View source on GitHub |
Solve systems of linear equations with upper or lower triangular matrices.
tf.linalg.triangular_solve(
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 sum_k matrix[..., i, k] * output[..., k, j] = rhs[..., i, j]
.
If adjoint
is False
then the
innermost matrices in output satisfy matrix equations
sum_k adjoint(matrix[..., i, k]) * output[..., k, j] = rhs[..., i, j]
.
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)>
tf.matmul(a, x)
<tf.Tensor: shape=(4, 1), dtype=float32, numpy=
array([[4.],
[2.],
[4.],
[2.]], dtype=float32)>
Returns | |
---|---|
A Tensor . Has the same type as matrix, and shape is [..., M, N] .
|