NAME

dsbmv - perform the matrix-vector operation y := alpha*A*x + beta*y

SYNOPSIS

  SUBROUTINE DSBMV( UPLO, N, NDIAG, ALPHA, A, LDA, X, INCX, BETA, Y, 
 *      INCY)
  CHARACTER * 1 UPLO
  INTEGER N, NDIAG, LDA, INCX, INCY
  DOUBLE PRECISION ALPHA, BETA
  DOUBLE PRECISION A(LDA,*), X(*), Y(*)

  SUBROUTINE DSBMV_64( UPLO, N, NDIAG, ALPHA, A, LDA, X, INCX, BETA, 
 *      Y, INCY)
  CHARACTER * 1 UPLO
  INTEGER*8 N, NDIAG, LDA, INCX, INCY
  DOUBLE PRECISION ALPHA, BETA
  DOUBLE PRECISION A(LDA,*), X(*), Y(*)

F95 INTERFACE

  SUBROUTINE SBMV( UPLO, [N], NDIAG, ALPHA, A, [LDA], X, [INCX], BETA, 
 *       Y, [INCY])
  CHARACTER(LEN=1) :: UPLO
  INTEGER :: N, NDIAG, LDA, INCX, INCY
  REAL(8) :: ALPHA, BETA
  REAL(8), DIMENSION(:) :: X, Y
  REAL(8), DIMENSION(:,:) :: A

  SUBROUTINE SBMV_64( UPLO, [N], NDIAG, ALPHA, A, [LDA], X, [INCX], 
 *       BETA, Y, [INCY])
  CHARACTER(LEN=1) :: UPLO
  INTEGER(8) :: N, NDIAG, LDA, INCX, INCY
  REAL(8) :: ALPHA, BETA
  REAL(8), DIMENSION(:) :: X, Y
  REAL(8), DIMENSION(:,:) :: A

C INTERFACE

#include <sunperf.h>

void dsbmv(char uplo, int n, int ndiag, double alpha, double *a, int lda, double *x, int incx, double beta, double *y, int incy);

void dsbmv_64(char uplo, long n, long ndiag, double alpha, double *a, long lda, double *x, long incx, double beta, double *y, long incy);

PURPOSE

dsbmv 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 symmetric band matrix, with ndiag super-diagonals.

ARGUMENTS

UPLO (input)
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 (input)
On entry, N specifies the order of the matrix A. N > = 0. Unchanged on exit.
NDIAG (input)
On entry, NDIAG specifies the number of super-diagonals of the matrix A. NDIAG > = 0. Unchanged on exit.
ALPHA (input)
On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
A (input)
Before entry with UPLO = 'U' or 'u', the leading ( ndiag + 1 ) by n part of the array A must contain the upper triangular band part of the symmetric matrix, supplied column by column, with the leading diagonal of the matrix in row ( ndiag + 1 ) of the array, the first super-diagonal starting at position 2 in row ndiag, and so on. The top left ndiag by ndiag triangle of the array A is not referenced. The following program segment will transfer the upper triangular part of a symmetric band matrix from conventional full matrix storage to band storage:
```
    DO 20, J = 1, N
      M = NDIAG + 1 - J
      DO 10, I = MAX( 1, J - NDIAG ), J
        A( M + I, J ) = matrix( I, J )
 10   CONTINUE
 20 CONTINUE
```
Before entry with UPLO = 'L' or 'l', the leading ( ndiag + 1 ) by n part of the array A must contain the lower triangular band part of the symmetric 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 ndiag by ndiag triangle of the array A is not referenced. The following program segment will transfer the lower triangular part of a symmetric 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 + NDIAG )
        A( M + 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 > = ( ndiag + 1 ). Unchanged on exit.
X (input)
( 1 + ( n - 1 )*abs( INCX ) ). 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. Unchanged on exit.
Y (input/output)
( 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 (input)
On entry, INCY specifies the increment for the elements of Y. INCY < > 0. Unchanged on exit.