Solves a system of equations with a square upper or lower triangular invertible matrix A A A and multiple right-hand sides b b b.
In symbols, it solves A X = b AX = b AX=b and assumes A A A 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 A contains 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 ( ∗ , m , k ) (*, m, k) (∗,m,k) where ∗ * ∗ is zero of more batch dimensions
A (Tensor) – the input triangular coefficient matrix of size ( ∗ , m , m ) (*, m, m) (∗,m,m) where ∗ * ∗ is zero or more batch dimensions
upper (bool, optional) – whether A A A is upper or lower triangular. Default: True.
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 False. Default: False.
unitriangular (bool, optional) – whether A A A is unit triangular. If True, the diagonal elements of A A A are assumed to be 1 and not referenced from A A A. Default: False.
out ((Tensor, Tensor), optional) – tuple of two tensors to write the output to. Ignored if None. Default: None.
A namedtuple (solution, cloned_coefficient) where cloned_coefficient is a clone of A A A and solution is the solution X X X to A X = b AX = b AX=b (or whatever variant of the system of equations, depending on the keyword arguments.)
Examples:
>>> 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]]))
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