SparseMatrixSparseCholesky

Computes the sparse Cholesky decomposition of `input`.

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`.

Constants

String

OP_NAME

The name of this op, as known by TensorFlow core engine

Public Methods

Output<TType>	asOutput() Returns the symbolic handle of the tensor.
static <T extends TType> SparseMatrixSparseCholesky	create(Scope scope, Operand<?> input, Operand<TInt32> permutation, Class<T> type) Factory method to create a class wrapping a new SparseMatrixSparseCholesky operation.
Output<?>	output() The sparse Cholesky decompsition of `input`.

Inherited Methods

From class org.tensorflow.op.RawOp

final boolean	equals(Object obj)
final int	hashCode()
Operation	op() Return this unit of computation as a single Operation.
final String	toString()

From class java.lang.Object

boolean	equals(Object arg0)
final Class<?>	getClass()
int	hashCode()
final void	notify()
final void	notifyAll()
String	toString()
final void	wait(long arg0, int arg1)
final void	wait(long arg0)
final void	wait()

From interface org.tensorflow.op.Op

abstract ExecutionEnvironment	env() Return the execution environment this op was created in.
abstract Operation	op() Return this unit of computation as a single Operation.

From interface org.tensorflow.Operand

abstract Output<TType>	asOutput() Returns the symbolic handle of the tensor.
abstract TType	asTensor() Returns the tensor at this operand.
abstract Shape	shape() Returns the (possibly partially known) shape of the tensor referred to by the Output of this operand.
abstract Class<TType>	type() Returns the tensor type of this operand

From interface org.tensorflow.ndarray.Shaped

abstract int	rank()
abstract Shape	shape()
abstract long	size() Computes and returns the total size of this container, in number of values.