help mata cholesky()
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Title
[M-5] cholesky() -- Cholesky square-root decomposition
Syntax
numeric matrix cholesky(numeric matrix A)
void _cholesky(numeric matrix A)
Description
cholesky(A) returns the Cholesky decomposition G of symmetric
(Hermitian), positive-definite matrix A. cholesky() returns a
lower-triangular matrix of missing values if A is not positive definite.
_cholesky(A) does the same thing, except that it overwrites A with the
Cholesky result.
Remarks
The Cholesky decomposition G of a symmetric, positive-definite matrix A
is
A = GG'
where G is lower triangular. When A is complex, A must be Hermitian, and
G', of course, is the conjugate transpose of G.
Decomposition is performed via [M-1] LAPACK.
Conformability
cholesky(A)
A: n x n
result: n x n
_cholesky(A)
input:
A: n x n
output:
A: n x n
Diagnostics
cholesky() returns a lower-triangular matrix of missing values if A
contains missing values or if A is not positive definite.
_cholesky(A) overwrites A with a lower-triangular matrix of missing
values if A contains missing values or if A is not positive definite.
Both functions use the elements from the lower triangle of A without
checking whether A is symmetric or, in the complex case, Hermitian.
Source code
cholesky.mata; _cholesky() is built in.
Also see
Manual: [M-5] cholesky()
Help: [M-5] lud(); [M-4] matrix
