Annotation of rpl/lapack/lapack/dpftrs.f, revision 1.12
1.7 bertrand 1: *> \brief \b DPFTRS
1.1 bertrand 2: *
1.7 bertrand 3: * =========== DOCUMENTATION ===========
1.1 bertrand 4: *
1.7 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.1 bertrand 7: *
1.7 bertrand 8: *> \htmlonly
9: *> Download DPFTRS + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpftrs.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpftrs.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpftrs.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER TRANSR, UPLO
25: * INTEGER INFO, LDB, N, NRHS
26: * ..
27: * .. Array Arguments ..
28: * DOUBLE PRECISION A( 0: * ), B( LDB, * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> DPFTRS solves a system of linear equations A*X = B with a symmetric
38: *> positive definite matrix A using the Cholesky factorization
39: *> A = U**T*U or A = L*L**T computed by DPFTRF.
40: *> \endverbatim
41: *
42: * Arguments:
43: * ==========
44: *
45: *> \param[in] TRANSR
46: *> \verbatim
47: *> TRANSR is CHARACTER*1
48: *> = 'N': The Normal TRANSR of RFP A is stored;
49: *> = 'T': The Transpose TRANSR of RFP A is stored.
50: *> \endverbatim
51: *>
52: *> \param[in] UPLO
53: *> \verbatim
54: *> UPLO is CHARACTER*1
55: *> = 'U': Upper triangle of RFP A is stored;
56: *> = 'L': Lower triangle of RFP A is stored.
57: *> \endverbatim
58: *>
59: *> \param[in] N
60: *> \verbatim
61: *> N is INTEGER
62: *> The order of the matrix A. N >= 0.
63: *> \endverbatim
64: *>
65: *> \param[in] NRHS
66: *> \verbatim
67: *> NRHS is INTEGER
68: *> The number of right hand sides, i.e., the number of columns
69: *> of the matrix B. NRHS >= 0.
70: *> \endverbatim
71: *>
72: *> \param[in] A
73: *> \verbatim
74: *> A is DOUBLE PRECISION array, dimension ( N*(N+1)/2 ).
75: *> The triangular factor U or L from the Cholesky factorization
76: *> of RFP A = U**T*U or RFP A = L*L**T, as computed by DPFTRF.
77: *> See note below for more details about RFP A.
78: *> \endverbatim
79: *>
80: *> \param[in,out] B
81: *> \verbatim
82: *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
83: *> On entry, the right hand side matrix B.
84: *> On exit, the solution matrix X.
85: *> \endverbatim
86: *>
87: *> \param[in] LDB
88: *> \verbatim
89: *> LDB is INTEGER
90: *> The leading dimension of the array B. LDB >= max(1,N).
91: *> \endverbatim
92: *>
93: *> \param[out] INFO
94: *> \verbatim
95: *> INFO is INTEGER
96: *> = 0: successful exit
97: *> < 0: if INFO = -i, the i-th argument had an illegal value
98: *> \endverbatim
99: *
100: * Authors:
101: * ========
102: *
103: *> \author Univ. of Tennessee
104: *> \author Univ. of California Berkeley
105: *> \author Univ. of Colorado Denver
106: *> \author NAG Ltd.
107: *
108: *> \date November 2011
109: *
110: *> \ingroup doubleOTHERcomputational
111: *
112: *> \par Further Details:
113: * =====================
114: *>
115: *> \verbatim
116: *>
117: *> We first consider Rectangular Full Packed (RFP) Format when N is
118: *> even. We give an example where N = 6.
119: *>
120: *> AP is Upper AP is Lower
121: *>
122: *> 00 01 02 03 04 05 00
123: *> 11 12 13 14 15 10 11
124: *> 22 23 24 25 20 21 22
125: *> 33 34 35 30 31 32 33
126: *> 44 45 40 41 42 43 44
127: *> 55 50 51 52 53 54 55
128: *>
129: *>
130: *> Let TRANSR = 'N'. RFP holds AP as follows:
131: *> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
132: *> three columns of AP upper. The lower triangle A(4:6,0:2) consists of
133: *> the transpose of the first three columns of AP upper.
134: *> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
135: *> three columns of AP lower. The upper triangle A(0:2,0:2) consists of
136: *> the transpose of the last three columns of AP lower.
137: *> This covers the case N even and TRANSR = 'N'.
