# zpotrf2.f - Man Page

SRC/zpotrf2.f

## Synopsis

### Functions/Subroutines

recursive subroutine **zpotrf2** (uplo, n, a, lda, info)**ZPOTRF2**

## Function/Subroutine Documentation

### recursive subroutine zpotrf2 (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer info)

**ZPOTRF2**

**Purpose:**

ZPOTRF2 computes the Cholesky factorization of a Hermitian positive definite matrix A using the recursive algorithm. The factorization has the form A = U**H * U, if UPLO = 'U', or A = L * L**H, if UPLO = 'L', where U is an upper triangular matrix and L is lower triangular. This is the recursive version of the algorithm. It divides the matrix into four submatrices: [ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2 A = [ -----|----- ] with n1 = n/2 [ A21 | A22 ] n2 = n-n1 The subroutine calls itself to factor A11. Update and scale A21 or A12, update A22 then call itself to factor A22.

**Parameters***UPLO*UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.

*N*N is INTEGER The order of the matrix A. N >= 0.

*A*A is COMPLEX*16 array, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if INFO = 0, the factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading principal minor of order i is not positive, and the factorization could not be completed.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **105** of file **zpotrf2.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zpotrf2(3) is an alias of zpotrf2.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK