solve_triangular(A, B, *, upper, left=True, unitriangular=False, out=None) → Tensor¶
Computes the solution of a triangular system of linear equations with a unique solution.
Letting be or , this function computes the solution of the linear system associated to the triangular matrix without zeros on the diagonal (that is, it is invertible) and the rectangular matrix , , which is defined as
uppersignals whether is upper or lower triangular.
left= False, this function returns the matrix that solves the system
upper= True (resp. False) just the upper (resp. lower) triangular half of
Awill be accessed. The elements below the main diagonal will be considered to be zero and will not be accessed.
unitriangular= True, the diagonal of
Ais assumed to be ones and will not be accessed.
The result may contain NaN s if the diagonal of
Acontains zeros or elements that are very close to zero and
unitriangular= False (default) or if the input matrix has very small eigenvalues.
Supports inputs of float, double, cfloat and cdouble dtypes. Also supports batches of matrices, and if the inputs are batches of matrices then the output has the same batch dimensions.
torch.linalg.solve()computes the solution of a general square system of linear equations with a unique solution.
- Keyword Arguments
upper (bool) – whether
Ais an upper or lower triangular matrix.
left (bool, optional) – whether to solve the system or . Default: True.
unitriangular (bool, optional) – if True, the diagonal elements of
Aare assumed to be all equal to 1. Default: False.
out (Tensor, optional) – output tensor. B may be passed as out and the result is computed in-place on B. Ignored if None. Default: None.
>>> A = torch.randn(3, 3).triu_() >>> b = torch.randn(3, 4) >>> X = torch.linalg.solve_triangular(A, B, upper=True) >>> torch.allclose(A @ X, B) True >>> A = torch.randn(2, 3, 3).tril_() >>> B = torch.randn(2, 3, 4) >>> X = torch.linalg.solve_triangular(A, B, upper=False) >>> torch.allclose(A @ X, B) True >>> A = torch.randn(2, 4, 4).tril_() >>> B = torch.randn(2, 3, 4) >>> X = torch.linalg.solve_triangular(A, B, upper=False, left=False) >>> torch.allclose(X @ A, B) True