From 57395f70dbc24d3ac5f97626520194f6773303e8 Mon Sep 17 00:00:00 2001
From: Penporn Koanantakool <penporn@google.com>
Date: Tue, 3 Sep 2019 15:39:06 -0700
Subject: [PATCH] Add CSRSparseMatrix ops.

PiperOrigin-RevId: 267029468
---
 tensorflow/core/BUILD                         |    4 +
 .../api_def_CSRSparseMatrixComponents.pbtxt   |   29 +
 .../api_def_CSRSparseMatrixToDense.pbtxt      |   13 +
 ...pi_def_CSRSparseMatrixToSparseTensor.pbtxt |   20 +
 .../api_def_DenseToCSRSparseMatrix.pbtxt      |   16 +
 .../base_api/api_def_SparseMatrixAdd.pbtxt    |   28 +
 .../base_api/api_def_SparseMatrixMatMul.pbtxt |   67 +
 .../base_api/api_def_SparseMatrixMul.pbtxt    |   26 +
 .../base_api/api_def_SparseMatrixNNZ.pbtxt    |   12 +
 .../api_def_SparseMatrixOrderingAMD.pbtxt     |   63 +
 .../api_def_SparseMatrixSoftmax.pbtxt         |   19 +
 .../api_def_SparseMatrixSoftmaxGrad.pbtxt     |   16 +
 .../api_def_SparseMatrixSparseCholesky.pbtxt  |   95 ++
 .../api_def_SparseMatrixSparseMatMul.pbtxt    |  110 ++
 .../api_def_SparseMatrixTranspose.pbtxt       |   20 +
 .../base_api/api_def_SparseMatrixZeros.pbtxt  |   12 +
 ...pi_def_SparseTensorToCSRSparseMatrix.pbtxt |   20 +
 tensorflow/core/kernels/BUILD                 |    3 +-
 tensorflow/core/kernels/cuda_sparse.cc        |  343 +++-
 tensorflow/core/kernels/cuda_sparse.h         |  247 ++-
 tensorflow/core/kernels/sparse/BUILD          |  100 ++
 tensorflow/core/kernels/sparse/add_op.cc      |  342 ++++
 tensorflow/core/kernels/sparse/conj_op.cc     |   98 ++
 .../sparse/csr_sparse_matrix_to_dense_op.cc   |  267 +++
 .../csr_sparse_matrix_to_sparse_tensor_op.cc  |  264 +++
 .../sparse/dense_to_csr_sparse_matrix_op.cc   |  398 +++++
 tensorflow/core/kernels/sparse/kernels.cc     |  100 ++
 tensorflow/core/kernels/sparse/kernels.h      |  247 +++
 .../core/kernels/sparse/kernels_gpu.cu.cc     |  676 ++++++++
 .../core/kernels/sparse/kernels_test.cc       |   82 +
 tensorflow/core/kernels/sparse/mat_mul_op.cc  |  436 +++++
 tensorflow/core/kernels/sparse/mul_op.cc      |  171 ++
 tensorflow/core/kernels/sparse/nnz_op.cc      |   78 +
 tensorflow/core/kernels/sparse/softmax_op.cc  |  225 +++
 .../core/kernels/sparse/sparse_cholesky_op.cc |  288 ++++
 .../core/kernels/sparse/sparse_mat_mul_op.cc  |  651 +++++++
 .../core/kernels/sparse/sparse_matrix.cc      |   43 +
 .../core/kernels/sparse/sparse_matrix.h       |  640 +++++++
 .../sparse/sparse_matrix_components_op.cc     |  150 ++
 .../kernels/sparse/sparse_ordering_amd_op.cc  |  131 ++
 .../sparse_tensor_to_csr_sparse_matrix_op.cc  |  345 ++++
 .../core/kernels/sparse/transpose_op.cc       |  189 +++
 tensorflow/core/kernels/sparse/transpose_op.h |   73 +
 tensorflow/core/kernels/sparse/zeros_op.cc    |   93 +
 tensorflow/core/kernels/sparse/zeros_op.h     |   88 +
 tensorflow/core/ops/sparse_csr_matrix_ops.cc  |  613 +++++++
 .../core/ops/sparse_csr_matrix_ops_test.cc    |  369 ++++
 tensorflow/opensource_only.files              |    3 +
 tensorflow/python/BUILD                       |    3 +
 tensorflow/python/kernel_tests/BUILD          |   56 +-
 .../kernel_tests/csr_sparse_matrix_test.py    |  266 +++
 ...arse_csr_matrix_dense_mat_mul_grad_test.py |  138 ++
 .../sparse_csr_matrix_grad_test.py            |  119 ++
 .../sparse_csr_matrix_ops_test.py             | 1511 +++++++++++++++++
 ...rse_csr_matrix_sparse_mat_mul_grad_test.py |  137 ++
 tensorflow/python/ops/linalg/sparse/BUILD     |   35 +
 .../python/ops/linalg/sparse/__init__.py      |    0
 tensorflow/python/ops/linalg/sparse/sparse.py |   25 +
 .../linalg/sparse/sparse_csr_matrix_grad.py   |  233 +++
 .../linalg/sparse/sparse_csr_matrix_ops.py    |  378 +++++
 tensorflow/tools/test/BUILD                   |    5 +
 third_party/eigen3/BUILD                      |    3 +
 third_party/eigen3/Eigen/OrderingMethods      |    1 +
 third_party/eigen3/Eigen/SparseCholesky       |    1 +
 third_party/eigen3/Eigen/SparseCore           |    1 +
 third_party/eigen3/LICENSE                    |    2 +
 66 files changed, 11215 insertions(+), 22 deletions(-)
 create mode 100644 tensorflow/core/api_def/base_api/api_def_CSRSparseMatrixComponents.pbtxt
 create mode 100644 tensorflow/core/api_def/base_api/api_def_CSRSparseMatrixToDense.pbtxt
 create mode 100644 tensorflow/core/api_def/base_api/api_def_CSRSparseMatrixToSparseTensor.pbtxt
 create mode 100644 tensorflow/core/api_def/base_api/api_def_DenseToCSRSparseMatrix.pbtxt
 create mode 100644 tensorflow/core/api_def/base_api/api_def_SparseMatrixAdd.pbtxt
 create mode 100644 tensorflow/core/api_def/base_api/api_def_SparseMatrixMatMul.pbtxt
 create mode 100644 tensorflow/core/api_def/base_api/api_def_SparseMatrixMul.pbtxt
 create mode 100644 tensorflow/core/api_def/base_api/api_def_SparseMatrixNNZ.pbtxt
 create mode 100644 tensorflow/core/api_def/base_api/api_def_SparseMatrixOrderingAMD.pbtxt
 create mode 100644 tensorflow/core/api_def/base_api/api_def_SparseMatrixSoftmax.pbtxt
 create mode 100644 tensorflow/core/api_def/base_api/api_def_SparseMatrixSoftmaxGrad.pbtxt
 create mode 100644 tensorflow/core/api_def/base_api/api_def_SparseMatrixSparseCholesky.pbtxt
 create mode 100644 tensorflow/core/api_def/base_api/api_def_SparseMatrixSparseMatMul.pbtxt
 create mode 100644 tensorflow/core/api_def/base_api/api_def_SparseMatrixTranspose.pbtxt
 create mode 100644 tensorflow/core/api_def/base_api/api_def_SparseMatrixZeros.pbtxt
 create mode 100644 tensorflow/core/api_def/base_api/api_def_SparseTensorToCSRSparseMatrix.pbtxt
 create mode 100644 tensorflow/core/kernels/sparse/BUILD
 create mode 100644 tensorflow/core/kernels/sparse/add_op.cc
 create mode 100644 tensorflow/core/kernels/sparse/conj_op.cc
 create mode 100644 tensorflow/core/kernels/sparse/csr_sparse_matrix_to_dense_op.cc
 create mode 100644 tensorflow/core/kernels/sparse/csr_sparse_matrix_to_sparse_tensor_op.cc
 create mode 100644 tensorflow/core/kernels/sparse/dense_to_csr_sparse_matrix_op.cc
 create mode 100644 tensorflow/core/kernels/sparse/kernels.cc
 create mode 100644 tensorflow/core/kernels/sparse/kernels.h
 create mode 100644 tensorflow/core/kernels/sparse/kernels_gpu.cu.cc
 create mode 100644 tensorflow/core/kernels/sparse/kernels_test.cc
 create mode 100644 tensorflow/core/kernels/sparse/mat_mul_op.cc
 create mode 100644 tensorflow/core/kernels/sparse/mul_op.cc
 create mode 100644 tensorflow/core/kernels/sparse/nnz_op.cc
 create mode 100644 tensorflow/core/kernels/sparse/softmax_op.cc
 create mode 100644 tensorflow/core/kernels/sparse/sparse_cholesky_op.cc
 create mode 100644 tensorflow/core/kernels/sparse/sparse_mat_mul_op.cc
 create mode 100644 tensorflow/core/kernels/sparse/sparse_matrix.cc
 create mode 100644 tensorflow/core/kernels/sparse/sparse_matrix.h
 create mode 100644 tensorflow/core/kernels/sparse/sparse_matrix_components_op.cc
 create mode 100644 tensorflow/core/kernels/sparse/sparse_ordering_amd_op.cc
 create mode 100644 tensorflow/core/kernels/sparse/sparse_tensor_to_csr_sparse_matrix_op.cc
 create mode 100644 tensorflow/core/kernels/sparse/transpose_op.cc
 create mode 100644 tensorflow/core/kernels/sparse/transpose_op.h
 create mode 100644 tensorflow/core/kernels/sparse/zeros_op.cc
 create mode 100644 tensorflow/core/kernels/sparse/zeros_op.h
 create mode 100644 tensorflow/core/ops/sparse_csr_matrix_ops.cc
 create mode 100644 tensorflow/core/ops/sparse_csr_matrix_ops_test.cc
 create mode 100644 tensorflow/python/kernel_tests/csr_sparse_matrix_test.py
 create mode 100644 tensorflow/python/kernel_tests/sparse_csr_matrix_dense_mat_mul_grad_test.py
 create mode 100644 tensorflow/python/kernel_tests/sparse_csr_matrix_grad_test.py
 create mode 100644 tensorflow/python/kernel_tests/sparse_csr_matrix_ops_test.py
 create mode 100644 tensorflow/python/kernel_tests/sparse_csr_matrix_sparse_mat_mul_grad_test.py
 create mode 100644 tensorflow/python/ops/linalg/sparse/BUILD
 create mode 100644 tensorflow/python/ops/linalg/sparse/__init__.py
 create mode 100644 tensorflow/python/ops/linalg/sparse/sparse.py
 create mode 100644 tensorflow/python/ops/linalg/sparse/sparse_csr_matrix_grad.py
 create mode 100644 tensorflow/python/ops/linalg/sparse/sparse_csr_matrix_ops.py
 create mode 100644 third_party/eigen3/Eigen/OrderingMethods
 create mode 100644 third_party/eigen3/Eigen/SparseCholesky
 create mode 100644 third_party/eigen3/Eigen/SparseCore

diff --git a/tensorflow/core/BUILD b/tensorflow/core/BUILD
index a7e65884923..efb943da1ef 100644
--- a/tensorflow/core/BUILD
+++ b/tensorflow/core/BUILD
@@ -1170,6 +1170,7 @@ tf_gen_op_libs(
         "set_ops",
         "script_ops",
         "sendrecv_ops",
+        "sparse_csr_matrix_ops",
         "sparse_ops",
         "spectral_ops",
         "state_ops",
@@ -1395,6 +1396,7 @@ cc_library(
         ":sdca_ops_op_lib",
         ":sendrecv_ops_op_lib",
         ":set_ops_op_lib",
+        ":sparse_csr_matrix_ops_op_lib",
         ":sparse_ops_op_lib",
         ":summary_ops_op_lib",
         ":spectral_ops_op_lib",
@@ -1584,6 +1586,7 @@ cc_library(
         "//tensorflow/core/kernels:summary_kernels",
         "//tensorflow/core/kernels:training_ops",
         "//tensorflow/core/kernels:word2vec_kernels",
+        "//tensorflow/core/kernels/sparse:kernels",
     ] + tf_additional_cloud_kernel_deps() + if_not_windows([
         "//tensorflow/core/kernels:fact_op",
         "//tensorflow/core/kernels:array_not_windows",
@@ -5179,6 +5182,7 @@ tf_cc_tests(
         "ops/rnn_ops_test.cc",
         "ops/set_ops_test.cc",
         "ops/shape_function_test.cc",
+        "ops/sparse_csr_matrix_ops_test.cc",
         "ops/sparse_ops_test.cc",
         "ops/spectral_ops_test.cc",
         "ops/state_ops_test.cc",
diff --git a/tensorflow/core/api_def/base_api/api_def_CSRSparseMatrixComponents.pbtxt b/tensorflow/core/api_def/base_api/api_def_CSRSparseMatrixComponents.pbtxt
new file mode 100644
index 00000000000..8964b60e33d
--- /dev/null
+++ b/tensorflow/core/api_def/base_api/api_def_CSRSparseMatrixComponents.pbtxt
@@ -0,0 +1,29 @@
+op {
+  graph_op_name: "CSRSparseMatrixComponents"
+  visibility: HIDDEN
+  in_arg {
+    name: "csr_sparse_matrix"
+    description: "A batched CSRSparseMatrix."
+  }
+  in_arg {
+    name: "index"
+    description: "The index in `csr_sparse_matrix`'s batch."
+  }
+  out_arg {
+    name: "row_ptrs"
+    description: "An array containing CSR matrix row pointers."
+  }
+  out_arg {
+    name: "col_inds"
+    description: "An array containing CSR matrix column indices."
+  }
+  out_arg {
+    name: "values"
+    description: "An array containing CSR matrix nonzero values."
+  }
+  summary: "Reads out the CSR components at batch `index`."
+  description: <<END
+This op is meant only for debugging / testing, and its interface is not expected
+to be stable.
+END
+}
diff --git a/tensorflow/core/api_def/base_api/api_def_CSRSparseMatrixToDense.pbtxt b/tensorflow/core/api_def/base_api/api_def_CSRSparseMatrixToDense.pbtxt
new file mode 100644
index 00000000000..8165f7efa3f
--- /dev/null
+++ b/tensorflow/core/api_def/base_api/api_def_CSRSparseMatrixToDense.pbtxt
@@ -0,0 +1,13 @@
+op {
+  graph_op_name: "CSRSparseMatrixToDense"
+  visibility: HIDDEN
+  in_arg {
+    name: "sparse_input"
+    description: "A batched CSRSparseMatrix."
+  }
+  out_arg {
+    name: "dense_output"
+    description: "A dense tensor."
+  }
+  summary: "Convert a (possibly batched) CSRSparseMatrix to dense."
+}
diff --git a/tensorflow/core/api_def/base_api/api_def_CSRSparseMatrixToSparseTensor.pbtxt b/tensorflow/core/api_def/base_api/api_def_CSRSparseMatrixToSparseTensor.pbtxt
new file mode 100644
index 00000000000..2b932378339
--- /dev/null
+++ b/tensorflow/core/api_def/base_api/api_def_CSRSparseMatrixToSparseTensor.pbtxt
@@ -0,0 +1,20 @@
+op {
+  graph_op_name: "CSRSparseMatrixToSparseTensor"
+  in_arg {
+    name: "sparse_matrix"
+    description: "A (possibly batched) CSRSparseMatrix."
+  }
+  out_arg {
+    name: "indices"
+    description: "SparseTensor indices."
+  }
+  out_arg {
+    name: "values"
+    description: "SparseTensor values."
+  }
+  out_arg {
+    name: "dense_shape"
+    description: "SparseTensor dense shape."
+  }
+  summary: "Converts a (possibly batched) CSRSparesMatrix to a SparseTensor."
+}
diff --git a/tensorflow/core/api_def/base_api/api_def_DenseToCSRSparseMatrix.pbtxt b/tensorflow/core/api_def/base_api/api_def_DenseToCSRSparseMatrix.pbtxt
new file mode 100644
index 00000000000..9e578c0f123
--- /dev/null
+++ b/tensorflow/core/api_def/base_api/api_def_DenseToCSRSparseMatrix.pbtxt
@@ -0,0 +1,16 @@
+op {
+  graph_op_name: "DenseToCSRSparseMatrix"
+  in_arg {
+    name: "dense_input"
+    description: "A Dense tensor."
+  }
+  in_arg {
+    name: "indices"
+    description: "Indices of nonzero elements."
+  }
+  out_arg {
+    name: "sparse_output"
+    description: "A (possibly batched) CSRSparseMatrix."
+  }
+  summary: "Converts a dense tensor to a (possibly batched) CSRSparseMatrix."
+}
diff --git a/tensorflow/core/api_def/base_api/api_def_SparseMatrixAdd.pbtxt b/tensorflow/core/api_def/base_api/api_def_SparseMatrixAdd.pbtxt
new file mode 100644
index 00000000000..78c20141b67
--- /dev/null
+++ b/tensorflow/core/api_def/base_api/api_def_SparseMatrixAdd.pbtxt
@@ -0,0 +1,28 @@
+op {
+  graph_op_name: "SparseMatrixAdd"
+  in_arg {
+    name: "a"
+    description: "A CSRSparseMatrix."
+  }
+  in_arg {
+    name: "b"
+    description: "A CSRSparseMatrix."
+  }
+  in_arg {
+    name: "alpha"
+    description: "A constant scalar."
+  }
+  in_arg {
+    name: "beta"
+    description: "A constant scalar."
+  }
+  out_arg {
+    name: "c"
+    description: "A CSRSparseMatrix."
+  }
+  summary: "Sparse addition of two CSR matrices, C = alpha * A + beta * B."
+  description: <<END
+The gradients of SparseMatrixAdd outputs with respect to alpha and beta are not
+currently defined (TensorFlow will return zeros for these entries).
+END
+}
diff --git a/tensorflow/core/api_def/base_api/api_def_SparseMatrixMatMul.pbtxt b/tensorflow/core/api_def/base_api/api_def_SparseMatrixMatMul.pbtxt
new file mode 100644
index 00000000000..8d4da45cd8a
--- /dev/null
+++ b/tensorflow/core/api_def/base_api/api_def_SparseMatrixMatMul.pbtxt
@@ -0,0 +1,67 @@
+op {
+  graph_op_name: "SparseMatrixMatMul"
+  in_arg {
+    name: "a"
+    description: "A CSRSparseMatrix."
+  }
+  in_arg {
+    name: "b"
+    description: "A dense tensor."
+  }
+  out_arg {
+    name: "output"
+    description: "A dense output tensor."
+  }
+  attr {
+    name: "transpose_a"
+    description: "Indicates whether `a` should be transposed."
+  }
+  attr {
+    name: "transpose_b"
+    description: "Indicates whether `b` should be transposed."
+  }
+  attr {
+    name: "adjoint_a"
+    description: "Indicates whether `a` should be conjugate-transposed."
+  }
+  attr {
+    name: "adjoint_b"
+    description: "Indicates whether `b` should be conjugate-transposed."
+  }
+  attr {
+    name: "transpose_output"
+    description: "Transposes the product of `a` and `b`."
+  }
+  attr {
+    name: "conjugate_output"
+    description: "Conjugates the product of `a` and `b`."
+  }
+  summary: "Matrix-multiplies a sparse matrix with a dense matrix."
+  description: <<END
+Returns a dense matrix.
+For inputs A and B, where A is CSR and B is dense; this op returns a dense C;
+
+If transpose_output is false, returns:
+```
+  C = A . B
+```
+
+If transpose_output is `true`, returns:
+```
+  C = transpose(A . B) = transpose(B) . transpose(A)
+```
+where the transposition is performed along the two innermost (matrix)
+dimensions.
+
+If conjugate_output is `true`, returns:
+```
+  C = conjugate(A . B) = conjugate(A) . conjugate(B)
+```
+
+If both conjugate_output and transpose_output are `true`, returns:
+```
+  C = conjugate(transpose(A . B)) = conjugate(transpose(B)) .
+                                    conjugate(transpose(A))
+```
+END
+}
diff --git a/tensorflow/core/api_def/base_api/api_def_SparseMatrixMul.pbtxt b/tensorflow/core/api_def/base_api/api_def_SparseMatrixMul.pbtxt
new file mode 100644
index 00000000000..0f9a8b30351
--- /dev/null
+++ b/tensorflow/core/api_def/base_api/api_def_SparseMatrixMul.pbtxt
@@ -0,0 +1,26 @@
+op {
+  graph_op_name: "SparseMatrixMul"
+  in_arg {
+    name: "a"
+    description: "A CSRSparseMatrix."
+  }
+  in_arg {
+    name: "b"
+    description: "A dense tensor."
+  }
+  out_arg {
+    name: "output"
+    description: "A dense output tensor."
+  }
+  summary: "Element-wise multiplication of a sparse matrix with a dense tensor."
+  description: <<END
+Returns a sparse matrix.
+
+The dense tensor `b` may be either a scalar; otherwise `a` must be a rank-3
+`SparseMatrix`; in this case `b` must be shaped `[batch_size, 1, 1]` and the
+multiply operation broadcasts.
+
+**NOTE** even if `b` is zero, the sparsity structure of the output does not
+change.
+END
+}
diff --git a/tensorflow/core/api_def/base_api/api_def_SparseMatrixNNZ.pbtxt b/tensorflow/core/api_def/base_api/api_def_SparseMatrixNNZ.pbtxt
new file mode 100644
index 00000000000..7e19822a6d7
--- /dev/null
+++ b/tensorflow/core/api_def/base_api/api_def_SparseMatrixNNZ.pbtxt
@@ -0,0 +1,12 @@
+op {
+  graph_op_name: "SparseMatrixNNZ"
+  in_arg {
+    name: "sparse_matrix"
+    description: "A CSRSparseMatrix."
+  }
+  out_arg {
+    name: "nnz"
+    description: "The number of nonzeroes of `sparse_matrix`."
+  }
+  summary: "Returns the number of nonzeroes of `sparse_matrix`."
+}
diff --git a/tensorflow/core/api_def/base_api/api_def_SparseMatrixOrderingAMD.pbtxt b/tensorflow/core/api_def/base_api/api_def_SparseMatrixOrderingAMD.pbtxt
new file mode 100644
index 00000000000..32704f2cf33
--- /dev/null
+++ b/tensorflow/core/api_def/base_api/api_def_SparseMatrixOrderingAMD.pbtxt
@@ -0,0 +1,63 @@
+op {
+  graph_op_name: "SparseMatrixOrderingAMD"
+  in_arg {
+    name: "input"
+    description: "A `CSRSparseMatrix`."
+  }
+  out_arg {
+    name: "output"
+    description: "The Approximate Minimum Degree (AMD) ordering of `input`."
+  }
+  summary: "Computes the Approximate Minimum Degree (AMD) ordering of `input`."
+  description: <<END
+Computes the Approximate Minimum Degree (AMD) ordering for a sparse matrix.
+
+The returned permutation may be used to permute the rows and columns of the
+given sparse matrix. This typically results in permuted sparse matrix's sparse
+Cholesky (or other decompositions) in having fewer zero fill-in compared to
+decomposition of the original matrix.
+
+The input sparse matrix may have rank 2 or rank 3. The output Tensor,
+representing would then have rank 1 or 2 respectively, with the same batch
+shape as the input.
+
+Each component of the input sparse matrix must represent a square symmetric
+matrix; only the lower triangular part of the matrix is read. The values of the
+sparse matrix does not affect the returned permutation, only the sparsity
+pattern of the sparse matrix is used. Hence, a single AMD ordering may be
+reused for the Cholesky decompositions of sparse matrices with the same sparsity
+pattern but with possibly different values.
+
+Each batch component of the output permutation represents a permutation of `N`
+elements, where the input sparse matrix components each have `N` rows. That is,
+the component contains each of the integers `{0, .. N-1}` exactly once. The
+`i`th element represents the row index that the `i`th row maps to.
+
+Usage example:
+
+```python
+    from tensorflow.python.ops.linalg.sparse import sparse_csr_matrix_ops
+
+    a_indices = np.array([[0, 0], [1, 1], [2, 1], [2, 2], [3, 3]])
+    a_values = np.array([1.0, 2.0, 1.0, 3.0, 4.0], np.float32)
+    a_dense_shape = [4, 4]
+
+    with tf.Session() as sess:
+      # Define (COO format) SparseTensor over Numpy array.
+      a_st = tf.SparseTensor(a_indices, a_values, a_dense_shape)
+
+      # Convert SparseTensors to CSR SparseMatrix.
+      a_sm = sparse_csr_matrix_ops.sparse_tensor_to_csr_sparse_matrix(
+          a_st.indices, a_st.values, a_st.dense_shape)
+
+      # Obtain the AMD Ordering for the CSR SparseMatrix.
+      ordering_amd = sparse_csr_matrix_ops.sparse_matrix_ordering_amd(sparse_matrix)
+
+      ordering_amd_value = sess.run(ordering_amd)
+```
+
+`ordering_amd_value` stores the AMD ordering: `[1 2 3 0]`.
+
+input: A `CSRSparseMatrix`.
+END
+}
diff --git a/tensorflow/core/api_def/base_api/api_def_SparseMatrixSoftmax.pbtxt b/tensorflow/core/api_def/base_api/api_def_SparseMatrixSoftmax.pbtxt
new file mode 100644
index 00000000000..bf868e5ff5c
--- /dev/null
+++ b/tensorflow/core/api_def/base_api/api_def_SparseMatrixSoftmax.pbtxt
@@ -0,0 +1,19 @@
+op {
+  graph_op_name: "SparseMatrixSoftmax"
+  in_arg {
+    name: "logits"
+    description: "A CSRSparseMatrix."
+  }
+  out_arg {
+    name: "softmax"
+    description: "A CSRSparseMatrix."
+  }
+  summary: "Calculates the softmax of a CSRSparseMatrix."
+  description: <<END
+Calculate the softmax of the innermost dimensions of a SparseMatrix.
+
+Missing values are treated as `-inf` (i.e., logits of zero probability); and
+the output has the same sparsity structure as the input (though missing values
+in the output may now be treated as having probability zero).
+END
+}
diff --git a/tensorflow/core/api_def/base_api/api_def_SparseMatrixSoftmaxGrad.pbtxt b/tensorflow/core/api_def/base_api/api_def_SparseMatrixSoftmaxGrad.pbtxt
new file mode 100644
index 00000000000..bb7961b94fd
--- /dev/null
+++ b/tensorflow/core/api_def/base_api/api_def_SparseMatrixSoftmaxGrad.pbtxt
@@ -0,0 +1,16 @@
+op {
+  graph_op_name: "SparseMatrixSoftmaxGrad"
+  in_arg {
+    name: "softmax"
+    description: "A CSRSparseMatrix."
+  }
+  in_arg {
+    name: "grad_softmax"
+    description: "The gradient of `softmax`."
+  }
+  out_arg {
+    name: "gradient"
+    description: "The output gradient."
+  }
+  summary: "Calculates the gradient of the SparseMatrixSoftmax op."
+}
diff --git a/tensorflow/core/api_def/base_api/api_def_SparseMatrixSparseCholesky.pbtxt b/tensorflow/core/api_def/base_api/api_def_SparseMatrixSparseCholesky.pbtxt
new file mode 100644
index 00000000000..e69814e9f91
--- /dev/null
+++ b/tensorflow/core/api_def/base_api/api_def_SparseMatrixSparseCholesky.pbtxt
@@ -0,0 +1,95 @@
+op {
+  graph_op_name: "SparseMatrixSparseCholesky"
+  in_arg {
+    name: "input"
+    description: "A `CSRSparseMatrix`."
+  }
+  in_arg {
+    name: "permutation"
+    description: "A fill-in reducing permutation matrix."
+  }
+  out_arg {
+    name: "output"
+    description: "The sparse Cholesky decompsition of `input`."
+  }
+  summary: "Computes the sparse Cholesky decomposition of `input`."
+  description: <<END
+Computes the Sparse Cholesky decomposition of a sparse matrix, with the given
+fill-in reducing permutation.
+
+The input sparse matrix and the fill-in reducing permutation `permutation` must
+have compatible shapes. If the sparse matrix has rank 3; with the batch
+dimension `B`, then the `permutation` must be of rank 2; with the same batch
+dimension `B`. There is no support for broadcasting.
+
+Furthermore, each component vector of `permutation` must be of length `N`,
+containing each of the integers {0, 1, ..., N - 1} exactly once, where `N` is
+the number of rows of each component of the sparse matrix.
+
+Each component of the input sparse matrix must represent a symmetric positive
+definite (SPD) matrix; although only the lower triangular part of the matrix is
+read. If any individual component is not SPD, then an InvalidArgument error is
+thrown.
+
+The returned sparse matrix has the same dense shape as the input sparse matrix.
+For each component `A` of the input sparse matrix, the corresponding output
+sparse matrix represents `L`, the lower triangular Cholesky factor satisfying
+the following identity:
+
+```
+  A = L * Lt
+```
+
+where Lt denotes the transpose of L (or its conjugate transpose, if `type` is
+`complex64` or `complex128`).
+
+The `type` parameter denotes the type of the matrix elements. The supported
+types are: `float32`, `float64`, `complex64` and `complex128`.
+
+Usage example:
+
+```python
+    from tensorflow.python.ops.linalg.sparse import sparse_csr_matrix_ops
+
+    a_indices = np.array([[0, 0], [1, 1], [2, 1], [2, 2], [3, 3]])
+    a_values = np.array([1.0, 2.0, 1.0, 3.0, 4.0], np.float32)
+    a_dense_shape = [4, 4]
+
+    with tf.Session() as sess:
+      # Define (COO format) SparseTensor over Numpy array.
+      a_st = tf.SparseTensor(a_indices, a_values, a_dense_shape)
+
+      # Convert SparseTensors to CSR SparseMatrix.
+      a_sm = sparse_csr_matrix_ops.sparse_tensor_to_csr_sparse_matrix(
+          a_st.indices, a_st.values, a_st.dense_shape)
+
+      # Obtain the Sparse Cholesky factor using AMD Ordering for reducing zero
+      # fill-in (number of structural non-zeros in the sparse Cholesky factor).
+      ordering_amd = sparse_csr_matrix_ops.sparse_matrix_ordering_amd(sparse_matrix)
+      cholesky_sparse_matrices = (
+          sparse_csr_matrix_ops.sparse_matrix_sparse_cholesky(
+              sparse_matrix, ordering_amd, type=tf.float32))
+
+      # Convert the CSRSparseMatrix Cholesky factor to a dense Tensor
+      dense_cholesky = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+          cholesky_sparse_matrices, tf.float32)
+
+      # Evaluate the dense Tensor value.
+      dense_cholesky_value = sess.run(dense_cholesky)
+```
+
+`dense_cholesky_value` stores the dense Cholesky factor:
+
+```
+    [[  1.  0.    0.    0.]
+     [  0.  1.41  0.    0.]
+     [  0.  0.70  1.58  0.]
+     [  0.  0.    0.    2.]]
+```
+
+
+input: A `CSRSparseMatrix`.
+permutation: A `Tensor`.
+type: The type of `input`.
+END
+}
diff --git a/tensorflow/core/api_def/base_api/api_def_SparseMatrixSparseMatMul.pbtxt b/tensorflow/core/api_def/base_api/api_def_SparseMatrixSparseMatMul.pbtxt
new file mode 100644
index 00000000000..8c9cc0ba151
--- /dev/null
+++ b/tensorflow/core/api_def/base_api/api_def_SparseMatrixSparseMatMul.pbtxt
@@ -0,0 +1,110 @@
+op {
+  graph_op_name: "SparseMatrixSparseMatMul"
+  in_arg {
+    name: "a"
+    description: "A CSRSparseMatrix."
+  }
+  in_arg {
+    name: "b"
+    description: "A CSRSparseMatrix."
+  }
+  out_arg {
+    name: "c"
+    description: "A CSRSparseMatrix."
+  }
+  attr {
+    name: "transpose_a"
+    description: "Indicates whether `a` should be transposed."
+  }
+  attr {
+    name: "transpose_b"
+    description: "Indicates whether `b` should be transposed."
+  }
+  attr {
+    name: "adjoint_a"
+    description: "Indicates whether `a` should be conjugate-transposed."
+  }
+  attr {
+    name: "adjoint_b"
+    description: "Indicates whether `b` should be conjugate-transposed."
+  }
+  summary: "Sparse-matrix-multiplies two CSR matrices `a` and `b`."
+  description: <<END
+Performs a matrix multiplication of a sparse matrix `a` with a sparse matrix
+`b`; returns a sparse matrix `a * b`, unless either `a` or `b` is transposed or
+adjointed.
+
+Each matrix may be transposed or adjointed (conjugated and transposed)
+according to the Boolean parameters `transpose_a`, `adjoint_a`, `transpose_b`
+and `adjoint_b`. At most one of `transpose_a` or `adjoint_a` may be True.
+Similarly, at most one of `transpose_b` or `adjoint_b` may be True.
+
+The inputs must have compatible shapes. That is, the inner dimension of `a`
+must be equal to the outer dimension of `b`. This requirement is adjusted
+according to whether either `a` or `b` is transposed or adjointed.
+
+The `type` parameter denotes the type of the matrix elements. Both `a` and `b`
+must have the same type. The supported types are: `float32`, `float64`,
+`complex64` and `complex128`.
+
+Both `a` and `b` must have the same rank. Broadcasting is not supported. If they
+have rank 3, each batch of 2D CSRSparseMatrices within `a` and `b` must have the
+same dense shape.
+
+The sparse matrix product may have numeric (non-structural) zeros.
+TODO(anudhyan): Consider adding a boolean attribute to control whether to prune
+zeros.
+
+Usage example:
+
+```python
+    from tensorflow.python.ops.linalg.sparse import sparse_csr_matrix_ops
+
+    a_indices = np.array([[0, 0], [2, 3], [2, 4], [3, 0]])
+    a_values = np.array([1.0, 5.0, -1.0, -2.0], np.float32)
+    a_dense_shape = [4, 5]
+
+    b_indices = np.array([[0, 0], [3, 0], [3, 1]])
+    b_values = np.array([2.0, 7.0, 8.0], np.float32)
+    b_dense_shape = [5, 3]
+
+    with tf.Session() as sess:
+      # Define (COO format) Sparse Tensors over Numpy arrays
+      a_st = tf.SparseTensor(a_indices, a_values, a_dense_shape)
+      b_st = tf.SparseTensor(b_indices, b_values, b_dense_shape)
+
+      # Convert SparseTensors to CSR SparseMatrix
+      a_sm = sparse_csr_matrix_ops.sparse_tensor_to_csr_sparse_matrix(
+          a_st.indices, a_st.values, a_st.dense_shape)
+      b_sm = sparse_csr_matrix_ops.sparse_tensor_to_csr_sparse_matrix(
+          b_st.indices, b_st.values, b_st.dense_shape)
+
+      # Compute the CSR SparseMatrix matrix multiplication
+      c_sm = sparse_csr_matrix_ops.sparse_matrix_sparse_mat_mul(
+          a=a_sm, b=b_sm, type=tf.float32)
+
+      # Convert the CSR SparseMatrix product to a dense Tensor
+      c_sm_dense = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+          c_sm, tf.float32)
+      # Evaluate the dense Tensor value
+      c_sm_dense_value = sess.run(c_sm_dense)
+```
+
+`c_sm_dense_value` stores the dense matrix product:
+
+```
+    [[  2.   0.   0.]
+     [  0.   0.   0.]
+     [ 35.  40.   0.]
+     [ -4.   0.   0.]]
+```
+
+a: A `CSRSparseMatrix`.
+b: A `CSRSparseMatrix` with the same type and rank as `a`.
+type: The type of both `a` and `b`.
+transpose_a: If True, `a` transposed before multiplication.
+transpose_b: If True, `b` transposed before multiplication.
+adjoint_a: If True, `a` adjointed before multiplication.
+adjoint_b: If True, `b` adjointed before multiplication.
+END
+}
diff --git a/tensorflow/core/api_def/base_api/api_def_SparseMatrixTranspose.pbtxt b/tensorflow/core/api_def/base_api/api_def_SparseMatrixTranspose.pbtxt
new file mode 100644
index 00000000000..5a3cfba8cce
--- /dev/null
+++ b/tensorflow/core/api_def/base_api/api_def_SparseMatrixTranspose.pbtxt
@@ -0,0 +1,20 @@
+op {
+  graph_op_name: "SparseMatrixTranspose"
+  in_arg {
+    name: "input"
+    description: "A CSRSparseMatrix."
+  }
+  out_arg {
+    name: "output"
+    description: "A CSRSparseMatrix."
+  }
+  attr {
+    name: "conjugate"
+    description: "Indicates whether `input` should be conjugated."
+  }
+  summary: "Transposes the inner (matrix) dimensions of a CSRSparseMatrix."
+  description: <<END
+Transposes the inner (matrix) dimensions of a SparseMatrix and optionally
+conjugates its values.
+END
+}
diff --git a/tensorflow/core/api_def/base_api/api_def_SparseMatrixZeros.pbtxt b/tensorflow/core/api_def/base_api/api_def_SparseMatrixZeros.pbtxt
new file mode 100644
index 00000000000..c535bba6876
--- /dev/null
+++ b/tensorflow/core/api_def/base_api/api_def_SparseMatrixZeros.pbtxt
@@ -0,0 +1,12 @@
+op {
+  graph_op_name: "SparseMatrixZeros"
+  in_arg {
+    name: "dense_shape"
+    description: "The desired matrix shape."
+  }
+  out_arg {
+    name: "sparse_matrix"
+    description: "An empty CSR matrix with shape `dense_shape`."
+  }
+  summary: "Creates an all-zeros CSRSparseMatrix with shape `dense_shape`."
+}
diff --git a/tensorflow/core/api_def/base_api/api_def_SparseTensorToCSRSparseMatrix.pbtxt b/tensorflow/core/api_def/base_api/api_def_SparseTensorToCSRSparseMatrix.pbtxt
new file mode 100644
index 00000000000..dc8c229056b
--- /dev/null
+++ b/tensorflow/core/api_def/base_api/api_def_SparseTensorToCSRSparseMatrix.pbtxt
@@ -0,0 +1,20 @@
+op {
+  graph_op_name: "SparseTensorToCSRSparseMatrix"
+  in_arg {
+    name: "indices"
+    description: "SparseTensor indices."
+  }
+  in_arg {
+    name: "values"
+    description: "SparseTensor values."
+  }
+  in_arg {
+    name: "dense_shape"
+    description: "SparseTensor dense shape."
+  }
+  out_arg {
+    name: "sparse_matrix"
+    description: "A (possibly batched) CSRSparseMatrix."
+  }
+  summary: "Converts a SparseTensor to a (possibly batched) CSRSparseMatrix."
+}
diff --git a/tensorflow/core/kernels/BUILD b/tensorflow/core/kernels/BUILD
index 6b233eabe46..dc99a569d94 100644
--- a/tensorflow/core/kernels/BUILD
+++ b/tensorflow/core/kernels/BUILD
@@ -3359,8 +3359,9 @@ tf_kernel_library(
     deps = [
         "//tensorflow/core:framework",
         "//tensorflow/core:lib",
+        "//tensorflow/core/kernels:cuda_solvers",
         "//tensorflow/stream_executor/cuda:cusparse_lib",
-    ],
+    ] + if_cuda(["@cub_archive//:cub"]),
 )
 
 LINALG_DEPS = [
diff --git a/tensorflow/core/kernels/cuda_sparse.cc b/tensorflow/core/kernels/cuda_sparse.cc
index dff78bc9c7e..7825dc5969f 100644
--- a/tensorflow/core/kernels/cuda_sparse.cc
+++ b/tensorflow/core/kernels/cuda_sparse.cc
@@ -1,21 +1,22 @@
 /* Copyright 2019 The TensorFlow Authors. All Rights Reserved.
 
-   Licensed under the Apache License, Version 2.0 (the "License");
-   you may not use this file except in compliance with the License.
-   You may obtain a copy of the License at
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
 
-   http://www.apache.org/licenses/LICENSE-2.0
+    http://www.apache.org/licenses/LICENSE-2.0
 
-   Unless required by applicable law or agreed to in writing, software
-   distributed under the License is distributed on an "AS IS" BASIS,
-   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-   See the License for the specific language governing permissions and
-   limitations under the License.
-   =============================================================================
-*/
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
 
 #ifdef GOOGLE_CUDA
 
+#include "tensorflow/core/kernels/cuda_sparse.h"
+
 #include <complex>
 #include <memory>
 #include <unordered_map>
@@ -26,7 +27,7 @@
 #include "tensorflow/core/common_runtime/gpu/gpu_event_mgr.h"
 #include "tensorflow/core/framework/op_kernel.h"
 #include "tensorflow/core/framework/types.h"
-#include "tensorflow/core/kernels/cuda_sparse.h"
+#include "tensorflow/core/kernels/cuda_solvers.h"
 #include "tensorflow/core/lib/core/blocking_counter.h"
 #include "tensorflow/core/lib/core/status.h"
 #include "tensorflow/core/lib/core/stringpiece.h"
@@ -37,6 +38,8 @@
 #include "tensorflow/core/platform/stream_executor.h"
 #include "tensorflow/core/platform/types.h"
 
+// TODO(rmlarsen,penporn): Investigate using newer kernels in CUDA 10.1+.
+
 namespace tensorflow {
 namespace {
 
@@ -126,6 +129,13 @@ class CudaSparseHandles {
   TF_DISALLOW_COPY_AND_ASSIGN(CudaSparseHandles);
 };
 
+// TODO(ebrevdo): Replace global mutex guarding CudaSparseHandles
+// lookup with one of:
+//    1. Adding the handle to the CudaStream structure; do the lookup there.
+//    2. Add a thread-local cusparse, set it to the current stream
+//       upon each call.
+// #1 seems like the cleanest option but will need to wait until this
+// is moved into TF core.
 static mutex handle_map_mutex(LINKER_INITIALIZED);
 
 using HandleMap = std::unordered_map<cudaStream_t, CudaSparseHandles>;
@@ -141,11 +151,13 @@ HandleMap* GetHandleMapSingleton() {
 
 CudaSparse::CudaSparse(OpKernelContext* context)
     : initialized_(false), context_(context) {
-  cuda_stream_ =
-      *reinterpret_cast<const cudaStream_t*>(context->op_device_context()
-                                                 ->stream()
-                                                 ->implementation()
-                                                 ->GpuStreamMemberHack());
+  auto cuda_stream_ptr =
+      reinterpret_cast<const cudaStream_t*>(context->op_device_context()
+                                                ->stream()
+                                                ->implementation()
+                                                ->GpuStreamMemberHack());
+  DCHECK(cuda_stream_ptr);
+  cuda_stream_ = *cuda_stream_ptr;
 }
 
 Status CudaSparse::Initialize() {
@@ -376,6 +388,303 @@ static inline Status Gtsv2StridedBatchBufferSizeImpl(
 
 TF_CALL_LAPACK_TYPES(GTSV2_STRIDED_BATCH_BUFFER_SIZE_INSTANCE);
 
+Status CudaSparse::Coo2csr(const int* cooRowInd, int nnz, int m,
+                           int* csrRowPtr) const {
+  // cusparseStatus_t CUSPARSEAPI cusparseXcoo2csr(cusparseHandle_t handle,
+  //                                               const int *cooRowInd,
+  //                                               int nnz,
+  //                                               int m,
+  //                                               int *csrSortedRowPtr,
+  //                                               cusparseIndexBase_t
+  //                                               idxBase);
+  DCHECK(initialized_);
+  TF_RETURN_IF_CUSPARSE_ERROR(cusparseXcoo2csr(*cusparse_handle_, cooRowInd,
+                                               nnz, m, csrRowPtr,
+                                               CUSPARSE_INDEX_BASE_ZERO));
+  return Status::OK();
+}
+
+Status CudaSparse::Csr2coo(const int* csrRowPtr, int nnz, int m,
+                           int* cooRowInd) const {
+  // cusparseStatus_t CUSPARSEAPI cusparseXcsr2coo(cusparseHandle_t handle,
+  //                                               const int *csrRowPtr,
+  //                                               int nnz,
+  //                                               int m,
+  //                                               int *cooRowInd,
+  //                                               cusparseIndexBase_t
+  //                                               idxBase);
+  DCHECK(initialized_);
+  TF_RETURN_IF_CUSPARSE_ERROR(cusparseXcsr2coo(*cusparse_handle_, csrRowPtr,
+                                               nnz, m, cooRowInd,
+                                               CUSPARSE_INDEX_BASE_ZERO));
+  return Status::OK();
+}
+
+Status CudaSparse::CsrgeamNnz(int m, int n, const cusparseMatDescr_t descrA,
+                              int nnzA, const int* csrSortedRowPtrA,
+                              const int* csrSortedColIndA,
+                              const cusparseMatDescr_t descrB, int nnzB,
+                              const int* csrSortedRowPtrB,
+                              const int* csrSortedColIndB,
+                              const cusparseMatDescr_t descrC,
+                              int* csrSortedRowPtrC, int* nnzTotalDevHostPtr) {
+  DCHECK(initialized_);
+  DCHECK(nnzTotalDevHostPtr != nullptr);
+  TF_RETURN_IF_CUSPARSE_ERROR(cusparseXcsrgeamNnz(
+      *cusparse_handle_, m, n, descrA, nnzA, csrSortedRowPtrA, csrSortedColIndA,
+      descrB, nnzB, csrSortedRowPtrB, csrSortedColIndB, descrC,
+      csrSortedRowPtrC, nnzTotalDevHostPtr));
+  return Status::OK();
+}
+
+template <typename Scalar, typename SparseFnT>
+static inline Status CsrmmImpl(
+    SparseFnT op, OpKernelContext* context, cusparseHandle_t cusparse_handle,
+    cusparseOperation_t transA, cusparseOperation_t transB, int m, int n, int k,
+    int nnz, const Scalar* alpha_host, const cusparseMatDescr_t descrA,
+    const Scalar* csrSortedValA, const int* csrSortedRowPtrA,
+    const int* csrSortedColIndA, const Scalar* B, int ldb,
+    const Scalar* beta_host, Scalar* C, int ldc) {
+  // cusparseStatus_t CUSPARSEAPI cusparseScsrmm2(
+  //     cusparseHandle_t handle, cusparseOperation_t transA,
+  //     cusparseOperation_t transB, int m, int n, int k, int nnz,
+  //     const float* alpha, const cusparseMatDescr_t descrA,
+  //     const float* csrSortedValA, const int* csrSortedRowPtrA,
+  //     const int* csrSortedColIndA, const float* B, int ldb, const float*
+  //     beta, float* C, int ldc);
+  TF_RETURN_IF_CUSPARSE_ERROR(op(
+      cusparse_handle, transA, transB, m, n, k, nnz, AsCudaComplex(alpha_host),
+      descrA, AsCudaComplex(csrSortedValA), csrSortedRowPtrA, csrSortedColIndA,
+      AsCudaComplex(B), ldb, AsCudaComplex(beta_host), AsCudaComplex(C), ldc));
+  return Status::OK();
+}
+
+#define CSRMM_INSTANCE(Scalar, sparse_prefix)                                \
+  template <>                                                                \
+  Status CudaSparse::Csrmm<Scalar>(                                          \
+      cusparseOperation_t transA, cusparseOperation_t transB, int m, int n,  \
+      int k, int nnz, const Scalar* alpha_host,                              \
+      const cusparseMatDescr_t descrA, const Scalar* csrSortedValA,          \
+      const int* csrSortedRowPtrA, const int* csrSortedColIndA,              \
+      const Scalar* B, int ldb, const Scalar* beta_host, Scalar* C, int ldc) \
+      const {                                                                \
+    DCHECK(initialized_);                                                    \
+    return CsrmmImpl(SPARSE_FN(csrmm2, sparse_prefix), context_,             \
+                     *cusparse_handle_, transA, transB, m, n, k, nnz,        \
+                     alpha_host, descrA, csrSortedValA, csrSortedRowPtrA,    \
+                     csrSortedColIndA, B, ldb, beta_host, C, ldc);           \
+  }
+
+TF_CALL_LAPACK_TYPES(CSRMM_INSTANCE);
+
+template <typename Scalar, typename SparseFnT>
+static inline Status CsrmvImpl(
+    SparseFnT op, OpKernelContext* context, cusparseHandle_t cusparse_handle,
+    cusparseOperation_t transA, int m, int n, int nnz, const Scalar* alpha_host,
+    const cusparseMatDescr_t descrA, const Scalar* csrSortedValA,
+    const int* csrSortedRowPtrA, const int* csrSortedColIndA, const Scalar* x,
+    const Scalar* beta_host, Scalar* y) {
+  TF_RETURN_IF_CUSPARSE_ERROR(
+      op(cusparse_handle, transA, m, n, nnz, AsCudaComplex(alpha_host), descrA,
+         AsCudaComplex(csrSortedValA), csrSortedRowPtrA, csrSortedColIndA,
+         AsCudaComplex(x), AsCudaComplex(beta_host), AsCudaComplex(y)));
+  return Status::OK();
+}
+
+// TODO(ebrevdo,rmlarsen): Use csrmv_mp for all cases when available in CUDA 9.
+#define CSRMV_INSTANCE(Scalar, sparse_prefix)                                \
+  template <>                                                                \
+  Status CudaSparse::Csrmv<Scalar>(                                          \
+      cusparseOperation_t transA, int m, int n, int nnz,                     \
+      const Scalar* alpha_host, const cusparseMatDescr_t descrA,             \
+      const Scalar* csrSortedValA, const int* csrSortedRowPtrA,              \
+      const int* csrSortedColIndA, const Scalar* x, const Scalar* beta_host, \
+      Scalar* y) const {                                                     \
+    DCHECK(initialized_);                                                    \
+    if (transA == CUSPARSE_OPERATION_NON_TRANSPOSE) {                        \
+      return CsrmvImpl(SPARSE_FN(csrmv_mp, sparse_prefix), context_,         \
+                       *cusparse_handle_, transA, m, n, nnz, alpha_host,     \
+                       descrA, csrSortedValA, csrSortedRowPtrA,              \
+                       csrSortedColIndA, x, beta_host, y);                   \
+    } else {                                                                 \
+      return CsrmvImpl(SPARSE_FN(csrmv, sparse_prefix), context_,            \
+                       *cusparse_handle_, transA, m, n, nnz, alpha_host,     \
+                       descrA, csrSortedValA, csrSortedRowPtrA,              \
+                       csrSortedColIndA, x, beta_host, y);                   \
+    }                                                                        \
+  }
+
+TF_CALL_LAPACK_TYPES(CSRMV_INSTANCE);
+
+template <typename Scalar, typename SparseFnT>
+static inline Status CsrgeamImpl(
+    SparseFnT op, OpKernelContext* context, cusparseHandle_t cusparse_handle,
+    int m, int n, const Scalar* alpha, const cusparseMatDescr_t descrA,
+    int nnzA, const Scalar* csrSortedValA, const int* csrSortedRowPtrA,
+    const int* csrSortedColIndA, const Scalar* beta,
+    const cusparseMatDescr_t descrB, int nnzB, const Scalar* csrSortedValB,
+    const int* csrSortedRowPtrB, const int* csrSortedColIndB,
+    const cusparseMatDescr_t descrC, Scalar* csrSortedValC,
+    int* csrSortedRowPtrC, int* csrSortedColIndC) {
+  TF_RETURN_IF_CUSPARSE_ERROR(
+      op(cusparse_handle, m, n, AsCudaComplex(alpha), descrA, nnzA,
+         AsCudaComplex(csrSortedValA), csrSortedRowPtrA, csrSortedColIndA,
+         AsCudaComplex(beta), descrB, nnzB, AsCudaComplex(csrSortedValB),
+         csrSortedRowPtrB, csrSortedColIndB, descrC,
+         AsCudaComplex(csrSortedValC), csrSortedRowPtrC, csrSortedColIndC));
+  return Status::OK();
+}
+
+#define CSRGEAM_INSTANCE(Scalar, sparse_prefix)                               \
+  template <>                                                                 \
+  Status CudaSparse::Csrgeam<Scalar>(                                         \
+      int m, int n, const Scalar* alpha, const cusparseMatDescr_t descrA,     \
+      int nnzA, const Scalar* csrSortedValA, const int* csrSortedRowPtrA,     \
+      const int* csrSortedColIndA, const Scalar* beta,                        \
+      const cusparseMatDescr_t descrB, int nnzB, const Scalar* csrSortedValB, \
+      const int* csrSortedRowPtrB, const int* csrSortedColIndB,               \
+      const cusparseMatDescr_t descrC, Scalar* csrSortedValC,                 \
+      int* csrSortedRowPtrC, int* csrSortedColIndC) {                         \
+    DCHECK(initialized_);                                                     \
+    return CsrgeamImpl(SPARSE_FN(csrgeam, sparse_prefix), context_,           \
+                       *cusparse_handle_, m, n, alpha, descrA, nnzA,          \
+                       csrSortedValA, csrSortedRowPtrA, csrSortedColIndA,     \
+                       beta, descrB, nnzB, csrSortedValB, csrSortedRowPtrB,   \
+                       csrSortedColIndB, descrC, csrSortedValC,               \
+                       csrSortedRowPtrC, csrSortedColIndC);                   \
+  }
+
+TF_CALL_LAPACK_TYPES(CSRGEAM_INSTANCE);
+
+Status CudaSparse::CsrgemmNnz(
+    cusparseOperation_t transA, cusparseOperation_t transB, int m, int k, int n,
+    const cusparseMatDescr_t descrA, int nnzA, const int* csrSortedRowPtrA,
+    const int* csrSortedColIndA, const cusparseMatDescr_t descrB, int nnzB,
+    const int* csrSortedRowPtrB, const int* csrSortedColIndB,
+    const cusparseMatDescr_t descrC, int* csrSortedRowPtrC,
+    int* nnzTotalDevHostPtr) {
+  DCHECK(initialized_);
+  DCHECK(nnzTotalDevHostPtr != nullptr);
+  TF_RETURN_IF_CUSPARSE_ERROR(cusparseXcsrgemmNnz(
+      *cusparse_handle_, transA, transB, m, k, n, descrA, nnzA,
+      csrSortedRowPtrA, csrSortedColIndA, descrB, nnzB, csrSortedRowPtrB,
+      csrSortedColIndB, descrC, csrSortedRowPtrC, nnzTotalDevHostPtr));
+  return Status::OK();
+}
+
+template <typename Scalar, typename SparseFnT>
+static inline Status CsrgemmImpl(
+    SparseFnT op, OpKernelContext* context, cusparseHandle_t cusparse_handle,
+    cusparseOperation_t transA, cusparseOperation_t transB, int m, int k, int n,
+    const cusparseMatDescr_t descrA, int nnzA, const Scalar* csrSortedValA,
+    const int* csrSortedRowPtrA, const int* csrSortedColIndA,
+    const cusparseMatDescr_t descrB, int nnzB, const Scalar* csrSortedValB,
+    const int* csrSortedRowPtrB, const int* csrSortedColIndB,
+    const cusparseMatDescr_t descrC, Scalar* csrSortedValC,
+    int* csrSortedRowPtrC, int* csrSortedColIndC) {
+  TF_RETURN_IF_CUSPARSE_ERROR(
+      op(cusparse_handle, transA, transB, m, k, n, descrA, nnzA,
+         AsCudaComplex(csrSortedValA), csrSortedRowPtrA, csrSortedColIndA,
+         descrB, nnzB, AsCudaComplex(csrSortedValB), csrSortedRowPtrB,
+         csrSortedColIndB, descrC, AsCudaComplex(csrSortedValC),
+         csrSortedRowPtrC, csrSortedColIndC));
+  return Status::OK();
+}
+
+#define CSRGEMM_INSTANCE(Scalar, sparse_prefix)                               \
+  template <>                                                                 \
+  Status CudaSparse::Csrgemm<Scalar>(                                         \
+      cusparseOperation_t transA, cusparseOperation_t transB, int m, int k,   \
+      int n, const cusparseMatDescr_t descrA, int nnzA,                       \
+      const Scalar* csrSortedValA, const int* csrSortedRowPtrA,               \
+      const int* csrSortedColIndA, const cusparseMatDescr_t descrB, int nnzB, \
+      const Scalar* csrSortedValB, const int* csrSortedRowPtrB,               \
+      const int* csrSortedColIndB, const cusparseMatDescr_t descrC,           \
+      Scalar* csrSortedValC, int* csrSortedRowPtrC, int* csrSortedColIndC) {  \
+    DCHECK(initialized_);                                                     \
+    return CsrgemmImpl(SPARSE_FN(csrgemm, sparse_prefix), context_,           \
+                       *cusparse_handle_, transA, transB, m, k, n, descrA,    \
+                       nnzA, csrSortedValA, csrSortedRowPtrA,                 \
+                       csrSortedColIndA, descrB, nnzB, csrSortedValB,         \
+                       csrSortedRowPtrB, csrSortedColIndB, descrC,            \
+                       csrSortedValC, csrSortedRowPtrC, csrSortedColIndC);    \
+  }
+
+TF_CALL_LAPACK_TYPES(CSRGEMM_INSTANCE);
+
+template <typename Scalar, typename BufferSizeFnT, typename SparseFnT>
+static inline Status Csru2csrImpl(SparseFnT op, BufferSizeFnT buffer_size_op,
+                                  OpKernelContext* context,
+                                  cusparseHandle_t cusparse_handle, int m,
+                                  int n, int nnz,
+                                  const cusparseMatDescr_t descrA,
+                                  Scalar* csrVal, const int* csrRowPtr,
+                                  int* csrColInd) {
+  CudaSparseCsrSortingConversionInfo info;
+  TF_RETURN_IF_ERROR(info.Initialize());
+
+  size_t pBufferSizeInBytes = 0;
+
+  TF_RETURN_IF_CUSPARSE_ERROR(
+      buffer_size_op(cusparse_handle, m, n, nnz, AsCudaComplex(csrVal),
+                     csrRowPtr, csrColInd, info.info(), &pBufferSizeInBytes));
+
+  Tensor pBuffer_t;
+  TF_RETURN_IF_ERROR(context->allocate_temp(
+      DT_INT8, TensorShape({static_cast<int64>(pBufferSizeInBytes)}),
+      &pBuffer_t));
+  auto pBuffer = pBuffer_t.flat<int8>();
+  DCHECK(pBuffer.data() != nullptr);
+
+  TF_RETURN_IF_CUSPARSE_ERROR(op(cusparse_handle, m, n, nnz, descrA,
+                                 AsCudaComplex(csrVal), csrRowPtr, csrColInd,
+                                 info.info(), pBuffer.data()));
+
+  return Status::OK();
+}
+
+#define CSRU2CSR_INSTANCE(Scalar, sparse_prefix)                              \
+  template <>                                                                 \
+  Status CudaSparse::Csru2csr<Scalar>(                                        \
+      int m, int n, int nnz, const cusparseMatDescr_t descrA, Scalar* csrVal, \
+      const int* csrRowPtr, int* csrColInd) {                                 \
+    DCHECK(initialized_);                                                     \
+    return Csru2csrImpl(SPARSE_FN(csru2csr, sparse_prefix),                   \
+                        BUFSIZE_FN(csru2csr, sparse_prefix), context_,        \
+                        *cusparse_handle_, m, n, nnz, descrA, csrVal,         \
+                        csrRowPtr, csrColInd);                                \
+  }
+
+TF_CALL_LAPACK_TYPES(CSRU2CSR_INSTANCE);
+
+template <typename Scalar, typename SparseFnT>
+static inline Status Csr2cscImpl(SparseFnT op, OpKernelContext* context,
+                                 cusparseHandle_t cusparse_handle, int m, int n,
+                                 int nnz, const Scalar* csrVal,
+                                 const int* csrRowPtr, const int* csrColInd,
+                                 Scalar* cscVal, int* cscRowInd, int* cscColPtr,
+                                 const cusparseAction_t copyValues) {
+  TF_RETURN_IF_CUSPARSE_ERROR(op(cusparse_handle, m, n, nnz,
+                                 AsCudaComplex(csrVal), csrRowPtr, csrColInd,
+                                 AsCudaComplex(cscVal), cscRowInd, cscColPtr,
+                                 copyValues, CUSPARSE_INDEX_BASE_ZERO));
+  return Status::OK();
+}
+
+#define CSR2CSC_INSTANCE(Scalar, sparse_prefix)                              \
+  template <>                                                                \
+  Status CudaSparse::Csr2csc<Scalar>(                                        \
+      int m, int n, int nnz, const Scalar* csrVal, const int* csrRowPtr,     \
+      const int* csrColInd, Scalar* cscVal, int* cscRowInd, int* cscColPtr,  \
+      const cusparseAction_t copyValues) {                                   \
+    DCHECK(initialized_);                                                    \
+    return Csr2cscImpl(SPARSE_FN(csr2csc, sparse_prefix), context_,          \
+                       *cusparse_handle_, m, n, nnz, csrVal, csrRowPtr,      \
+                       csrColInd, cscVal, cscRowInd, cscColPtr, copyValues); \
+  }
+
+TF_CALL_LAPACK_TYPES(CSR2CSC_INSTANCE);
+
 }  // namespace tensorflow
 
 #endif  // GOOGLE_CUDA
diff --git a/tensorflow/core/kernels/cuda_sparse.h b/tensorflow/core/kernels/cuda_sparse.h
index 4bdfb991200..f2ef99c67e6 100644
--- a/tensorflow/core/kernels/cuda_sparse.h
+++ b/tensorflow/core/kernels/cuda_sparse.h
@@ -11,8 +11,7 @@ distributed under the License is distributed on an "AS IS" BASIS,
 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 See the License for the specific language governing permissions and
 limitations under the License.
-==============================================================================
-*/
+==============================================================================*/
 
 #ifndef TENSORFLOW_CORE_KERNELS_CUDA_SPARSE_H_
 #define TENSORFLOW_CORE_KERNELS_CUDA_SPARSE_H_
@@ -76,6 +75,22 @@ inline string ConvertCUSparseErrorToString(const cusparseStatus_t status) {
     }                                                                      \
   } while (0)
 
+inline cusparseOperation_t TransposeAndConjugateToCuSparseOp(bool transpose,
+                                                             bool conjugate,
+                                                             Status* status) {
+  if (transpose) {
+    return conjugate ? CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE
+                     : CUSPARSE_OPERATION_TRANSPOSE;
+  } else {
+    if (conjugate) {
+      DCHECK(status != nullptr);
+      *status = errors::InvalidArgument(
+          "Conjugate == True and transpose == False is not supported.");
+    }
+    return CUSPARSE_OPERATION_NON_TRANSPOSE;
+  }
+}
+
 // The CudaSparse class provides a simplified templated API for cuSparse
 // (http://docs.nvidia.com/cuda/cusparse/index.html).
 // An object of this class wraps static cuSparse instances,
@@ -89,7 +104,7 @@ inline string ConvertCUSparseErrorToString(const cusparseStatus_t status) {
 class CudaSparse {
  public:
   // This object stores a pointer to context, which must outlive it.
-  explicit CudaSparse(OpKernelContext *context);
+  explicit CudaSparse(OpKernelContext* context);
   virtual ~CudaSparse() {}
 
   // This initializes the CudaSparse class if it hasn't
@@ -180,6 +195,119 @@ class CudaSparse {
                                         int batchStride,
                                         size_t *bufferSizeInBytes) const;
 
