Note: this is a BLAS routine and is not in libslatec.a
*DECK SSBMV
SUBROUTINE SSBMV (UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y,
$ INCY)
C***BEGIN PROLOGUE SSBMV
C***PURPOSE Multiply a real vector by a real symmetric band matrix.
C***LIBRARY SLATEC (BLAS)
C***CATEGORY D1B4
C***TYPE SINGLE PRECISION (SSBMV-S, DSBMV-D, CSBMV-C)
C***KEYWORDS LEVEL 2 BLAS, LINEAR ALGEBRA
C***AUTHOR Dongarra, J. J., (ANL)
C Du Croz, J., (NAG)
C Hammarling, S., (NAG)
C Hanson, R. J., (SNLA)
C***DESCRIPTION
C
C SSBMV performs the matrix-vector operation
C
C y := alpha*A*x + beta*y,
C
C where alpha and beta are scalars, x and y are n element vectors and
C A is an n by n symmetric band matrix, with k super-diagonals.
C
C Parameters
C ==========
C
C UPLO - CHARACTER*1.
C On entry, UPLO specifies whether the upper or lower
C triangular part of the band matrix A is being supplied as
C follows:
C
C UPLO = 'U' or 'u' The upper triangular part of A is
C being supplied.
C
C UPLO = 'L' or 'l' The lower triangular part of A is
C being supplied.
C
C Unchanged on exit.
C
C N - INTEGER.
C On entry, N specifies the order of the matrix A.
C N must be at least zero.
C Unchanged on exit.
C
C K - INTEGER.
C On entry, K specifies the number of super-diagonals of the
C matrix A. K must satisfy 0 .le. K.
C Unchanged on exit.
C
C ALPHA - REAL .
C On entry, ALPHA specifies the scalar alpha.
C Unchanged on exit.
C
C A - REAL array of DIMENSION ( LDA, n ).
C Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
C by n part of the array A must contain the upper triangular
C band part of the symmetric matrix, supplied column by
C column, with the leading diagonal of the matrix in row
C ( k + 1 ) of the array, the first super-diagonal starting at
C position 2 in row k, and so on. The top left k by k triangle
C of the array A is not referenced.
C The following program segment will transfer the upper
C triangular part of a symmetric band matrix from conventional
C full matrix storage to band storage:
C
C DO 20, J = 1, N
C M = K + 1 - J
C DO 10, I = MAX( 1, J - K ), J
C A( M + I, J ) = matrix( I, J )
C 10 CONTINUE
C 20 CONTINUE
C
C Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
C by n part of the array A must contain the lower triangular
C band part of the symmetric matrix, supplied column by
C column, with the leading diagonal of the matrix in row 1 of
C the array, the first sub-diagonal starting at position 1 in
C row 2, and so on. The bottom right k by k triangle of the
C array A is not referenced.
C The following program segment will transfer the lower
C triangular part of a symmetric band matrix from conventional
C full matrix storage to band storage:
C
C DO 20, J = 1, N
C M = 1 - J
C DO 10, I = J, MIN( N, J + K )
C A( M + I, J ) = matrix( I, J )
C 10 CONTINUE
C 20 CONTINUE
C
C Unchanged on exit.
C
C LDA - INTEGER.
C On entry, LDA specifies the first dimension of A as declared
C in the calling (sub) program. LDA must be at least
C ( k + 1 ).
C Unchanged on exit.
C
C X - REAL array of DIMENSION at least
C ( 1 + ( n - 1 )*abs( INCX ) ).
C Before entry, the incremented array X must contain the
C vector x.
C Unchanged on exit.
C
C INCX - INTEGER.
C On entry, INCX specifies the increment for the elements of
C X. INCX must not be zero.
C Unchanged on exit.
C
C BETA - REAL .
C On entry, BETA specifies the scalar beta.
C Unchanged on exit.
C
C Y - REAL array of DIMENSION at least
C ( 1 + ( n - 1 )*abs( INCY ) ).
C Before entry, the incremented array Y must contain the
C vector y. On exit, Y is overwritten by the updated vector y.
C
C INCY - INTEGER.
C On entry, INCY specifies the increment for the elements of
C Y. INCY must not be zero.
C Unchanged on exit.
C
C***REFERENCES Dongarra, J. J., Du Croz, J., Hammarling, S., and
C Hanson, R. J. An extended set of Fortran basic linear
C algebra subprograms. ACM TOMS, Vol. 14, No. 1,
C pp. 1-17, March 1988.
C***ROUTINES CALLED LSAME, XERBLA
C***REVISION HISTORY (YYMMDD)
C 861022 DATE WRITTEN
C 910605 Modified to meet SLATEC prologue standards. Only comment
C lines were modified. (BKS)
C***END PROLOGUE SSBMV