# torch.triangular_solve¶

torch.triangular_solve(b, A, upper=True, transpose=False, unitriangular=False) -> (Tensor, Tensor)

Solves a system of equations with a triangular coefficient matrix $A$ and multiple right-hand sides $b$.

In particular, solves $AX = b$ and assumes $A$ 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

Supports input of float, double, cfloat and cdouble data types.

Parameters
• b (Tensor) – multiple right-hand sides of size $(*, m, k)$ where $*$ is zero of more batch dimensions

• A (Tensor) – the input triangular coefficient matrix of size $(*, m, m)$ 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: True.

• transpose (bool, optional) – whether $A$ should be transposed before being sent into the solver. Default: False.

• unitriangular (bool, optional) – whether $A$ is unit triangular. If True, the diagonal elements of $A$ are assumed to be 1 and not referenced from $A$. Default: False.

Returns

A namedtuple (solution, cloned_coefficient) where cloned_coefficient is a clone of $A$ and solution is the solution $X$ to $AX = b$ (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]]))