Computes the inverse of a complex Hermitian or real symmetric positive-definite matrix given its Cholesky decomposition.
Let A A A be a complex Hermitian or real symmetric positive-definite matrix, and L L L its Cholesky decomposition such that:
A = L LH A = LL^{\text{H}} A=LLH
where LH L^{\text{H}} LH is the conjugate transpose when L L L is complex, and the transpose when L L L is real-valued.
Computes the inverse matrix A − 1 A^{-1} A−1.
Supports input of float, double, cfloat and cdouble dtypes. Also supports batches of matrices, and if A A A is a batch of matrices then the output has the same batch dimensions.
L (Tensor) – tensor of shape (*, n, n) where * is zero or more batch dimensions consisting of lower or upper triangular Cholesky decompositions of symmetric or Hermitian positive-definite matrices.
upper (bool, optional) – flag that indicates whether L L L is lower triangular or upper triangular. Default: False
out (Tensor, optional) – output tensor. Ignored if None. Default: None.
Example:
>>> A = torch.randn(3, 3)
>>> A = A @ A.T + torch.eye(3) * 1e-3 # Creates a symmetric positive-definite matrix
>>> L = torch.linalg.cholesky(A) # Extract Cholesky decomposition
>>> torch.cholesky_inverse(L)
tensor([[ 1.9314, 1.2251, -0.0889],
[ 1.2251, 2.4439, 0.2122],
[-0.0889, 0.2122, 0.1412]])
>>> A.inverse()
tensor([[ 1.9314, 1.2251, -0.0889],
[ 1.2251, 2.4439, 0.2122],
[-0.0889, 0.2122, 0.1412]])
>>> A = torch.randn(3, 2, 2, dtype=torch.complex64)
>>> A = A @ A.mH + torch.eye(2) * 1e-3 # Batch of Hermitian positive-definite matrices
>>> L = torch.linalg.cholesky(A)
>>> torch.dist(torch.inverse(A), torch.cholesky_inverse(L))
tensor(5.6358e-7)
RetroSearch is an open source project built by @garambo | Open a GitHub Issue
Search and Browse the WWW like it's 1997 | Search results from DuckDuckGo
HTML:
3.2
| Encoding:
UTF-8
| Version:
0.7.4