138: *>
139: *> RFP A RFP A
140: *>
141: *> 03 04 05 33 43 53
142: *> 13 14 15 00 44 54
143: *> 23 24 25 10 11 55
144: *> 33 34 35 20 21 22
145: *> 00 44 45 30 31 32
146: *> 01 11 55 40 41 42
147: *> 02 12 22 50 51 52
148: *>
149: *> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
150: *> transpose of RFP A above. One therefore gets:
151: *>
152: *>
153: *> RFP A RFP A
154: *>
155: *> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
156: *> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
157: *> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
158: *>
159: *>
160: *> We then consider Rectangular Full Packed (RFP) Format when N is
161: *> odd. We give an example where N = 5.
162: *>
163: *> AP is Upper AP is Lower
164: *>
165: *> 00 01 02 03 04 00
166: *> 11 12 13 14 10 11
167: *> 22 23 24 20 21 22
168: *> 33 34 30 31 32 33
169: *> 44 40 41 42 43 44
170: *>
171: *>
172: *> Let TRANSR = 'N'. RFP holds AP as follows:
173: *> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
174: *> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
175: *> the transpose of the first two columns of AP upper.
176: *> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
177: *> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
178: *> the transpose of the last two columns of AP lower.
179: *> This covers the case N odd and TRANSR = 'N'.
180: *>
181: *> RFP A RFP A
182: *>
183: *> 02 03 04 00 33 43
184: *> 12 13 14 10 11 44
185: *> 22 23 24 20 21 22
186: *> 00 33 34 30 31 32
187: *> 01 11 44 40 41 42
188: *>
189: *> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
190: *> transpose of RFP A above. One therefore gets:
191: *>
192: *> RFP A RFP A
193: *>
194: *> 02 12 22 00 01 00 10 20 30 40 50
195: *> 03 13 23 33 11 33 11 21 31 41 51
196: *> 04 14 24 34 44 43 44 22 32 42 52
197: *> \endverbatim
198: *>
199: * =====================================================================
200: SUBROUTINE DPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO )
201: *
202: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 203: * -- LAPACK is a software package provided by Univ. of Tennessee, --
204: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.7 bertrand 205: * November 2011
1.1 bertrand 206: *
207: * .. Scalar Arguments ..
208: CHARACTER TRANSR, UPLO
209: INTEGER INFO, LDB, N, NRHS
210: * ..
211: * .. Array Arguments ..
212: DOUBLE PRECISION A( 0: * ), B( LDB, * )
213: * ..
214: *
215: * =====================================================================
216: *
217: * .. Parameters ..
218: DOUBLE PRECISION ONE
219: PARAMETER ( ONE = 1.0D+0 )
220: * ..
221: * .. Local Scalars ..
222: LOGICAL LOWER, NORMALTRANSR
223: * ..
224: * .. External Functions ..
225: LOGICAL LSAME
226: EXTERNAL LSAME
227: * ..
228: * .. External Subroutines ..
229: EXTERNAL XERBLA, DTFSM
230: * ..
231: * .. Intrinsic Functions ..
232: INTRINSIC MAX
233: * ..
234: * .. Executable Statements ..
235: *
236: * Test the input parameters.
237: *
238: INFO = 0
239: NORMALTRANSR = LSAME( TRANSR, 'N' )
240: LOWER = LSAME( UPLO, 'L' )
241: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN
242: INFO = -1
243: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
244: INFO = -2
245: ELSE IF( N.LT.0 ) THEN
246: INFO = -3
247: ELSE IF( NRHS.LT.0 ) THEN
248: INFO = -4
249: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
250: INFO = -7
251: END IF
252: IF( INFO.NE.0 ) THEN
253: CALL XERBLA( 'DPFTRS', -INFO )
254: RETURN
255: END IF
256: *
257: * Quick return if possible
258: *
259: IF( N.EQ.0 .OR. NRHS.EQ.0 )
1.6 bertrand 260: $ RETURN
1.1 bertrand 261: *
262: * start execution: there are two triangular solves
263: *
264: IF( LOWER ) THEN
265: CALL DTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, ONE, A, B,
1.6 bertrand 266: $ LDB )
1.1 bertrand 267: CALL DTFSM( TRANSR, 'L', UPLO, 'T', 'N', N, NRHS, ONE, A, B,
1.6 bertrand 268: $ LDB )
1.1 bertrand 269: ELSE
270: CALL DTFSM( TRANSR, 'L', UPLO, 'T', 'N', N, NRHS, ONE, A, B,
1.6 bertrand 271: $ LDB )
1.1 bertrand 272: CALL DTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, ONE, A, B,
1.6 bertrand 273: $ LDB )
1.1 bertrand 274: END IF
275: *
276: RETURN
277: *
278: * End of DPFTRS
279: *
280: END
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