+  // Compresses the indices of rows or columns. It can be interpreted as a
+  // conversion from COO to CSR sparse storage format. See:
+  // http://docs.nvidia.com/cuda/cusparse/index.html#cusparse-lt-t-gt-csr2coo.
+  Status Csr2coo(const int* CsrRowPtr, int nnz, int m, int* cooRowInd) const;
+
+  // Uncompresses the indices of rows or columns. It can be interpreted as a
+  // conversion from CSR to COO sparse storage format. See:
+  // http://docs.nvidia.com/cuda/cusparse/index.html#cusparse-lt-t-gt-coo2csr.
+  Status Coo2csr(const int* cooRowInd, int nnz, int m, int* csrRowPtr) const;
+
+  // Sparse-dense matrix multiplication C = alpha * op(A) * op(B)  + beta * C,
+  // where A is a sparse matrix in CSR format, B and C are dense tall
+  // matrices.  This routine allows transposition of matrix B, which
+  // may improve performance.  See:
+  // http://docs.nvidia.com/cuda/cusparse/index.html#cusparse-lt-t-gt-csrmm2
+  //
+  // **NOTE** Matrices B and C are expected to be in column-major
+  // order; to make them consistent with TensorFlow they
+  // must be transposed (or the matmul op's pre/post-procesisng must take this
+  // into account).
+  //
+  // **NOTE** This is an in-place operation for data in C.
+  template <typename Scalar>
+  Status Csrmm(cusparseOperation_t transA, cusparseOperation_t transB, int m,
+               int n, int k, int nnz, const Scalar* alpha_host,
+               const cusparseMatDescr_t descrA, const Scalar* csrSortedValA,
+               const int* csrSortedRowPtrA, const int* csrSortedColIndA,
+               const Scalar* B, int ldb, const Scalar* beta_host, Scalar* C,
+               int ldc) const;
+
+  // Sparse-dense vector multiplication y = alpha * op(A) * x  + beta * y,
+  // where A is a sparse matrix in CSR format, x and y are dense vectors. See:
+  // http://docs.nvidia.com/cuda/cusparse/index.html#cusparse-lt-t-gt-csrmv_mergepath
+  //
+  // **NOTE** This is an in-place operation for data in y.
+  template <typename Scalar>
+  Status Csrmv(cusparseOperation_t transA, int m, int n, int nnz,
+               const Scalar* alpha_host, const cusparseMatDescr_t descrA,
+               const Scalar* csrSortedValA, const int* csrSortedRowPtrA,
+               const int* csrSortedColIndA, const Scalar* x,
+               const Scalar* beta_host, Scalar* y) const;
+
+  // Computes sparse-sparse matrix addition of matrices
+  // stored in CSR format.  This is part one: calculate nnz of the
+  // output.  csrSortedRowPtrC must be preallocated on device with
+  // m + 1 entries.  See:
+  // http://docs.nvidia.com/cuda/cusparse/index.html#cusparse-lt-t-gt-csrgeam.
+  Status CsrgeamNnz(int m, int n, const cusparseMatDescr_t descrA, int nnzA,
+                    const int* csrSortedRowPtrA, const int* csrSortedColIndA,
+                    const cusparseMatDescr_t descrB, int nnzB,
+                    const int* csrSortedRowPtrB, const int* csrSortedColIndB,
+                    const cusparseMatDescr_t descrC, int* csrSortedRowPtrC,
+                    int* nnzTotalDevHostPtr);
+
+  // Computes sparse - sparse matrix addition of matrices
+  // stored in CSR format.  This is part two: perform sparse-sparse
+  // addition.  csrValC and csrColIndC must be allocated on the device
+  // with nnzTotalDevHostPtr entries (as calculated by CsrgeamNnz).  See:
+  // http://docs.nvidia.com/cuda/cusparse/index.html#cusparse-lt-t-gt-csrgeam.
+  template <typename Scalar>
+  Status Csrgeam(int m, int n, const Scalar* alpha,
+                 const cusparseMatDescr_t descrA, int nnzA,
+                 const Scalar* csrSortedValA, const int* csrSortedRowPtrA,
+                 const int* csrSortedColIndA, const Scalar* beta,
+                 const cusparseMatDescr_t descrB, int nnzB,
+                 const Scalar* csrSortedValB, const int* csrSortedRowPtrB,
+                 const int* csrSortedColIndB, const cusparseMatDescr_t descrC,
+                 Scalar* csrSortedValC, int* csrSortedRowPtrC,
+                 int* csrSortedColIndC);
+
+  // Computes sparse-sparse matrix multiplication of matrices
+  // stored in CSR format.  This is part one: calculate nnz of the
+  // output.  csrSortedRowPtrC must be preallocated on device with
+  // m + 1 entries.  See:
+  // http://docs.nvidia.com/cuda/cusparse/index.html#cusparse-lt-t-gt-csrgemm.
+  Status CsrgemmNnz(cusparseOperation_t transA, cusparseOperation_t transB,
+                    int m, int k, int n, const cusparseMatDescr_t descrA,
+                    int nnzA, const int* csrSortedRowPtrA,
+                    const int* csrSortedColIndA,
+                    const cusparseMatDescr_t descrB, int nnzB,
+                    const int* csrSortedRowPtrB, const int* csrSortedColIndB,
+                    const cusparseMatDescr_t descrC, int* csrSortedRowPtrC,
+                    int* nnzTotalDevHostPtr);
+
+  // Computes sparse - sparse matrix matmul of matrices
+  // stored in CSR format.  This is part two: perform sparse-sparse
+  // addition.  csrValC and csrColIndC must be allocated on the device
+  // with nnzTotalDevHostPtr entries (as calculated by CsrgemmNnz).  See:
+  // http://docs.nvidia.com/cuda/cusparse/index.html#cusparse-lt-t-gt-csrgemm.
+  template <typename Scalar>
+  Status Csrgemm(cusparseOperation_t transA, cusparseOperation_t transB, int m,
+                 int k, int n, const cusparseMatDescr_t descrA, int nnzA,
+                 const Scalar* csrSortedValA, const int* csrSortedRowPtrA,
+                 const int* csrSortedColIndA, const cusparseMatDescr_t descrB,
+                 int nnzB, const Scalar* csrSortedValB,
+                 const int* csrSortedRowPtrB, const int* csrSortedColIndB,
+                 const cusparseMatDescr_t descrC, Scalar* csrSortedValC,
+                 int* csrSortedRowPtrC, int* csrSortedColIndC);
+
+  // In-place reordering of unsorted CSR to sorted CSR.
+  // http://docs.nvidia.com/cuda/cusparse/index.html#cusparse-lt-t-gt-csru2csr
+  template <typename Scalar>
+  Status Csru2csr(int m, int n, int nnz, const cusparseMatDescr_t descrA,
+                  Scalar* csrVal, const int* csrRowPtr, int* csrColInd);
+
+  // Converts from CSR to CSC format (equivalently, transpose).
+  // http://docs.nvidia.com/cuda/cusparse/index.html#cusparse-csr2cscEx
+  template <typename Scalar>
+  Status Csr2csc(int m, int n, int nnz, const Scalar* csrVal,
+                 const int* csrRowPtr, const int* csrColInd, Scalar* cscVal,
+                 int* cscRowInd, int* cscColPtr,
+                 const cusparseAction_t copyValues);
+
  private:
   bool initialized_;
   OpKernelContext *context_;  // not owned.
@@ -189,6 +317,119 @@ class CudaSparse {
   TF_DISALLOW_COPY_AND_ASSIGN(CudaSparse);
 };
 
+// A wrapper class to ensure that a CUDA sparse matrix descriptor is initialized
+// only once. For more details on the descriptor (cusparseMatDescr_t), see:
+// https://docs.nvidia.com/cuda/cusparse/index.html#cusparsematdescrt
+class CudaSparseMatrixDescriptor {
+ public:
+  explicit CudaSparseMatrixDescriptor() : initialized_(false) {}
+
+  CudaSparseMatrixDescriptor(CudaSparseMatrixDescriptor&& rhs)
+      : initialized_(rhs.initialized_), descr_(std::move(rhs.descr_)) {
+    rhs.initialized_ = false;
+  }
+
+  CudaSparseMatrixDescriptor& operator=(CudaSparseMatrixDescriptor&& rhs) {
+    if (this == &rhs) return *this;
+    Release();
+    initialized_ = rhs.initialized_;
+    descr_ = std::move(rhs.descr_);
+    rhs.initialized_ = false;
+    return *this;
+  }
+
+  ~CudaSparseMatrixDescriptor() { Release(); }
+
+  // Initializes the underlying descriptor.  Will fail on the second call if
+  // called more than once.
+  Status Initialize() {
+    DCHECK(!initialized_);
+    TF_RETURN_IF_CUSPARSE_ERROR(cusparseCreateMatDescr(&descr_));
+    initialized_ = true;
+    return Status::OK();
+  }
+
+  cusparseMatDescr_t& descr() {
+    DCHECK(initialized_);
+    return descr_;
+  }
+
+  const cusparseMatDescr_t& descr() const {
+    DCHECK(initialized_);
+    return descr_;
+  }
+
+ private:
+  void Release() {
+    if (initialized_) {
+      cusparseDestroyMatDescr(descr_);
+      initialized_ = false;
+    }
+  }
+
+  bool initialized_;
+  cusparseMatDescr_t descr_;
+
+  TF_DISALLOW_COPY_AND_ASSIGN(CudaSparseMatrixDescriptor);
+};
+
+// A wrapper class to ensure that an unsorted/sorted CSR conversion information
+// struct (csru2csrInfo_t) is initialized only once. See:
+// https://docs.nvidia.com/cuda/cusparse/index.html#csru2csr
+class CudaSparseCsrSortingConversionInfo {
+ public:
+  explicit CudaSparseCsrSortingConversionInfo() : initialized_(false) {}
+
+  CudaSparseCsrSortingConversionInfo(CudaSparseCsrSortingConversionInfo&& rhs)
+      : initialized_(rhs.initialized_), info_(std::move(rhs.info_)) {
+    rhs.initialized_ = false;
+  }
+
+  CudaSparseCsrSortingConversionInfo& operator=(
+      CudaSparseCsrSortingConversionInfo&& rhs) {
+    if (this == &rhs) return *this;
+    Release();
+    initialized_ = rhs.initialized_;
+    info_ = std::move(rhs.info_);
+    rhs.initialized_ = false;
+    return *this;
+  }
+
+  ~CudaSparseCsrSortingConversionInfo() { Release(); }
+
+  // Initializes the underlying info. Will fail on the second call if called
+  // more than once.
+  Status Initialize() {
+    DCHECK(!initialized_);
+    TF_RETURN_IF_CUSPARSE_ERROR(cusparseCreateCsru2csrInfo(&info_));
+    initialized_ = true;
+    return Status::OK();
+  }
+
+  csru2csrInfo_t& info() {
+    DCHECK(initialized_);
+    return info_;
+  }
+
+  const csru2csrInfo_t& info() const {
+    DCHECK(initialized_);
+    return info_;
+  }
+
+ private:
+  void Release() {
+    if (initialized_) {
+      cusparseDestroyCsru2csrInfo(info_);
+      initialized_ = false;
+    }
+  }
+
+  bool initialized_;
+  csru2csrInfo_t info_;
+
+  TF_DISALLOW_COPY_AND_ASSIGN(CudaSparseCsrSortingConversionInfo);
+};
+
 }  // namespace tensorflow
 
