maxframe.tensor.linalg.solve_triangular#

maxframe.tensor.linalg.solve_triangular(a, b, lower=False, sparse=None)[source]#

Solve the equation a x = b for x, assuming a is a triangular matrix.

Parameters:

  • a ((M, M) array_like) – A triangular matrix

  • b ((M,) or (M, N) array_like) – Right-hand side matrix in a x = b

  • lower (bool, optional) – Use only data contained in the lower triangle of a. Default is to use upper triangle.

  • sparse (bool, optional) – Return sparse value or not.

Returns:

x – Solution to the system a x = b. Shape of return matches b.

Return type:

(M,) or (M, N) ndarray

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 maxframe.tensor as mt
>>> a = mt.array([[3, 0, 0, 0], [2, 1, 0, 0], [1, 0, 1, 0], [1, 1, 1, 1]])
>>> b = mt.array([4, 2, 4, 2])
>>> x = mt.linalg.solve_triangular(a, b, lower=True)
>>> x.execute()
array([ 1.33333333, -0.66666667,  2.66666667, -1.33333333])

>>> a.dot(x).execute()  # Check the result
array([ 4.,  2.,  4.,  2.])