# cholesky_solve¶

paddle.linalg. cholesky_solve ( x, y, upper=False, name=None ) [source]

Solves a linear system of equations A @ X = B, given A’s Cholesky factor matrix u and matrix B.

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

Parameters
• x (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 or float64.

• y (Tensor) – The input matrix which is upper or lower triangular Cholesky factor of square matrix A. Its shape should be [*, M, M], where * is zero or more batch dimensions. Its data type should be float32 or float64.

• upper (bool, optional) – whether to consider the Cholesky factor as a lower or upper triangular matrix. Default: False.

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

Returns

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

Return type

Tensor

Examples

```>>> import paddle

>>> u = paddle.to_tensor([[1, 1, 1],
...                       [0, 2, 1],
...                       [0, 0,-1]], dtype="float64")
>>> b = paddle.to_tensor([[0], [-9], [5]], dtype="float64")
>>> out = paddle.linalg.cholesky_solve(b, u, upper=True)

>>> print(out)