zhbmv (3) - Linux Manuals

NAME

zhbmv.f -

SYNOPSIS


Functions/Subroutines


subroutine zhbmv (UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZHBMV

Function/Subroutine Documentation

subroutine zhbmv (characterUPLO, integerN, integerK, complex*16ALPHA, complex*16, dimension(lda,*)A, integerLDA, complex*16, dimension(*)X, integerINCX, complex*16BETA, complex*16, dimension(*)Y, integerINCY)

ZHBMV 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.


 

Parameters:

UPLO 

          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.


N 

          N is INTEGER
           On entry, N specifies the order of the matrix A.
           N must be at least zero.


K 

          K is INTEGER
           On entry, K specifies the number of super-diagonals of the
           matrix A. K must satisfy  0 .le. K.


ALPHA 

          ALPHA is COMPLEX*16
           On entry, ALPHA specifies the scalar alpha.


A 

          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.


LDA 

          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 ).


X 

          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.


INCX 

          INCX is INTEGER
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.


BETA 

          BETA is COMPLEX*16
           On entry, BETA specifies the scalar beta.


Y 

          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.


INCY 

          INCY is INTEGER
           On entry, INCY specifies the increment for the elements of
           Y. INCY must not be zero.


 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Further Details: 

  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.


 

Definition at line 188 of file zhbmv.f.

Author

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