NAME

zgbmv - 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 ZGBMV( TRANSA, M, N, NSUB, NSUPER, ALPHA, A, LDA, X, 
 *      INCX, BETA, Y, INCY)
  CHARACTER * 1 TRANSA
  DOUBLE COMPLEX ALPHA, BETA
  DOUBLE COMPLEX A(LDA,*), X(*), Y(*)
  INTEGER M, N, NSUB, NSUPER, LDA, INCX, INCY

  SUBROUTINE ZGBMV_64( TRANSA, M, N, NSUB, NSUPER, ALPHA, A, LDA, X, 
 *      INCX, BETA, Y, INCY)
  CHARACTER * 1 TRANSA
  DOUBLE COMPLEX ALPHA, BETA
  DOUBLE COMPLEX A(LDA,*), X(*), Y(*)
  INTEGER*8 M, N, NSUB, NSUPER, LDA, INCX, INCY

F95 INTERFACE

  SUBROUTINE GBMV( [TRANSA], [M], [N], NSUB, NSUPER, ALPHA, A, [LDA], 
 *       X, [INCX], BETA, Y, [INCY])
  CHARACTER(LEN=1) :: TRANSA
  COMPLEX(8) :: ALPHA, BETA
  COMPLEX(8), DIMENSION(:) :: X, Y
  COMPLEX(8), DIMENSION(:,:) :: A
  INTEGER :: M, N, NSUB, NSUPER, LDA, INCX, INCY

  SUBROUTINE GBMV_64( [TRANSA], [M], [N], NSUB, NSUPER, ALPHA, A, [LDA], 
 *       X, [INCX], BETA, Y, [INCY])
  CHARACTER(LEN=1) :: TRANSA
  COMPLEX(8) :: ALPHA, BETA
  COMPLEX(8), DIMENSION(:) :: X, Y
  COMPLEX(8), DIMENSION(:,:) :: A
  INTEGER(8) :: M, N, NSUB, NSUPER, LDA, INCX, INCY

C INTERFACE

#include <sunperf.h>

void zgbmv(char transa, int m, int n, int nsub, int nsuper, doublecomplex alpha, doublecomplex *a, int lda, doublecomplex *x, int incx, doublecomplex beta, doublecomplex *y, int incy);

void zgbmv_64(char transa, long m, long n, long nsub, long nsuper, doublecomplex alpha, doublecomplex *a, long lda, doublecomplex *x, long incx, doublecomplex beta, doublecomplex *y, long incy);

PURPOSE

zgbmv 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 nsub sub-diagonals and nsuper super-diagonals.

ARGUMENTS

TRANSA (input)
On entry, TRANSA specifies the operation to be performed as follows:
TRANSA = 'N' or 'n' y : = alpha*A*x + beta*y.

TRANSA = 'T' or 't' y : = alpha*A'*x + beta*y.

TRANSA = 'C' or 'c' y : = alpha*conjg( A' )*x + beta*y.

Unchanged on exit.
M (input)
On entry, M specifies the number of rows of the matrix A. M must be at least zero. Unchanged on exit.
N (input)
On entry, N specifies the number of columns of the matrix A. N must be at least zero. Unchanged on exit.
NSUB (input)
On entry, NSUB specifies the number of sub-diagonals of the matrix A. NSUB must satisfy 0 .le. NSUB. Unchanged on exit.
NSUPER (input)
On entry, NSUPER specifies the number of super-diagonals of the matrix A. NSUPER must satisfy 0 .le. NSUPER. Unchanged on exit.
ALPHA (input)
On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
A (input)
Before entry, the leading ( nsub + nsuper + 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 ( nsuper + 1 ) of the array, the first super-diagonal starting at position 2 in row nsuper, the first sub-diagonal starting at position 1 in row ( nsuper + 2 ), and so on. Elements in the array A that do not correspond to elements in the band matrix (such as the top left nsuper by nsuper 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 = NSUPER + 1 - J
      DO 10, I = MAX( 1, J - NSUPER ), MIN( M, J + NSUB )
        A( K + I, J ) = matrix( I, J )
 10   CONTINUE
 20 CONTINUE
```
Unchanged on exit.
LDA (input)
On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least ( nsub + nsuper + 1 ). Unchanged on exit.
X (input)
( 1 + ( n - 1 )*abs( INCX ) ) when TRANSA = '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 (input)
On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.
BETA (input)
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 (input/output)
( 1 + ( m - 1 )*abs( INCY ) ) when TRANSA = '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 (input)
On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit.