1
SUBROUTINE DTBSV( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX )
3
* -- Automatically Tuned Linear Algebra Software (ATLAS)
4
* (C) Copyright 2000 All Rights Reserved
6
* -- ATLAS routine -- F77 Interface -- Version 3.2 -- December 15, 2000
8
* -- Suggestions, comments, bugs reports should be sent to the follo-
9
* wing e-mail address: atlas@cs.utk.edu
11
* Author : Antoine P. Petitet
12
* University of Tennessee - Innovative Computing Laboratory
13
* Knoxville TN, 37996-1301, USA.
15
* ---------------------------------------------------------------------
17
* -- Copyright notice and Licensing terms:
19
* Redistribution and use in source and binary forms, with or without
20
* modification, are permitted provided that the following conditions
23
* 1. Redistributions of source code must retain the above copyright
24
* notice, this list of conditions and the following disclaimer.
25
* 2. Redistributions in binary form must reproduce the above copyright
26
* notice, this list of conditions, and the following disclaimer in
27
* the documentation and/or other materials provided with the distri-
29
* 3. The name of the University, the ATLAS group, or the names of its
30
* contributors may not be used to endorse or promote products deri-
31
* ved from this software without specific written permission.
35
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
36
* ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
37
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
38
* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE UNIVERSITY
39
* OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPE-
40
* CIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
41
* TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
42
* OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEO-
43
* RY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (IN-
44
* CLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
45
* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
47
* ---------------------------------------------------------------------
49
* .. Scalar Arguments ..
50
CHARACTER*1 DIAG, TRANS, UPLO
51
INTEGER INCX, K, LDA, N
53
* .. Array Arguments ..
54
DOUBLE PRECISION A( LDA, * ), X( * )
60
* DTBSV solves one of the systems of equations
62
* A*x = b, or A'*x = b,
64
* where b and x are n-element vectors and A is an n by n unit, or non-
65
* unit, upper or lower triangular band matrix, with (k+1) diagonals.
67
* No test for singularity or near-singularity is included in this
68
* routine. Such tests must be performed before calling this routine.
73
* UPLO (input) CHARACTER*1
74
* On entry, UPLO specifies whether the matrix is an upper or
75
* lower triangular matrix as follows:
77
* UPLO = 'U' or 'u' A is an upper triangular matrix.
79
* UPLO = 'L' or 'l' A is a lower triangular matrix.
83
* TRANS (input) CHARACTER*1.
84
* On entry, TRANS specifies the equations to be solved as fol-
87
* TRANS = 'N' or 'n' A *x = b,
89
* TRANS = 'T' or 't' A'*x = b,
91
* TRANS = 'T' or 't' A'*x = b.
95
* DIAG (input) CHARACTER*1
96
* On entry, DIAG specifies whether or not A is unit triangu-
99
* DIAG = 'U' or 'u' A is assumed to be unit triangular.
101
* DIAG = 'N' or 'n' A is not assumed to be unit
107
* On entry, N specifies the order of the matrix A. N must be at
108
* least zero. Unchanged on exit.
111
* On entry with UPLO = 'U' or 'u', K specifies the number of
112
* super-diagonals of the matrix A. On entry with UPLO = 'L' or
113
* 'l', K specifies the number of sub-diagonals of the matrix A.
114
* K must satisfy 0 .le. K. Unchanged on exit.
116
* A (input) DOUBLE PRECISION array
117
* On entry, A is an array of dimension ( LDA, n ). Before entry
118
* with UPLO = 'U' or 'u', the leading (k + 1) by n part of the
119
* array A must contain the upper triangular band part of the
120
* matrix of coefficients, supplied column by column, with the
121
* leading diagonal of the matrix in row ( k + 1 ) of the array,
122
* the first super-diagonal starting at position 2 in row k, and
123
* so on. The top left k by k triangle of the array A is not re-
124
* ferenced. The following program segment will transfer an up-
125
* per triangular band matrix from conventional full matrix
126
* storage to band storage:
130
* DO 10, I = MAX( 1, J - K ), J
131
* A( M + I, J ) = matrix( I, J )
135
* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) by
136
* n part of the array A must contain the lower triangular band
137
* part of the matrix of coefficients, supplied column by co-
138
* lumn, with the leading diagonal of the matrix in row 1 of the
139
* array, the first sub-diagonal starting at position 1 in row
140
* 2, and so on. The bottom right k by k triangle of the array A
141
* is not referenced. The following program segment will trans-
142
* fer a lower triangular band matrix from conventional full ma-
143
* trix storage to band storage:
147
* DO 10, I = J, MIN( N, J + K )
148
* A( M + I, J ) = matrix( I, J )
152
* Note that when DIAG = 'U' or 'u' the elements of the array A
153
* corresponding to the diagonal elements of the matrix are not
154
* referenced, but are assumed to be unity. Unchanged on exit.
