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dsbmv(3P)		    Sun Performance Library		     dsbmv(3P)

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

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

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

       SUBROUTINE DSBMV_64(UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y,
	     INCY)

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

   F95 INTERFACE
       SUBROUTINE SBMV(UPLO, [N], K, ALPHA, A, [LDA], X, [INCX], BETA,
	      Y, [INCY])

       CHARACTER(LEN=1) :: UPLO
       INTEGER :: N, K, LDA, INCX, INCY
       REAL(8) :: ALPHA, BETA
       REAL(8), DIMENSION(:) :: X, Y
       REAL(8), DIMENSION(:,:) :: A

       SUBROUTINE SBMV_64(UPLO, [N], K, ALPHA, A, [LDA], X, [INCX],
	      BETA, Y, [INCY])

       CHARACTER(LEN=1) :: UPLO
       INTEGER(8) :: N, K, 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 k, double alpha, double *a, int lda,
		 double *x, int incx, double beta, double *y, int incy);

       void dsbmv_64(char uplo, long n, long k, 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 k super-diagonals.

ARGUMENTS
       UPLO (input)
		 On entry, UPLO specifies whether the upper or lower  triangu‐
		 lar 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.

       K (input)
		 On entry, K specifies the number of  super-diagonals  of  the
		 matrix A. K >= 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 ( k + 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 ( 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 symmetric 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 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 k by k triangle of the array A is not
		 referenced.  The following program segment will transfer  the
		 lower triangular part of a symmetric band matrix from conven‐
		 tional 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

		 Unchanged on exit.

       LDA (input)
		 On entry, LDA specifies the first dimension of A as  declared
		 in the calling (sub) program. LDA >= ( k + 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.

				  6 Mar 2009			     dsbmv(3P)
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