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version 1.4, 2010/08/07 13:22:10 version 1.12, 2016/08/27 15:37:54
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   *> \brief \b ZHBMV
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
   * 
   *       .. Scalar Arguments ..
   *       COMPLEX*16 ALPHA,BETA
   *       INTEGER INCX,INCY,K,LDA,N
   *       CHARACTER UPLO
   *       ..
   *       .. Array Arguments ..
   *       COMPLEX*16 A(LDA,*),X(*),Y(*)
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZHBMV  performs the matrix-vector  operation
   *>
   *>    y := alpha*A*x + beta*y,
   *>
   *> where alpha and beta are scalars, x and y are n element vectors and
   *> A is an n by n hermitian band matrix, with k super-diagonals.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] UPLO
   *> \verbatim
   *>          UPLO is CHARACTER*1
   *>           On entry, UPLO specifies whether the upper or lower
   *>           triangular part of the band matrix A is being supplied as
   *>           follows:
   *>
   *>              UPLO = 'U' or 'u'   The upper triangular part of A is
   *>                                  being supplied.
   *>
   *>              UPLO = 'L' or 'l'   The lower triangular part of A is
   *>                                  being supplied.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>           On entry, N specifies the order of the matrix A.
   *>           N must be at least zero.
   *> \endverbatim
   *>
   *> \param[in] K
   *> \verbatim
   *>          K is INTEGER
   *>           On entry, K specifies the number of super-diagonals of the
   *>           matrix A. K must satisfy  0 .le. K.
   *> \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, n ).
   *>           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
   *>           by n part of the array A must contain the upper triangular
   *>           band part of the hermitian matrix, supplied column by
   *>           column, with the leading diagonal of the matrix in row
   *>           ( k + 1 ) of the array, the first super-diagonal starting at
   *>           position 2 in row k, and so on. The top left k by k triangle
   *>           of the array A is not referenced.
   *>           The following program segment will transfer the upper
   *>           triangular part of a hermitian band matrix from conventional
   *>           full matrix storage to band storage:
   *>
   *>                 DO 20, J = 1, N
   *>                    M = K + 1 - J
   *>                    DO 10, I = MAX( 1, J - K ), J
   *>                       A( M + I, J ) = matrix( I, J )
   *>              10    CONTINUE
   *>              20 CONTINUE
   *>
   *>           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
   *>           by n part of the array A must contain the lower triangular
   *>           band part of the hermitian matrix, supplied column by
   *>           column, with the leading diagonal of the matrix in row 1 of
   *>           the array, the first sub-diagonal starting at position 1 in
   *>           row 2, and so on. The bottom right k by k triangle of the
   *>           array A is not referenced.
   *>           The following program segment will transfer the lower
   *>           triangular part of a hermitian band matrix from conventional
   *>           full matrix storage to band storage:
   *>
   *>                 DO 20, J = 1, N
   *>                    M = 1 - J
   *>                    DO 10, I = J, MIN( N, J + K )
   *>                       A( M + I, J ) = matrix( I, J )
   *>              10    CONTINUE
   *>              20 CONTINUE
   *>
   *>           Note that the imaginary parts of the diagonal elements need
   *>           not be set and are assumed to be zero.
   *> \endverbatim
   *>
   *> \param[in] LDA
   *> \verbatim
   *>          LDA is INTEGER
   *>           On entry, LDA specifies the first dimension of A as declared
   *>           in the calling (sub) program. LDA must be at least
   *>           ( k + 1 ).
   *> \endverbatim
   *>
   *> \param[in] X
   *> \verbatim
   *>          X is COMPLEX*16 array of DIMENSION at least
   *>           ( 1 + ( n - 1 )*abs( INCX ) ).
   *>           Before entry, the incremented array X must contain the
   *>           vector x.
   *> \endverbatim
   *>
   *> \param[in] INCX
   *> \verbatim
   *>          INCX is INTEGER
   *>           On entry, INCX specifies the increment for the elements of
   *>           X. INCX must not be zero.
   *> \endverbatim
   *>
   *> \param[in] BETA
   *> \verbatim
   *>          BETA is COMPLEX*16
   *>           On entry, BETA specifies the scalar beta.
   *> \endverbatim
   *>
   *> \param[in,out] Y
   *> \verbatim
   *>          Y is COMPLEX*16 array of DIMENSION at least
   *>           ( 1 + ( n - 1 )*abs( INCY ) ).
   *>           Before entry, the incremented array Y must contain the
   *>           vector y. On exit, Y is overwritten by the updated vector y.
   *> \endverbatim
   *>
   *> \param[in] INCY
   *> \verbatim
   *>          INCY is INTEGER
   *>           On entry, INCY specifies the increment for the elements of
   *>           Y. INCY must not be zero.
   *> \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_level2
   *
   *> \par Further Details:
   *  =====================
   *>
   *> \verbatim
   *>
   *>  Level 2 Blas routine.
   *>  The vector and matrix arguments are not referenced when N = 0, or M = 0
   *>
   *>  -- Written on 22-October-1986.
   *>     Jack Dongarra, Argonne National Lab.
   *>     Jeremy Du Croz, Nag Central Office.
   *>     Sven Hammarling, Nag Central Office.
   *>     Richard Hanson, Sandia National Labs.
   *> \endverbatim
   *>
   *  =====================================================================
       SUBROUTINE ZHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)        SUBROUTINE ZHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
   *
   *  -- Reference BLAS level2 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
   *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       DOUBLE COMPLEX ALPHA,BETA        COMPLEX*16 ALPHA,BETA
       INTEGER INCX,INCY,K,LDA,N        INTEGER INCX,INCY,K,LDA,N
       CHARACTER UPLO        CHARACTER UPLO
 *     ..  *     ..