 #endif  // GOOGLE_CUDA
diff --git a/tensorflow/core/kernels/sparse/BUILD b/tensorflow/core/kernels/sparse/BUILD
new file mode 100644
index 00000000000..808a269b645
--- /dev/null
+++ b/tensorflow/core/kernels/sparse/BUILD
@@ -0,0 +1,100 @@
+# Description: Op kernels for sparse matrix operations.
+
+load(
+    "//tensorflow:tensorflow.bzl",
+    "tf_cc_test",
+    "tf_kernel_library",
+)
+load("@local_config_cuda//cuda:build_defs.bzl", "if_cuda")
+
+package(
+    default_visibility = ["//visibility:public"],
+    licenses = ["notice"],  # Apache 2.0
+)
+
+cc_library(
+    name = "sparse_matrix",
+    srcs = ["sparse_matrix.cc"],
+    hdrs = ["sparse_matrix.h"],
+    deps = [
+        "//tensorflow/core:framework",
+        "//third_party/eigen3",
+    ],
+)
+
+tf_kernel_library(
+    name = "kernels",
+    srcs = [
+        "add_op.cc",
+        "conj_op.cc",
+        "csr_sparse_matrix_to_dense_op.cc",
+        "csr_sparse_matrix_to_sparse_tensor_op.cc",
+        "dense_to_csr_sparse_matrix_op.cc",
+        "kernels.cc",
+        "mat_mul_op.cc",
+        "mul_op.cc",
+        "nnz_op.cc",
+        "softmax_op.cc",
+        "sparse_cholesky_op.cc",
+        "sparse_mat_mul_op.cc",
+        "sparse_matrix_components_op.cc",
+        "sparse_ordering_amd_op.cc",
+        "sparse_tensor_to_csr_sparse_matrix_op.cc",
+        "transpose_op.cc",
+        "zeros_op.cc",
+    ],
+    hdrs = [
+        "kernels.h",
+        "transpose_op.h",
+        "zeros_op.h",
+    ],
+    gpu_srcs = [
+        "zeros_op.h",
+        "kernels.h",
+        "kernels_gpu.cu.cc",
+    ],
+    deps = [
+        ":sparse_matrix",
+        "//third_party/eigen3",
+        "//tensorflow/core:array_ops_op_lib",
+        "//tensorflow/core:bitwise_ops_op_lib",
+        "//tensorflow/core:framework",
+        "//tensorflow/core:functional_ops_op_lib",
+        "//tensorflow/core:lib",
+        "//tensorflow/core:math_ops_op_lib",
+        "//tensorflow/core:nn_ops_op_lib",
+        "//tensorflow/core:no_op_op_lib",
+        "//tensorflow/core:sendrecv_ops_op_lib",
+        "//tensorflow/core:sparse_csr_matrix_ops_op_lib",
+        "//tensorflow/core:state_ops_op_lib",
+        "//tensorflow/core/kernels:concat_lib",
+        "//tensorflow/core/kernels:constant_op",
+        "//tensorflow/core/kernels:cwise_op",
+        "//tensorflow/core/kernels:dense_update_functor",
+        "//tensorflow/core/kernels:fill_functor",
+        "//tensorflow/core/kernels:gather_nd_op",
+        "//tensorflow/core/kernels:scatter_nd_op",
+        "//tensorflow/core/kernels:slice_op",
+        "//tensorflow/core/kernels:transpose_functor",
+    ] + if_cuda([
+        "//tensorflow/core/kernels:cuda_solvers",
+        "//tensorflow/core/kernels:cuda_sparse",
+    ]),
+    alwayslink = 1,
+)
+
+tf_cc_test(
+    name = "kernels_test",
+    size = "small",
+    srcs = [
+        "kernels_test.cc",
+    ],
+    deps = [
+        ":kernels",
+        "//tensorflow/core:framework",
+        "//tensorflow/core:lib",
+        "//tensorflow/core:test",
+        "//tensorflow/core:testlib",
+        "//third_party/eigen3",
+    ],
+)
diff --git a/tensorflow/core/kernels/sparse/add_op.cc b/tensorflow/core/kernels/sparse/add_op.cc
new file mode 100644
index 00000000000..95d69410d45
--- /dev/null
+++ b/tensorflow/core/kernels/sparse/add_op.cc
@@ -0,0 +1,342 @@
+/* Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+#define EIGEN_USE_THREADS
+
+#if GOOGLE_CUDA
+#define EIGEN_USE_GPU
+#endif
+
+#include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
+#include "tensorflow/core/framework/op.h"
+#include "tensorflow/core/framework/op_kernel.h"
+#include "tensorflow/core/framework/tensor_shape.h"
+#include "tensorflow/core/framework/tensor_types.h"
+#include "tensorflow/core/framework/tensor_util.h"
+#include "tensorflow/core/framework/variant_op_registry.h"
+#include "tensorflow/core/kernels/dense_update_functor.h"
+#include "tensorflow/core/kernels/sparse/kernels.h"
+#include "tensorflow/core/kernels/sparse/sparse_matrix.h"
+#include "tensorflow/core/kernels/fill_functor.h"
+
+#if GOOGLE_CUDA
+#include "tensorflow/core/kernels/cuda_solvers.h"
+#include "tensorflow/core/kernels/cuda_sparse.h"
+#endif
+
+namespace tensorflow {
+
+typedef Eigen::ThreadPoolDevice CPUDevice;
+typedef Eigen::GpuDevice GPUDevice;
+
+namespace {
+template <typename Device, typename T>
+class CSRSparseMatrixAddFunctor {
+ public:
+  explicit CSRSparseMatrixAddFunctor(OpKernelContext* ctx, const T alpha,
+                                     const T beta)
+      : ctx_(ctx), alpha_(alpha), beta_(beta) {}
+
+  Status operator()(const CSRSparseMatrix& a, const CSRSparseMatrix& b,
+                    CSRSparseMatrix* c) {
+    TensorShape a_tensor_shape;
+    TensorShape b_tensor_shape;
+    TF_RETURN_IF_ERROR(TensorShapeUtils::MakeShape(a.dense_shape().vec<int64>(),
+                                                   &a_tensor_shape));
+    TF_RETURN_IF_ERROR(TensorShapeUtils::MakeShape(b.dense_shape().vec<int64>(),
+                                                   &b_tensor_shape));
+
+    if (a_tensor_shape.dims() == 3) {
+      if ((a_tensor_shape.dims() != b_tensor_shape.dims()) ||
+          (a_tensor_shape.dim_size(0) != b_tensor_shape.dim_size(0))) {
+        return errors::InvalidArgument(
+            "Incompatible shapes of a and b, a.shape == ",
+            a_tensor_shape.DebugString(),
+            ", b.shape == ", b_tensor_shape.DebugString());
+      }
+    }
+    const int rank = a_tensor_shape.dims();
+    if ((a_tensor_shape.dim_size(rank - 2) !=
+         b_tensor_shape.dim_size(rank - 2)) ||
+        (a_tensor_shape.dim_size(rank - 1) !=
+         b_tensor_shape.dim_size(rank - 1))) {
+      return errors::InvalidArgument(
+          "Incompatible shapes of a and b, a.shape == ",
+          a_tensor_shape.DebugString(),
+          ", b.shape == ", b_tensor_shape.DebugString());
+    }
+
+    const int batch_size = a.batch_size();
+
+    // TODO(ebrevdo): Add support for broadcasting at least in the
+    // batch dimension.
+    auto a_dense_shape = a.dense_shape().vec<int64>();
+    auto b_dense_shape = b.dense_shape().vec<int64>();
+    Tensor c_dense_shape_t = a.dense_shape();
+
+    const int64 rows = a_dense_shape((rank == 2) ? 0 : 1);
+
+    functor::CSRSparseMatrixAdd<Device, T> csr_geam(ctx_, alpha_, beta_);
+    TF_RETURN_IF_ERROR(csr_geam.Initialize());
+
+    Tensor c_batch_ptr_t(cpu_allocator(), DT_INT32,
+                         TensorShape({batch_size + 1}));
+    auto c_batch_ptr = c_batch_ptr_t.vec<int32>();
+    c_batch_ptr(0) = 0;
+
+    Tensor c_row_ptr_t;
+    TF_RETURN_IF_ERROR(ctx_->allocate_temp(
+        DT_INT32, TensorShape({batch_size * (rows + 1)}), &c_row_ptr_t));
+    auto c_row_ptr = c_row_ptr_t.vec<int32>();
+
+    // Set the output row pointers to zero, in case we hit any empty
+    // combinations of rows in a and b.
+    functor::SetZeroFunctor<Device, int32> set_zero;
+    const Device& d = ctx_->eigen_device<Device>();
+    set_zero(d, c_row_ptr_t.flat<int32>());
+
+    for (int i = 0; i < batch_size; ++i) {
+      // Calculate output sizes for all minibatch entries.
+      // Store in c_batch_ptr and update c_row_ptrs.
+      if (a.nnz(i) == 0 && b.nnz(i) == 0) {
+        c_batch_ptr(i + 1) = c_batch_ptr(i);
+        continue;
+      }
+      ConstCSRComponent<T> a_comp{a.row_pointers_vec(i), a.col_indices_vec(i),
+                                  a.values_vec<T>(i), a_dense_shape};
+      ConstCSRComponent<T> b_comp{b.row_pointers_vec(i), b.col_indices_vec(i),
+                                  b.values_vec<T>(i), b_dense_shape};
+      TTypes<int32>::UnalignedVec c_row_ptr_i(&c_row_ptr(i * (rows + 1)),
+                                              rows + 1);
+      int c_nnz_i;
+      TF_RETURN_IF_ERROR(
+          csr_geam.GetOutputStructure(a_comp, b_comp, c_row_ptr_i, &c_nnz_i));
+      c_batch_ptr(i + 1) = c_batch_ptr(i) + c_nnz_i;
+    }
+
+    Tensor c_col_ind_t;
+    Tensor c_values_t;
+
+    const int total_nnz = c_batch_ptr(batch_size);
+
+    TF_RETURN_IF_ERROR(
+        ctx_->allocate_temp(DT_INT32, TensorShape({total_nnz}), &c_col_ind_t));
+    TF_RETURN_IF_ERROR(ctx_->allocate_temp(
+        DataTypeToEnum<T>::value, TensorShape({total_nnz}), &c_values_t));
+    TF_RETURN_IF_ERROR(CSRSparseMatrix::CreateCSRSparseMatrix(
+        DataTypeToEnum<T>::value, c_dense_shape_t, c_batch_ptr_t, c_row_ptr_t,
+        c_col_ind_t, c_values_t, c));
+
+    for (int i = 0; i < batch_size; ++i) {
+      if (a.nnz(i) == 0 && b.nnz(i) == 0) {
+        // Setting of c_row_pointers_vec(i) == 0 is already done.
+        continue;
+      }
+      ConstCSRComponent<T> a_comp{a.row_pointers_vec(i), a.col_indices_vec(i),
+                                  a.values_vec<T>(i), a_dense_shape};
+      ConstCSRComponent<T> b_comp{b.row_pointers_vec(i), b.col_indices_vec(i),
+                                  b.values_vec<T>(i), b_dense_shape};
+      CSRComponent<T> c_comp{c->row_pointers_vec(i), c->col_indices_vec(i),
+                             c->values_vec<T>(i), c_dense_shape_t.vec<int64>()};
+
+      TF_RETURN_IF_ERROR(csr_geam.Compute(a_comp, b_comp, &c_comp));
+    }
+
+    return Status::OK();
+  }
+
+ private:
+  OpKernelContext* ctx_;
+  const T alpha_;
+  const T beta_;
+};
+
+template <typename Device, typename T>
+class CSRSparseMatrixSumFunctor : public CSRSparseMatrixAddFunctor<Device, T> {
+ public:
+  // Same as above, but with alpha = beta = 1.0, so C = 1.0 * A + 1.0 * B.
+  explicit CSRSparseMatrixSumFunctor(OpKernelContext* ctx)
+      : CSRSparseMatrixAddFunctor<Device, T>(ctx, 1, 1) {}
+};
+
+}  // namespace
+
+template <typename Device, typename T>
+class CSRAddOp : public OpKernel {
+ public:
+  explicit CSRAddOp(OpKernelConstruction* c) : OpKernel(c) {}
+
+  void Compute(OpKernelContext* ctx) final {
+    const CSRSparseMatrix* a_matrix;
+    const CSRSparseMatrix* b_matrix;
+    OP_REQUIRES_OK(ctx, ExtractVariantFromInput(ctx, 0, &a_matrix));
+    OP_REQUIRES_OK(ctx, ExtractVariantFromInput(ctx, 1, &b_matrix));
+
+    OP_REQUIRES(
+        ctx, a_matrix->dtype() == DataTypeToEnum<T>::value,
+        errors::InvalidArgument("dtype of a is not equal to 'type': ",
+                                DataTypeString(a_matrix->dtype()), " vs. ",
+                                DataTypeString(DataTypeToEnum<T>::value)));
+    OP_REQUIRES(
+        ctx, b_matrix->dtype() == DataTypeToEnum<T>::value,
+        errors::InvalidArgument("dtype of b is not equal to 'type': ",
+                                DataTypeString(b_matrix->dtype()), " vs. ",
+                                DataTypeString(DataTypeToEnum<T>::value)));
+
+    const Tensor& alpha_t = ctx->input(2);
+    const Tensor& beta_t = ctx->input(3);
+    OP_REQUIRES(
+        ctx, TensorShapeUtils::IsScalar(alpha_t.shape()),
+        errors::InvalidArgument("Expected alpha to be a scalar, saw shape: ",
+                                alpha_t.shape().DebugString()));
+    OP_REQUIRES(
+        ctx, TensorShapeUtils::IsScalar(beta_t.shape()),
+        errors::InvalidArgument("Expected beta to be a scalar, saw shape: ",
+                                beta_t.shape().DebugString()));
+
+    const T host_alpha = alpha_t.scalar<T>()();
+    const T host_beta = beta_t.scalar<T>()();
+
+    Tensor c_t(cpu_allocator(), DT_VARIANT, TensorShape({}));
+    CSRSparseMatrix c_matrix;
+    CSRSparseMatrixAddFunctor<Device, T> add_functor(ctx, host_alpha,
+                                                     host_beta);
+    OP_REQUIRES_OK(ctx, add_functor(*a_matrix, *b_matrix, &c_matrix));
+    c_t.scalar<Variant>()() = std::move(c_matrix);
+    ctx->set_output(0, c_t);
+  }
+};
+
+#define REGISTER(DEV, T)                              \
+  REGISTER_KERNEL_BUILDER(Name("SparseMatrixAdd")     \
+                              .Device(DEVICE_##DEV)   \
+                              .TypeConstraint<T>("T") \
+                              .HostMemory("alpha")    \
+                              .HostMemory("beta"),    \
+                          CSRAddOp<DEV##Device, T>);
+
+#if GOOGLE_CUDA
+
+#define REGISTER_GPU(T) REGISTER(GPU, T)
+
+REGISTER_GPU(float)
+REGISTER_GPU(double)
+REGISTER_GPU(complex64)
+REGISTER_GPU(complex128)
+
+#undef REGISTER_GPU
+
+REGISTER_UNARY_VARIANT_BINARY_OP_FUNCTION(
+    ADD_VARIANT_BINARY_OP, DEVICE_GPU, CSRSparseMatrix,
+    (CSRSparseMatrixBinaryHelper<GPUDevice, CSRSparseMatrixSumFunctor>));
+
+#endif  // GOOGLE_CUDA
+
+#undef REGISTER
+
+#if GOOGLE_CUDA
+namespace functor {
+template <typename T>
+struct CSRSparseMatrixAdd<GPUDevice, T>
+    : public CSRStructureModifyingFunctor<GPUDevice, T> {
+  explicit CSRSparseMatrixAdd(OpKernelContext* ctx, const T alpha, const T beta)
+      : ctx_(ctx),
+        cuda_sparse_(ctx),
+        alpha_(alpha),
+        beta_(beta),
+        initialized_(false) {}
+
+  Status Initialize() {
+    TF_RETURN_IF_ERROR(cuda_sparse_.Initialize());
+    TF_RETURN_IF_ERROR(descrA_.Initialize());
+    TF_RETURN_IF_ERROR(descrB_.Initialize());
+    TF_RETURN_IF_ERROR(descrC_.Initialize());
+    initialized_ = true;
+    return Status::OK();
+  }
+
+  Status GetOutputStructure(const ConstCSRComponent<T>& a,
+                            const ConstCSRComponent<T>& b,
+                            TTypes<int32>::UnalignedVec c_row_ptr,
+                            int* output_nnz) {
+    DCHECK(initialized_);
+
+    const int m = a.row_ptr.size() - 1;
+    DCHECK_EQ(m, b.row_ptr.size() - 1);
+    const int row_dim = a.dense_shape_host.size() == 2 ? 0 : 1;
+    DCHECK_EQ(m, a.dense_shape_host(row_dim));
+    DCHECK_EQ(m, b.dense_shape_host(row_dim));
+    const int nnzA = a.col_ind.size();
+    const int nnzB = b.col_ind.size();
+    *output_nnz = -1;
+
+    const int n = a.dense_shape_host(row_dim + 1);
+    DCHECK_EQ(n, b.dense_shape_host(row_dim + 1));
+
+    TF_RETURN_IF_ERROR(cuda_sparse_.CsrgeamNnz(
+        m, n, descrA_.descr(), nnzA, a.row_ptr.data(), a.col_ind.data(),
+        descrB_.descr(), nnzB, b.row_ptr.data(), b.col_ind.data(),
+        descrC_.descr(), c_row_ptr.data(), output_nnz));
+
+    if (*output_nnz < 0) {
+      return errors::Internal(
+          "CSRAdd: CsrgeamNnz returned nnzTotalDevHostPtr < 0: ", *output_nnz);
+    }
+    return Status::OK();
+  }
+
+  Status Compute(const ConstCSRComponent<T>& a, const ConstCSRComponent<T>& b,
+                 CSRComponent<T>* c) {
+    DCHECK(initialized_);
+
+    const int m = a.row_ptr.size() - 1;
+    DCHECK_EQ(m, b.row_ptr.size() - 1);
+    const int row_dim = a.dense_shape_host.size() == 2 ? 0 : 1;
+    DCHECK_EQ(m, a.dense_shape_host(row_dim));
+    DCHECK_EQ(m, b.dense_shape_host(row_dim));
+    const int nnzA = a.col_ind.size();
+    const int nnzB = b.col_ind.size();
+
+    const int n = a.dense_shape_host(row_dim + 1);
+    DCHECK_EQ(n, b.dense_shape_host(row_dim + 1));
+
+    // Adding alpha * a + beta * b.
+    TF_RETURN_IF_ERROR(cuda_sparse_.Csrgeam(
+        m, n, &alpha_, descrA_.descr(), nnzA, a.values.data(), a.row_ptr.data(),
+        a.col_ind.data(), &beta_, descrB_.descr(), nnzB, b.values.data(),
+        b.row_ptr.data(), b.col_ind.data(), descrC_.descr(), c->values.data(),
+        c->row_ptr.data(), c->col_ind.data()));
+
+    return Status::OK();
+  }
+
+ private:
+  OpKernelContext* ctx_;
+  CudaSparse cuda_sparse_;
+  CudaSparseMatrixDescriptor descrA_;
+  CudaSparseMatrixDescriptor descrB_;
+  CudaSparseMatrixDescriptor descrC_;
+  const T alpha_;
+  const T beta_;
+  bool initialized_;
+
+  TF_DISALLOW_COPY_AND_ASSIGN(CSRSparseMatrixAdd);
+};
+
+}  // namespace functor
+
+#endif  // GOOGLE_CUDA
+
+}  // namespace tensorflow
diff --git a/tensorflow/core/kernels/sparse/conj_op.cc b/tensorflow/core/kernels/sparse/conj_op.cc
new file mode 100644
index 00000000000..3ebab4b2ebc
--- /dev/null
+++ b/tensorflow/core/kernels/sparse/conj_op.cc
@@ -0,0 +1,98 @@
+/* Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+#define EIGEN_USE_THREADS
+
+#if GOOGLE_CUDA
+#define EIGEN_USE_GPU
+#endif
+
+#include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
+#include "tensorflow/core/framework/op.h"
+#include "tensorflow/core/framework/op_kernel.h"
+#include "tensorflow/core/framework/tensor_shape.h"
+#include "tensorflow/core/framework/tensor_types.h"
+#include "tensorflow/core/framework/tensor_util.h"
+#include "tensorflow/core/framework/variant_op_registry.h"
+#include "tensorflow/core/kernels/cwise_ops.h"
+#include "tensorflow/core/kernels/sparse/kernels.h"
+#include "tensorflow/core/kernels/sparse/sparse_matrix.h"
+
+#if GOOGLE_CUDA
+#include "tensorflow/core/kernels/cuda_solvers.h"
+#include "tensorflow/core/kernels/cuda_sparse.h"
+#endif
+
+namespace tensorflow {
+
+typedef Eigen::ThreadPoolDevice CPUDevice;
+typedef Eigen::GpuDevice GPUDevice;
+
+namespace {
+template <typename Device, typename T>
+class CSRSparseMatrixConjFunctor {
+ public:
+  explicit CSRSparseMatrixConjFunctor(OpKernelContext* ctx) : ctx_(ctx) {}
+
+  Status operator()(const CSRSparseMatrix& a, CSRSparseMatrix* b) {
+    const int total_nnz = a.total_nnz();
+    Tensor b_values_t;
+    TF_RETURN_IF_ERROR(ctx_->allocate_temp(
+        DataTypeToEnum<T>::value, TensorShape({total_nnz}), &b_values_t));
+    TF_RETURN_IF_ERROR(CSRSparseMatrix::CreateCSRSparseMatrix(
+        DataTypeToEnum<T>::value, a.dense_shape(), a.batch_pointers(),
+        a.row_pointers(), a.col_indices(), b_values_t, b));
+
+    const Device& d = ctx_->eigen_device<Device>();
+    functor::UnaryFunctor<Device, functor::conj<T>> func;
+    func(d, b->values().flat<T>() /*out*/, a.values().flat<T>() /*in*/);
+
+    return Status::OK();
+  }
+
+ private:
+  OpKernelContext* ctx_;
+};
+
+// Partial specialization for real types where conjugation is a noop.
+#define NOOP_CONJ_FUNCTOR(T)                                             \
+  template <typename Device>                                             \
+  class CSRSparseMatrixConjFunctor<Device, T> {                          \
+   public:                                                               \
+    explicit CSRSparseMatrixConjFunctor(OpKernelContext* ctx) {}         \
+    Status operator()(const CSRSparseMatrix& a, CSRSparseMatrix* b) {    \
+      TF_RETURN_IF_ERROR(CSRSparseMatrix::CreateCSRSparseMatrix(         \
+          DataTypeToEnum<T>::value, a.dense_shape(), a.batch_pointers(), \
+          a.row_pointers(), a.col_indices(), a.values(), b));            \
+      return Status::OK();                                               \
+    }                                                                    \
+  };
+
+NOOP_CONJ_FUNCTOR(float);
+NOOP_CONJ_FUNCTOR(double);
+
+#undef NOOP_CONJ_FUNCTOR
+
+}  // namespace
+
+#if GOOGLE_CUDA
+
+REGISTER_UNARY_VARIANT_UNARY_OP_FUNCTION(
+    CONJ_VARIANT_UNARY_OP, DEVICE_GPU, CSRSparseMatrix,
+    (CSRSparseMatrixUnaryHelper<GPUDevice, CSRSparseMatrixConjFunctor>));
+
+#endif  // GOOGLE_CUDA
+
+}  // namespace tensorflow
diff --git a/tensorflow/core/kernels/sparse/csr_sparse_matrix_to_dense_op.cc b/tensorflow/core/kernels/sparse/csr_sparse_matrix_to_dense_op.cc
new file mode 100644
index 00000000000..68144a66c15
--- /dev/null
+++ b/tensorflow/core/kernels/sparse/csr_sparse_matrix_to_dense_op.cc
@@ -0,0 +1,267 @@
+/* Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+#define EIGEN_USE_THREADS
+
+#if GOOGLE_CUDA
+#define EIGEN_USE_GPU
+#endif
+
+#include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
+#include "tensorflow/core/framework/allocator.h"
+#include "tensorflow/core/framework/op.h"
+#include "tensorflow/core/framework/op_kernel.h"
+#include "tensorflow/core/framework/tensor_shape.h"
+#include "tensorflow/core/framework/tensor_types.h"
+#include "tensorflow/core/framework/variant_op_registry.h"
+#include "tensorflow/core/kernels/concat_lib.h"
+#include "tensorflow/core/kernels/fill_functor.h"
+#include "tensorflow/core/kernels/scatter_nd_op.h"
+#include "tensorflow/core/kernels/sparse/kernels.h"
+#include "tensorflow/core/kernels/sparse/sparse_matrix.h"
+#include "tensorflow/core/util/work_sharder.h"
+
+#if GOOGLE_CUDA
+#include "tensorflow/core/kernels/cuda_solvers.h"
+#include "tensorflow/core/kernels/cuda_sparse.h"
+#endif
+
+namespace tensorflow {
+
+typedef Eigen::ThreadPoolDevice CPUDevice;
+typedef Eigen::GpuDevice GPUDevice;
+
+// Op to convert a (batched) CSR SparseMatrix to dense Tensors on the CPU.
+// The resulting Tensor will have rank 2 or (if batched) 3. Missing values in
+// the CSR SparseMatrix are interpreted as zeros in the dense Tensor.
+template <typename Device, typename T>
+class CSRSparseMatrixToDenseCPUOp : public OpKernel {
+ public:
+  explicit CSRSparseMatrixToDenseCPUOp(OpKernelConstruction* c) : OpKernel(c) {}
+
+  void Compute(OpKernelContext* context) override {
+    const CSRSparseMatrix* csr_sparse_matrix;
+    OP_REQUIRES_OK(context,
+                   ExtractVariantFromInput(context, 0, &csr_sparse_matrix));
+
+    OP_REQUIRES(
+        context, csr_sparse_matrix->dtype() == DataTypeToEnum<T>::value,
+        errors::InvalidArgument(
+            "Asked for a CSRSparseMatrix of type ",
+            DataTypeString(DataTypeToEnum<T>::value),
+            " but saw dtype: ", DataTypeString(csr_sparse_matrix->dtype())));
+
+    const Tensor& dense_shape_t = csr_sparse_matrix->dense_shape();
+    const int rank = dense_shape_t.dim_size(0);
+    OP_REQUIRES(context, rank == 2 || rank == 3,
+                errors::InvalidArgument("sparse matrix must have rank 2 or 3; ",
+                                        "but dense_shape has size ", rank));
+
+    auto dense_shape = dense_shape_t.vec<int64>();
+    const int64 num_rows = dense_shape((rank == 2) ? 0 : 1);
+    const int64 num_cols = dense_shape((rank == 2) ? 1 : 2);
+
+    auto batch_ptrs = csr_sparse_matrix->batch_pointers().vec<int32>();
+    auto row_ptr = csr_sparse_matrix->row_pointers().vec<int32>();
+    auto col_ind = csr_sparse_matrix->col_indices().vec<int32>();
+    auto values = csr_sparse_matrix->values().vec<T>();
+
+    TensorShape dense_tensor_shape;
+    OP_REQUIRES_OK(context, TensorShapeUtils::MakeShape(dense_shape.data(),
+                                                        dense_shape.size(),
+                                                        &dense_tensor_shape));
+    Tensor dense_t(cpu_allocator(), DataTypeToEnum<T>::value,
+                   dense_tensor_shape);
+
+    // Fill the dense tensor with zeros.
+    functor::SetZeroFunctor<Device, T> set_zero;
+    set_zero(context->eigen_device<Device>(), dense_t.flat<T>());
+
+    auto dense_ptr = dense_t.flat<T>().data();
+
+    // Process the individual batches in parallel using a threadpool.
+    auto shard = [&](int64 batch_begin, int64 batch_end) {
+      for (int64 batch_idx = batch_begin; batch_idx < batch_end; ++batch_idx) {
+        const int64 csr_batch_offset = batch_ptrs(batch_idx);
+        const int64 dense_batch_offset = batch_idx * num_rows * num_cols;
+
+        for (int row_idx = 0; row_idx < num_rows; ++row_idx) {
+          const int64 row_offset = batch_idx * (num_rows + 1) + row_idx;
+          const int64 col_begin = row_ptr(row_offset);
+          const int64 col_end = row_ptr(row_offset + 1);
+          for (int64 i = col_begin; i < col_end; ++i) {
+            const int64 col_idx = col_ind(csr_batch_offset + i);
+            dense_ptr[dense_batch_offset + (row_idx * num_cols) + col_idx] =
+                values(csr_batch_offset + i);
+          }
+        }
+      }
+    };
+    const int batch_size = csr_sparse_matrix->batch_size();
+    auto worker_threads = *(context->device()->tensorflow_cpu_worker_threads());
+    Shard(worker_threads.num_threads, worker_threads.workers, batch_size,
+          csr_sparse_matrix->total_nnz() / batch_size /* cost per unit */,
+          shard);
+
+    context->set_output(0, dense_t);
+  }
+};
+
+template <typename Device, typename T>
+class CSRSparseMatrixToDenseGPUOp : public OpKernel {
+ public:
+  explicit CSRSparseMatrixToDenseGPUOp(OpKernelConstruction* c) : OpKernel(c) {}
+
+  void Compute(OpKernelContext* c) final {
+    const CSRSparseMatrix* csr_sparse_matrix;
+    OP_REQUIRES_OK(c, ExtractVariantFromInput(c, 0, &csr_sparse_matrix));
+
+    OP_REQUIRES(
+        c, csr_sparse_matrix->dtype() == DataTypeToEnum<T>::value,
+        errors::InvalidArgument(
+            "Asked for a CSRSparseMatrix of type ",
+            DataTypeString(DataTypeToEnum<T>::value),
+            " but saw dtype: ", DataTypeString(csr_sparse_matrix->dtype())));
+
+    const Tensor& dense_shape_t = csr_sparse_matrix->dense_shape();
+    const int rank = dense_shape_t.dim_size(0);
+    OP_REQUIRES(c, rank == 2 || rank == 3,
+                errors::InvalidArgument("sparse matrix must have rank 2 or 3; ",
+                                        "but dense_shape has size ", rank));
+
+    const int batch_size = csr_sparse_matrix->batch_size();
+    const int64 total_nnz = csr_sparse_matrix->total_nnz();
+
+    auto dense_shape = dense_shape_t.vec<int64>();
+    const int64 rows = dense_shape((rank == 2) ? 0 : 1);
+
+    Tensor indices_t;
+    OP_REQUIRES_OK(c, c->allocate_temp(DT_INT64, TensorShape({total_nnz, rank}),
+                                       &indices_t));
+
+    Tensor values_t;
+    OP_REQUIRES_OK(c, c->allocate_temp(DataTypeToEnum<T>::value,
+                                       TensorShape({total_nnz}), &values_t));
+
+    functor::CSRSparseMatrixToCOOSparseMatrix<Device> csr_to_coo;
+    auto indices = indices_t.matrix<int64>();
+
+    auto csr_row_ptr = csr_sparse_matrix->row_pointers().vec<int32>();
+    auto coo_col_ind = csr_sparse_matrix->col_indices().vec<int32>();
+    auto batch_ptrs = csr_sparse_matrix->batch_pointers().vec<int32>();
+
+    Tensor coo_row_ind_t;
+    OP_REQUIRES_OK(c, c->allocate_temp(DT_INT32, TensorShape({total_nnz}),
+                                       &coo_row_ind_t));
+    auto coo_row_ind = coo_row_ind_t.vec<int32>();
+
+    // TODO(ebrevdo): just write a custom kernel that converts from
+    // csr to dense.
+    for (int i = 0; i < batch_size; ++i) {
+      const int nnz_i = csr_sparse_matrix->nnz(i);
+      if (nnz_i == 0) {
+        // No copying required.  Avoid failure case below.
+        continue;
+      }
+      const TTypes<int32>::UnalignedConstVec csr_row_ptr_i(
+          &csr_row_ptr((rows + 1) * i), rows + 1);
+      const TTypes<int32>::UnalignedVec coo_row_ind_i(
+          &coo_row_ind(csr_sparse_matrix->batch_offset(i)), nnz_i);
+      OP_REQUIRES_OK(c, csr_to_coo(c, csr_row_ptr_i, coo_row_ind_i));
+    }
+
+    if (total_nnz > 0) {
+      functor::COOSparseMatrixToSparseTensor<Device> coo_to_st;
+      OP_REQUIRES_OK(c, coo_to_st(c, dense_shape, batch_ptrs, coo_row_ind,
+                                  coo_col_ind, indices));
+    }
+
+    values_t = csr_sparse_matrix->values();
+
+    Tensor dense_t;
+    TensorShape dense_tensor_shape;
+    OP_REQUIRES_OK(
+        c, TensorShapeUtils::MakeShape(dense_shape.data(), dense_shape.size(),
+                                       &dense_tensor_shape));
+    OP_REQUIRES_OK(
+        c,
+        functor::DoScatterNd<Device, T, int64, scatter_nd_op::UpdateOp::ASSIGN>(
+            c, indices_t, values_t, dense_tensor_shape, &dense_t,
+            true /*allocate*/));
+    c->set_output(0, dense_t);
+  }
+};
+
+#define REGISTER_GPU(T)                                   \
+  REGISTER_KERNEL_BUILDER(Name("CSRSparseMatrixToDense")  \
+                              .Device(DEVICE_GPU)         \
+                              .TypeConstraint<T>("type"), \
+                          CSRSparseMatrixToDenseGPUOp<GPUDevice, T>);
+
+#define REGISTER_CPU(T)                                   \
+  REGISTER_KERNEL_BUILDER(Name("CSRSparseMatrixToDense")  \
+                              .Device(DEVICE_CPU)         \
+                              .TypeConstraint<T>("type"), \
+                          CSRSparseMatrixToDenseCPUOp<CPUDevice, T>);
+REGISTER_CPU(float)
+REGISTER_CPU(double)
+REGISTER_CPU(complex64)
+REGISTER_CPU(complex128)
+
+#if GOOGLE_CUDA
+
+REGISTER_GPU(float)
+REGISTER_GPU(double)
+REGISTER_GPU(complex64)
+REGISTER_GPU(complex128)
+
+#endif  // GOOGLE_CUDA
+
+#undef REGISTER_CPU
+#undef REGISTER_GPU
+
+#if GOOGLE_CUDA
+
+namespace functor {
+template <>
+struct COOSparseMatrixToSparseTensor<GPUDevice> {
+  Status operator()(OpKernelContext* ctx,
+                    TTypes<int64>::ConstVec host_dense_shape,
+                    TTypes<int>::ConstVec host_batch_ptrs,
+                    TTypes<int>::Vec coo_row_ind,
+                    TTypes<int>::ConstVec coo_col_ind,
+                    TTypes<int64>::Matrix indices);
+};
+extern template struct COOSparseMatrixToSparseTensor<GPUDevice>;
+
+// TODO(ebrevdo): Write a custom batch-friendly impl of this to update
+// the SparseTensor indices directly.
+template <>
+Status CSRSparseMatrixToCOOSparseMatrix<GPUDevice>::operator()(
+    OpKernelContext* c, TTypes<const int>::UnalignedVec csr_row_ptr,
+    TTypes<int>::UnalignedVec coo_row_ind) {
+  CudaSparse cuda_sparse(c);
+  const int nnz = coo_row_ind.size();
+  TF_RETURN_IF_ERROR(cuda_sparse.Initialize());
+  const int m = csr_row_ptr.size() - 1;  // rows
+  return cuda_sparse.Csr2coo(csr_row_ptr.data(), nnz, m, coo_row_ind.data());
+}
+extern template struct CSRSparseMatrixToCOOSparseMatrix<GPUDevice>;
+
+}  // namespace functor
+
+#endif  // GOOGLE_CUDA
+
+}  // namespace tensorflow
diff --git a/tensorflow/core/kernels/sparse/csr_sparse_matrix_to_sparse_tensor_op.cc b/tensorflow/core/kernels/sparse/csr_sparse_matrix_to_sparse_tensor_op.cc
new file mode 100644
index 00000000000..839d6e35f6a
--- /dev/null
+++ b/tensorflow/core/kernels/sparse/csr_sparse_matrix_to_sparse_tensor_op.cc
@@ -0,0 +1,264 @@
+/* Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+#define EIGEN_USE_THREADS
+
+#if GOOGLE_CUDA
+#define EIGEN_USE_GPU
+#endif
+
+#include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
+#include "tensorflow/core/framework/op.h"
+#include "tensorflow/core/framework/op_kernel.h"
+#include "tensorflow/core/framework/tensor_shape.h"
+#include "tensorflow/core/framework/tensor_types.h"
+#include "tensorflow/core/framework/types.h"
+#include "tensorflow/core/framework/variant_op_registry.h"
+#include "tensorflow/core/kernels/concat_lib.h"
+#include "tensorflow/core/kernels/sparse/kernels.h"
+#include "tensorflow/core/kernels/sparse/sparse_matrix.h"
+#include "tensorflow/core/util/work_sharder.h"
+
+#if GOOGLE_CUDA
+#include "tensorflow/core/kernels/cuda_solvers.h"
+#include "tensorflow/core/kernels/cuda_sparse.h"
+#endif
+
+namespace tensorflow {
+namespace {
+
+using CPUDevice = Eigen::ThreadPoolDevice;
+using GPUDevice = Eigen::GpuDevice;
+
+// Validate that CSR SparseMatrix has the expected dtype and rank 2 or 3.
+Status ValidateCSRSparseMatrix(const CSRSparseMatrix& csr_sparse_matrix,
+                               DataType expected_dtype) {
+  if (csr_sparse_matrix.dtype() != expected_dtype) {
+    return errors::InvalidArgument(
+        "Expected a CSRSparseMatrix of type ", DataTypeString(expected_dtype),
+        " but saw type: ", DataTypeString(csr_sparse_matrix.dtype()));
+  }
+  const int rank = csr_sparse_matrix.dense_shape().dim_size(0);
+  if (rank != 2 && rank != 3) {
+    return errors::InvalidArgument("CSR SparseMatrix must have rank 2 or 3; ",
+                                   "but dense_shape has size ", rank);
+  }
+  return Status::OK();
+}
+}  // namespace
+
+// Op to convert a (batched) CSR SparseMatrix to SparseTensors on the CPU.
+// The resulting SparseTensor will have the same dense shape and non-zero values
+// as the CSR SparseMatrix. rank 2 or (if batched) 3. Moreover, the resulting
+// SparseTensor's indices will be present in the canonical, row-major ordering.
+template <typename T>
+class CSRSparseMatrixToSparseTensorCPUOp : public OpKernel {
+ public:
+  explicit CSRSparseMatrixToSparseTensorCPUOp(OpKernelConstruction* c)
+      : OpKernel(c) {}
+
+  void Compute(OpKernelContext* c) final {
+    const CSRSparseMatrix* csr_sparse_matrix;
+    OP_REQUIRES_OK(c, ExtractVariantFromInput(c, 0, &csr_sparse_matrix));
+    OP_REQUIRES_OK(c, ValidateCSRSparseMatrix(*csr_sparse_matrix,
+                                              DataTypeToEnum<T>::value));
+
+    // Copy the SparseTensor's dense_shape and values from the CSRSparseMatrix.
+    c->set_output(1, csr_sparse_matrix->values());
+    const Tensor& dense_shape = csr_sparse_matrix->dense_shape();
+    c->set_output(2, dense_shape);
+
+    const int batch_size = csr_sparse_matrix->batch_size();
+    const int64 total_nnz = csr_sparse_matrix->total_nnz();
+    const int rank = csr_sparse_matrix->dense_shape().dim_size(0);
+    auto dense_shape_vec = dense_shape.vec<int64>();
+    const int64 num_rows = dense_shape_vec((rank == 2) ? 0 : 1);
+
+    Tensor* indices;
+    OP_REQUIRES_OK(
+        c, c->allocate_output(0, TensorShape({total_nnz, rank}), &indices));
+    auto indices_flat = indices->template flat<int64>();
+
+    auto csr_row_ptr = csr_sparse_matrix->row_pointers().vec<int32>();
+    auto csr_col_ind = csr_sparse_matrix->col_indices().vec<int32>();
+    auto batch_ptrs = csr_sparse_matrix->batch_pointers().vec<int32>();
+
+    // Process the individual batches in parallel using a threadpool.
+    auto shard = [&](int64 batch_begin, int64 batch_end) {
+      for (int64 batch_idx = batch_begin; batch_idx < batch_end; ++batch_idx) {
+        const int64 csr_batch_offset = batch_ptrs(batch_idx);
+
+        for (int row_idx = 0; row_idx < num_rows; ++row_idx) {
+          const int64 row_offset = batch_idx * (num_rows + 1) + row_idx;
+
+          // The column indices of the current row lie in the range:
+          //  [csr_row_ptr[row_offset], csr_row_ptr[row_offset + 1])
+          const int64 col_begin = csr_row_ptr(row_offset);
+          const int64 col_end = csr_row_ptr(row_offset + 1);
+          for (int64 i = col_begin; i < col_end; ++i) {
+            const int64 col_idx = csr_col_ind(csr_batch_offset + i);
+            const int64 indices_offset = rank * (csr_batch_offset + i);
+
+            if (rank == 2) {
+              indices_flat(indices_offset) = row_idx;
+              indices_flat(indices_offset + 1) = col_idx;
+            } else {  // rank == 3
+              indices_flat(indices_offset) = batch_idx;
+              indices_flat(indices_offset + 1) = row_idx;
+              indices_flat(indices_offset + 2) = col_idx;
+            }
+          }
+        }
+      }
+    };
+    auto worker_threads = *(c->device()->tensorflow_cpu_worker_threads());
+    // TODO(anudhyan): Estimate the cost per unit based on Eigen::TensorOpCost
+    // units and scale based on benchmarks.
+    Shard(worker_threads.num_threads, worker_threads.workers, batch_size,
+          csr_sparse_matrix->total_nnz() / batch_size /* cost per unit */,
+          shard);
+  }
+};
+
+template <typename Device, typename T>
+class CSRSparseMatrixToSparseTensorGPUOp : public OpKernel {
+ public:
+  explicit CSRSparseMatrixToSparseTensorGPUOp(OpKernelConstruction* c)
+      : OpKernel(c) {}
+
+  void Compute(OpKernelContext* c) final {
+    const CSRSparseMatrix* csr_sparse_matrix;
+    OP_REQUIRES_OK(c, ExtractVariantFromInput(c, 0, &csr_sparse_matrix));
+    OP_REQUIRES_OK(c, ValidateCSRSparseMatrix(*csr_sparse_matrix,
+                                              DataTypeToEnum<T>::value));
+
+    const Tensor& dense_shape_t = csr_sparse_matrix->dense_shape();
+    c->set_output(2, dense_shape_t);
+    const int rank = dense_shape_t.dim_size(0);
+    const int batch_size = csr_sparse_matrix->batch_size();
+    const int64 total_nnz = csr_sparse_matrix->total_nnz();
+
+    auto dense_shape = dense_shape_t.vec<int64>();
+    const int64 rows = dense_shape((rank == 2) ? 0 : 1);
+
+    Tensor* indices_t;
+    OP_REQUIRES_OK(
+        c, c->allocate_output(0, TensorShape({total_nnz, rank}), &indices_t));
+
+    Tensor* values_t;
+    OP_REQUIRES_OK(c,
+                   c->allocate_output(1, TensorShape({total_nnz}), &values_t));
+
+    functor::CSRSparseMatrixToCOOSparseMatrix<Device> csr_to_coo;
+    auto indices = indices_t->matrix<int64>();
+
+    auto csr_row_ptr = csr_sparse_matrix->row_pointers().vec<int32>();
+    auto coo_col_ind = csr_sparse_matrix->col_indices().vec<int32>();
+    auto batch_ptrs = csr_sparse_matrix->batch_pointers().vec<int32>();
+
+    Tensor coo_row_ind_t;
+    OP_REQUIRES_OK(c, c->allocate_temp(DT_INT32, TensorShape({total_nnz}),
+                                       &coo_row_ind_t));
+    auto coo_row_ind = coo_row_ind_t.vec<int32>();
+
+    // TODO(ebrevdo): Convert to one or two single kernel calls,
+    // where the kernels are batch-friendly.
+    for (int i = 0; i < batch_size; ++i) {
+      const int nnz_i = csr_sparse_matrix->nnz(i);
+      if (nnz_i == 0) {
+        // No copying required.  Avoid failure case below.
+        continue;
+      }
+      const TTypes<int32>::UnalignedConstVec csr_row_ptr_i(
+          &csr_row_ptr((rows + 1) * i), rows + 1);
+      const TTypes<int32>::UnalignedVec coo_row_ind_i(
+          &coo_row_ind(csr_sparse_matrix->batch_offset(i)), nnz_i);
+      OP_REQUIRES_OK(c, csr_to_coo(c, csr_row_ptr_i, coo_row_ind_i));
+    }
+
+    if (total_nnz > 0) {
+      functor::COOSparseMatrixToSparseTensor<Device> coo_to_st;
+      OP_REQUIRES_OK(c, coo_to_st(c, dense_shape, batch_ptrs, coo_row_ind,
+                                  coo_col_ind, indices));
+    }
+
+    *values_t = csr_sparse_matrix->values();
+  }
+};
+
+#define REGISTER_GPU(T)                                         \
+  REGISTER_KERNEL_BUILDER(Name("CSRSparseMatrixToSparseTensor") \
+                              .Device(DEVICE_GPU)               \
+                              .TypeConstraint<T>("type")        \
+                              .HostMemory("dense_shape"),       \
+                          CSRSparseMatrixToSparseTensorGPUOp<GPUDevice, T>);
+
+#if GOOGLE_CUDA
+
+REGISTER_GPU(float)
+REGISTER_GPU(double)
+REGISTER_GPU(complex64)
+REGISTER_GPU(complex128)
+
+#endif  // GOOGLE_CUDA
+
+#undef REGISTER_GPU
+
+#if GOOGLE_CUDA
+
+namespace functor {
+template <>
+struct COOSparseMatrixToSparseTensor<GPUDevice> {
+  Status operator()(OpKernelContext* ctx,
+                    TTypes<int64>::ConstVec host_dense_shape,
+                    TTypes<int>::ConstVec host_batch_ptrs,
+                    TTypes<int>::Vec coo_row_ind,
+                    TTypes<int>::ConstVec coo_col_ind,
+                    TTypes<int64>::Matrix indices);
+};
+extern template struct COOSparseMatrixToSparseTensor<GPUDevice>;
+
+// TODO(ebrevdo): Write a custom batch-friendly impl of this to update
+// the SparseTensor indices directly.
+template <>
+Status CSRSparseMatrixToCOOSparseMatrix<GPUDevice>::operator()(
+    OpKernelContext* c, TTypes<const int>::UnalignedVec csr_row_ptr,
+    TTypes<int>::UnalignedVec coo_row_ind) {
+  CudaSparse cuda_sparse(c);
+  const int nnz = coo_row_ind.size();
+  TF_RETURN_IF_ERROR(cuda_sparse.Initialize());
+  const int m = csr_row_ptr.size() - 1;  // rows
+  return cuda_sparse.Csr2coo(csr_row_ptr.data(), nnz, m, coo_row_ind.data());
+}
+extern template struct CSRSparseMatrixToCOOSparseMatrix<GPUDevice>;
+
+}  // namespace functor
+
+#endif  // GOOGLE_CUDA
+
+#define REGISTER_CPU(T)                                         \
+  REGISTER_KERNEL_BUILDER(Name("CSRSparseMatrixToSparseTensor") \
+                              .Device(DEVICE_CPU)               \
+                              .TypeConstraint<T>("type"),       \
+                          CSRSparseMatrixToSparseTensorCPUOp<T>);
+
+REGISTER_CPU(float)
+REGISTER_CPU(double)
+REGISTER_CPU(complex64)
+REGISTER_CPU(complex128)
+
+#undef REGISTER_CPU
+
+}  // namespace tensorflow
diff --git a/tensorflow/core/kernels/sparse/dense_to_csr_sparse_matrix_op.cc b/tensorflow/core/kernels/sparse/dense_to_csr_sparse_matrix_op.cc
new file mode 100644
index 00000000000..94cbae3185f
--- /dev/null
+++ b/tensorflow/core/kernels/sparse/dense_to_csr_sparse_matrix_op.cc
@@ -0,0 +1,398 @@
+/* Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+#define EIGEN_USE_THREADS
+
+#if GOOGLE_CUDA
+#define EIGEN_USE_GPU
+#endif
+
+#include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
+#include "tensorflow/core/framework/op.h"
+#include "tensorflow/core/framework/op_kernel.h"
+#include "tensorflow/core/framework/tensor_shape.h"
+#include "tensorflow/core/framework/tensor_types.h"
+#include "tensorflow/core/framework/types.h"
+#include "tensorflow/core/framework/variant_op_registry.h"
+#include "tensorflow/core/kernels/dense_update_functor.h"
+#include "tensorflow/core/kernels/fill_functor.h"
+#include "tensorflow/core/kernels/gather_nd_op.h"
+#include "tensorflow/core/kernels/sparse/kernels.h"
+#include "tensorflow/core/kernels/sparse/sparse_matrix.h"
+
+#if GOOGLE_CUDA
+#include "tensorflow/core/common_runtime/gpu/gpu_event_mgr.h"
+#include "tensorflow/core/kernels/cuda_solvers.h"
+#include "tensorflow/core/kernels/cuda_sparse.h"
+#include "tensorflow/core/platform/cuda.h"
+
+using ::perftools::gputools::cuda::ScopedActivateExecutorContext;
+#endif
+
+namespace tensorflow {
+
+typedef Eigen::ThreadPoolDevice CPUDevice;
+typedef Eigen::GpuDevice GPUDevice;
+
+// Op to convert dense matrices to CSR SparseMatrices on the CPU.
+// Takes a Tensor of rank 2 or (if batched) 3 and a corresponding list of
+// indices as input.
+//
+// The (batched) CSR SparseMatrix is constructed using only
+// the values at the given indices. This implementation assumes that the indices
+// are sorted with respect to batch indices and are in row-major order.
+template <typename Device, typename T>
+class DenseToCSRSparseMatrixCPUOp : public OpKernel {
+ public:
+  explicit DenseToCSRSparseMatrixCPUOp(OpKernelConstruction* c) : OpKernel(c) {}
+
+  void Compute(OpKernelContext* ctx) override {
+    const Tensor& params = ctx->input(0);
+    const Tensor& indices = ctx->input(1);
+
+    // TODO(anudhyan): Factor out common input validation for CPU and GPU ops
+    // into a single function.
+    const TensorShape& dense_tensor_shape = params.shape();
+    const int rank = params.dims();
+    OP_REQUIRES(ctx, rank == 2 || rank == 3,
+                errors::InvalidArgument(
+                    "params must have rank == 2 or 3; ",
+                    "but saw shape: ", dense_tensor_shape.DebugString()));
+    OP_REQUIRES(
+        ctx, indices.dims() == 2,
+        errors::InvalidArgument("indices must be a matrix, but saw shape: ",
+                                indices.shape().DebugString()));
+    OP_REQUIRES(
+        ctx, indices.dim_size(1) == rank,
+        errors::InvalidArgument(
+            "indices.shape[1] must be equal to the rank of params, but saw: ",
+            indices.dim_size(1), " vs. ", rank));
+
+    Tensor dense_shape(cpu_allocator(), DT_INT64, TensorShape({rank}));
+    auto dense_shape_mutable = dense_shape.vec<int64>();
+    for (int i = 0; i < rank; ++i) {
+      dense_shape_mutable(i) = dense_tensor_shape.dim_size(i);
+    }
+
+    const int64 batch_size = (rank == 2) ? 1 : dense_tensor_shape.dim_size(0);
+    const int64 num_rows = dense_tensor_shape.dim_size((rank == 2) ? 0 : 1);
+    const int64 total_nnz = indices.NumElements() / rank;
+
+    Tensor values;
+    OP_REQUIRES_OK(ctx, functor::DoGatherNd<Device, T, int64>(
+                            ctx, params, indices, &values));
+
+    Tensor batch_ptr(cpu_allocator(), DT_INT32, TensorShape({batch_size + 1}));
+    Tensor csr_col_ind(cpu_allocator(), DT_INT32, TensorShape({total_nnz}));
+    Tensor csr_row_ptr(cpu_allocator(), DT_INT32,
+                       TensorShape({(num_rows + 1) * batch_size}));
+
+    // Fill the row pointers with zeros.
+    functor::SetZeroFunctor<Device, int32> set_zero;
+    set_zero(ctx->eigen_device<Device>(), csr_row_ptr.flat<int32>());
+
+    // Convert from COO to CSR format.
+    functor::SparseTensorToCSRSparseMatrixCPUFunctor coo_to_csr;
+    OP_REQUIRES_OK(ctx,
+                   coo_to_csr(batch_size, num_rows, indices.matrix<int64>(),
+                              batch_ptr.vec<int32>(), csr_row_ptr.vec<int32>(),
+                              csr_col_ind.vec<int32>()));
+
+    CSRSparseMatrix output_csr_matrix;
+    OP_REQUIRES_OK(ctx, CSRSparseMatrix::CreateCSRSparseMatrix(
+                            values.dtype(), dense_shape, batch_ptr, csr_row_ptr,
+                            csr_col_ind, values, &output_csr_matrix));
+    Tensor* output_csr_matrix_tensor;
+    AllocatorAttributes cpu_alloc;
+    cpu_alloc.set_on_host(true);
+    OP_REQUIRES_OK(
+        ctx, ctx->allocate_output(0, TensorShape({}), &output_csr_matrix_tensor,
+                                  cpu_alloc));
+    output_csr_matrix_tensor->scalar<Variant>()() =
+        std::move(output_csr_matrix);
+  }
+};
+
+#define REGISTER_CPU(T)                                  \
+  REGISTER_KERNEL_BUILDER(Name("DenseToCSRSparseMatrix") \
+                              .Device(DEVICE_CPU)        \
+                              .TypeConstraint<T>("T"),   \
+                          DenseToCSRSparseMatrixCPUOp<CPUDevice, T>);
+
+REGISTER_CPU(float)
+REGISTER_CPU(double)
+REGISTER_CPU(complex64)
+REGISTER_CPU(complex128)
+
+#undef REGISTER_CPU
+
+#if GOOGLE_CUDA
+
+template <typename Device, typename T>
+class DenseToCSRSparseMatrixGPUOp : public AsyncOpKernel {
+ public:
+  explicit DenseToCSRSparseMatrixGPUOp(OpKernelConstruction* c)
+      : AsyncOpKernel(c) {}
+
+  void ComputeAsync(OpKernelContext* c, DoneCallback done) final {
+    auto stream = c->op_device_context()->stream();
+    const Device& d = c->eigen_device<Device>();
+
+    const Tensor& params_t = c->input(0);
+    const Tensor& indices_t = c->input(1);
+    const TensorShape& dense_tensor_shape = params_t.shape();
+    const int rank = params_t.dims();
+    OP_REQUIRES_ASYNC(c, rank == 2 || rank == 3,
+                      errors::InvalidArgument(
+                          "params must have rank == 2 or 3; ",
+                          "but saw shape: ", dense_tensor_shape.DebugString()),
+                      done);
+    OP_REQUIRES_ASYNC(
+        c, indices_t.dims() == 2,
+        errors::InvalidArgument("indices must be a matrix, but saw shape: ",
+                                indices_t.shape().DebugString()),
+        done);
+    OP_REQUIRES_ASYNC(
+        c, indices_t.dim_size(1) == rank,
+        errors::InvalidArgument(
+            "indices.shape[1] must be equal to the rank of params, but saw: ",
+            indices_t.dim_size(1), " vs. ", rank),
+        done);
+    const int64 batch_size = (rank == 2) ? 1 : dense_tensor_shape.dim_size(0);
+    const int64 rows = dense_tensor_shape.dim_size((rank == 2) ? 0 : 1);
+    const int64 cols = dense_tensor_shape.dim_size((rank == 2) ? 1 : 2);
+
+    ScratchSpace<int32> nnz_per_batch_host(c, batch_size, /*on_host*/ true);
+
+    Tensor nnz_per_batch_device_t;
+    if (rank == 2) {
+      // Simple case.
+      nnz_per_batch_host.mutable_data()[0] = indices_t.dim_size(0);
+    } else {
+      OP_REQUIRES_OK_ASYNC(c,
+                           c->allocate_temp(DT_INT32, TensorShape({batch_size}),
+                                            &nnz_per_batch_device_t),
+                           done);
+      auto nnz_per_batch_device = nnz_per_batch_device_t.vec<int32>();
+
+      functor::CalculateNNZPerBatchMatrixFromIndices<Device>
+          calculate_nnz_from_indices;
+      auto indices = indices_t.matrix<int64>();
+      OP_REQUIRES_OK_ASYNC(
+          c, calculate_nnz_from_indices(c, indices, nnz_per_batch_device),
+          done);
+
+      perftools::gputools::DeviceMemoryBase nnz_per_batch_device_ptr(
+          static_cast<void*>(nnz_per_batch_device.data()));
+
+      OP_REQUIRES_ASYNC(
+          c,
+          stream
+              ->ThenMemcpy(nnz_per_batch_host.mutable_data() /*host_dst*/,
+                           nnz_per_batch_device_ptr /*gpu_src*/,
+                           batch_size * sizeof(int32) /*size*/)
+              .ok(),
+          errors::Internal("DenseToSparseMatrixGPUOp: failed to copy "
+                           "nnz_per_batch from device"),
+          done);
+    }
+
+    // TODO(ebrevdo): write a custom pair of kernels: one that
+    // calculates the batched csr_row_ptr vector, another that fills in
+    // the col_ind and values vectors.
+    TensorReference nnz_per_batch_device_ref(nnz_per_batch_device_t);
+    auto convert_to_csr = [this, c, rank, batch_size, nnz_per_batch_host,
+                           nnz_per_batch_device_ref, stream, &d, &params_t,
+                           &indices_t, dense_tensor_shape, rows, cols, done]() {
+      // The data has been copied out of the nnz_per_batch_device
+      // tensor by the time we get here; we can unreference it.
+      nnz_per_batch_device_ref.Unref();
+
+      auto nnz_per_batch = nnz_per_batch_host.tensor().vec<int32>();
+
+      // Ensure that within the callback, the proper GPU settings are
+      // configured.
+      ScopedActivateExecutorContext scoped_activation{stream->parent()};
+
+      // Extract out the values.
+      Tensor temp_values_t;
+      OP_REQUIRES_OK_ASYNC(c,
+                           (functor::DoGatherNd<Device, T, int64>(
+                               c, params_t, indices_t, &temp_values_t)),
+                           done);
+      const Tensor& values_t = const_cast<const Tensor&>(temp_values_t);
+
+      OP_REQUIRES_ASYNC(
+          c, TensorShapeUtils::IsVector(values_t.shape()),
+          errors::Internal("Expected values_t to be a vector, but saw shape: ",
+                           values_t.shape().DebugString()),
+          done);
+
+      Tensor dense_shape_t(cpu_allocator(), DT_INT64, TensorShape({rank}));
+      auto dense_shape_mutable = dense_shape_t.vec<int64>();
+      for (int i = 0; i < rank; ++i) {
+        dense_shape_mutable(i) = dense_tensor_shape.dim_size(i);
+      }
+      auto dense_shape = const_cast<const Tensor&>(dense_shape_t).vec<int64>();
+
+      Tensor batch_ptr_t(cpu_allocator(), DT_INT32,
+                         TensorShape({batch_size + 1}));
+      auto batch_ptr = batch_ptr_t.vec<int32>();
+      auto indices = indices_t.matrix<int64>();
+
+      batch_ptr(0) = 0;
+      for (int i = 0; i < batch_size; ++i) {
+        batch_ptr(i + 1) = batch_ptr(i) + nnz_per_batch(i);
+      }
+      int total_nnz = batch_ptr(batch_size);
+      OP_REQUIRES_ASYNC(
+          c, total_nnz == values_t.NumElements(),
+          errors::Internal("nnz returned by "
+                           "CalculateNNZPerBatchMatrixFromInd"
+                           "ices != len(values): ",
+                           total_nnz, " vs. ", values_t.NumElements()),
+          done);
+
+      Tensor coo_col_ind_t;
+      Tensor csr_row_ptr_t;
+      Tensor csr_values_t = values_t;
+
+      Tensor coo_row_ind_t;
+      OP_REQUIRES_OK_ASYNC(
+          c,
+          c->allocate_temp(DT_INT32, TensorShape({total_nnz}), &coo_row_ind_t),
+          done);
+      OP_REQUIRES_OK_ASYNC(
+          c,
+          c->allocate_temp(DT_INT32, TensorShape({total_nnz}), &coo_col_ind_t),
+          done);
+      OP_REQUIRES_OK_ASYNC(
+          c,
+          c->allocate_temp(DT_INT32, TensorShape({batch_size * (rows + 1)}),
+                           &csr_row_ptr_t),
+          done);
+
+      auto coo_row_ind = coo_row_ind_t.vec<int32>();
+      auto coo_col_ind = coo_col_ind_t.vec<int32>();
+      auto csr_row_ptr = csr_row_ptr_t.vec<int32>();
+
+      // Convert SparseTensor rep to coo row ind, coo col ind.
+      if (total_nnz > 0) {
+        functor::SparseTensorToCOOSparseMatrix<Device> st_to_coo;
+        st_to_coo(d, dense_shape, indices, coo_row_ind, coo_col_ind);
+      }
+
+      // Set all csr row pointers to zero, so that when iterating over
+      // batches converting coo to csr, we do not have to perform an
+      // unaligned SetZero for any nnz == 0 minibatches.  coo2csr has
+      // a bug if you have empty coo rows.
+      // TODO(ebrevdo): File bug w/ nvidia so coo2csr can handle
+      // zero-element input coo rows.
+      functor::SetZeroFunctor<Device, int32> set_zero;
+      set_zero(d, csr_row_ptr_t.flat<int32>());
+
+      functor::COOSparseMatrixToCSRSparseMatrix<Device> coo_to_csr;
+      for (int i = 0; i < batch_size; ++i) {
+        int nnz_i = batch_ptr(i + 1) - batch_ptr(i);
+        if (nnz_i == 0) {
+          // This is an empty minibatch; no call to coo2csr: it's
+          // handled by the SetZero above.
+        } else {
+          // Convert coo to csr.
+          auto coo_row_ind_i =
+              TTypes<int32>::UnalignedVec(&coo_row_ind(batch_ptr(i)), nnz_i);
+          auto csr_row_ptr_i = TTypes<int32>::UnalignedVec(
+              &csr_row_ptr((rows + 1) * i), rows + 1);
+          OP_REQUIRES_OK_ASYNC(
+              c, coo_to_csr(c, rows, cols, coo_row_ind_i, csr_row_ptr_i), done);
+        }
+      }
+
+      CSRSparseMatrix matrix;
+      OP_REQUIRES_OK_ASYNC(
+          c,
+          CSRSparseMatrix::CreateCSRSparseMatrix(
+              values_t.dtype(), dense_shape_t, batch_ptr_t, csr_row_ptr_t,
+              coo_col_ind_t, csr_values_t, &matrix),
+          done);
+      Tensor* matrix_t;
+      AllocatorAttributes cpu_alloc;
+      cpu_alloc.set_on_host(true);
+      OP_REQUIRES_OK_ASYNC(
+          c, c->allocate_output(0, TensorShape({}), &matrix_t, cpu_alloc),
+          done);
+      matrix_t->scalar<Variant>()() = std::move(matrix);
+
+      done();
+    };
+
+    if (rank == 2) {
+      convert_to_csr();
+    } else {
+      // Launch the GPU kernel to count nnz entries, then call convert_to_csr.
+      c->device()->tensorflow_gpu_device_info()->event_mgr->ThenExecute(
+          stream, convert_to_csr);
+    }
+  }
+};
+
+#define REGISTER_GPU(DEV, T)                             \
+  REGISTER_KERNEL_BUILDER(Name("DenseToCSRSparseMatrix") \
+                              .Device(DEVICE_##DEV)      \
+                              .TypeConstraint<T>("T"),   \
+                          DenseToCSRSparseMatrixGPUOp<DEV##Device, T>);
+
+REGISTER_GPU(GPU, float)
+REGISTER_GPU(GPU, double)
+REGISTER_GPU(GPU, complex64)
+REGISTER_GPU(GPU, complex128)
+
+namespace functor {
+
+template <>
+Status CalculateNNZPerBatchMatrixFromIndices<GPUDevice>::operator()(
+    OpKernelContext* c, TTypes<int64>::ConstMatrix indices,
+    TTypes<int32>::Vec nnz_per_batch);
+extern template struct CalculateNNZPerBatchMatrixFromIndices<GPUDevice>;
+
+template <>
+struct SparseTensorToCOOSparseMatrix<GPUDevice> {
+  void operator()(const GPUDevice& d, TTypes<int64>::ConstVec host_dense_shape,
+                  TTypes<int64>::ConstMatrix indices,
+                  TTypes<int>::Vec coo_row_ind, TTypes<int>::Vec coo_col_ind);
+};
+extern template struct SparseTensorToCOOSparseMatrix<GPUDevice>;
+
+template <>
+struct COOSparseMatrixToCSRSparseMatrix<GPUDevice> {
+  Status operator()(OpKernelContext* c, const int rows, const int cols,
+                    TTypes<int>::UnalignedVec coo_row_ind,
+                    TTypes<int>::UnalignedVec csr_row_ptr) {
+    CudaSparse cuda_sparse(c);
+    TF_RETURN_IF_ERROR(cuda_sparse.Initialize());
+    return cuda_sparse.Coo2csr(coo_row_ind.data(),
+                               /*nnz*/ coo_row_ind.size(),
+                               /*m == rows of A*/ rows, csr_row_ptr.data());
+  }
+};
+extern template struct COOSparseMatrixToCSRSparseMatrix<GPUDevice>;
+
+}  // namespace functor
+
+#endif  // GOOGLE_CUDA
+
+#undef REGISTER_GPU
+
+}  // namespace tensorflow
diff --git a/tensorflow/core/kernels/sparse/kernels.cc b/tensorflow/core/kernels/sparse/kernels.cc
new file mode 100644
index 00000000000..0eea9f1feed
--- /dev/null
+++ b/tensorflow/core/kernels/sparse/kernels.cc
@@ -0,0 +1,100 @@
+/* Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+#include "tensorflow/core/kernels/sparse/kernels.h"
+
+#include <numeric>
+
+#include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
+#include "tensorflow/core/framework/op_kernel.h"
+#include "tensorflow/core/framework/tensor_types.h"
+#include "tensorflow/core/lib/core/errors.h"
+#include "tensorflow/core/lib/core/status.h"
+
+namespace tensorflow {
+namespace functor {
+
+Status SparseTensorToCSRSparseMatrixCPUFunctor::operator()(
+    const int64 batch_size, const int num_rows,
+    TTypes<int64>::ConstMatrix indices, TTypes<int32>::Vec batch_ptr,
+    TTypes<int32>::Vec csr_row_ptr, TTypes<int32>::Vec csr_col_ind) {
+  // Validate inputs.
+  if (batch_ptr.size() != batch_size + 1) {
+    return errors::InvalidArgument(
+        "Expected batch_ptr.size() == batch_size + 1. Got: ", batch_ptr.size(),
+        " vs. ", batch_size + 1);
+  }
+  if (csr_row_ptr.size() != batch_size * (num_rows + 1)) {
+    return errors::InvalidArgument(
+        "Expected csr_row_ptr.size() == batch_size * (num_rows + 1). Got: ",
+        csr_row_ptr.size(), " vs. ", batch_size * (num_rows + 1));
+  }
+
+  const int64 total_nnz = indices.dimension(0);
+  const int rank = indices.dimension(1);
+  if (rank == 2 && batch_size != 1) {
+    return errors::InvalidArgument(
+        "Expected batch_size == 1 when rank is 2. Got batch_size: ",
+        batch_size);
+  }
+  if (csr_col_ind.size() != total_nnz) {
+    return errors::InvalidArgument(
+        "Expected csr_col_ind.size() == total_nnz. Got: ", csr_col_ind.size(),
+        " vs. ", total_nnz);
+  }
+
+  int prev_batch = -1;
+  if (rank == 2) {
+    // For a single batch, the batch_ptrs are {0, total_nnz}.
+    batch_ptr(0) = 0;
+    ++prev_batch;
+
+    for (int64 i = 0; i < total_nnz; ++i) {
+      // For now, the rows pointers store the corresponding row counts.
+      csr_row_ptr(indices(i, 0) + 1) += 1;
+      csr_col_ind(i) = indices(i, 1);
+    }
+  } else {  // rank == 3
+    for (int64 i = 0; i < total_nnz; ++i) {
+      const int cur_batch = indices(i, 0);
+      // For now, the rows pointers store the corresponding row counts.
+      csr_row_ptr(cur_batch * (num_rows + 1) + indices(i, 1) + 1) += 1;
+      csr_col_ind(i) = indices(i, 2);
+
+      // We're at a new batch and might have skipped over empty batches.
+      while (prev_batch < cur_batch) {
+        // The previous batch ends at position i.
+        batch_ptr(prev_batch + 1) = i;
+        ++prev_batch;
+      }
+    }
+  }
+  // Set the last element of batch_ptr and account for trailing empty batches.
+  while (prev_batch < batch_size) {
+    batch_ptr(prev_batch + 1) = total_nnz;
+    ++prev_batch;
+  }
+
+  // Compute the cumulative row counts for each batch.
+  for (int batch_idx = 0; batch_idx < batch_size; ++batch_idx) {
+    auto* row_ptr_batch = csr_row_ptr.data() + batch_idx * (num_rows + 1);
+    std::partial_sum(row_ptr_batch, row_ptr_batch + num_rows + 1,
+                     row_ptr_batch);
+  }
+  return Status::OK();
+}
+
+}  // namespace functor
+}  // namespace tensorflow
diff --git a/tensorflow/core/kernels/sparse/kernels.h b/tensorflow/core/kernels/sparse/kernels.h
new file mode 100644
index 00000000000..f795829af05
--- /dev/null
+++ b/tensorflow/core/kernels/sparse/kernels.h
@@ -0,0 +1,247 @@
+/* Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+#ifndef TENSORFLOW_CORE_KERNELS_SPARSE_KERNELS_H_
+#define TENSORFLOW_CORE_KERNELS_SPARSE_KERNELS_H_
+
+#include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
+#include "tensorflow/core/framework/op_kernel.h"
+#include "tensorflow/core/framework/tensor_types.h"
+#include "tensorflow/core/kernels/sparse/sparse_matrix.h"
+#include "tensorflow/core/lib/core/status.h"
+#include "tensorflow/core/platform/types.h"
+
+namespace tensorflow {
+
+namespace functor {
+
+// Calculates number of nonzero entries per batch of a sorted rank-3
+// SparseTensor's indices.  indices is expected to have columns
+// corresponding to [batch, row, column],  where indices[:,0] < B.
+//
+// REQUIRES:
+//  indices.dimension(1) == 3
+//  nnz_per_batch.dimension(0) == B
+template <typename Device>
+struct CalculateNNZPerBatchMatrixFromIndices {
+  Status operator()(OpKernelContext* c, TTypes<int64>::ConstMatrix indices,
+                    TTypes<int32>::Vec nnz_per_batch);
+};
+
+// Split a subset of a SparseTensors' indices into two vectors:
+// COO row inds and COO col inds.  Outputs are:
+//
+//   coo_row_ind = indices[:, row_dim]
+//   coo_col_ind = indices[:, row_dim + 1]
+//
+// where n = coo_row_ind.size()
+// and row_dim = #cols(indices) - 1
+//
+// REQUIRES:
+//   host_dense_shape.size() in [2, 3]
+//   indices.dim_size(1) == host_dense_shape.size()
+//   coo_row_ind.size() == coo_col_ind.size()
+//   coo_row_ind.size() == indices.dim_size(0)
+template <typename Device>
+struct SparseTensorToCOOSparseMatrix {
+  void operator()(const Device& d, TTypes<int64>::ConstVec host_dense_shape,
+                  TTypes<int64>::ConstMatrix indices,
+                  TTypes<int32>::Vec coo_row_ind,
+                  TTypes<int32>::Vec coo_col_ind);
+};
+
+// Write coo batch, row, and column vectors to output matrix indices:
+//
+//   indices[:, row_dim] = coo_row_ind
+//   indices[:, col_dim] = coo_col_ind
+//
+// where row_dim = #cols(indices) - 1 and n = coo_row_ind.size().
+// In addition, if #cols(indices) == 3, also store the batch:
+//
+//   indices[i, 0] = batch_of(i) where
+//      host_batch_ptrs(batch_of(i)) <= i < host_batch_ptrs(batch_of(i) + 1)
+//
+// REQUIRES:
+//
+//   host_dense_shape.size() in [2, 3]
+//   indices.dim_size(1) == host_dense_shape.size()
+//   host_batch_ptr.size() ==
+//   coo_row_ind.size() == coo_col_ind.size()
+//
+template <typename Device>
+struct COOSparseMatrixToSparseTensor {
+  Status operator()(OpKernelContext* c,
+                    TTypes<int64>::ConstVec host_dense_shape,
+                    TTypes<int32>::ConstVec host_batch_ptrs,
+                    TTypes<int32>::Vec coo_row_ind,
+                    TTypes<int32>::ConstVec coo_col_ind,
+                    TTypes<int64>::Matrix indices);
+};
+
+// Convert a vector of coo row indices to csr row pointers.
+//
+// REQUIRES:
+//
+//   csr_row_ptr.size() == rows + 1.
+//   max(coo_row_ptr) < rows.
+//
+template <typename Device>
+struct COOSparseMatrixToCSRSparseMatrix {
+  Status operator()(OpKernelContext* c, const int rows, const int cols,
+                    TTypes<int32>::UnalignedVec coo_row_ind,
+                    TTypes<int32>::UnalignedVec csr_row_ptr);
+};
+
+// Convert a matrix of (batched) coo row and column indices to CSR SparseMatrix
+// batch ptrs, csr row pointers and coo column indices.
+//
+// REQUIRES:
+//   batch_ptr.size() == batch_size + 1
+//   csr_row_ptr.size() == batch_size * (num_rows + 1)
+//   csr_col_ind.size() == total_nnz
+//   batch_size == 1 if rank == 2
+//
+//   where
+//     total_nnz = indices.dim_size(0)
+//     rank = indices.dim_size(1)
+//   Also csr_row_ptr should be initially filled with zeros.
+//
+struct SparseTensorToCSRSparseMatrixCPUFunctor {
+  Status operator()(const int64 batch_size, const int num_rows,
+                    TTypes<int64>::ConstMatrix indices,
+                    TTypes<int32>::Vec batch_ptr,
+                    TTypes<int32>::Vec csr_row_ptr,
+                    TTypes<int32>::Vec csr_col_ind);
+};
+
+// Convert a vector of csr row pointers to coo row indices.
+//
+// REQUIRES:
+//
+//   coo_row_ptr.size() == nnz.
+//   csr_row_ptr[-1] == nnz.
+//
+template <typename Device>
+struct CSRSparseMatrixToCOOSparseMatrix {
+  Status operator()(OpKernelContext* c,
+                    TTypes<int32>::UnalignedConstVec csr_row_ptr,
+                    TTypes<int32>::UnalignedVec coo_row_ind);
+};
+
+// Calculates C = matmul(A, B) or C = matmul(A, B)^T, where A is in CSR format
+// and B and C are dense.
+template <typename Device, typename T>
+struct CSRSparseMatrixMatMul {
+  explicit CSRSparseMatrixMatMul(const bool transpose_output);
+  Status Compute(OpKernelContext* ctx, const ConstCSRComponent<T>& a,
+                 typename TTypes<T>::ConstMatrix b,
+                 typename TTypes<T>::Matrix c);
+};
+
+// Calculates y = A * x, y = A^T * x, or y = A^H * x, where A is in CSR format
+// and x and y are dense vectors.
+template <typename Device, typename T>
+class CSRSparseMatrixMatVec {
+  CSRSparseMatrixMatVec(bool transpose_a, bool adjoint_a);
+  Status Compute(OpKernelContext* ctx, const ConstCSRComponent<T>& a,
+                 const T* x, T* y);
+};
+
+// Calculates C = functor(A, B) where A and B are CSR and C is CSR
+// with a different sparsity pattern.
+template <typename Device, typename T>
+struct CSRStructureModifyingFunctor {
+  virtual ~CSRStructureModifyingFunctor() {}
+
+  virtual Status Initialize() = 0;
+
+  virtual Status GetOutputStructure(const ConstCSRComponent<T>& a,
+                                    const ConstCSRComponent<T>& b,
+                                    TTypes<int32>::UnalignedVec c_row_ptr,
+                                    int* output_nnz) = 0;
+
+  virtual Status Compute(const ConstCSRComponent<T>& a,
+                         const ConstCSRComponent<T>& b, CSRComponent<T>* c) = 0;
+};
+
+// Calculates C = alpha * A + beta * B, where A and B are in CSR
+// format, and alpha and beta are scalars on the host.
+template <typename Device, typename T>
+struct CSRSparseMatrixAdd : public CSRStructureModifyingFunctor<Device, T> {
+  explicit CSRSparseMatrixAdd(OpKernelContext* ctx, const T alpha,
+                              const T beta);
+};
+
+// Calculates C = matmul(A, B), where A, B, and C are in CSR format.
+template <typename Device, typename T>
+struct CSRSparseSparseMatrixMatMul
+    : public CSRStructureModifyingFunctor<Device, T> {
+  explicit CSRSparseSparseMatrixMatMul(OpKernelContext* ctx, bool transpose_a,
+                                       bool transpose_b);
+};
+
+// Calculates Y = transpose(X) where X and Y are CSR format components.
+template <typename Device, typename T>
+struct CSRSparseMatrixTransposeComponent {
+  Status operator()(OpKernelContext* ctx, const ConstCSRComponent<T>& x,
+                    CSRComponent<T>* y);
+};
+
+// Calculates Y = transpose(X) where X and Y are in CSR format.
+template <typename Device, typename T>
+struct CSRSparseMatrixTranspose {
+  Status operator()(OpKernelContext* ctx, bool conjugate,
+                    const CSRSparseMatrix& input_matrix,
+                    CSRSparseMatrix* output_matrix);
+};
+
+// Calculates Y = softmax(X) where X and Y are in CSR format;
+// missing coefficients in X are treates as -inf (logits of 0 probability).
+template <typename Device, typename T>
+struct CSRSparseMatrixSoftmax {
+  Status operator()(OpKernelContext* ctx, const CSRSparseMatrix& logits,
+                    typename TTypes<T>::Vec softmax_values);
+};
+
+template <typename Device, typename T>
+struct CSRSparseMatrixSoftmaxGrad {
+  Status operator()(OpKernelContext* ctx, const CSRSparseMatrix& softmax,
+                    const CSRSparseMatrix& grad_softmax,
+                    typename TTypes<T>::Vec gradient_values);
+};
+
+template <typename Device, typename T>
+class CSRSparseMatrixMulScalar {
+ public:
+  explicit CSRSparseMatrixMulScalar() {}
+
+  Status Compute(OpKernelContext* ctx, const CSRSparseMatrix& a,
+                 typename TTypes<T>::ConstScalar b, CSRSparseMatrix* c);
+};
+
+template <typename Device, typename T>
+class CSRSparseMatrixBatchMulVec {
+ public:
+  explicit CSRSparseMatrixBatchMulVec() {}
+
+  Status Compute(OpKernelContext* ctx, const CSRSparseMatrix& a,
+                 typename TTypes<T>::ConstFlat b, CSRSparseMatrix* c);
+};
+
+}  // namespace functor
+
+}  // namespace tensorflow
+
+#endif  // TENSORFLOW_CORE_KERNELS_SPARSE_KERNELS_H_
diff --git a/tensorflow/core/kernels/sparse/kernels_gpu.cu.cc b/tensorflow/core/kernels/sparse/kernels_gpu.cu.cc
new file mode 100644
index 00000000000..518fdd55ff2
--- /dev/null
+++ b/tensorflow/core/kernels/sparse/kernels_gpu.cu.cc
@@ -0,0 +1,676 @@
+/* Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+#if GOOGLE_CUDA
+
+#define EIGEN_USE_GPU
+
+#include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
+#include "third_party/cub/device/device_histogram.cuh"
+#include "third_party/cub/iterator/counting_input_iterator.cuh"
+#include "third_party/cub/iterator/transform_input_iterator.cuh"
+#include "third_party/gpus/cuda/include/cusparse.h"
+#include "tensorflow/core/framework/register_types.h"
+#include "tensorflow/core/framework/tensor_types.h"
+#include "tensorflow/core/kernels/gpu_device_array.h"
+#include "tensorflow/core/kernels/gpu_device_array_gpu.h"
+#include "tensorflow/core/kernels/sparse/kernels.h"
+#include "tensorflow/core/lib/core/errors.h"
+#include "tensorflow/core/platform/types.h"
+#include "tensorflow/core/util/gpu_kernel_helper.h"
+
+namespace tensorflow {
+
+typedef Eigen::GpuDevice GPUDevice;
+
+namespace functor {
+
+namespace {
+struct StridedDataReader {
+  StridedDataReader(const int64* begin, int stride)
+      : begin_(begin), stride_(stride) {}
+
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE int operator()(int idx) const {
+    return static_cast<int>(ldg(begin_ + idx * stride_));
+  }
+
+  const int64* begin_;
+  const int stride_;
+};
+}  // namespace
+
+template <>
+Status CalculateNNZPerBatchMatrixFromIndices<GPUDevice>::operator()(
+    OpKernelContext* c, TTypes<int64>::ConstMatrix indices,
+    TTypes<int32>::Vec nnz_per_batch) {
+  const auto& cu_stream = GetGpuStream(c);
+
+  const int total_nnz = indices.dimension(0);
+  const int size = nnz_per_batch.size();
+
+  DCHECK_EQ(indices.rank(), 2);
+  DCHECK_EQ(indices.dimension(1), 3);  // batch, row, col
+
+  const int rank = indices.dimension(1);
+  cub::CountingInputIterator<int> row_counter(0);
+  cub::TransformInputIterator<int, StridedDataReader,
+                              cub::CountingInputIterator<int>>
+      indices_first_column(row_counter,
+                           StridedDataReader(indices.data(), rank));
+
