Annotation of rpl/lapack/lapack/dgetrs.f, revision 1.16
1.9 bertrand 1: *> \brief \b DGETRS
2: *
3: * =========== DOCUMENTATION ===========
4: *
1.15 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.9 bertrand 7: *
8: *> \htmlonly
1.15 bertrand 9: *> Download DGETRS + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgetrs.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgetrs.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgetrs.f">
1.9 bertrand 15: *> [TXT]</a>
1.15 bertrand 16: *> \endhtmlonly
1.9 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
1.15 bertrand 22: *
1.9 bertrand 23: * .. Scalar Arguments ..
24: * CHARACTER TRANS
25: * INTEGER INFO, LDA, LDB, N, NRHS
26: * ..
27: * .. Array Arguments ..
28: * INTEGER IPIV( * )
29: * DOUBLE PRECISION A( LDA, * ), B( LDB, * )
30: * ..
1.15 bertrand 31: *
1.9 bertrand 32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> DGETRS solves a system of linear equations
39: *> A * X = B or A**T * X = B
40: *> with a general N-by-N matrix A using the LU factorization computed
41: *> by DGETRF.
42: *> \endverbatim
43: *
44: * Arguments:
45: * ==========
46: *
47: *> \param[in] TRANS
48: *> \verbatim
49: *> TRANS is CHARACTER*1
50: *> Specifies the form of the system of equations:
51: *> = 'N': A * X = B (No transpose)
52: *> = 'T': A**T* X = B (Transpose)
53: *> = 'C': A**T* X = B (Conjugate transpose = Transpose)
54: *> \endverbatim
55: *>
56: *> \param[in] N
57: *> \verbatim
58: *> N is INTEGER
59: *> The order of the matrix A. N >= 0.
60: *> \endverbatim
61: *>
62: *> \param[in] NRHS
63: *> \verbatim
64: *> NRHS is INTEGER
65: *> The number of right hand sides, i.e., the number of columns
66: *> of the matrix B. NRHS >= 0.
67: *> \endverbatim
68: *>
69: *> \param[in] A
70: *> \verbatim
71: *> A is DOUBLE PRECISION array, dimension (LDA,N)
72: *> The factors L and U from the factorization A = P*L*U
73: *> as computed by DGETRF.
74: *> \endverbatim
75: *>
76: *> \param[in] LDA
77: *> \verbatim
78: *> LDA is INTEGER
79: *> The leading dimension of the array A. LDA >= max(1,N).
80: *> \endverbatim
81: *>
82: *> \param[in] IPIV
83: *> \verbatim
84: *> IPIV is INTEGER array, dimension (N)
85: *> The pivot indices from DGETRF; for 1<=i<=N, row i of the
86: *> matrix was interchanged with row IPIV(i).
87: *> \endverbatim
88: *>
89: *> \param[in,out] B
90: *> \verbatim
91: *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
92: *> On entry, the right hand side matrix B.
93: *> On exit, the solution matrix X.
94: *> \endverbatim
95: *>
96: *> \param[in] LDB
97: *> \verbatim
98: *> LDB is INTEGER
99: *> The leading dimension of the array B. LDB >= max(1,N).
100: *> \endverbatim
101: *>
102: *> \param[out] INFO
103: *> \verbatim
104: *> INFO is INTEGER
105: *> = 0: successful exit
106: *> < 0: if INFO = -i, the i-th argument had an illegal value
107: *> \endverbatim
108: *
109: * Authors:
110: * ========
111: *
1.15 bertrand 112: *> \author Univ. of Tennessee
113: *> \author Univ. of California Berkeley
114: *> \author Univ. of Colorado Denver
115: *> \author NAG Ltd.
1.9 bertrand 116: *
1.15 bertrand 117: *> \date December 2016
1.9 bertrand 118: *
119: *> \ingroup doubleGEcomputational
120: *
121: * =====================================================================
1.1 bertrand 122: SUBROUTINE DGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO )
123: *
1.15 bertrand 124: * -- LAPACK computational routine (version 3.7.0) --
1.1 bertrand 125: * -- LAPACK is a software package provided by Univ. of Tennessee, --
126: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.15 bertrand 127: * December 2016
1.1 bertrand 128: *
129: * .. Scalar Arguments ..
130: CHARACTER TRANS
131: INTEGER INFO, LDA, LDB, N, NRHS
132: * ..
133: * .. Array Arguments ..
134: INTEGER IPIV( * )
135: DOUBLE PRECISION A( LDA, * ), B( LDB, * )
136: * ..
137: *
138: * =====================================================================
139: *
140: * .. Parameters ..
141: DOUBLE PRECISION ONE
142: PARAMETER ( ONE = 1.0D+0 )
143: * ..
144: * .. Local Scalars ..
145: LOGICAL NOTRAN
146: * ..
147: * .. External Functions ..
148: LOGICAL LSAME
149: EXTERNAL LSAME
150: * ..
151: * .. External Subroutines ..
152: EXTERNAL DLASWP, DTRSM, XERBLA
153: * ..
154: * .. Intrinsic Functions ..
155: INTRINSIC MAX
156: * ..
157: * .. Executable Statements ..
158: *
159: * Test the input parameters.
160: *
161: INFO = 0
162: NOTRAN = LSAME( TRANS, 'N' )
163: IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT.
164: $ LSAME( TRANS, 'C' ) ) THEN
165: INFO = -1
166: ELSE IF( N.LT.0 ) THEN
167: INFO = -2
168: ELSE IF( NRHS.LT.0 ) THEN
169: INFO = -3
170: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
171: INFO = -5
172: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
173: INFO = -8
174: END IF
175: IF( INFO.NE.0 ) THEN
176: CALL XERBLA( 'DGETRS', -INFO )
177: RETURN
178: END IF
179: *
180: * Quick return if possible
181: *
182: IF( N.EQ.0 .OR. NRHS.EQ.0 )
183: $ RETURN
184: *
185: IF( NOTRAN ) THEN
186: *
187: * Solve A * X = B.
188: *
189: * Apply row interchanges to the right hand sides.
190: *
191: CALL DLASWP( NRHS, B, LDB, 1, N, IPIV, 1 )
192: *
193: * Solve L*X = B, overwriting B with X.
194: *
195: CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Unit', N, NRHS,
196: $ ONE, A, LDA, B, LDB )
197: *
198: * Solve U*X = B, overwriting B with X.
199: *
200: CALL DTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', N,
201: $ NRHS, ONE, A, LDA, B, LDB )
202: ELSE
203: *
1.8 bertrand 204: * Solve A**T * X = B.
1.1 bertrand 205: *
1.8 bertrand 206: * Solve U**T *X = B, overwriting B with X.
1.1 bertrand 207: *
208: CALL DTRSM( 'Left', 'Upper', 'Transpose', 'Non-unit', N, NRHS,
209: $ ONE, A, LDA, B, LDB )
210: *
1.8 bertrand 211: * Solve L**T *X = B, overwriting B with X.
1.1 bertrand 212: *
213: CALL DTRSM( 'Left', 'Lower', 'Transpose', 'Unit', N, NRHS, ONE,
214: $ A, LDA, B, LDB )
215: *
216: * Apply row interchanges to the solution vectors.
217: *
218: CALL DLASWP( NRHS, B, LDB, 1, N, IPIV, -1 )
219: END IF
220: *
221: RETURN
222: *
223: * End of DGETRS
224: *
225: END
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