Annotation of rpl/lapack/lapack/dtrtrs.f, revision 1.10
1.9 bertrand 1: *> \brief \b DTRTRS
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DTRTRS + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtrtrs.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtrtrs.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtrtrs.f">
15: *> [TXT]</a>
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: * =====================================================================
1.1 bertrand 140: SUBROUTINE DTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB,
141: $ INFO )
142: *
1.9 bertrand 143: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 144: * -- LAPACK is a software package provided by Univ. of Tennessee, --
145: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 bertrand 146: * November 2011
1.1 bertrand 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: *
1.8 bertrand 217: * Solve A * x = b or A**T * x = b.
1.1 bertrand 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
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