+  std::size_t temp_storage_bytes = 0;
+
+  DCHECK_NE(indices.data(), nullptr);
+  DCHECK_NE(nnz_per_batch.data(), nullptr);
+
+  auto first_success = cub::DeviceHistogram::HistogramEven(
+      /*d_temp_storage*/ nullptr,
+      /*temp_storage_bytes&*/ temp_storage_bytes,
+      /*d_samples*/ indices_first_column,
+      /*d_histogram*/ nnz_per_batch.data(),
+      /*num_levels*/ size + 1,
+      /*lower_level*/ 0,
+      /*upper_level*/ size,
+      /*num_samples*/ total_nnz,
+      /*stream*/ cu_stream);
+
+  if (first_success != cudaSuccess) {
+    return errors::Internal(
+        "SparseTensorToCSRSparseMatrix: Could not launch "
+        "cub::DeviceHistogram::HistogramEven "
+        "to calculate temp_storage_bytes, status: ",
+        cudaGetErrorString(first_success));
+  }
+
+  Tensor temp_storage;
+  TF_RETURN_IF_ERROR(c->allocate_temp(
+      DT_INT8, TensorShape({static_cast<int64>(temp_storage_bytes)}),
+      &temp_storage));
+  DCHECK_NE(temp_storage.flat<int8>().data(), nullptr);
+  auto second_success = cub::DeviceHistogram::HistogramEven(
+      /*d_temp_storage*/ temp_storage.flat<int8>().data(),
+      /*temp_storage_bytes&*/ temp_storage_bytes,
+      /*d_samples*/ indices_first_column,
+      /*d_histogram*/ nnz_per_batch.data(),
+      /*num_levels*/ size + 1,
+      /*lower_level*/ 0,
+      /*upper_level*/ size,
+      /*num_samples*/ total_nnz,
+      /*stream*/ cu_stream);
+
+  if (second_success != cudaSuccess) {
+    return errors::Internal(
+        "SparseTensorToCSRSparseMatrix: Could not launch "
+        "cub::DeviceHistogram::HistogramEven "
+        "to count nnz entries per batch.  temp_storage_bytes: ",
+        temp_storage_bytes, ", status: ", cudaGetErrorString(second_success));
+  }
+
+  return Status::OK();
+}
+
+template <int stride>
+__global__ void SparseTensorToCOOMatrixKernel(const int64* indices,
+                                              int* coo_rows_out,
+                                              int* coo_cols_out, int size) {
+  const int offset = (stride == 3) ? 1 : 0;
+  CUDA_1D_KERNEL_LOOP(i, size) {
+    coo_rows_out[i] = static_cast<int>(ldg(indices + i * stride + offset));
+    coo_cols_out[i] = static_cast<int>(ldg(indices + i * stride + offset + 1));
+  }
+}
+
+template <>
+void SparseTensorToCOOSparseMatrix<GPUDevice>::operator()(
+    const GPUDevice& d, TTypes<int64>::ConstVec host_dense_shape,
+    TTypes<int64>::ConstMatrix indices, TTypes<int>::Vec coo_row_ind,
+    TTypes<int>::Vec coo_col_ind) {
+  const int stride = host_dense_shape.size();
+  DCHECK(stride == 2 || stride == 3);
+  DCHECK_EQ(stride, indices.dimension(1));
+  const int size = coo_row_ind.dimension(0);
+  GpuLaunchConfig config = GetGpuLaunchConfig(size, d);
+  if (stride == 2) {
+    SparseTensorToCOOMatrixKernel<2>
+        <<<config.block_count, config.thread_per_block, 0, d.stream()>>>(
+            indices.data(), coo_row_ind.data(), coo_col_ind.data(), size);
+  } else {
+    SparseTensorToCOOMatrixKernel<3>
+        <<<config.block_count, config.thread_per_block, 0, d.stream()>>>(
+            indices.data(), coo_row_ind.data(), coo_col_ind.data(), size);
+  }
+}
+
+__global__ void COOMatrixToSparseTensorKernel2D(const int* coo_rows,
+                                                const int* coo_cols,
+                                                int64* indices_out, int size) {
+  CUDA_1D_KERNEL_LOOP(i, size) {
+    indices_out[i * 2] = static_cast<int64>(ldg(coo_rows + i));
+    indices_out[i * 2 + 1] = static_cast<int64>(ldg(coo_cols + i));
+  }
+}
+
+__device__ inline int BinarySearchRange(int* range, int n, int x) {
+  int left = 0;
+  int right = n - 1;
+  while (left < right) {
+    int mid = left + (right - left) / 2;
+    if (x < range[mid])
+      right = mid - 1;
+    else if (range[mid + 1] <= x)
+      left = mid + 1;
+    else
+      return mid;  // range[mid] <= x < range[mid + 1].
+  }
+  return left;
+}
+
+__global__ void COOMatrixToSparseTensorKernel3D(
+    const int* coo_rows, const int* coo_cols, int64* indices_out,
+    GpuDeviceArrayStruct<int> batch_ptr_s, const int batch_size,
+    const int size) {
+  // Step 1: access the batch ptrs and copy to shared memory.
+  const int* batch_ptr = GetGpuDeviceArrayOnDevice(&batch_ptr_s);
+  extern __shared__ int local_batch_ptr[];
+  for (int i = threadIdx.x; i < batch_size + 1; i += blockDim.x) {
+    local_batch_ptr[i] = batch_ptr[i];
+  }
+  __syncthreads();
+
+  CUDA_1D_KERNEL_LOOP(i, size) {
+    // TODO(ebrevdo): Consider special casing batch_size <= 3,
+    // alternatively doing linear instead of binary search.  Requires
+    // some benchmarks.
+    const int b = BinarySearchRange(local_batch_ptr, batch_size, i);
+    indices_out[i * 3] = static_cast<int64>(b);
+    indices_out[i * 3 + 1] = static_cast<int64>(ldg(coo_rows + i));
+    indices_out[i * 3 + 2] = static_cast<int64>(ldg(coo_cols + i));
+  }
+}
+
+template <>
+Status COOSparseMatrixToSparseTensor<GPUDevice>::operator()(
+    OpKernelContext* c, TTypes<int64>::ConstVec host_dense_shape,
+    TTypes<int>::ConstVec host_batch_ptr, TTypes<int>::Vec coo_row_ind,
+    TTypes<int>::ConstVec coo_col_ind, TTypes<int64>::Matrix indices) {
+  const int ndims = indices.dimension(1);
+  DCHECK(ndims == 2 || ndims == 3);
+  DCHECK_EQ(ndims, host_dense_shape.size());
+  DCHECK_NE(coo_row_ind.data(), nullptr);
+  DCHECK_NE(coo_col_ind.data(), nullptr);
+  DCHECK_NE(indices.data(), nullptr);
+  const GPUDevice& d = c->eigen_device<GPUDevice>();
+  const int size = coo_row_ind.size();
+  DCHECK_EQ(size, coo_col_ind.size());
+  DCHECK_EQ(size, indices.dimension(0));
+  if (ndims == 2) {
+    GpuLaunchConfig config = GetGpuLaunchConfig(size, d);
+    COOMatrixToSparseTensorKernel2D<<<config.block_count,
+                                      config.thread_per_block, 0, d.stream()>>>(
+        coo_row_ind.data(), coo_col_ind.data(), indices.data(), size);
+    return Status::OK();
+  } else {
+    const int batch_size = host_dense_shape(0);
+    GpuDeviceArrayOnHost<int> batch_ptr_copy(c, host_batch_ptr.size());
+    TF_RETURN_IF_ERROR(batch_ptr_copy.Init());
+    for (int i = 0; i < batch_size; ++i) {
+      batch_ptr_copy.Set(i, host_batch_ptr(i));
+    }
+    TF_RETURN_IF_ERROR(batch_ptr_copy.Finalize());
+    GpuLaunchConfig config = GetGpuLaunchConfig(size, d);
+    // shared memory stores the batch pointers.
+    const size_t shared_memory_size = sizeof(int) * (batch_size + 1);
+    COOMatrixToSparseTensorKernel3D<<<config.block_count,
+                                      config.thread_per_block,
+                                      shared_memory_size, d.stream()>>>(
+        coo_row_ind.data(), coo_col_ind.data(), indices.data(),
+        batch_ptr_copy.data(), batch_size, size);
+    return Status::OK();
+  }
+}
+
+template <typename T>
+__global__ void CSRSparseMatrixBatchMulVecKernel3D(
+    const T* a_values, const T* b_batch_values, T* c_values,
+    GpuDeviceArrayStruct<int> batch_ptr_s, const int batch_size,
+    const int total_nnz) {
+  // Step 1: Access the batch ptrs and copy to shared memory.
+  //         Also copy the per-batch multipliers into shared memory.
+  const int* batch_ptr = GetGpuDeviceArrayOnDevice(&batch_ptr_s);
+  extern __shared__ int local_batch_ptr[];
+  T* local_batch_values =
+      reinterpret_cast<T*>(local_batch_ptr + batch_size + 1);
+  for (int i = threadIdx.x; i < batch_size + 1; i += blockDim.x) {
+    local_batch_ptr[i] = batch_ptr[i];
+    if (i < batch_size) {
+      local_batch_values[i] = b_batch_values[i];
+    }
+  }
+  __syncthreads();
+
+  CUDA_1D_KERNEL_LOOP(i, total_nnz) {
+    const int b = BinarySearchRange(local_batch_ptr, batch_size, i);
+    c_values[i] = ldg(a_values + i) * local_batch_values[b];
+  }
+}
+
+template <typename T>
+Status CSRSparseMatrixBatchMulVecImpl(OpKernelContext* ctx,
+                                      const CSRSparseMatrix& a,
+                                      typename TTypes<T>::ConstFlat b,
+                                      CSRSparseMatrix* c) {
+  DCHECK_EQ(a.dims(), 3);
+  const int total_nnz = a.total_nnz();
+  Tensor c_values_t;
+  TF_RETURN_IF_ERROR(ctx->allocate_temp(DataTypeToEnum<T>::value,
+                                        TensorShape({total_nnz}), &c_values_t));
+  TF_RETURN_IF_ERROR(CSRSparseMatrix::CreateCSRSparseMatrix(
+      DataTypeToEnum<T>::value, a.dense_shape(), a.batch_pointers(),
+      a.row_pointers(), a.col_indices(), c_values_t, c));
+
+  auto a_values = a.values().flat<T>();
+  auto c_values = c_values_t.flat<T>();
+
+  auto host_dense_shape = a.dense_shape().vec<int64>();
+  auto host_batch_ptr = a.batch_pointers().vec<int>();
+
+  const GPUDevice& d = ctx->eigen_device<GPUDevice>();
+
+  const int batch_size = host_dense_shape(0);
+  DCHECK_EQ(b.size(), batch_size);
+
+  GpuDeviceArrayOnHost<int> batch_ptr_copy(ctx, host_batch_ptr.size());
+  TF_RETURN_IF_ERROR(batch_ptr_copy.Init());
+  for (int i = 0; i < batch_size; ++i) {
+    batch_ptr_copy.Set(i, host_batch_ptr(i));
+  }
+  TF_RETURN_IF_ERROR(batch_ptr_copy.Finalize());
+  GpuLaunchConfig config = GetGpuLaunchConfig(total_nnz, d);
+  // shared memory stores the batch pointers.
+  const size_t shared_memory_size =
+      (sizeof(int) * (batch_size + 1)  // local batch_pointers.
+       + sizeof(T) * batch_size);      // local copy of b.
+  CSRSparseMatrixBatchMulVecKernel3D<T>
+      <<<config.block_count, config.thread_per_block, shared_memory_size,
+         d.stream()>>>(a_values.data(), b.data(), c_values.data(),
+                       batch_ptr_copy.data(), batch_size, total_nnz);
+
+  return Status::OK();
+}
+
+#define DEFINE_SPARSE_MUL_VEC_GPU(T)                                        \
+  template <>                                                               \
+  CSRSparseMatrixBatchMulVec<GPUDevice, T>::CSRSparseMatrixBatchMulVec() {} \
+  template <>                                                               \
+  Status CSRSparseMatrixBatchMulVec<GPUDevice, T>::Compute(                 \
+      OpKernelContext* ctx, const CSRSparseMatrix& a,                       \
+      typename TTypes<T>::ConstFlat b, CSRSparseMatrix* c) {                \
+    return CSRSparseMatrixBatchMulVecImpl<T>(ctx, a, b, c);                 \
+  }
+
+DEFINE_SPARSE_MUL_VEC_GPU(float);
+DEFINE_SPARSE_MUL_VEC_GPU(double);
+DEFINE_SPARSE_MUL_VEC_GPU(std::complex<float>);
+DEFINE_SPARSE_MUL_VEC_GPU(std::complex<double>);
+
+#undef DEFINE_SPARSE_MUL_VEC_GPU
+
+template <typename T>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC void CalculateRowSoftmax(const int begin,
+                                                               const int end,
+                                                               const T* logits,
+                                                               T* softmax) {
+  // For each row, calculate the vector:
+  //   softmax[row] = exp(shifted_logits[row]) / sum(exp(shifted_logits[row]))
+  // where
+  //   shifted_logits[row] = logits[row] - max(logits[row])
+  // are the logits normalized for stability.
+  T row_max = Eigen::NumTraits<T>::lowest();
+  for (int r_i = begin; r_i < end; ++r_i) {
+    row_max = Eigen::numext::maxi(row_max, ldg(logits + r_i));
+  }
+  T sum_exp = 0;
+  for (int r_i = begin; r_i < end; ++r_i) {
+    const T exp_i = Eigen::numext::exp(ldg(logits + r_i) - row_max);
+    softmax[r_i] = exp_i;
+    sum_exp += exp_i;
+  }
+  for (int r_i = begin; r_i < end; ++r_i) {
+    softmax[r_i] = softmax[r_i] / sum_exp;
+  }
+}
+
+template <typename T>
+__global__ void CSRSparseMatrixSoftmaxKernel2D(const int rows,
+                                               const int* row_ptr,
+                                               const T* logits, T* softmax) {
+  // TODO(ebrevdo): consider something like a merge-path based
+  // algorithm to distribute the work in case the row sizes are
+  // uneven:
+  //   http://images.nvidia.com/events/sc15/pdfs/sc15-Merge-Based-Parallel-Sparse-Matrix-Vector-Multiplication-merrill.pdf
+  CUDA_1D_KERNEL_LOOP(row, rows) {
+    CalculateRowSoftmax(ldg(row_ptr + row), ldg(row_ptr + row + 1), logits,
+                        softmax);
+  }
+}
+
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void CopyFromGpuDeviceArrayToLocal(
+    GpuDeviceArrayStruct<int> cuda_ptr_s, int* local_ptr, int length) {
+#ifdef __CUDA_ARCH__
+  const int* cuda_ptr = GetGpuDeviceArrayOnDevice(&cuda_ptr_s);
+  for (int i = threadIdx.x; i < length; i += blockDim.x) {
+    local_ptr[i] = cuda_ptr[i];
+  }
+  __syncthreads();
+#endif
+}
+
+template <typename T>
+__global__ void CSRSparseMatrixSoftmaxKernel3D(
+    const int size, const int rows, GpuDeviceArrayStruct<int> batch_ptr_s,
+    const int* row_ptr, const T* logits, T* softmax) {
+  // TODO(ebrevdo): consider something like a merge-path based
+  // algorithm to distribute the work in case the row sizes are
+  // uneven:
+  //   http://images.nvidia.com/events/sc15/pdfs/sc15-Merge-Based-Parallel-Sparse-Matrix-Vector-Multiplication-merrill.pdf
+  const int batch_size = size / rows;
+  extern __shared__ int local_batch_ptr[];
+  CopyFromGpuDeviceArrayToLocal(std::move(batch_ptr_s), local_batch_ptr,
+                                batch_size + 1);
+
+  CUDA_1D_KERNEL_LOOP(i, size) {
+    const int batch = i / rows;
+    const int row = i % rows;
+    const int batch_offset = local_batch_ptr[batch];
+    const int row_offset = batch * (rows + 1) + row;
+    CalculateRowSoftmax(batch_offset + ldg(row_ptr + row_offset),
+                        batch_offset + ldg(row_ptr + row_offset + 1), logits,
+                        softmax);
+  }
+}
+
+template <typename T>
+Status CSRSparseMatrixSoftmaxGPUImpl(OpKernelContext* ctx,
+                                     const CSRSparseMatrix& logits,
+                                     typename TTypes<T>::Vec softmax_values) {
+  auto host_dense_shape = logits.dense_shape().vec<int64>();
+  auto host_batch_ptr = logits.batch_pointers().vec<int32>();
+  auto row_ptr = logits.row_pointers().vec<int32>();
+  auto logits_values = logits.values().vec<T>();
+
+  const int ndims = host_dense_shape.size();
+  DCHECK(ndims == 2 || ndims == 3);
+  const GPUDevice& d = ctx->eigen_device<GPUDevice>();
+  if (ndims == 2) {
+    const int rows = host_dense_shape(0);
+    DCHECK_EQ(rows, row_ptr.size() - 1);
+    GpuLaunchConfig config = GetGpuLaunchConfig(rows /*size*/, d);
+    CSRSparseMatrixSoftmaxKernel2D<T>
+        <<<config.block_count, config.thread_per_block, 0, d.stream()>>>(
+            rows /*size*/, row_ptr.data(), logits_values.data(),
+            softmax_values.data());
+  } else {
+    const int batch_size = host_dense_shape(0);
+    const int rows = host_dense_shape(1);
+    DCHECK_EQ(batch_size, host_batch_ptr.size() - 1);
+    DCHECK_EQ((rows + 1) * batch_size, row_ptr.size());
+    const int size = rows * batch_size;
+
+    GpuDeviceArrayOnHost<int> batch_ptr_copy(ctx, host_batch_ptr.size());
+    TF_RETURN_IF_ERROR(batch_ptr_copy.Init());
+    for (int i = 0; i < host_batch_ptr.size(); ++i) {
+      batch_ptr_copy.Set(i, host_batch_ptr(i));
+    }
+    TF_RETURN_IF_ERROR(batch_ptr_copy.Finalize());
+
+    GpuLaunchConfig config = GetGpuLaunchConfig(size, d);
+    // shared memory stores the batch pointers.
+    const size_t shared_memory_size = sizeof(int) * (batch_size + 1);
+    CSRSparseMatrixSoftmaxKernel3D<T>
+        <<<config.block_count, config.thread_per_block, shared_memory_size,
+           d.stream()>>>(size, rows, batch_ptr_copy.data(), row_ptr.data(),
+                         logits_values.data(), softmax_values.data());
+  }
+
+  return Status::OK();
+}
+
+#define DEFINE_SOFTMAX_GPU(T)                                             \
+  template <>                                                             \
+  Status CSRSparseMatrixSoftmax<GPUDevice, T>::operator()(                \
+      OpKernelContext* ctx, const CSRSparseMatrix& logits,                \
+      typename TTypes<T>::Vec softmax_values) {                           \
+    return CSRSparseMatrixSoftmaxGPUImpl<T>(ctx, logits, softmax_values); \
+  }
+
+DEFINE_SOFTMAX_GPU(float);
+DEFINE_SOFTMAX_GPU(double);
+
+#undef DEFINE_SOFTMAX_GPU
+
+template <typename T>
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC void CalculateRowSoftmaxGrad(
+    const int softmax_begin, const int softmax_end, const int* softmax_col_ind,
+    const T* softmax, const int grad_softmax_begin, const int grad_softmax_end,
+    const int* grad_softmax_col_ind, const T* grad_softmax, T* gradient) {
+  // Iterate from
+  //   softmax_col_ind[softmax_begin] to
+  //   softmax_col_ind[softmax_end]
+  // and from
+  //  grad_softmax_col_ind[grad_softmax_begin] to
+  //  grad_softmax_col_ind[grad_softmax_end]
+  //
+  // looking for for matching indices.  In the softmax indices only, perform:
+  //
+  //   gradient = (grad_softmax - sum(grad_softmax * softmax)) * softmax
+  //
+  // where the sum is along the given row.
+  T sum_prod = 0;
+  for (int i = softmax_begin, j = grad_softmax_begin;
+       i < softmax_end && j < grad_softmax_end;) {
+    const int softmax_col = ldg(softmax_col_ind + i);
+    const int grad_softmax_col = ldg(grad_softmax_col_ind + j);
+    if (softmax_col == grad_softmax_col) {
+      sum_prod += ldg(softmax + i) * ldg(grad_softmax + j);
+      ++i;
+      ++j;
+    } else if (softmax_col > grad_softmax_col) {
+      ++j;
+    } else {
+      ++i;
+    }
+  }
+
+  // Find an upper bound on the column numbers in this row; for use in
+  // the special case of a empty grad_softmax row and a non-empty
+  // softmax row.
+  const int softmax_col_upper_bound =
+      (softmax_begin == softmax_end)
+          ? -1
+          : ldg(softmax_col_ind + softmax_end - 1) + 1;
+  for (int i = softmax_begin, j = grad_softmax_begin; i < softmax_end;) {
+    const int softmax_col = ldg(softmax_col_ind + i);
+    // We need to keep a large grad_softmax_col value if we're at the
+    // end of the grad_softmax row, so we can fill in the remainder of
+    // the gradients row (the last if branch in this loop).
+    const int grad_softmax_col = (j == grad_softmax_end)
+                                     ? softmax_col_upper_bound
+                                     : ldg(grad_softmax_col_ind + j);
+
+    if (softmax_col == grad_softmax_col) {
+      gradient[i] = (ldg(grad_softmax + j) - sum_prod) * ldg(softmax + i);
+      ++i;
+      ++j;
+    } else if (softmax_col > grad_softmax_col) {
+      // grad_softmax is nonzero here, but since softmax is zero, the
+      // gradient is 0; so we skip it since the sparsity structure
+      // already encodes this zero.
+      ++j;
+    } else {
+      // grad_softmax is zero but softmax is not.
+      gradient[i] = -sum_prod * ldg(softmax + i);
+      ++i;
+    }
+  }
+}
+
+template <typename T>
+__global__ void CSRSparseMatrixSoftmaxGradKernel2D(
+    const int rows, const int* softmax_row_ptr, const int* softmax_col_ind,
+    const T* softmax, const int* grad_softmax_row_ptr,
+    const int* grad_softmax_col_ind, const T* grad_softmax, T* gradient) {
+  // TODO(ebrevdo): consider something like a merge-path based
+  // algorithm to distribute the work in case the row sizes are
+  // uneven:
+  //   http://images.nvidia.com/events/sc15/pdfs/sc15-Merge-Based-Parallel-Sparse-Matrix-Vector-Multiplication-merrill.pdf
+  CUDA_1D_KERNEL_LOOP(row, rows) {
+    CalculateRowSoftmaxGrad(
+        ldg(softmax_row_ptr + row) /*softmax_begin*/,
+        ldg(softmax_row_ptr + row + 1) /*softmax_end*/, softmax_col_ind,
+        softmax, ldg(grad_softmax_row_ptr + row) /*grad_softmax_begin*/,
+        ldg(grad_softmax_row_ptr + row + 1) /*grad_softmax_end*/,
+        grad_softmax_col_ind, grad_softmax, gradient);
+  }
+}
+
+template <typename T>
+__global__ void CSRSparseMatrixSoftmaxGradKernel3D(
+    const int size, const int rows,
+    GpuDeviceArrayStruct<int> softmax_and_grad_batch_ptr_s,
+    const int* softmax_row_ptr, const int* softmax_col_ind, const T* softmax,
+    const int* grad_softmax_row_ptr, const int* grad_softmax_col_ind,
+    const T* grad_softmax, T* gradient) {
+  // TODO(ebrevdo): consider something like a merge-path based
+  // algorithm to distribute the work in case the row sizes are
+  // uneven:
+  //   http://images.nvidia.com/events/sc15/pdfs/sc15-Merge-Based-Parallel-Sparse-Matrix-Vector-Multiplication-merrill.pdf
+
+  const int batch_size = size / rows;
+  extern __shared__ int local_batch_ptr[];
+  CopyFromGpuDeviceArrayToLocal(std::move(softmax_and_grad_batch_ptr_s),
+                                local_batch_ptr, 2 * (batch_size + 1));
+
+#define SOFTMAX_BATCH_PTR(i) local_batch_ptr[i];
+#define GRAD_SOFTMAX_BATCH_PTR(i) local_batch_ptr[batch_size + 1 + i];
+
+  CUDA_1D_KERNEL_LOOP(i, size) {
+    const int batch = i / rows;
+    const int row = i % rows;
+    const int softmax_batch_offset = SOFTMAX_BATCH_PTR(batch);
+    const int grad_softmax_batch_offset = GRAD_SOFTMAX_BATCH_PTR(batch);
+    const int row_offset = batch * (rows + 1) + row;
+    CalculateRowSoftmaxGrad(
+        softmax_batch_offset +
+            ldg(softmax_row_ptr + row_offset) /*softmax_begin*/,
+        softmax_batch_offset +
+            ldg(softmax_row_ptr + row_offset + 1) /*softmax_end*/,
+        softmax_col_ind, softmax,
+        grad_softmax_batch_offset +
+            ldg(grad_softmax_row_ptr + row_offset) /*grad_softmax_begin*/,
+        grad_softmax_batch_offset +
+            ldg(grad_softmax_row_ptr + row_offset + 1) /*grad_softmax_end*/,
+        grad_softmax_col_ind, grad_softmax, gradient);
+  }
+
+#undef SOFTMAX_BATCH_PTR
+#undef GRAD_SOFTMAX_BATCH_PTR
+}
+
+template <typename T>
+Status CSRSparseMatrixSoftmaxGradGPUImpl(
+    OpKernelContext* ctx, const CSRSparseMatrix& softmax,
+    const CSRSparseMatrix& grad_softmax,
+    typename TTypes<T>::Vec gradient_values) {
+  auto host_dense_shape = softmax.dense_shape().vec<int64>();
+  auto softmax_host_batch_ptr = softmax.batch_pointers().vec<int32>();
+  auto softmax_row_ptr = softmax.row_pointers().vec<int32>();
+  auto softmax_col_ind = softmax.col_indices().vec<int32>();
+  auto softmax_values = softmax.values().vec<T>();
+  auto grad_softmax_host_batch_ptr = grad_softmax.batch_pointers().vec<int32>();
+  auto grad_softmax_row_ptr = grad_softmax.row_pointers().vec<int32>();
+  auto grad_softmax_col_ind = grad_softmax.col_indices().vec<int32>();
+  auto grad_softmax_values = grad_softmax.values().vec<T>();
+
+  const int ndims = host_dense_shape.size();
+  DCHECK(ndims == 2 || ndims == 3);
+  const int rows = host_dense_shape(0);
+  const GPUDevice& d = ctx->eigen_device<GPUDevice>();
+  if (ndims == 2) {
+    DCHECK_EQ(rows + 1, softmax_row_ptr.size());
+    DCHECK_EQ(rows + 1, grad_softmax_row_ptr.size());
+    GpuLaunchConfig config = GetGpuLaunchConfig(rows /*size*/, d);
+    CSRSparseMatrixSoftmaxGradKernel2D<T>
+        <<<config.block_count, config.thread_per_block, 0, d.stream()>>>(
+            rows /*size*/, softmax_row_ptr.data(), softmax_col_ind.data(),
+            softmax_values.data(), grad_softmax_row_ptr.data(),
+            grad_softmax_col_ind.data(), grad_softmax_values.data(),
+            gradient_values.data());
+  } else {
+    const int batch_size = host_dense_shape(0);
+    const int rows = host_dense_shape(1);
+    DCHECK_EQ(batch_size, softmax_host_batch_ptr.size() - 1);
+    DCHECK_EQ(batch_size, grad_softmax_host_batch_ptr.size() - 1);
+    DCHECK_EQ((rows + 1) * batch_size, softmax_row_ptr.size());
+    DCHECK_EQ((rows + 1) * batch_size, grad_softmax_row_ptr.size());
+    const int size = rows * batch_size;
+    // The length of softmax_and_grad_batch_ptr_copy is 2 * (batch_size + 1)
+    // The first (batch_size + 1) entries contain softmax_batch_ptr and
+    // the second (batch_size + 1) entries contain grad_softmax_batch_ptr.
+    GpuDeviceArrayOnHost<int> softmax_and_grad_batch_ptr_copy(
+        ctx, 2 * softmax_host_batch_ptr.size());
+    TF_RETURN_IF_ERROR(softmax_and_grad_batch_ptr_copy.Init());
+    for (int i = 0; i < softmax_host_batch_ptr.size(); ++i) {
+      softmax_and_grad_batch_ptr_copy.Set(i, softmax_host_batch_ptr(i));
+      softmax_and_grad_batch_ptr_copy.Set(batch_size + 1 + i,
+                                          grad_softmax_host_batch_ptr(i));
+    }
+    TF_RETURN_IF_ERROR(softmax_and_grad_batch_ptr_copy.Finalize());
+
+    GpuLaunchConfig config = GetGpuLaunchConfig(size, d);
+    // shared memory stores two copies of batch pointers: one for the
+    // softmax CSR matrix, one for the grad_softmax CSR matrix.
+    const size_t shared_memory_size = 2 * sizeof(int) * (batch_size + 1);
+    CSRSparseMatrixSoftmaxGradKernel3D<T>
+        <<<config.block_count, config.thread_per_block, shared_memory_size,
+           d.stream()>>>(size, rows, softmax_and_grad_batch_ptr_copy.data(),
+                         softmax_row_ptr.data(), softmax_col_ind.data(),
+                         softmax_values.data(), grad_softmax_row_ptr.data(),
+                         grad_softmax_col_ind.data(),
+                         grad_softmax_values.data(), gradient_values.data());
+  }
+
+  return Status::OK();
+}
+
+#define DEFINE_SOFTMAX_GRAD_GPU(T)                                          \
+  template <>                                                               \
+  Status CSRSparseMatrixSoftmaxGrad<GPUDevice, T>::operator()(              \
+      OpKernelContext* ctx, const CSRSparseMatrix& softmax,                 \
+      const CSRSparseMatrix& grad_softmax,                                  \
+      typename TTypes<T>::Vec gradient_values) {                            \
+    return CSRSparseMatrixSoftmaxGradGPUImpl<T>(ctx, softmax, grad_softmax, \
+                                                gradient_values);           \
+  }
+
+DEFINE_SOFTMAX_GRAD_GPU(float);
+DEFINE_SOFTMAX_GRAD_GPU(double);
+
+#undef DEFINE_SOFTMAX_GRAD_GPU
+
+}  // namespace functor
+
+}  // namespace tensorflow
+
+#endif  // GOOGLE_CUDA
diff --git a/tensorflow/core/kernels/sparse/kernels_test.cc b/tensorflow/core/kernels/sparse/kernels_test.cc
new file mode 100644
index 00000000000..116a80aca0b
--- /dev/null
+++ b/tensorflow/core/kernels/sparse/kernels_test.cc
@@ -0,0 +1,82 @@
+/* Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+#include "tensorflow/core/kernels/sparse/kernels.h"
+
+#include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
+#include "tensorflow/core/framework/tensor.h"
+#include "tensorflow/core/framework/tensor_shape.h"
+#include "tensorflow/core/framework/tensor_testutil.h"
+#include "tensorflow/core/framework/tensor_types.h"
+#include "tensorflow/core/lib/core/status_test_util.h"
+#include "tensorflow/core/platform/test.h"
+
+namespace tensorflow {
+namespace {
+
+TEST(SparseTensorToCSRSparseMatrix, SingleBatchConversion) {
+  const auto indices =
+      test::AsTensor<int64>({0, 0, 2, 3, 2, 4, 3, 0}, TensorShape({4, 2}));
+  Tensor batch_ptr(DT_INT32, {2});
+  Tensor csr_col_ind(DT_INT32, {4});
+  auto csr_row_ptr = test::AsTensor<int32>({0, 0, 0, 0, 0});
+
+  functor::SparseTensorToCSRSparseMatrixCPUFunctor coo_to_csr;
+  TF_EXPECT_OK(coo_to_csr(1 /* batch_size */, 4 /* num_rows */,
+                          indices.template matrix<int64>(),
+                          batch_ptr.vec<int32>(), csr_row_ptr.vec<int32>(),
+                          csr_col_ind.vec<int32>()));
+
+  test::ExpectTensorEqual<int32>(batch_ptr, test::AsTensor<int32>({0, 4}));
+  test::ExpectTensorEqual<int32>(csr_row_ptr,
+                                 test::AsTensor<int32>({0, 1, 1, 3, 4}));
+  test::ExpectTensorEqual<int32>(csr_col_ind,
+                                 test::AsTensor<int32>({0, 3, 4, 0}));
+}
+
+TEST(SparseTensorToCSRSparseMatrix, BatchConversion) {
+  // Batch of 3 matrices, each having dimension [3, 4] with 3 non-zero elements.
+  const auto indices = test::AsTensor<int64>({0, 0, 0,  //
+                                              0, 2, 3,  //
+                                              2, 0, 1},
+                                             TensorShape({3, 3}));
+  Tensor batch_ptr(DT_INT32, {4});
+  Tensor csr_col_ind(DT_INT32, {3});
+  // row pointers have size = batch_size * (num_rows + 1) = 3 * 4 = 12
+  Tensor csr_row_ptr(DT_INT32, {12});
+  test::FillFn<int32>(&csr_row_ptr, [](int unused) { return 0; });
+
+  functor::SparseTensorToCSRSparseMatrixCPUFunctor coo_to_csr;
+  TF_EXPECT_OK(coo_to_csr(3 /* batch_size */, 3 /* num_rows */,
+                          indices.template matrix<int64>(),
+                          batch_ptr.vec<int32>(), csr_row_ptr.vec<int32>(),
+                          csr_col_ind.vec<int32>()));
+
+  test::ExpectTensorEqual<int32>(batch_ptr,
+                                 test::AsTensor<int32>({0, 2, 2, 3}));
+  test::ExpectTensorEqual<int32>(csr_row_ptr,
+                                 test::AsTensor<int32>({0, 1, 1, 2,  //
+                                                        0, 0, 0, 0,  //
+                                                        0, 1, 1, 1}));
+  test::ExpectTensorEqual<int32>(csr_col_ind, test::AsTensor<int32>({0, 3, 1}));
+}
+
+}  // namespace
+}  // namespace tensorflow
+
+int main(int argc, char** argv) {
+  ::testing::InitGoogleTest(&argc, argv);
+  return RUN_ALL_TESTS();
+}
diff --git a/tensorflow/core/kernels/sparse/mat_mul_op.cc b/tensorflow/core/kernels/sparse/mat_mul_op.cc
new file mode 100644
index 00000000000..2fa007873c8
--- /dev/null
+++ b/tensorflow/core/kernels/sparse/mat_mul_op.cc
@@ -0,0 +1,436 @@
+/* Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+#define EIGEN_USE_THREADS
+
+#if GOOGLE_CUDA
+#define EIGEN_USE_GPU
+#endif
+
+#include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
+#include "tensorflow/core/framework/op.h"
+#include "tensorflow/core/framework/op_kernel.h"
+#include "tensorflow/core/framework/tensor_types.h"
+#include "tensorflow/core/framework/variant_op_registry.h"
+#include "tensorflow/core/kernels/dense_update_functor.h"
+#include "tensorflow/core/kernels/fill_functor.h"
+#include "tensorflow/core/kernels/sparse/kernels.h"
+#include "tensorflow/core/kernels/sparse/sparse_matrix.h"
+#include "tensorflow/core/kernels/sparse/transpose_op.h"
+#include "tensorflow/core/kernels/transpose_functor.h"
+
+#if GOOGLE_CUDA
+#include "tensorflow/core/kernels/cuda_solvers.h"
+#include "tensorflow/core/kernels/cuda_sparse.h"
+#endif
+
+namespace tensorflow {
+
+typedef Eigen::ThreadPoolDevice CPUDevice;
+typedef Eigen::GpuDevice GPUDevice;
+
+template <typename Device, typename T>
+class CSRMatMulOp : public OpKernel {
+ public:
+  explicit CSRMatMulOp(OpKernelConstruction* c) : OpKernel(c) {
+    OP_REQUIRES_OK(c, c->GetAttr("transpose_a", &transpose_a_));
+    OP_REQUIRES_OK(c, c->GetAttr("transpose_b", &transpose_b_));
+    bool adjoint_a;
+    OP_REQUIRES_OK(c, c->GetAttr("adjoint_a", &adjoint_a));
+    OP_REQUIRES(c, !(adjoint_a && transpose_a_),
+                errors::InvalidArgument(
+                    "Only one of adjoint_a and transpose_a may be true."));
+    bool adjoint_b;
+    OP_REQUIRES_OK(c, c->GetAttr("adjoint_b", &adjoint_b));
+    OP_REQUIRES(c, !(adjoint_b && transpose_b_),
+                errors::InvalidArgument(
+                    "Only one of adjoint_b and transpose_b may be true."));
+    OP_REQUIRES_OK(c, c->GetAttr("transpose_output", &transpose_output_));
+    OP_REQUIRES_OK(c, c->GetAttr("conjugate_output", &conjugate_output_));
+    conjugate_a_ = adjoint_a;
+    conjugate_b_ = adjoint_b;
+    transpose_a_ = transpose_a_ || adjoint_a;
+    transpose_b_ = transpose_b_ || adjoint_b;
+  }
+
+  void Compute(OpKernelContext* ctx) final {
+    const CSRSparseMatrix* a_matrix;
+    OP_REQUIRES_OK(ctx, ExtractVariantFromInput(ctx, 0, &a_matrix));
+    const Tensor& b_t = ctx->input(1);
+
+    OP_REQUIRES(ctx, a_matrix->dtype() == b_t.dtype(),
+                errors::InvalidArgument(
+                    "Input types don't match.  a.dtype == ",
+                    DataTypeString(a_matrix->dtype()),
+                    " vs. b.dtype == ", DataTypeString(b_t.dtype())));
+
+    const int a_rank = a_matrix->dims();
+    const int b_rank = b_t.dims();
+    const int64 batch_size = (b_rank == 2) ? 1 : b_t.dim_size(0);
+
+    // TODO(ebrevdo): Add support for broadcasting matmul.
+    OP_REQUIRES(ctx, a_rank == b_rank,
+                errors::InvalidArgument("Ranks of a and b must match, saw: ",
+                                        a_rank, " vs. ", b_rank, "."));
+    OP_REQUIRES(ctx, a_matrix->batch_size() == batch_size,
+                errors::InvalidArgument(
+                    "Batch sizes of a and b must match, saw: ",
+                    a_matrix->batch_size(), " vs. ", batch_size, "."));
+
+    const Tensor& a_dense_shape_t = a_matrix->dense_shape();
+    TensorShape a_dense_tensor_shape;
+    auto a_dense_shape = a_dense_shape_t.vec<int64>();
+    OP_REQUIRES_OK(
+        ctx, TensorShapeUtils::MakeShape(a_dense_shape, &a_dense_tensor_shape));
+
+    const int row_dim = (a_rank == 2) ? 0 : 1;
+    const int64 a_inner_dim =
+        a_dense_tensor_shape.dim_size(transpose_a_ ? row_dim : row_dim + 1);
+    const int64 b_inner_dim =
+        b_t.shape().dim_size(transpose_b_ ? row_dim + 1 : row_dim);
+    const int64 b_outer_dim =
+        b_t.shape().dim_size(transpose_b_ ? row_dim : row_dim + 1);
+    const int64 b_slice_size = b_inner_dim * b_outer_dim;
+
+    OP_REQUIRES(
+        ctx, a_inner_dim == b_inner_dim,
+        errors::InvalidArgument(
+            "Inner product dimensions of A and B do not agree.  Shapes are: ",
+            a_dense_tensor_shape.DebugString(), " vs. ",
+            b_t.shape().DebugString()));
+
+    TensorShape c_shape;
+    if (a_rank == 3) c_shape.AddDim(batch_size);
+    if (transpose_output_) {
+      c_shape.AddDim(b_t.dim_size(transpose_b_ ? row_dim : row_dim + 1));
+      c_shape.AddDim(
+          a_dense_tensor_shape.dim_size(transpose_a_ ? row_dim + 1 : row_dim));
+    } else {
+      c_shape.AddDim(
+          a_dense_tensor_shape.dim_size(transpose_a_ ? row_dim + 1 : row_dim));
+      c_shape.AddDim(b_t.dim_size(transpose_b_ ? row_dim : row_dim + 1));
+    }
+
+    const int64 c_matrix_lhs = c_shape.dim_size(row_dim);
+    const int64 c_matrix_rhs = c_shape.dim_size(row_dim + 1);
+    const int64 c_slice_size = c_matrix_lhs * c_matrix_rhs;
+    Tensor* c_t;
+    OP_REQUIRES_OK(ctx, ctx->allocate_output(0, c_shape, &c_t));
+
+    const Device& d = ctx->eigen_device<Device>();
+
+    if (b_outer_dim == 1) {
+      // Call matrix-vector multiply if b is a vector.
+      TTypes<int64>::ConstVec a_dense_shape_comp(a_dense_shape.data() + row_dim,
+                                                 2);
+      Tensor b_conj_t;
+      const T* b_base_ptr = b_t.template flat<T>().data();
+      bool conjugate_a = conjugate_a_;
+      bool conjugate_output = conjugate_output_;
+      if (conjugate_b_) {
+        if (conjugate_a) {
+          // In this case we can use the identity
+          //   conj(a) * conj(b) = conj(a * b)
+          // instead of creating a conjugated copy of b.
+          conjugate_a = false;
+          conjugate_output = !conjugate_output;
+        } else {
+          OP_REQUIRES_OK(
+              ctx, ctx->forward_input_or_allocate_temp(
+                       {1}, DataTypeToEnum<T>::value, b_t.shape(), &b_conj_t));
+          functor::maybe_conj<Device, T>::run(d, b_t, &b_conj_t);
+          b_base_ptr = b_conj_t.template flat<T>().data();
+        }
+      }
+
+      functor::CSRSparseMatrixMatVec<Device, T> csr_spmv(transpose_a_,
+                                                         conjugate_a);
+      for (int i = 0; i < batch_size; ++i) {
+        auto a_row_ptr = a_matrix->row_pointers_vec(i);
+        auto a_col_ind = a_matrix->col_indices_vec(i);
+        auto a_values = a_matrix->values_vec<T>(i);
+        ConstCSRComponent<T> a_comp{a_row_ptr, a_col_ind, a_values,
+                                    a_dense_shape_comp};
+        const T* b_i = b_base_ptr + i * b_slice_size;
+        T* c_i = &c_t->template flat<T>()(i * c_slice_size);
+        Status s = csr_spmv.Compute(ctx, a_comp, b_i, c_i);
+        OP_REQUIRES_OK(ctx, s);
+      }
+      if (conjugate_output) {
+        functor::maybe_conj_inplace<Device, T>::run(d, c_t);
+      }
+      return;
+    }
+
+    functor::CSRSparseMatrixMatMul<Device, T> csr_spmmadd(transpose_output_);
+
+    Tensor c_mat_col_major_t;
+    if (!transpose_output_) {
+      // If transpose_output is false, we'll need to transpose the (col
+      // major) output of the csrgemm call to get proper (row-major)
+      // output.  Which means we need to keep a temporary buffer to
+      // store the intermediate gemm output.
+      TensorShape c_mat_col_major_shape;
+      if (a_rank == 2) {
+        c_mat_col_major_shape = TensorShape({c_matrix_rhs, c_matrix_lhs});
+      } else {
+        c_mat_col_major_shape =
+            TensorShape({batch_size, c_matrix_rhs, c_matrix_lhs});
+      }
+      OP_REQUIRES_OK(
+          ctx, ctx->allocate_temp(DataTypeToEnum<T>::value,
+                                  c_mat_col_major_shape, &c_mat_col_major_t));
+    }
+
+    // If transpose_output is true, return the direct (column-major i.e.,
+    // transposed) output of the csrgemm call.  Otherwise we'll need
+    // to transpose it to row major format.
+    auto c_mat_col_major =
+        (transpose_output_) ? c_t->flat<T>() : c_mat_col_major_t.flat<T>();
+
+    // Possibly transpose a.
+    const CSRSparseMatrix* a_input_matrix;
+    // If we need to transpose a, we will store the result temporarily
+    // in the object below.
+    CSRSparseMatrix a_matrix_transposed;
+    if (!transpose_a_) {
+      a_input_matrix = a_matrix;
+    } else {
+      functor::CSRSparseMatrixTranspose<Device, T> transpose;
+      OP_REQUIRES_OK(
+          ctx, transpose(ctx, conjugate_a_, *a_matrix, &a_matrix_transposed));
+      a_input_matrix = &a_matrix_transposed;
+    }
+
+    auto a_input_dense_shape = a_input_matrix->dense_shape().vec<int64>();
+
+    // Possibly transpose b.
+    Tensor b_t_input;
+    if (!transpose_b_) {
+      b_t_input = b_t;
+    } else {
+      TensorShape b_t_transposed_shape;
+      if (a_rank == 3) {
+        b_t_transposed_shape.AddDim(batch_size);
+      }
+      b_t_transposed_shape.AddDim(b_t.dim_size(row_dim + 1));
+      b_t_transposed_shape.AddDim(b_t.dim_size(row_dim));
+      OP_REQUIRES_OK(ctx, ctx->allocate_temp(DataTypeToEnum<T>::value,
+                                             b_t_transposed_shape, &b_t_input));
+      const Device& d = ctx->eigen_device<Device>();
+      if (conjugate_b_) {
+        OP_REQUIRES_OK(ctx, DoConjugateMatrixTranspose(d, b_t /*input*/,
+                                                       &b_t_input /*output*/));
+      } else {
+        OP_REQUIRES_OK(
+            ctx, DoMatrixTranspose(d, b_t /*input*/, &b_t_input /*output*/));
+      }
+    }
+
+    // Dense shape of a batch component of A.
+    TTypes<int64>::ConstVec a_input_dense_shape_comp(
+        a_input_dense_shape.data() + row_dim, 2);
+
+    auto b = b_t_input.flat<T>();
+
+    for (int i = 0; i < batch_size; ++i) {
+      auto a_row_ptr = a_input_matrix->row_pointers_vec(i);
+      auto a_col_ind = a_input_matrix->col_indices_vec(i);
+      auto a_values = a_input_matrix->values_vec<T>(i);
+      typename TTypes<T>::UnalignedConstMatrix b_i(b.data() + i * b_slice_size,
+                                                   {b_inner_dim, b_outer_dim});
+      typename TTypes<T>::UnalignedMatrix c_mat_col_major_i(
+          c_mat_col_major.data() + i * c_slice_size,
+          {c_matrix_lhs, c_matrix_rhs});
+      ConstCSRComponent<T> a_comp{a_row_ptr, a_col_ind, a_values,
+                                  a_input_dense_shape_comp};
+      Status s = csr_spmmadd.Compute(ctx, a_comp, b_i, c_mat_col_major_i);
+      OP_REQUIRES_OK(ctx, s);
+    }
+
+    if (!transpose_output_) {
+      // We need to return values in row major format, so transpose
+      // the column-major values in c_mat_col_major_t to row-major output c_t.
+      OP_REQUIRES_OK(ctx, DoMatrixTranspose(d, /*input=*/c_mat_col_major_t,
+                                            /*output=*/c_t));
+    }
+    if (conjugate_output_) {
+      functor::maybe_conj_inplace<Device, T>::run(d, c_t);
+    }
+  }
+
+ private:
+  bool transpose_a_;
+  bool transpose_b_;
+  bool conjugate_a_;
+  bool conjugate_b_;
+  bool transpose_output_;
+  bool conjugate_output_;
+};
+
+#define REGISTER(DEV, T)                                                      \
+  REGISTER_KERNEL_BUILDER(                                                    \
+      Name("SparseMatrixMatMul").Device(DEVICE_##DEV).TypeConstraint<T>("T"), \
+      CSRMatMulOp<DEV##Device, T>);
+
+#if GOOGLE_CUDA
+
+#define REGISTER_GPU(T) REGISTER(GPU, T)
+
+REGISTER_GPU(float)
+REGISTER_GPU(double)
+REGISTER_GPU(complex64)
+REGISTER_GPU(complex128)
+
+#undef REGISTER_GPU
+
+#endif  // GOOGLE_CUDA
+
+#undef REGISTER
+
+#if GOOGLE_CUDA
+
+namespace functor {
+
+template <typename T>
+class CSRSparseMatrixMatMul<GPUDevice, T> {
+ public:
+  explicit CSRSparseMatrixMatMul(const bool transpose_output)
+      : transpose_output_(transpose_output) {}
+
+  Status Compute(OpKernelContext* ctx, const ConstCSRComponent<T>& a,
+                 typename TTypes<T>::UnalignedConstMatrix b,
+                 typename TTypes<T>::UnalignedMatrix c) {
+    CudaSparse cuda_sparse(ctx);
+    TF_RETURN_IF_ERROR(cuda_sparse.Initialize());
+    {
+      // Use Csrmm to calculate:
+      //   C = alpha * op(A) * op(B) + beta * C
+      // where alpha = 1.0, beta = 0.0, A is sparse and B and C are dense.
+      // Note that Csrmm assumes B and C are in column-major form; so we
+      // use transB == true, and manually transpose the output in place
+      // using blas<t>geam.
+      // TODO(ebrevdo,rmlarsen): Add support for transposition and adjoint.
+
+      // Create alpha and beta scalars; alpha = 1.0, beta = 0.0
+      // TODO(ebrevdo,rmlarsen): Add support for non-trivial alpha and beta.
+      const T alpha = 1;
+      const T beta = 0;
+
+      // transA must be non-transpose if transB is transpose (cusparse
+      // limitation).
+      const cusparseOperation_t transA = CUSPARSE_OPERATION_NON_TRANSPOSE;
+
+      // transB: b is row-major, and cusparse requires col-major b (or
+      // equivalently transB == transpose).  this version is actually more
+      // efficient.
+      const cusparseOperation_t transB = CUSPARSE_OPERATION_TRANSPOSE;
+
+      cusparseMatDescr_t descrA;
+      TF_RETURN_IF_CUSPARSE_ERROR(cusparseCreateMatDescr(&descrA));
+      TF_RETURN_IF_CUSPARSE_ERROR(
+          cusparseSetMatType(descrA, CUSPARSE_MATRIX_TYPE_GENERAL));
+      TF_RETURN_IF_CUSPARSE_ERROR(
+          cusparseSetMatIndexBase(descrA, CUSPARSE_INDEX_BASE_ZERO));
+
+      // A is (m, k), Bt is (ldb, k) and Ct is (ldc, n)
+      const int k = b.dimension(0);
+      DCHECK_EQ(k, a.dense_shape_host(1));
+
+      // If transpose_output_ is true, then the c matrix we receive
+      // here is the direct row major output (into which we will store
+      // csrgemm's col major output).  Otherwise it's a
+      // temporary tensor that will store the column major output that
+      // will eventually be transposed.
+      const int m = c.dimension(transpose_output_ ? 1 : 0);
+      const int n = c.dimension(transpose_output_ ? 0 : 1);
+      DCHECK_EQ(m, a.dense_shape_host(0));
+      DCHECK_EQ(n, b.dimension(1));
+      const int nnz = a.values.size();
+      DCHECK_EQ(nnz, a.col_ind.size());
+
+      // ldb: leading dimension of B. If op(B)=B, it must be at least max(1, k)
+      // if op(A) = A and at least max (1, m) otherwise. If op(B) != B, it must
+      // be at least max(1, n).
+      const int ldb = n;
+      // ldc: leading dimension of C. It must be at least max(1, m) if
+      // op(A) = A and at least max(1, k) otherwise.
+      const int ldc = m;
+
+      TF_RETURN_IF_ERROR(
+          cuda_sparse.Csrmm(transA, transB, m, n, k, nnz, &alpha, descrA,
+                            a.values.data(), a.row_ptr.data(), a.col_ind.data(),
+                            b.data(), ldb, &beta, c.data(), ldc));
+    }
+
+    return Status::OK();
+  }
+
+ private:
+  bool transpose_output_;
+};
+
+template <typename T>
+class CSRSparseMatrixMatVec<GPUDevice, T> {
+ public:
+  CSRSparseMatrixMatVec(bool transpose_a, bool conjugate_a)
+      : transA_(TransposeAndConjugateToCuSparseOp(transpose_a, conjugate_a,
+                                                  &status_)) {}
+
+  Status Compute(OpKernelContext* ctx, const ConstCSRComponent<T>& a,
+                 const T* x, T* y) {
+    TF_RETURN_IF_ERROR(status_);
+    CudaSparse cuda_sparse(ctx);
+    TF_RETURN_IF_ERROR(cuda_sparse.Initialize());
+    {
+      // Use Csrmv to calculate:
+      //   y = alpha * op(A) * x + beta * y
+      // where alpha = 1.0, beta = 0.0, A is a sparse matrix and x and y are
+      // dense vectors.
+
+      // Create alpha and beta scalars; alpha = 1.0, beta = 0.0
+      // TODO(rmlarsen,ebrevdo): Add support for general alpha, beta.
+      const T alpha = 1;
+      const T beta = 0;
+
+      cusparseMatDescr_t descrA;
+      TF_RETURN_IF_CUSPARSE_ERROR(cusparseCreateMatDescr(&descrA));
+      TF_RETURN_IF_CUSPARSE_ERROR(
+          cusparseSetMatType(descrA, CUSPARSE_MATRIX_TYPE_GENERAL));
+      TF_RETURN_IF_CUSPARSE_ERROR(
+          cusparseSetMatIndexBase(descrA, CUSPARSE_INDEX_BASE_ZERO));
+
+      const int m = a.dense_shape_host(0);
+      const int n = a.dense_shape_host(1);
+      const int nnz = a.values.size();
+      DCHECK_EQ(nnz, a.col_ind.size());
+      TF_RETURN_IF_ERROR(cuda_sparse.Csrmv(transA_, m, n, nnz, &alpha, descrA,
+                                           a.values.data(), a.row_ptr.data(),
+                                           a.col_ind.data(), x, &beta, y));
+    }
+
+    return Status::OK();
+  }
+
+ private:
+  Status status_;
+  const cusparseOperation_t transA_;
+};
+
+}  // namespace functor
+
+#endif  // GOOGLE_CUDA
+
+}  // namespace tensorflow
diff --git a/tensorflow/core/kernels/sparse/mul_op.cc b/tensorflow/core/kernels/sparse/mul_op.cc
new file mode 100644
index 00000000000..d63512252f7
--- /dev/null
+++ b/tensorflow/core/kernels/sparse/mul_op.cc
@@ -0,0 +1,171 @@
+/* Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+#define EIGEN_USE_THREADS
+
+#if GOOGLE_CUDA
+#define EIGEN_USE_GPU
+#endif
+
+#include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
+#include "tensorflow/core/framework/op.h"
+#include "tensorflow/core/framework/op_kernel.h"
+#include "tensorflow/core/framework/tensor_types.h"
+#include "tensorflow/core/framework/variant_op_registry.h"
+#include "tensorflow/core/kernels/cwise_ops.h"
+#include "tensorflow/core/kernels/sparse/kernels.h"
+#include "tensorflow/core/kernels/sparse/sparse_matrix.h"
+
+#if GOOGLE_CUDA
+#include "tensorflow/core/kernels/cuda_sparse.h"
+#endif
+
+namespace tensorflow {
+
+typedef Eigen::ThreadPoolDevice CPUDevice;
+typedef Eigen::GpuDevice GPUDevice;
+
+template <typename Device, typename T>
+class CSRMulOp : public OpKernel {
+ public:
+  explicit CSRMulOp(OpKernelConstruction* c) : OpKernel(c) {}
+
+  void Compute(OpKernelContext* ctx) final {
+    const CSRSparseMatrix* a_matrix;
+    OP_REQUIRES_OK(ctx, ExtractVariantFromInput(ctx, 0, &a_matrix));
+    const Tensor& b_t = ctx->input(1);
+
+    OP_REQUIRES(ctx, a_matrix->dtype() == b_t.dtype(),
+                errors::InvalidArgument(
+                    "Input types don't match.  a.dtype == ",
+                    DataTypeString(a_matrix->dtype()),
+                    " vs. b.dtype == ", DataTypeString(b_t.dtype())));
+
+    const int b_rank = b_t.dims();
+
+    const Tensor& a_dense_shape_t = a_matrix->dense_shape();
+    auto a_dense_shape = a_dense_shape_t.vec<int64>();
+    const int batch_size = a_dense_shape(0);
+    if (b_rank == 3) {
+      OP_REQUIRES(
+          ctx,
+          ((a_matrix->dims() == 3) && (b_t.dim_size(0) == batch_size) &&
+           (b_t.NumElements() == batch_size)),
+          errors::InvalidArgument(
+              "If b is a rank-3 tensor, then a must be a rank 3 and the size "
+              "of b be "
+              "[batch_size, 1, 1].  But the shape of b is: ",
+              b_t.shape().DebugString(),
+              " and the shape of a is: ", a_dense_shape_t.DebugString()));
+    } else {
+      OP_REQUIRES(ctx, b_rank == 0,
+                  errors::Unimplemented(
+                      "Multiplying by a 2D+ dense tensor is not currently "
+                      "supported, but shape of b is: ",
+                      b_t.shape().DebugString()));
+    }
+
+    Tensor c_t(cpu_allocator(), DT_VARIANT, TensorShape({}));
+    CSRSparseMatrix c_matrix;
+    if (b_rank == 0) {
+      auto b = b_t.scalar<T>();
+      // TODO(ebrevdo): call other functor if b is nonscalar.
+      functor::CSRSparseMatrixMulScalar<Device, T> csrmul_scalar;
+      OP_REQUIRES_OK(ctx, csrmul_scalar.Compute(ctx, *a_matrix, b, &c_matrix));
+    } else {
+      // b_rank == 1 and a_matrix is rank-3.
+      auto b = b_t.flat<T>();
+      functor::CSRSparseMatrixBatchMulVec<Device, T> csrmul_batch_vec;
+      OP_REQUIRES_OK(ctx,
+                     csrmul_batch_vec.Compute(ctx, *a_matrix, b, &c_matrix));
+    }
+    c_t.scalar<Variant>()() = std::move(c_matrix);
+    ctx->set_output(0, c_t);
+  }
+};
+
+#define REGISTER(DEV, T)                                                   \
+  REGISTER_KERNEL_BUILDER(                                                 \
+      Name("SparseMatrixMul").Device(DEVICE_##DEV).TypeConstraint<T>("T"), \
+      CSRMulOp<DEV##Device, T>);
+
+#if GOOGLE_CUDA
+
+#define REGISTER_GPU(T) REGISTER(GPU, T)
+
+REGISTER_GPU(float)
+REGISTER_GPU(double)
+REGISTER_GPU(complex64)
+REGISTER_GPU(complex128)
+
+#undef REGISTER_GPU
+
+#endif  // GOOGLE_CUDA
+
+#undef REGISTER
+
+#if GOOGLE_CUDA
+
+namespace functor {
+
+template <typename T>
+class CSRSparseMatrixMulScalar<GPUDevice, T> {
+ public:
+  explicit CSRSparseMatrixMulScalar() {}
+
+  Status Compute(OpKernelContext* ctx, const CSRSparseMatrix& a,
+                 typename TTypes<T>::ConstScalar b, CSRSparseMatrix* c) {
+    const int total_nnz = a.total_nnz();
+    Tensor c_values_t;
+    TF_RETURN_IF_ERROR(ctx->allocate_temp(
+        DataTypeToEnum<T>::value, TensorShape({total_nnz}), &c_values_t));
+    TF_RETURN_IF_ERROR(CSRSparseMatrix::CreateCSRSparseMatrix(
+        DataTypeToEnum<T>::value, a.dense_shape(), a.batch_pointers(),
+        a.row_pointers(), a.col_indices(), c_values_t, c));
+
+    auto a_values = a.values().flat<T>();
+    auto c_values = c_values_t.flat<T>();
+
+    const GPUDevice& d = ctx->eigen_device<GPUDevice>();
+    bool error;
+    bool* const error_ptr = functor::mul<T>::has_errors ? &error : nullptr;
+
+    // tensor * scalar
+    functor::BinaryFunctor<GPUDevice, functor::mul<T>, 1>().Right(
+        d, c_values, a_values, b, error_ptr);
+
+    return Status::OK();
+  }
+};
+
+#define DECLARE_GPU_SPEC(T)                                 \
+  template <>                                               \
+  Status CSRSparseMatrixBatchMulVec<GPUDevice, T>::Compute( \
+      OpKernelContext* ctx, const CSRSparseMatrix& a,       \
+      typename TTypes<T>::ConstFlat b, CSRSparseMatrix* c); \
+  extern template struct CSRSparseMatrixBatchMulVec<GPUDevice, T>;
+
+DECLARE_GPU_SPEC(float);
+DECLARE_GPU_SPEC(double);
+DECLARE_GPU_SPEC(std::complex<float>);
+DECLARE_GPU_SPEC(std::complex<double>);
+
+#undef DECLARE_GPU_SPEC
+
+}  // namespace functor
+
+#endif  // GOOGLE_CUDA
+
+}  // namespace tensorflow
diff --git a/tensorflow/core/kernels/sparse/nnz_op.cc b/tensorflow/core/kernels/sparse/nnz_op.cc
new file mode 100644
index 00000000000..e38b39916c3
--- /dev/null
+++ b/tensorflow/core/kernels/sparse/nnz_op.cc
@@ -0,0 +1,78 @@
+/* Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+#define EIGEN_USE_THREADS
+
+#if GOOGLE_CUDA
+#define EIGEN_USE_GPU
+#endif
+
+#include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
+#include "tensorflow/core/framework/op.h"
+#include "tensorflow/core/framework/op_kernel.h"
+#include "tensorflow/core/framework/tensor_types.h"
+#include "tensorflow/core/framework/variant_op_registry.h"
+#include "tensorflow/core/kernels/dense_update_functor.h"
+#include "tensorflow/core/kernels/sparse/kernels.h"
+#include "tensorflow/core/kernels/sparse/sparse_matrix.h"
+
+#if GOOGLE_CUDA
+#include "tensorflow/core/kernels/cuda_solvers.h"
+#include "tensorflow/core/kernels/cuda_sparse.h"
+#endif
+
+namespace tensorflow {
+
+typedef Eigen::ThreadPoolDevice CPUDevice;
+typedef Eigen::GpuDevice GPUDevice;
+
+template <typename Device>
+class CSRNNZOp : public OpKernel {
+ public:
+  explicit CSRNNZOp(OpKernelConstruction* c) : OpKernel(c) {}
+
+  void Compute(OpKernelContext* c) final {
+    const CSRSparseMatrix* csr_sparse_matrix;
+    OP_REQUIRES_OK(c, ExtractVariantFromInput(c, 0, &csr_sparse_matrix));
+    Tensor* nnz_t;
+    TensorShape nnz_shape;
+    if (csr_sparse_matrix->dims() == 3) {
+      nnz_shape.AddDim(csr_sparse_matrix->batch_size());
+    }
+    OP_REQUIRES_OK(c, c->allocate_output(0, nnz_shape, &nnz_t));
+    auto nnz = nnz_t->flat<int32>();
+    for (int i = 0; i < csr_sparse_matrix->batch_size(); ++i) {
+      nnz(i) = csr_sparse_matrix->nnz(i);
+    }
+  }
+};
+
+#define REGISTER(DEV)                                      \
+  REGISTER_KERNEL_BUILDER(Name("SparseMatrixNNZ")          \
+                              .Device(DEVICE_##DEV)        \
+                              .HostMemory("nnz"),          \
+                          CSRNNZOp<DEV##Device>);
+
+REGISTER(CPU)
+
+#if GOOGLE_CUDA
+
+REGISTER(GPU)
+
+#endif  // GOOGLE_CUDA
+
+#undef REGISTER
+
+}  // namespace tensorflow
diff --git a/tensorflow/core/kernels/sparse/softmax_op.cc b/tensorflow/core/kernels/sparse/softmax_op.cc
new file mode 100644
index 00000000000..0195eb474e9
--- /dev/null
+++ b/tensorflow/core/kernels/sparse/softmax_op.cc
@@ -0,0 +1,225 @@
+/* Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+// Implements the kernel for the CSRSoftmax op, which performs softmax
+// along the innermost (col) dimension of a CSRSparseMatrix object
+// stored in a DT_VARIANT.
+
+#define EIGEN_USE_THREADS
+
+#if GOOGLE_CUDA
+#include "tensorflow/core/kernels/cuda_sparse.h"
+#define EIGEN_USE_GPU
+#endif
+
+#include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
+#include "tensorflow/core/framework/op.h"
+#include "tensorflow/core/framework/op_kernel.h"
+#include "tensorflow/core/framework/tensor_types.h"
+#include "tensorflow/core/framework/variant_op_registry.h"
+#include "tensorflow/core/kernels/dense_update_functor.h"
+#include "tensorflow/core/kernels/fill_functor.h"
+#include "tensorflow/core/kernels/slice_op.h"
+#include "tensorflow/core/kernels/sparse/kernels.h"
+#include "tensorflow/core/kernels/sparse/sparse_matrix.h"
+
+namespace tensorflow {
+
+typedef Eigen::ThreadPoolDevice CPUDevice;
+typedef Eigen::GpuDevice GPUDevice;
+
+template <typename Device, typename T>
+class CSRSoftmaxOp : public OpKernel {
+ public:
+  explicit CSRSoftmaxOp(OpKernelConstruction* ctx) : OpKernel(ctx) {}
+
+  void Compute(OpKernelContext* ctx) override {
+    const CSRSparseMatrix* logits_matrix;
+    OP_REQUIRES_OK(ctx, ExtractVariantFromInput(ctx, 0, &logits_matrix));
+    OP_REQUIRES(
+        ctx, logits_matrix->dtype() == DataTypeToEnum<T>::value,
+        errors::InvalidArgument("dtype of logits is not equal to 'type': ",
+                                DataTypeString(logits_matrix->dtype()), " vs. ",
+                                DataTypeString(DataTypeToEnum<T>::value)));
+
+    // Allocate output shapes
+    const int total_nnz = logits_matrix->total_nnz();
+    Tensor output_values_t;
+    OP_REQUIRES_OK(
+        ctx, ctx->allocate_temp(DataTypeToEnum<T>::value,
+                                TensorShape({total_nnz}), &output_values_t));
+
+    CSRSparseMatrix output_matrix;
+
+    Tensor dense_shape_t = logits_matrix->dense_shape();
+
+    OP_REQUIRES_OK(
+        ctx,
+        CSRSparseMatrix::CreateCSRSparseMatrix(
+            DataTypeToEnum<T>::value, dense_shape_t,
+            logits_matrix->batch_pointers(), logits_matrix->row_pointers(),
+            logits_matrix->col_indices(), output_values_t, &output_matrix));
+
+    if (total_nnz > 0) {
+      functor::CSRSparseMatrixSoftmax<Device, T> softmax;
+      OP_REQUIRES_OK(
+          ctx, softmax(ctx, *logits_matrix, output_matrix.values().vec<T>()));
+    }
+
+    Tensor output_t(cpu_allocator(), DT_VARIANT, TensorShape({}));
+    output_t.scalar<Variant>()() = std::move(output_matrix);
+    ctx->set_output(0, output_t);
+  }
+};
+
+#ifdef GOOGLE_CUDA
+#define REGISTER(DEV, T)                                  \
+  REGISTER_KERNEL_BUILDER(Name("SparseMatrixSoftmax")     \
+                              .Device(DEVICE_##DEV)       \
+                              .TypeConstraint<T>("type"), \
+                          CSRSoftmaxOp<DEV##Device, T>);
+
+REGISTER(GPU, float)
+REGISTER(GPU, double)
+
+#undef REGISTER
+
+namespace functor {
+#define DECLARE_GPU_SPEC(T)                                \
+  template <>                                              \
+  Status CSRSparseMatrixSoftmax<GPUDevice, T>::operator()( \
+      OpKernelContext* ctx, const CSRSparseMatrix& logits, \
+      typename TTypes<T>::Vec softmax_values);             \
+  extern template struct CSRSparseMatrixSoftmax<GPUDevice, T>;
+
+DECLARE_GPU_SPEC(float);
+DECLARE_GPU_SPEC(double);
+
+#undef DECLARE_GPU_SPEC
+}  // namespace functor
+
+#endif  // GOOGLE_CUDA
+
+template <typename Device, typename T>
+class CSRSoftmaxGradOp : public OpKernel {
+ public:
+  explicit CSRSoftmaxGradOp(OpKernelConstruction* ctx) : OpKernel(ctx) {}
+
+  void Compute(OpKernelContext* ctx) override {
+    const CSRSparseMatrix* softmax_matrix;
+    OP_REQUIRES_OK(ctx, ExtractVariantFromInput(ctx, 0, &softmax_matrix));
+    OP_REQUIRES(ctx, softmax_matrix->dtype() == DataTypeToEnum<T>::value,
+                errors::InvalidArgument(
+                    "dtype of softmax is not equal to 'type': ",
+                    DataTypeString(softmax_matrix->dtype()), " vs. ",
+                    DataTypeString(DataTypeToEnum<T>::value)));
+
+    const CSRSparseMatrix* grad_softmax_matrix;
+    OP_REQUIRES_OK(ctx, ExtractVariantFromInput(ctx, 1, &grad_softmax_matrix));
+    OP_REQUIRES(ctx, grad_softmax_matrix->dtype() == DataTypeToEnum<T>::value,
+                errors::InvalidArgument(
+                    "dtype of grad_softmax is not equal to 'type': ",
+                    DataTypeString(grad_softmax_matrix->dtype()), " vs. ",
+                    DataTypeString(DataTypeToEnum<T>::value)));
+
+    OP_REQUIRES(
+        ctx, softmax_matrix->dims() == grad_softmax_matrix->dims(),
+        errors::InvalidArgument(
+            "Ranks of softmax and grad_softmax matrices differ: ",
+            softmax_matrix->dims(), " vs. ", grad_softmax_matrix->dims()));
+
+    OP_REQUIRES(
+        ctx, softmax_matrix->dims() == grad_softmax_matrix->dims(),
+        errors::InvalidArgument(
+            "Ranks of softmax and grad_softmax matrices differ: ",
+            softmax_matrix->dims(), " vs. ", grad_softmax_matrix->dims()));
+
+    Tensor dense_shape_t = softmax_matrix->dense_shape();
+    auto host_dense_shape =
+        static_cast<const Tensor>(dense_shape_t).vec<int64>();
+
+    auto host_grad_dense_shape =
+        grad_softmax_matrix->dense_shape().vec<int64>();
+
+    for (int i = 0; i < host_dense_shape.size(); ++i) {
+      OP_REQUIRES(ctx, host_dense_shape(i) == host_grad_dense_shape(i),
+                  errors::InvalidArgument(
+                      "Shapes of softmax and grad_softmax matrices differ: ",
+                      dense_shape_t.SummarizeValue(3), " vs. ",
+                      grad_softmax_matrix->dense_shape().SummarizeValue(3)));
+    }
+
+    // Allocate output shapes.  Note that since the Softmax Gradient
+    // tensor is the elementwise product of some function with the
+    // softmax value, it will keep the sparsity structure of the softmax.
+    const int total_nnz = softmax_matrix->total_nnz();
+    PersistentTensor gradient_values_pt;
+    Tensor* gradient_values_t;
+    OP_REQUIRES_OK(ctx, ctx->allocate_persistent(
+                            DataTypeToEnum<T>::value, TensorShape({total_nnz}),
+                            &gradient_values_pt, &gradient_values_t));
+
+    CSRSparseMatrix gradient_matrix;
+
+    OP_REQUIRES_OK(
+        ctx, CSRSparseMatrix::CreateCSRSparseMatrix(
+                 DataTypeToEnum<T>::value, dense_shape_t,
+                 softmax_matrix->batch_pointers(),
+                 softmax_matrix->row_pointers(), softmax_matrix->col_indices(),
+                 *gradient_values_t, &gradient_matrix));
+
+    if (total_nnz > 0) {
+      functor::CSRSparseMatrixSoftmaxGrad<Device, T> softmax_grad;
+      OP_REQUIRES_OK(ctx,
+                     softmax_grad(ctx, *softmax_matrix, *grad_softmax_matrix,
+                                  gradient_matrix.values().vec<T>()));
+    }
+
+    Tensor gradient_t(cpu_allocator(), DT_VARIANT, TensorShape({}));
+    gradient_t.scalar<Variant>()() = std::move(gradient_matrix);
+    ctx->set_output(0, gradient_t);
+  }
+};
+
+#ifdef GOOGLE_CUDA
+#define REGISTER(DEV, T)                                  \
+  REGISTER_KERNEL_BUILDER(Name("SparseMatrixSoftmaxGrad") \
+                              .Device(DEVICE_##DEV)       \
+                              .TypeConstraint<T>("type"), \
+                          CSRSoftmaxGradOp<DEV##Device, T>);
+
+REGISTER(GPU, float)
+REGISTER(GPU, double)
+
+#undef REGISTER
+
+namespace functor {
+#define DECLARE_GPU_SPEC(T)                                    \
+  template <>                                                  \
+  Status CSRSparseMatrixSoftmaxGrad<GPUDevice, T>::operator()( \
+      OpKernelContext* ctx, const CSRSparseMatrix& softmax,    \
+      const CSRSparseMatrix& grad_softmax,                     \
+      typename TTypes<T>::Vec gradient_values);                \
+  extern template struct CSRSparseMatrixSoftmaxGrad<GPUDevice, T>;
+
+DECLARE_GPU_SPEC(float);
+DECLARE_GPU_SPEC(double);
+
+#undef DECLARE_GPU_SPEC
+}  // namespace functor
+
+#endif  // GOOGLE_CUDA
+
+}  // namespace tensorflow
diff --git a/tensorflow/core/kernels/sparse/sparse_cholesky_op.cc b/tensorflow/core/kernels/sparse/sparse_cholesky_op.cc
new file mode 100644
index 00000000000..bd62fa2a296
--- /dev/null
+++ b/tensorflow/core/kernels/sparse/sparse_cholesky_op.cc
@@ -0,0 +1,288 @@
+/* Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+#include <atomic>
+#include <numeric>
+#include <vector>
+
+#define EIGEN_USE_THREADS
+
+#include "third_party/eigen3/Eigen/Core"
+#include "third_party/eigen3/Eigen/SparseCholesky"
+#include "third_party/eigen3/Eigen/SparseCore"
+#include "third_party/eigen3/Eigen/OrderingMethods"
+#include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
+#include "tensorflow/core/framework/op.h"
+#include "tensorflow/core/framework/op_kernel.h"
+#include "tensorflow/core/framework/tensor_types.h"
+#include "tensorflow/core/framework/variant_op_registry.h"
+#include "tensorflow/core/kernels/sparse/kernels.h"
+#include "tensorflow/core/kernels/sparse/sparse_matrix.h"
+#include "tensorflow/core/util/work_sharder.h"
+
+namespace tensorflow {
+
+// Op to compute the sparse Cholesky factorization of a sparse matrix.
+//
+// Implements a CPU kernel which returns the lower triangular sparse Cholesky
+// factor of a CSRSparseMatrix, using the fill-in reducing permutation.
+//
+// The CSRSparseMatrix may represent a single sparse matrix (rank 2) or a batch
+// of sparse matrices (rank 3). Each component must represent a symmetric
+// positive definite (SPD) matrix. In particular, this means the component
+// matrices must be square. We don't actually check if the input is symmetric,
+// only the lower triangular part of each component is read.
+//
+// The associated permutation must be a Tensor of rank (R - 1), where the
+// CSRSparseMatrix has rank R. Additionally, the batch dimension of the
+// CSRSparseMatrix and the permutation must be the same. Each batch of
+// the permutation should the contain each of the integers [0,..,N - 1] exactly
+// once, where N is the number of rows of each CSR SparseMatrix component.
+// TODO(anudhyan): Add checks to throw an InvalidArgument error if the
+// permutation is not valid.
+//
+// Returns a CSRSparseMatrix representing the lower triangular (batched)
+// Cholesky factors. It has the same shape as the input CSRSparseMatrix. For
+// each component sparse matrix A, the corresponding output sparse matrix L
+// satisfies the identity:
+//   A = L * Lt
+// where Lt denotes the adjoint of L.
+//
+// TODO(b/126472741): Due to the multiple batches of a 3D CSRSparseMatrix being
+// laid out in contiguous memory, this implementation allocates memory to store
+// a temporary copy of the Cholesky factor. Consequently, it uses roughly twice
+// the amount of memory that it needs to. This may cause a memory blowup for
+// sparse matrices with a high number of non-zero elements.
+template <typename T>
+class CSRSparseCholeskyCPUOp : public OpKernel {
+  // Note: We operate in column major (CSC) format in this Op since the
+  // SimplicialLLT returns the factor in column major.
+  using SparseMatrix = Eigen::SparseMatrix<T, Eigen::ColMajor>;
+
+ public:
+  explicit CSRSparseCholeskyCPUOp(OpKernelConstruction* c) : OpKernel(c) {}
+
+  void Compute(OpKernelContext* ctx) final {
+    // Extract inputs and valididate shapes and types.
+    const CSRSparseMatrix* input_matrix;
+    OP_REQUIRES_OK(ctx, ExtractVariantFromInput(ctx, 0, &input_matrix));
+    const Tensor& input_permutation_indices = ctx->input(1);
+
+    int64 num_rows;
+    int batch_size;
+    ValidateInputs(ctx, *input_matrix, input_permutation_indices, &batch_size,
+                   &num_rows);
+
+    // Allocate batch pointers.
+    Tensor batch_ptr(cpu_allocator(), DT_INT32, TensorShape({batch_size + 1}));
+    auto batch_ptr_vec = batch_ptr.vec<int32>();
+    batch_ptr_vec(0) = 0;
+
+    // Temporary vector of Eigen SparseMatrices to store the Sparse Cholesky
+    // factors.
+    // Note: we use column-compressed (CSC) SparseMatrix because SimplicialLLT
+    // returns the factors in column major format. Since our input should be
+    // symmetric, column major and row major is identical in storage. We just
+    // have to switch to reading the upper triangular part of the input, which
+    // corresponds to the lower triangular part in row major format.
+    std::vector<SparseMatrix> sparse_cholesky_factors(batch_size);
+
+    // TODO(anudhyan): Tune the cost per unit based on benchmarks.
+    const double nnz_per_row =
+        (input_matrix->total_nnz() / batch_size) / num_rows;
+    const int64 sparse_cholesky_cost_per_batch =
+        nnz_per_row * nnz_per_row * num_rows;
+    // Perform sparse Cholesky factorization of each batch in parallel.
+    auto worker_threads = *(ctx->device()->tensorflow_cpu_worker_threads());
+    std::atomic<int64> invalid_input_index(-1);
+    Shard(worker_threads.num_threads, worker_threads.workers, batch_size,
+          sparse_cholesky_cost_per_batch,
+          [&](int64 batch_begin, int64 batch_end) {
+            for (int64 batch_index = batch_begin; batch_index < batch_end;
+                 ++batch_index) {
+              // Define an Eigen SparseMatrix Map to operate on the
+              // CSRSparseMatrix component without copying the data.
+              Eigen::Map<const SparseMatrix> sparse_matrix(
+                  num_rows, num_rows, input_matrix->nnz(batch_index),
+                  input_matrix->row_pointers_vec(batch_index).data(),
+                  input_matrix->col_indices_vec(batch_index).data(),
+                  input_matrix->values_vec<T>(batch_index).data());
+
+              Eigen::SimplicialLLT<SparseMatrix, Eigen::Upper,
+                                   Eigen::NaturalOrdering<int>>
+                  solver;
+              auto permutation_indices_flat =
+                  input_permutation_indices.flat<int32>().data();
+
+              // Invert the fill-in reducing ordering and apply it to the input
+              // sparse matrix.
+              Eigen::Map<
+                  Eigen::PermutationMatrix<Eigen::Dynamic, Eigen::Dynamic, int>>
+                  permutation(permutation_indices_flat + batch_index * num_rows,
+                              num_rows);
+              auto permutation_inverse = permutation.inverse();
+
+              SparseMatrix permuted_sparse_matrix;
+              permuted_sparse_matrix.template selfadjointView<Eigen::Upper>() =
+                  sparse_matrix.template selfadjointView<Eigen::Upper>()
+                      .twistedBy(permutation_inverse);
+
+              // Compute the Cholesky decomposition.
+              solver.compute(permuted_sparse_matrix);
+              if (solver.info() != Eigen::Success) {
+                invalid_input_index = batch_index;
+                return;
+              }
+
+              // Get the upper triangular factor, which would end up in the
+              // lower triangular part of the output CSRSparseMatrix when
+              // interpreted in row major format.
+              sparse_cholesky_factors[batch_index] =
+                  solver.matrixU().twistedBy(permutation);
+
+              // For now, batch_ptr contains the number of nonzeros in each
+              // batch.
+              batch_ptr_vec(batch_index + 1) =
+                  sparse_cholesky_factors[batch_index].nonZeros();
+            }
+          });
+
+    // Check for invalid input.
+    OP_REQUIRES(
+        ctx, invalid_input_index == -1,
+        errors::InvalidArgument(
+            "Sparse Cholesky factorization failed for batch index ",
