*DECK DSBMV
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
C .. Scalar Arguments ..
DOUBLE PRECISION ALPHA, BETA
INTEGER INCX, INCY, K, LDA, N
CHARACTER*1 UPLO
C .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), X( * ), Y( * )
C .. Parameters ..
DOUBLE PRECISION ONE , ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
C .. Local Scalars ..
DOUBLE PRECISION TEMP1, TEMP2
INTEGER I, INFO, IX, IY, J, JX, JY, KPLUS1, KX, KY, L
C .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
C .. External Subroutines ..
EXTERNAL XERBLA
C .. Intrinsic Functions ..
INTRINSIC MAX, MIN
C***FIRST EXECUTABLE STATEMENT DSBMV
C
C Test the input parameters.
C
INFO = 0
IF ( .NOT.LSAME( UPLO, 'U' ).AND.
$ .NOT.LSAME( UPLO, 'L' ) )THEN
INFO = 1
ELSE IF( N.LT.0 )THEN
INFO = 2
ELSE IF( K.LT.0 )THEN
INFO = 3
ELSE IF( LDA.LT.( K + 1 ) )THEN
INFO = 6
ELSE IF( INCX.EQ.0 )THEN
INFO = 8
ELSE IF( INCY.EQ.0 )THEN
INFO = 11
END IF
IF( INFO.NE.0 )THEN
CALL XERBLA( 'DSBMV ', INFO )
RETURN
END IF
C
C Quick return if possible.
C
IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
$ RETURN
C
C Set up the start points in X and Y.
C
IF( INCX.GT.0 )THEN
KX = 1
ELSE
KX = 1 - ( N - 1 )*INCX
END IF
IF( INCY.GT.0 )THEN
KY = 1
ELSE
KY = 1 - ( N - 1 )*INCY
END IF
C
C Start the operations. In this version the elements of the array A
C are accessed sequentially with one pass through A.
C
C First form y := beta*y.
C
IF( BETA.NE.ONE )THEN
IF( INCY.EQ.1 )THEN
IF( BETA.EQ.ZERO )THEN
DO 10, I = 1, N
Y( I ) = ZERO
10 CONTINUE
ELSE
DO 20, I = 1, N
Y( I ) = BETA*Y( I )
20 CONTINUE
END IF
ELSE
IY = KY
IF( BETA.EQ.ZERO )THEN
DO 30, I = 1, N
Y( IY ) = ZERO
IY = IY + INCY
30 CONTINUE
ELSE
DO 40, I = 1, N
Y( IY ) = BETA*Y( IY )
IY = IY + INCY
40 CONTINUE
END IF
END IF
END IF
IF( ALPHA.EQ.ZERO )
$ RETURN
IF( LSAME( UPLO, 'U' ) )THEN
C
C Form y when upper triangle of A is stored.
C
KPLUS1 = K + 1
IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
DO 60, J = 1, N
TEMP1 = ALPHA*X( J )
TEMP2 = ZERO
L = KPLUS1 - J
DO 50, I = MAX( 1, J - K ), J - 1
Y( I ) = Y( I ) + TEMP1*A( L + I, J )
TEMP2 = TEMP2 + A( L + I, J )*X( I )
50 CONTINUE
Y( J ) = Y( J ) + TEMP1*A( KPLUS1, J ) + ALPHA*TEMP2
60 CONTINUE
ELSE
JX = KX
JY = KY
DO 80, J = 1, N
TEMP1 = ALPHA*X( JX )
TEMP2 = ZERO
IX = KX
IY = KY
L = KPLUS1 - J
DO 70, I = MAX( 1, J - K ), J - 1
Y( IY ) = Y( IY ) + TEMP1*A( L + I, J )
TEMP2 = TEMP2 + A( L + I, J )*X( IX )
IX = IX + INCX
IY = IY + INCY
70 CONTINUE
Y( JY ) = Y( JY ) + TEMP1*A( KPLUS1, J ) + ALPHA*TEMP2
JX = JX + INCX
JY = JY + INCY
IF( J.GT.K )THEN
KX = KX + INCX
KY = KY + INCY
END IF
80 CONTINUE
END IF
ELSE
C
C Form y when lower triangle of A is stored.
C
IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
DO 100, J = 1, N
TEMP1 = ALPHA*X( J )
TEMP2 = ZERO
Y( J ) = Y( J ) + TEMP1*A( 1, J )
L = 1 - J
DO 90, I = J + 1, MIN( N, J + K )
Y( I ) = Y( I ) + TEMP1*A( L + I, J )
TEMP2 = TEMP2 + A( L + I, J )*X( I )
90 CONTINUE
Y( J ) = Y( J ) + ALPHA*TEMP2
100 CONTINUE
ELSE
JX = KX
JY = KY
DO 120, J = 1, N
TEMP1 = ALPHA*X( JX )
TEMP2 = ZERO
Y( JY ) = Y( JY ) + TEMP1*A( 1, J )
L = 1 - J
IX = JX
IY = JY
DO 110, I = J + 1, MIN( N, J + K )
IX = IX + INCX
IY = IY + INCY
Y( IY ) = Y( IY ) + TEMP1*A( L + I, J )
TEMP2 = TEMP2 + A( L + I, J )*X( IX )
110 CONTINUE
Y( JY ) = Y( JY ) + ALPHA*TEMP2
JX = JX + INCX
JY = JY + INCY
120 CONTINUE
END IF
END IF
C
RETURN
C
C End of DSBMV .
C
END