Note: this is a BLAS routine and is not in libslatec.a
*DECK SGBMV
SUBROUTINE SGBMV (TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX,
$ BETA, Y, INCY)
C***BEGIN PROLOGUE SGBMV
C***PURPOSE Multiply a real vector by a real general band matrix.
C***LIBRARY SLATEC (BLAS)
C***CATEGORY D1B4
C***TYPE SINGLE PRECISION (SGBMV-S, DGBMV-D, CGBMV-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 SGBMV performs one of the matrix-vector operations
C
C y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y,
C
C where alpha and beta are scalars, x and y are vectors and A is an
C m by n band matrix, with kl sub-diagonals and ku super-diagonals.
C
C Parameters
C ==========
C
C TRANS - CHARACTER*1.
C On entry, TRANS specifies the operation to be performed as
C follows:
C
C TRANS = 'N' or 'n' y := alpha*A*x + beta*y.
C
C TRANS = 'T' or 't' y := alpha*A'*x + beta*y.
C
C TRANS = 'C' or 'c' y := alpha*A'*x + beta*y.
C
C Unchanged on exit.
C
C M - INTEGER.
C On entry, M specifies the number of rows of the matrix A.
C M must be at least zero.
C Unchanged on exit.
C
C N - INTEGER.
C On entry, N specifies the number of columns of the matrix A.
C N must be at least zero.
C Unchanged on exit.
C
C KL - INTEGER.
C On entry, KL specifies the number of sub-diagonals of the
C matrix A. KL must satisfy 0 .le. KL.
C Unchanged on exit.
C
C KU - INTEGER.
C On entry, KU specifies the number of super-diagonals of the
C matrix A. KU must satisfy 0 .le. KU.
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, the leading ( kl + ku + 1 ) by n part of the
C array A must contain the matrix of coefficients, supplied
C column by column, with the leading diagonal of the matrix in
C row ( ku + 1 ) of the array, the first super-diagonal
C starting at position 2 in row ku, the first sub-diagonal
C starting at position 1 in row ( ku + 2 ), and so on.
C Elements in the array A that do not correspond to elements
C in the band matrix (such as the top left ku by ku triangle)
C are not referenced.
C The following program segment will transfer a band matrix
C from conventional full matrix storage to band storage:
C
C DO 20, J = 1, N
C K = KU + 1 - J
C DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
C A( K + 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 ( kl + ku + 1 ).
C Unchanged on exit.
C
C X - REAL array of DIMENSION at least
C ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
C and at least
C ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
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. When BETA is
C supplied as zero then Y need not be set on input.
C Unchanged on exit.
C
C Y - REAL array of DIMENSION at least
C ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
C and at least
C ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
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 SGBMV