tf.linalg.triangular_solve
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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)>
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,
N].
|
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, and shape is [..., M, N].
|
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Last updated 2024-04-26 UTC.
[null,null,["Last updated 2024-04-26 UTC."],[],[],null,["# tf.linalg.triangular_solve\n\n\u003cbr /\u003e\n\n|-----------------------------------------------------------------------------------------------------------------------------|\n| [View source on GitHub](https://github.com/tensorflow/tensorflow/blob/v2.16.1/tensorflow/python/ops/linalg_ops.py#L84-L144) |\n\nSolve systems of linear equations with upper or lower triangular matrices.\n\n#### View aliases\n\n\n**Compat aliases for migration**\n\nSee\n[Migration guide](https://www.tensorflow.org/guide/migrate) for\nmore details.\n\n[`tf.compat.v1.linalg.triangular_solve`](https://www.tensorflow.org/api_docs/python/tf/linalg/triangular_solve), [`tf.compat.v1.matrix_triangular_solve`](https://www.tensorflow.org/api_docs/python/tf/linalg/triangular_solve)\n\n\u003cbr /\u003e\n\n tf.linalg.triangular_solve(\n matrix, rhs, lower=True, adjoint=False, name=None\n )\n\n`matrix` is a tensor of shape `[..., M, M]` whose inner-most 2 dimensions form\nsquare matrices. If `lower` is `True` then the strictly upper triangular part\nof each inner-most matrix is assumed to be zero and not accessed. If `lower`\nis `False` then the strictly lower triangular part of each inner-most matrix\nis assumed to be zero and not accessed. `rhs` is a tensor of shape\n`[..., M, N]`.\n\nThe output is a tensor of shape `[..., M, N]`. If `adjoint` is `True` then the\ninnermost matrices in output satisfy matrix equations `sum_k matrix[..., i, k] * output[..., k, j] = rhs[..., i, j]`.\nIf `adjoint` is `False` then the\ninnermost matrices in output satisfy matrix equations\n`sum_k adjoint(matrix[..., i, k]) * output[..., k, j] = rhs[..., i, j]`.\n\n#### Example:\n\n a = tf.constant([[3, 0, 0, 0],\n [2, 1, 0, 0],\n [1, 0, 1, 0],\n [1, 1, 1, 1]], dtype=tf.float32)\n\n b = tf.constant([[4], [2], [4], [2]], dtype=tf.float32)\n x = tf.linalg.triangular_solve(a, b, lower=True)\n x\n \u003ctf.Tensor: shape=(4, 1), dtype=float32, numpy=\n array([[ 1.3333334 ],\n [-0.66666675],\n [ 2.6666665 ],\n [-1.3333331 ]], dtype=float32)\u003e\n tf.matmul(a, x)\n \u003ctf.Tensor: shape=(4, 1), dtype=float32, numpy=\n array([[4.],\n [2.],\n [4.],\n [2.]], dtype=float32)\u003e\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n| Args ---- ||\n|-----------|------------------------------------------------------------------------------------------------------------------------------------|\n| `matrix` | A `Tensor`. Must be one of the following types: `float64`, `float32`, `half`, `complex64`, `complex128`. Shape is `[..., M, M]`. |\n| `rhs` | A `Tensor`. Must have the same type as `matrix`. Shape is `[..., M, N]`. |\n| `lower` | An optional `bool`. Defaults to `True`. Boolean indicating whether the innermost matrices in matrix are lower or upper triangular. |\n| `adjoint` | An optional `bool`. Defaults to `False`. Boolean indicating whether to solve with matrix or its (block-wise) adjoint. |\n| `name` | A name for the operation (optional). |\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n\u003cbr /\u003e\n\n| Returns ------- ||\n|---|---|\n| A `Tensor`. Has the same type as matrix, and shape is `[..., M, N]`. ||\n\n\u003cbr /\u003e"]]
View source on GitHub