TriangularSolve

public final class TriangularSolve

Solves systems of linear equations with upper or lower triangular matrices by backsubstitution.

`matrix` is a tensor of shape `[..., M, M]` whose inner-most 2 dimensions form square matrices. If `lower` is `True` then the strictly upper triangular part of each inner-most matrix is assumed to be zero and not accessed. If `lower` is False then the strictly lower triangular part of each inner-most matrix is assumed to be zero and not accessed. `rhs` is a tensor of shape `[..., M, N]`.

The output is a tensor of shape `[..., M, N]`. If `adjoint` is `True` then the innermost matrices in `output` satisfy matrix equations `matrix[..., :, :] * output[..., :, :] = rhs[..., :, :]`. If `adjoint` is `False` then the strictly then the innermost matrices in `output` satisfy matrix equations `adjoint(matrix[..., i, k]) * output[..., k, j] = rhs[..., i, j]`.

Note, the batch shapes for the inputs only need to broadcast.

Example:

a = tf.constant([[3,  0,  0,  0],
                  [2,  1,  0,  0],
                  [1,  0,  1,  0],
                  [1,  1,  1,  1]], dtype=tf.float32)
 
 b = tf.constant([[4],
                  [2],
                  [4],
                  [2]], dtype=tf.float32)
 
 x = tf.linalg.triangular_solve(a, b, lower=True)
 x
 # <tf.Tensor: shape=(4, 1), dtype=float32, numpy=
 # array([[ 1.3333334 ],
 #        [-0.66666675],
 #        [ 2.6666665 ],
 #        [-1.3333331 ]], dtype=float32)>
 
 # in python3 one can use `a@x`
 tf.matmul(a, x)
 # <tf.Tensor: shape=(4, 1), dtype=float32, numpy=
 # array([[4.       ],
 #        [2.       ],
 #        [4.       ],
 #        [1.9999999]], dtype=float32)>

Nested Classes

class TriangularSolve.Options Optional attributes for TriangularSolve

Constants

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

Public Methods

static TriangularSolve.Options	adjoint(Boolean adjoint)
Output<T>	asOutput() Returns the symbolic handle of the tensor.
static <T extends TType> TriangularSolve<T>	create(Scope scope, Operand<T> matrix, Operand<T> rhs, Options... options) Factory method to create a class wrapping a new TriangularSolve operation.
static TriangularSolve.Options	lower(Boolean lower)
Output<T>	output() Shape is `[..., M, K]`.

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<T>	asOutput() Returns the symbolic handle of the tensor.
abstract T	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<T>	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.

Constants

public static final String OP_NAME

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

Constant Value: "MatrixTriangularSolve"

Public Methods

public static TriangularSolve.Options adjoint (Boolean adjoint)

Parameters

adjoint	Boolean indicating whether to solve with `matrix` or its (block-wise) adjoint.

public Output<T> asOutput ()

Returns the symbolic handle of the tensor.

Inputs to TensorFlow operations are outputs of another TensorFlow operation. This method is used to obtain a symbolic handle that represents the computation of the input.

public static TriangularSolve<T> create (Scope scope, Operand<T> matrix, Operand<T> rhs, Options... options)

Factory method to create a class wrapping a new TriangularSolve operation.

Parameters

scope	current scope
matrix	Shape is `[..., M, M]`.
rhs	Shape is `[..., M, K]`.
options	carries optional attributes values

Returns

a new instance of TriangularSolve

public static TriangularSolve.Options lower (Boolean lower)

Parameters

lower	Boolean indicating whether the innermost matrices in `matrix` are lower or upper triangular.

public Output<T> output ()

Shape is `[..., M, K]`.