SUBROUTINE DGBMV( TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, $ BETA, Y, INCY ) * * -- Automatically Tuned Linear Algebra Software (ATLAS) * (C) Copyright 2000 All Rights Reserved * * -- ATLAS routine -- F77 Interface -- Version 3.2 -- December 25, 2000 * * -- Suggestions, comments, bugs reports should be sent to the follo- * wing e-mail address: atlas@cs.utk.edu * * Author : Antoine P. Petitet * University of Tennessee - Innovative Computing Laboratory * Knoxville TN, 37996-1301, USA. * * --------------------------------------------------------------------- * * -- Copyright notice and Licensing terms: * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions, and the following disclaimer in * the documentation and/or other materials provided with the distri- * bution. * 3. The name of the University, the ATLAS group, or the names of its * contributors may not be used to endorse or promote products deri- * ved from this software without specific written permission. * * -- Disclaimer: * * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE UNIVERSITY * OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPE- * CIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED * TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, * OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEO- * RY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (IN- * CLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. * * --------------------------------------------------------------------- * * .. Scalar Arguments .. CHARACTER*1 TRANS INTEGER INCX, INCY, KL, KU, LDA, M, N DOUBLE PRECISION ALPHA, BETA * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * DGBMV performs one of the matrix-vector operations * * y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, * * where alpha and beta are scalars, x and y are vectors and A is an m * by n band matrix, with kl sub-diagonals and ku super-diagonals. * * Arguments * ========= * * TRANS (input) CHARACTER*1 * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n', y := alpha*A *x + beta*y, * * TRANS = 'T' or 't', y := alpha*A'*x + beta*y, * * TRANS = 'C' or 'c', y := alpha*A'*x + beta*y. * * Unchanged on exit. * * M (input) INTEGER * On entry, M specifies the number of rows of the matrix A. * M must be at least zero. Unchanged on exit. * * N (input) INTEGER * On entry, N specifies the number of columns of the matrix A. * N must be at least zero. Unchanged on exit. * * KL (input) INTEGER * On entry, KL specifies the number of sub-diagonals of the ma- * trix A. KL must satisfy 0 .le. KL. Unchanged on exit. * * KU (input) INTEGER * On entry, KU specifies the number of super-diagonals of the * matrix A. KU must satisfy 0 .le. KU. Unchanged on exit. * * ALPHA (input) DOUBLE PRECISION * On entry, ALPHA specifies the scalar alpha. When ALPHA is * supplied as zero then A and X need not be set on input. Un- * changed on exit. * * A (input) DOUBLE PRECISION array * On entry, A is an array of DIMENSION ( LDA, n ). Before en- * try, the leading (kl+ku+1) by n part of the array A must con- * tain the matrix of coefficients, supplied column by column, * with the leading diagonal of the matrix in row (ku+1) of the * array, the first super-diagonal starting at position 2 in row * ku, the first sub-diagonal starting at position 1 in row * (ku+2), and so on. Elements in the array A that do not cor- * respond to elements in the band matrix (such as the top left * ku by ku triangle) are not referenced. * The following program segment will transfer a band matrix * from conventional full matrix storage to band storage: * * DO 20, J = 1, N * K = KU + 1 - J * DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) * A( K + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Unchanged on exit. * * LDA (input) INTEGER * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least (kl+ku+1). * Unchanged on exit. * * X (input) DOUBLE PRECISION array * On entry, X is an incremented array of dimension at least * ( 1 + ( n - 1 ) * abs( INCX ) ) when TRANS = 'N' or 'n' and * at least ( 1 + ( m - 1 ) * abs( INCX ) ) otherwise. Before * entry, the incremented array X must contain the vector x. Un- * changed on exit. * * INCX (input) INTEGER * On entry, INCX specifies the increment for the elements of X. * INCX must not be zero. Unchanged on exit. * * BETA (input) DOUBLE PRECISION * On entry, BETA specifies the scalar beta. When BETA is * supplied as zero then Y need not be set on input. Unchanged * on exit. * * Y (input/output) DOUBLE PRECISION array * On entry, Y is an incremented array of dimension at least * ( 1 + ( m - 1 ) * abs( INCY ) ) when TRANS = 'N' or 'n' and * at least ( 1 + ( n - 1 ) * abs( INCY ) ) otherwise. Before * entry with BETA non-zero, the incremented array Y must con- * tain the vector y. On exit, Y is overwritten by the updated * vector y. * * INCY (input) INTEGER * On entry, INCY specifies the increment for the elements of Y. * INCY must not be zero. Unchanged on exit. * * Further Details * =============== * * For further information on the Level 1 BLAS specification, see: * * ``A Proposal for Standard Linear Algebra Subprograms'' by R. Hanson, * F. Krogh and C. Lawson, ACM SIGNUM Newsl., 8(16), 1973, * * ``Basic Linear Algebra Subprograms for Fortran Usage'' by C. Lawson, * R. Hanson, D. Kincaid and F. Krogh, ACM Transactions on Mathematical * Software, 5(3) pp 308-323, 1979. * * For further information on the Level 2 BLAS specification, see: * * ``An Extended Set of FORTRAN Basic Linear Algebra Subprograms'' by * J. Dongarra, J. Du Croz, S. Hammarling and R. Hanson, ACM Transac- * tions on Mathematical Software, 14(1) pp 1-17, 1988. * * ``Algorithm 656: An extended Set of Basic Linear Algebra Subprograms: * Model Implementation and Test Programs'' by J. Dongarra, J. Du Croz, * S. Hammarling and R. Hanson, ACM Transactions on Mathematical Soft- * ware, 14(1) pp 18-32, 1988. * * For further information on the Level 3 BLAS specification, see: * * ``A Set of Level 3 Basic Linear Algebra Subprograms'' by J. Dongarra, * J. Du Croz, I. Duff and S. Hammarling, ACM Transactions on Mathemati- * cal Software, 16(1), pp 1-17, 1990. * * ===================================================================== * * .. Parameters .. INTEGER ICOTRAN, INOTRAN, ITRAN PARAMETER ( INOTRAN = 111, ITRAN = 112, ICOTRAN = 113 ) * .. * .. Local Scalars .. INTEGER INFO, ITRANS * .. * .. External Subroutines .. EXTERNAL ATL_F77WRAP_DGBMV, XERBLA * .. * .. External Functions .. EXTERNAL LSAME LOGICAL LSAME * .. * .. Executable Statements .. * INFO = 0 * IF( LSAME( TRANS, 'N' ) ) THEN ITRANS = INOTRAN ELSE IF( LSAME( TRANS, 'T' ) ) THEN ITRANS = ITRAN ELSE IF( LSAME( TRANS, 'C' ) ) THEN ITRANS = ICOTRAN ELSE IF( INFO.EQ.0 ) THEN INFO = 1 END IF * IF( INFO.EQ.0 ) THEN 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 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DGBMV ', INFO ) RETURN END IF * CALL ATL_F77WRAP_DGBMV( ITRANS, M, N, KL, KU, ALPHA, A, LDA, $ X, INCX, BETA, Y, INCY ) * RETURN * * End of DGBMV * END