+            invalid_input_index.load(), ". The input might not be valid."));
+
+    // Compute a cumulative sum to obtain the batch pointers.
+    std::partial_sum(batch_ptr_vec.data(),
+                     batch_ptr_vec.data() + batch_size + 1,
+                     batch_ptr_vec.data());
+
+    // Allocate output Tensors.
+    const int64 total_nnz = batch_ptr_vec(batch_size);
+    Tensor output_row_ptr(cpu_allocator(), DT_INT32,
+                          TensorShape({(num_rows + 1) * batch_size}));
+    Tensor output_col_ind(cpu_allocator(), DT_INT32, TensorShape({total_nnz}));
+    Tensor output_values(cpu_allocator(), DataTypeToEnum<T>::value,
+                         TensorShape({total_nnz}));
+    auto output_row_ptr_ptr = output_row_ptr.flat<int32>().data();
+    auto output_col_ind_ptr = output_col_ind.flat<int32>().data();
+    auto output_values_ptr = output_values.flat<T>().data();
+
+    // Copy the output matrices from each batch into the CSRSparseMatrix
+    // Tensors.
+    // TODO(b/129906419): Factor out the copy from Eigen SparseMatrix to
+    // CSRSparseMatrix into common utils. This is also used in
+    // SparseMatrixSparseMatMul.
+    Shard(worker_threads.num_threads, worker_threads.workers, batch_size,
+          (3 * total_nnz) / batch_size /* cost per unit */,
+          [&](int64 batch_begin, int64 batch_end) {
+            for (int64 batch_index = batch_begin; batch_index < batch_end;
+                 ++batch_index) {
+              const SparseMatrix& cholesky_factor =
+                  sparse_cholesky_factors[batch_index];
+              const int64 nnz = cholesky_factor.nonZeros();
+
+              std::copy(cholesky_factor.outerIndexPtr(),
+                        cholesky_factor.outerIndexPtr() + num_rows + 1,
+                        output_row_ptr_ptr + batch_index * (num_rows + 1));
+              std::copy(cholesky_factor.innerIndexPtr(),
+                        cholesky_factor.innerIndexPtr() + nnz,
+                        output_col_ind_ptr + batch_ptr_vec(batch_index));
+              std::copy(cholesky_factor.valuePtr(),
+                        cholesky_factor.valuePtr() + nnz,
+                        output_values_ptr + batch_ptr_vec(batch_index));
+            }
+          });
+
+    // Create the CSRSparseMatrix instance from its component Tensors and
+    // prepare the Variant output Tensor.
+    CSRSparseMatrix output_csr_matrix;
+    OP_REQUIRES_OK(
+        ctx,
+        CSRSparseMatrix::CreateCSRSparseMatrix(
+            DataTypeToEnum<T>::value, input_matrix->dense_shape(), batch_ptr,
+            output_row_ptr, output_col_ind, output_values, &output_csr_matrix));
+    Tensor* output_csr_matrix_tensor;
+    AllocatorAttributes cpu_alloc;
+    cpu_alloc.set_on_host(true);
+    OP_REQUIRES_OK(
+        ctx, ctx->allocate_output(0, TensorShape({}), &output_csr_matrix_tensor,
+                                  cpu_alloc));
+    output_csr_matrix_tensor->scalar<Variant>()() =
+        std::move(output_csr_matrix);
+  }
+
+ private:
+  void ValidateInputs(OpKernelContext* ctx,
+                      const CSRSparseMatrix& sparse_matrix,
+                      const Tensor& permutation_indices, int* batch_size,
+                      int64* num_rows) {
+    OP_REQUIRES(ctx, sparse_matrix.dtype() == DataTypeToEnum<T>::value,
+                errors::InvalidArgument(
+                    "Asked for a CSRSparseMatrix of type ",
+                    DataTypeString(DataTypeToEnum<T>::value),
+                    " but saw dtype: ", DataTypeString(sparse_matrix.dtype())));
+
+    const Tensor& dense_shape = sparse_matrix.dense_shape();
+    const int rank = dense_shape.dim_size(0);
+    OP_REQUIRES(ctx, rank == 2 || rank == 3,
+                errors::InvalidArgument("sparse matrix must have rank 2 or 3; ",
+                                        "but dense_shape has size ", rank));
+    const int row_dim = (rank == 2) ? 0 : 1;
+    auto dense_shape_vec = dense_shape.vec<int64>();
+    *num_rows = dense_shape_vec(row_dim);
+    const int64 num_cols = dense_shape_vec(row_dim + 1);
+    OP_REQUIRES(ctx, *num_rows == num_cols,
+                errors::InvalidArgument("sparse matrix must be square; got: ",
+                                        *num_rows, " != ", num_cols));
+    const TensorShape& perm_shape = permutation_indices.shape();
+    OP_REQUIRES(
+        ctx, perm_shape.dims() + 1 == rank,
+        errors::InvalidArgument(
+            "sparse matrix must have the same rank as permutation; got: ", rank,
+            " != ", perm_shape.dims(), " + 1."));
+    OP_REQUIRES(
+        ctx, perm_shape.dim_size(rank - 2) == *num_rows,
+        errors::InvalidArgument(
+            "permutation must have the same number of elements in each batch "
+            "as the number of rows in sparse matrix; got: ",
+            perm_shape.dim_size(rank - 2), " != ", *num_rows));
+
+    *batch_size = sparse_matrix.batch_size();
+    if (*batch_size > 1) {
+      OP_REQUIRES(
+          ctx, perm_shape.dim_size(0) == *batch_size,
+          errors::InvalidArgument("permutation must have the same batch size "
+                                  "as sparse matrix; got: ",
+                                  perm_shape.dim_size(0), " != ", *batch_size));
+    }
+  }
+};
+
+#define REGISTER_CPU(T)                                      \
+  REGISTER_KERNEL_BUILDER(Name("SparseMatrixSparseCholesky") \
+                              .Device(DEVICE_CPU)            \
+                              .TypeConstraint<T>("type"),    \
+                          CSRSparseCholeskyCPUOp<T>);
+REGISTER_CPU(float);
+REGISTER_CPU(double);
+REGISTER_CPU(complex64);
+REGISTER_CPU(complex128);
+
+#undef REGISTER_CPU
+
+}  // namespace tensorflow
diff --git a/tensorflow/core/kernels/sparse/sparse_mat_mul_op.cc b/tensorflow/core/kernels/sparse/sparse_mat_mul_op.cc
new file mode 100644
index 00000000000..53f9fbff377
--- /dev/null
+++ b/tensorflow/core/kernels/sparse/sparse_mat_mul_op.cc
@@ -0,0 +1,651 @@
+/* Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+#define EIGEN_USE_THREADS
+
+#if GOOGLE_CUDA
+#define EIGEN_USE_GPU
+#endif
+
+#include <memory>
+#include <numeric>
+
+#include "third_party/eigen3/Eigen/SparseCore"
+#include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
+#include "tensorflow/core/framework/op.h"
+#include "tensorflow/core/framework/op_kernel.h"
+#include "tensorflow/core/framework/tensor_shape.h"
+#include "tensorflow/core/framework/tensor_types.h"
+#include "tensorflow/core/framework/types.h"
+#include "tensorflow/core/framework/variant_op_registry.h"
+#include "tensorflow/core/kernels/dense_update_functor.h"
+#include "tensorflow/core/kernels/sparse/kernels.h"
+#include "tensorflow/core/kernels/sparse/sparse_matrix.h"
+#include "tensorflow/core/util/work_sharder.h"
+
+#if GOOGLE_CUDA
+#include "tensorflow/core/kernels/cuda_solvers.h"
+#include "tensorflow/core/kernels/cuda_sparse.h"
+#endif
+
+namespace tensorflow {
+
+typedef Eigen::ThreadPoolDevice CPUDevice;
+typedef Eigen::GpuDevice GPUDevice;
+
+namespace {
+
+// Swaps the dim sizes at two given dimensions of a TensorShape.
+// Callers are responsible for making sure the given dimensions are within the
+// valid dimension range of the TensorShape.
+void SwapDimSizes(const int dim_a, const int dim_b, TensorShape* shape) {
+  const int64 size_a = shape->dim_size(dim_a);
+  const int64 size_b = shape->dim_size(dim_b);
+  shape->set_dim(dim_a, size_b);
+  shape->set_dim(dim_b, size_a);
+}
+
+}  // namespace
+
+// Op to compute the matrix multiplication of two CSR Sparse Matrices.
+//
+// Implements a CPU kernel to perform matrix multiplication using Eigen
+// SparseMatrix and its Sparse-Sparse matmul. Supports transposing and
+// adjointing on the fly for both the inputs without actually constructing the
+// transpose or adjoint.
+//
+// This implementation does not support broadcasting. Hence both the input
+// CSRSparseMatrices must have the same rank. (Either rank 2 or rank 3).
+//
+// The output sparse have numeric (non-structural) zeros.
+// TODO(anudhyan): Consider exposing whether to prune zeros as an attribute in
+// the op's interface.
+//
+// If multiple threads are available, we parallelize across multiple batches
+// using Eigen ThreadPool. Within a single batch, we run in single threaded mode
+// because Eigen's Sparse-Sparse matmul doesn't support multithreading.
+//
+// TODO(b/126472741): Due to the multiple batches of a 3D CSRSparseMatrix being
+// laid out in contiguous memory, this implementation allocates memory to store
+// a temporary copy of the matrix product. Consequently, it uses roughly twice
+// the amount of memory that it needs to. This may cause a memory blowup for
+// sparse matrices with a high number of non-zero elements.
+template <typename T>
+class CSRSparseMatMulCPUOp : public OpKernel {
+  using SparseMatrix = Eigen::SparseMatrix<T, Eigen::RowMajor>;
+
+ public:
+  explicit CSRSparseMatMulCPUOp(OpKernelConstruction* c) : OpKernel(c) {
+    OP_REQUIRES_OK(c, c->GetAttr("transpose_a", &transpose_a_));
+    OP_REQUIRES_OK(c, c->GetAttr("transpose_b", &transpose_b_));
+    OP_REQUIRES_OK(c, c->GetAttr("adjoint_a", &adjoint_a_));
+    OP_REQUIRES(c, !(adjoint_a_ && transpose_a_),
+                errors::InvalidArgument(
+                    "Only one of adjoint_a and transpose_a may be true."));
+    OP_REQUIRES_OK(c, c->GetAttr("adjoint_b", &adjoint_b_));
+    OP_REQUIRES(c, !(adjoint_b_ && transpose_b_),
+                errors::InvalidArgument(
+                    "Only one of adjoint_b and transpose_b may be true."));
+  }
+
+  void Compute(OpKernelContext* ctx) final {
+    const CSRSparseMatrix* input_matrix_a;
+    const CSRSparseMatrix* input_matrix_b;
+    // TODO(anudhyan): Factor out common validation logic in CPU and GPU Ops
+    // into a common base class.
+    OP_REQUIRES_OK(ctx, ExtractVariantFromInput(ctx, 0, &input_matrix_a));
+    OP_REQUIRES_OK(ctx, ExtractVariantFromInput(ctx, 1, &input_matrix_b));
+    OP_REQUIRES(ctx, input_matrix_a->dtype() == DataTypeToEnum<T>::value,
+                errors::InvalidArgument(
+                    "dtype of a is not equal to 'type': ",
+                    DataTypeString(input_matrix_a->dtype()), " vs. ",
+                    DataTypeString(DataTypeToEnum<T>::value)));
+    OP_REQUIRES(ctx, input_matrix_b->dtype() == DataTypeToEnum<T>::value,
+                errors::InvalidArgument(
+                    "dtype of b is not equal to 'type': ",
+                    DataTypeString(input_matrix_b->dtype()), " vs. ",
+                    DataTypeString(DataTypeToEnum<T>::value)));
+    OP_REQUIRES(ctx,
+                input_matrix_a->batch_size() == input_matrix_b->batch_size(),
+                errors::InvalidArgument(
+                    "Batch sizes of A and B do not agree.  Batch sizes are: ",
+                    input_matrix_a->batch_size(), " vs. ",
+                    input_matrix_b->batch_size()));
+
+    // Validate input_matrix_a's and input_matrix_b's shapes
+    TensorShape a_shape;
+    TensorShape b_shape;
+    OP_REQUIRES_OK(ctx,
+                   TensorShapeUtils::MakeShape(
+                       input_matrix_a->dense_shape().vec<int64>(), &a_shape));
+    OP_REQUIRES_OK(ctx,
+                   TensorShapeUtils::MakeShape(
+                       input_matrix_b->dense_shape().vec<int64>(), &b_shape));
+
+    const int rank = a_shape.dims();
+    const int row_dim = (rank == 2) ? 0 : 1;
+    if (transpose_a_ || adjoint_a_)
+      SwapDimSizes(row_dim, row_dim + 1, &a_shape);
+    if (transpose_b_ || adjoint_b_)
+      SwapDimSizes(row_dim, row_dim + 1, &b_shape);
+
+    OP_REQUIRES(
+        ctx, a_shape.dim_size(row_dim + 1) == b_shape.dim_size(row_dim),
+        errors::InvalidArgument(
+            "Inner product dimensions of A and B do not agree.  Shapes are: ",
+            a_shape.DebugString(), " vs. ", b_shape.DebugString()));
+
+    // Infer the output shape of the matrix product.
+    // TODO(ebrevdo): MatMul support for broadcasting at least in the
+    // batch dimension.
+    const int batch_size = input_matrix_a->batch_size();
+    Tensor output_shape(cpu_allocator(), DT_INT64, TensorShape({rank}));
+    auto output_shape_vec = output_shape.vec<int64>();
+    if (rank == 3) output_shape_vec(0) = batch_size;
+    output_shape_vec(row_dim) = a_shape.dim_size(row_dim);
+    output_shape_vec(row_dim + 1) = b_shape.dim_size(row_dim + 1);
+
+    // Set batch pointers.
+    Tensor batch_ptr(cpu_allocator(), DT_INT32, TensorShape({batch_size + 1}));
+    auto batch_ptr_vec = batch_ptr.vec<int32>();
+    batch_ptr_vec(0) = 0;
+
+    // Store intermediate matrix products for each batch.
+    // TODO(b/126472741): For a single batch, consider reusing the
+    // SparseMatrices' buffers to construct the CSRSparseMatrix to prevent 2x
+    // memory usage.
+    std::vector<SparseMatrix> output_matrices(batch_size);
+
+    auto worker_threads = *(ctx->device()->tensorflow_cpu_worker_threads());
+    // Estimate the cost per batch per as num_output_rows times the product of
+    // average number of nonzeros per row.
+    const int64 num_output_rows = output_shape_vec(row_dim);
+    const double avg_nnz_per_row_a =
+        input_matrix_a->total_nnz() /
+        static_cast<double>(a_shape.dim_size(row_dim) * batch_size);
+    const double avg_nnz_per_row_b =
+        input_matrix_b->total_nnz() /
+        static_cast<double>(b_shape.dim_size(row_dim) * batch_size);
+    const int64 matmul_cost_per_batch =
+        num_output_rows * (avg_nnz_per_row_a * avg_nnz_per_row_b);
+
+    // Parallelize matrix multiplication across batches.
+    Shard(worker_threads.num_threads, worker_threads.workers, batch_size,
+          matmul_cost_per_batch, [&](int64 batch_begin, int64 batch_end) {
+            for (int64 batch_idx = batch_begin; batch_idx < batch_end;
+                 ++batch_idx) {
+              // For each batch, map the CSRSparseMatrix as Eigen SparseMatrix
+              // without copying the underlying data.
+              auto a_ref = GetSparseMatrixRef(*input_matrix_a, rank, batch_idx,
+                                              transpose_a_, adjoint_a_);
+              auto b_ref = GetSparseMatrixRef(*input_matrix_b, rank, batch_idx,
+                                              transpose_b_, adjoint_b_);
+
+              // Matrix multiply while *not* pruning numerical zeros on the fly.
+              // Allocates output SparseMatrix and moves it to our list of
+              // output_matrices.
+              output_matrices[batch_idx] = a_ref * b_ref;
+
+              // For now, batch_ptr contains the number of nonzeros in each
+              // batch.
+              batch_ptr_vec(batch_idx + 1) =
+                  output_matrices[batch_idx].nonZeros();
+            }
+          });
+
+    // Compute the cumulative sum to obtain the batch pointers.
+    std::partial_sum(batch_ptr_vec.data(),
+                     batch_ptr_vec.data() + batch_size + 1,
+                     batch_ptr_vec.data());
+    const int64 total_nnz = batch_ptr_vec(batch_size);
+
+    // Allocate output tensors.
+    Tensor output_row_ptr(cpu_allocator(), DT_INT32,
+                          TensorShape({(num_output_rows + 1) * batch_size}));
+    Tensor output_col_ind(cpu_allocator(), DT_INT32, TensorShape({total_nnz}));
+    Tensor output_values(cpu_allocator(), DataTypeToEnum<T>::value,
+                         TensorShape({total_nnz}));
+    auto output_row_ptr_ptr = output_row_ptr.flat<int32>().data();
+    auto output_col_ind_ptr = output_col_ind.flat<int32>().data();
+    auto output_values_ptr = output_values.flat<T>().data();
+
+    // Copy the output matrices from each batch into the CSRSparseMatrix
+    // tensors.
+    Shard(worker_threads.num_threads, worker_threads.workers, batch_size,
+          (3 * total_nnz) / batch_size /* cost per unit */,
+          [&](int64 batch_begin, int64 batch_end) {
+            for (int64 batch_idx = batch_begin; batch_idx < batch_end;
+                 ++batch_idx) {
+              const SparseMatrix& output_matrix = output_matrices[batch_idx];
+              const int64 nnz = output_matrix.nonZeros();
+              std::copy(output_matrix.outerIndexPtr(),
+                        output_matrix.outerIndexPtr() + num_output_rows + 1,
+                        output_row_ptr_ptr + batch_idx * (num_output_rows + 1));
+              std::copy(output_matrix.innerIndexPtr(),
+                        output_matrix.innerIndexPtr() + nnz,
+                        output_col_ind_ptr + batch_ptr_vec(batch_idx));
+              std::copy(output_matrix.valuePtr(),
+                        output_matrix.valuePtr() + nnz,
+                        output_values_ptr + batch_ptr_vec(batch_idx));
+            }
+          });
+
+    // Create the CSRSparseMatrix object from its component Tensors and prepare
+    // the Variant output Tensor.
+    CSRSparseMatrix output_csr_matrix;
+    OP_REQUIRES_OK(ctx, CSRSparseMatrix::CreateCSRSparseMatrix(
+                            DataTypeToEnum<T>::value, output_shape, batch_ptr,
+                            output_row_ptr, output_col_ind, output_values,
+                            &output_csr_matrix));
+    Tensor* output_csr_matrix_tensor;
+    AllocatorAttributes cpu_alloc;
+    cpu_alloc.set_on_host(true);
+    OP_REQUIRES_OK(
+        ctx, ctx->allocate_output(0, TensorShape({}), &output_csr_matrix_tensor,
+                                  cpu_alloc));
+    output_csr_matrix_tensor->scalar<Variant>()() =
+        std::move(output_csr_matrix);
+  }
+
+ private:
+  // Returns an Eigen::Ref expression of a SparseMatrix; which points to the
+  // underlying memory of the given CSRSparseMatrix.
+  Eigen::Ref<const SparseMatrix> GetSparseMatrixRef(
+      const CSRSparseMatrix& csr_matrix, const int rank, const int batch_index,
+      const bool transpose, const bool adjoint) {
+    const auto dense_shape = csr_matrix.dense_shape().vec<int64>();
+    const int64 num_rows = dense_shape(rank == 2 ? 0 : 1);
+    const int64 num_cols = dense_shape(rank == 2 ? 1 : 2);
+
+    Eigen::Map<const SparseMatrix> sparse_matrix(
+        num_rows, num_cols, csr_matrix.nnz(batch_index),
+        csr_matrix.row_pointers_vec(batch_index).data(),
+        csr_matrix.col_indices_vec(batch_index).data(),
+        csr_matrix.values_vec<T>(batch_index).data());
+
+    // The transpose/adjoint expressions are not actually evaluated until
+    // necessary. Hence we don't create copies or modify the input matrix
+    // inplace.
+    if (transpose) return sparse_matrix.transpose();
+    if (adjoint) return sparse_matrix.adjoint();
+    return sparse_matrix;
+  }
+
+  bool transpose_a_;
+  bool transpose_b_;
+  bool adjoint_a_;
+  bool adjoint_b_;
+};
+
+template <typename Device, typename T>
+class CSRSparseMatMulGPUOp : public OpKernel {
+ public:
+  explicit CSRSparseMatMulGPUOp(OpKernelConstruction* c) : OpKernel(c) {
+    OP_REQUIRES_OK(c, c->GetAttr("transpose_a", &transpose_a_));
+    OP_REQUIRES_OK(c, c->GetAttr("transpose_b", &transpose_b_));
+    bool adjoint_a;
+    OP_REQUIRES_OK(c, c->GetAttr("adjoint_a", &adjoint_a));
+    OP_REQUIRES(c, !(adjoint_a && transpose_a_),
+                errors::InvalidArgument(
+                    "Only one of adjoint_a and transpose_a may be true."));
+    bool adjoint_b;
+    OP_REQUIRES_OK(c, c->GetAttr("adjoint_b", &adjoint_b));
+    OP_REQUIRES(c, !(adjoint_b && transpose_b_),
+                errors::InvalidArgument(
+                    "Only one of adjoint_b and transpose_b may be true."));
+    conjugate_a_ = adjoint_a;
+    conjugate_b_ = adjoint_b;
+    transpose_a_ = transpose_a_ || adjoint_a;
+    transpose_b_ = transpose_b_ || adjoint_b;
+  }
+
+  void Compute(OpKernelContext* ctx) final {
+    const CSRSparseMatrix* a_matrix;
+    const CSRSparseMatrix* b_matrix;
+    OP_REQUIRES_OK(ctx, ExtractVariantFromInput(ctx, 0, &a_matrix));
+    OP_REQUIRES_OK(ctx, ExtractVariantFromInput(ctx, 1, &b_matrix));
+    OP_REQUIRES(
+        ctx, a_matrix->dtype() == DataTypeToEnum<T>::value,
+        errors::InvalidArgument("dtype of a is not equal to 'type': ",
+                                DataTypeString(a_matrix->dtype()), " vs. ",
+                                DataTypeString(DataTypeToEnum<T>::value)));
+    OP_REQUIRES(
+        ctx, b_matrix->dtype() == DataTypeToEnum<T>::value,
+        errors::InvalidArgument("dtype of b is not equal to 'type': ",
+                                DataTypeString(b_matrix->dtype()), " vs. ",
+                                DataTypeString(DataTypeToEnum<T>::value)));
+
+    // TODO(ebrevdo): MatMul support for broadcasting at least in the
+    // batch dimension.
+    auto a_dense_shape = a_matrix->dense_shape().vec<int64>();
+    auto b_dense_shape = b_matrix->dense_shape().vec<int64>();
+
+    TensorShape a_tensor_shape;
+    TensorShape b_tensor_shape;
+    OP_REQUIRES_OK(ctx,
+                   TensorShapeUtils::MakeShape(a_dense_shape, &a_tensor_shape));
+    OP_REQUIRES_OK(ctx,
+                   TensorShapeUtils::MakeShape(b_dense_shape, &b_tensor_shape));
+
+    const int rank = a_tensor_shape.dims();
+    const int row_dim = (rank == 2) ? 0 : 1;
+
+    const int64 a_inner_dim =
+        a_tensor_shape.dim_size(transpose_a_ ? row_dim : row_dim + 1);
+    const int64 b_inner_dim =
+        b_tensor_shape.dim_size(transpose_b_ ? row_dim + 1 : row_dim);
+
+    const int batch_size = a_matrix->batch_size();
+
+    OP_REQUIRES(
+        ctx, a_inner_dim == b_inner_dim,
+        errors::InvalidArgument(
+            "Inner product dimensions of A and B do not agree.  Shapes are: ",
+            a_tensor_shape.DebugString(), " vs. ",
+            b_tensor_shape.DebugString()));
+
+    Tensor c_dense_shape_t(cpu_allocator(), DT_INT64, TensorShape({rank}));
+    auto c_dense_shape = c_dense_shape_t.vec<int64>();
+
+    if (rank == 3) c_dense_shape(0) = batch_size;
+    c_dense_shape(row_dim) =
+        a_tensor_shape.dim_size(transpose_a_ ? row_dim + 1 : row_dim);
+    c_dense_shape(row_dim + 1) =
+        b_tensor_shape.dim_size(transpose_b_ ? row_dim : row_dim + 1);
+
+    const int64 rows = c_dense_shape((rank == 2) ? 0 : 1);
+
+    CSRSparseMatrix c;
+    Tensor c_row_ptrs;
+    Tensor c_col_inds;
+    Tensor c_values;
+
+    // TODO(ebrevdo): Re-enable transposing within the GEMM kernel when cuSparse
+    // stops spitting out CUSPARSE_STATUS_INTERNAL_ERROR values for transposes.
+    functor::CSRSparseSparseMatrixMatMul<Device, T> csr_gemm(
+        ctx, /*transpose_a=*/false, /*adjoint_a=*/false, /*transpose_b=*/false);
+    OP_REQUIRES_OK(ctx, csr_gemm.Initialize());
+
+    Tensor c_batch_ptr_t(cpu_allocator(), DT_INT32,
+                         TensorShape({batch_size + 1}));
+    auto c_batch_ptr = c_batch_ptr_t.vec<int32>();
+    c_batch_ptr(0) = 0;
+
+    Tensor c_row_ptr_t;
+    OP_REQUIRES_OK(ctx, ctx->allocate_temp(
+                            DT_INT32, TensorShape({batch_size * (rows + 1)}),
+                            &c_row_ptr_t));
+    auto c_row_ptr = c_row_ptr_t.vec<int32>();
+
+    // Possibly transpose a.
+    const CSRSparseMatrix* a_input_matrix;
+    // If we need to transpose a, we will store the result temporarily
+    // in the object below.
+    CSRSparseMatrix a_matrix_transposed;
+    if (!transpose_a_) {
+      a_input_matrix = a_matrix;
+    } else {
+      functor::CSRSparseMatrixTranspose<Device, T> transpose;
+      OP_REQUIRES_OK(
+          ctx, transpose(ctx, conjugate_a_, *a_matrix, &a_matrix_transposed));
+      a_input_matrix = &a_matrix_transposed;
+    }
+    auto a_input_dense_shape = a_input_matrix->dense_shape().vec<int64>();
+
+    // Possibly transpose b.
+    const CSRSparseMatrix* b_input_matrix;
+    // If we need to transpose a, we will store the result temporarily
+    // in the object below.
+    CSRSparseMatrix b_matrix_transposed;
+    if (!transpose_b_) {
+      b_input_matrix = b_matrix;
+    } else {
+      functor::CSRSparseMatrixTranspose<Device, T> transpose;
+      OP_REQUIRES_OK(
+          ctx, transpose(ctx, conjugate_b_, *b_matrix, &b_matrix_transposed));
+      b_input_matrix = &b_matrix_transposed;
+    }
+    auto b_input_dense_shape = b_input_matrix->dense_shape().vec<int64>();
+
+    for (int i = 0; i < batch_size; ++i) {
+      // Calculate output sizes for all minibatch entries.
+      // Store in c_batch_ptr and update c_row_ptrs.
+      ConstCSRComponent<T> a_comp{a_input_matrix->row_pointers_vec(i),
+                                  a_input_matrix->col_indices_vec(i),
+                                  a_input_matrix->values_vec<T>(i),
+                                  a_input_dense_shape};
+      ConstCSRComponent<T> b_comp{b_input_matrix->row_pointers_vec(i),
+                                  b_input_matrix->col_indices_vec(i),
+                                  b_input_matrix->values_vec<T>(i),
+                                  b_input_dense_shape};
+
+      TTypes<int32>::UnalignedVec c_row_ptr_i(&c_row_ptr(i * (rows + 1)),
+                                              rows + 1);
+
+      int c_nnz_i;
+      OP_REQUIRES_OK(ctx, csr_gemm.GetOutputStructure(a_comp, b_comp,
+                                                      c_row_ptr_i, &c_nnz_i));
+      c_batch_ptr(i + 1) = c_batch_ptr(i) + c_nnz_i;
+    }
+
+    Tensor c_col_ind_t;
+    Tensor c_values_t;
+
+    const int total_nnz = c_batch_ptr(batch_size);
+
+    OP_REQUIRES_OK(ctx, ctx->allocate_temp(DT_INT32, TensorShape({total_nnz}),
+                                           &c_col_ind_t));
+    OP_REQUIRES_OK(ctx,
+                   ctx->allocate_temp(DataTypeToEnum<T>::value,
+                                      TensorShape({total_nnz}), &c_values_t));
+    OP_REQUIRES_OK(ctx,
+                   CSRSparseMatrix::CreateCSRSparseMatrix(
+                       DataTypeToEnum<T>::value, c_dense_shape_t, c_batch_ptr_t,
+                       c_row_ptr_t, c_col_ind_t, c_values_t, &c));
+
+    for (int i = 0; i < batch_size; ++i) {
+      ConstCSRComponent<T> a_comp{a_input_matrix->row_pointers_vec(i),
+                                  a_input_matrix->col_indices_vec(i),
+                                  a_input_matrix->values_vec<T>(i),
+                                  a_input_dense_shape};
+      ConstCSRComponent<T> b_comp{b_input_matrix->row_pointers_vec(i),
+                                  b_input_matrix->col_indices_vec(i),
+                                  b_input_matrix->values_vec<T>(i),
+                                  b_input_dense_shape};
+      CSRComponent<T> c_comp{c.row_pointers_vec(i), c.col_indices_vec(i),
+                             c.values_vec<T>(i), c_dense_shape};
+      OP_REQUIRES_OK(ctx, csr_gemm.Compute(a_comp, b_comp, &c_comp));
+    }
+
+    Tensor c_t(cpu_allocator(), DT_VARIANT, TensorShape({}));
+    c_t.scalar<Variant>()() = std::move(c);
+    ctx->set_output(0, c_t);
+  }
+
+ private:
+  bool transpose_a_;
+  bool transpose_b_;
+  bool conjugate_a_;
+  bool conjugate_b_;
+};
+
+#define REGISTER_CPU(T)                                    \
+  REGISTER_KERNEL_BUILDER(Name("SparseMatrixSparseMatMul") \
+                              .Device(DEVICE_CPU)          \
+                              .TypeConstraint<T>("type"),  \
+                          CSRSparseMatMulCPUOp<T>);
+
+REGISTER_CPU(float)
+REGISTER_CPU(double)
+REGISTER_CPU(complex64)
+REGISTER_CPU(complex128)
+
+#undef REGISTER_CPU
+
+#define REGISTER(DEV, T)                                   \
+  REGISTER_KERNEL_BUILDER(Name("SparseMatrixSparseMatMul") \
+                              .Device(DEVICE_##DEV)        \
+                              .TypeConstraint<T>("type"),  \
+                          CSRSparseMatMulGPUOp<DEV##Device, T>);
+
+#if GOOGLE_CUDA
+
+#define REGISTER_GPU(T) REGISTER(GPU, T)
+
+REGISTER_GPU(float)
+REGISTER_GPU(double)
+REGISTER_GPU(complex64)
+REGISTER_GPU(complex128)
+
+#undef REGISTER_GPU
+
+#endif  // GOOGLE_CUDA
+
+#undef REGISTER
+
+#if GOOGLE_CUDA
+namespace functor {
+template <typename T>
+struct CSRSparseSparseMatrixMatMul<GPUDevice, T>
+    : public CSRStructureModifyingFunctor<GPUDevice, T> {
+  explicit CSRSparseSparseMatrixMatMul(OpKernelContext* ctx, bool transpose_a,
+                                       bool adjoint_a, bool transpose_b)
+      : ctx_(ctx),
+        cuda_sparse_(ctx),
+        initialized_(false),
+        transpose_a_(transpose_a),
+        adjoint_a_(adjoint_a),
+        transpose_b_(transpose_b) {
+    // TODO(ebrevdo): Figure out why transposed implementations crash cuSparse.
+    transA_ = transpose_a ? (adjoint_a ? CUSPARSE_OPERATION_TRANSPOSE
+                                       : CUSPARSE_OPERATION_CONJUGATE_TRANSPOSE)
+                          : CUSPARSE_OPERATION_NON_TRANSPOSE;
+    transB_ = transpose_b ? CUSPARSE_OPERATION_TRANSPOSE
+                          : CUSPARSE_OPERATION_NON_TRANSPOSE;
+  }
+
+  Status Initialize() {
+    if (adjoint_a_ && transpose_a_) {
+      return errors::InvalidArgument(
+          "Only one of adjoint_a and transpose_a may be true.");
+    }
+
+    TF_RETURN_IF_ERROR(cuda_sparse_.Initialize());
+    TF_RETURN_IF_ERROR(descrA_.Initialize());
+    TF_RETURN_IF_ERROR(descrB_.Initialize());
+    TF_RETURN_IF_ERROR(descrC_.Initialize());
+    initialized_ = true;
+    return Status::OK();
+  }
+
+  Status GetOutputStructure(const ConstCSRComponent<T>& a,
+                            const ConstCSRComponent<T>& b,
+                            TTypes<int32>::UnalignedVec c_row_ptr,
+                            int* output_nnz) {
+    DCHECK(initialized_);
+
+    const int m =
+        a.dense_shape_host(a.dense_shape_host.size() - (transpose_a_ ? 1 : 2));
+    if (!transpose_a_) {
+      DCHECK_EQ(m, a.row_ptr.size() - 1);
+    }
+    DCHECK_EQ(m, c_row_ptr.size() - 1);
+    const int k =
+        a.dense_shape_host(a.dense_shape_host.size() - (transpose_a_ ? 2 : 1));
+    if (!transpose_b_) {
+      DCHECK_EQ(k, b.row_ptr.size() - 1);
+    }
+    const int nnzA = a.col_ind.size();
+    const int nnzB = b.col_ind.size();
+
+    const int n =
+        b.dense_shape_host(b.dense_shape_host.size() - (transpose_b_ ? 2 : 1));
+
+    *output_nnz = -1;
+
+    TF_RETURN_IF_ERROR(cuda_sparse_.CsrgemmNnz(
+        transA_, transB_, m, n, k, descrA_.descr(), nnzA, a.row_ptr.data(),
+        a.col_ind.data(), descrB_.descr(), nnzB, b.row_ptr.data(),
+        b.col_ind.data(), descrC_.descr(), c_row_ptr.data(), output_nnz));
+
+    if (*output_nnz < 0) {
+      return errors::Internal(
+          "CSRMatMul: CsrgemmNnz returned nnzTotalDevHostPtr < 0: ",
+          *output_nnz);
+    }
+    return Status::OK();
+  }
+
+  Status Compute(const ConstCSRComponent<T>& a, const ConstCSRComponent<T>& b,
+                 CSRComponent<T>* c) {
+    DCHECK(initialized_);
+
+    const int m =
+        a.dense_shape_host(a.dense_shape_host.size() - (transpose_a_ ? 1 : 2));
+    if (!transpose_a_) {
+      DCHECK_EQ(m, a.row_ptr.size() - 1);
+    }
+    DCHECK_EQ(m, c->dense_shape_host(c->dense_shape_host.size() - 2));
+    DCHECK_EQ(m, c->row_ptr.size() - 1);
+    const int k =
+        a.dense_shape_host(a.dense_shape_host.size() - (transpose_a_ ? 2 : 1));
+    if (!transpose_b_) {
+      DCHECK_EQ(k, b.row_ptr.size() - 1);
+    }
+    const int nnzA = a.col_ind.size();
+    const int nnzB = b.col_ind.size();
+
+    const int n =
+        b.dense_shape_host(b.dense_shape_host.size() - (transpose_b_ ? 2 : 1));
+    DCHECK_EQ(n, c->dense_shape_host(c->dense_shape_host.size() - 1));
+
+    TF_RETURN_IF_ERROR(cuda_sparse_.Csrgemm(
+        transA_, transB_, m, k, n, descrA_.descr(), nnzA, a.values.data(),
+        a.row_ptr.data(), a.col_ind.data(), descrB_.descr(), nnzB,
+        b.values.data(), b.row_ptr.data(), b.col_ind.data(), descrC_.descr(),
+        c->values.data(), c->row_ptr.data(), c->col_ind.data()));
+
+    // TODO(ebrevdo): Add a flag to CSRSparseMatrix whether matrix
+    // columns are sorted?  Above operation leads to unsorted columns.
+    // For now, here is an example of how to ensure the output columns
+    // are sorted.  Leaving here in case we realize we need to ensure
+    // sorted columns in the future.
+    //
+    // TF_RETURN_IF_ERROR(cuda_sparse.Csru2csr(
+    //     m, n, nnzTotalDevHostPtr, descrA_.descr(), c->values.data(),
+    //     c->row_ptr.data(), c->col_ind.data()));
+
+    return Status::OK();
+  }
+
+ private:
+  OpKernelContext* ctx_;
+  CudaSparse cuda_sparse_;
+  bool initialized_;
+  bool transpose_a_;
+  bool adjoint_a_;
+  bool transpose_b_;
+  CudaSparseMatrixDescriptor descrA_;
+  CudaSparseMatrixDescriptor descrB_;
+  CudaSparseMatrixDescriptor descrC_;
+  cusparseOperation_t transA_;
+  cusparseOperation_t transB_;
+};
+
+}  // namespace functor
+
+#endif  // GOOGLE_CUDA
+
+}  // namespace tensorflow
diff --git a/tensorflow/core/kernels/sparse/sparse_matrix.cc b/tensorflow/core/kernels/sparse/sparse_matrix.cc
new file mode 100644
index 00000000000..0871ba2b121
--- /dev/null
+++ b/tensorflow/core/kernels/sparse/sparse_matrix.cc
@@ -0,0 +1,43 @@
+/* Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+#define EIGEN_USE_THREADS
+
+#if GOOGLE_CUDA
+#define EIGEN_USE_GPU
+#endif
+
+#include "tensorflow/core/framework/variant_op_registry.h"
+#include "tensorflow/core/kernels/sparse/sparse_matrix.h"
+
+namespace tensorflow {
+
+constexpr const char CSRSparseMatrix::kTypeName[];
+
+// Register variant decoding function for TF's RPC.
+REGISTER_UNARY_VARIANT_DECODE_FUNCTION(CSRSparseMatrix,
+                                       CSRSparseMatrix::kTypeName);
+
+#define REGISTER_CSR_COPY(DIRECTION)                    \
+  INTERNAL_REGISTER_UNARY_VARIANT_DEVICE_COPY_FUNCTION( \
+      CSRSparseMatrix, DIRECTION, CSRSparseMatrix::DeviceCopy)
+
+REGISTER_CSR_COPY(VariantDeviceCopyDirection::HOST_TO_DEVICE);
+REGISTER_CSR_COPY(VariantDeviceCopyDirection::DEVICE_TO_HOST);
+REGISTER_CSR_COPY(VariantDeviceCopyDirection::DEVICE_TO_DEVICE);
+
+#undef REGISTER_CSR_COPY
+
+}  // namespace tensorflow
diff --git a/tensorflow/core/kernels/sparse/sparse_matrix.h b/tensorflow/core/kernels/sparse/sparse_matrix.h
new file mode 100644
index 00000000000..1cf1da8da06
--- /dev/null
+++ b/tensorflow/core/kernels/sparse/sparse_matrix.h
@@ -0,0 +1,640 @@
+/* Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+#ifndef TENSORFLOW_CORE_KERNELS_SPARSE_SPARSE_MATRIX_H_
+#define TENSORFLOW_CORE_KERNELS_SPARSE_SPARSE_MATRIX_H_
+
+#define EIGEN_USE_THREADS
+
+#if GOOGLE_CUDA
+#define EIGEN_USE_GPU
+#endif
+
+#include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
+#include "tensorflow/core/framework/op_kernel.h"
+#include "tensorflow/core/framework/tensor.h"
+#include "tensorflow/core/framework/tensor_types.h"
+#include "tensorflow/core/framework/variant.h"
+#include "tensorflow/core/framework/variant_encode_decode.h"
+#include "tensorflow/core/framework/variant_op_registry.h"
+
+namespace tensorflow {
+
+class CSRSparseMatrix {
+  // CreateCSRSparseMatrix is the main method used to construct a
+  // CSRSparseMatrix.  The representations for both 2D and 3D
+  // (batched) CSR Sparse Matrices are the same:
+  //
+  // dtype: The datatype of the values.
+  // dense_shape: The dense shape of the matrix.
+  //   * Host int64 vector, size 2 or 3.
+  //   * Takes on values: (rows, cols) or (batch_size, rows, cols).
+  // batch_pointers: Batch offset pointers into col_indices and values.
+  //   * Host int32 vector, size (batch_size + 1).
+  //   * Takes on values: (0, nnz[0], nnz[0] + nnz[1], ..., total_nnz).
+  // row_pointers: Row offset pointers into col_indices and values.
+  //   * Device int32 vector, size ((rows + 1) * batch_size).
+  //   * Each block of size (rows + 1) takes on values:
+  //     (0, num_rows{b}[0], num_rows{b}[0] + num_rows{b}[1], ..., nnz[b]).
+  //     for b = 0 .. batch_size - 1.
+  // col_indices: Column values for the given row and column index.
+  //   * Device int32 vector, size total_nnz.
+  // values: Actual values for the given row and column index.
+  //   * Device dtype vector, size total_nnz.
+  //
+  // The storage agreement is such that for a given (batch, row, ix):
+  //   offset = batch_pointers(batch) + row_pointers(batch * (rows + 1) + row)
+  //   col = col_indices(offset + ix)
+  //   val = values(offset + ix)
+  // where ix < #nnz columns in (batch, row).
+  // Then:
+  //   matrix(batch, row, col) = val.
+  //
+  // All other elements in the dense representation are treated as 0 / empty.
+  //
+  // For example, for a 2D sparse matrix m shaped (3, 4) such that:
+  //
+  //   m[0, 0] = 1.0
+  //   m[0, 1] = 2.0
+  //   m[0, 2] = 3.0
+  //   m[2, 2] = 4.0
+  //   m[2, 3] = 5.0
+  //
+  // The corresponding representation is:
+  //
+  //   dtype: DT_FLOAT
+  //   dense_shape: (3, 4)
+  //   batch_pointers: (0, 5)
+  //   row_pointers: (0, 3, 3, 5)
+  //   col_indices: concat((0, 1, 2), (), (2, 3))
+  //   values: concat((1.0, 2.0, 3.0), (), (4.0, 5.0))
+  //
+  // For a 3D sparse matrix m shaped (2, 3, 4) such that:
+  //
+  //   m[0, 0, 0] = 1.0
+  //   m[0, 0, 2] = 2.0
+  //   m[0, 2, 3] = 3.0
+  //   m[1, 0, 3] = 4.0
+  //   m[1, 1, 0] = 5.0
+  //
+  // The corresponding representation is:
+  //   dtype: DT_FLOAT
+  //   dense_shape: (2, 3, 4)
+  //   batch_pointers: (0, 3, 5)
+  //   row_pointers: concat((0, 2, 2, 3), (0, 1, 2, 2))
+  //   col_indices: concat(concat((0, 2), (), (3,)),
+  //                       concat((3,),   (), (0,)))
+  //   values: concat(concat((1.0, 2.0), (3.0,), ()),
+  ///                 concat((4.0,),     (5.0,), ()))
+  //
+ public:
+  static constexpr const char kTypeName[] = "tensorflow::CSRSparseMatrix";
+
+  CSRSparseMatrix() : metadata_{false, DT_INVALID} {}
+
+  CSRSparseMatrix(const CSRSparseMatrix& rhs)
+      : metadata_(rhs.metadata_),
+        dense_shape_(rhs.dense_shape_),
+        batch_pointers_(rhs.batch_pointers_),
+        row_pointers_(rhs.row_pointers_),
+        col_indices_(rhs.col_indices_),
+        values_(rhs.values_) {
+    SetupVecs();
+  }
+
+  CSRSparseMatrix(CSRSparseMatrix&& rhs)
+      : metadata_(rhs.metadata_),
+        dense_shape_(std::move(rhs.dense_shape_)),
+        batch_pointers_(std::move(rhs.batch_pointers_)),
+        row_pointers_(std::move(rhs.row_pointers_)),
+        col_indices_(std::move(rhs.col_indices_)),
+        values_(std::move(rhs.values_)) {
+    SetupVecs();
+    rhs.metadata_.validated = false;
+    rhs.metadata_.dtype = DT_INVALID;
+    rhs.ClearVecs();
+  }
+
+  CSRSparseMatrix& operator=(CSRSparseMatrix&& rhs) {
+    if (this == &rhs) return *this;
+    metadata_ = rhs.metadata_;
+    metadata_.validated = rhs.metadata_.validated;
+    dense_shape_ = std::move(rhs.dense_shape_);
+    batch_pointers_ = std::move(rhs.batch_pointers_);
+    row_pointers_ = std::move(rhs.row_pointers_);
+    col_indices_ = std::move(rhs.col_indices_);
+    values_ = std::move(rhs.values_);
+    SetupVecs();
+    rhs.metadata_ = {false, DT_INVALID};
+    rhs.ClearVecs();
+    return *this;
+  }
+
+  static Status CreateCSRSparseMatrix(DataType dtype,
+                                      const Tensor& dense_shape,     // on host
+                                      const Tensor& batch_pointers,  // on host
+                                      const Tensor& row_pointers,
+                                      const Tensor& col_indices,
+                                      const Tensor& values,
+                                      CSRSparseMatrix* matrix) {
+    *matrix = CSRSparseMatrix(dtype, dense_shape, batch_pointers, row_pointers,
+                              col_indices, values);
+    Status s = matrix->Validate();
+    matrix->metadata_.validated = s.ok();
+    matrix->SetupVecs();
+    return s;
+  }
+
+  Status Validate() const {
+    return ValidateTypesAndShapes(metadata_.dtype, dense_shape_,
+                                  batch_pointers_, row_pointers_, col_indices_,
+                                  values_);
+  }
+
+  void Clear() {
+    metadata_ = {false, DT_INVALID};
+    dense_shape_ = Tensor();
+    batch_pointers_ = Tensor();
+    row_pointers_ = Tensor();
+    col_indices_ = Tensor();
+    values_ = Tensor();
+    ClearVecs();
+  }
+
+  bool valid() const {
+    return metadata_.validated && dense_shape_.IsInitialized() &&
+           batch_pointers_.IsInitialized() && row_pointers_.IsInitialized() &&
+           col_indices_.IsInitialized() && values_.IsInitialized() &&
+           dense_shape_.NumElements() > 1 &&
+           batch_pointers_.NumElements() > 0 && row_pointers_.NumElements() > 0;
+  }
+
+  DataType dtype() const {
+    DCHECK(valid());
+    return metadata_.dtype;
+  }
+
+  inline int dims() const {
+    DCHECK(valid());
+    return dense_shape_.NumElements();
+  }
+
+  inline int nnz(int batch) const {
+    DCHECK_LT(batch, batch_size());
+    return (*batch_pointers_vec_)(batch + 1) - (*batch_pointers_vec_)(batch);
+  }
+
+  inline int batch_offset(int batch) const {
+    DCHECK_LT(batch, batch_size());
+    return (*batch_pointers_vec_)(batch);
+  }
+
+  inline int total_nnz() const {
+    DCHECK(valid());
+    return (*batch_pointers_vec_)(batch_size());
+  }
+
+  inline Tensor& dense_shape() {
+    DCHECK(valid());
+    return dense_shape_;
+  }
+
+  inline const Tensor& dense_shape() const {
+    DCHECK(valid());
+    return dense_shape_;
+  }
+
+  inline TTypes<int32>::UnalignedVec row_pointers_vec(int batch) {
+    DCHECK(valid());
+    DCHECK_LT(batch, batch_size());
+    const int64 rows = dense_shape().vec<int64>()((dims() == 2) ? 0 : 1);
+    const int offset = batch * (rows + 1);
+    return TTypes<int32>::UnalignedVec(row_pointers_vec_->data() + offset,
+                                       rows + 1);
+  }
+
+  inline TTypes<int32>::UnalignedConstVec row_pointers_vec(int batch) const {
+    DCHECK(valid());
+    DCHECK_LT(batch, batch_size());
+    const int64 rows = dense_shape().vec<int64>()((dims() == 2) ? 0 : 1);
+    const int offset = batch * (rows + 1);
+    return TTypes<int32>::UnalignedConstVec(row_pointers_vec_->data() + offset,
+                                            rows + 1);
+  }
+
+  inline TTypes<int32>::UnalignedVec col_indices_vec(int batch) {
+    DCHECK(valid());
+    DCHECK_LT(batch, batch_size());
+    const int offset = (*batch_pointers_vec_)(batch);
+    const int nnz_in_batch = nnz(batch);
+    return TTypes<int32>::UnalignedVec(col_indices_vec_->data() + offset,
+                                       nnz_in_batch);
+  }
+
+  inline TTypes<int32>::UnalignedConstVec col_indices_vec(int batch) const {
+    DCHECK(valid());
+    DCHECK_LT(batch, batch_size());
+    const int offset = (*batch_pointers_vec_)(batch);
+    const int nnz_in_batch = nnz(batch);
+    return TTypes<int32>::UnalignedConstVec(col_indices_vec_->data() + offset,
+                                            nnz_in_batch);
+  }
+
+  template <typename T>
+  inline typename TTypes<T>::UnalignedVec values_vec(int batch) {
+    DCHECK(valid());
+    DCHECK_LT(batch, batch_size());
+    const int offset = (*batch_pointers_vec_)(batch);
+    const int nnz_in_batch = nnz(batch);
+    return typename TTypes<T>::UnalignedVec(&(values().vec<T>()(offset)),
+                                            nnz_in_batch);
+  }
+
+  template <typename T>
+  inline typename TTypes<T>::UnalignedConstVec values_vec(int batch) const {
+    DCHECK(valid());
+    DCHECK_LT(batch, batch_size());
+    const int offset = (*batch_pointers_vec_)(batch);
+    const int nnz_in_batch = nnz(batch);
+    return typename TTypes<T>::UnalignedConstVec(&(values().vec<T>()(offset)),
+                                                 nnz_in_batch);
+  }
+
+  inline Tensor& row_pointers() {
+    DCHECK(valid());
+    return row_pointers_;
+  }
+
+  inline const Tensor& row_pointers() const {
+    DCHECK(valid());
+    return row_pointers_;
+  }
+
+  inline Tensor& col_indices() {
+    DCHECK(valid());
+    return col_indices_;
+  }
+
+  inline const Tensor& col_indices() const {
+    DCHECK(valid());
+    return col_indices_;
+  }
+
+  inline Tensor& values() {
+    DCHECK(valid());
+    return values_;
+  }
+
+  inline const Tensor& values() const {
+    DCHECK(valid());
+    return values_;
+  }
+
+  inline Tensor& batch_pointers() {
+    DCHECK(valid());
+    return batch_pointers_;
+  }
+
+  inline const Tensor& batch_pointers() const {
+    DCHECK(valid());
+    return batch_pointers_;
+  }
+
+  string TypeName() const { return kTypeName; }
+
+  // TODO(ebrevdo): A better debug string.
+  string DebugString() const { return dense_shape_.DebugString(); }
+
+  // Returns the number of elements.  This is equal to 1 if the
+  // CSRSparseMatrix is a singleton matrix (dense_shape is length 2).
+  int batch_size() const {
+    DCHECK(valid());
+    return batch_pointers_.NumElements() - 1;
+  }
+
+  bool Decode(const VariantTensorData& p) {
+    if (p.tensors_.empty()) return false;
+    Metadata metadata;
+    if (!p.get_metadata(&metadata)) return false;
+    const bool validated = metadata.validated;
+    const DataType dtype = metadata.dtype;
+
+    // p.tensors_ should contain tensors {dense_shape, batch_pointers,
+    // row_pointers, col_indices, values}.
+    if (p.tensors_.size() != 5) return false;
+
+    Tensor dense_shape = p.tensors_[0];
+    if (dense_shape.dtype() != DT_INT64) return false;
+    if (dense_shape.dims() != 1) return false;
+    int rank = dense_shape.dim_size(0);
+    if (rank < 2 || rank > 3) return false;
+
+    Tensor batch_pointers(p.tensors_[1]);
+    Tensor row_pointers(p.tensors_[2]);
+    Tensor col_indices(p.tensors_[3]);
+    Tensor values(p.tensors_[4]);
+
+    // Check that the validated bool is consistent with the data.
+    Status s = ValidateTypesAndShapes(dtype, dense_shape, batch_pointers,
+                                      row_pointers, col_indices, values);
+    if (s.ok() != validated) return false;
+
+    // Save to this object.
+    metadata_ = metadata;
+    dense_shape_ = std::move(dense_shape);
+    batch_pointers_ = std::move(batch_pointers);
+    row_pointers_ = std::move(row_pointers);
+    col_indices_ = std::move(col_indices);
+    values_ = std::move(values);
+    SetupVecs();
+    return true;
+  }
+
+  void Encode(VariantTensorData* p) const {
+    DCHECK(valid());
+
+    // Store metadata_ to p's metadata
+    p->set_metadata(metadata_);
+
+    // Store dense_shape, row_pointers, col_indices, and values to p->tensors_.
+    p->tensors_.reserve(5);
+    p->tensors_.push_back(dense_shape_);
+    p->tensors_.push_back(batch_pointers_);
+    p->tensors_.push_back(row_pointers_);
+    p->tensors_.push_back(col_indices_);
+    p->tensors_.push_back(values_);
+  }
+
+  // This static method copies CSRSparseMatrices in all directions:
+  //   Host->Device, Device->Host, and Device->Device.
+  static Status DeviceCopy(
+      const CSRSparseMatrix& from, CSRSparseMatrix* to,
+      const UnaryVariantOpRegistry::AsyncTensorDeviceCopyFn& copy) {
+    VLOG(2) << "DeviceCopy from type: " << DataTypeString(from.dtype())
+            << " and shape: " << from.dense_shape().DebugString();
+    Tensor to_row_ptr(DT_INT32);
+    Tensor to_col_ind(DT_INT32);
+    Tensor to_values(from.dtype());
+    TF_RETURN_IF_ERROR(copy(from.row_pointers(), &to_row_ptr));
+    TF_RETURN_IF_ERROR(copy(from.col_indices(), &to_col_ind));
+    TF_RETURN_IF_ERROR(copy(from.values(), &to_values));
+    return CreateCSRSparseMatrix(from.dtype(),
+                                 from.dense_shape(),     // Always on host.
+                                 from.batch_pointers(),  // Always on host.
+                                 to_row_ptr, to_col_ind, to_values, to);
+  }
+
+ private:
+  CSRSparseMatrix(DataType dtype, const Tensor& dense_shape,
+                  const Tensor& batch_pointers, const Tensor& row_pointers,
+                  const Tensor& col_indices, const Tensor& values)
+      : metadata_{false, dtype},
+        dense_shape_(dense_shape),
+        batch_pointers_(batch_pointers),
+        row_pointers_(row_pointers),
+        col_indices_(col_indices),
+        values_(values) {}
+
+  void SetupVecs() {
+    if (!metadata_.validated) return;
+    batch_pointers_vec_.reset(
+        new TTypes<int32>::Vec(batch_pointers_.vec<int32>()));
+    row_pointers_vec_.reset(new TTypes<int32>::Vec(row_pointers_.vec<int32>()));
+    col_indices_vec_.reset(new TTypes<int32>::Vec(col_indices_.vec<int32>()));
+  }
+
+  void ClearVecs() {
+    batch_pointers_vec_.reset();
+    row_pointers_vec_.reset();
+    col_indices_vec_.reset();
+  }
+
+  static Status ValidateTypesAndShapes(DataType dtype,
+                                       const Tensor& dense_shape,
+                                       const Tensor& batch_pointers,
+                                       const Tensor& row_pointers,
+                                       const Tensor& col_indices,
+                                       const Tensor& values) {
+    // TODO(ebrevdo): Consider adding support for other floating point types
+    // (namely, float16).
+    if (dtype != DT_FLOAT && dtype != DT_DOUBLE && dtype != DT_COMPLEX64 &&
+        dtype != DT_COMPLEX128) {
+      return errors::InvalidArgument(
+          "CSRSparseMatrix::Validate: dtype = ", DataTypeString(dtype),
+          " not in {float32, float64, complex64, complex128}");
+    }
+    // dense_shape checks
+    if (dense_shape.dtype() != DT_INT64) {
+      return errors::InvalidArgument(
+          "CSRSparseMatrix::Validate: dense_shape.dtype() = ",
+          DataTypeString(dense_shape.dtype()), " != int64");
+    }
+    if (dense_shape.dims() != 1) {
+      return errors::InvalidArgument(
+          "CSRSparseMatrix::Validate: dense_shape should be a vector, but saw "
+          "tensor: ",
+          dense_shape.DebugString());
+    }
+    int rank = dense_shape.dim_size(0);
+    if (rank < 2 || rank > 3) {
+      return errors::InvalidArgument(
+          "CSRSparseMatrix::Validate: dense_shape should be a 2- or 3- vector, "
+          "but saw: ",
+          dense_shape.SummarizeValue(5));
+    }
+    auto dense_shape_t = dense_shape.vec<int64>();
+    int batch_size = (rank == 2) ? 1 : dense_shape_t(0);
+
+    if (batch_pointers.dtype() != DT_INT32) {
+      return errors::InvalidArgument(
+          "CSRSparseMatrix::Validate: batch_pointers.dtype() = ",
+          DataTypeString(batch_pointers.dtype()), " != int32");
+    }
+    if (batch_pointers.dims() != 1) {
+      return errors::InvalidArgument(
+          "CSRSparseMatrix::Validate: batch_indices is not a vector, saw "
+          "shape: ",
+          batch_pointers.shape().DebugString());
+    }
+
+    // batch size checks
+    if (batch_size != batch_pointers.NumElements() - 1) {
+      return errors::InvalidArgument(
+          "CSRSparseMatrix::Validate: dense_shape is ",
+          dense_shape.SummarizeValue(5),
+          " but batch pointers implies batch size is ",
+          batch_pointers.NumElements() - 1);
+    }
+
+    if (row_pointers.dtype() != DT_INT32) {
+      return errors::InvalidArgument(
+          "CSRSparseMatrix::Validate: row_indices.dtype() = ",
+          DataTypeString(row_pointers.dtype()), " != int32");
+    }
+    if (row_pointers.dims() != 1) {
+      return errors::InvalidArgument(
+          "CSRSparseMatrix::Validate: row_indices is not a vector, saw shape: ",
+          row_pointers.shape().DebugString());
+    }
+    if (col_indices.dtype() != DT_INT32) {
+      return errors::InvalidArgument(
+          "CSRSparseMatrix::Validate: col_indices.dtype() = ",
+          DataTypeString(col_indices.dtype()), " != int32");
+    }
+    if (col_indices.dims() != 1) {
+      return errors::InvalidArgument(
+          "CSRSparseMatrix::Validate: col_indices is not a vector, saw shape: ",
+          col_indices.shape().DebugString());
+    }
+    if (values.dtype() != dtype) {
+      return errors::InvalidArgument(
+          "CSRSparseMatrix::Validate: values.dtype() = ",
+          DataTypeString(values.dtype()),
+          " != dtype = ", DataTypeString(dtype));
+    }
+    if (values.dims() != 1) {
+      return errors::InvalidArgument(
+          "CSRSparseMatrix::Validate: values is not a vector, saw shape: ",
+          values.shape().DebugString());
+    }
+    if (col_indices.dim_size(0) != values.dim_size(0)) {
+      return errors::InvalidArgument(
+          "CSRSparseMatrix::Validate: size(col_indices) = ",
+          col_indices.dim_size(0), " != size(values) = ", values.dim_size(0));
+    }
+    return Status::OK();
+  }
+
+  struct Metadata {
+    bool validated;
+    DataType dtype;
+  };
+  Metadata metadata_;
+  Tensor dense_shape_;
+  Tensor batch_pointers_;
+  Tensor row_pointers_;
+  Tensor col_indices_;
+  Tensor values_;
+  std::unique_ptr<TTypes<int32>::Vec> batch_pointers_vec_;
+  std::unique_ptr<TTypes<int32>::Vec> row_pointers_vec_;
+  std::unique_ptr<TTypes<int32>::Vec> col_indices_vec_;
+};
+
+// Call BinaryFunctor<Device, T>()(ctx, a, b, c)
+// where T depends on a.dtype().  T will be one of: float, double,
+// complex64, complex128.
+template <typename Device, template <typename, typename> class BinaryFunctor>
+Status CSRSparseMatrixBinaryHelper(OpKernelContext* ctx,
+                                   const CSRSparseMatrix& a,
+                                   const CSRSparseMatrix& b,
+                                   CSRSparseMatrix* c) {
+  DataType dt = a.dtype();
+  if (dt != b.dtype()) {
+    return errors::InvalidArgument(
+        "CSRSparseMatrixBinaryHelper: Inconsistent dtypes for input matrices, "
+        "a "
+        "dtype: ",
+        DataTypeString(dt), ", b dtype: ", DataTypeString(b.dtype()));
+  }
+  switch (dt) {
+    case DT_FLOAT: {
+      BinaryFunctor<Device, float> functor(ctx);
+      return functor(a, b, c);
+    }
+    case DT_DOUBLE: {
+      BinaryFunctor<Device, double> functor(ctx);
+      return functor(a, b, c);
+    }
+    case DT_COMPLEX64: {
+      BinaryFunctor<Device, complex64> functor(ctx);
+      return functor(a, b, c);
+    }
+    case DT_COMPLEX128: {
+      BinaryFunctor<Device, complex128> functor(ctx);
+      return functor(a, b, c);
+    }
+    default:
+      return errors::InvalidArgument(
+          "CSRSparseMatrixBinaryHelper: a.dtype (", DataTypeString(dt),
+          ") is not one of: float, double, complex64, complex128");
+  }
+}
+
+// Call UnaryFunctor<Device, T>()(ctx, a, b)
+// where T depends on a.dtype().  T will be one of: float, double,
+// complex64, complex128.
+template <typename Device, template <typename, typename> class UnaryFunctor>
+Status CSRSparseMatrixUnaryHelper(OpKernelContext* ctx,
+                                  const CSRSparseMatrix& a,
+                                  CSRSparseMatrix* b) {
+  DataType dt = a.dtype();
+  switch (dt) {
+    case DT_FLOAT: {
+      UnaryFunctor<Device, float> functor(ctx);
+      return functor(a, b);
+    }
+    case DT_DOUBLE: {
+      UnaryFunctor<Device, double> functor(ctx);
+      return functor(a, b);
+    }
+    case DT_COMPLEX64: {
+      UnaryFunctor<Device, complex64> functor(ctx);
+      return functor(a, b);
+    }
+    case DT_COMPLEX128: {
+      UnaryFunctor<Device, complex128> functor(ctx);
+      return functor(a, b);
+    }
+    default:
+      return errors::InvalidArgument(
+          "CSRSparseMatrixUnaryHelper: a.dtype (", DataTypeString(dt),
+          ") is not one of: float, double, complex64, complex128");
+  }
+}
+
+template <typename T>
+struct ConstCSRComponent {
+  TTypes<int32>::UnalignedConstVec row_ptr;
+  TTypes<int32>::UnalignedConstVec col_ind;
+  typename TTypes<T>::UnalignedConstVec values;
+  TTypes<int64>::ConstVec dense_shape_host;
+};
+
+template <typename T>
+struct CSRComponent {
+  TTypes<int32>::UnalignedVec row_ptr;
+  TTypes<int32>::UnalignedVec col_ind;
+  typename TTypes<T>::UnalignedVec values;
+  TTypes<int64>::Vec dense_shape_host;
+};
+
+template <typename T>
+Status ExtractVariantFromInput(OpKernelContext* ctx, int index,
+                               const T** value) {
+  const Tensor& input_t = ctx->input(index);
+  const Variant& input_variant = input_t.scalar<Variant>()();
+  *value = input_variant.get<T>();
+  if (*value == nullptr) {
+    return errors::InvalidArgument("Could not retrieve Variant input ", index);
+  }
+  if (!(*value)->valid()) {
+    return errors::InvalidArgument("Variant input ", index, " is not valid.");
+  }
+  return Status::OK();
+}
+
+}  // namespace tensorflow
+
+#endif  // TENSORFLOW_CORE_KERNELS_SPARSE_SPARSE_MATRIX_H_
diff --git a/tensorflow/core/kernels/sparse/sparse_matrix_components_op.cc b/tensorflow/core/kernels/sparse/sparse_matrix_components_op.cc
new file mode 100644
index 00000000000..e72c85184d1
--- /dev/null
+++ b/tensorflow/core/kernels/sparse/sparse_matrix_components_op.cc
@@ -0,0 +1,150 @@
+/* Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+#define EIGEN_USE_THREADS
+
+#if GOOGLE_CUDA
+#define EIGEN_USE_GPU
+#endif
+
+#include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
+#include "tensorflow/core/framework/op.h"
+#include "tensorflow/core/framework/op_kernel.h"
+#include "tensorflow/core/framework/tensor_types.h"
+#include "tensorflow/core/framework/variant_op_registry.h"
+#include "tensorflow/core/kernels/dense_update_functor.h"
+#include "tensorflow/core/kernels/slice_op.h"
+#include "tensorflow/core/kernels/sparse/kernels.h"
+#include "tensorflow/core/kernels/sparse/sparse_matrix.h"
+
+#if GOOGLE_CUDA
+#include "tensorflow/core/kernels/cuda_solvers.h"
+#include "tensorflow/core/kernels/cuda_sparse.h"
+#endif
+
+namespace tensorflow {
+
+typedef Eigen::ThreadPoolDevice CPUDevice;
+typedef Eigen::GpuDevice GPUDevice;
+
+template <typename Device, typename T>
+class CSRSparseMatrixComponentsOp : public OpKernel {
+ public:
+  explicit CSRSparseMatrixComponentsOp(OpKernelConstruction* c) : OpKernel(c) {}
+
+  void Compute(OpKernelContext* c) final {
+    const CSRSparseMatrix* csr_sparse_matrix;
+    OP_REQUIRES_OK(c, ExtractVariantFromInput(c, 0, &csr_sparse_matrix));
+
+    const Tensor& index_t = c->input(1);
+    OP_REQUIRES(c, DataTypeToEnum<T>::value == csr_sparse_matrix->dtype(),
+                errors::InvalidArgument(
+                    "dtype of input is not equal to 'type': ",
+                    DataTypeString(csr_sparse_matrix->dtype()), " vs. ",
+                    DataTypeString(DataTypeToEnum<T>::value)));
+    OP_REQUIRES(c, index_t.dims() == 0,
+                errors::InvalidArgument("index should be a scalar, but saw: ",
+                                        index_t.DebugString()));
+    int32 index = index_t.scalar<int32>()();
+    OP_REQUIRES(c, index >= 0 && index < csr_sparse_matrix->batch_size(),
+                errors::InvalidArgument("index (", index, ") not in [0, ",
+                                        csr_sparse_matrix->batch_size(), ")"));
+
+    if (csr_sparse_matrix->dims() == 2) {
+      c->set_output(0, csr_sparse_matrix->row_pointers());
+      c->set_output(1, csr_sparse_matrix->col_indices());
+      c->set_output(2, csr_sparse_matrix->values());
+    } else {
+      auto batch_ptrs = csr_sparse_matrix->batch_pointers().vec<int32>();
+      auto dense_shape = csr_sparse_matrix->dense_shape().vec<int64>();
+      int64 rows = dense_shape(1);
+      int nnz = batch_ptrs(index + 1) - batch_ptrs(index);
+      Tensor* row_ptrs_t;
+      Tensor* col_inds_t;
+      Tensor* values_t;
+      OP_REQUIRES_OK(
+          c, c->allocate_output(0, TensorShape({rows + 1}), &row_ptrs_t));
+      OP_REQUIRES_OK(c, c->allocate_output(1, TensorShape({nnz}), &col_inds_t));
+      OP_REQUIRES_OK(c, c->allocate_output(2, TensorShape({nnz}), &values_t));
+      auto row_ptrs = row_ptrs_t->vec<int32>();
+      auto col_inds = col_inds_t->vec<int32>();
+      auto values = values_t->vec<T>();
+
+      functor::Slice<Device, int32, 1> slice_int;
+      functor::Slice<Device, T, 1> slice_t;
+      typedef Eigen::DSizes<Eigen::DenseIndex, 1> EVec;
+      const Device& d = c->eigen_device<Device>();
+      slice_int(d,
+                /*output*/ row_ptrs,
+                /*input*/ csr_sparse_matrix->row_pointers().vec<int32>(),
+                /*slice_indices*/ EVec{index * (rows + 1)},
+                /*slice_sizes*/ EVec{rows + 1});
+      slice_int(d,
+                /*output*/ col_inds,
+                /*input*/ csr_sparse_matrix->col_indices().vec<int32>(),
+                /*slice_indices*/ EVec{batch_ptrs(index)},
+                /*slice_sizes*/ EVec{nnz});
+      slice_t(d,
+              /*output*/ values, /*input*/ csr_sparse_matrix->values().vec<T>(),
+              /*slice_indices*/ EVec{batch_ptrs(index)},
+              /*slice_sizes*/ EVec{nnz});
+    }
+  }
+};
+
+#define REGISTER(DEV, T)                                    \
+  REGISTER_KERNEL_BUILDER(Name("CSRSparseMatrixComponents") \
+                              .Device(DEVICE_##DEV)         \
+                              .TypeConstraint<T>("type")    \
+                              .HostMemory("index"),         \
+                          CSRSparseMatrixComponentsOp<DEV##Device, T>);
+
+REGISTER(CPU, float)
+REGISTER(CPU, double)
+REGISTER(CPU, complex64)
+REGISTER(CPU, complex128)
+
+#if GOOGLE_CUDA
+
+REGISTER(GPU, float)
+REGISTER(GPU, double)
+REGISTER(GPU, complex64)
+REGISTER(GPU, complex128)
+
+#undef REGISTER
+
+namespace functor {
+// TODO(ebrevdo): This should move to a slice_functor.cc
+#define DECLARE_GPU_SPEC(T)                                     \
+  template <>                                                   \
+  void Slice<GPUDevice, T, 1>::operator()(                      \
+      const GPUDevice& d, typename TTypes<T, 1>::Tensor output, \
+      typename TTypes<T, 1>::ConstTensor input,                 \
+      const Eigen::DSizes<Eigen::DenseIndex, 1>& indices,       \
+      const Eigen::DSizes<Eigen::DenseIndex, 1>& sizes);        \
+  extern template struct Slice<GPUDevice, T, 1>;
+
+DECLARE_GPU_SPEC(int32);
+DECLARE_GPU_SPEC(float);
+DECLARE_GPU_SPEC(double);
+DECLARE_GPU_SPEC(complex64);
+DECLARE_GPU_SPEC(complex128);
+
+#undef DECLARE_GPU_SPEC
+}  // namespace functor
+
+#endif  // GOOGLE_CUDA
+
+}  // namespace tensorflow
diff --git a/tensorflow/core/kernels/sparse/sparse_ordering_amd_op.cc b/tensorflow/core/kernels/sparse/sparse_ordering_amd_op.cc
new file mode 100644
index 00000000000..cf8b003ab9d
--- /dev/null
+++ b/tensorflow/core/kernels/sparse/sparse_ordering_amd_op.cc
@@ -0,0 +1,131 @@
+/* Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+#include <vector>
+
+#define EIGEN_USE_THREADS
+
+#include "third_party/eigen3/Eigen/Core"
+#include "third_party/eigen3/Eigen/SparseCholesky"
+#include "third_party/eigen3/Eigen/SparseCore"
+#include "third_party/eigen3/Eigen/OrderingMethods"
+#include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
+#include "tensorflow/core/framework/allocator.h"
+#include "tensorflow/core/framework/op.h"
+#include "tensorflow/core/framework/op_kernel.h"
+#include "tensorflow/core/framework/variant_op_registry.h"
+#include "tensorflow/core/kernels/sparse/kernels.h"
+#include "tensorflow/core/kernels/sparse/sparse_matrix.h"
+#include "tensorflow/core/util/work_sharder.h"
+
+namespace tensorflow {
+
+// Op to compute the Approximate Minimum Degree (AMD) ordering for a sparse
+// matrix.
+//
+// Accepts a CSRSparseMatrix which may represent a single sparse matrix (rank 2)
+// or a batch of sparse matrices (rank 3). Each component must be a square
+// matrix. The input is assumed to be symmetric; only the lower triangular part
+// of each component matrix is read. The numeric values of the sparse matrix
+// does not affect the returned AMD ordering; only the sparsity pattern does.
+//
+// For each component sparse matrix A, the corresponding output Tensor
+// represents the AMD ordering of A's rows and columns. The ordering is returned
+// as a 1D Tensor (per batch) containing the list of indices, i.e. it contains
+// each of the integers {0, .. N-1} exactly once; where N is the number of rows
+// of the sparse matrix. The ith element represents the index of the row that
+// the ith row should map to.
+
+// If P represents the permutation matrix corresponding to the indices, then the
+// matrix:
+//   P^{-1} * A * P
+// would have a sparse Cholesky decomposition with fewer structural non-zero
+// elements than the sparse Cholesky decomposition of A itself.
+class CSROrderingAMDCPUOp : public OpKernel {
+  using SparseMatrix = Eigen::SparseMatrix<int, Eigen::RowMajor>;
+  using Indices =
+      Eigen::Matrix<int, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>;
+  using IndicesMap = Eigen::Map<Indices>;
+  using ConstIndicesMap = Eigen::Map<const Indices>;
+
+ public:
+  explicit CSROrderingAMDCPUOp(OpKernelConstruction* c) : OpKernel(c) {}
+
+  void Compute(OpKernelContext* ctx) final {
+    // Extract the input CSRSparseMatrix.
+    const CSRSparseMatrix* input_matrix;
+    OP_REQUIRES_OK(ctx, ExtractVariantFromInput(ctx, 0, &input_matrix));
+
+    const Tensor& dense_shape = input_matrix->dense_shape();
+    const int rank = dense_shape.dim_size(0);
+    OP_REQUIRES(ctx, rank == 2 || rank == 3,
+                errors::InvalidArgument("sparse matrix must have rank 2 or 3; ",
+                                        "but dense_shape has size ", rank));
+
+    auto dense_shape_vec = dense_shape.vec<int64>();
+    const int64 num_rows = dense_shape_vec((rank == 2) ? 0 : 1);
+    const int64 num_cols = dense_shape_vec((rank == 2) ? 1 : 2);
+
+    OP_REQUIRES(ctx, num_rows == num_cols,
+                errors::InvalidArgument("sparse matrix must be square; got: ",
+                                        num_rows, " != ", num_cols));
+
+    // Allocate the output permutation indices.
+    const int batch_size = input_matrix->batch_size();
+    TensorShape permutation_indices_shape =
+        (rank == 2) ? TensorShape{num_rows} : TensorShape{batch_size, num_rows};
+    Tensor permutation_indices(cpu_allocator(), DT_INT32,
+                               permutation_indices_shape);
+    ctx->set_output(0, permutation_indices);
+
+    // Parallelize AMD computation across batches using a threadpool.
+    auto worker_threads = *(ctx->device()->tensorflow_cpu_worker_threads());
+    const int64 amd_cost_per_batch =
+        10 * num_rows * (input_matrix->total_nnz() / batch_size);
+    Shard(
+        worker_threads.num_threads, worker_threads.workers, batch_size,
+        amd_cost_per_batch, [&](int64 batch_begin, int64 batch_end) {
+          for (int64 batch_index = batch_begin; batch_index < batch_end;
+               ++batch_index) {
+            // Define an Eigen SparseMatrix Map to operate on the
+            // CSRSparseMatrix component without copying the data.
+            // The values doesn't matter for computing the ordering, hence we
+            // reuse the column pointers as dummy values.
+            Eigen::Map<const SparseMatrix> sparse_matrix(
+                num_rows, num_rows, input_matrix->nnz(batch_index),
+                input_matrix->row_pointers_vec(batch_index).data(),
+                input_matrix->col_indices_vec(batch_index).data(),
+                input_matrix->col_indices_vec(batch_index).data());
+            Eigen::PermutationMatrix<Eigen::Dynamic, Eigen::Dynamic, int>
+                permutation_matrix;
+            // Compute the AMD ordering.
+            Eigen::AMDOrdering<int> amd_ordering;
+            amd_ordering(sparse_matrix.template selfadjointView<Eigen::Lower>(),
+                         permutation_matrix);
+            // Define an Eigen Map over the allocated output Tensor so that it
+            // can be mutated in place.
+            IndicesMap permutation_map(
+                permutation_indices.flat<int>().data() + batch_index * num_rows,
+                num_rows, 1);
+            permutation_map = permutation_matrix.indices();
+          }
+        });
+  }
+};
+
+REGISTER_KERNEL_BUILDER(Name("SparseMatrixOrderingAMD").Device(DEVICE_CPU),
+                        CSROrderingAMDCPUOp);
+
+}  // namespace tensorflow
diff --git a/tensorflow/core/kernels/sparse/sparse_tensor_to_csr_sparse_matrix_op.cc b/tensorflow/core/kernels/sparse/sparse_tensor_to_csr_sparse_matrix_op.cc
new file mode 100644
index 00000000000..f791b6c5105
--- /dev/null
+++ b/tensorflow/core/kernels/sparse/sparse_tensor_to_csr_sparse_matrix_op.cc
@@ -0,0 +1,345 @@
+/* Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+#define EIGEN_USE_THREADS
+
+#if GOOGLE_CUDA
+#define EIGEN_USE_GPU
+#endif
+
+#include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
+#include "tensorflow/core/framework/op.h"
+#include "tensorflow/core/framework/op_kernel.h"
+#include "tensorflow/core/framework/tensor_shape.h"
+#include "tensorflow/core/framework/tensor_types.h"
+#include "tensorflow/core/framework/variant_op_registry.h"
+#include "tensorflow/core/kernels/dense_update_functor.h"
+#include "tensorflow/core/kernels/fill_functor.h"
+#include "tensorflow/core/kernels/sparse/kernels.h"
+#include "tensorflow/core/kernels/sparse/sparse_matrix.h"
+
+#if GOOGLE_CUDA
+#include "tensorflow/core/common_runtime/gpu/gpu_event_mgr.h"
+#include "tensorflow/core/kernels/cuda_solvers.h"
+#include "tensorflow/core/kernels/cuda_sparse.h"
+#include "tensorflow/core/platform/cuda.h"
+
+using ::perftools::gputools::cuda::ScopedActivateExecutorContext;
+#endif
+
+namespace tensorflow {
+
+typedef Eigen::ThreadPoolDevice CPUDevice;
+typedef Eigen::GpuDevice GPUDevice;
+
+// Op to convert SparseTensors to CSR SparseMatrices on the CPU.
+// Takes a SparseTensor of rank 2 or (if batched) 3 as the input. The
+// SparseTensor's indices must be present in the canonical, row-major ordering.
+//
+// Returns a (batched) CSR SparseMatrix with the same dense shape and non-zero
+// values.
+template <typename T>
+class SparseTensorToCSRSparseMatrixCPUOp : public OpKernel {
+ public:
