triangular_solve

paddle.linalg. triangular_solve ( x: Tensor, y: Tensor, upper: bool = True, transpose: bool = False, unitriangular: bool = False, name: str | None = None ) → Tensor [source]

Computes the solution of a system of equations with a triangular coefficient. x is coefficient matrix y is multiple right-hand sides of equations.

Input x and y is 2D matrices or batches of 2D matrices. If the inputs are batches, the outputs is also batches.

Equations can be described as:

\[x * Out = y\]

Solution of Equations is:

\[Out = x ^ {-1} * y\]

Parameters

• x (Tensor) – The input triangular coefficient matrix. Its shape should be [*, M, M], where * is zero or more batch dimensions. Its data type should be float32, float64, complex64, complex128.

• y (Tensor) – Multiple right-hand sides of system of equations. Its shape should be [*, M, K], where * is zero or more batch dimensions. Its data type should be float32, float64, complex64, complex128.

• 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 x should be transposed before calculation. Default: False.

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

• name (str|None, optional) – Name for the operation (optional, default is None). For more information, please refer to api_guide_Name.

Returns

The solution of the system of equations. Its data type should be the same as that of x.

Return type

Tensor

Examples

>>> # a square system of linear equations:
>>> # x1 +   x2  +   x3 = 0
>>> #      2*x2  +   x3 = -9
>>> #               -x3 = 5

>>> import paddle
>>> x = paddle.to_tensor([[1, 1, 1],
...                       [0, 2, 1],
...                       [0, 0,-1]], dtype="float64")
>>> y = paddle.to_tensor([[0], [-9], [5]], dtype="float64")
>>> out = paddle.linalg.triangular_solve(x, y, upper=True)

>>> print(out)
Tensor(shape=[3, 1], dtype=float64, place=Place(cpu), stop_gradient=True,
[[ 7.],
 [-2.],
 [-5.]])