NAME

zhbmv - perform the matrix-vector operation y := alpha∗A∗x + beta∗y

SYNOPSIS

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

COMPLEX∗16 ALPHA, BETA

INTEGER INCX, INCY, K, LDA, N

CHARACTER∗1 UPLO

COMPLEX∗16 A( LDA, ∗ ), X( ∗ ), Y( ∗ )

#include <sunperf.h>

void zhbmv(char uplo, int n, int k, doublecomplex ∗alpha, doublecomplex ∗za, int lda, doublecomplex ∗zx, int incx, doublecomplex ∗zbeta, doublecomplex ∗zy, int incy) ;

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 - 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.

SunOS 5.0  —  Last change: 10 Dec 1998