triangular_solve(b, A, upper=True, transpose=False, unitriangular=False, *, out=None)¶
Solves a system of equations with a triangular coefficient matrix and multiple right-hand sides .
In particular, solves and assumes is upper-triangular with the default keyword arguments.
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.
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 to solve the upper-triangular system of equations (default) or the lower-triangular system of equations. Default:
transpose (bool, optional) – whether should be transposed before being sent into the solver. Default:
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]]))