1: *> \brief \b DPFTRS
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
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: *> \ingroup doubleOTHERcomputational
109: *
110: *> \par Further Details:
111: * =====================
112: *>
113: *> \verbatim
114: *>
115: *> We first consider Rectangular Full Packed (RFP) Format when N is
116: *> even. We give an example where N = 6.
117: *>
118: *> AP is Upper AP is Lower
119: *>
120: *> 00 01 02 03 04 05 00
121: *> 11 12 13 14 15 10 11
122: *> 22 23 24 25 20 21 22
123: *> 33 34 35 30 31 32 33
124: *> 44 45 40 41 42 43 44
125: *> 55 50 51 52 53 54 55
126: *>
127: *>
128: *> Let TRANSR = 'N'. RFP holds AP as follows:
129: *> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
130: *> three columns of AP upper. The lower triangle A(4:6,0:2) consists of
131: *> the transpose of the first three columns of AP upper.
132: *> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
133: *> three columns of AP lower. The upper triangle A(0:2,0:2) consists of
134: *> the transpose of the last three columns of AP lower.
135: *> This covers the case N even and TRANSR = 'N'.
136: *>
137: *> RFP A RFP A
138: *>
139: *> 03 04 05 33 43 53
140: *> 13 14 15 00 44 54
141: *> 23 24 25 10 11 55
142: *> 33 34 35 20 21 22
143: *> 00 44 45 30 31 32
144: *> 01 11 55 40 41 42
145: *> 02 12 22 50 51 52
146: *>
147: *> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
148: *> transpose of RFP A above. One therefore gets:
149: *>
150: *>
151: *> RFP A RFP A
152: *>
153: *> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
154: *> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
155: *> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
156: *>
157: *>
158: *> We then consider Rectangular Full Packed (RFP) Format when N is
159: *> odd. We give an example where N = 5.
160: *>
161: *> AP is Upper AP is Lower
162: *>
163: *> 00 01 02 03 04 00
164: *> 11 12 13 14 10 11
165: *> 22 23 24 20 21 22
166: *> 33 34 30 31 32 33
167: *> 44 40 41 42 43 44
168: *>
169: *>
170: *> Let TRANSR = 'N'. RFP holds AP as follows:
171: *> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
172: *> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
173: *> the transpose of the first two columns of AP upper.
174: *> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
175: *> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
176: *> the transpose of the last two columns of AP lower.
177: *> This covers the case N odd and TRANSR = 'N'.
178: *>
179: *> RFP A RFP A
180: *>
181: *> 02 03 04 00 33 43
182: *> 12 13 14 10 11 44
183: *> 22 23 24 20 21 22
184: *> 00 33 34 30 31 32
185: *> 01 11 44 40 41 42
186: *>
187: *> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
188: *> transpose of RFP A above. One therefore gets:
189: *>
190: *> RFP A RFP A
191: *>
192: *> 02 12 22 00 01 00 10 20 30 40 50
193: *> 03 13 23 33 11 33 11 21 31 41 51
194: *> 04 14 24 34 44 43 44 22 32 42 52
195: *> \endverbatim
196: *>
197: * =====================================================================
198: SUBROUTINE DPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO )
199: *
200: * -- LAPACK computational routine --
201: * -- LAPACK is a software package provided by Univ. of Tennessee, --
202: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
203: *
204: * .. Scalar Arguments ..
205: CHARACTER TRANSR, UPLO
206: INTEGER INFO, LDB, N, NRHS
207: * ..
208: * .. Array Arguments ..
209: DOUBLE PRECISION A( 0: * ), B( LDB, * )
210: * ..
211: *
212: * =====================================================================
213: *
214: * .. Parameters ..
215: DOUBLE PRECISION ONE
216: PARAMETER ( ONE = 1.0D+0 )
217: * ..
218: * .. Local Scalars ..
219: LOGICAL LOWER, NORMALTRANSR
220: * ..
221: * .. External Functions ..
222: LOGICAL LSAME
223: EXTERNAL LSAME
224: * ..
225: * .. External Subroutines ..
226: EXTERNAL XERBLA, DTFSM
227: * ..
228: * .. Intrinsic Functions ..
229: INTRINSIC MAX
230: * ..
231: * .. Executable Statements ..
232: *
233: * Test the input parameters.
234: *
235: INFO = 0
236: NORMALTRANSR = LSAME( TRANSR, 'N' )
237: LOWER = LSAME( UPLO, 'L' )
238: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN
239: INFO = -1
240: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
241: INFO = -2
242: ELSE IF( N.LT.0 ) THEN
243: INFO = -3
244: ELSE IF( NRHS.LT.0 ) THEN
245: INFO = -4
246: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
247: INFO = -7
248: END IF
249: IF( INFO.NE.0 ) THEN
250: CALL XERBLA( 'DPFTRS', -INFO )
251: RETURN
252: END IF
253: *
254: * Quick return if possible
255: *
256: IF( N.EQ.0 .OR. NRHS.EQ.0 )
257: $ RETURN
258: *
259: * start execution: there are two triangular solves
260: *
261: IF( LOWER ) THEN
262: CALL DTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, ONE, A, B,
263: $ LDB )
264: CALL DTFSM( TRANSR, 'L', UPLO, 'T', 'N', N, NRHS, ONE, A, B,
265: $ LDB )
266: ELSE
267: CALL DTFSM( TRANSR, 'L', UPLO, 'T', 'N', N, NRHS, ONE, A, B,
268: $ LDB )
269: CALL DTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, ONE, A, B,
270: $ LDB )
271: END IF
272: *
273: RETURN
274: *
275: * End of DPFTRS
276: *
277: END
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