+  explicit SparseTensorToCSRSparseMatrixCPUOp(OpKernelConstruction* c)
+      : OpKernel(c) {}
+
+  void Compute(OpKernelContext* ctx) final {
+    const Tensor& indices = ctx->input(0);
+    const Tensor& values = ctx->input(1);
+    const Tensor& dense_shape = ctx->input(2);
+    const int rank = dense_shape.NumElements();
+    OP_REQUIRES(ctx, rank == 2 || rank == 3,
+                errors::InvalidArgument("SparseTensor must have rank 2 or 3; ",
+                                        "but indices has rank: ", rank));
+    auto dense_shape_vec = dense_shape.vec<int64>();
+    const int64 batch_size = (rank == 2) ? 1 : dense_shape_vec(0);
+    const int64 num_rows = dense_shape_vec((rank == 2) ? 0 : 1);
+    const int64 total_nnz = values.NumElements();
+
+    // Allocate output Tensors.
+    Tensor batch_ptr(cpu_allocator(), DT_INT32, TensorShape({batch_size + 1}));
+    Tensor csr_col_ind(cpu_allocator(), DT_INT32, TensorShape({total_nnz}));
+    Tensor csr_row_ptr(cpu_allocator(), DT_INT32,
+                       TensorShape({(num_rows + 1) * batch_size}));
+
+    // Fill the row pointers with zeros.
+    functor::SetZeroFunctor<CPUDevice, int32> set_zero;
+    set_zero(ctx->eigen_device<CPUDevice>(), csr_row_ptr.flat<int32>());
+
+    // Convert from COO to CSR format.
+    functor::SparseTensorToCSRSparseMatrixCPUFunctor coo_to_csr;
+    OP_REQUIRES_OK(
+        ctx, coo_to_csr(batch_size, num_rows, indices.template matrix<int64>(),
+                        batch_ptr.vec<int32>(), csr_row_ptr.vec<int32>(),
+                        csr_col_ind.vec<int32>()));
+
+    // Create the CSRSparseMatrix object from its component Tensors and prepare
+    // the Variant output Tensor.
+    CSRSparseMatrix output_csr_matrix;
+    OP_REQUIRES_OK(
+        ctx, CSRSparseMatrix::CreateCSRSparseMatrix(
+                 DataTypeToEnum<T>::value, dense_shape, batch_ptr, csr_row_ptr,
+                 csr_col_ind, values, &output_csr_matrix));
+    Tensor* output_csr_matrix_tensor;
+    AllocatorAttributes cpu_alloc;
+    cpu_alloc.set_on_host(true);
+    OP_REQUIRES_OK(
+        ctx, ctx->allocate_output(0, TensorShape({}), &output_csr_matrix_tensor,
+                                  cpu_alloc));
+    output_csr_matrix_tensor->scalar<Variant>()() =
+        std::move(output_csr_matrix);
+  }
+};
+
+#if GOOGLE_CUDA
+
+template <typename Device, typename T>
+class SparseTensorToCSRSparseMatrixGPUOp : public AsyncOpKernel {
+ public:
+  explicit SparseTensorToCSRSparseMatrixGPUOp(OpKernelConstruction* c)
+      : AsyncOpKernel(c) {}
+
+  void ComputeAsync(OpKernelContext* c, DoneCallback done) final {
+    auto stream = c->op_device_context()->stream();
+    const Device& d = c->eigen_device<Device>();
+
+    const Tensor& indices_t = c->input(0);
+    const Tensor& values_t = c->input(1);
+    const Tensor& dense_shape_t = c->input(2);
+    const int rank = dense_shape_t.NumElements();
+    OP_REQUIRES_ASYNC(
+        c, rank == 2 || rank == 3,
+        errors::InvalidArgument("sparse tensor must have rank == 2 or 3; ",
+                                "but indices has ", rank, " columns"),
+        done);
+    auto dense_shape = dense_shape_t.vec<int64>();
+    const int64 batch_size = (rank == 2) ? 1 : dense_shape(0);
+    const int64 rows = dense_shape((rank == 2) ? 0 : 1);
+    const int64 cols = dense_shape((rank == 2) ? 1 : 2);
+
+    ScratchSpace<int32> nnz_per_batch_host(c, batch_size, /*on_host*/ true);
+
+    Tensor nnz_per_batch_device_t;
+    if (rank == 2) {
+      // Simple case.
+      nnz_per_batch_host.mutable_data()[0] = indices_t.dim_size(0);
+    } else {
+      OP_REQUIRES_OK_ASYNC(c,
+                           c->allocate_temp(DT_INT32, TensorShape({batch_size}),
+                                            &nnz_per_batch_device_t),
+                           done);
+      auto nnz_per_batch_device = nnz_per_batch_device_t.vec<int32>();
+
+      functor::CalculateNNZPerBatchMatrixFromIndices<Device>
+          calculate_nnz_from_indices;
+      auto indices = indices_t.matrix<int64>();
+      OP_REQUIRES_OK_ASYNC(
+          c, calculate_nnz_from_indices(c, indices, nnz_per_batch_device),
+          done);
+
+      perftools::gputools::DeviceMemoryBase nnz_per_batch_device_ptr(
+          static_cast<void*>(nnz_per_batch_device.data()));
+
+      OP_REQUIRES_ASYNC(
+          c,
+          stream
+              ->ThenMemcpy(nnz_per_batch_host.mutable_data() /*host_dst*/,
+                           nnz_per_batch_device_ptr /*gpu_src*/,
+                           batch_size * sizeof(int32) /*size*/)
+              .ok(),
+          errors::Internal("SparseTensorToSparseMatrixGPUOp: failed to copy "
+                           "nnz_per_batch from device"),
+          done);
+    }
+
+    TensorReference nnz_per_batch_device_ref(nnz_per_batch_device_t);
+    auto convert_to_csr = [this, c, batch_size, nnz_per_batch_host,
+                           nnz_per_batch_device_ref, stream, &d, &values_t,
+                           &indices_t, &dense_shape_t, dense_shape, rows, cols,
+                           rank, done]() {
+      // The data has been copied out of the nnz_per_batch_device
+      // tensor by the time we get here; we can unreference it.
+      nnz_per_batch_device_ref.Unref();
+
+      auto nnz_per_batch = nnz_per_batch_host.tensor().vec<int32>();
+
+      // Ensure that within the callback, the proper GPU settings are
+      // configured.
+      ScopedActivateExecutorContext scoped_activation{stream->parent()};
+      Tensor batch_ptr_t(cpu_allocator(), DT_INT32,
+                         TensorShape({batch_size + 1}));
+
+      auto batch_ptr = batch_ptr_t.vec<int32>();
+      auto indices = indices_t.matrix<int64>();
+
+      batch_ptr(0) = 0;
+      for (int i = 0; i < batch_size; ++i) {
+        batch_ptr(i + 1) = batch_ptr(i) + nnz_per_batch(i);
+      }
+      int total_nnz = batch_ptr(batch_size);
+      OP_REQUIRES_ASYNC(
+          c, total_nnz == values_t.NumElements(),
+          errors::Internal("nnz returned by "
+                           "CalculateNNZPerBatchMatrixFromInd"
+                           "ices != len(values): ",
+                           total_nnz, " vs. ", values_t.NumElements()),
+          done);
+
+      Tensor coo_col_ind_t;
+      Tensor csr_row_ptr_t;
+      Tensor csr_values_t = values_t;
+
+      Tensor coo_row_ind_t;
+      OP_REQUIRES_OK_ASYNC(
+          c,
+          c->allocate_temp(DT_INT32, TensorShape({total_nnz}), &coo_row_ind_t),
+          done);
+      OP_REQUIRES_OK_ASYNC(
+          c,
+          c->allocate_temp(DT_INT32, TensorShape({total_nnz}), &coo_col_ind_t),
+          done);
+      OP_REQUIRES_OK_ASYNC(
+          c,
+          c->allocate_temp(DT_INT32, TensorShape({batch_size * (rows + 1)}),
+                           &csr_row_ptr_t),
+          done);
+
+      auto coo_row_ind = coo_row_ind_t.vec<int32>();
+      auto coo_col_ind = coo_col_ind_t.vec<int32>();
+      auto csr_row_ptr = csr_row_ptr_t.vec<int32>();
+
+      // Convert SparseTensor rep to coo row ind, coo col ind.
+      if (total_nnz > 0) {
+        functor::SparseTensorToCOOSparseMatrix<Device> st_to_coo;
+        st_to_coo(d, dense_shape, indices, coo_row_ind, coo_col_ind);
+      }
+
+      // Set all csr row pointers to zero, so that when iterating over
+      // batches converting coo to csr, we do not have to perform an
+      // unaligned SetZero for any nnz == 0 minibatches.  coo2csr has
+      // a bug if you have empty coo rows.
+      // TODO(ebrevdo): File bug w/ nvidia so coo2csr can handle
+      // zero-element input coo rows.
+      functor::SetZeroFunctor<Device, int32> set_zero;
+      set_zero(d, csr_row_ptr_t.flat<int32>());
+
+      functor::COOSparseMatrixToCSRSparseMatrix<Device> coo_to_csr;
+      for (int i = 0; i < batch_size; ++i) {
+        int nnz_i = batch_ptr(i + 1) - batch_ptr(i);
+        if (nnz_i == 0) {
+          // This is an empty minibatch; no call to coo2csr: it's
+          // handled by the SetZero above.
+        } else {
+          // Convert coo to csr.
+          auto coo_row_ind_i =
+              TTypes<int32>::UnalignedVec(&coo_row_ind(batch_ptr(i)), nnz_i);
+          auto csr_row_ptr_i = TTypes<int32>::UnalignedVec(
+              &csr_row_ptr((rows + 1) * i), rows + 1);
+          OP_REQUIRES_OK_ASYNC(
+              c, coo_to_csr(c, rows, cols, coo_row_ind_i, csr_row_ptr_i), done);
+        }
+      }
+
+      CSRSparseMatrix matrix;
+      OP_REQUIRES_OK_ASYNC(
+          c,
+          CSRSparseMatrix::CreateCSRSparseMatrix(
+              values_t.dtype(), dense_shape_t, batch_ptr_t, csr_row_ptr_t,
+              coo_col_ind_t, csr_values_t, &matrix),
+          done);
+      Tensor* matrix_t;
+      AllocatorAttributes cpu_alloc;
+      cpu_alloc.set_on_host(true);
+      OP_REQUIRES_OK_ASYNC(
+          c, c->allocate_output(0, TensorShape({}), &matrix_t, cpu_alloc),
+          done);
+      matrix_t->scalar<Variant>()() = std::move(matrix);
+
+      done();
+    };
+
+    if (rank == 2) {
+      convert_to_csr();
+    } else {
+      // Launch the GPU kernel to count nnz entries, then call convert_to_csr.
+      c->device()->tensorflow_gpu_device_info()->event_mgr->ThenExecute(
+          stream, convert_to_csr);
+    }
+  }
+};
+
+namespace functor {
+
+template <>
+Status CalculateNNZPerBatchMatrixFromIndices<GPUDevice>::operator()(
+    OpKernelContext* c, TTypes<int64>::ConstMatrix indices,
+    TTypes<int32>::Vec nnz_per_batch);
+extern template struct CalculateNNZPerBatchMatrixFromIndices<GPUDevice>;
+
+template <>
+struct SparseTensorToCOOSparseMatrix<GPUDevice> {
+  void operator()(const GPUDevice& d, TTypes<int64>::ConstVec host_dense_shape,
+                  TTypes<int64>::ConstMatrix indices,
+                  TTypes<int>::Vec coo_row_ind, TTypes<int>::Vec coo_col_ind);
+};
+extern template struct SparseTensorToCOOSparseMatrix<GPUDevice>;
+
+template <>
+struct COOSparseMatrixToCSRSparseMatrix<GPUDevice> {
+  Status operator()(OpKernelContext* c, const int rows, const int cols,
+                    TTypes<int>::UnalignedVec coo_row_ind,
+                    TTypes<int>::UnalignedVec csr_row_ptr) {
+    CudaSparse cuda_sparse(c);
+    TF_RETURN_IF_ERROR(cuda_sparse.Initialize());
+    return cuda_sparse.Coo2csr(coo_row_ind.data(),
+                               /*nnz*/ coo_row_ind.size(),
+                               /*m == rows of A*/ rows, csr_row_ptr.data());
+  }
+};
+extern template struct COOSparseMatrixToCSRSparseMatrix<GPUDevice>;
+
+}  // namespace functor
+
+#define REGISTER_GPU(T)                                         \
+  REGISTER_KERNEL_BUILDER(Name("SparseTensorToCSRSparseMatrix") \
+                              .Device(DEVICE_GPU)               \
+                              .TypeConstraint<T>("T")           \
+                              .HostMemory("dense_shape"),       \
+                          SparseTensorToCSRSparseMatrixGPUOp<GPUDevice, T>);
+
+REGISTER_GPU(float)
+REGISTER_GPU(double)
+REGISTER_GPU(complex64)
+REGISTER_GPU(complex128)
+
+#undef REGISTER_GPU
+
+#endif  // GOOGLE_CUDA
+
+#define REGISTER_CPU(T)                                         \
+  REGISTER_KERNEL_BUILDER(Name("SparseTensorToCSRSparseMatrix") \
+                              .Device(DEVICE_CPU)               \
+                              .TypeConstraint<T>("T"),          \
+                          SparseTensorToCSRSparseMatrixCPUOp<T>);
+
+REGISTER_CPU(float)
+REGISTER_CPU(double)
+REGISTER_CPU(complex64)
+REGISTER_CPU(complex128)
+
+#undef REGISTER_CPU
+
+}  // namespace tensorflow
diff --git a/tensorflow/core/kernels/sparse/transpose_op.cc b/tensorflow/core/kernels/sparse/transpose_op.cc
new file mode 100644
index 00000000000..74084094b67
--- /dev/null
+++ b/tensorflow/core/kernels/sparse/transpose_op.cc
@@ -0,0 +1,189 @@
+/* Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+// Implements the kernel for the CSRTranspose op, which transposes the
+// two innermost dimensions of a CSRSparseMatrix object stored in a
+// DT_VARIANT.
+
+#define EIGEN_USE_THREADS
+
+#if GOOGLE_CUDA
+#include "tensorflow/core/kernels/cuda_sparse.h"
+#define EIGEN_USE_GPU
+#endif
+
+#include "tensorflow/core/kernels/sparse/transpose_op.h"
+
+#include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
+#include "tensorflow/core/framework/op.h"
+#include "tensorflow/core/framework/op_kernel.h"
+#include "tensorflow/core/framework/tensor_types.h"
+#include "tensorflow/core/framework/variant_op_registry.h"
+#include "tensorflow/core/kernels/cwise_ops.h"
+#include "tensorflow/core/kernels/dense_update_functor.h"
+#include "tensorflow/core/kernels/fill_functor.h"
+#include "tensorflow/core/kernels/slice_op.h"
+#include "tensorflow/core/kernels/sparse/kernels.h"
+#include "tensorflow/core/kernels/sparse/sparse_matrix.h"
+
+namespace tensorflow {
+
+typedef Eigen::ThreadPoolDevice CPUDevice;
+typedef Eigen::GpuDevice GPUDevice;
+
+template <typename Device, typename T>
+class CSRTransposeOp : public OpKernel {
+ public:
+  explicit CSRTransposeOp(OpKernelConstruction* ctx) : OpKernel(ctx) {
+    OP_REQUIRES_OK(ctx, ctx->GetAttr("conjugate", &conjugate_));
+  }
+
+  void Compute(OpKernelContext* ctx) override {
+    const CSRSparseMatrix* input_matrix;
+    OP_REQUIRES_OK(ctx, ExtractVariantFromInput(ctx, 0, &input_matrix));
+    OP_REQUIRES(
+        ctx, input_matrix->dtype() == DataTypeToEnum<T>::value,
+        errors::InvalidArgument("dtype of input is not equal to 'type': ",
+                                DataTypeString(input_matrix->dtype()), " vs. ",
+                                DataTypeString(DataTypeToEnum<T>::value)));
+
+    // Allocate output shapes
+    functor::CSRSparseMatrixTranspose<Device, T> transpose;
+    CSRSparseMatrix output_matrix;
+    OP_REQUIRES_OK(ctx,
+                   transpose(ctx, conjugate_, *input_matrix, &output_matrix));
+    Tensor output_t(cpu_allocator(), DT_VARIANT, TensorShape({}));
+    output_t.scalar<Variant>()() = std::move(output_matrix);
+    ctx->set_output(0, output_t);
+  }
+
+ private:
+  bool conjugate_;
+};
+
+#ifdef GOOGLE_CUDA
+#define REGISTER(DEV, T)                                  \
+  REGISTER_KERNEL_BUILDER(Name("SparseMatrixTranspose")   \
+                              .Device(DEVICE_##DEV)       \
+                              .TypeConstraint<T>("type"), \
+                          CSRTransposeOp<DEV##Device, T>);
+
+REGISTER(GPU, float)
+REGISTER(GPU, double)
+REGISTER(GPU, complex64)
+REGISTER(GPU, complex128)
+
+#undef REGISTER
+#endif  // GOOGLE_CUDA
+
+namespace functor {
+
+template <typename Device, typename T>
+Status CSRSparseMatrixTranspose<Device, T>::operator()(
+    OpKernelContext* ctx, bool conjugate, const CSRSparseMatrix& input_matrix,
+    CSRSparseMatrix* output_matrix) {
+  const int rank = input_matrix.dims();
+  Tensor output_dense_shape_t(cpu_allocator(), DT_INT64, TensorShape({rank}));
+  const Tensor& input_dense_shape_t = input_matrix.dense_shape();
+  auto input_dense_shape = input_dense_shape_t.vec<int64>();
+  auto output_dense_shape = output_dense_shape_t.vec<int64>();
+  const int64 batch_size = input_matrix.batch_size();
+  if (rank == 3) {
+    output_dense_shape(0) = batch_size;
+  }
+  output_dense_shape(rank - 2) = input_dense_shape(rank - 1);
+  output_dense_shape(rank - 1) = input_dense_shape(rank - 2);
+  const int64 output_rows = output_dense_shape(rank - 2);
+
+  // nnzs per batch do not change with matrix transposition.
+  Tensor batch_ptr_t = input_matrix.batch_pointers();
+  const int total_nnz = input_matrix.total_nnz();
+
+  Tensor output_row_ptr_t;
+  Tensor output_col_ind_t;
+  Tensor output_values_t;
+
+  TF_RETURN_IF_ERROR(ctx->allocate_temp(
+      DT_INT32, TensorShape({batch_size * (output_rows + 1)}),
+      &output_row_ptr_t));
+  TF_RETURN_IF_ERROR(ctx->allocate_temp(DT_INT32, TensorShape({total_nnz}),
+                                        &output_col_ind_t));
+  TF_RETURN_IF_ERROR(ctx->allocate_temp(
+      DataTypeToEnum<T>::value, TensorShape({total_nnz}), &output_values_t));
+
+  TF_RETURN_IF_ERROR(CSRSparseMatrix::CreateCSRSparseMatrix(
+      DataTypeToEnum<T>::value, output_dense_shape_t, batch_ptr_t,
+      output_row_ptr_t, output_col_ind_t, output_values_t, output_matrix));
+
+  // Set the output row pointers to zero, in case we hit any empty
+  // input batches.
+  functor::SetZeroFunctor<Device, int32> set_zero;
+  const Device& d = ctx->eigen_device<Device>();
+  set_zero(d, output_row_ptr_t.flat<int32>());
+
+  functor::CSRSparseMatrixTransposeComponent<Device, T> transpose_component;
+  for (int i = 0; i < batch_size; ++i) {
+    if (output_matrix->nnz(i) == 0) {
+      continue;
+    }
+    ConstCSRComponent<T> input_comp{
+        input_matrix.row_pointers_vec(i), input_matrix.col_indices_vec(i),
+        input_matrix.values_vec<T>(i), input_dense_shape};
+    CSRComponent<T> output_comp{
+        output_matrix->row_pointers_vec(i), output_matrix->col_indices_vec(i),
+        output_matrix->values_vec<T>(i), output_dense_shape};
+
+    TF_RETURN_IF_ERROR(transpose_component(ctx, input_comp, &output_comp));
+  }
+  if (conjugate) {
+    // conjugate all values with a single kernel launch.
+    maybe_conj_inplace<Device, T>::run(d, &output_values_t);
+  }
+
+  return Status::OK();
+}
+
+#ifdef GOOGLE_CUDA
+
+template <typename T>
+struct CSRSparseMatrixTransposeComponent<GPUDevice, T> {
+  Status operator()(OpKernelContext* ctx, const ConstCSRComponent<T>& x,
+                    CSRComponent<T>* y) {
+    CudaSparse cuda_sparse(ctx);
+    TF_RETURN_IF_ERROR(cuda_sparse.Initialize());
+    const cusparseAction_t copyValues = CUSPARSE_ACTION_NUMERIC;
+    const int rank = x.dense_shape_host.size();
+    const int m = x.row_ptr.size() - 1;
+    const int n = x.dense_shape_host(rank - 1);
+    const int nnz = x.col_ind.size();
+    DCHECK_EQ(nnz, x.values.size());
+    DCHECK_EQ(n, y->row_ptr.size() - 1);
+    DCHECK_EQ(rank, y->dense_shape_host.size());
+    DCHECK_EQ(m, y->dense_shape_host(rank - 1));
+    DCHECK_EQ(nnz, y->col_ind.size());
+    DCHECK_EQ(nnz, y->values.size());
+
+    return cuda_sparse.Csr2csc(
+        m, n, nnz, x.values.data() /*csrVal*/, x.row_ptr.data() /*csrRowPtr*/,
+        x.col_ind.data() /*csrColInd*/, y->values.data() /*cscVal*/,
+        y->col_ind.data() /*cscRowInd*/, y->row_ptr.data() /*cscColPtr*/,
+        copyValues);
+    return Status::OK();
+  }
+};
+#endif  // GOOGLE_CUDA
+}  // namespace functor
+
+}  // namespace tensorflow
diff --git a/tensorflow/core/kernels/sparse/transpose_op.h b/tensorflow/core/kernels/sparse/transpose_op.h
new file mode 100644
index 00000000000..2a8f067121d
--- /dev/null
+++ b/tensorflow/core/kernels/sparse/transpose_op.h
@@ -0,0 +1,73 @@
+/* Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+#ifndef TENSORFLOW_CORE_KERNELS_SPARSE_TRANSPOSE_OP_H_
+#define TENSORFLOW_CORE_KERNELS_SPARSE_TRANSPOSE_OP_H_
+
+#include "tensorflow/core/framework/tensor.h"
+#include "tensorflow/core/framework/tensor_types.h"
+#include "tensorflow/core/kernels/cwise_ops.h"
+
+namespace tensorflow {
+namespace functor {
+
+template <typename Device, typename T>
+struct maybe_conj_inplace {
+  static void run(const Device& d, Tensor* t) {}
+};
+
+template <typename Device>
+struct maybe_conj_inplace<Device, complex64> {
+  static void run(const Device& d, Tensor* t) {
+    functor::UnaryFunctor<Device, functor::conj<complex64>> conj;
+    conj(d, t->flat<complex64>() /*out*/,
+         const_cast<const Tensor*>(t)->flat<complex64>() /*in*/);
+  }
+};
+
+template <typename Device>
+struct maybe_conj_inplace<Device, complex128> {
+  static void run(const Device& d, Tensor* t) {
+    functor::UnaryFunctor<Device, functor::conj<complex128>> conj;
+    conj(d, t->flat<complex128>() /*out*/,
+         const_cast<const Tensor*>(t)->flat<complex128>() /*in*/);
+  }
+};
+
+template <typename Device, typename T>
+struct maybe_conj {
+  static void run(const Device& d, const Tensor& in, Tensor* out) { *out = in; }
+};
+
+template <typename Device>
+struct maybe_conj<Device, complex64> {
+  static void run(const Device& d, const Tensor& in, Tensor* out) {
+    functor::UnaryFunctor<Device, functor::conj<complex64>> conj;
+    conj(d, out->flat<complex64>() /*out*/, in.flat<complex64>() /*in*/);
+  }
+};
+
+template <typename Device>
+struct maybe_conj<Device, complex128> {
+  static void run(const Device& d, const Tensor& in, Tensor* out) {
+    functor::UnaryFunctor<Device, functor::conj<complex128>> conj;
+    conj(d, out->flat<complex128>() /*out*/, in.flat<complex128>() /*in*/);
+  }
+};
+
+}  // namespace functor
+}  // namespace tensorflow
+
+#endif  // TENSORFLOW_CORE_KERNELS_SPARSE_TRANSPOSE_OP_H_
diff --git a/tensorflow/core/kernels/sparse/zeros_op.cc b/tensorflow/core/kernels/sparse/zeros_op.cc
new file mode 100644
index 00000000000..2eb1a768364
--- /dev/null
+++ b/tensorflow/core/kernels/sparse/zeros_op.cc
@@ -0,0 +1,93 @@
+/* Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+#define EIGEN_USE_THREADS
+
+#if GOOGLE_CUDA
+#define EIGEN_USE_GPU
+#endif
+
+#include "tensorflow/core/kernels/sparse/zeros_op.h"
+
+#include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
+#include "tensorflow/core/framework/op.h"
+#include "tensorflow/core/framework/op_kernel.h"
+#include "tensorflow/core/framework/tensor_types.h"
+#include "tensorflow/core/framework/variant_op_registry.h"
+#include "tensorflow/core/kernels/dense_update_functor.h"
+#include "tensorflow/core/kernels/fill_functor.h"
+#include "tensorflow/core/kernels/slice_op.h"
+#include "tensorflow/core/kernels/sparse/kernels.h"
+#include "tensorflow/core/kernels/sparse/sparse_matrix.h"
+
+namespace tensorflow {
+
+typedef Eigen::ThreadPoolDevice CPUDevice;
+typedef Eigen::GpuDevice GPUDevice;
+
+template <typename Device>
+class CSRZerosOp : public OpKernel {
+ public:
+  explicit CSRZerosOp(OpKernelConstruction* c) : OpKernel(c) {
+    OP_REQUIRES_OK(c, c->GetAttr("type", &dtype_));
+  }
+
+  void Compute(OpKernelContext* c) override {
+    const Tensor& dense_shape_t = c->input(0);
+    CSRSparseMatrix matrix;
+    functor::CSRSparseMatrixZeros<Device> csr_sparse_matrix_zeros;
+    OP_REQUIRES_OK(c,
+                   csr_sparse_matrix_zeros(c, dtype_, dense_shape_t, &matrix));
+    Tensor* matrix_t;
+    AllocatorAttributes cpu_alloc;
+    cpu_alloc.set_on_host(true);
+    OP_REQUIRES_OK(
+        c, c->allocate_output(0, TensorShape({}), &matrix_t, cpu_alloc));
+    matrix_t->scalar<Variant>()() = matrix;
+  }
+
+ private:
+  DataType dtype_;
+};
+
+namespace {
+
+template <typename Device>
+Status CSRSparseMatrixZerosLikeHelper(OpKernelContext* ctx,
+                                      const CSRSparseMatrix& x,
+                                      CSRSparseMatrix* y) {
+  functor::CSRSparseMatrixZeros<Device> csr_sparse_matrix_zeros;
+  return csr_sparse_matrix_zeros(ctx, x.dtype(), x.dense_shape(), y);
+}
+
+}  // namespace
+
+#ifdef GOOGLE_CUDA
+#define REGISTER(DEV)                                     \
+  REGISTER_KERNEL_BUILDER(Name("SparseMatrixZeros")       \
+                              .Device(DEVICE_##DEV)       \
+                              .HostMemory("dense_shape"), \
+                          CSRZerosOp<DEV##Device>);
+
+REGISTER(GPU)
+
+REGISTER_UNARY_VARIANT_UNARY_OP_FUNCTION(
+    ZEROS_LIKE_VARIANT_UNARY_OP, DEVICE_GPU, CSRSparseMatrix,
+    CSRSparseMatrixZerosLikeHelper<GPUDevice>);
+
+#undef REGISTER
+#endif  // GOOGLE_CUDA
+
+}  // namespace tensorflow
diff --git a/tensorflow/core/kernels/sparse/zeros_op.h b/tensorflow/core/kernels/sparse/zeros_op.h
new file mode 100644
index 00000000000..66cba071c94
--- /dev/null
+++ b/tensorflow/core/kernels/sparse/zeros_op.h
@@ -0,0 +1,88 @@
+/* Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+#ifndef TENSORFLOW_CORE_KERNELS_SPARSE_ZEROS_OP_H_
+#define TENSORFLOW_CORE_KERNELS_SPARSE_ZEROS_OP_H_
+
+#define EIGEN_USE_THREADS
+
+#if GOOGLE_CUDA
+#define EIGEN_USE_GPU
+#endif
+
+#include "third_party/eigen3/unsupported/Eigen/CXX11/Tensor"
+#include "tensorflow/core/framework/op.h"
+#include "tensorflow/core/framework/op_kernel.h"
+#include "tensorflow/core/framework/tensor_types.h"
+#include "tensorflow/core/framework/variant_op_registry.h"
+#include "tensorflow/core/kernels/dense_update_functor.h"
+#include "tensorflow/core/kernels/fill_functor.h"
+#include "tensorflow/core/kernels/sparse/sparse_matrix.h"
+
+namespace tensorflow {
+
+typedef Eigen::ThreadPoolDevice CPUDevice;
+typedef Eigen::GpuDevice GPUDevice;
+
+namespace functor {
+
+template <typename Device>
+struct CSRSparseMatrixZeros {
+  Status operator()(OpKernelContext* c, DataType dtype,
+                    const Tensor& dense_shape_t, CSRSparseMatrix* matrix) {
+    auto dense_shape = dense_shape_t.vec<int64>();
+    const int rank = dense_shape.size();
+    if (!(rank == 2 || rank == 3)) {
+      return errors::InvalidArgument("sparse tensor must have rank == 2 or 3; ",
+                                     "but dense shape has ", rank, " entries");
+    }
+    const int64 batch_size = (rank == 2) ? 1 : dense_shape(0);
+    const int64 rows = dense_shape((rank == 2) ? 0 : 1);
+
+    Tensor batch_ptr_t(cpu_allocator(), DT_INT32,
+                       TensorShape({batch_size + 1}));
+    batch_ptr_t.vec<int32>().setZero();  // On host.
+
+    Allocator* allocator = c->device()->GetAllocator(AllocatorAttributes());
+    // An all-zeros CSR matrix is composed of an empty set of column
+    // indices, an empty set of values, and a vector of all zero row
+    // pointers.  The length of the row pointers vector is #rows + 1.
+    // Each row pointer is just an offset into the cols and
+    // values vectors, and those are empty, all coefficients are zero.
+    Tensor csr_row_ptr_t;
+    Tensor coo_col_ind_t(allocator, DT_INT32, TensorShape({0}));
+    Tensor csr_values_t(allocator, dtype, TensorShape({0}));
+    const Device& d = c->eigen_device<Device>();
+    functor::SetZeroFunctor<Device, int32> set_zero;
+    Tensor* csr_row_ptr_t_ptr;
+    PersistentTensor csr_row_ptr_pt;
+    TF_RETURN_IF_ERROR(
+        c->allocate_persistent(DT_INT32, TensorShape({batch_size * (rows + 1)}),
+                               &csr_row_ptr_pt, &csr_row_ptr_t_ptr));
+    set_zero(d, csr_row_ptr_t_ptr->flat<int32>());
+    csr_row_ptr_t = std::move(*csr_row_ptr_t_ptr);
+
+    TF_RETURN_IF_ERROR(CSRSparseMatrix::CreateCSRSparseMatrix(
+        dtype, dense_shape_t, batch_ptr_t, csr_row_ptr_t, coo_col_ind_t,
+        csr_values_t, matrix));
+
+    return Status::OK();
+  }
+};
+
+}  // namespace functor
+}  // namespace tensorflow
+
+#endif  // TENSORFLOW_CORE_KERNELS_SPARSE_ZEROS_OP_H_
diff --git a/tensorflow/core/ops/sparse_csr_matrix_ops.cc b/tensorflow/core/ops/sparse_csr_matrix_ops.cc
new file mode 100644
index 00000000000..7214f7e0188
--- /dev/null
+++ b/tensorflow/core/ops/sparse_csr_matrix_ops.cc
@@ -0,0 +1,613 @@
+/* Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+#include "tensorflow/core/framework/common_shape_fns.h"
+#include "tensorflow/core/framework/numeric_op.h"
+#include "tensorflow/core/framework/op.h"
+#include "tensorflow/core/framework/shape_inference.h"
+#include "tensorflow/core/lib/core/errors.h"
+
+namespace tensorflow {
+
+using shape_inference::DimensionHandle;
+using shape_inference::InferenceContext;
+using shape_inference::ShapeAndType;
+using shape_inference::ShapeHandle;
+
+Status GetVariantInput(InferenceContext* c, int index,
+                       ShapeAndType* shape_and_type) {
+  ShapeHandle variant;
+  TF_RETURN_IF_ERROR(c->WithRank(c->input(index), 0, &variant));
+  auto* shapes_and_types = c->input_handle_shapes_and_types(index);
+  if (shapes_and_types == nullptr || shapes_and_types->size() != 1) {
+    return errors::InvalidArgument(
+        "Unable to access shape and type info from variant input ", index);
+  }
+  *shape_and_type = shapes_and_types->at(0);
+  return Status::OK();
+}
+
+// Validates that a shape represents a (rank-2) square matrix or a (rank-3)
+// batch of square matrices.
+Status ValidateSquareMatrixShape(InferenceContext* c,
+                                 const ShapeHandle& matrix_shape,
+                                 DimensionHandle* matrix_dimension) {
+  ShapeHandle out;
+  TF_RETURN_IF_ERROR(c->WithRankAtLeast(matrix_shape, 2, &out));
+  TF_RETURN_IF_ERROR(c->WithRankAtMost(matrix_shape, 3, &out));
+  if (!c->RankKnown(matrix_shape)) {
+    return errors::Internal("Sparse matrix has an unknown rank.");
+  }
+
+  TF_RETURN_IF_ERROR(c->Merge(c->Dim(matrix_shape, -2),
+                              c->Dim(matrix_shape, -1), matrix_dimension));
+  return Status::OK();
+}
+
+REGISTER_OP("SparseTensorToCSRSparseMatrix")
+    .Input("indices: int64")
+    .Input("values: T")
+    .Input("dense_shape: int64")
+    .Attr("T: {float, double, complex64, complex128}")
+    .Output("sparse_matrix: variant")
+    .SetShapeFn([](InferenceContext* c) {
+      TF_RETURN_IF_ERROR(shape_inference::ValidateSparseTensor(
+          c, c->input(0), c->input(1), c->input(2)));
+      auto rank = c->Value(c->Dim(c->input(0), 1));
+      ShapeHandle dense_shape;
+      TF_RETURN_IF_ERROR(c->MakeShapeFromShapeTensor(2, &dense_shape));
+      TF_RETURN_IF_ERROR(c->WithRank(dense_shape, rank, &dense_shape));
+      if (!c->RankKnown(dense_shape) || c->Rank(dense_shape) < 2 ||
+          c->Rank(dense_shape) > 3) {
+        return errors::InvalidArgument(
+            "Invalid rank: ", c->Rank(dense_shape),
+            ".  Expected a known rank of either 2 or 3.");
+      }
+
+      DataType dtype;
+      TF_RETURN_IF_ERROR(c->GetAttr("T", &dtype));
+      c->set_output(0, c->Scalar());
+      c->set_output_handle_shapes_and_types(0,
+                                            {ShapeAndType{dense_shape, dtype}});
+      return Status::OK();
+    });
+
+REGISTER_OP("CSRSparseMatrixToSparseTensor")
+    .Input("sparse_matrix: variant")
+    .Output("indices: int64")
+    .Output("values: type")
+    .Output("dense_shape: int64")
+    .Attr("type: {float, double, complex64, complex128}")
+    .SetShapeFn([](InferenceContext* c) {
+      ShapeAndType sparse_matrix_shape_and_type;
+      TF_RETURN_IF_ERROR(GetVariantInput(c, 0, &sparse_matrix_shape_and_type));
+      ShapeHandle sparse_matrix = sparse_matrix_shape_and_type.shape;
+      TF_RETURN_IF_ERROR(c->WithRankAtMost(sparse_matrix, 3, &sparse_matrix));
+      if (!c->RankKnown(sparse_matrix)) {
+        return errors::InvalidArgument("sparse_matrix has an unknown rank.");
+      }
+      int rank = c->Rank(sparse_matrix);
+      ShapeHandle indices = c->Matrix(c->UnknownDim(), rank);
+      ShapeHandle values = c->Vector(c->UnknownDim());
+      ShapeHandle dense_shape = c->Vector(rank);
+      c->set_output(0, indices);
+      c->set_output(1, values);
+      c->set_output(2, dense_shape);
+      return Status::OK();
+    });
+
+REGISTER_OP("DenseToCSRSparseMatrix")
+    .Input("dense_input: T")
+    .Input("indices: int64")
+    .Attr("T: {float, double, complex64, complex128}")
+    .Output("sparse_output: variant")
+    .SetShapeFn([](InferenceContext* c) {
+      ShapeHandle dense_shape = c->input(0);
+      if (!c->RankKnown(dense_shape) || c->Rank(dense_shape) < 2 ||
+          c->Rank(dense_shape) > 3) {
+        return errors::InvalidArgument(
+            "Invalid rank of dense: ", c->Rank(dense_shape),
+            ".  Expected a known rank of either 2 or 3.");
+      }
+      auto rank = c->Rank(dense_shape);
+
+      ShapeHandle indices = c->input(1);
+      if (!c->RankKnown(indices) || c->Rank(indices) != 2) {
+        return errors::InvalidArgument(
+            "indices must be a matrix; but its rank is not 2: ",
+            c->Rank(indices));
+      }
+      auto indices_col = c->Dim(indices, 1);
+      if (!c->ValueKnown(indices_col) || c->Value(indices_col) != rank) {
+        return errors::InvalidArgument(
+            "indices.shape[1] must match rank of dense; saw: ",
+            c->Value(indices_col), " vs. ", rank);
+      }
+      ShapeHandle fake_values_vec = c->Vector(c->Dim(indices, 0));
+      ShapeHandle fake_shape_shape = c->Vector(rank);
+      TF_RETURN_IF_ERROR(shape_inference::ValidateSparseTensor(
+          c, indices /*indices_shape*/, fake_values_vec /*values_shape*/,
+          fake_shape_shape /*shape_shape*/));
+      DataType dtype;
+      TF_RETURN_IF_ERROR(c->GetAttr("T", &dtype));
+      c->set_output_handle_shapes_and_types(0,
+                                            {ShapeAndType{dense_shape, dtype}});
+      c->set_output(0, c->Scalar());
+      return Status::OK();
+    });
+
+REGISTER_OP("CSRSparseMatrixToDense")
+    .Input("sparse_input: variant")
+    .Output("dense_output: type")
+    .Attr("type: {float, double, complex64, complex128}")
+    .SetShapeFn([](InferenceContext* c) {
+      ShapeAndType sparse_matrix_shape_and_type;
+      TF_RETURN_IF_ERROR(GetVariantInput(c, 0, &sparse_matrix_shape_and_type));
+      ShapeHandle sparse_matrix = sparse_matrix_shape_and_type.shape;
+      TF_RETURN_IF_ERROR(c->WithRankAtMost(sparse_matrix, 3, &sparse_matrix));
+      if (!c->RankKnown(sparse_matrix)) {
+        return errors::InvalidArgument("sparse_matrix has an unknown rank.");
+      }
+      c->set_output(0, sparse_matrix);
+      return Status::OK();
+    });
+
+REGISTER_OP("CSRSparseMatrixComponents")
+    .Input("csr_sparse_matrix: variant")
+    .Input("index: int32")
+    .Output("row_ptrs: int32")
+    .Output("col_inds: int32")
+    .Output("values: type")
+    .Attr("type: {float, double, complex64, complex128}")
+    .SetShapeFn([](InferenceContext* c) {
+      ShapeAndType sparse_matrix_shape_and_type;
+      TF_RETURN_IF_ERROR(GetVariantInput(c, 0, &sparse_matrix_shape_and_type));
+      ShapeHandle csr_sparse_matrix = sparse_matrix_shape_and_type.shape;
+      TF_RETURN_IF_ERROR(
+          c->WithRankAtLeast(csr_sparse_matrix, 2, &csr_sparse_matrix));
+      TF_RETURN_IF_ERROR(
+          c->WithRankAtMost(csr_sparse_matrix, 3, &csr_sparse_matrix));
+      ShapeHandle index;
+      if (c->Rank(c->input(1)) != 0) {
+        return errors::InvalidArgument("index must be a scalar.");
+      }
+      if (!c->RankKnown(csr_sparse_matrix)) {
+        return errors::InvalidArgument(
+            "csr_sparse_matrix has an unknown rank.");
+      }
+      auto row_ptrs_dh = c->Dim(csr_sparse_matrix, -2);
+      TF_RETURN_IF_ERROR(c->Add(row_ptrs_dh, 1, &row_ptrs_dh));
+      ShapeHandle row_ptrs = c->Vector(row_ptrs_dh);
+      c->set_output(0, row_ptrs);
+      c->set_output(1, c->Vector(c->UnknownDim()));
+      c->set_output(2, c->Vector(c->UnknownDim()));
+      return Status::OK();
+    });
+
+REGISTER_OP("SparseMatrixNNZ")
+    .Input("sparse_matrix: variant")
+    .Output("nnz: int32")
+    .SetShapeFn([](InferenceContext* c) {
+      ShapeAndType sparse_matrix_shape_and_type;
+      TF_RETURN_IF_ERROR(GetVariantInput(c, 0, &sparse_matrix_shape_and_type));
+      ShapeHandle sparse_matrix = sparse_matrix_shape_and_type.shape;
+      TF_RETURN_IF_ERROR(c->WithRankAtLeast(sparse_matrix, 2, &sparse_matrix));
+      TF_RETURN_IF_ERROR(c->WithRankAtMost(sparse_matrix, 3, &sparse_matrix));
+      if (!c->RankKnown(sparse_matrix)) {
+        return errors::InvalidArgument("sparse_matrix has an unknown rank.");
+      }
+      ShapeHandle out;
+      if (c->Rank(sparse_matrix) == 3) {
+        out = c->Vector(c->Dim(sparse_matrix, 0));
+      } else {
+        out = c->Scalar();
+      }
+      c->set_output(0, out);
+      return Status::OK();
+    });
+
+REGISTER_OP("SparseMatrixMatMul")
+    .Input("a: variant")
+    .Input("b: T")
+    .Attr("T: type")
+    .Attr("transpose_a: bool = false")
+    .Attr("transpose_b: bool = false")
+    .Attr("adjoint_a: bool = false")
+    .Attr("adjoint_b: bool = false")
+    .Attr("transpose_output: bool = false")
+    .Attr("conjugate_output: bool = false")
+    .Output("output: T")
+    .SetShapeFn([](InferenceContext* c) {
+      ShapeAndType sparse_matrix_shape_and_type;
+      TF_RETURN_IF_ERROR(GetVariantInput(c, 0, &sparse_matrix_shape_and_type));
+      ShapeHandle a_shape = sparse_matrix_shape_and_type.shape;
+      TF_RETURN_IF_ERROR(c->WithRankAtLeast(a_shape, 2, &a_shape));
+      TF_RETURN_IF_ERROR(c->WithRankAtMost(a_shape, 3, &a_shape));
+      if (!c->RankKnown(a_shape)) {
+        return errors::Internal("a has an unknown rank.");
+      }
+      ShapeHandle b_shape;
+      TF_RETURN_IF_ERROR(c->WithRankAtLeast(c->input(1), 2, &b_shape));
+      TF_RETURN_IF_ERROR(c->WithRankAtMost(b_shape, 3, &b_shape));
+
+      bool transpose_a = false;
+      bool transpose_b = false;
+      bool transpose_output = false;
+
+      // TODO(ebrevdo): Add transpose support.
+      TF_RETURN_IF_ERROR(c->GetAttr("transpose_a", &transpose_a));
+      TF_RETURN_IF_ERROR(c->GetAttr("transpose_b", &transpose_b));
+      TF_RETURN_IF_ERROR(c->GetAttr("transpose_output", &transpose_output));
+
+      bool adjoint_a = false;
+      bool adjoint_b = false;
+      TF_RETURN_IF_ERROR(c->GetAttr("adjoint_a", &adjoint_a));
+      TF_RETURN_IF_ERROR(c->GetAttr("adjoint_b", &adjoint_b));
+      if (adjoint_a && transpose_a) {
+        return errors::InvalidArgument(
+            "Only one of adjoint_a and transpose_a may be true.");
+      }
+      if (adjoint_b && transpose_b) {
+        return errors::InvalidArgument(
+            "Only one of adjoint_b and transpose_b may be true.");
+      }
+      transpose_a = transpose_a || adjoint_a;
+      transpose_b = transpose_b || adjoint_b;
+
+      auto output_rows = c->Dim(a_shape, transpose_a ? -1 : -2);
+      auto output_cols = c->Dim(b_shape, transpose_b ? -2 : -1);
+      if (transpose_output) {
+        std::tie(output_rows, output_cols) =
+            std::make_tuple(output_cols, output_rows);
+      }
+
+      // Batch dims match between inputs.
+      ShapeHandle a_batch_dims;
+      ShapeHandle b_batch_dims;
+      ShapeHandle batch_dims;
+      TF_RETURN_IF_ERROR(c->Subshape(a_shape, 0, -2, &a_batch_dims));
+      TF_RETURN_IF_ERROR(c->Subshape(b_shape, 0, -2, &b_batch_dims));
+      TF_RETURN_IF_ERROR(c->Merge(a_batch_dims, b_batch_dims, &batch_dims));
+
+      // Assert inner dims match.
+      shape_inference::DimensionHandle unused;
+      TF_RETURN_IF_ERROR(c->Merge(c->Dim(a_shape, transpose_a ? -2 : -1),
+                                  c->Dim(b_shape, transpose_b ? -1 : -2),
+                                  &unused));
+
+      ShapeHandle out;
+      TF_RETURN_IF_ERROR(c->Concatenate(
+          batch_dims, c->Matrix(output_rows, output_cols), &out));
+
+      c->set_output(0, out);
+      return Status::OK();
+    });
+
+REGISTER_OP("SparseMatrixMul")
+    .Input("a: variant")
+    .Input("b: T")
+    .Attr("T: type")
+    .Output("output: variant")
+    .SetShapeFn([](InferenceContext* c) {
+      ShapeAndType sparse_matrix_shape_and_type;
+      TF_RETURN_IF_ERROR(GetVariantInput(c, 0, &sparse_matrix_shape_and_type));
+      ShapeHandle a_shape = sparse_matrix_shape_and_type.shape;
+      TF_RETURN_IF_ERROR(c->WithRankAtMost(a_shape, 3, &a_shape));
+      if (!c->RankKnown(a_shape)) {
+        return errors::Internal("a has an unknown rank.");
+      }
+      ShapeHandle b_shape;
+      TF_RETURN_IF_ERROR(c->WithRankAtMost(c->input(1), 3, &b_shape));
+      if (!c->RankKnown(b_shape)) {
+        return errors::Internal("b has an unknown rank.");
+      }
+      ShapeHandle out;
+      if (c->Rank(b_shape) == 0) {
+        out = a_shape;
+      } else if (c->Rank(b_shape) == 3) {
+        if (c->Rank(a_shape) != 3) {
+          return errors::Unimplemented("rank of b is 3 but rank of a is not.");
+        }
+        if (!(c->Value(c->Dim(b_shape, 1)) == 1 &&
+              c->Value(c->Dim(b_shape, 2)) == 1)) {
+          return errors::Unimplemented(
+              "b must be a scalar or shaped [batch_size, 1, 1]");
+        }
+        DimensionHandle batch_size = c->Dim(a_shape, 0);
+        TF_RETURN_IF_ERROR(
+            c->Merge(batch_size, c->Dim(b_shape, 0), &batch_size));
+        TF_RETURN_IF_ERROR(c->ReplaceDim(b_shape, 0, batch_size, &b_shape));
+        TF_RETURN_IF_ERROR(c->ReplaceDim(a_shape, 0, batch_size, &a_shape));
+        out = a_shape;
+      } else {
+        return errors::Unimplemented(
+            "b must be a scalar or shaped [batch_size, 1, 1]");
+      }
+      c->set_output_handle_shapes_and_types(
+          0, {ShapeAndType{out, sparse_matrix_shape_and_type.dtype}});
+      c->set_output(0, c->Scalar());
+      return Status::OK();
+    });
+
+REGISTER_OP("SparseMatrixAdd")
+    .Input("a: variant")
+    .Input("b: variant")
+    .Input("alpha: T")
+    .Input("beta: T")
+    .Attr("T: {float, double, complex64, complex128}")
+    .Output("c: variant")
+    .SetShapeFn([](InferenceContext* c) {
+      // alpha and beta are scalars.
+      ShapeHandle unused_scalar_shape;
+      TF_RETURN_IF_ERROR(c->WithRank(c->input(2), 0, &unused_scalar_shape));
+      TF_RETURN_IF_ERROR(c->WithRank(c->input(3), 0, &unused_scalar_shape));
+
+      ShapeAndType sparse_matrix_shape_and_type;
+      TF_RETURN_IF_ERROR(GetVariantInput(c, 0, &sparse_matrix_shape_and_type));
+      ShapeHandle a_shape = sparse_matrix_shape_and_type.shape;
+      TF_RETURN_IF_ERROR(c->WithRankAtLeast(a_shape, 2, &a_shape));
+      TF_RETURN_IF_ERROR(c->WithRankAtMost(a_shape, 3, &a_shape));
+      if (!c->RankKnown(a_shape)) {
+        return errors::InvalidArgument("a has an unknown rank.");
+      }
+
+      TF_RETURN_IF_ERROR(GetVariantInput(c, 1, &sparse_matrix_shape_and_type));
+      ShapeHandle b_shape = sparse_matrix_shape_and_type.shape;
+      TF_RETURN_IF_ERROR(c->WithRankAtLeast(b_shape, 2, &b_shape));
+      TF_RETURN_IF_ERROR(c->WithRankAtMost(b_shape, 3, &b_shape));
+      if (!c->RankKnown(b_shape)) {
+        return errors::InvalidArgument("b has an unknown rank.");
+      }
+      ShapeHandle out;
+      TF_RETURN_IF_ERROR(c->Merge(a_shape, b_shape, &out));
+      c->set_output_handle_shapes_and_types(
+          0, {ShapeAndType{out, sparse_matrix_shape_and_type.dtype}});
+      c->set_output(0, c->Scalar());
+      return Status::OK();
+    });
+
+REGISTER_OP("SparseMatrixSparseMatMul")
+    .Input("a: variant")
+    .Input("b: variant")
+    .Attr("type: {float, double, complex64, complex128}")
+    .Attr("transpose_a: bool = false")
+    .Attr("transpose_b: bool = false")
+    .Attr("adjoint_a: bool = false")
+    .Attr("adjoint_b: bool = false")
+    .Output("c: variant")
+    .SetShapeFn([](InferenceContext* c) {
+      ShapeAndType sparse_matrix_shape_and_type;
+      TF_RETURN_IF_ERROR(GetVariantInput(c, 0, &sparse_matrix_shape_and_type));
+      ShapeHandle a_shape = sparse_matrix_shape_and_type.shape;
+      TF_RETURN_IF_ERROR(c->WithRankAtLeast(a_shape, 2, &a_shape));
+      TF_RETURN_IF_ERROR(c->WithRankAtMost(a_shape, 3, &a_shape));
+      if (!c->RankKnown(a_shape)) {
+        return errors::Internal("a has an unknown rank.");
+      }
+
+      TF_RETURN_IF_ERROR(GetVariantInput(c, 1, &sparse_matrix_shape_and_type));
+      ShapeHandle b_shape = sparse_matrix_shape_and_type.shape;
+      TF_RETURN_IF_ERROR(c->WithRankAtLeast(b_shape, 2, &b_shape));
+      TF_RETURN_IF_ERROR(c->WithRankAtMost(b_shape, 3, &b_shape));
+      if (!c->RankKnown(b_shape)) {
+        return errors::Internal("b has an unknown rank.");
+      }
+
+      bool transpose_a = false;
+      bool transpose_b = false;
+      TF_RETURN_IF_ERROR(c->GetAttr("transpose_a", &transpose_a));
+      TF_RETURN_IF_ERROR(c->GetAttr("transpose_b", &transpose_b));
+      bool adjoint_a = false;
+      bool adjoint_b = false;
+      TF_RETURN_IF_ERROR(c->GetAttr("adjoint_a", &adjoint_a));
+      TF_RETURN_IF_ERROR(c->GetAttr("adjoint_b", &adjoint_b));
+      if (adjoint_a && transpose_a) {
+        return errors::InvalidArgument(
+            "Only one of adjoint_a and transpose_a may be true.");
+      } else if (adjoint_b && transpose_b) {
+        return errors::InvalidArgument(
+            "Only one of adjoint_b and transpose_b may be true.");
+      }
+      transpose_a = transpose_a || adjoint_a;
+      transpose_b = transpose_b || adjoint_b;
+
+      auto output_rows = c->Dim(a_shape, transpose_a ? -1 : -2);
+      auto output_cols = c->Dim(b_shape, transpose_b ? -2 : -1);
+
+      // Batch dims match between inputs.
+      ShapeHandle a_batch_dims;
+      ShapeHandle b_batch_dims;
+      ShapeHandle batch_dims;
+      TF_RETURN_IF_ERROR(c->Subshape(a_shape, 0, -2, &a_batch_dims));
+      TF_RETURN_IF_ERROR(c->Subshape(b_shape, 0, -2, &b_batch_dims));
+      TF_RETURN_IF_ERROR(c->Merge(a_batch_dims, b_batch_dims, &batch_dims));
+
+      // Assert inner dims match.
+      shape_inference::DimensionHandle unused;
+      TF_RETURN_IF_ERROR(c->Merge(c->Dim(a_shape, transpose_a ? -2 : -1),
+                                  c->Dim(b_shape, transpose_b ? -1 : -2),
+                                  &unused));
+
+      ShapeHandle out;
+      TF_RETURN_IF_ERROR(c->Concatenate(
+          batch_dims, c->Matrix(output_rows, output_cols), &out));
+
+      c->set_output_handle_shapes_and_types(
+          0, {ShapeAndType{out, sparse_matrix_shape_and_type.dtype}});
+      c->set_output(0, c->Scalar());
+      return Status::OK();
+    });
+
+REGISTER_OP("SparseMatrixZeros")
+    .Input("dense_shape: int64")
+    .Attr("type: {float, double, complex64, complex128}")
+    .Output("sparse_matrix: variant")
+    .SetShapeFn([](InferenceContext* c) {
+      auto rank = c->NumElements(c->input(0));
+      ShapeHandle dense_shape;
+      TF_RETURN_IF_ERROR(c->MakeShapeFromShapeTensor(0, &dense_shape));
+      TF_RETURN_IF_ERROR(
+          c->WithRank(dense_shape, c->Value(rank), &dense_shape));
+      if (!c->RankKnown(dense_shape) || c->Rank(dense_shape) < 2 ||
+          c->Rank(dense_shape) > 3) {
+        return errors::InvalidArgument(
+            "Invalid rank: ", c->Rank(dense_shape),
+            ".  Expected a known rank of either 2 or 3.");
+      }
+      DataType dtype;
+      TF_RETURN_IF_ERROR(c->GetAttr("type", &dtype));
+      c->set_output_handle_shapes_and_types(0,
+                                            {ShapeAndType{dense_shape, dtype}});
+      c->set_output(0, c->Scalar());
+      return Status::OK();
+    });
+
+REGISTER_OP("SparseMatrixTranspose")
+    .Input("input: variant")
+    .Attr("conjugate: bool = false")
+    .Attr("type: {float, double, complex64, complex128}")
+    .Output("output: variant")
+    .SetShapeFn([](InferenceContext* c) {
+      ShapeAndType sparse_matrix_shape_and_type;
+      TF_RETURN_IF_ERROR(GetVariantInput(c, 0, &sparse_matrix_shape_and_type));
+      ShapeHandle input = sparse_matrix_shape_and_type.shape;
+      TF_RETURN_IF_ERROR(c->WithRankAtLeast(input, 2, &input));
+      TF_RETURN_IF_ERROR(c->WithRankAtMost(input, 3, &input));
+      if (!c->RankKnown(input)) {
+        return errors::InvalidArgument("input has an unknown rank.");
+      }
+      ShapeHandle output;
+      if (c->Rank(input) == 2) {
+        output = c->Matrix(c->Dim(input, 1), c->Dim(input, 0));
+      } else {
+        output = c->MakeShape(
+            {c->Dim(input, 0), c->Dim(input, 2), c->Dim(input, 1)});
+      }
+      c->set_output_handle_shapes_and_types(
+          0, {ShapeAndType{output, sparse_matrix_shape_and_type.dtype}});
+      c->set_output(0, c->Scalar());
+
+      return Status::OK();
+    });
+
+REGISTER_OP("SparseMatrixSoftmax")
+    .Input("logits: variant")
+    .Attr("type: {float, double}")
+    .Output("softmax: variant")
+    .SetShapeFn([](InferenceContext* c) {
+      ShapeAndType sparse_matrix_shape_and_type;
+      TF_RETURN_IF_ERROR(GetVariantInput(c, 0, &sparse_matrix_shape_and_type));
+      ShapeHandle logits = sparse_matrix_shape_and_type.shape;
+      TF_RETURN_IF_ERROR(c->WithRankAtLeast(logits, 2, &logits));
+      TF_RETURN_IF_ERROR(c->WithRankAtMost(logits, 3, &logits));
+      if (!c->RankKnown(logits)) {
+        return errors::InvalidArgument("logits has an unknown rank.");
+      }
+      c->set_output_handle_shapes_and_types(
+          0, {ShapeAndType{logits, sparse_matrix_shape_and_type.dtype}});
+      c->set_output(0, c->Scalar());
+      return Status::OK();
+    });
+
+REGISTER_OP("SparseMatrixSoftmaxGrad")
+    .Input("softmax: variant")
+    .Input("grad_softmax: variant")
+    .Attr("type: {float, double}")
+    .Output("gradient: variant")
+    .SetShapeFn([](InferenceContext* c) {
+      ShapeAndType sparse_matrix_shape_and_type;
+      TF_RETURN_IF_ERROR(GetVariantInput(c, 0, &sparse_matrix_shape_and_type));
+      ShapeHandle softmax = sparse_matrix_shape_and_type.shape;
+      TF_RETURN_IF_ERROR(c->WithRankAtLeast(softmax, 2, &softmax));
+      TF_RETURN_IF_ERROR(c->WithRankAtMost(softmax, 3, &softmax));
+      if (!c->RankKnown(softmax)) {
+        return errors::InvalidArgument("softmax has an unknown rank.");
+      }
+      TF_RETURN_IF_ERROR(GetVariantInput(c, 1, &sparse_matrix_shape_and_type));
+      ShapeHandle grad_softmax = sparse_matrix_shape_and_type.shape;
+      TF_RETURN_IF_ERROR(c->WithRankAtLeast(grad_softmax, 2, &grad_softmax));
+      TF_RETURN_IF_ERROR(c->WithRankAtMost(grad_softmax, 3, &grad_softmax));
+      if (!c->RankKnown(grad_softmax)) {
+        return errors::InvalidArgument("grad_softmax has an unknown rank.");
+      }
+      TF_RETURN_IF_ERROR(c->Merge(softmax, grad_softmax, &softmax));
+      c->set_output_handle_shapes_and_types(
+          0, {ShapeAndType{softmax, sparse_matrix_shape_and_type.dtype}});
+      c->set_output(0, c->Scalar());
+      return Status::OK();
+    });
+
+REGISTER_OP("SparseMatrixOrderingAMD")
+    .Input("input: variant")
+    .Output("output: int32")
+    .SetShapeFn([](InferenceContext* c) {
+      ShapeAndType sparse_matrix_shape_and_type;
+      TF_RETURN_IF_ERROR(GetVariantInput(c, 0, &sparse_matrix_shape_and_type));
+      ShapeHandle matrix_shape = sparse_matrix_shape_and_type.shape;
+      DimensionHandle n;
+      TF_RETURN_IF_ERROR(ValidateSquareMatrixShape(c, matrix_shape, &n));
+
+      ShapeHandle output;
+      if (c->Rank(matrix_shape) == 2) {
+        output = c->Vector(c->Dim(matrix_shape, 0));
+      } else {
+        output = c->Matrix(c->Dim(matrix_shape, 0), c->Dim(matrix_shape, 1));
+      }
+      c->set_output(0, output);
+      return Status::OK();
+    });
+
+REGISTER_OP("SparseMatrixSparseCholesky")
+    .Input("input: variant")
+    .Input("permutation: int32")
+    .Attr("type: {float, double, complex64, complex128}")
+    .Output("output: variant")
+    .SetShapeFn([](InferenceContext* c) {
+      ShapeAndType sparse_matrix_shape_and_type;
+      TF_RETURN_IF_ERROR(GetVariantInput(c, 0, &sparse_matrix_shape_and_type));
+      ShapeHandle matrix_shape = sparse_matrix_shape_and_type.shape;
+      DimensionHandle n;
+      TF_RETURN_IF_ERROR(ValidateSquareMatrixShape(c, matrix_shape, &n));
+
+      ShapeHandle perm_shape;
+      TF_RETURN_IF_ERROR(c->WithRankAtLeast(c->input(1), 1, &perm_shape));
+      TF_RETURN_IF_ERROR(c->WithRankAtMost(c->input(1), 2, &perm_shape));
+      if (!c->RankKnown(perm_shape)) {
+        return errors::Internal("permutation has an unknown rank.");
+      }
+
+      // Each batch component of permutation must have the same number of
+      // elements as number of rows of sparse_matrix.
+      TF_RETURN_IF_ERROR(c->Merge(n, c->Dim(perm_shape, -1), &n));
+      ShapeHandle matrix_batch_shape;
+      ShapeHandle perm_batch_shape;
+
+      // Make the common batch subshape.
+      TF_RETURN_IF_ERROR(c->Subshape(matrix_shape, 0, -2, &matrix_batch_shape));
+      TF_RETURN_IF_ERROR(c->Subshape(perm_shape, 0, -1, &perm_shape));
+      // Make sure the batch dimensions match between sparse_matrix and
+      // permutation.
+      TF_RETURN_IF_ERROR(
+          c->Merge(matrix_batch_shape, perm_batch_shape, &matrix_batch_shape));
+
+      ShapeHandle out = matrix_shape;
+      c->set_output_handle_shapes_and_types(
+          0, {ShapeAndType{out, sparse_matrix_shape_and_type.dtype}});
+      c->set_output(0, c->Scalar());
+
+      return Status::OK();
+    });
+
+}  // namespace tensorflow
diff --git a/tensorflow/core/ops/sparse_csr_matrix_ops_test.cc b/tensorflow/core/ops/sparse_csr_matrix_ops_test.cc
new file mode 100644
index 00000000000..39b2bb66398
--- /dev/null
+++ b/tensorflow/core/ops/sparse_csr_matrix_ops_test.cc
@@ -0,0 +1,369 @@
+/* Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+==============================================================================*/
+
+#include "tensorflow/core/framework/node_def_builder.h"
+#include "tensorflow/core/framework/node_def_util.h"
+#include "tensorflow/core/framework/op.h"
+#include "tensorflow/core/framework/shape_inference.h"
+#include "tensorflow/core/framework/shape_inference_testutil.h"
+#include "tensorflow/core/framework/tensor_testutil.h"
+#include "tensorflow/core/lib/core/status_test_util.h"
+#include "tensorflow/core/platform/test.h"
+#include "tensorflow/core/public/version.h"
+
+namespace tensorflow {
+
+TEST(SparseMatrixOpsTest, SparseTensorToCSRSparseMatrix_ShapeFn) {
+  ShapeInferenceTestOp op("SparseTensorToCSRSparseMatrix");
+  (*op.node_def.mutable_attr())["T"].set_type(DT_FLOAT);
+  op.input_tensors.resize(3);
+  // inputs: indices, values, dense_shape
+  INFER_ERROR("Expected a known rank", op, "?;?;?");
+  INFER_ERROR("either 2 or 3", op, "[?,4];?;?");
+  INFER_OK(op, "[?,2];?;?", "[]");
+  INFER_OK(op, "[?,3];?;?", "[]");
+  Tensor dense_shape_t = test::AsTensor<int64>({5, 6});
+  op.input_tensors[2] = &dense_shape_t;
+  INFER_ERROR("Shape must be rank 3 but is rank 2 for", op, "[?,3];?;?");
+  INFER_OK(op, "[?,2];?;?", "[]");
+}
+
+TEST(SparseMatrixOpsTest, CSRSparseMatrixToSparseTensor_ShapeFn) {
+  ShapeInferenceTestOp op("CSRSparseMatrixToSparseTensor");
+  std::vector<ShapeInferenceTestOp::ShapeAndType> shapes_and_types(1);
+  shapes_and_types[0].second = DT_FLOAT;
+  op.input_resource_handle_shapes_and_types.push_back(&shapes_and_types);
+  // outputs: indices, values, dense_shape
+  shapes_and_types[0].first = "[4,5]";
+  INFER_OK(op, "[]", "[?,2];[?];[2]");
+  shapes_and_types[0].first = "[?,?]";
+  INFER_OK(op, "[]", "[?,2];[?];[2]");
+  shapes_and_types[0].first = "[4,5,6]";
+  INFER_OK(op, "[]", "[?,3];[?];[3]");
+  shapes_and_types[0].first = "[?,?,?]";
+  INFER_OK(op, "[]", "[?,3];[?];[3]");
+}
+
+TEST(SparseMatrixOpsTest, DenseToCSRSparseMatrix_ShapeFn) {
+  ShapeInferenceTestOp op("DenseToCSRSparseMatrix");
+  (*op.node_def.mutable_attr())["T"].set_type(DT_FLOAT);
+  INFER_ERROR("Expected a known rank", op, "?;?");
+  INFER_ERROR("either 2 or 3", op, "[?];?");
+  INFER_OK(op, "[?,?];[?,2]", "[]");
+  INFER_OK(op, "[?,?,?];[?,3]", "[]");
+  INFER_ERROR("indices.shape[1] must match rank of dense; saw: 2 vs. 3", op,
+              "[?,?,?];[?,2]");
+}
+
+TEST(SparseMatrixOpsTest, CSRSparseMatrixToDense_ShapeFn) {
+  ShapeInferenceTestOp op("CSRSparseMatrixToDense");
+  std::vector<ShapeInferenceTestOp::ShapeAndType> shapes_and_types(1);
+  shapes_and_types[0].second = DT_FLOAT;
+  op.input_resource_handle_shapes_and_types.push_back(&shapes_and_types);
+  // outputs: dense
+  shapes_and_types[0].first = "[?,?]";
+  INFER_OK(op, "[]", "[?,?]");
+  shapes_and_types[0].first = "[?,?,?]";
+  INFER_OK(op, "[]", "[?,?,?]");
+}
+
+TEST(SparseMatrixOpsTest, CSRSparseMatrixComponents_ShapeFn) {
+  ShapeInferenceTestOp op("CSRSparseMatrixComponents");
+  std::vector<ShapeInferenceTestOp::ShapeAndType> shapes_and_types(1);
+  shapes_and_types[0].second = DT_FLOAT;
+  op.input_resource_handle_shapes_and_types.push_back(&shapes_and_types);
+  op.input_resource_handle_shapes_and_types.push_back(nullptr);
+  // inputs: csr_sparse_matrix, index
+  // outputs: row_ptrs, col_inds, values
+  shapes_and_types[0].first = "[4,5]";
+  INFER_OK(op, "[];[]", "[5];[?];[?]");
+  shapes_and_types[0].first = "[?,?]";
+  INFER_OK(op, "[];[]", "[?];[?];[?]");
+  shapes_and_types[0].first = "[19,34,55]";
+  INFER_OK(op, "[];[]", "[35];[?];[?]");
+  shapes_and_types[0].first = "[?,?,?]";
+  INFER_OK(op, "[];[]", "[?];[?];[?]");
+  shapes_and_types[0].first = "[?,?,?]";
+  INFER_ERROR("index must be a scalar", op, "[];?");
+}
+
+TEST(SparseMatrixOpsTest, SparseMatrixMatMul_ShapeFn) {
+  ShapeInferenceTestOp op("SparseMatrixMatMul");
+  std::vector<ShapeInferenceTestOp::ShapeAndType> a_shapes_and_types(1);
+  a_shapes_and_types[0].second = DT_FLOAT;
+  op.input_resource_handle_shapes_and_types.push_back(&a_shapes_and_types);
+  op.input_resource_handle_shapes_and_types.push_back(nullptr);
+  auto set_options = [&op](bool transpose_a, bool transpose_b, bool adjoint_a,
+                           bool adjoint_b, bool transpose_output) {
+    TF_ASSERT_OK(NodeDefBuilder("test", "SparseMatrixMatMul")
+                     .Input("a", 0, DT_VARIANT)
+                     .Input("b", 1, DT_FLOAT)
+                     .Attr("transpose_a", transpose_a)
+                     .Attr("transpose_b", transpose_b)
+                     .Attr("adjoint_a", adjoint_a)
+                     .Attr("adjoint_b", adjoint_b)
+                     .Attr("transpose_output", transpose_output)
+                     .Finalize(&op.node_def));
+  };
+  // inputs: a <CSR>, b <T>
+  // output: matmul(a, b)
+  set_options(false, false, false, false, false /*transpose_output*/);
+  a_shapes_and_types[0].first = "?";
+  INFER_ERROR("a has an unknown rank", op, "[];?");
+  a_shapes_and_types[0].first = "[?]";
+  INFER_ERROR("must be at least rank 2 but is rank 1", op, "[];?");
+  a_shapes_and_types[0].first = "[?,?]";
+  INFER_OK(op, "[];?", "[?,?]");
+  a_shapes_and_types[0].first = "[?,?,?]";
+  INFER_OK(op, "[];?", "[?,?,?]");
+  a_shapes_and_types[0].first = "[?,3,?]";
+  INFER_OK(op, "[];[?,?,?]", "[?,3,d1_2]");
+  a_shapes_and_types[0].first = "[?,3,?]";
+  INFER_OK(op, "[];[?,?,4]", "[?,3,d1_2]");  // [B,3,?] . [B,?,4]
+  a_shapes_and_types[0].first = "[?,?,6]";
+  INFER_OK(op, "[];[?,6,?]", "[?,?,d1_2]");  // [B,?,6] . [B,6,?]
+  a_shapes_and_types[0].first = "[?,?,5]";
+  INFER_ERROR("must be equal, but are 5 and 6 for", op, "[];[?,6,?]");
+
+  set_options(false, false, false, false, true /*transpose_output*/);
+  a_shapes_and_types[0].first = "[?,3,?]";
+  INFER_OK(op, "[];[?,?,4]", "[?,d1_2,3]");
+  a_shapes_and_types[0].first = "[3,?]";
+  INFER_OK(op, "[];[?,4]", "[d1_1,3]");
+
+  set_options(/*transpose_a=*/true, /*transpose_b=*/true,
+              /*adjoint_a=*/false, /*adjoint_b=*/false,
+              false /*transpose_output*/);
+  // t([B,W,X]) . t([B,Y,Z]) => [B,X,Y]
+  a_shapes_and_types[0].first = "[?,?,?]";
+  INFER_OK(op, "[];[?,?,?]", "[?,?,d1_1]");
+
+  set_options(/*transpose_a=*/false, /*transpose_b=*/false,
+              /*adjoint_a=*/true, /*adjoint_b=*/true,
+              false /*transpose_output*/);
+  // adj([B,W,X]) . adj([B,Y,Z]) => [B,X,Y]
+  a_shapes_and_types[0].first = "[?,?,?]";
+  INFER_OK(op, "[];[?,?,?]", "[?,?,d1_1]");
+
+  set_options(true /*transpose_a*/, true /*transpose_b*/,
+              /*adjoint_a=*/false, /*adjoint_b=*/false,
+              true /*transpose_output*/);
+  // t(t([B,W,X]) . t([B,Y,Z])) => [B,Y,X]
+  a_shapes_and_types[0].first = "[?,?,?]";
+  INFER_OK(op, "[];[?,?,?]", "[?,d1_1,?]");
+
+  set_options(/*transpose_a=*/true, /*transpose_b=*/false,
+              /*adjoint_a=*/true, /*adjoint_b=*/true,
+              false /*transpose_output*/);
+  a_shapes_and_types[0].first = "[?,?,?]";
+  INFER_ERROR("Only one of adjoint_a and transpose_a", op, "[];[?,?,?]");
+  set_options(/*transpose_a=*/false, /*transpose_b=*/true,
+              /*adjoint_a=*/true, /*adjoint_b=*/true,
+              false /*transpose_output*/);
+  a_shapes_and_types[0].first = "[?,?,?]";
+  INFER_ERROR("Only one of adjoint_b and transpose_b", op, "[];[?,?,?]");
+}
+
+TEST(SparseMatrixOpsTest, SparseMatrixAdd_ShapeFn) {
+  // inputs: a <CSR>, b <CSR>, alpha <scalar>, beta <scalar>
+  // output: alpha * a + beta * b
+  ShapeInferenceTestOp op("SparseMatrixAdd");
+  std::vector<ShapeInferenceTestOp::ShapeAndType> a_shapes_and_types(1);
+  std::vector<ShapeInferenceTestOp::ShapeAndType> b_shapes_and_types(1);
+  a_shapes_and_types[0].second = DT_FLOAT;
+  b_shapes_and_types[0].second = DT_FLOAT;
+  op.input_resource_handle_shapes_and_types.push_back(&a_shapes_and_types);
+  op.input_resource_handle_shapes_and_types.push_back(&b_shapes_and_types);
+  op.input_resource_handle_shapes_and_types.push_back(nullptr);
+  op.input_resource_handle_shapes_and_types.push_back(nullptr);
+  auto set_shapes = [&a_shapes_and_types, &b_shapes_and_types](
+                        const string& a_shape, const string& b_shape) {
+    a_shapes_and_types[0].first = a_shape;
+    b_shapes_and_types[0].first = b_shape;
+  };
+  // TODO(ebrevdo): Update shape_inference_testutil to be able to properly test
+  // output handle shapes and types.
+  set_shapes("[?,?]", "[?,?]");
+  INFER_OK(op, "[];[];?;?", "[]");  // output handle: [?,?]
+  set_shapes("[?,?,?]", "[?,?,?]");
+  INFER_OK(op, "[];[];?;?", "[]");  // output handle: [?,?,?]
+  set_shapes("[3,4]", "[3,4]");
+  INFER_OK(op, "[];[];?;?", "[]");  // output handle: [3,4]
+  set_shapes("[3,4,5]", "[3,4,5]");
+  INFER_OK(op, "[];[];?;?", "[]");  // output handle: [3,4,5]
+  set_shapes("[?,?,?]", "[?,?,?]");
+  INFER_OK(op, "[];[];[];[]", "[]");  // output handle: [?,?,?]
+  // non-scalar beta.
+  set_shapes("[?,?]", "[?,?]");
+  INFER_ERROR("must be rank 0 but is rank 1", op, "[];[];?;[?]");
+  // unknown rank b.
+  set_shapes("[?,?,?]", "?");
+  INFER_ERROR("b has an unknown rank", op, "[];[];?;?");
+  // different ranks of a and b.
+  set_shapes("[?,?,?]", "[?,?]");
+  INFER_ERROR("must be equal", op, "[];[];?;?");
+}
+
+TEST(SparseMatrixOpsTest, SparseMatrixSparseMatMul_ShapeFn) {
+  ShapeInferenceTestOp op("SparseMatrixSparseMatMul");
+  std::vector<ShapeInferenceTestOp::ShapeAndType> a_shapes_and_types(1);
+  std::vector<ShapeInferenceTestOp::ShapeAndType> b_shapes_and_types(1);
+  a_shapes_and_types[0].second = DT_FLOAT;
+  b_shapes_and_types[0].second = DT_FLOAT;
+  op.input_resource_handle_shapes_and_types.push_back(&a_shapes_and_types);
+  op.input_resource_handle_shapes_and_types.push_back(&b_shapes_and_types);
+  auto set_shapes = [&a_shapes_and_types, &b_shapes_and_types](
+                        const string& a_shape, const string& b_shape) {
+    a_shapes_and_types[0].first = a_shape;
+    b_shapes_and_types[0].first = b_shape;
+  };
+  auto set_options = [&op](bool transpose_a, bool transpose_b, bool adjoint_a,
+                           bool adjoint_b) {
+    TF_ASSERT_OK(NodeDefBuilder("test", "SparseMatrixMatMul")
+                     .Input("a", 0, DT_VARIANT)
+                     .Input("b", 1, DT_FLOAT)
+                     .Attr("transpose_a", transpose_a)
+                     .Attr("transpose_b", transpose_b)
+                     .Attr("adjoint_a", adjoint_a)
+                     .Attr("adjoint_b", adjoint_b)
+                     .Finalize(&op.node_def));
+  };
+  // inputs: a <CSR>, b <CSR>
+  // output: matmul(a, b) <CSR>
+  set_options(false, false, false, false);
+  set_shapes("?", "?");
+  INFER_ERROR("has an unknown rank", op, "[];[]");
+  set_shapes("[?]", "[?,?]");
+  INFER_ERROR("must be at least rank 2 but is rank 1", op, "[];[]");
+  set_shapes("[?,?]", "[?,?]");
+  INFER_OK(op, "[];[]", "[]");  // [d0_0,d1_1]"
+  set_shapes("[?,?,?]", "[?,?]");
+  INFER_ERROR("must be equal rank, but are", op, "[];[]");
+  set_shapes("[?,?,?]", "[?,?,?]");
+  INFER_OK(op, "[];[]", "[]");  // "[d0_0,d0_1,d1_2]"
+  set_shapes("[?,3,?]", "[?,?,?]");
+  INFER_OK(op, "[];[]", "[]");  // "[d0_0,d0_1,d1_2]"
+  set_shapes("[?,3,?]", "[?,?,4]");
+  INFER_OK(op, "[];[]", "[]");  // [d0_0,d0_1,d1_2]"
+  set_shapes("[?,?,6]", "[?,6,?]");
+  INFER_OK(op, "[];[]", "[]");  // "[d0_0,d0_1,d1_2]"
+  set_shapes("[?,?,5]", "[?,6,?]");
+  INFER_ERROR("must be equal, but are 5 and 6 for", op, "[];[]");
+
+  set_options(/*transpose_a=*/true, /*transpose_b=*/true, /*adjoint_a=*/false,
+              /*adjoint_b=*/false);
+  // t([B,W,X]) . t([B,Y,Z]) => [B,X,Y]
+  set_shapes("[?,?,?]", "[?,?,?]");
+  INFER_OK(op, "[];[]", "[]");  // [d0_0,d0_2,d1_1]"
+
+  set_options(/*transpose_a=*/false, /*transpose_b=*/false, /*adjoint_a=*/true,
+              /*adjoint_b=*/true);
+  // adj([B,W,X]) . adj([B,Y,Z]) => [B,X,Y]
+  set_shapes("[?,?,?]", "[?,?,?]");
+  INFER_OK(op, "[];[]", "[]");  // "[d0_0,d0_2,d1_1]"
+
+  set_options(/*transpose_a=*/true, /*transpose_b=*/false,
+              /*adjoint_a=*/true, /*adjoint_b=*/true);
+  set_shapes("[?,?,?]", "[?,?,?]");
+  INFER_ERROR("Only one of adjoint_a and transpose_a", op, "[];[]");
+  set_options(/*transpose_a=*/false, /*transpose_b=*/true,
+              /*adjoint_a=*/true, /*adjoint_b=*/true);
+  set_shapes("[?,?,?]", "[?,?,?]");
+  INFER_ERROR("Only one of adjoint_b and transpose_b", op, "[];[]");
+}
+
+TEST(SparseMatrixOpsTest, SparseMatrixTranspose_ShapeFn) {
+  ShapeInferenceTestOp op("SparseMatrixTranspose");
+  // inputs: input
+  // outputs: output
+  std::vector<ShapeInferenceTestOp::ShapeAndType> shapes_and_types(1);
+  shapes_and_types[0].second = DT_FLOAT;
+  op.input_resource_handle_shapes_and_types.push_back(&shapes_and_types);
+  shapes_and_types[0].first = "[3,4,5]";
+  INFER_OK(op, "[]", "[]");  // [3,5,4]"
+  shapes_and_types[0].first = "[3,4]";
+  INFER_OK(op, "[]", "[]");  // "[4, 3]";
+  shapes_and_types[0].first = "?";
+  INFER_ERROR("input has an unknown rank", op, "[]");
+}
+
+TEST(SparseMatrixOpsTest, SparseMatrixSoftmax_ShapeFn) {
+  ShapeInferenceTestOp op("SparseMatrixSoftmax");
+  // inputs: logits
+  // outputs: softmax
+  std::vector<ShapeInferenceTestOp::ShapeAndType> shapes_and_types(1);
+  shapes_and_types[0].second = DT_FLOAT;
+  op.input_resource_handle_shapes_and_types.push_back(&shapes_and_types);
+  shapes_and_types[0].first = "[?,?,?]";
+  INFER_OK(op, "[]", "[]");  // "in0"
+  shapes_and_types[0].first = "[?,?]";
+  INFER_OK(op, "[]", "[]");  // "in0"
+  shapes_and_types[0].first = "?";
+  INFER_ERROR("logits has an unknown rank", op, "[]");
+}
+
+TEST(SparseMatrixOpsTest, SparseMatrixSoftmaxGrad_ShapeFn) {
+  ShapeInferenceTestOp op("SparseMatrixSoftmaxGrad");
+  // inputs: softmax, grad_softmax
+  // outputs: gradient
+  std::vector<ShapeInferenceTestOp::ShapeAndType> a_shapes_and_types(1);
+  std::vector<ShapeInferenceTestOp::ShapeAndType> b_shapes_and_types(1);
+  a_shapes_and_types[0].second = DT_FLOAT;
+  b_shapes_and_types[0].second = DT_FLOAT;
+  op.input_resource_handle_shapes_and_types.push_back(&a_shapes_and_types);
+  op.input_resource_handle_shapes_and_types.push_back(&b_shapes_and_types);
+  auto set_shapes = [&a_shapes_and_types, &b_shapes_and_types](
+                        const string& a_shape, const string& b_shape) {
+    a_shapes_and_types[0].first = a_shape;
+    b_shapes_and_types[0].first = b_shape;
+  };
+  set_shapes("[?,?,?]", "[?,?,?]");
+  INFER_OK(op, "[];[]", "[]");  // "in0"
+  set_shapes("[?,?]", "[?,?]");
+  INFER_OK(op, "[];[]", "[]");  // "in0"
+  set_shapes("[3,4]", "[5,6]");
+  INFER_ERROR("Dimension 0 in both shapes must be equal, but are 3 and 5", op,
+              "[];[]");
+  set_shapes("?", "[?,?]");
+  INFER_ERROR("softmax has an unknown rank", op, "[];[]");
+  set_shapes("[?,?,?]", "?");
+  INFER_ERROR("grad_softmax has an unknown rank", op, "[];[]");
+}
+
+TEST(SparseMatrixOpsTest, SparseMatrixMul_ShapeFn) {
+  ShapeInferenceTestOp op("SparseMatrixMul");
+  // inputs: a <CSR>, b <dense>
+  // output: a * b
+  std::vector<ShapeInferenceTestOp::ShapeAndType> shapes_and_types(1);
+  shapes_and_types[0].second = DT_FLOAT;
+  op.input_resource_handle_shapes_and_types.push_back(&shapes_and_types);
+  op.input_resource_handle_shapes_and_types.push_back(nullptr);
+  shapes_and_types[0].first = "[3,4]";
+  INFER_OK(op, "[];[]", "[]");  // "[3,4]"
+  shapes_and_types[0].first = "[5,3,4]";
+  INFER_OK(op, "[];[?,1,1]", "[]");  // "[5,3,4]"
+  // b not scalar, doesn't match a.
+  shapes_and_types[0].first = "[?,?,?]";
+  INFER_ERROR("b must be a scalar or shaped [batch_size, 1, 1]", op,
+              "[];[3,4]");
+  shapes_and_types[0].first = "[3,4]";
+  INFER_ERROR("b must be a scalar or shaped", op, "[];[3,4]");
+  shapes_and_types[0].first = "[3,4,5]";
+  INFER_ERROR("b must be a scalar or shaped", op, "[];[3,4,5]");
+  shapes_and_types[0].first = "[3,4,5]";
+  INFER_ERROR("must be equal, but are 3 and 4", op, "[];[4,1,1]");
+}
+
+}  // namespace tensorflow
diff --git a/tensorflow/opensource_only.files b/tensorflow/opensource_only.files
index ec66f4947c2..9b1efb68491 100644
--- a/tensorflow/opensource_only.files
+++ b/tensorflow/opensource_only.files
@@ -38,8 +38,11 @@ tensorflow/third_party/eigen3/Eigen/Cholesky
 tensorflow/third_party/eigen3/Eigen/Core
 tensorflow/third_party/eigen3/Eigen/Eigenvalues
 tensorflow/third_party/eigen3/Eigen/LU
+tensorflow/third_party/eigen3/Eigen/OrderingMethods
 tensorflow/third_party/eigen3/Eigen/QR
 tensorflow/third_party/eigen3/Eigen/SVD
+tensorflow/third_party/eigen3/Eigen/SparseCholesky
+tensorflow/third_party/eigen3/Eigen/SparseCore
 tensorflow/third_party/eigen3/LICENSE
 tensorflow/third_party/eigen3/gpu_packet_math.patch
 tensorflow/third_party/eigen3/unsupported/Eigen/CXX11/FixedPoint
diff --git a/tensorflow/python/BUILD b/tensorflow/python/BUILD
index 2362ce91620..c1efe03a904 100644
--- a/tensorflow/python/BUILD
+++ b/tensorflow/python/BUILD
@@ -184,6 +184,7 @@ py_library(
         "//tensorflow/python/module",
         "//tensorflow/python/ops/distributions",
         "//tensorflow/python/ops/linalg",
+        "//tensorflow/python/ops/linalg/sparse",
         "//tensorflow/python/ops/losses",
         "//tensorflow/python/ops/parallel_for",
         "//tensorflow/python/ops/ragged",
@@ -2875,6 +2876,7 @@ py_library(
         ":tensor_array_ops",
         ":unconnected_gradients",
         ":util",
+        "//tensorflow/python/ops/linalg/sparse",
     ],
 )
 
