NAME

sgbmv - perform one of the matrix-vector operations y := alpha*A*x + beta*y or y := alpha*A'*x + beta*y

SYNOPSIS

  SUBROUTINE SGBMV( TRANSA, M, N, NSUB, NSUPER, ALPHA, A, LDA, X, 
 *      INCX, BETA, Y, INCY)
  CHARACTER * 1 TRANSA
  INTEGER M, N, NSUB, NSUPER, LDA, INCX, INCY
  REAL ALPHA, BETA
  REAL A(LDA,*), X(*), Y(*)

  SUBROUTINE SGBMV_64( TRANSA, M, N, NSUB, NSUPER, ALPHA, A, LDA, X, 
 *      INCX, BETA, Y, INCY)
  CHARACTER * 1 TRANSA
  INTEGER*8 M, N, NSUB, NSUPER, LDA, INCX, INCY
  REAL ALPHA, BETA
  REAL A(LDA,*), X(*), Y(*)

F95 INTERFACE

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

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

C INTERFACE

#include <sunperf.h>

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

void sgbmv_64(char transa, long m, long n, long nsub, long nsuper, float alpha, float *a, long lda, float *x, long incx, float beta, float *y, long incy);

PURPOSE

sgbmv performs one of the matrix-vector operations y := alpha*A*x + beta*y or y := alpha*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*A'*x + beta*y.

Unchanged on exit.
M (input)
On entry, M specifies the number of rows of the matrix A. M > = 0. Unchanged on exit.
N (input)
On entry, N specifies the number of columns of the matrix A. N > = 0. Unchanged on exit.
NSUB (input)
On entry, NSUB specifies the number of sub-diagonals of the matrix A. NSUB > = 0. Unchanged on exit.
NSUPER (input)
On entry, NSUPER specifies the number of super-diagonals of the matrix A. NSUPER > = 0. 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 > = ( 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 < > 0. 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 < > 0. Unchanged on exit.