LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
dtrtrs.f
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1 *> \brief \b DTRTRS
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
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16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE DTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB,
22 * INFO )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER DIAG, TRANS, UPLO
26 * INTEGER INFO, LDA, LDB, N, NRHS
27 * ..
28 * .. Array Arguments ..
29 * DOUBLE PRECISION A( LDA, * ), B( LDB, * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> DTRTRS solves a triangular system of the form
39 *>
40 *> A * X = B or A**T * X = B,
41 *>
42 *> where A is a triangular matrix of order N, and B is an N-by-NRHS
43 *> matrix. A check is made to verify that A is nonsingular.
44 *> \endverbatim
45 *
46 * Arguments:
47 * ==========
48 *
49 *> \param[in] UPLO
50 *> \verbatim
51 *> UPLO is CHARACTER*1
52 *> = 'U': A is upper triangular;
53 *> = 'L': A is lower triangular.
54 *> \endverbatim
55 *>
56 *> \param[in] TRANS
57 *> \verbatim
58 *> TRANS is CHARACTER*1
59 *> Specifies the form of the system of equations:
60 *> = 'N': A * X = B (No transpose)
61 *> = 'T': A**T * X = B (Transpose)
62 *> = 'C': A**H * X = B (Conjugate transpose = Transpose)
63 *> \endverbatim
64 *>
65 *> \param[in] DIAG
66 *> \verbatim
67 *> DIAG is CHARACTER*1
68 *> = 'N': A is non-unit triangular;
69 *> = 'U': A is unit triangular.
70 *> \endverbatim
71 *>
72 *> \param[in] N
73 *> \verbatim
74 *> N is INTEGER
75 *> The order of the matrix A. N >= 0.
76 *> \endverbatim
77 *>
78 *> \param[in] NRHS
79 *> \verbatim
80 *> NRHS is INTEGER
81 *> The number of right hand sides, i.e., the number of columns
82 *> of the matrix B. NRHS >= 0.
83 *> \endverbatim
84 *>
85 *> \param[in] A
86 *> \verbatim
87 *> A is DOUBLE PRECISION array, dimension (LDA,N)
88 *> The triangular matrix A. If UPLO = 'U', the leading N-by-N
89 *> upper triangular part of the array A contains the upper
90 *> triangular matrix, and the strictly lower triangular part of
91 *> A is not referenced. If UPLO = 'L', the leading N-by-N lower
92 *> triangular part of the array A contains the lower triangular
93 *> matrix, and the strictly upper triangular part of A is not
94 *> referenced. If DIAG = 'U', the diagonal elements of A are
95 *> also not referenced and are assumed to be 1.
96 *> \endverbatim
97 *>
98 *> \param[in] LDA
99 *> \verbatim
100 *> LDA is INTEGER
101 *> The leading dimension of the array A. LDA >= max(1,N).
102 *> \endverbatim
103 *>
104 *> \param[in,out] B
105 *> \verbatim
106 *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
107 *> On entry, the right hand side matrix B.
108 *> On exit, if INFO = 0, the solution matrix X.
109 *> \endverbatim
110 *>
111 *> \param[in] LDB
112 *> \verbatim
113 *> LDB is INTEGER
114 *> The leading dimension of the array B. LDB >= max(1,N).
115 *> \endverbatim
116 *>
117 *> \param[out] INFO
118 *> \verbatim
119 *> INFO is INTEGER
120 *> = 0: successful exit
121 *> < 0: if INFO = -i, the i-th argument had an illegal value
122 *> > 0: if INFO = i, the i-th diagonal element of A is zero,
123 *> indicating that the matrix is singular and the solutions
124 *> X have not been computed.
125 *> \endverbatim
126 *
127 * Authors:
128 * ========
129 *
130 *> \author Univ. of Tennessee
131 *> \author Univ. of California Berkeley
132 *> \author Univ. of Colorado Denver
133 *> \author NAG Ltd.
134 *
135 *> \date November 2011
136 *
137 *> \ingroup doubleOTHERcomputational
138 *
139 * =====================================================================
140  SUBROUTINE dtrtrs( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB,
141  \$ info )
142 *
143 * -- LAPACK computational routine (version 3.4.0) --
144 * -- LAPACK is a software package provided by Univ. of Tennessee, --
145 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
146 * November 2011
147 *
148 * .. Scalar Arguments ..
149  CHARACTER DIAG, TRANS, UPLO
150  INTEGER INFO, LDA, LDB, N, NRHS
151 * ..
152 * .. Array Arguments ..
153  DOUBLE PRECISION A( lda, * ), B( ldb, * )
154 * ..
155 *
156 * =====================================================================
157 *
158 * .. Parameters ..
159  DOUBLE PRECISION ZERO, ONE
160  parameter ( zero = 0.0d+0, one = 1.0d+0 )
161 * ..
162 * .. Local Scalars ..
163  LOGICAL NOUNIT
164 * ..
165 * .. External Functions ..
166  LOGICAL LSAME
167  EXTERNAL lsame
168 * ..
169 * .. External Subroutines ..
170  EXTERNAL dtrsm, xerbla
171 * ..
172 * .. Intrinsic Functions ..
173  INTRINSIC max
174 * ..
175 * .. Executable Statements ..
176 *
177 * Test the input parameters.
178 *
179  info = 0
180  nounit = lsame( diag, 'N' )
181  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
182  info = -1
183  ELSE IF( .NOT.lsame( trans, 'N' ) .AND. .NOT.
184  \$ lsame( trans, 'T' ) .AND. .NOT.lsame( trans, 'C' ) ) THEN
185  info = -2
186  ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
187  info = -3
188  ELSE IF( n.LT.0 ) THEN
189  info = -4
190  ELSE IF( nrhs.LT.0 ) THEN
191  info = -5
192  ELSE IF( lda.LT.max( 1, n ) ) THEN
193  info = -7
194  ELSE IF( ldb.LT.max( 1, n ) ) THEN
195  info = -9
196  END IF
197  IF( info.NE.0 ) THEN
198  CALL xerbla( 'DTRTRS', -info )
199  RETURN
200  END IF
201 *
202 * Quick return if possible
203 *
204  IF( n.EQ.0 )
205  \$ RETURN
206 *
207 * Check for singularity.
208 *
209  IF( nounit ) THEN
210  DO 10 info = 1, n
211  IF( a( info, info ).EQ.zero )
212  \$ RETURN
213  10 CONTINUE
214  END IF
215  info = 0
216 *
217 * Solve A * x = b or A**T * x = b.
218 *
219  CALL dtrsm( 'Left', uplo, trans, diag, n, nrhs, one, a, lda, b,
220  \$ ldb )
221 *
222  RETURN
223 *
224 * End of DTRTRS
225 *
226  END
subroutine dtrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRSM
Definition: dtrsm.f:183
subroutine dtrtrs(UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, INFO)
DTRTRS
Definition: dtrtrs.f:142
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62