1: *> \brief \b ZPFTRS
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZPFTRS + dependencies
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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: *> \ingroup complex16OTHERcomputational
109: *
110: *> \par Further Details:
111: * =====================
112: *>
113: *> \verbatim
114: *>
115: *> We first consider Standard Packed Format when N is even.
116: *> 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: *> conjugate-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: *> conjugate-transpose of the last three columns of AP lower.
135: *> To denote conjugate we place -- above the element. This covers the
136: *> case N even and TRANSR = 'N'.
137: *>
138: *> RFP A RFP A
139: *>
140: *> -- -- --
141: *> 03 04 05 33 43 53
142: *> -- --
143: *> 13 14 15 00 44 54
144: *> --
145: *> 23 24 25 10 11 55
146: *>
147: *> 33 34 35 20 21 22
148: *> --
149: *> 00 44 45 30 31 32
150: *> -- --
151: *> 01 11 55 40 41 42
152: *> -- -- --
153: *> 02 12 22 50 51 52
154: *>
155: *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
156: *> transpose of RFP A above. One therefore gets:
157: *>
158: *>
159: *> RFP A RFP A
160: *>
161: *> -- -- -- -- -- -- -- -- -- --
162: *> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
163: *> -- -- -- -- -- -- -- -- -- --
164: *> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
165: *> -- -- -- -- -- -- -- -- -- --
166: *> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
167: *>
168: *>
169: *> We next consider Standard Packed Format when N is odd.
170: *> We give an example where N = 5.
171: *>
172: *> AP is Upper AP is Lower
173: *>
174: *> 00 01 02 03 04 00
175: *> 11 12 13 14 10 11
176: *> 22 23 24 20 21 22
177: *> 33 34 30 31 32 33
178: *> 44 40 41 42 43 44
179: *>
180: *>
181: *> Let TRANSR = 'N'. RFP holds AP as follows:
182: *> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
183: *> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
184: *> conjugate-transpose of the first two columns of AP upper.
185: *> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
186: *> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
187: *> conjugate-transpose of the last two columns of AP lower.
188: *> To denote conjugate we place -- above the element. This covers the
189: *> case N odd and TRANSR = 'N'.
190: *>
191: *> RFP A RFP A
192: *>
193: *> -- --
194: *> 02 03 04 00 33 43
195: *> --
196: *> 12 13 14 10 11 44
197: *>
198: *> 22 23 24 20 21 22
199: *> --
200: *> 00 33 34 30 31 32
201: *> -- --
202: *> 01 11 44 40 41 42
203: *>
204: *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
205: *> transpose of RFP A above. One therefore gets:
206: *>
207: *>
208: *> RFP A RFP A
209: *>
210: *> -- -- -- -- -- -- -- -- --
211: *> 02 12 22 00 01 00 10 20 30 40 50
212: *> -- -- -- -- -- -- -- -- --
213: *> 03 13 23 33 11 33 11 21 31 41 51
214: *> -- -- -- -- -- -- -- -- --
215: *> 04 14 24 34 44 43 44 22 32 42 52
216: *> \endverbatim
217: *>
218: * =====================================================================
219: SUBROUTINE ZPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO )
220: *
221: * -- LAPACK computational routine --
222: * -- LAPACK is a software package provided by Univ. of Tennessee, --
223: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
224: *
225: * .. Scalar Arguments ..
226: CHARACTER TRANSR, UPLO
227: INTEGER INFO, LDB, N, NRHS
228: * ..
229: * .. Array Arguments ..
230: COMPLEX*16 A( 0: * ), B( LDB, * )
231: * ..
232: *
233: * =====================================================================
234: *
235: * .. Parameters ..
236: COMPLEX*16 CONE
237: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
238: * ..
239: * .. Local Scalars ..
240: LOGICAL LOWER, NORMALTRANSR
241: * ..
242: * .. External Functions ..
243: LOGICAL LSAME
244: EXTERNAL LSAME
245: * ..
246: * .. External Subroutines ..
247: EXTERNAL XERBLA, ZTFSM
248: * ..
249: * .. Intrinsic Functions ..
250: INTRINSIC MAX
251: * ..
252: * .. Executable Statements ..
253: *
254: * Test the input parameters.
255: *
256: INFO = 0
257: NORMALTRANSR = LSAME( TRANSR, 'N' )
258: LOWER = LSAME( UPLO, 'L' )
259: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
260: INFO = -1
261: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
262: INFO = -2
263: ELSE IF( N.LT.0 ) THEN
264: INFO = -3
265: ELSE IF( NRHS.LT.0 ) THEN
266: INFO = -4
267: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
268: INFO = -7
269: END IF
270: IF( INFO.NE.0 ) THEN
271: CALL XERBLA( 'ZPFTRS', -INFO )
272: RETURN
273: END IF
274: *
275: * Quick return if possible
276: *
277: IF( N.EQ.0 .OR. NRHS.EQ.0 )
278: $ RETURN
279: *
280: * start execution: there are two triangular solves
281: *
282: IF( LOWER ) THEN
283: CALL ZTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, CONE, A, B,
284: $ LDB )
285: CALL ZTFSM( TRANSR, 'L', UPLO, 'C', 'N', N, NRHS, CONE, A, B,
286: $ LDB )
287: ELSE
288: CALL ZTFSM( TRANSR, 'L', UPLO, 'C', 'N', N, NRHS, CONE, A, B,
289: $ LDB )
290: CALL ZTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, CONE, A, B,
291: $ LDB )
292: END IF
293: *
294: RETURN
295: *
296: * End of ZPFTRS
297: *
298: END
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