triangular_solve(b, A, upper=True, transpose=False, unitriangular=False, *, out=None)¶
Solves a system of equations with a square upper or lower triangular invertible matrix and multiple right-hand sides .
In symbols, it solves and assumes is square upper-triangular (or lower-triangular if
upper= False) and does not have zeros on the diagonal.
torch.triangular_solve(b, A) can take in 2D inputs b, A or inputs that are batches of 2D matrices. If the inputs are batches, then returns batched outputs X
If the diagonal of
Acontains zeros or elements that are very close to zero and
unitriangular= False (default) or if the input matrix is badly conditioned, the result may contain NaN s.
Supports input of float, double, cfloat and cdouble data types.
torch.triangular_solve()is deprecated in favor of
torch.linalg.solve_triangular()and will be removed in a future PyTorch release.
torch.linalg.solve_triangular()has its arguments reversed and does not return a copy of one of the inputs.
X = torch.triangular_solve(B, A).solutionshould be replaced with
X = torch.linalg.solve_triangular(A, B)
b (Tensor) – multiple right-hand sides of size where is zero of more batch dimensions
A (Tensor) – the input triangular coefficient matrix of size where is zero or more batch dimensions
upper (bool, optional) – whether is upper or lower triangular. Default:
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
unitriangular (bool, optional) – whether is unit triangular. If True, the diagonal elements of are assumed to be 1 and not referenced from . Default:
- Keyword Arguments
A namedtuple (solution, cloned_coefficient) where cloned_coefficient is a clone of and solution is the solution to (or whatever variant of the system of equations, depending on the keyword arguments.)
>>> A = torch.randn(2, 2).triu() >>> A tensor([[ 1.1527, -1.0753], [ 0.0000, 0.7986]]) >>> b = torch.randn(2, 3) >>> b tensor([[-0.0210, 2.3513, -1.5492], [ 1.5429, 0.7403, -1.0243]]) >>> torch.triangular_solve(b, A) torch.return_types.triangular_solve( solution=tensor([[ 1.7841, 2.9046, -2.5405], [ 1.9320, 0.9270, -1.2826]]), cloned_coefficient=tensor([[ 1.1527, -1.0753], [ 0.0000, 0.7986]]))