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version 1.7, 2011/07/22 07:38:02 version 1.8, 2011/11/21 20:37:08
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       SUBROUTINE ZGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)  *> \brief \b ZGEMM
 *     .. Scalar Arguments ..  
       DOUBLE COMPLEX ALPHA,BETA  
       INTEGER K,LDA,LDB,LDC,M,N  
       CHARACTER TRANSA,TRANSB  
 *     ..  
 *     .. Array Arguments ..  
       DOUBLE COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)  
 *     ..  
 *  *
 *  Purpose  *  =========== DOCUMENTATION ===========
 *  =======  
 *  *
 *  ZGEMM  performs one of the matrix-matrix operations  * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
 *  *
 *     C := alpha*op( A )*op( B ) + beta*C,  *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
   * 
   *       .. Scalar Arguments ..
   *       COMPLEX*16 ALPHA,BETA
   *       INTEGER K,LDA,LDB,LDC,M,N
   *       CHARACTER TRANSA,TRANSB
   *       ..
   *       .. Array Arguments ..
   *       COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*)
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZGEMM  performs one of the matrix-matrix operations
   *>
   *>    C := alpha*op( A )*op( B ) + beta*C,
   *>
   *> where  op( X ) is one of
   *>
   *>    op( X ) = X   or   op( X ) = X**T   or   op( X ) = X**H,
   *>
   *> alpha and beta are scalars, and A, B and C are matrices, with op( A )
   *> an m by k matrix,  op( B )  a  k by n matrix and  C an m by n matrix.
   *> \endverbatim
 *  *
 *  where  op( X ) is one of  *  Arguments:
 *  *  ==========
 *     op( X ) = X   or   op( X ) = X**T   or   op( X ) = X**H,  
 *  *
 *  alpha and beta are scalars, and A, B and C are matrices, with op( A )  *> \param[in] TRANSA
 *  an m by k matrix,  op( B )  a  k by n matrix and  C an m by n matrix.  *> \verbatim
   *>          TRANSA is CHARACTER*1
   *>           On entry, TRANSA specifies the form of op( A ) to be used in
   *>           the matrix multiplication as follows:
   *>
   *>              TRANSA = 'N' or 'n',  op( A ) = A.
   *>
   *>              TRANSA = 'T' or 't',  op( A ) = A**T.
   *>
   *>              TRANSA = 'C' or 'c',  op( A ) = A**H.
   *> \endverbatim
   *>
   *> \param[in] TRANSB
   *> \verbatim
   *>          TRANSB is CHARACTER*1
   *>           On entry, TRANSB specifies the form of op( B ) to be used in
   *>           the matrix multiplication as follows:
   *>
   *>              TRANSB = 'N' or 'n',  op( B ) = B.
   *>
   *>              TRANSB = 'T' or 't',  op( B ) = B**T.
   *>
   *>              TRANSB = 'C' or 'c',  op( B ) = B**H.
   *> \endverbatim
   *>
   *> \param[in] M
   *> \verbatim
   *>          M is INTEGER
   *>           On entry,  M  specifies  the number  of rows  of the  matrix
   *>           op( A )  and of the  matrix  C.  M  must  be at least  zero.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>           On entry,  N  specifies the number  of columns of the matrix
   *>           op( B ) and the number of columns of the matrix C. N must be
   *>           at least zero.
   *> \endverbatim
   *>
   *> \param[in] K
   *> \verbatim
   *>          K is INTEGER
   *>           On entry,  K  specifies  the number of columns of the matrix
   *>           op( A ) and the number of rows of the matrix op( B ). K must
   *>           be at least  zero.
   *> \endverbatim
   *>
   *> \param[in] ALPHA
   *> \verbatim
   *>          ALPHA is COMPLEX*16
   *>           On entry, ALPHA specifies the scalar alpha.
   *> \endverbatim
   *>
   *> \param[in] A
   *> \verbatim
   *>          A is COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is
   *>           k  when  TRANSA = 'N' or 'n',  and is  m  otherwise.
   *>           Before entry with  TRANSA = 'N' or 'n',  the leading  m by k
   *>           part of the array  A  must contain the matrix  A,  otherwise
   *>           the leading  k by m  part of the array  A  must contain  the
   *>           matrix A.
   *> \endverbatim
   *>
   *> \param[in] LDA
   *> \verbatim
   *>          LDA is INTEGER
   *>           On entry, LDA specifies the first dimension of A as declared
   *>           in the calling (sub) program. When  TRANSA = 'N' or 'n' then
   *>           LDA must be at least  max( 1, m ), otherwise  LDA must be at
   *>           least  max( 1, k ).
