*DECK DGBMV SUBROUTINE DGBMV (TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, $ BETA, Y, INCY) C***BEGIN PROLOGUE DGBMV C***PURPOSE Perform one of the matrix-vector operations. C***LIBRARY SLATEC (BLAS) C***CATEGORY D1B4 C***TYPE DOUBLE 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 DGBMV 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 - 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, 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 - DOUBLE PRECISION 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 - DOUBLE PRECISION. 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 - DOUBLE PRECISION 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 DGBMV C .. Scalar Arguments .. DOUBLE PRECISION ALPHA, BETA INTEGER INCX, INCY, KL, KU, LDA, M, N CHARACTER*1 TRANS C .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), X( * ), Y( * ) DOUBLE PRECISION ONE , ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) C .. Local Scalars .. DOUBLE PRECISION 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 DGBMV 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( 'DGBMV ', 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 DGBMV . C END