Letting be or , the Cholesky decomposition of a complex Hermitian or real symmetric positive-definite matrix is defined as
linalg_cholesky(A)(Tensor): tensor of shape (*, n, n) where * is zero or more batch dimensions
consisting of symmetric or Hermitian positive-definite matrices.
torch:::math_to_rd(" A = LL^{H}\\mathrlap{\\qquad L \\in \\mathbb{K}^{n \\times n}} ")
where is a lower triangular matrix and is the conjugate transpose when is complex, and the transpose when is real-valued.
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.
linalg_cholesky_ex() for a version of this operation that
skips the (slow) error checking by default and instead returns the debug
information. This makes it a faster way to check if a matrix is
positive-definite.
linalg_eigh() for a different decomposition of a Hermitian matrix.
The eigenvalue decomposition gives more information about the matrix but it
slower to compute than the Cholesky decomposition.
Other linalg:
linalg_cholesky_ex(),
linalg_det(),
linalg_eigh(),
linalg_eigvalsh(),
linalg_eigvals(),
linalg_eig(),
linalg_householder_product(),
linalg_inv_ex(),
linalg_inv(),
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_svdvals(),
linalg_svd(),
linalg_tensorinv(),
linalg_tensorsolve(),
linalg_vector_norm()
if (torch_is_installed()) {
a <- torch_eye(10)
linalg_cholesky(a)
}
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