   *> \endverbatim
   *>
   *> \param[in] B
   *> \verbatim
   *>          B is COMPLEX*16 array of DIMENSION ( LDB, kb ), where kb is
   *>           n  when  TRANSB = 'N' or 'n',  and is  k  otherwise.
   *>           Before entry with  TRANSB = 'N' or 'n',  the leading  k by n
   *>           part of the array  B  must contain the matrix  B,  otherwise
   *>           the leading  n by k  part of the array  B  must contain  the
   *>           matrix B.
   *> \endverbatim
   *>
   *> \param[in] LDB
   *> \verbatim
   *>          LDB is INTEGER
   *>           On entry, LDB specifies the first dimension of B as declared
   *>           in the calling (sub) program. When  TRANSB = 'N' or 'n' then
   *>           LDB must be at least  max( 1, k ), otherwise  LDB must be at
   *>           least  max( 1, n ).
   *> \endverbatim
   *>
   *> \param[in] BETA
   *> \verbatim
   *>          BETA is COMPLEX*16
   *>           On entry,  BETA  specifies the scalar  beta.  When  BETA  is
   *>           supplied as zero then C need not be set on input.
   *> \endverbatim
   *>
   *> \param[in,out] C
   *> \verbatim
   *>          C is COMPLEX*16 array of DIMENSION ( LDC, n ).
   *>           Before entry, the leading  m by n  part of the array  C must
   *>           contain the matrix  C,  except when  beta  is zero, in which
   *>           case C need not be set on entry.
   *>           On exit, the array  C  is overwritten by the  m by n  matrix
   *>           ( alpha*op( A )*op( B ) + beta*C ).
   *> \endverbatim
   *>
   *> \param[in] LDC
   *> \verbatim
   *>          LDC is INTEGER
   *>           On entry, LDC specifies the first dimension of C as declared
   *>           in  the  calling  (sub)  program.   LDC  must  be  at  least
   *>           max( 1, m ).
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup complex16_blas_level3
   *
   *> \par Further Details:
   *  =====================
   *>
   *> \verbatim
   *>
   *>  Level 3 Blas routine.
   *>
   *>  -- Written on 8-February-1989.
   *>     Jack Dongarra, Argonne National Laboratory.
   *>     Iain Duff, AERE Harwell.
   *>     Jeremy Du Croz, Numerical Algorithms Group Ltd.
   *>     Sven Hammarling, Numerical Algorithms Group Ltd.
   *> \endverbatim
   *>
   *  =====================================================================
         SUBROUTINE ZGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
 *  *
 *  Arguments  *  -- Reference BLAS level3 routine (version 3.4.0) --
 *  ==========  *  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
   *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
   *     November 2011
 *  *
 *  TRANSA - CHARACTER*1.  *     .. Scalar Arguments ..
 *           On entry, TRANSA specifies the form of op( A ) to be used in        COMPLEX*16 ALPHA,BETA
 *           the matrix multiplication as follows:        INTEGER K,LDA,LDB,LDC,M,N
 *        CHARACTER TRANSA,TRANSB
 *              TRANSA = 'N' or 'n',  op( A ) = A.  *     ..
 *  *     .. Array Arguments ..
 *              TRANSA = 'T' or 't',  op( A ) = A**T.        COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*)
 *  *     ..
 *              TRANSA = 'C' or 'c',  op( A ) = A**H.  
 *  
 *           Unchanged on exit.  
 *  
 *  TRANSB - CHARACTER*1.  
 *           On entry, TRANSB specifies the form of op( B ) to be used in  
 *           the matrix multiplication as follows:  
 *  
 *              TRANSB = 'N' or 'n',  op( B ) = B.  
 *  
 *              TRANSB = 'T' or 't',  op( B ) = B**T.  
 *  
 *              TRANSB = 'C' or 'c',  op( B ) = B**H.  
 *  
 *           Unchanged on exit.  
 *  
 *  M      - INTEGER.  
 *           On entry,  M  specifies  the number  of rows  of the  matrix  
 *           op( A )  and of the  matrix  C.  M  must  be at least  zero.  
 *           Unchanged on exit.  
 *  
 *  N      - INTEGER.  
 *           On entry,  N  specifies the number  of columns of the matrix  
 *           op( B ) and the number of columns of the matrix C. N must be  
 *           at least zero.  
 *           Unchanged on exit.  
 *  
 *  K      - INTEGER.  
