Annotation of rpl/lapack/lapack/zpftrs.f, revision 1.9
1.7 bertrand 1: *> \brief \b ZPFTRS
2: *
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 ZPFTRS + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpftrs.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpftrs.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpftrs.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZPFTRS( 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: * COMPLEX*16 A( 0: * ), B( LDB, * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> ZPFTRS solves a system of linear equations A*X = B with a Hermitian
38: *> positive definite matrix A using the Cholesky factorization
39: *> A = U**H*U or A = L*L**H computed by ZPFTRF.
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: *> = 'C': The Conjugate-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 COMPLEX*16 array, dimension ( N*(N+1)/2 );
75: *> The triangular factor U or L from the Cholesky factorization
76: *> of RFP A = U**H*U or RFP A = L*L**H, as computed by ZPFTRF.
77: *> See note below for more details about RFP A.
78: *> \endverbatim
79: *>
80: *> \param[in,out] B
81: *> \verbatim
82: *> B is COMPLEX*16 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 complex16OTHERcomputational
111: *
112: *> \par Further Details:
113: * =====================
114: *>
115: *> \verbatim
116: *>
117: *> We first consider Standard Packed Format when N is even.
118: *> 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: *> conjugate-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: *> conjugate-transpose of the last three columns of AP lower.
137: *> To denote conjugate we place -- above the element. This covers the
138: *> case N even and TRANSR = 'N'.
139: *>
140: *> RFP A RFP A
141: *>
142: *> -- -- --
143: *> 03 04 05 33 43 53
144: *> -- --
145: *> 13 14 15 00 44 54
146: *> --
147: *> 23 24 25 10 11 55
148: *>
149: *> 33 34 35 20 21 22
150: *> --
151: *> 00 44 45 30 31 32
152: *> -- --
153: *> 01 11 55 40 41 42
154: *> -- -- --
155: *> 02 12 22 50 51 52
156: *>
157: *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
158: *> transpose of RFP A above. One therefore gets:
159: *>
160: *>
161: *> RFP A RFP A
162: *>
163: *> -- -- -- -- -- -- -- -- -- --
164: *> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
165: *> -- -- -- -- -- -- -- -- -- --
166: *> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
167: *> -- -- -- -- -- -- -- -- -- --
168: *> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
169: *>
170: *>
171: *> We next consider Standard Packed Format when N is odd.
172: *> We give an example where N = 5.
173: *>
174: *> AP is Upper AP is Lower
175: *>
176: *> 00 01 02 03 04 00
177: *> 11 12 13 14 10 11
178: *> 22 23 24 20 21 22
179: *> 33 34 30 31 32 33
180: *> 44 40 41 42 43 44
181: *>
182: *>
183: *> Let TRANSR = 'N'. RFP holds AP as follows:
184: *> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
185: *> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
186: *> conjugate-transpose of the first two columns of AP upper.
187: *> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
188: *> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
189: *> conjugate-transpose of the last two columns of AP lower.
190: *> To denote conjugate we place -- above the element. This covers the
191: *> case N odd and TRANSR = 'N'.
192: *>
193: *> RFP A RFP A
194: *>
195: *> -- --
196: *> 02 03 04 00 33 43
197: *> --
198: *> 12 13 14 10 11 44
199: *>
200: *> 22 23 24 20 21 22
201: *> --
202: *> 00 33 34 30 31 32
203: *> -- --
204: *> 01 11 44 40 41 42
205: *>
206: *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
207: *> transpose of RFP A above. One therefore gets:
208: *>
209: *>
210: *> RFP A RFP A
211: *>
212: *> -- -- -- -- -- -- -- -- --
213: *> 02 12 22 00 01 00 10 20 30 40 50
214: *> -- -- -- -- -- -- -- -- --
215: *> 03 13 23 33 11 33 11 21 31 41 51
216: *> -- -- -- -- -- -- -- -- --
217: *> 04 14 24 34 44 43 44 22 32 42 52
218: *> \endverbatim
219: *>
220: * =====================================================================
221: SUBROUTINE ZPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO )
1.1 bertrand 222: *
1.7 bertrand 223: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 224: * -- LAPACK is a software package provided by Univ. of Tennessee, --
225: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.7 bertrand 226: * November 2011
1.1 bertrand 227: *
228: * .. Scalar Arguments ..
229: CHARACTER TRANSR, UPLO
230: INTEGER INFO, LDB, N, NRHS
231: * ..
232: * .. Array Arguments ..
233: COMPLEX*16 A( 0: * ), B( LDB, * )
234: * ..
235: *
236: * =====================================================================
237: *
238: * .. Parameters ..
239: COMPLEX*16 CONE
240: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
241: * ..
242: * .. Local Scalars ..
243: LOGICAL LOWER, NORMALTRANSR
244: * ..
245: * .. External Functions ..
246: LOGICAL LSAME
247: EXTERNAL LSAME
248: * ..
249: * .. External Subroutines ..
250: EXTERNAL XERBLA, ZTFSM
251: * ..
252: * .. Intrinsic Functions ..
253: INTRINSIC MAX
254: * ..
255: * .. Executable Statements ..
256: *
257: * Test the input parameters.
258: *
259: INFO = 0
260: NORMALTRANSR = LSAME( TRANSR, 'N' )
261: LOWER = LSAME( UPLO, 'L' )
262: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
263: INFO = -1
264: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
265: INFO = -2
266: ELSE IF( N.LT.0 ) THEN
267: INFO = -3
268: ELSE IF( NRHS.LT.0 ) THEN
269: INFO = -4
270: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
271: INFO = -7
272: END IF
273: IF( INFO.NE.0 ) THEN
274: CALL XERBLA( 'ZPFTRS', -INFO )
275: RETURN
276: END IF
277: *
278: * Quick return if possible
279: *
280: IF( N.EQ.0 .OR. NRHS.EQ.0 )
1.6 bertrand 281: $ RETURN
1.1 bertrand 282: *
283: * start execution: there are two triangular solves
284: *
285: IF( LOWER ) THEN
286: CALL ZTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, CONE, A, B,
1.6 bertrand 287: $ LDB )
1.1 bertrand 288: CALL ZTFSM( TRANSR, 'L', UPLO, 'C', 'N', N, NRHS, CONE, A, B,
1.6 bertrand 289: $ LDB )
1.1 bertrand 290: ELSE
291: CALL ZTFSM( TRANSR, 'L', UPLO, 'C', 'N', N, NRHS, CONE, A, B,
1.6 bertrand 292: $ LDB )
1.1 bertrand 293: CALL ZTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, CONE, A, B,
1.6 bertrand 294: $ LDB )
1.1 bertrand 295: END IF
296: *
297: RETURN
298: *
299: * End of ZPFTRS
300: *
301: END
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