 *     .. Array Arguments ..  *     .. Array Arguments ..
       DOUBLE COMPLEX A(LDA,*),X(*),Y(*)        COMPLEX*16 A(LDA,*),X(*),Y(*)
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZHBMV  performs the matrix-vector  operation  
 *  
 *     y := alpha*A*x + beta*y,  
 *  
 *  where alpha and beta are scalars, x and y are n element vectors and  
 *  A is an n by n hermitian band matrix, with k super-diagonals.  
 *  
 *  Arguments  
 *  ==========  
 *  
 *  UPLO   - CHARACTER*1.  
 *           On entry, UPLO specifies whether the upper or lower  
 *           triangular part of the band matrix A is being supplied as  
 *           follows:  
 *  
 *              UPLO = 'U' or 'u'   The upper triangular part of A is  
 *                                  being supplied.  
 *  
 *              UPLO = 'L' or 'l'   The lower triangular part of A is  
 *                                  being supplied.  
 *  
 *           Unchanged on exit.  
 *  
 *  N      - INTEGER.  
 *           On entry, N specifies the order of the matrix A.  
 *           N must be at least zero.  
 *           Unchanged on exit.  
 *  
 *  K      - INTEGER.  
 *           On entry, K specifies the number of super-diagonals of the  
 *           matrix A. K must satisfy  0 .le. K.  
 *           Unchanged on exit.  
 *  
 *  ALPHA  - COMPLEX*16      .  
 *           On entry, ALPHA specifies the scalar alpha.  
 *           Unchanged on exit.  
 *  
 *  A      - COMPLEX*16       array of DIMENSION ( LDA, n ).  
 *           Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )  
 *           by n part of the array A must contain the upper triangular  
 *           band part of the hermitian matrix, supplied column by  
 *           column, with the leading diagonal of the matrix in row  
 *           ( k + 1 ) of the array, the first super-diagonal starting at  
 *           position 2 in row k, and so on. The top left k by k triangle  
 *           of the array A is not referenced.  
 *           The following program segment will transfer the upper  
 *           triangular part of a hermitian band matrix from conventional  
 *           full matrix storage to band storage:  
 *  
 *                 DO 20, J = 1, N  
 *                    M = K + 1 - J  
 *                    DO 10, I = MAX( 1, J - K ), J  
 *                       A( M + I, J ) = matrix( I, J )  
 *              10    CONTINUE  
 *              20 CONTINUE  
 *  
 *           Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )  
 *           by n part of the array A must contain the lower triangular  
 *           band part of the hermitian matrix, supplied column by  
 *           column, with the leading diagonal of the matrix in row 1 of  
 *           the array, the first sub-diagonal starting at position 1 in  
 *           row 2, and so on. The bottom right k by k triangle of the  
 *           array A is not referenced.  
 *           The following program segment will transfer the lower  
 *           triangular part of a hermitian band matrix from conventional  
 *           full matrix storage to band storage:  
 *  
 *                 DO 20, J = 1, N  
 *                    M = 1 - J  
 *                    DO 10, I = J, MIN( N, J + K )  
 *                       A( M + I, J ) = matrix( I, J )  
 *              10    CONTINUE  
 *              20 CONTINUE  
 *  
 *           Note that the imaginary parts of the diagonal elements need  
 *           not be set and are assumed to be zero.  
 *           Unchanged on exit.  
 *  
 *  LDA    - INTEGER.  
 *           On entry, LDA specifies the first dimension of A as declared  
 *           in the calling (sub) program. LDA must be at least  
 *           ( k + 1 ).  
 *           Unchanged on exit.  
 *  
 *  X      - COMPLEX*16       array of DIMENSION at least  
 *           ( 1 + ( n - 1 )*abs( INCX ) ).  
 *           Before entry, the incremented array X must contain the  
 *           vector x.  
 *           Unchanged on exit.  
 *  
 *  INCX   - INTEGER.  
 *           On entry, INCX specifies the increment for the elements of  
 *           X. INCX must not be zero.  
 *           Unchanged on exit.  
 *  
 *  BETA   - COMPLEX*16      .  
 *           On entry, BETA specifies the scalar beta.  
 *           Unchanged on exit.  
 *  
 *  Y      - COMPLEX*16       array of DIMENSION at least  
 *           ( 1 + ( n - 1 )*abs( INCY ) ).  
 *           Before entry, the incremented array Y must contain the  
 *           vector y. On exit, Y is overwritten by the updated vector y.  
 *  
 *  INCY   - INTEGER.  
 *           On entry, INCY specifies the increment for the elements of  
 *           Y. INCY must not be zero.  
 *           Unchanged on exit.  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  Level 2 Blas routine.  
 *  
 *  -- Written on 22-October-1986.  
 *     Jack Dongarra, Argonne National Lab.  
 *     Jeremy Du Croz, Nag Central Office.  
 *     Sven Hammarling, Nag Central Office.  
 *     Richard Hanson, Sandia National Labs.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. 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))
 *     ..  *     ..
 *     .. Local Scalars ..  *     .. Local Scalars ..
       DOUBLE COMPLEX TEMP1,TEMP2        COMPLEX*16 TEMP1,TEMP2
       INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L        INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L
 *     ..  *     ..
 *     .. External Functions ..  *     .. External Functions ..
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