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RedHat 9 (Linux i386) - man page for dsbmv (redhat section l)

DSBMV(l)				   BLAS routine 				 DSBMV(l)

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 )

	   DOUBLE	PRECISION ALPHA, BETA

	   INTEGER	INCX, INCY, K, LDA, N

	   CHARACTER*1	UPLO

	   DOUBLE	PRECISION A( LDA, * ), X( * ), Y( * )

PURPOSE
       DSBMV  performs the matrix-vector  operation

       where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmet-
       ric band matrix, with k super-diagonals.

PARAMETERS
       UPLO   - CHARACTER*1.
	      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      - INTEGER.
	      On  entry,  N  specifies	the  order  of	the  matrix  A.  N must be at least zero.
	      Unchanged on exit.

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

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

       A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
	      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  col-
	      umn  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 seg-
	      ment will transfer the upper triangular part of a symmetric band matrix  from  con-
	      ventional 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 col-
	      umn 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 conventional
	      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    - INTEGER.
	      On  entry,  LDA specifies the first dimension of A as declared in the calling (sub)
	      program. LDA must be at least ( k + 1 ).	Unchanged on exit.

       X      - DOUBLE PRECISION array of DIMENSION at least
	      ( 1 + ( n - 1 )*abs( INCX ) ).  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   - DOUBLE PRECISION.
	      On entry, BETA specifies the scalar beta.  Unchanged on exit.

       Y      - DOUBLE PRECISION array of DIMENSION at least
	      ( 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   - INTEGER.
	      On  entry,  INCY	specifies  the	increment for the elements of Y. INCY must not be
	      zero.  Unchanged on exit.

	      Level 2 Blas routine.

	      -- Written on 22-October-1986.  Jack Dongarra, Argonne  National	Lab.   Jeremy  Du
	      Croz,  Nag  Central  Office.  Sven Hammarling, Nag Central Office.  Richard Hanson,
	      Sandia National Labs.

BLAS routine				 16 October 1992				 DSBMV(l)


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