Solves systems of linear equations with upper or lower triangular matrices by backsubstitution.
tf.raw_ops.MatrixTriangularSolve(
matrix, rhs, lower=True, adjoint=False, name=None
)
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)>
Args | |
---|---|
matrix
|
A Tensor . Must be one of the following types: float64 , float32 , half , complex64 , complex128 .
Shape is [..., M, M] .
|
rhs
|
A Tensor . Must have the same type as matrix .
Shape is [..., M, K] .
|
lower
|
An optional bool . Defaults to True .
Boolean indicating whether the innermost matrices in matrix are
lower or upper triangular.
|
adjoint
|
An optional bool . Defaults to False .
Boolean indicating whether to solve with matrix or its (block-wise)
adjoint.
|
name
|
A name for the operation (optional). |
Returns | |
---|---|
A Tensor . Has the same type as matrix .
|
Numpy Compatibility
Equivalent to scipy.linalg.solve_triangular