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SUBROUTINE DTBSV( 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 15, 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 ..
DOUBLE PRECISION A( LDA, * ), X( * )
* ..
*
* Purpose
* =======
*
* DTBSV solves one of the systems of equations
*
* A*x = b, or 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 = 'T' or 't' 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) 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
* 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) 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 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_DTBSV, 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( 'DTBSV ', INFO )
RETURN
END IF
*
CALL ATL_F77WRAP_DTBSV( IUPLO, ITRANS, IDIAG, N, K, A, LDA,
$ X, INCX )
*
RETURN
*
* End of DTBSV
*
END
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