tf.raw_ops.SparseMatrixSparseCholesky

Computes the sparse Cholesky decomposition of input.

tf.raw_ops.SparseMatrixSparseCholesky(
    input, permutation, type, name=None
)

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:

    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.