mindspore.mint.triangular_solve

mindspore.mint.triangular_solve(b, A, upper=True, transpose=False, unitriangular=False)

Solves a system of equations with a square upper or lower triangular invertible matrix A and multiple right-hand sides b.

In symbols, it solves \(A X = b\) and assumes A is square upper-triangular (or lower-triangular if upper = False) and does not have zeros on the diagonal.

Warning

This is an experimental API that is subject to change or deletion.

Parameters

• b (Tensor) – A Tensor of shape \((*, M, K)\) where * is zero of more batch dimensions.

• A (Tensor) – A Tensor of shape \((*, M, M)\) where * is zero of more batch dimensions.

• upper (bool, optional) – Whether A is upper or lower triangular. Default: True.

• transpose (bool, optional) – Solves \(op(A) X = b\) where \(op(A) = A^T\) if this flag is True, and \(op(A) = A\) if it is False, Default: False.

• unitriangular (bool, optional) – Whether A is unit triangular. If True, the diagonal elements of A are assumed to be 1 and not referenced from A. Default: False.

Returns

A tuple of X and A.

Raises

• TypeError – If argument b is not Tensor.

• TypeError – If argument A is not Tensor.

• TypeError – If upper is not bool.

• TypeError – If transpose is not bool.

• TypeError – If unitriangular is not bool.

• ValueError – If the rank of b or A is not in the range of \([2, 6]\).

• ValueError – If the shapes of b and A are not matched.

Supported Platforms:

Ascend

Examples

>>> import numpy as np
>>> from mindspore import mint
>>> from mindspore import Tensor
>>> b = Tensor(np.ones((2, 3, 4), dtype=np.float32))
>>> A = Tensor(np.ones((2, 3, 3), dtype=np.float32))
>>> output = mint.triangular_solve(b, A)
>>> print(output[0])
[[[ 0.  0.  0.  0.]
  [ 0.  0.  0.  0.]
  [ 1.  1.  1.  1.]]
 [[ 0.  0.  0.  0.]
  [ 0.  0.  0.  0.]
  [ 1.  1.  1.  1.]]]