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.sparse.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
.
Args | |
---|---|
input
|
A Tensor of type variant . A CSRSparseMatrix .
|
permutation
|
A Tensor of type int32 .
A fill-in reducing permutation matrix.
|
type
|
A tf.DType from: tf.float32, tf.float64, tf.complex64, tf.complex128 .
|
name
|
A name for the operation (optional). |
Returns | |
---|---|
A Tensor of type variant .
|