LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
ztrtrs.f
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1 *> \brief \b ZTRTRS
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
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14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztrtrs.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZTRTRS( 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 * COMPLEX*16 A( LDA, * ), B( LDB, * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> ZTRTRS solves a triangular system of the form
39 *>
40 *> A * X = B, A**T * X = B, or A**H * 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)
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 COMPLEX*16 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 COMPLEX*16 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 December 2016
136 *
137 *> \ingroup complex16OTHERcomputational
138 *
139 * =====================================================================
140  SUBROUTINE ztrtrs( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB,
141  $ INFO )
142 *
143 * -- LAPACK computational routine (version 3.7.0) --
144 * -- LAPACK is a software package provided by Univ. of Tennessee, --
145 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
146 * December 2016
147 *
148 * .. Scalar Arguments ..
149  CHARACTER DIAG, TRANS, UPLO
150  INTEGER INFO, LDA, LDB, N, NRHS
151 * ..
152 * .. Array Arguments ..
153  COMPLEX*16 A( lda, * ), B( ldb, * )
154 * ..
155 *
156 * =====================================================================
157 *
158 * .. Parameters ..
159  COMPLEX*16 ZERO, ONE
160  parameter( zero = ( 0.0d+0, 0.0d+0 ),
161  $ one = ( 1.0d+0, 0.0d+0 ) )
162 * ..
163 * .. Local Scalars ..
164  LOGICAL NOUNIT
165 * ..
166 * .. External Functions ..
167  LOGICAL LSAME
168  EXTERNAL lsame
169 * ..
170 * .. External Subroutines ..
171  EXTERNAL xerbla, ztrsm
172 * ..
173 * .. Intrinsic Functions ..
174  INTRINSIC max
175 * ..
176 * .. Executable Statements ..
177 *
178 * Test the input parameters.
179 *
180  info = 0
181  nounit = lsame( diag, 'N' )
182  IF( .NOT.lsame( uplo, 'U' ) .AND. .NOT.lsame( uplo, 'L' ) ) THEN
183  info = -1
184  ELSE IF( .NOT.lsame( trans, 'N' ) .AND. .NOT.
185  $ lsame( trans, 'T' ) .AND. .NOT.lsame( trans, 'C' ) ) THEN
186  info = -2
187  ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
188  info = -3
189  ELSE IF( n.LT.0 ) THEN
190  info = -4
191  ELSE IF( nrhs.LT.0 ) THEN
192  info = -5
193  ELSE IF( lda.LT.max( 1, n ) ) THEN
194  info = -7
195  ELSE IF( ldb.LT.max( 1, n ) ) THEN
196  info = -9
197  END IF
198  IF( info.NE.0 ) THEN
199  CALL xerbla( 'ZTRTRS', -info )
200  RETURN
201  END IF
202 *
203 * Quick return if possible
204 *
205  IF( n.EQ.0 )
206  $ RETURN
207 *
208 * Check for singularity.
209 *
210  IF( nounit ) THEN
211  DO 10 info = 1, n
212  IF( a( info, info ).EQ.zero )
213  $ RETURN
214  10 CONTINUE
215  END IF
216  info = 0
217 *
218 * Solve A * x = b, A**T * x = b, or A**H * x = b.
219 *
220  CALL ztrsm( 'Left', uplo, trans, diag, n, nrhs, one, a, lda, b,
221  $ ldb )
222 *
223  RETURN
224 *
225 * End of ZTRTRS
226 *
227  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine ztrtrs(UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, INFO)
ZTRTRS
Definition: ztrtrs.f:142
subroutine ztrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
ZTRSM
Definition: ztrsm.f:182