 *           On entry,  K  specifies  the number of columns of the matrix  
 *           op( A ) and the number of rows of the matrix op( B ). K must  
 *           be at least  zero.  
 *           Unchanged on exit.  
 *  
 *  ALPHA  - COMPLEX*16      .  
 *           On entry, ALPHA specifies the scalar alpha.  
 *           Unchanged on exit.  
 *  
 *  A      - COMPLEX*16       array of DIMENSION ( LDA, ka ), where ka is  
 *           k  when  TRANSA = 'N' or 'n',  and is  m  otherwise.  
 *           Before entry with  TRANSA = 'N' or 'n',  the leading  m by k  
 *           part of the array  A  must contain the matrix  A,  otherwise  
 *           the leading  k by m  part of the array  A  must contain  the  
 *           matrix A.  
 *           Unchanged on exit.  
 *  
 *  LDA    - INTEGER.  
 *           On entry, LDA specifies the first dimension of A as declared  
 *           in the calling (sub) program. When  TRANSA = 'N' or 'n' then  
 *           LDA must be at least  max( 1, m ), otherwise  LDA must be at  
 *           least  max( 1, k ).  
 *           Unchanged on exit.  
 *  
 *  B      - COMPLEX*16       array of DIMENSION ( LDB, kb ), where kb is  
 *           n  when  TRANSB = 'N' or 'n',  and is  k  otherwise.  
 *           Before entry with  TRANSB = 'N' or 'n',  the leading  k by n  
 *           part of the array  B  must contain the matrix  B,  otherwise  
 *           the leading  n by k  part of the array  B  must contain  the  
 *           matrix B.  
 *           Unchanged on exit.  
 *  
 *  LDB    - INTEGER.  
 *           On entry, LDB specifies the first dimension of B as declared  
 *           in the calling (sub) program. When  TRANSB = 'N' or 'n' then  
 *           LDB must be at least  max( 1, k ), otherwise  LDB must be at  
 *           least  max( 1, n ).  
 *           Unchanged on exit.  
 *  
 *  BETA   - COMPLEX*16      .  
 *           On entry,  BETA  specifies the scalar  beta.  When  BETA  is  
 *           supplied as zero then C need not be set on input.  
 *           Unchanged on exit.  
 *  
 *  C      - COMPLEX*16       array of DIMENSION ( LDC, n ).  
 *           Before entry, the leading  m by n  part of the array  C must  
 *           contain the matrix  C,  except when  beta  is zero, in which  
 *           case C need not be set on entry.  
 *           On exit, the array  C  is overwritten by the  m by n  matrix  
 *           ( alpha*op( A )*op( B ) + beta*C ).  
 *  
 *  LDC    - INTEGER.  
 *           On entry, LDC specifies the first dimension of C as declared  
 *           in  the  calling  (sub)  program.   LDC  must  be  at  least  
 *           max( 1, m ).  
 *           Unchanged on exit.  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  Level 3 Blas routine.  
 *  
 *  -- Written on 8-February-1989.  
 *     Jack Dongarra, Argonne National Laboratory.  
 *     Iain Duff, AERE Harwell.  
 *     Jeremy Du Croz, Numerical Algorithms Group Ltd.  
 *     Sven Hammarling, Numerical Algorithms Group Ltd.  
 *  *
 *  =====================================================================  *  =====================================================================
 *  *
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       INTRINSIC DCONJG,MAX        INTRINSIC DCONJG,MAX
 *     ..  *     ..
 *     .. Local Scalars ..  *     .. Local Scalars ..
       DOUBLE COMPLEX TEMP        COMPLEX*16 TEMP
       INTEGER I,INFO,J,L,NCOLA,NROWA,NROWB        INTEGER I,INFO,J,L,NCOLA,NROWA,NROWB
       LOGICAL CONJA,CONJB,NOTA,NOTB        LOGICAL CONJA,CONJB,NOTA,NOTB
 *     ..  *     ..
 *     .. Parameters ..  *     .. Parameters ..
       DOUBLE COMPLEX ONE        COMPLEX*16 ONE
       PARAMETER (ONE= (1.0D+0,0.0D+0))        PARAMETER (ONE= (1.0D+0,0.0D+0))
       DOUBLE COMPLEX ZERO        COMPLEX*16 ZERO
       PARAMETER (ZERO= (0.0D+0,0.0D+0))        PARAMETER (ZERO= (0.0D+0,0.0D+0))
 *     ..  *     ..
 *  *
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  Added in v.1.8

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