@@ -3861,6 +3863,7 @@ py_library(
         "//tensorflow/python/eager:wrap_function",
         "//tensorflow/python/ops/distributions",
         "//tensorflow/python/ops/linalg",
+        "//tensorflow/python/ops/linalg/sparse",
         "//tensorflow/python/ops/ragged",
     ],
 )
diff --git a/tensorflow/python/kernel_tests/BUILD b/tensorflow/python/kernel_tests/BUILD
index e5b741b8077..e87894fdccc 100644
--- a/tensorflow/python/kernel_tests/BUILD
+++ b/tensorflow/python/kernel_tests/BUILD
@@ -8,7 +8,7 @@ package(
     licenses = ["notice"],  # Apache 2.0
 )
 
-# CPU only tests should use tf_py_test, GPU tests use cuda_py_test
+# CPU-only tests should use tf_py_test, GPU tests use cuda_py_test
 # Please avoid the py_tests and cuda_py_tests (plural) while we
 # fix the shared/overbroad dependencies.
 
@@ -3878,3 +3878,57 @@ cuda_py_test(
     tags = ["no_rocm"],
     xla_enable_strict_auto_jit = True,
 )
+
+cuda_py_test(
+    name = "sparse_csr_matrix_ops_test",
+    size = "medium",
+    srcs = ["sparse_csr_matrix_ops_test.py"],
+    additional_deps = [
+        "//tensorflow/python/ops/linalg/sparse",
+        "//tensorflow/python/ops/linalg/sparse:gen_sparse_csr_matrix_ops",
+    ],
+    main = "sparse_csr_matrix_ops_test.py",
+)
+
+cuda_py_test(
+    name = "csr_sparse_matrix_test",
+    size = "medium",
+    srcs = ["csr_sparse_matrix_test.py"],
+    additional_deps = [
+        "//tensorflow/python/ops/linalg/sparse",
+    ],
+    main = "csr_sparse_matrix_test.py",
+)
+
+cuda_py_test(
+    name = "sparse_csr_matrix_grad_test",
+    size = "medium",
+    srcs = ["sparse_csr_matrix_grad_test.py"],
+    additional_deps = [
+        "//tensorflow/python/ops/linalg/sparse",
+    ],
+    main = "sparse_csr_matrix_grad_test.py",
+    shard_count = 50,
+)
+
+cuda_py_test(
+    name = "sparse_csr_matrix_dense_mat_mul_grad_test",
+    size = "medium",
+    srcs = ["sparse_csr_matrix_dense_mat_mul_grad_test.py"],
+    additional_deps = [
+        "//tensorflow/python/ops/linalg/sparse",
+    ],
+    main = "sparse_csr_matrix_dense_mat_mul_grad_test.py",
+    shard_count = 50,
+)
+
+cuda_py_test(
+    name = "sparse_csr_matrix_sparse_mat_mul_grad_test",
+    size = "medium",
+    srcs = ["sparse_csr_matrix_sparse_mat_mul_grad_test.py"],
+    additional_deps = [
+        "//tensorflow/python/ops/linalg/sparse",
+    ],
+    main = "sparse_csr_matrix_sparse_mat_mul_grad_test.py",
+    shard_count = 50,
+)
diff --git a/tensorflow/python/kernel_tests/csr_sparse_matrix_test.py b/tensorflow/python/kernel_tests/csr_sparse_matrix_test.py
new file mode 100644
index 00000000000..74456229b49
--- /dev/null
+++ b/tensorflow/python/kernel_tests/csr_sparse_matrix_test.py
@@ -0,0 +1,266 @@
+# Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+# ==============================================================================
+"""CSR sparse matrix tests."""
+
+from __future__ import absolute_import
+from __future__ import division
+from __future__ import print_function
+
+import itertools
+
+import numpy as np
+
+from tensorflow.python.framework import dtypes
+from tensorflow.python.framework import sparse_tensor
+from tensorflow.python.framework import test_util
+from tensorflow.python.ops import math_ops
+from tensorflow.python.ops.linalg.sparse import sparse_csr_matrix_ops
+from tensorflow.python.platform import test
+
+
+class CSRSparseMatrixTest(test.TestCase):
+
+  @classmethod
+  def setUpClass(cls):  # pylint: disable=g-missing-super-call
+    cls._gpu_available = test_util.is_gpu_available()
+
+  @test_util.run_in_graph_and_eager_modes
+  def testConstructorFromSparseTensor(self):
+    if not self._gpu_available:
+      return
+
+    a_indices = np.array([[0, 0], [2, 3], [2, 4], [3, 0]])
+    a_values = [1.0, 5.0, -1.0, -2.0]
+    a_dense_shape = [5, 6]
+
+    a_st = sparse_tensor.SparseTensor(a_indices, a_values, a_dense_shape)
+    a_st = math_ops.cast(a_st, dtypes.float32)
+    a_sm = sparse_csr_matrix_ops.CSRSparseMatrix(a_st)
+    self.assertEqual(a_sm.shape, a_dense_shape)
+
+    a_st_rt = a_sm.to_sparse_tensor()
+    a_st_rt = self.evaluate(a_st_rt)
+
+    self.assertAllEqual(a_indices, a_st_rt.indices)
+    self.assertAllClose(a_values, a_st_rt.values)
+    self.assertAllEqual(a_dense_shape, a_st_rt.dense_shape)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testConstructorFromDenseTensorNoIndices(self):
+    if not self._gpu_available:
+      return
+
+    sparsify = lambda m: m * (m > 0)
+    dense_shape = [5, 7, 13]
+    a_mats = sparsify(np.random.randn(*dense_shape)).astype(np.float32)
+
+    a_sm = sparse_csr_matrix_ops.CSRSparseMatrix(a_mats)
+    self.assertEqual(a_sm.shape, a_mats.shape)
+
+    a_sm_rt = a_sm.to_dense()
+    a_sm_nnz = a_sm.nnz()
+    a_sm_nnz, a_sm_rt = self.evaluate([a_sm_nnz, a_sm_rt])
+
+    # Count number of nonzero entries for each batch using bincount.
+    nz = np.bincount(a_mats.nonzero()[0], minlength=a_mats.shape[0])
+    self.assertAllEqual(nz, a_sm_nnz)
+    self.assertAllClose(a_mats, a_sm_rt)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testConstructorFromDenseTensorWithIndices(self):
+    if not self._gpu_available:
+      return
+
+    dense_shape = [5, 7, 13]
+    a_mats = np.random.randn(*dense_shape).astype(np.float32)
+    indices = np.array([[0, 0, 0],
+                        [1, 0, 0]], dtype=np.int64)
+
+    a_sm = sparse_csr_matrix_ops.CSRSparseMatrix(a_mats, indices=indices)
+    self.assertEqual(a_sm.shape, a_mats.shape)
+
+    a_sm_st = a_sm.to_sparse_tensor()
+    a_sm_st = self.evaluate(a_sm_st)
+
+    # Count number of nonzero entries for each batch using bincount.
+    self.assertAllEqual(indices, a_sm_st.indices)
+    self.assertAllEqual(dense_shape, a_sm.shape)
+    self.assertAllEqual(dense_shape, a_sm_st.dense_shape)
+    self.assertAllClose([a_mats[tuple(x)] for x in indices], a_sm_st.values)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testConj(self):
+    if not self._gpu_available:
+      return
+
+    sparsify = lambda m: m * (m.real > 0)
+    dense_shape = [5, 7, 13]
+    a_mats = sparsify(
+        (np.random.randn(*dense_shape) + 1.j * np.random.randn(*dense_shape))
+        .astype(np.complex64))
+    a_sm = sparse_csr_matrix_ops.CSRSparseMatrix(a_mats)
+    a_sm_conj = a_sm.conj()
+    self.assertIsInstance(a_sm_conj, sparse_csr_matrix_ops.CSRSparseMatrix)
+    a_sm_conj_dense = a_sm_conj.to_dense()
+    a_sm_conj_dense = self.evaluate(a_sm_conj_dense)
+    self.assertAllClose(a_mats.conj(), a_sm_conj_dense)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testTranspose(self):
+    if not self._gpu_available:
+      return
+
+    for conjugate in False, True:
+      sparsify = lambda m: m * (m > 0)
+      dense_shape = [5, 7, 13]
+      a_mats = sparsify((np.random.randn(*dense_shape) +
+                         1.j * np.random.randn(*dense_shape))).astype(
+                             np.complex64)
+      expected = np.transpose(a_mats, (0, 2, 1))
+      if conjugate:
+        expected = np.conj(expected)
+      a_sm = sparse_csr_matrix_ops.CSRSparseMatrix(a_mats)
+      if conjugate:
+        a_sm_t = a_sm.hermitian_transpose()
+      else:
+        a_sm_t = a_sm.transpose()
+      self.assertIsInstance(a_sm_t, sparse_csr_matrix_ops.CSRSparseMatrix)
+      a_sm_t_dense = a_sm_t.to_dense()
+      a_sm_t_dense = self.evaluate(a_sm_t_dense)
+      self.assertAllClose(expected, a_sm_t_dense)
+
+
+class SparseMatrixMatmulTest(test.TestCase):
+
+  @classmethod
+  def setUpClass(cls):  # pylint: disable=g-missing-super-call
+    cls._gpu_available = test_util.is_gpu_available()
+
+  def _testSparseSparse(self, transpose_a, transpose_b, adjoint_a, adjoint_b):
+    if not self._gpu_available:
+      return
+    sparsify = lambda m: m * (m > 0)
+    dense_shape_a = [5, 13, 7] if transpose_a or adjoint_a else [5, 7, 13]
+    dense_shape_b = [5, 15, 13] if transpose_b or adjoint_b else [5, 13, 15]
+    for dtype in np.float32, np.complex64:
+      a_mats = sparsify((np.random.randn(*dense_shape_a) +
+                         1.j * np.random.randn(*dense_shape_a))).astype(dtype)
+      b_mats = sparsify((np.random.randn(*dense_shape_b) +
+                         1.j * np.random.randn(*dense_shape_b))).astype(dtype)
+      a_sm = sparse_csr_matrix_ops.CSRSparseMatrix(a_mats)
+      b_sm = sparse_csr_matrix_ops.CSRSparseMatrix(b_mats)
+      c_dense = math_ops.matmul(
+          a_mats,
+          b_mats,
+          transpose_a=transpose_a,
+          transpose_b=transpose_b,
+          adjoint_a=adjoint_a,
+          adjoint_b=adjoint_b)
+      c_sm = sparse_csr_matrix_ops.matmul(
+          a_sm,
+          b_sm,
+          transpose_a=transpose_a,
+          transpose_b=transpose_b,
+          adjoint_a=adjoint_a,
+          adjoint_b=adjoint_b)
+      self.assertIsInstance(c_sm, sparse_csr_matrix_ops.CSRSparseMatrix)
+      c_sm_dense = c_sm.to_dense()
+      c_dense, c_sm_dense = self.evaluate([c_dense, c_sm_dense])
+      self.assertAllClose(c_dense, c_sm_dense)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testSparseSparse(self):
+    for (t_a, t_b, adj_a, adj_b) in itertools.product(*(([False, True],) * 4)):
+      if (t_a and adj_a) or (t_b and adj_b):
+        continue
+      self._testSparseSparse(t_a, t_b, adj_a, adj_b)
+
+  def _testSparseDense(self, transpose_a, transpose_b, adjoint_a, adjoint_b):
+    if not self._gpu_available:
+      return
+
+    sparsify = lambda m: m * (m > 0)
+    dense_shape_a = [5, 13, 7] if transpose_a or adjoint_a else [5, 7, 13]
+    dense_shape_b = [5, 15, 13] if transpose_b or adjoint_b else [5, 13, 15]
+    for dtype in np.float32, np.complex64:
+      a_mats = sparsify((np.random.randn(*dense_shape_a) +
+                         1.j * np.random.randn(*dense_shape_a))).astype(dtype)
+      b_mats = (np.random.randn(*dense_shape_b) +
+                1.j * np.random.randn(*dense_shape_b)).astype(dtype)
+      a_sm = sparse_csr_matrix_ops.CSRSparseMatrix(a_mats)
+      c_dense = math_ops.matmul(
+          a_mats,
+          b_mats,
+          transpose_a=transpose_a,
+          transpose_b=transpose_b,
+          adjoint_a=adjoint_a,
+          adjoint_b=adjoint_b)
+      c_sm_dense = sparse_csr_matrix_ops.matmul(
+          a_sm,
+          b_mats,
+          transpose_a=transpose_a,
+          transpose_b=transpose_b,
+          adjoint_a=adjoint_a,
+          adjoint_b=adjoint_b)
+      c_dense, c_sm_dense = self.evaluate([c_dense, c_sm_dense])
+      self.assertAllClose(c_dense, c_sm_dense)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testSparseDense(self):
+    for (t_a, t_b, adj_a, adj_b) in itertools.product(*(([False, True],) * 4)):
+      if (t_a and adj_a) or (t_b and adj_b):
+        continue
+      self._testSparseDense(t_a, t_b, adj_a, adj_b)
+
+  def _testDenseSparse(self, transpose_a, transpose_b, adjoint_a, adjoint_b):
+    if not self._gpu_available:
+      return
+
+    sparsify = lambda m: m * (m > 0)
+    dense_shape_a = [5, 13, 7] if transpose_a or adjoint_a else [5, 7, 13]
+    dense_shape_b = [5, 15, 13] if transpose_b or adjoint_b else [5, 13, 15]
+    for dtype in np.float32, np.complex64:
+      a_mats = (np.random.randn(*dense_shape_a) +
+                1.j * np.random.randn(*dense_shape_a)).astype(dtype)
+      b_mats = sparsify((np.random.randn(*dense_shape_b) +
+                         1.j * np.random.randn(*dense_shape_b))).astype(dtype)
+      b_sm = sparse_csr_matrix_ops.CSRSparseMatrix(b_mats)
+      c_dense = math_ops.matmul(
+          a_mats,
+          b_mats,
+          transpose_a=transpose_a,
+          transpose_b=transpose_b,
+          adjoint_a=adjoint_a,
+          adjoint_b=adjoint_b)
+      c_sm_dense = sparse_csr_matrix_ops.matmul(
+          a_mats,
+          b_sm,
+          transpose_a=transpose_a,
+          transpose_b=transpose_b,
+          adjoint_a=adjoint_a,
+          adjoint_b=adjoint_b)
+      c_dense, c_sm_dense = self.evaluate([c_dense, c_sm_dense])
+      self.assertAllClose(c_dense, c_sm_dense)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testDenseSparse(self):
+    for (t_a, t_b, adj_a, adj_b) in itertools.product(*(([False, True],) * 4)):
+      if (t_a and adj_a) or (t_b and adj_b):
+        continue
+      self._testDenseSparse(t_a, t_b, adj_a, adj_b)
+
+
+if __name__ == "__main__":
+  test.main()
diff --git a/tensorflow/python/kernel_tests/sparse_csr_matrix_dense_mat_mul_grad_test.py b/tensorflow/python/kernel_tests/sparse_csr_matrix_dense_mat_mul_grad_test.py
new file mode 100644
index 00000000000..c56ac88249f
--- /dev/null
+++ b/tensorflow/python/kernel_tests/sparse_csr_matrix_dense_mat_mul_grad_test.py
@@ -0,0 +1,138 @@
+# Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+# ==============================================================================
+"""CSR sparse matrix tests."""
+
+from __future__ import absolute_import
+from __future__ import division
+from __future__ import print_function
+
+import itertools
+
+import numpy as np
+
+from tensorflow.python.framework import ops
+from tensorflow.python.framework import test_util
+from tensorflow.python.ops import array_ops
+from tensorflow.python.ops import gradient_checker
+from tensorflow.python.ops import math_ops
+from tensorflow.python.ops.linalg.sparse import sparse_csr_matrix_grad  # pylint: disable=unused-import
+from tensorflow.python.ops.linalg.sparse import sparse_csr_matrix_ops
+from tensorflow.python.platform import test
+from tensorflow.python.platform import tf_logging
+
+
+def dense_to_csr_sparse_matrix(dense):
+  dense_t = ops.convert_to_tensor(dense)
+  locs = array_ops.stop_gradient(array_ops.where(math_ops.abs(dense_t) > 0))
+  return sparse_csr_matrix_ops.dense_to_csr_sparse_matrix(dense_t, locs)
+
+
+def _add_test(test, op_name, testcase_name, fn):  # pylint: disable=redefined-outer-name
+  if fn is None:
+    return
+  test_name = "_".join(["test", op_name, testcase_name])
+  if hasattr(test, test_name):
+    raise RuntimeError("Test %s defined more than once" % test_name)
+  setattr(test, test_name, fn)
+
+
+class CSRSparseMatrixDenseMatMulGradTest(test.TestCase):
+
+  @classmethod
+  def setUpClass(cls):
+    super(CSRSparseMatrixDenseMatMulGradTest, cls).setUpClass()
+    cls._gpu_available = test_util.is_gpu_available()
+
+  # TODO(penporn): Make these tests runnable on eager mode.
+  # (tf.gradients and gradient_checker only run in graph mode.)
+  @test_util.run_deprecated_v1
+  def _testLargeBatchSparseMatrixMatMulGrad(self, datatype, transpose_a,
+                                            transpose_b, adjoint_a, adjoint_b,
+                                            transpose_output, conjugate_output):
+    if not self._gpu_available:
+      return
+
+    sparsify = lambda m: m * (m > 0)
+    a_mats_val = sparsify(
+        np.random.randn(3, 5, 11) +
+        1.j * np.random.randn(3, 5, 11)).astype(datatype)
+    if transpose_a or adjoint_a:
+      a_mats_val = np.transpose(a_mats_val, (0, 2, 1))
+    if adjoint_a:
+      a_mats_val = np.conj(a_mats_val)
+    b_mats_val = (np.random.randn(3, 11, 13) +
+                  1.j * np.random.randn(3, 11, 13)).astype(datatype)
+    if transpose_b or adjoint_b:
+      b_mats_val = np.transpose(b_mats_val, (0, 2, 1))
+    if adjoint_b:
+      b_mats_val = np.conj(b_mats_val)
+    with self.test_session(use_gpu=True):
+      a_mats = ops.convert_to_tensor(a_mats_val, dtype=datatype)
+      b_mats = ops.convert_to_tensor(b_mats_val, dtype=datatype)
+      a_sm = dense_to_csr_sparse_matrix(a_mats)
+      c_mats = sparse_csr_matrix_ops.sparse_matrix_mat_mul(
+          a_sm,
+          b_mats,
+          transpose_a=transpose_a,
+          transpose_b=transpose_b,
+          adjoint_a=adjoint_a,
+          adjoint_b=adjoint_b,
+          transpose_output=transpose_output,
+          conjugate_output=conjugate_output)
+      for [ten, val, nn] in [[a_mats, a_mats_val, "a"],
+                             [b_mats, b_mats_val, "b"]]:
+        tf_logging.info("Testing gradients for %s" % nn)
+        theoretical, numerical = gradient_checker.compute_gradient(
+            ten,
+            ten.get_shape().as_list(),
+            c_mats,
+            c_mats.get_shape().as_list(),
+            x_init_value=val,
+            delta=1e-3)
+        self.assertAllClose(theoretical, numerical, atol=1e-3, rtol=1e-3)
+
+
+# These tests are refactored from sparse_csr_matrix_grad_test to keep its size
+# "medium".
+for dtype in (np.float32, np.complex64):
+  for (t_a, t_b, adj_a, adj_b, t_out,
+       conj_out) in itertools.product(*(([False, True],) * 6)):
+
+    def create_mat_mul_test_fn(dtype_, t_a_, t_b_, adj_a_, adj_b_, t_out_,
+                               conj_out_):
+      # Skip invalid cases.
+      if (t_a_ and adj_a_) or (t_b_ and adj_b_):
+        return
+      # Skip cases where we conjugate real matrices.
+      if dtype_ == np.float32 and (adj_a_ or adj_b_ or conj_out_):
+        return
+
+      def test_fn(self):
+        self._testLargeBatchSparseMatrixMatMulGrad(dtype_, t_a_, t_b_, adj_a_,
+                                                   adj_b_, t_out_, conj_out_)
+
+      return test_fn
+
+    name = (
+        "_testLargeBatchSparseMatrixMatMulGrad_dtype_%s_t_a_%s_t_b_%s_adj_a_%s_"
+        "adj_b_%s_t_out_%s_conj_out_%s" %
+        (dtype.__name__, t_a, t_b, adj_a, adj_b, t_out, conj_out))
+
+    _add_test(
+        CSRSparseMatrixDenseMatMulGradTest, "CSRSparseMatrixGradTest", name,
+        create_mat_mul_test_fn(dtype, t_a, t_b, adj_a, adj_b, t_out, conj_out))
+
+if __name__ == "__main__":
+  test.main()
diff --git a/tensorflow/python/kernel_tests/sparse_csr_matrix_grad_test.py b/tensorflow/python/kernel_tests/sparse_csr_matrix_grad_test.py
new file mode 100644
index 00000000000..e6425fcdc94
--- /dev/null
+++ b/tensorflow/python/kernel_tests/sparse_csr_matrix_grad_test.py
@@ -0,0 +1,119 @@
+# Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+# ==============================================================================
+"""CSR sparse matrix tests."""
+
+from __future__ import absolute_import
+from __future__ import division
+from __future__ import print_function
+
+import numpy as np
+
+from tensorflow.python.framework import dtypes
+from tensorflow.python.framework import ops
+from tensorflow.python.framework import test_util
+from tensorflow.python.ops import array_ops
+from tensorflow.python.ops import gradients_impl
+from tensorflow.python.ops import math_ops
+from tensorflow.python.ops.linalg.sparse import sparse_csr_matrix_grad  # pylint: disable=unused-import
+from tensorflow.python.ops.linalg.sparse import sparse_csr_matrix_ops
+from tensorflow.python.platform import test
+from tensorflow.python.platform import tf_logging
+
+
+def dense_to_csr_sparse_matrix(dense):
+  dense_t = ops.convert_to_tensor(dense)
+  locs = array_ops.stop_gradient(array_ops.where(math_ops.abs(dense_t) > 0))
+  return sparse_csr_matrix_ops.dense_to_csr_sparse_matrix(dense_t, locs)
+
+
+def _add_test(test, op_name, testcase_name, fn):  # pylint: disable=redefined-outer-name
+  if fn is None:
+    return
+  test_name = "_".join(["test", op_name, testcase_name])
+  if hasattr(test, test_name):
+    raise RuntimeError("Test %s defined more than once" % test_name)
+  setattr(test, test_name, fn)
+
+
+class CSRSparseMatrixGradTest(test.TestCase):
+
+  @classmethod
+  def setUpClass(cls):
+    super(CSRSparseMatrixGradTest, cls).setUpClass()
+    cls._gpu_available = test_util.is_gpu_available()
+
+  # TODO(penporn): Make these tests runnable on eager mode.
+  # (tf.gradients and gradient_checker only run in graph mode.)
+  @test_util.run_deprecated_v1
+  def testLargeBatchConversionGrad(self):
+    if not self._gpu_available:
+      return
+
+    sparsify = lambda m: m * (m > 0)
+    for dense_shape in ([53, 65, 127], [127, 65]):
+      mats_val = sparsify(np.random.randn(*dense_shape))
+      with self.test_session(use_gpu=True) as sess:
+        mats = math_ops.cast(mats_val, dtype=dtypes.float32)
+        sparse_mats = dense_to_csr_sparse_matrix(mats)
+        dense_mats = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+            sparse_mats, dtypes.float32)
+        grad_vals = np.random.randn(*dense_shape).astype(np.float32)
+        grad_out = gradients_impl.gradients([dense_mats], [mats],
+                                            [grad_vals])[0]
+        self.assertEqual(grad_out.dtype, dtypes.float32)
+        self.assertEqual(grad_out.shape, dense_shape)
+        grad_out_value = sess.run(grad_out)
+        tf_logging.info("testLargeBatchConversionGrad: Testing shape %s" %
+                        dense_shape)
+        self.assertAllEqual(grad_vals, grad_out_value)
+
+  @test_util.run_deprecated_v1
+  def testLargeBatchSparseMatrixAddGrad(self):
+    if not self._gpu_available:
+      return
+
+    sparsify = lambda m: m * (m > 0)
+    for dense_shape in ([53, 65, 127], [127, 65]):
+      a_mats_val = sparsify(np.random.randn(*dense_shape))
+      b_mats_val = sparsify(np.random.randn(*dense_shape))
+      alpha = np.float32(0.5)
+      beta = np.float32(-1.5)
+      grad_vals = np.random.randn(*dense_shape).astype(np.float32)
+      expected_a_grad = alpha * grad_vals
+      expected_b_grad = beta * grad_vals
+      with self.test_session(use_gpu=True) as sess:
+        a_mats = math_ops.cast(a_mats_val, dtype=dtypes.float32)
+        b_mats = math_ops.cast(b_mats_val, dtype=dtypes.float32)
+        a_sm = dense_to_csr_sparse_matrix(a_mats)
+        b_sm = dense_to_csr_sparse_matrix(b_mats)
+        c_sm = sparse_csr_matrix_ops.sparse_matrix_add(
+            a_sm, b_sm, alpha=alpha, beta=beta)
+        c_dense = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+            c_sm, dtypes.float32)
+        a_grad, b_grad = gradients_impl.gradients([c_dense], [a_mats, b_mats],
+                                                  [grad_vals])
+        self.assertEqual(a_grad.dtype, dtypes.float32)
+        self.assertEqual(b_grad.dtype, dtypes.float32)
+        self.assertEqual(a_grad.shape, dense_shape)
+        self.assertEqual(b_grad.shape, dense_shape)
+        a_grad_value, b_grad_value = sess.run((a_grad, b_grad))
+        tf_logging.info("testLargeBatchConversionGrad: Testing shape %s" %
+                        dense_shape)
+        self.assertAllEqual(expected_a_grad, a_grad_value)
+        self.assertAllEqual(expected_b_grad, b_grad_value)
+
+
+if __name__ == "__main__":
+  test.main()
diff --git a/tensorflow/python/kernel_tests/sparse_csr_matrix_ops_test.py b/tensorflow/python/kernel_tests/sparse_csr_matrix_ops_test.py
new file mode 100644
index 00000000000..ad564ea631f
--- /dev/null
+++ b/tensorflow/python/kernel_tests/sparse_csr_matrix_ops_test.py
@@ -0,0 +1,1511 @@
+# Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+# ==============================================================================
+"""CSR sparse matrix tests."""
+
+from __future__ import absolute_import
+from __future__ import division
+from __future__ import print_function
+
+import numpy as np
+from scipy import sparse
+
+from tensorflow.core.framework import tensor_pb2
+from tensorflow.core.protobuf import config_pb2
+from tensorflow.python.client import session
+from tensorflow.python.framework import constant_op
+from tensorflow.python.framework import dtypes
+from tensorflow.python.framework import errors
+from tensorflow.python.framework import ops
+from tensorflow.python.framework import sparse_tensor
+from tensorflow.python.framework import tensor_shape
+from tensorflow.python.framework import tensor_util
+from tensorflow.python.framework import test_util
+from tensorflow.python.ops import array_ops
+from tensorflow.python.ops import linalg_ops
+from tensorflow.python.ops import math_ops
+from tensorflow.python.ops import nn_ops
+from tensorflow.python.ops import random_ops
+from tensorflow.python.ops import state_ops
+from tensorflow.python.ops import variable_scope
+from tensorflow.python.ops.linalg.sparse import sparse_csr_matrix_ops
+from tensorflow.python.platform import test
+from tensorflow.python.platform import tf_logging
+
+CPU = "/device:CPU:0"
+GPU = "/device:GPU:0"
+
+
+def dense_to_csr_sparse_matrix(dense):
+  dense_t = ops.convert_to_tensor(dense)
+  locs = array_ops.stop_gradient(array_ops.where(math_ops.abs(dense_t) > 0))
+  return sparse_csr_matrix_ops.dense_to_csr_sparse_matrix(dense_t, locs)
+
+
+def _swap(a, i, j):
+  a[i], a[j] = a[j], a[i]
+
+
+class CSRSparseMatrixOpsTest(test.TestCase):
+
+  @classmethod
+  def setUpClass(cls):  # pylint: disable=g-missing-super-call
+    cls._gpu_available = test_util.is_gpu_available()
+
+  # TODO(ebrevdo): This will work once we find a way to get rendezvous
+  # working for CSRSparseMatrix and can remove the HostMemory
+  # annotations for the other ops.
+  @test_util.run_in_graph_and_eager_modes
+  def DISABLEDtestFromProto(self):
+    if not self._gpu_available:
+      return
+
+    a_indices = np.array([[0, 0], [2, 3]])
+    a_values = np.asarray([1.0, 5.0], dtype=np.float32)
+    a_dense_shape = np.asarray([5, 6], dtype=np.int64)
+    a_sparse_mat = sparse.coo_matrix((a_values,
+                                      (a_indices[:, 0], a_indices[:, 1])),
+                                     shape=a_dense_shape)
+    a_csr_mat = a_sparse_mat.tocsr()
+    a_col_inds = a_csr_mat.indices
+    a_row_ptrs = a_csr_mat.indptr
+
+    # Format of SparseMatrix:
+    #  type_name == "tensorflow::CSRSparseMatrix"
+    #  metadata == b (validated)
+    #  tensors == [dense_shape, row_ptrs, col_indices, values]
+    dense_shape_proto = tensor_util.make_tensor_proto(a_dense_shape)
+    row_ptrs_proto = tensor_util.make_tensor_proto(a_row_ptrs)
+    col_inds_proto = tensor_util.make_tensor_proto(a_col_inds)
+    values_proto = tensor_util.make_tensor_proto(a_values)
+    variant_tensor_data = tensor_pb2.VariantTensorDataProto(
+        type_name="tensorflow::CSRSparseMatrix",
+        metadata=np.asarray(True).tobytes(),
+        tensors=[
+            dense_shape_proto, row_ptrs_proto, col_inds_proto, values_proto
+        ])
+    tensor_proto = tensor_pb2.TensorProto(
+        dtype=dtypes.variant.as_datatype_enum,
+        tensor_shape=tensor_shape.TensorShape([]).as_proto())
+    tensor_proto.variant_val.extend([variant_tensor_data])
+    a_sm = constant_op.constant(tensor_proto)
+    a_rt = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+        a_sm, type=dtypes.float32)
+    self.evaluate(a_rt)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testSparseTensorConversion(self):
+    a_indices = np.array([[0, 0], [2, 3], [2, 4], [3, 0]])
+    a_values = [1.0, 5.0, -1.0, -2.0]
+    a_dense_shape = [5, 6]
+    a_sparse_mat = sparse.coo_matrix((a_values,
+                                      (a_indices[:, 0], a_indices[:, 1])),
+                                     shape=a_dense_shape)
+    a_csr_mat = a_sparse_mat.tocsr()
+
+    # Convert 2D SparseTensor to CSR Matrix
+    a_st = sparse_tensor.SparseTensor(a_indices, a_values, a_dense_shape)
+    a_st = math_ops.cast(a_st, dtypes.float32)
+    a_sm = sparse_csr_matrix_ops.sparse_tensor_to_csr_sparse_matrix(
+        a_st.indices, a_st.values, a_st.dense_shape)
+
+    # Get row indices and columns for batch 0.
+    a_sm_row_ptrs, a_sm_col_inds, a_sm_values = (
+        sparse_csr_matrix_ops.csr_sparse_matrix_components(
+            a_sm, 0, type=a_st.dtype))
+
+    a_sm_row_ptrs_values, a_sm_col_inds_values, a_sm_values_values = (
+        self.evaluate((a_sm_row_ptrs, a_sm_col_inds, a_sm_values)))
+
+    self.assertAllEqual(a_csr_mat.indices, a_sm_col_inds_values)
+    self.assertAllEqual(a_csr_mat.indptr, a_sm_row_ptrs_values)
+    self.assertAllClose(a_values, a_sm_values_values)
+
+    # Convert CSR Matrix to 2D SparseTensor
+    a_st_rt = sparse_csr_matrix_ops.csr_sparse_matrix_to_sparse_tensor(
+        a_sm, type=a_st.dtype)
+    a_st_rt_value = self.evaluate(a_st_rt)
+
+    self.assertAllEqual(a_indices, a_st_rt_value.indices)
+    self.assertAllClose(a_values, a_st_rt_value.values)
+    self.assertAllEqual(a_dense_shape, a_st_rt_value.dense_shape)
+
+  # TODO(b/139491352): Add handle_data propagation to array_ops.identity.
+  @test_util.run_deprecated_v1
+  def testCSRSparseMatrixResourceVariable(self):
+    if not self._gpu_available:
+      return
+
+    sparsify = lambda m: m * (m > 0)
+    dense_shape = [53, 65, 127]
+    a_mats = sparsify(np.random.randn(*dense_shape)).astype(np.float32)
+
+    a_sm = dense_to_csr_sparse_matrix(a_mats)
+    with ops.device("/gpu:0"):
+      v = variable_scope.get_variable("sm", initializer=a_sm, use_resource=True)
+      v_id = array_ops.identity(v)
+      self.assertEqual(
+          sparse_csr_matrix_ops.dense_shape_and_type(v_id).shape, a_mats.shape)
+      a_rt = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+          v, type=dtypes.float32)
+    v_reassign = state_ops.assign(v, v_id).op
+    with self.assertRaisesOpError("Error while reading resource variable sm"):
+      self.evaluate(a_rt)
+    self.evaluate(v.initializer)
+    a_rt_value = self.evaluate(a_rt)
+    self.assertAllClose(a_mats, a_rt_value)
+    self.evaluate(v_reassign)
+    a_rt_reassigned_value = self.evaluate(a_rt)
+    self.assertAllClose(a_mats, a_rt_reassigned_value)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testBatchSparseTensorConversion(self):
+    a_indices = np.array([[0, 0, 0], [0, 2, 3], [2, 0, 1]])
+    a_values = [1.0, 5.0, 6.0]
+    a_dense_shape = [3, 5, 6]
+    a_sparse_mats = [
+        sparse.coo_matrix(([1.0, 5.0], ([0, 2], [0, 3])),
+                          shape=a_dense_shape[1:]),
+        sparse.coo_matrix(([], ([], [])), shape=a_dense_shape[1:]),
+        sparse.coo_matrix(([6.0], ([0], [1])), shape=a_dense_shape[1:])
+    ]
+    a_csr_mats = [m.tocsr() for m in a_sparse_mats]
+
+    # Convert 3D SparseTensor to CSR Matrix
+    a_st = sparse_tensor.SparseTensor(a_indices, a_values, a_dense_shape)
+    a_st = math_ops.cast(a_st, dtypes.float32)
+    a_sm = sparse_csr_matrix_ops.sparse_tensor_to_csr_sparse_matrix(
+        a_st.indices, a_st.values, a_st.dense_shape)
+
+    # Get row indices and columns for batches.
+    a_sm_components = [
+        sparse_csr_matrix_ops.csr_sparse_matrix_components(
+            a_sm, i, type=a_st.dtype) for i in range(3)
+    ]
+
+    a_sm_values = self.evaluate(a_sm_components)
+
+    for i, (a_sm_val, a_csr_mat) in enumerate(zip(a_sm_values, a_csr_mats)):
+      tf_logging.info("Comparing batch %d" % i)
+      self.assertAllEqual(a_csr_mat.indptr, a_sm_val.row_ptrs)
+      self.assertAllEqual(a_csr_mat.indices, a_sm_val.col_inds)
+      self.assertAllClose(a_csr_mat.data, a_sm_val.values)
+
+    # Convert CSR batched Matrix to 3D SparseTensor
+    a_st_rt = sparse_csr_matrix_ops.csr_sparse_matrix_to_sparse_tensor(
+        a_sm, type=a_st.dtype)
+    a_st_rt_value = self.evaluate(a_st_rt)
+
+    self.assertAllEqual(a_indices, a_st_rt_value.indices)
+    self.assertAllClose(a_values, a_st_rt_value.values)
+    self.assertAllEqual(a_dense_shape, a_st_rt_value.dense_shape)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testLargeBatchSparseTensorConversion(self):
+    # Test two sets of conversions to check behavior of the ops in a
+    # concurrent environment (parallel executions of the ST -> SM ops).
+
+    sparsify = lambda m: m * (m > 0)
+    dense_shape = [53, 65, 127]
+
+    mats = [
+        sparsify(np.random.randn(*dense_shape)).astype(np.float32)
+        for _ in range(2)
+    ]
+    csr_mats = [list(map(sparse.csr_matrix, mat)) for mat in mats]
+    mats_t = [ops.convert_to_tensor(mat) for mat in mats]
+    mats_locs = [array_ops.where(mat_t > 0) for mat_t in mats_t]
+    sparse_tensors = list()
+    for mat_t, mat_loc in zip(mats_t, mats_locs):
+      sparse_tensors.append(
+          sparse_tensor.SparseTensor(mat_loc,
+                                     array_ops.gather_nd(mat_t,
+                                                         mat_loc), dense_shape))
+    sparse_matrices = [
+        sparse_csr_matrix_ops.sparse_tensor_to_csr_sparse_matrix(
+            st.indices, st.values, st.dense_shape) for st in sparse_tensors
+    ]
+    sm_nnz = [
+        sparse_csr_matrix_ops.sparse_matrix_nnz(sm) for sm in sparse_matrices
+    ]
+
+    # Get row indices and columns for batches.
+    sm_components = list()
+    for sm in sparse_matrices:
+      sm_components.append([
+          sparse_csr_matrix_ops.csr_sparse_matrix_components(
+              sm, i, type=dtypes.float32) for i in range(dense_shape[0])
+      ])
+
+    sm_nnz_values, sm_values = self.evaluate((sm_nnz, sm_components))
+
+    for i, (sm_values_i, csr_mats_i) in enumerate(zip(sm_values, csr_mats)):
+      for b, (sm_val, csr_mat) in enumerate(zip(sm_values_i, csr_mats_i)):
+        tf_logging.info("Comparing matrix %d batch %d" % (i, b))
+        self.assertEqual(csr_mat.nnz, sm_nnz_values[i][b])
+        self.assertAllEqual(csr_mat.indptr, sm_val.row_ptrs)
+        self.assertAllEqual(csr_mat.indices, sm_val.col_inds)
+        self.assertAllClose(csr_mat.data, sm_val.values)
+
+    # Convert CSR batched Matrix to 3D SparseTensor
+    st_rt = [
+        sparse_csr_matrix_ops.csr_sparse_matrix_to_sparse_tensor(
+            sm, type=dtypes.float32) for sm in sparse_matrices
+    ]
+
+    st_values, st_rt_values = self.evaluate((sparse_tensors, st_rt))
+
+    for (st_value, st_rt_value) in zip(st_values, st_rt_values):
+      self.assertAllEqual(st_value.indices, st_rt_value.indices)
+      self.assertAllClose(st_value.values, st_rt_value.values)
+      self.assertAllEqual(dense_shape, st_rt_value.dense_shape)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testDenseConversion(self):
+    a_indices = np.array([[0, 0], [2, 3], [2, 4], [3, 0]])
+    a_values = np.array([1.0, 5.0, -1.0, -2.0]).astype(np.float32)
+    a_dense_shape = [5, 6]
+    a_sparse_mat = sparse.coo_matrix((a_values,
+                                      (a_indices[:, 0], a_indices[:, 1])),
+                                     shape=a_dense_shape)
+    a_csr_mat = a_sparse_mat.tocsr()
+    a_dense = a_sparse_mat.todense()
+
+    # Convert 2D SparseTensor to CSR Matrix
+    a_sm = dense_to_csr_sparse_matrix(a_dense)
+
+    # Get row indices and columns for batch 0.
+    a_sm_row_ptrs, a_sm_col_inds, a_sm_values = (
+        sparse_csr_matrix_ops.csr_sparse_matrix_components(
+            a_sm, 0, type=dtypes.float32))
+
+    a_sm_row_ptrs_values, a_sm_col_inds_values, a_sm_values_values = (
+        self.evaluate((a_sm_row_ptrs, a_sm_col_inds, a_sm_values)))
+
+    self.assertAllEqual(a_csr_mat.indices, a_sm_col_inds_values)
+    self.assertAllEqual(a_csr_mat.indptr, a_sm_row_ptrs_values)
+    self.assertAllClose(a_values, a_sm_values_values)
+
+    # Convert CSR Matrix to 2D dense matrix
+    a_rt = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+        a_sm, dtypes.float32)
+    a_rt_value = self.evaluate(a_rt)
+
+    self.assertAllEqual(a_dense, a_rt_value)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testBatchDenseConversion(self):
+    a_dense_shape = [4, 5, 6]
+    a_sparse_mats = [
+        sparse.coo_matrix(([1.0, 5.0], ([0, 2], [0, 3])),
+                          shape=a_dense_shape[1:]),
+        sparse.coo_matrix(([], ([], [])), shape=a_dense_shape[1:]),
+        sparse.coo_matrix(([6.0], ([0], [1])), shape=a_dense_shape[1:]),
+        sparse.coo_matrix(([], ([], [])), shape=a_dense_shape[1:]),
+    ]
+    a_csr_mats = [m.tocsr() for m in a_sparse_mats]
+    a_dense = np.asarray([m.todense() for m in a_sparse_mats], dtype=np.float32)
+
+    # Convert 3D SparseTensor to CSR Matrix
+    a_sm = dense_to_csr_sparse_matrix(a_dense)
+
+    # Get row indices and columns for batches.
+    a_sm_components = [
+        sparse_csr_matrix_ops.csr_sparse_matrix_components(
+            a_sm, i, type=dtypes.float32) for i in range(3)
+    ]
+
+    a_sm_values = self.evaluate(a_sm_components)
+
+    for i, (a_sm_val, a_csr_mat) in enumerate(zip(a_sm_values, a_csr_mats)):
+      tf_logging.info("Comparing batch %d" % i)
+      self.assertAllEqual(a_csr_mat.indptr, a_sm_val.row_ptrs)
+      self.assertAllEqual(a_csr_mat.indices, a_sm_val.col_inds)
+      self.assertAllClose(a_csr_mat.data, a_sm_val.values)
+
+    # Convert CSR batched Matrix to 3D SparseTensor
+    a_rt = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+        a_sm, type=dtypes.float32)
+    a_rt_value = self.evaluate(a_rt)
+
+    self.assertAllEqual(a_dense, a_rt_value)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testLargeBatchDenseConversion(self):
+    # Test two sets of conversions to check behavior of the ops in a
+    # concurrent environment (parallel executions of the ST -> SM
+    # ops).
+
+    sparsify = lambda m: m * (m > 0)
+    dense_shape = [53, 65, 127]
+
+    mats = [
+        sparsify(np.random.randn(*dense_shape)).astype(np.float32)
+        for _ in range(2)
+    ]
+    csr_mats = [[sparse.csr_matrix(m) for m in mat] for mat in mats]
+    mats_t = [ops.convert_to_tensor(mat) for mat in mats]
+    mats_locs = [array_ops.where(mat_t > 0) for mat_t in mats_t]
+    sparse_matrices = [
+        sparse_csr_matrix_ops.dense_to_csr_sparse_matrix(mat, mat_loc)
+        for (mat, mat_loc) in zip(mats_t, mats_locs)
+    ]
+    sm_nnz = [
+        sparse_csr_matrix_ops.sparse_matrix_nnz(sm) for sm in sparse_matrices
+    ]
+
+    # Get row indices and columns for batches.
+    sm_components = []
+    for sm in sparse_matrices:
+      sm_components.append([
+          sparse_csr_matrix_ops.csr_sparse_matrix_components(
+              sm, i, type=dtypes.float32) for i in range(dense_shape[0])
+      ])
+
+    sm_nnz_values, sm_values = self.evaluate((sm_nnz, sm_components))
+
+    for i, (sm_values_i, csr_mats_i) in enumerate(zip(sm_values, csr_mats)):
+      for b, (sm_val, csr_mat) in enumerate(zip(sm_values_i, csr_mats_i)):
+        tf_logging.info("Comparing matrix %d batch %d" % (i, b))
+        self.assertEqual(csr_mat.nnz, sm_nnz_values[i][b])
+        self.assertAllEqual(csr_mat.indptr, sm_val.row_ptrs)
+        self.assertAllEqual(csr_mat.indices, sm_val.col_inds)
+        self.assertAllClose(csr_mat.data, sm_val.values)
+
+    # Convert CSR batched Matrix to 3D dense tensor
+    sm_rt = [
+        sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+            sm, type=dtypes.float32) for sm in sparse_matrices
+    ]
+
+    sm_rt_values = self.evaluate(sm_rt)
+
+    for (mat, sm_rt_value) in zip(mats, sm_rt_values):
+      self.assertAllEqual(mat, sm_rt_value)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testSparseMatrixAdd(self):
+    if not self._gpu_available:
+      return
+
+    a_indices = np.array([[0, 0], [2, 3]])
+    a_values = np.array([1.0, 5.0]).astype(np.float32)
+    a_dense_shape = [5, 6]
+    a_sparse_mat = sparse.coo_matrix((a_values,
+                                      (a_indices[:, 0], a_indices[:, 1])),
+                                     shape=a_dense_shape)
+    a_dense = a_sparse_mat.todense()
+
+    b_indices = np.array([[1, 0], [1, 4], [2, 3], [4, 1]])
+    b_values = np.array([1.0, 0.5, -5.0, 2.0]).astype(np.float32)
+    b_dense_shape = [5, 6]
+    b_sparse_mat = sparse.coo_matrix((b_values,
+                                      (b_indices[:, 0], b_indices[:, 1])),
+                                     shape=b_dense_shape)
+    b_dense = b_sparse_mat.todense()
+
+    for (alpha, beta) in [(1.0, 1.0), (1.0, -1.0), (0.25, 0.5)]:
+      a_sum_b_sparse_mat = alpha * a_sparse_mat + beta * b_sparse_mat
+
+      # Convert 2D SparseTensor to CSR Matrix
+      a_sm = dense_to_csr_sparse_matrix(a_dense)
+      b_sm = dense_to_csr_sparse_matrix(b_dense)
+      alpha = np.float32(alpha)
+      beta = np.float32(beta)
+      c_sm = sparse_csr_matrix_ops.sparse_matrix_add(
+          a_sm, b_sm, alpha=alpha, beta=beta)
+      c_dense = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+          c_sm, dtypes.float32)
+      c_dense_value = self.evaluate(c_dense)
+
+      self.assertAllClose(a_sum_b_sparse_mat.todense(), c_dense_value)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testLargeBatchSparseMatrixAdd(self):
+    if not self._gpu_available:
+      return
+
+    sparsify = lambda m: m * (m > 0)
+    dense_shape = [53, 65, 127]
+    a_mats = sparsify(np.random.randn(*dense_shape)).astype(np.float32)
+    b_mats = sparsify(np.random.randn(*dense_shape)).astype(np.float32)
+    for (alpha, beta) in [(1.0, 1.0), (1.0, -1.0), (0.25, 0.5)]:
+      tf_logging.info("testLargeBatchSparseMatrixAdd, comparing "
+                      "alpha, beta (%d, %d)" % (alpha, beta))
+      a_sm = dense_to_csr_sparse_matrix(a_mats)
+      b_sm = dense_to_csr_sparse_matrix(b_mats)
+      alpha = np.float32(alpha)
+      beta = np.float32(beta)
+      c_sm = sparse_csr_matrix_ops.sparse_matrix_add(
+          a_sm, b_sm, alpha=alpha, beta=beta)
+      c_dense = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+          c_sm, dtypes.float32)
+      c_dense_value = self.evaluate(c_dense)
+
+      self.assertAllClose(c_dense_value, alpha * a_mats + beta * b_mats)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testSparseMatrixMatMul(self):
+    if not self._gpu_available:
+      return
+    for shapes in [[(5, 6), (6, 1)], [(5, 6), (6, 2)]]:
+      a_indices = np.array([[0, 0], [2, 3]])
+      a_values = np.array([1.0, 5.0]).astype(np.float32)
+      a_dense_shape = shapes[0]
+      a_sparse_mat = sparse.coo_matrix((a_values,
+                                        (a_indices[:, 0], a_indices[:, 1])),
+                                       shape=a_dense_shape)
+      a_dense = a_sparse_mat.todense()
+
+      # Will multiply sparse a (shape=shapes[0]) by dense b (shape=shapes[1]).
+      b = np.random.randn(*shapes[1]).astype(np.float32)
+
+      a_sm = dense_to_csr_sparse_matrix(a_dense)
+      c = sparse_csr_matrix_ops.sparse_matrix_mat_mul(a=a_sm, b=b)
+      c_value = self.evaluate(c)
+
+      expected_c_value = a_sparse_mat.dot(b)
+      self.assertAllClose(expected_c_value, c_value)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testLargeBatchSparseMatrixMatMul(self):
+    if not self._gpu_available:
+      return
+
+    sparsify = lambda m: m * (m > 0)
+    for dtype in np.float32, np.complex64:
+      for (transpose_a, transpose_b) in ((False, False), (False, True),
+                                         (True, False), (True, True)):
+        for (adjoint_a, adjoint_b) in ((False, False), (False, True),
+                                       (True, False), (True, True)):
+          if (transpose_a and adjoint_a) or (transpose_b and adjoint_b):
+            continue
+          for shapes in [[[53, 127, 65], [53, 65, 1]],
+                         [[53, 127, 1], [53, 1, 65]],
+                         [[53, 127, 65], [53, 65, 127]]]:
+            a_dense_shape = shapes[0]
+            b_dense_shape = shapes[1]
+            if transpose_a or adjoint_a:
+              _swap(a_dense_shape, -2, -1)
+            if transpose_b or adjoint_b:
+              _swap(b_dense_shape, -2, -1)
+            a_mats = sparsify(
+                (np.random.randn(*a_dense_shape) +
+                 1.j * np.random.randn(*a_dense_shape))).astype(dtype)
+            b_mats = (np.random.randn(*b_dense_shape) +
+                      1.j * np.random.randn(*b_dense_shape)).astype(dtype)
+            tf_logging.info(
+                "testLargeBatchSparseMatrixMatMul transpose_a %s transpose_b "
+                "%s adjoint_a %s adjoint_b %s" %
+                (transpose_a, transpose_b, adjoint_a, adjoint_b))
+            a_sm = dense_to_csr_sparse_matrix(a_mats)
+            c_t = sparse_csr_matrix_ops.sparse_matrix_mat_mul(
+                a_sm,
+                b_mats,
+                transpose_output=False,
+                conjugate_output=False,
+                transpose_a=transpose_a,
+                transpose_b=transpose_b,
+                adjoint_a=adjoint_a,
+                adjoint_b=adjoint_b)
+            c_dense_t = math_ops.matmul(
+                a_mats,
+                b_mats,
+                transpose_a=transpose_a,
+                transpose_b=transpose_b,
+                adjoint_a=adjoint_a,
+                adjoint_b=adjoint_b)
+            self.assertAllEqual(c_dense_t.shape, c_t.shape)
+            c_t_value, c_dense_t_value = self.evaluate((c_t, c_dense_t))
+
+            self.assertAllClose(
+                c_t_value, c_dense_t_value, rtol=1e-6, atol=1e-5)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testLargeBatchSparseMatrixMatMulTransposed(self):
+    if not self._gpu_available:
+      return
+
+    sparsify = lambda m: m * (m > 0)
+    for dtype in np.float32, np.complex64:
+      for (transpose_a, transpose_b) in ((False, False), (False, True),
+                                         (True, False), (True, True)):
+        for (adjoint_a, adjoint_b) in ((False, False), (False, True),
+                                       (True, False), (True, True)):
+          if (transpose_a and adjoint_a) or (transpose_b and adjoint_b):
+            continue
+          for shapes in [[[53, 127, 65], [53, 65, 1]],
+                         [[53, 127, 1], [53, 1, 65]],
+                         [[53, 127, 65], [53, 65, 127]]]:
+            a_dense_shape = shapes[0]
+            b_dense_shape = shapes[1]
+            if transpose_a or adjoint_a:
+              _swap(a_dense_shape, -2, -1)
+            if transpose_b or adjoint_b:
+              _swap(b_dense_shape, -2, -1)
+            a_mats = sparsify(
+                (np.random.randn(*a_dense_shape) +
+                 1.j * np.random.randn(*a_dense_shape))).astype(dtype)
+            b_mats = (np.random.randn(*b_dense_shape) +
+                      1.j * np.random.randn(*b_dense_shape)).astype(dtype)
+            tf_logging.info(
+                "testLargeBatchSparseMatrixMatMul transpose_a %s transpose_b "
+                "%s adjoint_a %s adjoint_b %s" %
+                (transpose_a, transpose_b, adjoint_a, adjoint_b))
+            a_sm = dense_to_csr_sparse_matrix(a_mats)
+            c_t = sparse_csr_matrix_ops.sparse_matrix_mat_mul(
+                a_sm,
+                b_mats,
+                transpose_output=True,
+                conjugate_output=False,
+                transpose_a=transpose_a,
+                transpose_b=transpose_b,
+                adjoint_a=adjoint_a,
+                adjoint_b=adjoint_b)
+
+            # Example: t(adj(a) . b) = t(b) . conj(a)
+            c_dense_t = math_ops.matmul(
+                math_ops.conj(b_mats) if adjoint_b else b_mats,
+                math_ops.conj(a_mats) if adjoint_a else a_mats,
+                transpose_a=not (transpose_b or adjoint_b),
+                transpose_b=not (transpose_a or adjoint_a),
+                adjoint_a=False,
+                adjoint_b=False)
+            self.assertAllEqual(c_t.shape, c_dense_t.shape)
+            c_t_value, c_dense_t_value = self.evaluate((c_t, c_dense_t))
+            self.assertAllClose(
+                c_t_value, c_dense_t_value, rtol=1e-6, atol=1e-5)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testLargeBatchSparseMatrixMatMulConjugate(self):
+    if not self._gpu_available:
+      return
+
+    sparsify = lambda m: m * (m > 0)
+    a_dense_shape = [53, 65, 127]
+    b_dense_shape = [53, 127, 67]
+    a_mats = sparsify(
+        (np.random.randn(*a_dense_shape) +
+         1.j * np.random.randn(*a_dense_shape))).astype(np.complex64)
+    b_mats = (np.random.randn(*b_dense_shape) +
+              1.j * np.random.randn(*b_dense_shape)).astype(np.complex64)
+    a_sm = dense_to_csr_sparse_matrix(a_mats)
+    c_t = sparse_csr_matrix_ops.sparse_matrix_mat_mul(
+        a_sm, b_mats, conjugate_output=True)
+
+    c_dense_t = math_ops.conj(math_ops.matmul(a_mats, b_mats))
+    self.assertAllEqual(c_t.shape, c_dense_t.shape)
+    c_t_value, c_dense_t_value = self.evaluate((c_t, c_dense_t))
+
+    self.assertAllClose(c_t_value, c_dense_t_value, atol=1e-5, rtol=1e-5)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testSparseMatrixSparseMatMul(self):
+    a_indices = np.array([[0, 0], [2, 3]])
+    a_values = np.array([1.0, 5.0]).astype(np.float32)
+    a_dense_shape = [5, 6]
+    a_sparse_mat = sparse.coo_matrix((a_values,
+                                      (a_indices[:, 0], a_indices[:, 1])),
+                                     shape=a_dense_shape)
+    a_dense = a_sparse_mat.todense()
+
+    b_indices = np.array([[0, 0], [3, 0], [3, 1]])
+    b_values = np.array([2.0, 7.0, 8.0]).astype(np.float32)
+    b_dense_shape = [6, 7]
+    b_sparse_mat = sparse.coo_matrix((b_values,
+                                      (b_indices[:, 0], b_indices[:, 1])),
+                                     shape=b_dense_shape)
+    b_dense = b_sparse_mat.todense()
+
+    a_sm = dense_to_csr_sparse_matrix(a_dense)
+    b_sm = dense_to_csr_sparse_matrix(b_dense)
+    c_sm = sparse_csr_matrix_ops.sparse_matrix_sparse_mat_mul(
+        a=a_sm, b=b_sm, type=dtypes.float32)
+
+    c_sm_dense = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+        c_sm, dtypes.float32)
+    c_sm_dense_value = self.evaluate(c_sm_dense)
+
+    expected_c_value = a_sparse_mat.dot(b_sparse_mat).todense()
+    self.assertAllClose(expected_c_value, c_sm_dense_value)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testSparseMatrixSparseMatMul_NumericZerosNotPruned(self):
+    # Tests that numeric zeros appearing from the sparse-sparse matrix
+    # multiplication are not pruned from the sparse structural
+    a_indices = np.array([[0, 0], [0, 2]])
+    a_values = np.array([2.0, -1.0]).astype(np.float32)
+    a_dense_shape = [2, 3]
+    a_sparse_mat = sparse.coo_matrix((a_values,
+                                      (a_indices[:, 0], a_indices[:, 1])),
+                                     shape=a_dense_shape)
+    a_dense = a_sparse_mat.todense()
+
+    b_indices = np.array([[0, 1], [2, 1]])
+    b_values = np.array([3.0, 6.0]).astype(np.float32)
+    b_dense_shape = [3, 2]
+    b_sparse_mat = sparse.coo_matrix((b_values,
+                                      (b_indices[:, 0], b_indices[:, 1])),
+                                     shape=b_dense_shape)
+    b_dense = b_sparse_mat.todense()
+
+    # Convert to CSRSparseMatrix while removing numeric zeros from the
+    # structural representation.
+    a_sm = dense_to_csr_sparse_matrix(a_dense)
+    b_sm = dense_to_csr_sparse_matrix(b_dense)
+
+    # Compute the matmul.
+    c_sm = sparse_csr_matrix_ops.sparse_matrix_sparse_mat_mul(
+        a=a_sm, b=b_sm, type=dtypes.float32)
+    c_nnz = sparse_csr_matrix_ops.sparse_matrix_nnz(c_sm)
+    c_nnz_value = self.evaluate(c_nnz)
+
+    # Expect that there is a single numeric zero at index (0, 1) if zeros are
+    # not pruned, since 2.0 * 3.0 + (-1.0) * 6.0 = 0.0.
+    self.assertAllClose(1, c_nnz_value)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testLargeBatchSparseMatrixSparseMatMul(self):
+    sparsify = lambda m: m * (m > 0)
+
+    for (transpose_a, transpose_b) in ((False, False), (False, True),
+                                       (True, False), (True, True)):
+      for (adjoint_a, adjoint_b) in ((False, False), (False, True),
+                                     (True, False), (True, True)):
+        if (transpose_a and adjoint_a) or (transpose_b and adjoint_b):
+          continue
+
+        a_dense_shape = ([53, 127, 65]
+                         if transpose_a or adjoint_a else [53, 65, 127])
+        b_dense_shape = ([53, 67, 127]
+                         if transpose_b or adjoint_b else [53, 127, 67])
+
+        a_mats = sparsify(np.random.randn(*a_dense_shape)).astype(np.float32)
+        b_mats = sparsify(np.random.randn(*b_dense_shape).astype(np.float32))
+
+        a_sm = dense_to_csr_sparse_matrix(a_mats)
+        b_sm = dense_to_csr_sparse_matrix(b_mats)
+        c_sm = sparse_csr_matrix_ops.sparse_matrix_sparse_mat_mul(
+            a_sm,
+            b_sm,
+            type=dtypes.float32,
+            transpose_a=transpose_a,
+            adjoint_a=adjoint_a,
+            transpose_b=transpose_b,
+            adjoint_b=adjoint_b)
+        c_sm_dense = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+            c_sm, dtypes.float32)
+        c_dense_t = math_ops.matmul(
+            a_mats,
+            b_mats,
+            transpose_a=transpose_a,
+            adjoint_a=adjoint_a,
+            transpose_b=transpose_b,
+            adjoint_b=adjoint_b)
+        c_dense_t_value, c_sm_dense_value = self.evaluate(
+            (c_dense_t, c_sm_dense))
+
+        self.assertAllClose(c_sm_dense_value, c_dense_t_value)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testLargeBatchRegisteredAddN(self):
+    if not self._gpu_available:
+      return
+
+    sparsify = lambda m: m * (m > 0)
+    dense_shape = [53, 65, 127]
+    matrices = [
+        sparsify(np.random.randn(*dense_shape)).astype(np.float32)
+        for _ in range(16)
+    ]
+    sparse_matrices = [dense_to_csr_sparse_matrix(mat) for mat in matrices]
+    sparse_matrices_sum = math_ops.add_n(sparse_matrices)
+    sparse_matrices_sum_dense = \
+        sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+            sparse_matrices_sum, dtypes.float32)
+    sparse_matrices_sum_dense_value = self.evaluate(sparse_matrices_sum_dense)
+
+    # Ensure that the dense (numpy) sum across all batches matches the result
+    # of add_n converted back to dense.
+    expected_sum = np.sum(matrices, axis=0)
+    self.assertAllClose(expected_sum, sparse_matrices_sum_dense_value)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testCSRZeros(self):
+    if not self._gpu_available:
+      return
+    a_dense_shape = [65, 127]
+    b_dense_shape = [53, 127, 67]
+    data_types = [
+        dtypes.float32, dtypes.float64, dtypes.complex64, dtypes.complex128
+    ]
+    for dtype in data_types:
+      # Check both rank-2 and rank-3 tensors.
+      a_sm = sparse_csr_matrix_ops.sparse_matrix_zeros(
+          a_dense_shape, type=dtype)
+      b_sm = sparse_csr_matrix_ops.sparse_matrix_zeros(
+          b_dense_shape, type=dtype)
+      a_rt = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(a_sm, type=dtype)
+      b_rt = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(b_sm, type=dtype)
+      a_rt_value, b_rt_value = self.evaluate((a_rt, b_rt))
+
+      self.assertAllEqual(a_rt_value, np.zeros(a_dense_shape))
+      self.assertAllEqual(b_rt_value, np.zeros(b_dense_shape))
+
+  @test_util.run_in_graph_and_eager_modes
+  def testLargeBatchZerosLike(self):
+    if not self._gpu_available:
+      return
+
+    batch_size = 53
+    rows = 128
+    cols = 67
+    dense_shape = [batch_size, rows, cols]
+    data_types = [
+        dtypes.float32, dtypes.float64, dtypes.complex64, dtypes.complex128
+    ]
+    for dtype in data_types:
+      sparse_matrices = sparse_csr_matrix_ops.sparse_matrix_zeros(
+          dense_shape, type=dtype)
+      zeros_like_sparse_matrices = array_ops.zeros_like(sparse_matrices)
+      zeros_like_components = [
+          sparse_csr_matrix_ops.csr_sparse_matrix_components(
+              zeros_like_sparse_matrices, i, type=dtype)
+          for i in range(batch_size)
+      ]
+      zeros_like_components_values = self.evaluate(zeros_like_components)
+      for component in zeros_like_components_values:
+        self.assertAllEqual(component.row_ptrs, np.zeros(rows + 1, np.int32))
+        self.assertAllEqual(component.col_inds, np.empty([0], np.int32))
+        self.assertAllEqual(component.values, np.empty([0],
+                                                       dtype.as_numpy_dtype))
+
+  @test_util.run_in_graph_and_eager_modes
+  def testTranspose(self):
+    if not self._gpu_available:
+      return
+
+    sparsify = lambda m: m * (m > 0)
+    dense_shape = [127, 65]
+    data_types = [
+        dtypes.float32, dtypes.float64, dtypes.complex64, dtypes.complex128
+    ]
+    for dtype in data_types:
+      mats = sparsify(
+          (np.random.randn(*dense_shape) +
+           1.j * np.random.randn(*dense_shape))).astype(dtype.as_numpy_dtype)
+      for conjugate in False, True:
+        expected = np.transpose(mats)
+        if conjugate:
+          expected = np.conj(expected)
+        matrices = math_ops.cast(mats, dtype)
+        sparse_matrices = dense_to_csr_sparse_matrix(matrices)
+        transpose_sparse_matrices = \
+            sparse_csr_matrix_ops.sparse_matrix_transpose(
+                sparse_matrices, conjugate=conjugate, type=dtype)
+        dense_transposed = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+            transpose_sparse_matrices, dtype)
+        dense_transposed_values = self.evaluate(dense_transposed)
+        self.assertAllClose(expected, dense_transposed_values)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testLargeBatchTranspose(self):
+    if not self._gpu_available:
+      return
+
+    sparsify = lambda m: m * (m > 0)
+    dense_shape = [53, 65, 127]
+    data_types = [
+        dtypes.float32, dtypes.float64, dtypes.complex64, dtypes.complex128
+    ]
+    for dtype in data_types:
+      mats = sparsify(
+          (np.random.randn(*dense_shape) +
+           1.j * np.random.randn(*dense_shape))).astype(dtype.as_numpy_dtype)
+      expected = np.transpose(mats, (0, 2, 1))
+      for conjugate in False, True:
+        if conjugate:
+          expected = np.conj(expected)
+        matrices = math_ops.cast(mats, dtype)
+        sparse_matrices = dense_to_csr_sparse_matrix(matrices)
+        transpose_sparse_matrices = \
+            sparse_csr_matrix_ops.sparse_matrix_transpose(
+                sparse_matrices, conjugate=conjugate, type=dtype)
+        dense_transposed = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+            transpose_sparse_matrices, dtype)
+        dense_transposed_values = self.evaluate(dense_transposed)
+        self.assertAllClose(expected, dense_transposed_values)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testSoftmax(self):
+    if not self._gpu_available:
+      return
+
+    sparsify = lambda m: m * (m > 0)
+    dense_shape = [127, 65]
+    logits = sparsify(np.random.randn(*dense_shape))
+    logits_with_ninf = np.copy(logits)
+    logits_with_ninf[logits == 0] = -np.inf
+    data_types = [dtypes.float32, dtypes.float64]
+    for dtype in data_types:
+      logits_t = math_ops.cast(logits, dtype)
