mindspore.scipy.linalg.solve_triangular

mindspore.scipy.linalg.solve_triangular(a, b, trans=0, lower=False, unit_diagonal=False, overwrite_b=False, debug=None, check_finite=True)[source]

Assuming a is a batched triangular matrix, solve the equation

\[a x = b\]

Note

solve_triangular is not supported on Windows platform yet.
Only float32, float64, int32, int64 are supported Tensor dtypes. If Tensor with dtype int32 or int64 is passed, it will be cast to mstype.float64.
The floating point error will accumulate when the size of input matrix gets larger. Substituting result x back into \(a x = b\) would be a way to evaluate the result. If the input shape is large enough, using float64 instead of float32 is also a way to mitigate the error.

Parameters

a (Tensor) – A non-singular triangular matrix of shape \((M, M)\).
b (Tensor) – A Tensor of shape \((M,)\) or \((M, N)\). Right-hand side matrix in \(a x = b\).
lower (bool, optional) – Use only data contained in the lower triangle of a. Default: False.
trans (0, 1, 2, 'N', 'T', 'C', optional) –
Type of system to solve. Default: 0.

trans

system

0 or ‘N’

a x = b

1 or ‘T’

a^T x = b

2 or ‘C’

a^H x = b
unit_diagonal (bool, optional) – If True, diagonal elements of \(a\) are assumed to be 1 and will not be referenced. Default: False.
overwrite_b (bool, optional) – Allow overwriting data in \(b\) (may enhance performance). Default: False.
debug (None) – Not implemented now. Default: None.
check_finite (bool, optional) – Whether to check that the input matrices contain only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs. Default: True.

Returns

Tensor of shape \((M,)\) or \((M, N)\), which is the solution to the system \(a x = b\). Shape of \(x\) matches \(b\).

Raises

TypeError – If a is not Tensor.
ValueError – If a is not 2 dimension.
TypeError – If b is not Tensor.
ValueError – If b is not 1 or 2 dimension.
TypeError – If dtype of a and b are not the same.
ValueError – If the shape of a and b are not matched.
TypeError – If trans is not int or str.
ValueError – If trans is not in set {0, 1, 2, ‘N’, ‘T’, ‘C’}.
TypeError – If lower is not bool.
TypeError – If unit_diagonal is not bool.
TypeError – If overwrite_b is not bool.
TypeError – If check_finite is not bool.
ValueError – If debug is not None.
ValueError – If a is singular matrix.

Supported Platforms:: CPU GPU

Examples

Solve the lower triangular system \(a x = b\), where:

     [3  0  0  0]       [4]
a =  [2  1  0  0]   b = [2]
     [1  0  1  0]       [4]
     [1  1  1  1]       [2]

>>> import numpy as onp
>>> from mindspore.common import Tensor
>>> import mindspore.numpy as mnp
>>> from mindspore.scipy.linalg import solve_triangular
>>> a = Tensor(onp.array([[3, 0, 0, 0], [2, 1, 0, 0], [1, 0, 1, 0], [1, 1, 1, 1]], onp.float64))
>>> b = Tensor(onp.array([4, 2, 4, 2], onp.float64))
>>> x = solve_triangular(a, b, lower=True, unit_diagonal=False, trans='N')
>>> print(x)
[ 1.33333333 -0.66666667  2.66666667 -1.33333333]
>>> print(mnp.dot(a, x))  # Check the result
[4. 2. 4. 2.]

trans	system
0 or ‘N’	a x = b
1 or ‘T’	a^T x = b
2 or ‘C’	a^H x = b