SUBROUTINE DSBMV (UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, $ INCY) C***BEGIN PROLOGUE DSBMV C***PURPOSE Perform the matrix-vector operation. C***LIBRARY SLATEC (BLAS) C***CATEGORY D1B4 C***TYPE DOUBLE 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 DSBMV 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 - DOUBLE PRECISION. C On entry, ALPHA specifies the scalar alpha. C Unchanged on exit. C C A - DOUBLE PRECISION 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 - DOUBLE PRECISION 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 - DOUBLE PRECISION. C On entry, BETA specifies the scalar beta. C Unchanged on exit. C C Y - DOUBLE PRECISION 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 DSBMV