SUBROUTINE ZTBSV( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX ) * * -- 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 DIAG, TRANS, UPLO INTEGER INCX, K, LDA, N * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), X( * ) * .. * * Purpose * ======= * * ZTBSV solves one of the systems of equations * * A*x = b, or A'*x = b, or conjg( A' )*x = b, * * where b and x are n-element vectors and A is an n by n unit, or non- * unit, upper or lower triangular band matrix, with (k+1) diagonals. * * No test for singularity or near-singularity is included in this * routine. Such tests must be performed before calling this routine. * * Arguments * ========= * * UPLO (input) CHARACTER*1 * On entry, UPLO specifies whether the matrix is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * TRANS (input) CHARACTER*1. * On entry, TRANS specifies the equations to be solved as fol- * lows: * * TRANS = 'N' or 'n' A *x = b, * * TRANS = 'T' or 't' A'*x = b, * * TRANS = 'C' or 'c' conjg( A' )*x = b. * * Unchanged on exit. * * DIAG (input) CHARACTER*1 * On entry, DIAG specifies whether or not A is unit triangu- * lar as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * 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 with UPLO = 'U' or 'u', K specifies the number of * super-diagonals of the matrix A. On entry with UPLO = 'L' or * 'l', K specifies the number of sub-diagonals of the matrix A. * K must satisfy 0 .le. K. Unchanged on exit. * * A (input) COMPLEX*16 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 * matrix of coefficients, 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 re- * ferenced. The following program segment will transfer an up- * per triangular 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 matrix of coefficients, supplied column by co- * lumn, 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 trans- * fer a lower triangular band matrix from conventional full ma- * trix 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 * * Note that when DIAG = 'U' or 'u' the elements of the array A * corresponding to the diagonal elements of the matrix are not * referenced, but are assumed to be unity. 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 ). * Unchanged on exit. * * X (input/output) COMPLEX*16 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 n element right-hand side vector * b. On exit, X is overwritten with the solution vector x. * * INCX (input) INTEGER * On entry, INCX specifies the increment for the elements of X. * INCX 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 ) INTEGER ICOTRAN, INOTRAN, ITRAN PARAMETER ( INOTRAN = 111, ITRAN = 112, ICOTRAN = 113 ) INTEGER INONUNIT, IUNIT PARAMETER ( INONUNIT = 131, IUNIT = 132 ) * .. * .. Local Scalars .. INTEGER IDIAG, INFO, ITRANS, IUPLO * .. * .. External Subroutines .. EXTERNAL ATL_F77WRAP_ZTBSV, 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( 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 = 2 END IF * IF( LSAME( DIAG , 'N' ) ) THEN IDIAG = INONUNIT ELSE IF( LSAME( DIAG , 'U' ) ) THEN IDIAG = IUNIT ELSE IF( INFO.EQ.0 ) THEN INFO = 3 END IF * IF( INFO.EQ.0 ) THEN IF( N.LT.0 ) THEN INFO = 4 ELSE IF( K.LT.0 ) THEN INFO = 5 ELSE IF( LDA.LT.( K + 1 ) ) THEN INFO = 7 ELSE IF( INCX.EQ.0 ) THEN INFO = 9 END IF END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZTBSV ', INFO ) RETURN END IF * CALL ATL_F77WRAP_ZTBSV( IUPLO, ITRANS, IDIAG, N, K, A, LDA, $ X, INCX ) * RETURN * * End of ZTBSV * END