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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)

Assuming a is a batched triangular matrix, solve the equation

$$ax=b$$

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 $ax=b$ 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 $ax=b$.

• 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 $ax=b$. 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 $ax=b$, 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.]