cholesky_inverse¶

paddle.linalg. cholesky_inverse ( x: Tensor, upper: bool = False, name: str | None = None ) → Tensor [source]

Using the Cholesky factor U to calculate the inverse matrix of a symmetric positive definite matrix, returns the matrix inv.

If upper is False, U is lower triangular matrix:

\[inv = (UU^{T})^{-1}\]

If upper is True, U is upper triangular matrix:

\[inv = (U^{T}U)^{-1}\]

Parameters

• x (Tensor) – A tensor of lower or upper triangular Cholesky decompositions of symmetric matrix with shape [N, N]. The data type of the x should be one of float32, float64.

• upper (bool, optional) – If upper is False, x is lower triangular matrix, or is upper triangular matrix. Default: False.

• name (str|None, optional) – For details, please refer to Name. Generally, no setting is required. Default: None.

Returns

Tensor. Computes the inverse matrix.

Examples

>>> import paddle

>>> # lower triangular matrix
>>> x = paddle.to_tensor([[3.,.0,.0], [5.,3.,.0], [-1.,1.,2.]])
>>> out = paddle.linalg.cholesky_inverse(x)
>>> print(out)
Tensor(shape=[3, 3], dtype=float32, place=Place(gpu:0), stop_gradient=True,
[[ 0.61728382, -0.25925916,  0.22222219],
 [-0.25925916,  0.13888884, -0.08333331],
 [ 0.22222218, -0.08333331,  0.25000000]])

>>> # upper triangular matrix
>>> out = paddle.linalg.cholesky_inverse(x.T, upper=True)
>>> print(out)
Tensor(shape=[3, 3], dtype=float32, place=Place(gpu:0), stop_gradient=True,
[[ 0.61728382, -0.25925916,  0.22222219],
 [-0.25925916,  0.13888884, -0.08333331],
 [ 0.22222218, -0.08333331,  0.25000000]])