SSBMV or DSBMV Subroutine

Purpose

Performs matrix-vector operations using symmetric band matrix.

Library

BLAS Library (libblas.a)

FORTRAN Syntax

SUBROUTINE SSBMV(UPLO, N, K, ALPHA, A, LDA,
X, INCX, BETA, Y, INCY)
REAL  ALPHA, BETA
INTEGER  INCX, INCY, K, LDA, N
CHARACTER*1  UPLO
REAL  A(LDA,*),  X(*),  Y(*)

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(*)

Description

The SSBMV or DSBMV subroutine 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

Item Description
UPLO 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 On entry, N specifies the order of the matrix A; N must be at least 0; unchanged on exit.
K On entry, K specifies the number of superdiagonals of the matrix A; K must satisfy 0 .le. K; unchanged on exit.
ALPHA On entry, ALPHA specifies the scalar alpha; unchanged on exit.
A An array of dimension ( LDA, N ); on 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 superdiagonal 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 transfers 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

On 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 subdiagonal 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 transfers 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 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 A vector of dimension at least (1 + (N-1) * abs( INCX ) ); on entry, the incremented array X must contain the vector x; unchanged on exit.
INCX On entry, INCX specifies the increment for the elements of X; INCX must not be 0; unchanged on exit.
BETA On entry, BETA specifies the scalar beta; unchanged on exit.
Y A vector of dimension at least (1 + (N-1) * abs( INCY ) ); on entry, the incremented array Y must contain the vector y; on exit, Y is overwritten by the updated vector y.
INCY On entry, INCY specifies the increment for the elements of Y; INCY must not be 0; unchanged on exit.