--- rpl/lapack/lapack/zpstf2.f 2010/08/07 13:21:11 1.1
+++ rpl/lapack/lapack/zpstf2.f 2023/08/07 08:39:35 1.17
@@ -1,8 +1,148 @@
+*> \brief \b ZPSTF2 computes the Cholesky factorization with complete pivoting of a complex Hermitian positive semidefinite matrix.
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZPSTF2 + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZPSTF2( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO )
+*
+* .. Scalar Arguments ..
+* DOUBLE PRECISION TOL
+* INTEGER INFO, LDA, N, RANK
+* CHARACTER UPLO
+* ..
+* .. Array Arguments ..
+* COMPLEX*16 A( LDA, * )
+* DOUBLE PRECISION WORK( 2*N )
+* INTEGER PIV( N )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZPSTF2 computes the Cholesky factorization with complete
+*> pivoting of a complex Hermitian positive semidefinite matrix A.
+*>
+*> The factorization has the form
+*> P**T * A * P = U**H * U , if UPLO = 'U',
+*> P**T * A * P = L * L**H, if UPLO = 'L',
+*> where U is an upper triangular matrix and L is lower triangular, and
+*> P is stored as vector PIV.
+*>
+*> This algorithm does not attempt to check that A is positive
+*> semidefinite. This version of the algorithm calls level 2 BLAS.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> Specifies whether the upper or lower triangular part of the
+*> symmetric 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 symmetric 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 as above.
+*> \endverbatim
+*>
+*> \param[out] PIV
+*> \verbatim
+*> PIV is INTEGER array, dimension (N)
+*> PIV is such that the nonzero entries are P( PIV(K), K ) = 1.
+*> \endverbatim
+*>
+*> \param[out] RANK
+*> \verbatim
+*> RANK is INTEGER
+*> The rank of A given by the number of steps the algorithm
+*> completed.
+*> \endverbatim
+*>
+*> \param[in] TOL
+*> \verbatim
+*> TOL is DOUBLE PRECISION
+*> User defined tolerance. If TOL < 0, then N*U*MAX( A( K,K ) )
+*> will be used. The algorithm terminates at the (K-1)st step
+*> if the pivot <= TOL.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is DOUBLE PRECISION array, dimension (2*N)
+*> Work space.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> < 0: If INFO = -K, the K-th argument had an illegal value,
+*> = 0: algorithm completed successfully, and
+*> > 0: the matrix A is either rank deficient with computed rank
+*> as returned in RANK, or is not positive semidefinite. See
+*> Section 7 of LAPACK Working Note #161 for further
+*> information.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \ingroup complex16OTHERcomputational
+*
+* =====================================================================
SUBROUTINE ZPSTF2( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO )
*
-* -- LAPACK PROTOTYPE routine (version 3.2.2) --
-* Craig Lucas, University of Manchester / NAG Ltd.
-* October, 2008
+* -- LAPACK computational routine --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
DOUBLE PRECISION TOL
@@ -15,70 +155,6 @@
INTEGER PIV( N )
* ..
*
-* Purpose
-* =======
-*
-* ZPSTF2 computes the Cholesky factorization with complete
-* pivoting of a complex Hermitian positive semidefinite matrix A.
-*
-* The factorization has the form
-* P' * A * P = U' * U , if UPLO = 'U',
-* P' * A * P = L * L', if UPLO = 'L',
-* where U is an upper triangular matrix and L is lower triangular, and
-* P is stored as vector PIV.
-*
-* This algorithm does not attempt to check that A is positive
-* semidefinite. This version of the algorithm calls level 2 BLAS.
-*
-* Arguments
-* =========
-*
-* UPLO (input) CHARACTER*1
-* Specifies whether the upper or lower triangular part of the
-* symmetric 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 symmetric 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 as above.
-*
-* PIV (output) INTEGER array, dimension (N)
-* PIV is such that the nonzero entries are P( PIV(K), K ) = 1.
-*
-* RANK (output) INTEGER
-* The rank of A given by the number of steps the algorithm
-* completed.
-*
-* TOL (input) DOUBLE PRECISION
-* User defined tolerance. If TOL < 0, then N*U*MAX( A( K,K ) )
-* will be used. The algorithm terminates at the (K-1)st step
-* if the pivot <= TOL.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,N).
-*
-* WORK (workspace) DOUBLE PRECISION array, dimension (2*N)
-* Work space.
-*
-* INFO (output) INTEGER
-* < 0: If INFO = -K, the K-th argument had an illegal value,
-* = 0: algorithm completed successfully, and
-* > 0: the matrix A is either rank deficient with computed rank
-* as returned in RANK, or is indefinite. See Section 7 of
-* LAPACK Working Note #161 for further information.
-*
* =====================================================================
*
* .. Parameters ..
@@ -140,7 +216,7 @@
110 CONTINUE
PVT = MAXLOC( WORK( 1:N ), 1 )
AJJ = DBLE( A( PVT, PVT ) )
- IF( AJJ.EQ.ZERO.OR.DISNAN( AJJ ) ) THEN
+ IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN
RANK = 0
INFO = 1
GO TO 200
@@ -162,7 +238,7 @@
*
IF( UPPER ) THEN
*
-* Compute the Cholesky factorization P' * A * P = U' * U
+* Compute the Cholesky factorization P**T * A * P = U**H* U
*
DO 150 J = 1, N
*
@@ -173,7 +249,7 @@
DO 130 I = J, N
*
IF( J.GT.1 ) THEN
- WORK( I ) = WORK( I ) +
+ WORK( I ) = WORK( I ) +
$ DBLE( DCONJG( A( J-1, I ) )*
$ A( J-1, I ) )
END IF
@@ -234,7 +310,7 @@
*
ELSE
*
-* Compute the Cholesky factorization P' * A * P = L * L'
+* Compute the Cholesky factorization P**T * A * P = L * L**H
*
DO 180 J = 1, N
*
@@ -245,7 +321,7 @@
DO 160 I = J, N
*
IF( J.GT.1 ) THEN
- WORK( I ) = WORK( I ) +
+ WORK( I ) = WORK( I ) +
$ DBLE( DCONJG( A( I, J-1 ) )*
$ A( I, J-1 ) )
END IF