--- rpl/lapack/lapack/zhegs2.f	2010/12/21 13:53:46	1.7
+++ rpl/lapack/lapack/zhegs2.f	2023/08/07 08:39:23	1.20
@@ -1,9 +1,134 @@
+*> \brief \b ZHEGS2 reduces a Hermitian definite generalized eigenproblem to standard form, using the factorization results obtained from cpotrf (unblocked algorithm).
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZHEGS2 + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhegs2.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhegs2.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhegs2.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE ZHEGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
+*
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            INFO, ITYPE, LDA, LDB, N
+*       ..
+*       .. Array Arguments ..
+*       COMPLEX*16         A( LDA, * ), B( LDB, * )
+*       ..
+*
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> ZHEGS2 reduces a complex Hermitian-definite generalized
+*> eigenproblem to standard form.
+*>
+*> If ITYPE = 1, the problem is A*x = lambda*B*x,
+*> and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H)
+*>
+*> If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
+*> B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H *A*L.
+*>
+*> B must have been previously factorized as U**H *U or L*L**H by ZPOTRF.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] ITYPE
+*> \verbatim
+*>          ITYPE is INTEGER
+*>          = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H);
+*>          = 2 or 3: compute U*A*U**H or L**H *A*L.
+*> \endverbatim
+*>
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          Specifies whether the upper or lower triangular part of the
+*>          Hermitian matrix A is stored, and how B has been factorized.
+*>          = 'U':  Upper triangular
+*>          = 'L':  Lower triangular
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrices A and B.  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 transformed matrix, stored in the
+*>          same format as A.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*>          LDA is INTEGER
+*>          The leading dimension of the array A.  LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*>          B is COMPLEX*16 array, dimension (LDB,N)
+*>          The triangular factor from the Cholesky factorization of B,
+*>          as returned by ZPOTRF.
+*>          B is modified by the routine but restored on exit.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*>          LDB is INTEGER
+*>          The leading dimension of the array B.  LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0:  successful exit.
+*>          < 0:  if INFO = -i, the i-th argument had an illegal value.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \ingroup complex16HEcomputational
+*
+*  =====================================================================
       SUBROUTINE ZHEGS2( ITYPE, UPLO, N, A, LDA, B, LDB, 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
@@ -13,62 +138,6 @@
       COMPLEX*16         A( LDA, * ), B( LDB, * )
 *     ..
 *
-*  Purpose
-*  =======
-*
-*  ZHEGS2 reduces a complex Hermitian-definite generalized
-*  eigenproblem to standard form.
-*
-*  If ITYPE = 1, the problem is A*x = lambda*B*x,
-*  and A is overwritten by inv(U')*A*inv(U) or inv(L)*A*inv(L')
-*
-*  If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
-*  B*A*x = lambda*x, and A is overwritten by U*A*U` or L'*A*L.
-*
-*  B must have been previously factorized as U'*U or L*L' by ZPOTRF.
-*
-*  Arguments
-*  =========
-*
-*  ITYPE   (input) INTEGER
-*          = 1: compute inv(U')*A*inv(U) or inv(L)*A*inv(L');
-*          = 2 or 3: compute U*A*U' or L'*A*L.
-*
-*  UPLO    (input) CHARACTER*1
-*          Specifies whether the upper or lower triangular part of the
-*          Hermitian matrix A is stored, and how B has been factorized.
-*          = 'U':  Upper triangular
-*          = 'L':  Lower triangular
-*
-*  N       (input) INTEGER
-*          The order of the matrices A and B.  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 transformed matrix, stored in the
-*          same format as A.
-*
-*  LDA     (input) INTEGER
-*          The leading dimension of the array A.  LDA >= max(1,N).
-*
-*  B       (input) COMPLEX*16 array, dimension (LDB,N)
-*          The triangular factor from the Cholesky factorization of B,
-*          as returned by ZPOTRF.
-*
-*  LDB     (input) INTEGER
-*          The leading dimension of the array B.  LDB >= max(1,N).
-*
-*  INFO    (output) INTEGER
-*          = 0:  successful exit.
-*          < 0:  if INFO = -i, the i-th argument had an illegal value.
-*
 *  =====================================================================
 *
 *     .. Parameters ..
@@ -119,14 +188,14 @@
       IF( ITYPE.EQ.1 ) THEN
          IF( UPPER ) THEN
 *
-*           Compute inv(U')*A*inv(U)
+*           Compute inv(U**H)*A*inv(U)
 *
             DO 10 K = 1, N
 *
 *              Update the upper triangle of A(k:n,k:n)
 *
-               AKK = A( K, K )
-               BKK = B( K, K )
+               AKK = DBLE( A( K, K ) )
+               BKK = DBLE( B( K, K ) )
                AKK = AKK / BKK**2
                A( K, K ) = AKK
                IF( K.LT.N ) THEN
@@ -149,14 +218,14 @@
    10       CONTINUE
          ELSE
 *
-*           Compute inv(L)*A*inv(L')
+*           Compute inv(L)*A*inv(L**H)
 *
             DO 20 K = 1, N
 *
 *              Update the lower triangle of A(k:n,k:n)
 *
-               AKK = A( K, K )
-               BKK = B( K, K )
+               AKK = DBLE( A( K, K ) )
+               BKK = DBLE( B( K, K ) )
                AKK = AKK / BKK**2
                A( K, K ) = AKK
                IF( K.LT.N ) THEN
@@ -174,14 +243,14 @@
       ELSE
          IF( UPPER ) THEN
 *
-*           Compute U*A*U'
+*           Compute U*A*U**H
 *
             DO 30 K = 1, N
 *
 *              Update the upper triangle of A(1:k,1:k)
 *
-               AKK = A( K, K )
-               BKK = B( K, K )
+               AKK = DBLE( A( K, K ) )
+               BKK = DBLE( B( K, K ) )
                CALL ZTRMV( UPLO, 'No transpose', 'Non-unit', K-1, B,
      $                     LDB, A( 1, K ), 1 )
                CT = HALF*AKK
@@ -194,14 +263,14 @@
    30       CONTINUE
          ELSE
 *
-*           Compute L'*A*L
+*           Compute L**H *A*L
 *
             DO 40 K = 1, N
 *
 *              Update the lower triangle of A(1:k,1:k)
 *
-               AKK = A( K, K )
-               BKK = B( K, K )
+               AKK = DBLE( A( K, K ) )
+               BKK = DBLE( B( K, K ) )
                CALL ZLACGV( K-1, A( K, 1 ), LDA )
                CALL ZTRMV( UPLO, 'Conjugate transpose', 'Non-unit', K-1,
      $                     B, LDB, A( K, 1 ), LDA )