--- rpl/lapack/lapack/zpotf2.f 2010/08/06 15:29:00 1.3
+++ rpl/lapack/lapack/zpotf2.f 2023/08/07 08:39:34 1.19
@@ -1,9 +1,115 @@
+*> \brief \b ZPOTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix (unblocked algorithm).
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZPOTF2 + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZPOTF2( UPLO, N, A, LDA, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER INFO, LDA, N
+* ..
+* .. Array Arguments ..
+* COMPLEX*16 A( LDA, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZPOTF2 computes the Cholesky factorization of a complex Hermitian
+*> positive definite matrix A.
+*>
+*> 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 unblocked version of the algorithm, calling Level 2 BLAS.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> Specifies whether the upper or lower triangular part of the
+*> Hermitian matrix A is stored.
+*> = 'U': Upper triangular
+*> = 'L': Lower triangular
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> 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.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -k, the k-th argument had an illegal value
+*> > 0: if INFO = k, the leading minor of order k is not
+*> positive definite, and the factorization could not be
+*> completed.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \ingroup complex16POcomputational
+*
+* =====================================================================
SUBROUTINE ZPOTF2( UPLO, N, A, LDA, INFO )
*
-* -- LAPACK routine (version 3.2) --
+* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2006
*
* .. Scalar Arguments ..
CHARACTER UPLO
@@ -13,53 +119,6 @@
COMPLEX*16 A( LDA, * )
* ..
*
-* Purpose
-* =======
-*
-* ZPOTF2 computes the Cholesky factorization of a complex Hermitian
-* positive definite matrix A.
-*
-* The factorization has the form
-* A = U' * U , if UPLO = 'U', or
-* A = L * L', if UPLO = 'L',
-* where U is an upper triangular matrix and L is lower triangular.
-*
-* This is the unblocked version of the algorithm, calling Level 2 BLAS.
-*
-* Arguments
-* =========
-*
-* UPLO (input) CHARACTER*1
-* Specifies whether the upper or lower triangular part of the
-* Hermitian matrix A is stored.
-* = 'U': Upper triangular
-* = 'L': Lower triangular
-*
-* N (input) INTEGER
-* The order of the matrix A. N >= 0.
-*
-* A (input/output) 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'*U or A = L*L'.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,N).
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -k, the k-th argument had an illegal value
-* > 0: if INFO = k, the leading minor of order k is not
-* positive definite, and the factorization could not be
-* completed.
-*
* =====================================================================
*
* .. Parameters ..
@@ -109,14 +168,14 @@
*
IF( UPPER ) THEN
*
-* Compute the Cholesky factorization A = U'*U.
+* Compute the Cholesky factorization A = U**H *U.
*
DO 10 J = 1, N
*
* Compute U(J,J) and test for non-positive-definiteness.
*
- AJJ = DBLE( A( J, J ) ) - ZDOTC( J-1, A( 1, J ), 1,
- $ A( 1, J ), 1 )
+ AJJ = DBLE( A( J, J ) ) - DBLE( ZDOTC( J-1, A( 1, J ), 1,
+ $ A( 1, J ), 1 ) )
IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN
A( J, J ) = AJJ
GO TO 30
@@ -136,14 +195,14 @@
10 CONTINUE
ELSE
*
-* Compute the Cholesky factorization A = L*L'.
+* Compute the Cholesky factorization A = L*L**H.
*
DO 20 J = 1, N
*
* Compute L(J,J) and test for non-positive-definiteness.
*
- AJJ = DBLE( A( J, J ) ) - ZDOTC( J-1, A( J, 1 ), LDA,
- $ A( J, 1 ), LDA )
+ AJJ = DBLE( A( J, J ) ) - DBLE( ZDOTC( J-1, A( J, 1 ), LDA,
+ $ A( J, 1 ), LDA ) )
IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN
A( J, J ) = AJJ
GO TO 30