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Computes the Cholesky decomposition of a complex Hermitian or real symmetric positive-definite matrix.

Source: R/linalg.R
linalg_cholesky_ex.Rd

This function skips the (slow) error checking and error message construction of linalg_cholesky(), instead directly returning the LAPACK error codes as part of a named tuple (L, info). This makes this function a faster way to check if a matrix is positive-definite, and it provides an opportunity to handle decomposition errors more gracefully or performantly than linalg_cholesky() does. Supports input of float, double, cfloat and cdouble dtypes. Also supports batches of matrices, and if A is a batch of matrices then the output has the same batch dimensions. If A is not a Hermitian positive-definite matrix, or if it's a batch of matrices and one or more of them is not a Hermitian positive-definite matrix, then info stores a positive integer for the corresponding matrix. The positive integer indicates the order of the leading minor that is not positive-definite, and the decomposition could not be completed. info filled with zeros indicates that the decomposition was successful. If check_errors=TRUE and info contains positive integers, then a RuntimeError is thrown.

Usage

linalg_cholesky_ex(A, check_errors = FALSE)

Arguments

A

(Tensor): the Hermitian n \times n matrix or the batch of such matrices of size (*, n, n) where * is one or more batch dimensions.

check_errors

(bool, optional): controls whether to check the content of infos. Default: FALSE.

Note

If A is on a CUDA device, this function may synchronize that device with the CPU.

This function is "experimental" and it may change in a future PyTorch release.

See also

linalg_cholesky() is a NumPy compatible variant that always checks for errors.

Other linalg: linalg_cholesky(), linalg_det(), linalg_eig(), linalg_eigh(), linalg_eigvals(), linalg_eigvalsh(), linalg_householder_product(), linalg_inv(), linalg_inv_ex(), linalg_lstsq(), linalg_matrix_norm(), linalg_matrix_power(), linalg_matrix_rank(), linalg_multi_dot(), linalg_norm(), linalg_pinv(), linalg_qr(), linalg_slogdet(), linalg_solve(), linalg_solve_triangular(), linalg_svd(), linalg_svdvals(), linalg_tensorinv(), linalg_tensorsolve(), linalg_vector_norm()

Examples

if (torch_is_installed()) {
A <- torch_randn(2, 2)
out <- linalg_cholesky_ex(A)
out
}
#> $L
#> torch_tensor
#> -0.2854  0.0000
#> -0.5645 -0.8628
#> [ CPUFloatType{2,2} ]
#> 
#> $info
#> torch_tensor
#> 1
#> [ CPUIntType{} ]
#>