# tensorplay.functional.triangular_solve

Source: https://www.tensorplay.cn/docs/generated/tensorplay.functional.triangular_solve.html

```python
tensorplay.functional.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 $A$
and multiple right-hand sides $b$.

In symbols, it solves $AX = b$ and assumes $A$ is square upper-triangular
(or lower-triangular if upper= False) and does not have zeros on the diagonal.

tensorplay.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.

> **Warning**
>
> tensorplay.triangular_solve() is deprecated in favor of tensorplay.linalg.solve_triangular() tensorplay.linalg.solve_triangular() has its arguments reversed and does not return a copy of one of the inputs. X = tensorplay.triangular_solve(B, A).solution should be replaced with @@TPBLOCK_0@@

Parameters:

- b ([Tensor](/docs/generated/tensorplay.Tensor.html#tensorplay.Tensor)) – multiple right-hand sides of size $(*, m, k)$ where $*$ is zero of more batch dimensions

- A ([Tensor](/docs/generated/tensorplay.Tensor.html#tensorplay.Tensor)) – the input triangular coefficient matrix of size $(*, m, m)$ where $*$ is zero or more batch dimensions

- upper ([bool](https://docs.python.org/3/builtins/functions.html#bool), optional) – whether $A$ is upper or lower triangular. Default: True.

- transpose ([bool](https://docs.python.org/3/builtins/functions.html#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](https://docs.python.org/3/builtins/functions.html#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.

Keyword Arguments:

out (([Tensor](/docs/generated/tensorplay.Tensor.html#tensorplay.Tensor), [Tensor](/docs/generated/tensorplay.Tensor.html#tensorplay.Tensor)), optional) – tuple of two tensors to write
the output to. Ignored if None. Default: None.

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 = tensorplay.randn(2, 2).triu()
>>> A
tensor([[ 1.1527, -1.0753],
        [ 0.0000,  0.7986]])
>>> b = tensorplay.randn(2, 3)
>>> b
tensor([[-0.0210,  2.3513, -1.5492],
        [ 1.5429,  0.7403, -1.0243]])
>>> tensorplay.triangular_solve(b, A)
tensorplay.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]]))
```