156
* LDA (input) INTEGER
157
* On entry, LDA specifies the first dimension of A as declared
158
* in the calling (sub) program. LDA must be at least ( k + 1 ).
161
* X (input/output) DOUBLE PRECISION array
162
* On entry, X is an incremented array of dimension at least
163
* ( 1 + ( n - 1 ) * abs( INCX ) ). Before entry, the incremen-
164
* ted array X must contain the n element right-hand side vector
165
* b. On exit, X is overwritten with the solution vector x.
167
* INCX (input) INTEGER
168
* On entry, INCX specifies the increment for the elements of X.
169
* INCX must not be zero. Unchanged on exit.
174
* For further information on the Level 1 BLAS specification, see:
176
* ``A Proposal for Standard Linear Algebra Subprograms'' by R. Hanson,
177
* F. Krogh and C. Lawson, ACM SIGNUM Newsl., 8(16), 1973,
179
* ``Basic Linear Algebra Subprograms for Fortran Usage'' by C. Lawson,
180
* R. Hanson, D. Kincaid and F. Krogh, ACM Transactions on Mathematical
181
* Software, 5(3) pp 308-323, 1979.
183
* For further information on the Level 2 BLAS specification, see:
185
* ``An Extended Set of FORTRAN Basic Linear Algebra Subprograms'' by
186
* J. Dongarra, J. Du Croz, S. Hammarling and R. Hanson, ACM Transac-
187
* tions on Mathematical Software, 14(1) pp 1-17, 1988.
189
* ``Algorithm 656: An extended Set of Basic Linear Algebra Subprograms:
190
* Model Implementation and Test Programs'' by J. Dongarra, J. Du Croz,
191
* S. Hammarling and R. Hanson, ACM Transactions on Mathematical Soft-
192
* ware, 14(1) pp 18-32, 1988.
194
* For further information on the Level 3 BLAS specification, see:
196
* ``A Set of Level 3 Basic Linear Algebra Subprograms'' by J. Dongarra,
197
* J. Du Croz, I. Duff and S. Hammarling, ACM Transactions on Mathemati-
198
* cal Software, 16(1), pp 1-17, 1990.
200
* =====================================================================
203
INTEGER ILOWER, IUPPER
204
PARAMETER ( IUPPER = 121, ILOWER = 122 )
205
INTEGER ICOTRAN, INOTRAN, ITRAN
206
PARAMETER ( INOTRAN = 111, ITRAN = 112, ICOTRAN = 113 )
207
INTEGER INONUNIT, IUNIT
208
PARAMETER ( INONUNIT = 131, IUNIT = 132 )
210
* .. Local Scalars ..
211
INTEGER IDIAG, INFO, ITRANS, IUPLO
213
* .. External Subroutines ..
214
EXTERNAL ATL_F77WRAP_DTBSV, XERBLA
216
* .. External Functions ..
220
* .. Executable Statements ..
224
IF( LSAME( UPLO , 'U' ) ) THEN
226
ELSE IF( LSAME( UPLO , 'L' ) ) THEN
228
ELSE IF( INFO.EQ.0 ) THEN
232
IF( LSAME( TRANS, 'N' ) ) THEN
234
ELSE IF( LSAME( TRANS, 'T' ) ) THEN
236
ELSE IF( LSAME( TRANS, 'C' ) ) THEN
238
ELSE IF( INFO.EQ.0 ) THEN
242
IF( LSAME( DIAG , 'N' ) ) THEN
244
ELSE IF( LSAME( DIAG , 'U' ) ) THEN
246
ELSE IF( INFO.EQ.0 ) THEN
253
ELSE IF( K.LT.0 ) THEN
255
ELSE IF( LDA.LT.( K + 1 ) ) THEN
257
ELSE IF( INCX.EQ.0 ) THEN
263
CALL XERBLA( 'DTBSV ', INFO )
267
CALL ATL_F77WRAP_DTBSV( IUPLO, ITRANS, IDIAG, N, K, A, LDA,
added
removed
interfaces/blas/F77/src/dtbsv.f
