*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
C .. Scalar Arguments ..
REAL ALPHA, BETA
INTEGER INCX, INCY, KL, KU, LDA, M, N
CHARACTER*1 TRANS
C .. Array Arguments ..
REAL A( LDA, * ), X( * ), Y( * )
REAL ONE , ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
C .. Local Scalars ..
REAL TEMP
INTEGER I, INFO, IX, IY, J, JX, JY, K, KUP1, KX, KY,
$ LENX, LENY
C .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
C .. External Subroutines ..
EXTERNAL XERBLA
C .. Intrinsic Functions ..
INTRINSIC MAX, MIN
C***FIRST EXECUTABLE STATEMENT SGBMV
C
C Test the input parameters.
C
INFO = 0
IF ( .NOT.LSAME( TRANS, 'N' ).AND.
$ .NOT.LSAME( TRANS, 'T' ).AND.
$ .NOT.LSAME( TRANS, 'C' ) )THEN
INFO = 1
ELSE IF( M.LT.0 )THEN
INFO = 2
ELSE IF( N.LT.0 )THEN
INFO = 3
ELSE IF( KL.LT.0 )THEN
INFO = 4
ELSE IF( KU.LT.0 )THEN
INFO = 5
ELSE IF( LDA.LT.( KL + KU + 1 ) )THEN
INFO = 8
ELSE IF( INCX.EQ.0 )THEN
INFO = 10
ELSE IF( INCY.EQ.0 )THEN
INFO = 13
END IF
IF( INFO.NE.0 )THEN
CALL XERBLA( 'SGBMV ', INFO )
RETURN
END IF
C
C Quick return if possible.
C
IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.
$ ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
$ RETURN
C
C Set LENX and LENY, the lengths of the vectors x and y, and set
C up the start points in X and Y.
C
IF( LSAME( TRANS, 'N' ) )THEN
LENX = N
LENY = M
ELSE
LENX = M
LENY = N
END IF
IF( INCX.GT.0 )THEN
KX = 1
ELSE
KX = 1 - ( LENX - 1 )*INCX
END IF
IF( INCY.GT.0 )THEN
KY = 1
ELSE
KY = 1 - ( LENY - 1 )*INCY
END IF
C
C Start the operations. In this version the elements of A are
C accessed sequentially with one pass through the band part of 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, LENY
Y( I ) = ZERO
10 CONTINUE
ELSE
DO 20, I = 1, LENY
Y( I ) = BETA*Y( I )
20 CONTINUE
END IF
ELSE
IY = KY
IF( BETA.EQ.ZERO )THEN
DO 30, I = 1, LENY
Y( IY ) = ZERO
IY = IY + INCY
30 CONTINUE
ELSE
DO 40, I = 1, LENY
Y( IY ) = BETA*Y( IY )
IY = IY + INCY
40 CONTINUE
END IF
END IF
END IF
IF( ALPHA.EQ.ZERO )
$ RETURN
KUP1 = KU + 1
IF( LSAME( TRANS, 'N' ) )THEN
C
C Form y := alpha*A*x + y.
C
JX = KX
IF( INCY.EQ.1 )THEN
DO 60, J = 1, N
IF( X( JX ).NE.ZERO )THEN
TEMP = ALPHA*X( JX )
K = KUP1 - J
DO 50, I = MAX( 1, J - KU ), MIN( M, J + KL )
Y( I ) = Y( I ) + TEMP*A( K + I, J )
50 CONTINUE
END IF
JX = JX + INCX
60 CONTINUE
ELSE
DO 80, J = 1, N
IF( X( JX ).NE.ZERO )THEN
TEMP = ALPHA*X( JX )
IY = KY
K = KUP1 - J
DO 70, I = MAX( 1, J - KU ), MIN( M, J + KL )
Y( IY ) = Y( IY ) + TEMP*A( K + I, J )
IY = IY + INCY
70 CONTINUE
END IF
JX = JX + INCX
IF( J.GT.KU )
$ KY = KY + INCY
80 CONTINUE
END IF
ELSE
C
C Form y := alpha*A'*x + y.
C
JY = KY
IF( INCX.EQ.1 )THEN
DO 100, J = 1, N
TEMP = ZERO
K = KUP1 - J
DO 90, I = MAX( 1, J - KU ), MIN( M, J + KL )
TEMP = TEMP + A( K + I, J )*X( I )
90 CONTINUE
Y( JY ) = Y( JY ) + ALPHA*TEMP
JY = JY + INCY
100 CONTINUE
ELSE
DO 120, J = 1, N
TEMP = ZERO
IX = KX
K = KUP1 - J
DO 110, I = MAX( 1, J - KU ), MIN( M, J + KL )
TEMP = TEMP + A( K + I, J )*X( IX )
IX = IX + INCX
110 CONTINUE
Y( JY ) = Y( JY ) + ALPHA*TEMP
JY = JY + INCY
IF( J.GT.KU )
$ KX = KX + INCX
120 CONTINUE
END IF
END IF
C
RETURN
C
C End of SGBMV .
C
END