NAME

cgbmv - perform one of the matrix-vector operations   y := alpha∗A∗x + beta∗y, or y := alpha∗A’∗x + beta∗y, or   y := alpha∗conjg( A’ )∗x + beta∗y

SYNOPSIS

SUBROUTINE CGBMV ( TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )

COMPLEX ALPHA, BETA

INTEGER INCX, INCY, KL, KU, LDA, M, N

CHARACTER∗1 TRANS

COMPLEX A( LDA, ∗ ), X( ∗ ), Y( ∗ )

#include <sunperf.h>

void cgbmv(char trans, int m, int n, int kl, int ku, complex alpha, complex ∗ca, int lda, complex ∗cx, int incx, complex beta, complex ∗cy, int incy);

PURPOSE

CGBMV  performs one of the matrix-vector operations y := alpha∗A∗x + beta∗y, or y := alpha∗A’∗x + beta∗y, or   y := alpha∗conjg( A’ )∗x + beta∗y where alpha and beta are scalars, x and y are vectors and A is an m by n band matrix, with kl sub-diagonals and ku super-diagonals. 
 

PARAMETERS

TRANS - CHARACTER∗1. 
On entry, TRANS specifies the operation to be performed as follows:
TRANS = ’N’ or ’n’   y := alpha∗A∗x + beta∗y.
TRANS = ’T’ or ’t’   y := alpha∗A’∗x + beta∗y.
TRANS = ’C’ or ’c’   y := alpha∗conjg( A’ )∗x + beta∗y.
Unchanged on exit.

M - INTEGER. 
On entry, M specifies the number of rows of the matrix A.  M must be at least zero.  Unchanged on exit.

N - INTEGER. 
On entry, N specifies the number of columns of the matrix A.  N must be at least zero.  Unchanged on exit.

KL - INTEGER. 
On entry, KL specifies the number of sub-diagonals of the matrix A. KL must satisfy  0 .le. KL.  Unchanged on exit.

KU - INTEGER. 
On entry, KU specifies the number of super-diagonals of the matrix A. KU must satisfy  0 .le. KU.  Unchanged on exit.

ALPHA - COMPLEX. 
On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

A - COMPLEX array of DIMENSION ( LDA, n ). 
Before entry, the leading ( kl + ku + 1 ) by n part of the array A must contain the matrix of coefficients, supplied column by column, with the leading diagonal of the matrix in row ( ku + 1 ) of the array, the first super-diagonal starting at position 2 in row ku, the first sub-diagonal starting at position 1 in row ( ku + 2 ), and so on.  Elements in the array A that do not correspond to elements in the band matrix (such as the top left ku by ku triangle) are not referenced.  The following program segment will transfer a band matrix from conventional full matrix storage to band storage:
 
DO 20, J = 1, N K = KU + 1 - J DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) A( K + I, J ) = matrix( I, J ) 10    CONTINUE 20 CONTINUE
 
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 ( kl + ku + 1 ).  Unchanged on exit.

X - COMPLEX array of DIMENSION at least
( 1 + ( n - 1 )∗abs( INCX ) ) when TRANS = ’N’ or ’n’ and at least ( 1 + ( m - 1 )∗abs( INCX ) ) otherwise.  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         . 
On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input.  Unchanged on exit.

Y - COMPLEX array of DIMENSION at least
( 1 + ( m - 1 )∗abs( INCY ) ) when TRANS = ’N’ or ’n’ and at least ( 1 + ( n - 1 )∗abs( INCY ) ) otherwise.  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