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version 1.1, 2010/01/26 15:22:46 version 1.20, 2023/08/07 08:39:23
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   *> \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 )        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,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     November 2006  
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          UPLO        CHARACTER          UPLO
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       COMPLEX*16         A( LDA, * ), B( LDB, * )        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 ..  *     .. Parameters ..
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       IF( ITYPE.EQ.1 ) THEN        IF( ITYPE.EQ.1 ) THEN
          IF( UPPER ) THEN           IF( UPPER ) THEN
 *  *
 *           Compute inv(U')*A*inv(U)  *           Compute inv(U**H)*A*inv(U)
 *  *
             DO 10 K = 1, N              DO 10 K = 1, N
 *  *
 *              Update the upper triangle of A(k:n,k:n)  *              Update the upper triangle of A(k:n,k:n)
 *  *
                AKK = A( K, K )                 AKK = DBLE( A( K, K ) )
                BKK = B( K, K )                 BKK = DBLE( B( K, K ) )
                AKK = AKK / BKK**2                 AKK = AKK / BKK**2
                A( K, K ) = AKK                 A( K, K ) = AKK
                IF( K.LT.N ) THEN                 IF( K.LT.N ) THEN
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    10       CONTINUE     10       CONTINUE
          ELSE           ELSE
 *  *
 *           Compute inv(L)*A*inv(L')  *           Compute inv(L)*A*inv(L**H)
 *  *
             DO 20 K = 1, N              DO 20 K = 1, N
 *  *
 *              Update the lower triangle of A(k:n,k:n)  *              Update the lower triangle of A(k:n,k:n)
 *  *
                AKK = A( K, K )                 AKK = DBLE( A( K, K ) )
                BKK = B( K, K )                 BKK = DBLE( B( K, K ) )
                AKK = AKK / BKK**2                 AKK = AKK / BKK**2
                A( K, K ) = AKK                 A( K, K ) = AKK
                IF( K.LT.N ) THEN                 IF( K.LT.N ) THEN
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       ELSE        ELSE
          IF( UPPER ) THEN           IF( UPPER ) THEN
 *  *
 *           Compute U*A*U'  *           Compute U*A*U**H
 *  *
             DO 30 K = 1, N              DO 30 K = 1, N
 *  *
 *              Update the upper triangle of A(1:k,1:k)  *              Update the upper triangle of A(1:k,1:k)
 *  *
                AKK = A( K, K )                 AKK = DBLE( A( K, K ) )
                BKK = B( K, K )                 BKK = DBLE( B( K, K ) )
                CALL ZTRMV( UPLO, 'No transpose', 'Non-unit', K-1, B,                 CALL ZTRMV( UPLO, 'No transpose', 'Non-unit', K-1, B,
      $                     LDB, A( 1, K ), 1 )       $                     LDB, A( 1, K ), 1 )
                CT = HALF*AKK                 CT = HALF*AKK
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    30       CONTINUE     30       CONTINUE
          ELSE           ELSE
 *  *
 *           Compute L'*A*L  *           Compute L**H *A*L
 *  *
             DO 40 K = 1, N              DO 40 K = 1, N
 *  *
 *              Update the lower triangle of A(1:k,1:k)  *              Update the lower triangle of A(1:k,1:k)
 *  *
                AKK = A( K, K )                 AKK = DBLE( A( K, K ) )
                BKK = B( K, K )                 BKK = DBLE( B( K, K ) )
                CALL ZLACGV( K-1, A( K, 1 ), LDA )                 CALL ZLACGV( K-1, A( K, 1 ), LDA )
                CALL ZTRMV( UPLO, 'Conjugate transpose', 'Non-unit', K-1,                 CALL ZTRMV( UPLO, 'Conjugate transpose', 'Non-unit', K-1,
      $                     B, LDB, A( K, 1 ), LDA )       $                     B, LDB, A( K, 1 ), LDA )
Removed from v.1.1  
changed lines
  Added in v.1.20

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