+      logits_t_with_ninf = math_ops.cast(logits_with_ninf, dtype)
+      expected = nn_ops.softmax(logits_t_with_ninf)
+      sparse_logits_t = dense_to_csr_sparse_matrix(logits_t)
+      softmax_sparse_logits_t = sparse_csr_matrix_ops.sparse_matrix_softmax(
+          sparse_logits_t, type=dtype)
+      dense_softmax = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+          softmax_sparse_logits_t, dtype)
+      dense_softmax_values, expected_values = self.evaluate(
+          (dense_softmax, expected))
+      self.assertAllClose(expected_values, dense_softmax_values)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testLargeBatchSoftmax(self):
+    if not self._gpu_available:
+      return
+
+    sparsify = lambda m: m * (m > 0)
+    dense_shape = [53, 65, 127]
+    logits = sparsify(np.random.randn(*dense_shape))
+    logits_with_ninf = np.copy(logits)
+    logits_with_ninf[logits == 0] = -np.inf
+    data_types = [dtypes.float32, dtypes.float64]
+    for dtype in data_types:
+      logits_t = math_ops.cast(logits, dtype)
+      logits_t_with_ninf = math_ops.cast(logits_with_ninf, dtype)
+      expected = nn_ops.softmax(logits_t_with_ninf)
+      sparse_logits_t = dense_to_csr_sparse_matrix(logits_t)
+      softmax_sparse_logits_t = sparse_csr_matrix_ops.sparse_matrix_softmax(
+          sparse_logits_t, type=dtype)
+      dense_softmax = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+          softmax_sparse_logits_t, dtype)
+      dense_softmax_values, expected_values = self.evaluate(
+          (dense_softmax, expected))
+      self.assertAllClose(expected_values, dense_softmax_values)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testLargeBatchSoftmaxEmpty(self):
+    if not self._gpu_available:
+      return
+
+    dense_shape = [53, 65, 127]
+    sparse_logits_t = sparse_csr_matrix_ops.sparse_matrix_zeros(
+        dense_shape, type=dtypes.float32)
+    softmax_sparse_logits_t = sparse_csr_matrix_ops.sparse_matrix_softmax(
+        sparse_logits_t, type=dtypes.float32)
+    dense_softmax = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+        softmax_sparse_logits_t, dtypes.float32)
+    dense_softmax_values = self.evaluate(dense_softmax)
+    self.assertAllEqual(
+        np.zeros_like(dense_softmax_values), dense_softmax_values)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testSoftmaxGrad(self):
+    if not self._gpu_available:
+      return
+
+    sparsify = lambda m: m * (m > 0)
+    dense_shape = [127, 65]
+    softmax = sparsify(np.random.randn(*dense_shape))
+    grad_softmax = sparsify(np.random.randn(*dense_shape))
+    expected = (
+        (grad_softmax - np.sum(grad_softmax * softmax, -1, keepdims=True)) *
+        softmax)
+    data_types = [dtypes.float32, dtypes.float64]
+    for dtype in data_types:
+      softmax_t = math_ops.cast(softmax, dtype)
+      grad_softmax_t = math_ops.cast(grad_softmax, dtype)
+      softmax_sparse = dense_to_csr_sparse_matrix(softmax_t)
+      grad_softmax_sparse = dense_to_csr_sparse_matrix(grad_softmax_t)
+      gradients_sparse = sparse_csr_matrix_ops.sparse_matrix_softmax_grad(
+          softmax_sparse, grad_softmax_sparse, dtype)
+      dense_gradients = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+          gradients_sparse, dtype)
+      dense_gradients_values = self.evaluate((dense_gradients))
+      self.assertAllClose(expected, dense_gradients_values)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testLargeBatchSoftmaxGrad(self):
+    if not self._gpu_available:
+      return
+
+    sparsify = lambda m: m * (m > 0)
+    dense_shape = [53, 65, 127]
+    softmax = sparsify(np.random.randn(*dense_shape))
+    grad_softmax = sparsify(np.random.randn(*dense_shape))
+    expected = (
+        (grad_softmax - np.sum(grad_softmax * softmax, -1, keepdims=True)) *
+        softmax)
+    data_types = [dtypes.float32, dtypes.float64]
+    for dtype in data_types:
+      softmax_t = math_ops.cast(softmax, dtype)
+      grad_softmax_t = math_ops.cast(grad_softmax, dtype)
+      softmax_sparse = dense_to_csr_sparse_matrix(softmax_t)
+      grad_softmax_sparse = dense_to_csr_sparse_matrix(grad_softmax_t)
+      gradients_sparse = sparse_csr_matrix_ops.sparse_matrix_softmax_grad(
+          softmax_sparse, grad_softmax_sparse, dtype)
+      dense_gradients = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+          gradients_sparse, dtype)
+      dense_gradients_values = self.evaluate((dense_gradients))
+      self.assertAllClose(expected, dense_gradients_values)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testLargeBatchSoftmaxGradEmpty(self):
+    if not self._gpu_available:
+      return
+
+    sparsify = lambda m: m * (m > 0)
+    dense_shape = [53, 65, 127]
+    not_empty = sparsify(np.random.randn(*dense_shape)).astype(np.float32)
+    sparse_empty = sparse_csr_matrix_ops.sparse_matrix_zeros(
+        dense_shape, type=dtypes.float32)
+    sparse_not_empty = dense_to_csr_sparse_matrix(not_empty)
+    gradients_empty_softmax = sparse_csr_matrix_ops.sparse_matrix_softmax_grad(
+        sparse_empty, sparse_not_empty, dtypes.float32)
+    gradients_empty_grad_softmax = (
+        sparse_csr_matrix_ops.sparse_matrix_softmax_grad(
+            sparse_not_empty, sparse_empty, dtypes.float32))
+    gradients_empty_both = sparse_csr_matrix_ops.sparse_matrix_softmax_grad(
+        sparse_empty, sparse_empty, dtypes.float32)
+    ges = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+        gradients_empty_softmax, dtypes.float32)
+    gegs = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+        gradients_empty_grad_softmax, dtypes.float32)
+    geb = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+        gradients_empty_both, dtypes.float32)
+    ges_v, gegs_v, geb_v = self.evaluate((ges, gegs, geb))
+    for v in (ges_v, gegs_v, geb_v):
+      self.assertAllEqual(np.zeros(dense_shape), v)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testLargeBatchConj(self):
+    if not self._gpu_available:
+      return
+
+    sparsify = lambda m: m * (np.real(m) > 0)
+    dense_shape = [53, 65, 127]
+    matrices = (
+        sparsify(np.random.randn(*dense_shape)) +
+        1j * np.random.randn(*dense_shape))
+    data_types = [
+        dtypes.float32, dtypes.float64, dtypes.complex64, dtypes.complex128
+    ]
+    for dtype in data_types:
+      matrices_t = matrices.astype(dtype.as_numpy_dtype)
+      expected = np.conj(matrices_t)
+      sparse_matrices = dense_to_csr_sparse_matrix(matrices_t)
+      conj_sparse_matrices = math_ops.conj(sparse_matrices)
+      dense_conj_matrices = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+          conj_sparse_matrices, dtype)
+      conj_values = self.evaluate(dense_conj_matrices)
+      self.assertAllClose(expected, conj_values)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testLargeBatchSparseMatrixMulScalar(self):
+    if not self._gpu_available:
+      return
+
+    sparsify = lambda m: m * (m > 0)
+    a_dense_shape = [53, 65, 127]
+    a_mats = sparsify(np.random.randn(*a_dense_shape)).astype(np.float32)
+    b = np.float32(3.5)
+    expected = a_mats * b
+    a_sm = dense_to_csr_sparse_matrix(a_mats)
+    c_t = sparse_csr_matrix_ops.sparse_matrix_mul(a_sm, b)
+    c_dense_t = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+        c_t, dtypes.float32)
+    c_dense_t_value = self.evaluate(c_dense_t)
+
+    self.assertAllClose(expected, c_dense_t_value)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testLargeBatchSparseMatrixMulVec(self):
+    if not self._gpu_available:
+      return
+
+    sparsify = lambda m: m * (m > 0)
+    a_dense_shape = [53, 65, 127]
+    a_mats = sparsify(np.random.randn(*a_dense_shape)).astype(np.float32)
+    b = np.random.randn(53, 1, 1).astype(np.float32)
+    expected = a_mats * b
+    a_sm = dense_to_csr_sparse_matrix(a_mats)
+    c_t = sparse_csr_matrix_ops.sparse_matrix_mul(a_sm, b)
+    c_dense_t = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+        c_t, dtypes.float32)
+    c_dense_t_value = self.evaluate(c_dense_t)
+
+    self.assertAllClose(expected, c_dense_t_value)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testSparseCholesky(self):
+    dense_matrix = np.array([
+        [2, 0, 0, 0, 0, 0],
+        [0, 3, 0, 0, 0, 0],
+        [1, 1, 7, 0, 0, 0],
+        [0, 0, 0, 4, 0, 0],
+        [0, 0, 1, 0, 5, 0],
+        [0, 0, 2, 0, 1, 6],
+    ]).astype(np.complex128)
+
+    data_types = [
+        dtypes.float32, dtypes.float64, dtypes.complex64, dtypes.complex128
+    ]
+    for dtype in data_types:
+      with test_util.force_cpu():
+        if dtype.is_complex:
+          dense_matrix += 0.5j * np.tril(dense_matrix, -1)
+
+        sparse_matrix = dense_to_csr_sparse_matrix(
+            math_ops.cast(dense_matrix, dtype))
+        # Obtain the Sparse Cholesky factor using AMD Ordering for reducing
+        # fill-in.
+        ordering_amd = sparse_csr_matrix_ops.sparse_matrix_ordering_amd(
+            sparse_matrix)
+        cholesky_sparse_matrices = (
+            sparse_csr_matrix_ops.sparse_matrix_sparse_cholesky(
+                sparse_matrix, ordering_amd, type=dtype))
+        dense_cholesky = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+            cholesky_sparse_matrices, dtype)
+        # Compute L * Lh where L is the Sparse Cholesky factor.
+        verification = math_ops.matmul(
+            dense_cholesky, array_ops.transpose(dense_cholesky, conjugate=True))
+        # Assert that input matrix A satisfies A = L * Lh.
+        verification_values = self.evaluate(verification)
+        full_dense_matrix = (
+            dense_matrix +
+            np.conjugate(np.transpose(np.tril(dense_matrix, -1))))
+        self.assertAllClose(full_dense_matrix, verification_values)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testBatchSparseCholesky(self):
+    dense_mat = np.array([
+        # A diagonal matrix.
+        [
+            [1, 0, 0, 0],  #
+            [0, 2, 0, 0],  #
+            [0, 0, 3, 0],  #
+            [0, 0, 0, 4],
+        ],  #
+        # A tridiagonal hermitian matrix.
+        [
+            [5 + 0j, 1 + 0j, 0 + 0j, 0 + 0j],  #
+            [1 + 0j, 4 + 0j, 1 + 2j, 0 + 0j],  #
+            [0 + 0j, 1 - 2j, 9 + 0j, 3 - 3j],  #
+            [0 + 0j, 0 + 0j, 3 + 3j, 7 + 0j],
+        ],  #
+        # A diagonal matrix with a corner element; for which
+        # OrderingAMD returns a non-identity permutation.
+        [
+            [1, 0, 0, 1.],  #
+            [0, 2, 0, 0.],  #
+            [0, 0, 3, 0.],  #
+            [1, 0, 0, 4.],
+        ]  #
+    ]).astype(np.complex128)
+
+    data_types = [
+        dtypes.float32, dtypes.float64, dtypes.complex64, dtypes.complex128
+    ]
+    for dtype in data_types:
+      sparse_matrix = dense_to_csr_sparse_matrix(
+          math_ops.cast(dense_mat, dtype))
+      ordering_amd = sparse_csr_matrix_ops.sparse_matrix_ordering_amd(
+          sparse_matrix)
+
+      cholesky_sparse_matrix = (
+          sparse_csr_matrix_ops.sparse_matrix_sparse_cholesky(
+              sparse_matrix, ordering_amd, type=dtype))
+      dense_cholesky = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+          cholesky_sparse_matrix, dtype)
+
+      # Compute L * Lh.
+      verification = math_ops.matmul(
+          dense_cholesky,
+          array_ops.transpose(dense_cholesky, perm=[0, 2, 1], conjugate=True))
+
+      verification_values = self.evaluate(verification)
+      self.assertAllClose(
+          dense_mat.astype(dtype.as_numpy_dtype), verification_values)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testLargeBatchSparseCholesky(self):
+    sparsity = 0.1
+    sparsify = lambda m: m * (m > 1 - sparsity)
+
+    batch_size = 53
+    num_rows = 147
+    dense_shape = [batch_size, num_rows, num_rows]
+
+    dense_matrix = sparsify(np.random.uniform(size=dense_shape)).astype(
+        np.float32)
+
+    # Create a "random" SPD matrix, by choosing each entry of A between
+    # 0 and 1 at the specified density, and computing 0.5(A + At) + n*I.
+    # This ensures diagonal dominance which implies positive-definiteness.
+    dense_matrix = (
+        0.5 *
+        (dense_matrix + array_ops.transpose(dense_matrix, perm=[0, 2, 1])) +
+        num_rows * linalg_ops.eye(dense_shape[-1], batch_shape=[batch_size]))
+    # Compute the fill-in reducing permutation and use it to perform
+    # the Sparse Cholesky factorization.
+    sparse_matrix = dense_to_csr_sparse_matrix(dense_matrix)
+    ordering_amd = sparse_csr_matrix_ops.sparse_matrix_ordering_amd(
+        sparse_matrix)
+
+    cholesky_sparse_matrix = \
+        sparse_csr_matrix_ops.sparse_matrix_sparse_cholesky(
+            sparse_matrix, ordering_amd, type=dtypes.float32)
+    dense_cholesky = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+        cholesky_sparse_matrix, dtypes.float32)
+
+    # Compute L * Lh.
+    verification = math_ops.matmul(
+        dense_cholesky, array_ops.transpose(dense_cholesky, perm=[0, 2, 1]))
+    verification_values = self.evaluate(verification)
+    self.assertAllClose(dense_matrix, verification_values, atol=1e-5, rtol=1e-5)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testSparseCholesky_InvalidMatrix(self):
+    # Verify that non-SPD matrices result in an Invalid Argument error.
+    invalid_matrices = [
+        # zero matrix.
+        np.array([
+            [0., 0., 0., 0.],  #
+            [0., 0., 0., 0.],  #
+            [0., 0., 0., 0.],  #
+            [0., 0., 0., 0.]  #
+        ]),
+        # zero diagonal entry.
+        np.array([
+            [9., 0., 5., 0.],  #
+            [0., 0., 0., 1.],  #
+            [5., 0., 8., 0.],  #
+            [0., 1., 0., 7.]  #
+        ]),
+        # not positive definite.
+        np.array([
+            [2., -2., 0., 0.],  #
+            [-2., 2., 0., 0.],  #
+            [0., 0., 3., -3.],  #
+            [0., 0., -3., 3.]  #
+        ]),
+    ]
+
+    with test_util.force_cpu():
+      for invalid_matrix in invalid_matrices:
+        with self.assertRaises(errors.InvalidArgumentError):
+          sparse_matrix = dense_to_csr_sparse_matrix(
+              invalid_matrix.astype(np.float32))
+          # Compute the fill-in reducing permutation and use it to perform
+          # the Sparse Cholesky factorization.
+          ordering_amd = sparse_csr_matrix_ops.sparse_matrix_ordering_amd(
+              sparse_matrix)
+          cholesky_sparse_matrices = (
+              sparse_csr_matrix_ops.sparse_matrix_sparse_cholesky(
+                  sparse_matrix, ordering_amd, type=dtypes.float32))
+          # Convert the Cholesky factor to a dense matrix to be evaluated.
+          dense_cholesky = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+              cholesky_sparse_matrices, type=dtypes.float32)
+          self.evaluate(dense_cholesky)
+
+  @test_util.run_in_graph_and_eager_modes
+  def testOrderingAMD(self):
+    num_rows = 6
+    # An SPD matrix where AMD ordering can reduce fill-in for Cholesky factor.
+    dense_matrix = np.array([
+        [7, 0, 0, 0, 0, 0],
+        [1, 4, 0, 0, 0, 0],
+        [1, 1, 3, 0, 0, 0],
+        [0, 0, 0, 4, 0, 0],
+        [2, 0, 0, 0, 5, 0],
+        [1, 2, 2, 0, 0, 6],
+    ]).astype(np.float32)
+
+    with test_util.force_cpu():
+      sparse_matrix = dense_to_csr_sparse_matrix(dense_matrix)
+
+      # Obtain the Sparse Cholesky factor with the identity permutation as the
+      # fill-in reducing ordering.
+      cholesky_without_ordering = (
+          sparse_csr_matrix_ops.sparse_matrix_sparse_cholesky(
+              sparse_matrix, math_ops.range(num_rows), type=dtypes.float32))
+      cholesky_without_ordering_nnz = sparse_csr_matrix_ops.sparse_matrix_nnz(
+          cholesky_without_ordering)
+
+      # Obtain the Sparse Cholesky factor using AMD Ordering for reducing
+      # fill-in.
+      ordering_amd = sparse_csr_matrix_ops.sparse_matrix_ordering_amd(
+          sparse_matrix)
+      cholesky_with_amd = sparse_csr_matrix_ops.sparse_matrix_sparse_cholesky(
+          sparse_matrix, ordering_amd, type=dtypes.float32)
+      cholesky_with_amd_nnz = sparse_csr_matrix_ops.sparse_matrix_nnz(
+          cholesky_with_amd)
+
+      (ordering_amd_value, cholesky_with_amd_nnz_value,
+       cholesky_without_ordering_nnz_value) = self.evaluate(
+           [ordering_amd, cholesky_with_amd_nnz, cholesky_without_ordering_nnz])
+
+      # AMD ordering should return a valid permutation.
+      self.assertAllClose(np.arange(num_rows), np.sort(ordering_amd_value))
+      # Check that cholesky with AMD ordering has a strictly lower nonzero count
+      # for this matrix.
+      self.assertLess(cholesky_with_amd_nnz_value,
+                      cholesky_without_ordering_nnz_value)
+
+
+class CSRSparseMatrixOpsBenchmark(test.Benchmark):
+
+  def benchmark_sparse_matrix_mat_mul_gpu(self):
+    if not test_util.is_gpu_available():
+      return
+
+    sparsify = lambda m: array_ops.where(m > 2, m, array_ops.zeros_like(m))
+
+    # XW, X dense and W sparse
+    # X is shaped [{1, 8, 16}, 2000]
+    # W is shaped [2000, 4000]
+
+    for batch_size in [1, 8, 16]:
+      x_dense_shape = [batch_size, 2000]
+      w_dense_shape = [2000, 4000]
+
+      with ops.Graph().as_default(), ops.device("/gpu:0"):
+        x_mats = random_ops.random_normal(x_dense_shape, dtype=dtypes.float32)
+        w_mats = sparsify(
+            random_ops.random_normal(w_dense_shape, dtype=dtypes.float32))
+        nnz = array_ops.shape(array_ops.where(w_mats))[0]
+        ratio = math_ops.cast(nnz, dtypes.float32) / np.prod(w_dense_shape)
+        w_sm = dense_to_csr_sparse_matrix(w_mats)
+        with ops.name_scope("w_sm_var"):
+          w_sm_var = variable_scope.get_variable(
+              "sm", initializer=w_sm, use_resource=True)
+          w_sm_var_v = w_sm_var.read_value()
+        with ops.name_scope("w_var"):
+          w_var = variable_scope.get_variable(
+              "sm_dense", initializer=w_mats, use_resource=True)
+          w_var_v = w_var.read_value()
+        with ops.name_scope("b"):
+          x = variable_scope.get_variable(
+              "b", initializer=x_mats, use_resource=True)
+          x_v = x.read_value()
+        # X*W = (W'*X')'
+        xw_sparse = sparse_csr_matrix_ops.sparse_matrix_mat_mul(
+            w_sm_var_v,
+            x_v,
+            transpose_a=True,
+            transpose_b=True,
+            transpose_output=True)
+        xw_dense = math_ops.matmul(x_v, w_var_v)
+
+        with session.Session() as sess:
+          self.evaluate(
+              [w_var.initializer, w_sm_var.initializer, x.initializer])
+          nnz_value, ratio_value = self.evaluate((nnz, ratio))
+          name_template = (
+              "sparse_matrix_mat_mul_gpu_%s_W_2000x4000_batch_size_%d")
+          self.run_op_benchmark(
+              sess,
+              xw_sparse.op,
+              name=name_template % ("sparse", batch_size),
+              extras={
+                  "percentage_nonzero": ratio_value,
+                  "num_nonzero": nnz_value
+              },
+              min_iters=50)
+          self.run_op_benchmark(
+              sess,
+              xw_dense.op,
+              name=name_template % ("dense", batch_size),
+              extras={
+                  "percentage_nonzero": ratio_value,
+                  "num_nonzero": nnz_value
+              },
+              min_iters=50)
+
+  def benchmark_sparse_matrix_sparse_matmul(self):
+    density = 0.05
+    # pylint: disable=g-long-lambda
+    sparsify = lambda m: array_ops.where(m > 1. - density, m,
+                                         array_ops.zeros_like(m))
+    # pylint: enable=g-long-lambda
+
+    for batch_size in [1, 16]:
+      for num_threads in [1, 4, 12]:
+        dense_shape = [batch_size, 250, 250]
+
+        for device in [CPU, GPU]:
+          if device == GPU and not test_util.is_gpu_available():
+            continue
+
+          with ops.Graph().as_default(), ops.device(device):
+            x_mats = sparsify(
+                random_ops.random_uniform(dense_shape, dtype=dtypes.float32))
+            y_mats = sparsify(
+                random_ops.random_uniform(dense_shape, dtype=dtypes.float32))
+
+            nnz = array_ops.shape(array_ops.where(x_mats))[0] + array_ops.shape(
+                array_ops.where(y_mats))[0]
+            ratio = math_ops.cast(nnz,
+                                  dtypes.float32) / (2 * np.prod(dense_shape))
+
+            x_sm = dense_to_csr_sparse_matrix(x_mats)
+            y_sm = dense_to_csr_sparse_matrix(y_mats)
+
+            xy_sparse = sparse_csr_matrix_ops.sparse_matrix_sparse_mat_mul(
+                x_sm, y_sm, type=dtypes.float32)
+
+            with session.Session(
+                config=config_pb2.ConfigProto(
+                    intra_op_parallelism_threads=num_threads)) as sess:
+              nnz_value, ratio_value = self.evaluate((nnz, ratio))
+              name_template = (
+                  "sparse_matrix_sparse_matmul_%s_N_%d_batch_size_%d_threads_%d"
+              )
+              device_str = "cpu" if device == CPU else "gpu"
+              self.run_op_benchmark(
+                  sess,
+                  xy_sparse.op,
+                  name=name_template %
+                  (device_str, dense_shape[-1], batch_size, num_threads),
+                  extras={
+                      "percentage_nonzero": ratio_value,
+                      "num_nonzero": nnz_value
+                  },
+                  min_iters=50)
+
+  def benchmark_sparse_dense_conversion(self):
+    sparsity = 0.05
+
+    for batch_size in [1, 16]:
+      for num_threads in [1, 4, 12]:
+        dense_shape = [batch_size, 750, 750]
+
+        for device in [CPU, GPU]:
+          if device == GPU and not test_util.is_gpu_available():
+            continue
+
+          with ops.Graph().as_default(), ops.device(device):
+            mats = random_ops.random_uniform(dense_shape, dtype=dtypes.float32)
+            mats_locs = array_ops.where(mats > 1.0 - sparsity)
+
+            sparse_matrices = sparse_csr_matrix_ops.dense_to_csr_sparse_matrix(
+                mats, mats_locs)
+            dense_matrices = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+                sparse_matrices, type=dtypes.float32)
+            nnz = math_ops.reduce_sum(
+                sparse_csr_matrix_ops.sparse_matrix_nnz(sparse_matrices))
+            ratio = math_ops.cast(nnz, dtypes.float32) / np.prod(dense_shape)
+
+            with session.Session(
+                config=config_pb2.ConfigProto(
+                    intra_op_parallelism_threads=num_threads)) as sess:
+              nnz_value, ratio_value = self.evaluate((nnz, ratio))
+              device_str = "cpu" if device == CPU else "gpu"
+              name_template = (
+                  "dense_to_sparse_matrix_%s_N_%d_batch_size_%d_num_threads_%d")
+              self.run_op_benchmark(
+                  sess,
+                  sparse_matrices.op,
+                  name=name_template %
+                  (device_str, dense_shape[-1], batch_size, num_threads),
+                  extras={
+                      "percentage_nonzero": ratio_value,
+                      "num_nonzero": nnz_value,
+                  },
+                  min_iters=50)
+              name_template = (
+                  "sparse_matrix_to_dense_%s_N_%d_batch_size_%d_num_threads_%d")
+              self.run_op_benchmark(
+                  sess,
+                  dense_matrices.op,
+                  name=name_template %
+                  (device_str, dense_shape[-1], batch_size, num_threads),
+                  extras={
+                      "percentage_nonzero": ratio_value,
+                      "num_nonzero": nnz_value,
+                  },
+                  min_iters=50)
+
+  def benchmark_sparse_cholesky(self):
+    # TODO(anudhyan): Use conversions from SparseTensor instead of to get this
+    # benchmark working for larger matrices. For this to work without GPU, we
+    # need to write CPU kernels for SparseTensor conversions.
+    num_rows = 500
+    density = 0.01
+    # pylint: disable=g-long-lambda
+    sparsify = lambda m: array_ops.where(m > 1. - density, m,
+                                         array_ops.zeros_like(m))
+    # pylint: enable=g-long-lambda
+
+    for batch_size in [1, 16]:
+      for num_threads in [1, 4, 12]:
+        dense_shape = [batch_size, num_rows, num_rows]
+
+        with ops.Graph().as_default(), ops.device(CPU):
+          # Create a "random" SPD matrix, by choosing each entry of A between
+          # 0 and 1 at the specified density, and computing 0.5(A + At) + n*I.
+          # This ensures diagonal dominance which implies positive-definiteness.
+          dense_matrix = sparsify(
+              random_ops.random_uniform(dense_shape, dtype=dtypes.float32))
+          spd_dense_matrix = (
+              0.5 *
+              (dense_matrix + array_ops.transpose(dense_matrix, perm=[0, 2, 1]))
+              + num_rows *
+              linalg_ops.eye(dense_shape[-1], batch_shape=[batch_size]))
+
+          # Convert to SparseMatrix and invoke Sparse Cholesky factorization
+          # with AMD Ordering.
+          sparse_matrix = dense_to_csr_sparse_matrix(spd_dense_matrix)
+          ordering_amd = sparse_csr_matrix_ops.sparse_matrix_ordering_amd(
+              sparse_matrix)
+          cholesky_sparse_matrix = (
+              sparse_csr_matrix_ops.sparse_matrix_sparse_cholesky(
+                  sparse_matrix, ordering_amd, type=dtypes.float32))
+
+          nnz = math_ops.reduce_sum(
+              sparse_csr_matrix_ops.sparse_matrix_nnz(sparse_matrix))
+          ratio = math_ops.cast(nnz, dtypes.float32) / np.prod(dense_shape)
+          ordering_amd_name_template = (
+              "sparse_matrix_ordering_amd_cpu_N_%d_batch_size_%d_threads_%d")
+          sparse_cholesky_name_template = (
+              "sparse_matrix_sparse_cholesky_cpu_N_%d_batch_size_%d_threads_%d")
+          with session.Session(
+              config=config_pb2.ConfigProto(
+                  intra_op_parallelism_threads=num_threads)) as sess:
+            nnz_value, ratio_value = self.evaluate((nnz, ratio))
+            self.run_op_benchmark(
+                sess,
+                ordering_amd.op,
+                name=ordering_amd_name_template %
+                (dense_shape[-1], batch_size, num_threads),
+                extras={
+                    "percentage_nonzero": ratio_value,
+                    "num_nonzero": nnz_value
+                },
+                min_iters=25)
+            self.run_op_benchmark(
+                sess,
+                cholesky_sparse_matrix.op,
+                name=sparse_cholesky_name_template %
+                (dense_shape[-1], batch_size, num_threads),
+                extras={
+                    "percentage_nonzero": ratio_value,
+                    "num_nonzero": nnz_value
+                },
+                min_iters=25)
+
+
+if __name__ == "__main__":
+  test.main()
diff --git a/tensorflow/python/kernel_tests/sparse_csr_matrix_sparse_mat_mul_grad_test.py b/tensorflow/python/kernel_tests/sparse_csr_matrix_sparse_mat_mul_grad_test.py
new file mode 100644
index 00000000000..07d1e6a2a06
--- /dev/null
+++ b/tensorflow/python/kernel_tests/sparse_csr_matrix_sparse_mat_mul_grad_test.py
@@ -0,0 +1,137 @@
+# Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+# ==============================================================================
+"""CSR sparse matrix tests."""
+
+from __future__ import absolute_import
+from __future__ import division
+from __future__ import print_function
+
+import itertools
+
+import numpy as np
+
+from tensorflow.python.framework import ops
+from tensorflow.python.framework import test_util
+from tensorflow.python.ops import array_ops
+from tensorflow.python.ops import gradient_checker
+from tensorflow.python.ops import math_ops
+from tensorflow.python.ops.linalg.sparse import sparse_csr_matrix_grad  # pylint: disable=unused-import
+from tensorflow.python.ops.linalg.sparse import sparse_csr_matrix_ops
+from tensorflow.python.platform import test
+from tensorflow.python.platform import tf_logging
+
+
+def dense_to_csr_sparse_matrix(dense):
+  dense_t = ops.convert_to_tensor(dense)
+  locs = array_ops.stop_gradient(array_ops.where(math_ops.abs(dense_t) > 0))
+  return sparse_csr_matrix_ops.dense_to_csr_sparse_matrix(dense_t, locs)
+
+
+def _add_test(test, op_name, testcase_name, fn):  # pylint: disable=redefined-outer-name
+  if fn is None:
+    return
+  test_name = "_".join(["test", op_name, testcase_name])
+  if hasattr(test, test_name):
+    raise RuntimeError("Test %s defined more than once" % test_name)
+  setattr(test, test_name, fn)
+
+
+class CSRSparseMatrixGradTest(test.TestCase):
+
+  @classmethod
+  def setUpClass(cls):
+    super(CSRSparseMatrixGradTest, cls).setUpClass()
+    cls._gpu_available = test_util.is_gpu_available()
+
+  # TODO(penporn): Make these tests runnable on eager mode.
+  # (tf.gradients and gradient_checker only run in graph mode.)
+  @test_util.run_deprecated_v1
+  def _testLargeBatchSparseMatrixSparseMatMulGrad(self, datatype, transpose_a,
+                                                  transpose_b, adjoint_a,
+                                                  adjoint_b):
+    if not self._gpu_available:
+      return
+
+    sparsify = lambda m: m * (m > 0)
+    a_mats_val = sparsify(
+        np.random.randn(3, 5, 11) +
+        1.j * np.random.randn(3, 5, 11)).astype(datatype)
+    if transpose_a or adjoint_a:
+      a_mats_val = np.transpose(a_mats_val, (0, 2, 1))
+    if adjoint_a:
+      a_mats_val = np.conj(a_mats_val)
+    b_mats_val = sparsify(
+        np.random.randn(3, 11, 13) +
+        1.j * np.random.randn(3, 11, 13)).astype(datatype)
+    if transpose_b or adjoint_b:
+      b_mats_val = np.transpose(b_mats_val, (0, 2, 1))
+    if adjoint_b:
+      b_mats_val = np.conj(b_mats_val)
+    with self.test_session(use_gpu=True):
+      a_mats = ops.convert_to_tensor(a_mats_val, dtype=datatype)
+      b_mats = ops.convert_to_tensor(b_mats_val, dtype=datatype)
+      a_sm = dense_to_csr_sparse_matrix(a_mats)
+      b_sm = dense_to_csr_sparse_matrix(b_mats)
+      c_sm = sparse_csr_matrix_ops.sparse_matrix_sparse_mat_mul(
+          a_sm,
+          b_sm,
+          transpose_a=transpose_a,
+          transpose_b=transpose_b,
+          adjoint_a=adjoint_a,
+          adjoint_b=adjoint_b,
+          type=datatype)
+      c_dense = sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+          c_sm, type=datatype)
+      for ten, val, nn in [[a_mats, a_mats_val, "a"], [b_mats, b_mats_val,
+                                                       "b"]]:
+        tf_logging.info("Testing gradients for %s" % nn)
+        theoretical, numerical = gradient_checker.compute_gradient(
+            ten,
+            ten.get_shape().as_list(),
+            c_dense,
+            c_dense.get_shape().as_list(),
+            x_init_value=val,
+            delta=1e-3)
+        self.assertAllClose(theoretical, numerical, atol=1e-3, rtol=1e-3)
+
+
+# These tests are refactored from sparse_csr_matrix_grad_test to keep its size
+# "medium".
+for dtype in (np.float32, np.complex64):
+  for (t_a, t_b, adj_a, adj_b) in itertools.product(*(([False, True],) * 4)):
+
+    def create_sparse_mat_mul_test_fn(dtype_, t_a_, t_b_, adj_a_, adj_b_):
+      # Skip invalid cases.
+      if (t_a_ and adj_a_) or (t_b_ and adj_b_):
+        return
+      # Skip cases where we conjugate real matrices.
+      if dtype_ == np.float32 and (adj_a_ or adj_b_):
+        return
+
+      def test_fn(self):
+        self._testLargeBatchSparseMatrixSparseMatMulGrad(
+            dtype_, t_a_, t_b_, adj_a_, adj_b_)
+
+      return test_fn
+
+    name = (
+        "_testLargeBatchSparseMatrixSparseMatMulGrad_dtype_%s_t_a_%s_t_b_%s_"
+        "adj_a_%s_adj_b_%s" % (dtype.__name__, t_a, t_b, adj_a, adj_b))
+
+    _add_test(CSRSparseMatrixGradTest, "CSRSparseMatrixSparseGradTest", name,
+              create_sparse_mat_mul_test_fn(dtype, t_a, t_b, adj_a, adj_b))
+
+if __name__ == "__main__":
+  test.main()
diff --git a/tensorflow/python/ops/linalg/sparse/BUILD b/tensorflow/python/ops/linalg/sparse/BUILD
new file mode 100644
index 00000000000..bbe8341e722
--- /dev/null
+++ b/tensorflow/python/ops/linalg/sparse/BUILD
@@ -0,0 +1,35 @@
+# Description: Sparse CSR support for TensorFlow.
+load("//tensorflow:tensorflow.bzl", "tf_gen_op_wrapper_py")
+
+package(
+    default_visibility = ["//tensorflow:internal"],
+    licenses = ["notice"],  # Apache 2.0
+)
+
+tf_gen_op_wrapper_py(
+    name = "gen_sparse_csr_matrix_ops",
+    out = "gen_sparse_csr_matrix_ops.py",
+    api_def_srcs = ["//tensorflow/core/api_def:base_api_def"],
+    visibility = [
+        "//learning/brain/python/ops:__pkg__",
+        "//tensorflow/compiler/tests:__pkg__",
+        "//tensorflow/contrib/quantization:__pkg__",
+        "//tensorflow/python/kernel_tests:__pkg__",
+    ],
+    deps = ["//tensorflow/core:sparse_csr_matrix_ops_op_lib"],
+)
+
+py_library(
+    name = "sparse",
+    srcs = [
+        "__init__.py",
+        "sparse.py",
+        "sparse_csr_matrix_grad.py",
+        "sparse_csr_matrix_ops.py",
+    ],
+    srcs_version = "PY2AND3",
+    deps = [
+        ":gen_sparse_csr_matrix_ops",
+        "//third_party/py/numpy",
+    ],
+)
diff --git a/tensorflow/python/ops/linalg/sparse/__init__.py b/tensorflow/python/ops/linalg/sparse/__init__.py
new file mode 100644
index 00000000000..e69de29bb2d
diff --git a/tensorflow/python/ops/linalg/sparse/sparse.py b/tensorflow/python/ops/linalg/sparse/sparse.py
new file mode 100644
index 00000000000..d00142ae131
--- /dev/null
+++ b/tensorflow/python/ops/linalg/sparse/sparse.py
@@ -0,0 +1,25 @@
+# Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+# ==============================================================================
+"""Public API for tf.linalg.sparse namespace."""
+
+from __future__ import absolute_import
+from __future__ import division
+from __future__ import print_function
+
+# go/tf-wildcard-import
+# pylint: disable=wildcard-import
+from tensorflow.python.ops.linalg.sparse.sparse_csr_matrix_grad import *
+from tensorflow.python.ops.linalg.sparse.sparse_csr_matrix_ops import *
+# pylint: enable=wildcard-import
diff --git a/tensorflow/python/ops/linalg/sparse/sparse_csr_matrix_grad.py b/tensorflow/python/ops/linalg/sparse/sparse_csr_matrix_grad.py
new file mode 100644
index 00000000000..7c9f7dae858
--- /dev/null
+++ b/tensorflow/python/ops/linalg/sparse/sparse_csr_matrix_grad.py
@@ -0,0 +1,233 @@
+# Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+# ==============================================================================
+"""CSR Sparse Matrix Gradients."""
+
+from __future__ import absolute_import
+from __future__ import division
+from __future__ import print_function
+
+from tensorflow.python.framework import ops
+from tensorflow.python.ops import array_ops
+from tensorflow.python.ops import math_ops
+from tensorflow.python.ops.linalg.sparse import sparse_csr_matrix_ops
+
+
+@ops.RegisterGradient("DenseToCSRSparseMatrix")
+def _DenseToCSRSparseMatrixGrad(op, grad):
+  """Gradient for dense_to_csr_sparse_matrix op."""
+  grad_values = (
+      sparse_csr_matrix_ops.csr_sparse_matrix_to_dense(
+          grad, type=op.get_attr("T")))
+  # inputs to fw op were: params, indices.
+  return (grad_values, None)
+
+
+@ops.RegisterGradient("CSRSparseMatrixToDense")
+def _CSRSparseMatrixToDenseGrad(op, grad):
+  """Gradient for csr_sparse_matrix_to_dense op."""
+  del op  # Unused
+  return sparse_csr_matrix_ops.dense_to_csr_sparse_matrix(
+      grad, array_ops.stop_gradient(array_ops.where(math_ops.abs(grad) > 0)))
+
+
+ops.NotDifferentiable("SparseMatrixNNZ")
+
+ops.NotDifferentiable("SparseMatrixZeros")
+
+
+@ops.RegisterGradient("SparseMatrixAdd")
+def _SparseMatrixAddGrad(op, grad):
+  """Gradient for sparse_matrix_add op."""
+  # input to sparse_matrix_add is (a, b, alpha, beta)
+  # with a, b CSR and alpha beta scalars.
+  # output is: alpha * a + beta * b
+
+  # d(a*A + b*B)/dA . grad = a * grad
+
+  # May have gotten the transposes wrong below.
+  # d(a*A + b*B)/da . grad = tr(A' . grad)
+
+  # For now, only implement gradients w.r.t. A and B.
+  # TODO(ebrevdo): Implement reduce_sum for SparseMatrix so that we
+  # can implement gradients w.r.t. a and b.
+  (_, _, alpha, beta) = op.inputs
+  return (sparse_csr_matrix_ops.sparse_matrix_mul(grad, alpha),
+          sparse_csr_matrix_ops.sparse_matrix_mul(grad, beta), None, None)
+
+
+@ops.RegisterGradient("SparseMatrixTranspose")
+def _SparseMatrixTransposeGrad(op, grad):
+  """Gradient for sparse_matrix_transpose op."""
+  return sparse_csr_matrix_ops.sparse_matrix_transpose(
+      grad, type=op.get_attr("type"), conjugate=op.get_attr("conjugate"))
+
+
+@ops.RegisterGradient("SparseMatrixSoftmax")
+def _SparseMatrixSoftmaxGrad(op, grad_softmax):
+  """Gradient for sparse_matrix_softmax op."""
+  softmax = op.outputs[0]
+  return sparse_csr_matrix_ops.sparse_matrix_softmax_grad(
+      softmax, grad_softmax, type=op.get_attr("type"))
+
+
+@ops.RegisterGradient("SparseMatrixMatMul")
+def _SparseMatrixMatMulGrad(op, grad):
+  """Gradient for sparse_matrix_mat_mul op."""
+  # input to sparse_matrix_mat_mul is (A, B) with CSR A and dense B.
+  # Output is dense:
+  #   C = opA(A) . opB(B) if transpose_output = false
+  #   C = (opA(A) . opB(B))' = opB(B)' . opA(A)' if transpose_output = true.
+  # where opA = transpose if transpose_a = True else identity
+  # and   opB = transpose if transpose_b = True else identity
+
+  t_a = op.get_attr("transpose_a")
+  t_b = op.get_attr("transpose_b")
+  adj_a = op.get_attr("adjoint_a")
+  adj_b = op.get_attr("adjoint_b")
+  transpose_output = op.get_attr("transpose_output")
+  conjugate_output = op.get_attr("conjugate_output")
+  a = op.inputs[0]  # sparse matrix
+  b = op.inputs[1]  # dense matrix
+  conj = math_ops.conj
+  sparse_matmul = sparse_csr_matrix_ops.sparse_matrix_mat_mul
+  matmul = math_ops.matmul
+
+  if conjugate_output:
+    grad = conj(grad)
+  if not transpose_output:
+    # C = opA(A) . opB(B)
+    if not adj_a and not adj_b:
+      a = conj(a)
+      b = conj(b)
+      if not t_a:
+        grad_a_dense = matmul(grad, b, transpose_b=not t_b)
+      else:
+        grad_a_dense = matmul(b, grad, transpose_a=t_b, transpose_b=True)
+      grad_b = sparse_matmul(a, grad, transpose_a=not t_a, transpose_output=t_b)
+    elif not t_a and not t_b:
+      if not adj_a:
+        grad_a_dense = matmul(grad, b, adjoint_b=not adj_b)
+      else:
+        grad_a_dense = matmul(b, grad, adjoint_a=adj_b, adjoint_b=True)
+      grad_b = sparse_matmul(
+          a,
+          grad,
+          adjoint_a=not adj_a,
+          transpose_output=adj_b,
+          conjugate_output=adj_b)
+    elif adj_a and t_b:
+      grad_a_dense = matmul(b, grad, transpose_a=True, adjoint_b=True)
+      grad_b = sparse_matmul(a, grad, transpose_output=True)
+    elif t_a and adj_b:
+      grad_a_dense = matmul(b, grad, transpose_a=True, transpose_b=True)
+      grad_b = sparse_matmul(
+          conj(a), grad, transpose_output=True, conjugate_output=True)
+  else:
+    # C = (opA(A) . opB(B))' =  opB(B)' . opA(A)'
+    if not adj_a and not adj_b:
+      a = conj(a)
+      b = conj(b)
+      if not t_a:
+        grad_a_dense = matmul(grad, b, transpose_a=True, transpose_b=not t_b)
+      else:
+        grad_a_dense = matmul(b, grad, transpose_a=t_b)
+      grad_b = sparse_matmul(
+          a, grad, transpose_a=not t_a, transpose_b=True, transpose_output=t_b)
+    elif not t_a and not t_b:
+      if not adj_a:
+        grad_a_dense = matmul(grad, b, transpose_a=True, adjoint_b=not adj_b)
+      else:
+        grad_a_dense = matmul(b, conj(grad), adjoint_a=adj_b)
+      grad_b = sparse_matmul(
+          a,
+          grad,
+          adjoint_a=not adj_a,
+          transpose_b=True,
+          transpose_output=adj_b,
+          conjugate_output=adj_b)
+    elif adj_a and t_b:
+      grad_a_dense = matmul(b, conj(grad), transpose_a=True)
+      grad_b = sparse_matmul(a, grad, transpose_b=True, transpose_output=True)
+    elif t_a and adj_b:
+      grad_a_dense = matmul(b, grad, transpose_a=True)
+      grad_b = sparse_matmul(a, grad, adjoint_b=True, transpose_output=True)
+
+  grad_a = sparse_csr_matrix_ops.dense_to_csr_sparse_matrix(
+      grad_a_dense, array_ops.where(math_ops.abs(grad_a_dense) > 0))
+  return (grad_a, grad_b)
+
+
+@ops.RegisterGradient("SparseMatrixSparseMatMul")
+def _SparseMatrixSparseMatMulGrad(op, grad):
+  """Gradient for sparse_matrix_sparse_mat_mul op."""
+  t_a = op.get_attr("transpose_a")
+  t_b = op.get_attr("transpose_b")
+  adj_a = op.get_attr("adjoint_a")
+  adj_b = op.get_attr("adjoint_b")
+  dtype = op.get_attr("type")
+
+  # input to sparse_matrix_sparse_mat_mul is (A, B) with CSR A and B.
+  # Output is CSR:
+  #   C = opA(A) . opB(B)
+  # where opA = transpose if transpose_a = True else identity
+  # and   opB = transpose if transpose_b = True else identity
+  a = op.inputs[0]
+  b = op.inputs[1]
+  conj = math_ops.conj
+  matmul = sparse_csr_matrix_ops.sparse_matrix_sparse_mat_mul
+  if not t_a and not t_b:
+    if not adj_a:
+      if not adj_b:
+        grad_a = matmul(grad, b, adjoint_b=True, type=dtype)
+        grad_b = matmul(a, grad, adjoint_a=True, type=dtype)
+      else:
+        grad_a = matmul(grad, b, type=dtype)
+        grad_b = matmul(grad, a, adjoint_a=True, type=dtype)
+    else:
+      if not adj_b:
+        grad_a = matmul(b, grad, adjoint_b=True, type=dtype)
+        grad_b = matmul(a, grad, type=dtype)
+      else:
+        grad_a = matmul(b, grad, adjoint_a=True, adjoint_b=True, type=dtype)
+        grad_b = matmul(grad, a, adjoint_a=True, adjoint_b=True, type=dtype)
+  elif not adj_a and not adj_b:
+    if not t_a and t_b:
+      grad_a = matmul(grad, conj(b), type=dtype)
+      grad_b = matmul(grad, conj(a), transpose_a=True, type=dtype)
+    elif t_a and not t_b:
+      grad_a = matmul(conj(b), grad, transpose_b=True, type=dtype)
+      grad_b = matmul(conj(a), grad, type=dtype)
+    else:
+      grad_a = matmul(b, grad, adjoint_a=True, transpose_b=True, type=dtype)
+      grad_b = matmul(grad, a, transpose_a=True, adjoint_b=True, type=dtype)
+  elif adj_a and t_b:
+    grad_a = matmul(b, grad, transpose_a=True, adjoint_b=True, type=dtype)
+    grad_b = matmul(grad, a, transpose_a=True, transpose_b=True, type=dtype)
+  elif t_a and adj_b:
+    grad_a = matmul(b, grad, transpose_a=True, transpose_b=True, type=dtype)
+    grad_b = matmul(grad, a, adjoint_a=True, transpose_b=True, type=dtype)
+
+  return (grad_a, grad_b)
+
+
+@ops.RegisterGradient("SparseMatrixMul")
+def _SparseMatrixMulGrad(op, grad):
+  """Gradient for sparse_matrix_mul op."""
+  # input to sparse_matrix_mul is (A, B) with CSR A and dense B.
+  # Output is CSR:
+  #   C = A .* B
+  del op
+  del grad
+  raise NotImplementedError
diff --git a/tensorflow/python/ops/linalg/sparse/sparse_csr_matrix_ops.py b/tensorflow/python/ops/linalg/sparse/sparse_csr_matrix_ops.py
new file mode 100644
index 00000000000..2dc54047fe7
--- /dev/null
+++ b/tensorflow/python/ops/linalg/sparse/sparse_csr_matrix_ops.py
@@ -0,0 +1,378 @@
+# Copyright 2019 The TensorFlow Authors. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+# ==============================================================================
+"""CSR Sparse Matrix Operations."""
+
+from __future__ import absolute_import
+from __future__ import division
+from __future__ import print_function
+
+import abc
+import collections
+
+import six
+
+# pylint: disable=g-direct-tensorflow-import, wildcard-import
+from tensorflow.python.eager import context
+from tensorflow.python.framework import cpp_shape_inference_pb2
+from tensorflow.python.framework import dtypes
+from tensorflow.python.framework import ops
+from tensorflow.python.framework import sparse_tensor
+from tensorflow.python.framework import tensor_shape
+from tensorflow.python.ops import array_ops
+from tensorflow.python.ops import math_ops
+from tensorflow.python.ops import resource_variable_ops
+from tensorflow.python.ops.linalg.sparse import gen_sparse_csr_matrix_ops as sm_ops
+from tensorflow.python.ops.linalg.sparse.gen_sparse_csr_matrix_ops import *
+
+
+__all__ = [
+    "SparseMatrix",
+    "CSRSparseMatrix",
+    "matmul",
+    "dense_shape_and_type",
+]
+# pylint: disable=invalid-name
+__all__ += [_x for _x in dir(sm_ops) if not _x.startswith("_")]
+
+
+class DenseShapeAndType(
+    collections.namedtuple("DenseShapeAndType", ("shape", "dtype"))):
+  pass
+
+
+def _get_handle_data(tensor):
+  return resource_variable_ops.get_eager_safe_handle_data(tensor)
+
+
+def _create_handle_data_proto(shape_proto, dtype_enum):
+  """Create handle data based on shape and dtype protos."""
+  variant_shape_and_type_data = \
+    cpp_shape_inference_pb2.CppShapeInferenceResult.HandleData()
+  variant_shape_and_type_data.is_set = True
+  # NOTE(ebrevdo): shape_and_type lacks append() in some versions of protobuf.
+  variant_shape_and_type_data.shape_and_type.extend([
+      cpp_shape_inference_pb2.CppShapeInferenceResult.HandleShapeAndType(
+          shape=shape_proto, dtype=dtype_enum)
+  ])
+  return variant_shape_and_type_data
+
+
+def _make_handle_data(tensor):
+  """Create handle data based on tensor shape and dtype."""
+  return _create_handle_data_proto(tensor.shape.as_proto(),
+                                   tensor.dtype.as_datatype_enum)
+
+
+def get_shape_and_type(matrix):
+  """Return matrix's shape and type if available."""
+  handle_data = getattr(matrix, "_handle_data", None)
+  if handle_data is None:
+    return None
+  if len(handle_data.shape_and_type) != 1:
+    raise ValueError(
+        "shape_and_type array in _handle_data must have length one, but saw: %d"
+        % len(handle_data.shape_and_type))
+  return handle_data.shape_and_type[0]
+
+
+def dense_shape_and_type(matrix):
+  """Get dense shape and dtype of the tf.Tensor containing the matrix.
+
+  Args:
+    matrix: A `tf.Tensor` of type `tf.variant` storing a sparse matrix.
+
+  Returns:
+    An instance of `ShapeAndType` with properties `shape` (a `tf.TensorShape`)
+    and `dtype` (a `tf.DType`).
+
+  Raises:
+    TypeError: if `matrix` is not a tensor or its dtype is not variant.
+    ValueError: if `matrix` lacks static handle data containing the dense
+      shape and dtype.
+  """
+  if not isinstance(matrix, ops.Tensor):
+    raise TypeError("matrix should be a tensor, but saw: %s" % (matrix,))
+  if matrix.dtype != dtypes.variant:
+    raise TypeError(
+        "expected matrix to be type tf.variant, but saw: %s" % (matrix.dtype,))
+  handle_data = _get_handle_data(matrix)
+  if not handle_data or not handle_data.is_set:
+    raise ValueError("matrix has missing handle data: %s" % (matrix,))
+  if len(handle_data.shape_and_type) != 1:
+    raise ValueError("len(matrix.handle_data.shape_and_type) != 1: '%s'" %
+                     (handle_data.shape_and_type,))
+  return DenseShapeAndType(
+      tensor_shape.TensorShape(handle_data.shape_and_type[0].shape),
+      dtypes.DType(handle_data.shape_and_type[0].dtype))
+
+
+def matmul_shape_inference(a, b, c, transpose_a, transpose_b, adjoint_a,
+                           adjoint_b):
+  """Helper function for matmul to set the result matrix's handle data."""
+  c_handle = getattr(c, "_handle_data", None)
+  a_shape_and_type = get_shape_and_type(a)
+  b_shape_and_type = get_shape_and_type(b)
+  if (c_handle is None and a_shape_and_type is not None and
+      b_shape_and_type is not None):
+
+    transpose_a = transpose_a or adjoint_a
+    transpose_b = transpose_b or adjoint_b
+
+    a_shape = a_shape_and_type.shape
+    b_shape = b_shape_and_type.shape
+    rank = len(a_shape.dim)
+
+    # Creates the output shape.
+    c_rows = a_shape.dim[rank - (1 if transpose_a else 2)].size
+    c_cols = b_shape.dim[rank - (2 if transpose_b else 1)].size
+    c_shape = tensor_shape.TensorShape(a_shape)
+    c_shape = tensor_shape.TensorShape(c_shape[:rank - 2] + [c_rows, c_cols])
+    c_handle = _create_handle_data_proto(c_shape.as_proto(),
+                                         a_shape_and_type.dtype)
+  return c_handle
+
+
+def matmul(a,
+           b,
+           transpose_a=False,
+           transpose_b=False,
+           adjoint_a=False,
+           adjoint_b=False,
+           name=None):
+  """Perform a sparse matrix matmul between `a` and `b`.
+
+  Performs a contraction between `a` and `b` along the two innermost dimensions.
+  If both `a` and `b` are instances of `SparseMatrix`, returns a new instance
+  of `SparseMatrix` (same type as `a`).  If one is not an instance of
+  `SparseMatrix`, returns a dense `Tensor`:
+
+  ```
+  c = opA(a) . opB(b)
+  ```
+  where `opA` (resp. `opB`) is the transpose or hermitian transpose depending
+  on the values of `transpose_a` (resp. `transpose_b`) and `adjoint_a`
+  (resp. `adjoint_b`).
+
+  Args:
+    a: `Tensor` or `SparseMatrix`, having rank `2` or `3`.
+    b: `Tensor` or `SparseMatrix`, having rank `2` or `3`.
+    transpose_a: Python `bool`.
+    transpose_b: Python `bool`.
+    adjoint_a: Python `bool`.
+    adjoint_b: Python `bool`.
+    name: Optional name to use when creating ops.
+
+  Returns:
+    A `SparseMatrix` if both `a` and `b` are instances of `SparseMatrix`,
+    otherwise a dense `Tensor`.
+  """
+  if not isinstance(a, SparseMatrix) and not isinstance(b, SparseMatrix):
+    return math_ops.matmul(
+        a,
+        b,
+        transpose_a=transpose_a,
+        transpose_b=transpose_b,
+        adjoint_a=adjoint_a,
+        adjoint_b=adjoint_b,
+        name=name)
+
+  # pylint: disable=protected-access
+  a_matrix = a._matrix if isinstance(a, SparseMatrix) else a
+  b_matrix = b._matrix if isinstance(b, SparseMatrix) else b
+  with ops.name_scope(name, "SparseMatrixMatMul", [a_matrix, b_matrix]):
+    if isinstance(a, SparseMatrix) and isinstance(b, SparseMatrix):
+      if not (isinstance(a, type(b)) or isinstance(b, type(a))):
+        raise TypeError("SparseMatrix types don't inherit from each other: "
+                        "%s and %s" % (type(a), type(b)))
+      c = sm_ops.sparse_matrix_sparse_mat_mul(
+          a_matrix,
+          b_matrix,
+          transpose_a=transpose_a,
+          transpose_b=transpose_b,
+          adjoint_a=adjoint_a,
+          adjoint_b=adjoint_b,
+          type=a.dtype)
+
+      # In eager mode, shape inference functions are not called, and the output
+      # shape is not set. We have to infer the output shape here.
+      # TODO(penporn): Set this from the C++ kernel instead.
+      c_handle = matmul_shape_inference(a_matrix, b_matrix, c, transpose_a,
+                                        transpose_b, adjoint_a, adjoint_b)
+      return a._from_matrix(c, handle_data=c_handle)
+
+    elif isinstance(a, SparseMatrix):
+      return sm_ops.sparse_matrix_mat_mul(
+          a_matrix,
+          b,
+          transpose_a=transpose_a,
+          transpose_b=transpose_b,
+          adjoint_a=adjoint_a,
+          adjoint_b=adjoint_b)
+    else:
+      # opA(A) . opB(B) = t(nopB(B) . nopA(A))
+      if not adjoint_a and not adjoint_b:
+        return sm_ops.sparse_matrix_mat_mul(
+            b_matrix,
+            a,
+            transpose_a=not transpose_b,
+            transpose_b=not transpose_a,
+            transpose_output=True)
+      elif not transpose_a and not transpose_b:
+        return sm_ops.sparse_matrix_mat_mul(
+            b_matrix,
+            a,
+            adjoint_a=not adjoint_b,
+            adjoint_b=not adjoint_a,
+            transpose_output=True,
+            conjugate_output=True)
+      else:
+        return sm_ops.sparse_matrix_mat_mul(
+            b_matrix,
+            math_ops.conj(a),
+            transpose_output=True,
+            conjugate_output=adjoint_b)
+
+
+class SparseMatrix(six.with_metaclass(abc.ABCMeta)):
+  """Abstract class for sparse matrix types."""
+
+  @abc.abstractmethod
+  def __init__(self):
+    self._eager_mode = context.executing_eagerly()
+
+  @abc.abstractproperty
+  def _matrix(self):
+    pass
+
+  @abc.abstractmethod
+  def _from_matrix(self, matrix, handle_data=None):
+    pass
+
+  @abc.abstractmethod
+  def to_dense(self):
+    pass
+
+  @abc.abstractmethod
+  def to_sparse_tensor(self):
+    pass
+
+  @property
+  def graph(self):
+    return self._matrix.graph
+
+  @property
+  def shape(self):
+    return dense_shape_and_type(self._matrix).shape
+
+  @property
+  def dtype(self):
+    return dense_shape_and_type(self._matrix).dtype
+
+  @property
+  def eager_handle_data(self):
+    """Return the matrix's handle data iff in eager mode."""
+    return _get_handle_data(self._matrix) if self._eager_mode else None
+
+  def conj(self):
+    return self._from_matrix(
+        math_ops.conj(self._matrix), self.eager_handle_data)
+
+  def hermitian_transpose(self):
+    """Return the hermitian transpose of the matrix."""
+    return self._from_matrix(
+        sm_ops.sparse_matrix_transpose(
+            self._matrix, conjugate=True, type=self.dtype),
+        self.eager_handle_data)
+
+  def nnz(self):
+    """Number of stored values, including explicit zeros."""
+    return sm_ops.sparse_matrix_nnz(self._matrix)
+
+  nonzero = nnz
+
+  def sorted_indices(self):
+    # TODO(ebrevdo): A more efficient implementation?
+    return self.to_sparse_tensor().indices
+
+  def transpose(self):
+    return self._from_matrix(
+        sm_ops.sparse_matrix_transpose(self._matrix, type=self.dtype),
+        self.eager_handle_data)
+
+
+class CSRSparseMatrix(SparseMatrix):
+  """(Optionally batched) CSR Sparse Matrix."""
+
+  def __init__(self, value, indices=None, name=None):
+    """Construct a CSRSparseMatrix from a dense matrix or SparseTensor.
+
+    Args:
+      value: A dense `2D` or `3D` Tensor or `SparseTensor`.
+      indices: The nonzero indices of `value`
+        (if `value` is not a `SparseTensor`).
+      name: Optional op name.
+
+    Raises:
+      ValueError: if `value` is a `SparseTensor` and `indices` is not `None`.
+    """
+    super(CSRSparseMatrix, self).__init__()
+    if isinstance(value, sparse_tensor.SparseTensor):
+      if indices is not None:
+        raise ValueError("indices must be None if value is a SparseTensor.")
+      self._dtype = value.dtype
+      self._csr_matrix = sm_ops.sparse_tensor_to_csr_sparse_matrix(
+          indices=value.indices,
+          values=value.values,
+          dense_shape=value.dense_shape)
+    else:
+      value = ops.convert_to_tensor(value)
+      self._dtype = value.dtype
+      if indices is not None:
+        indices = ops.convert_to_tensor(indices, dtype=dtypes.int64)
+      else:
+        indices = array_ops.stop_gradient(array_ops.where(value))
+      self._csr_matrix = sm_ops.dense_to_csr_sparse_matrix(value, indices)
+
+    # Eager mode doesn't call shape inference functions, so we have to set the
+    # shape and dtype handle data directly.
+    if self._eager_mode:
+      # pylint: disable=protected-access
+      self._csr_matrix._handle_data = _make_handle_data(value)
+      # pylint: enable=protected-access
+
+  @property
+  def _matrix(self):
+    return self._csr_matrix
+
+  def _from_matrix(self, matrix, handle_data=None):
+    assert isinstance(matrix, ops.Tensor) and matrix.dtype == dtypes.variant
+    ret = type(self).__new__(type(self))
+    # pylint: disable=protected-access
+    ret._dtype = self._dtype
+    if self._eager_mode:
+      if matrix._handle_data is None:
+        matrix._handle_data = handle_data
+      assert matrix._handle_data is not None
+    ret._csr_matrix = matrix
+    # pylint: enable=protected-access
+    return ret
+
+  def to_dense(self):
+    return sm_ops.csr_sparse_matrix_to_dense(self._matrix, type=self.dtype)
+
+  def to_sparse_tensor(self):
+    r = sm_ops.csr_sparse_matrix_to_sparse_tensor(self._matrix, type=self.dtype)
+    return sparse_tensor.SparseTensor(
+        indices=r.indices, values=r.values, dense_shape=r.dense_shape)
diff --git a/tensorflow/tools/test/BUILD b/tensorflow/tools/test/BUILD
index 20cbcd18b20..5607fe73361 100644
--- a/tensorflow/tools/test/BUILD
+++ b/tensorflow/tools/test/BUILD
@@ -102,3 +102,8 @@ tf_py_logged_benchmark(
     name = "rnn_op_benchmark",
     target = "//tensorflow/python/kernel_tests:rnn_test",
 )
+
+tf_py_logged_benchmark(
+    name = "sparse_csr_matrix_ops_benchmark",
+    target = "//tensorflow/python/kernel_tests:sparse_csr_matrix_ops_test_py",
+)
diff --git a/third_party/eigen3/BUILD b/third_party/eigen3/BUILD
index bd6cb868a90..595321fda8d 100644
--- a/third_party/eigen3/BUILD
+++ b/third_party/eigen3/BUILD
@@ -18,7 +18,10 @@ EIGEN3_THIRD_PARTY_HEADERS = [
     "Eigen/LU",
     "Eigen/Cholesky",
     "Eigen/Eigenvalues",
+    "Eigen/OrderingMethods",
     "Eigen/QR",
+    "Eigen/SparseCholesky",
+    "Eigen/SparseCore",
     "Eigen/SVD",
     "unsupported/Eigen/MatrixFunctions",
     "unsupported/Eigen/SpecialFunctions",
diff --git a/third_party/eigen3/Eigen/OrderingMethods b/third_party/eigen3/Eigen/OrderingMethods
new file mode 100644
index 00000000000..190fc224bbd
--- /dev/null
+++ b/third_party/eigen3/Eigen/OrderingMethods
@@ -0,0 +1 @@
+#include "Eigen/OrderingMethods"
\ No newline at end of file
diff --git a/third_party/eigen3/Eigen/SparseCholesky b/third_party/eigen3/Eigen/SparseCholesky
new file mode 100644
index 00000000000..a6d362b9cdd
--- /dev/null
+++ b/third_party/eigen3/Eigen/SparseCholesky
@@ -0,0 +1 @@
+#include "Eigen/SparseCholesky"
\ No newline at end of file
diff --git a/third_party/eigen3/Eigen/SparseCore b/third_party/eigen3/Eigen/SparseCore
new file mode 100644
index 00000000000..3c60745d09e
--- /dev/null
+++ b/third_party/eigen3/Eigen/SparseCore
@@ -0,0 +1 @@
+#include "Eigen/SparseCore"
\ No newline at end of file
diff --git a/third_party/eigen3/LICENSE b/third_party/eigen3/LICENSE
index a25d8e6fc6a..c355a5ec0f6 100644
--- a/third_party/eigen3/LICENSE
+++ b/third_party/eigen3/LICENSE
@@ -533,10 +533,12 @@ Following applies to:
 ./Eigen/src/MetisSupport/MetisSupport.h
 ./Eigen/StdVector
 ./Eigen/Core
+./Eigen/OrderingMethods
 ./Eigen/SparseLU
 ./Eigen/StdList
 ./Eigen/StdDeque
 ./Eigen/SparseCholesky
+./Eigen/SparseCore
 ./scripts/relicense.py
 ./scripts/relicense.py
 ./blas/BandTriangularSolver.h