SSBMV(3)

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

NAME
ssbmv - Multiply a real vector by a real symmetric band matrix.

LIBRARY
SLATEC (BLAS)

CATEGORY
D1B4

TYPE
SINGLE PRECISION (SSBMV-S, DSBMV-D, CSBMV-C)

KEYWORDS
LEVEL 2 BLAS, LINEAR ALGEBRA

AUTHOR
Dongarra, J. J., (ANL) Du Croz, J., (NAG) Hammarling, S., (NAG) Hanson, R. J., (SNLA)

DESCRIPTION
SSBMV 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. 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 - REAL . On entry, ALPHA specifies the scalar alpha. Unchanged on exit. A - REAL 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 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 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 - REAL 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 - REAL . On entry, BETA specifies the scalar beta. Unchanged on exit. Y - REAL 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.

REFERENCES
Dongarra, J. J., Du Croz, J., Hammarling, S., and Hanson, R. J. An extended set of Fortran basic linear algebra subprograms. ACM TOMS, Vol. 14, No. 1, pp. 1-17, March 1988.

ROUTINES CALLED
LSAME, XERBLA

REVISION HISTORY (YYMMDD)
861022 DATE WRITTEN
910605 Modified to meet SLATEC prologue standards. Only comment lines were modified. (BKS)