SUBROUTINE DSBMV( UPLO, N, K, 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 UPLO INTEGER INCX, INCY, K, LDA, N DOUBLE PRECISION ALPHA, BETA * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * DSBMV performs the matrix-vector operation * * y := alpha*A*x + beta*y, * * where alpha and beta are scalars, x and y are n-element vectors and A * is an n by n symmetric band matrix, with k super-diagonals. * * Arguments * ========= * * UPLO (input) CHARACTER*1 * On entry, UPLO specifies whether the upper or lower triangu- * lar part of the band matrix A is being supplied as follows: * * UPLO = 'U' or 'u' The upper triangular part of A is * being supplied. * * UPLO = 'L' or 'l' The lower triangular part of A is * being supplied. * * Unchanged on exit. * * N (input) INTEGER * On entry, N specifies the order of the matrix A. N must be at * least zero. Unchanged on exit. * * K (input) INTEGER * On entry, K specifies the number of super-diagonals of the * matrix A. K must satisfy 0 .le. K. 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 entry * with UPLO = 'U' or 'u', the leading (k + 1) by n part of the * array A must contain the upper triangular band part of the * symmetric matrix, supplied column by column, with the leading * diagonal of the matrix in row (k + 1) of the array, the first * super-diagonal starting at position 2 in row k, and so on. * The top left k by k triangle of the array A is not referen- * ced. The following program segment will transfer the upper * triangular part of a symmetric band matrix from conventional * full matrix storage to band storage: * * DO 20, J = 1, N * M = K + 1 - J * DO 10, I = MAX( 1, J - K ), J * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Before entry with UPLO = 'L' or 'l', the leading (k+1) by n * part of the array A must contain the lower triangular band * part of the symmetric matrix, supplied column by column, with * the leading diagonal of the matrix in row 1 of the array, the * first sub-diagonal starting at position 1 in row 2, and so * on. The bottom right k by k triangle of the array A is not * referenced. The following program segment will transfer the * lower triangular part of a symmetric band matrix from conven- * tional full matrix storage to band storage: * * DO 20, J = 1, N * M = 1 - J * DO 10, I = J, MIN( N, J + K ) * A( M + 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 k + 1. Un- * changed on exit. * * X (input) DOUBLE PRECISION array * On entry, X is an incremented array of dimension at least * ( 1 + ( n - 1 ) * abs( INCX ) ). Before entry, the incremen- * ted array X must contain the vector x. Unchanged 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 + ( n - 1 ) * abs( INCY ) ). Before entry with BETA non- * zero, the incremented array Y must contain 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 ILOWER, IUPPER PARAMETER ( IUPPER = 121, ILOWER = 122 ) * .. * .. Local Scalars .. INTEGER INFO, IUPLO * .. * .. External Subroutines .. EXTERNAL ATL_F77WRAP_DSBMV, XERBLA * .. * .. External Functions .. EXTERNAL LSAME LOGICAL LSAME * .. * .. Executable Statements .. * INFO = 0 * IF( LSAME( UPLO , 'U' ) ) THEN IUPLO = IUPPER ELSE IF( LSAME( UPLO , 'L' ) ) THEN IUPLO = ILOWER ELSE IF( INFO.EQ.0 ) THEN INFO = 1 END IF * IF( INFO.EQ.0 ) THEN 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 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DSBMV ', INFO ) RETURN END IF * CALL ATL_F77WRAP_DSBMV( IUPLO, N, K, ALPHA, A, LDA, X, INCX, $ BETA, Y, INCY ) * RETURN * * End of DSBMV * END