Annotation of rpl/lapack/lapack/dpftri.f, revision 1.10
1.7 bertrand 1: *> \brief \b DPFTRI
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 DPFTRI + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpftri.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpftri.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpftri.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DPFTRI( TRANSR, UPLO, N, A, INFO )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER TRANSR, UPLO
25: * INTEGER INFO, N
26: * .. Array Arguments ..
27: * DOUBLE PRECISION A( 0: * )
28: * ..
29: *
30: *
31: *> \par Purpose:
32: * =============
33: *>
34: *> \verbatim
35: *>
36: *> DPFTRI computes the inverse of a (real) symmetric positive definite
37: *> matrix A using the Cholesky factorization A = U**T*U or A = L*L**T
38: *> computed by DPFTRF.
39: *> \endverbatim
40: *
41: * Arguments:
42: * ==========
43: *
44: *> \param[in] TRANSR
45: *> \verbatim
46: *> TRANSR is CHARACTER*1
47: *> = 'N': The Normal TRANSR of RFP A is stored;
48: *> = 'T': The Transpose TRANSR of RFP A is stored.
49: *> \endverbatim
50: *>
51: *> \param[in] UPLO
52: *> \verbatim
53: *> UPLO is CHARACTER*1
54: *> = 'U': Upper triangle of A is stored;
55: *> = 'L': Lower triangle of A is stored.
56: *> \endverbatim
57: *>
58: *> \param[in] N
59: *> \verbatim
60: *> N is INTEGER
61: *> The order of the matrix A. N >= 0.
62: *> \endverbatim
63: *>
64: *> \param[in,out] A
65: *> \verbatim
66: *> A is DOUBLE PRECISION array, dimension ( N*(N+1)/2 )
67: *> On entry, the symmetric matrix A in RFP format. RFP format is
68: *> described by TRANSR, UPLO, and N as follows: If TRANSR = 'N'
69: *> then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is
70: *> (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'T' then RFP is
71: *> the transpose of RFP A as defined when
72: *> TRANSR = 'N'. The contents of RFP A are defined by UPLO as
73: *> follows: If UPLO = 'U' the RFP A contains the nt elements of
74: *> upper packed A. If UPLO = 'L' the RFP A contains the elements
75: *> of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR =
76: *> 'T'. When TRANSR is 'N' the LDA is N+1 when N is even and N
77: *> is odd. See the Note below for more details.
78: *>
79: *> On exit, the symmetric inverse of the original matrix, in the
80: *> same storage format.
81: *> \endverbatim
82: *>
83: *> \param[out] INFO
84: *> \verbatim
85: *> INFO is INTEGER
86: *> = 0: successful exit
87: *> < 0: if INFO = -i, the i-th argument had an illegal value
88: *> > 0: if INFO = i, the (i,i) element of the factor U or L is
89: *> zero, and the inverse could not be computed.
90: *> \endverbatim
91: *
92: * Authors:
93: * ========
94: *
95: *> \author Univ. of Tennessee
96: *> \author Univ. of California Berkeley
97: *> \author Univ. of Colorado Denver
98: *> \author NAG Ltd.
99: *
100: *> \date November 2011
101: *
102: *> \ingroup doubleOTHERcomputational
103: *
104: *> \par Further Details:
105: * =====================
106: *>
107: *> \verbatim
108: *>
109: *> We first consider Rectangular Full Packed (RFP) Format when N is
110: *> even. We give an example where N = 6.
111: *>
112: *> AP is Upper AP is Lower
113: *>
114: *> 00 01 02 03 04 05 00
115: *> 11 12 13 14 15 10 11
116: *> 22 23 24 25 20 21 22
117: *> 33 34 35 30 31 32 33
118: *> 44 45 40 41 42 43 44
119: *> 55 50 51 52 53 54 55
120: *>
121: *>
122: *> Let TRANSR = 'N'. RFP holds AP as follows:
123: *> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
124: *> three columns of AP upper. The lower triangle A(4:6,0:2) consists of
125: *> the transpose of the first three columns of AP upper.
126: *> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
127: *> three columns of AP lower. The upper triangle A(0:2,0:2) consists of
128: *> the transpose of the last three columns of AP lower.
129: *> This covers the case N even and TRANSR = 'N'.
130: *>
131: *> RFP A RFP A
132: *>
133: *> 03 04 05 33 43 53
134: *> 13 14 15 00 44 54
135: *> 23 24 25 10 11 55
136: *> 33 34 35 20 21 22
137: *> 00 44 45 30 31 32
138: *> 01 11 55 40 41 42
139: *> 02 12 22 50 51 52
140: *>
141: *> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
142: *> transpose of RFP A above. One therefore gets:
143: *>
144: *>
145: *> RFP A RFP A
146: *>
147: *> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
148: *> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
149: *> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
150: *>
151: *>
152: *> We then consider Rectangular Full Packed (RFP) Format when N is
153: *> odd. We give an example where N = 5.
154: *>
155: *> AP is Upper AP is Lower
156: *>
157: *> 00 01 02 03 04 00
158: *> 11 12 13 14 10 11
159: *> 22 23 24 20 21 22
160: *> 33 34 30 31 32 33
161: *> 44 40 41 42 43 44
162: *>
163: *>
164: *> Let TRANSR = 'N'. RFP holds AP as follows:
165: *> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
166: *> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
167: *> the transpose of the first two columns of AP upper.
168: *> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
169: *> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
170: *> the transpose of the last two columns of AP lower.
171: *> This covers the case N odd and TRANSR = 'N'.
172: *>
173: *> RFP A RFP A
174: *>
175: *> 02 03 04 00 33 43
176: *> 12 13 14 10 11 44
177: *> 22 23 24 20 21 22
178: *> 00 33 34 30 31 32
179: *> 01 11 44 40 41 42
180: *>
181: *> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
182: *> transpose of RFP A above. One therefore gets:
183: *>
184: *> RFP A RFP A
185: *>
186: *> 02 12 22 00 01 00 10 20 30 40 50
187: *> 03 13 23 33 11 33 11 21 31 41 51
188: *> 04 14 24 34 44 43 44 22 32 42 52
189: *> \endverbatim
190: *>
191: * =====================================================================
192: SUBROUTINE DPFTRI( TRANSR, UPLO, N, A, INFO )
1.1 bertrand 193: *
1.7 bertrand 194: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 195: * -- LAPACK is a software package provided by Univ. of Tennessee, --
196: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.7 bertrand 197: * November 2011
1.1 bertrand 198: *
199: * .. Scalar Arguments ..
200: CHARACTER TRANSR, UPLO
201: INTEGER INFO, N
202: * .. Array Arguments ..
203: DOUBLE PRECISION A( 0: * )
204: * ..
205: *
206: * =====================================================================
207: *
208: * .. Parameters ..
209: DOUBLE PRECISION ONE
210: PARAMETER ( ONE = 1.0D+0 )
211: * ..
212: * .. Local Scalars ..
213: LOGICAL LOWER, NISODD, NORMALTRANSR
214: INTEGER N1, N2, K
215: * ..
216: * .. External Functions ..
217: LOGICAL LSAME
218: EXTERNAL LSAME
219: * ..
220: * .. External Subroutines ..
221: EXTERNAL XERBLA, DTFTRI, DLAUUM, DTRMM, DSYRK
222: * ..
223: * .. Intrinsic Functions ..
224: INTRINSIC MOD
225: * ..
226: * .. Executable Statements ..
227: *
228: * Test the input parameters.
229: *
230: INFO = 0
231: NORMALTRANSR = LSAME( TRANSR, 'N' )
232: LOWER = LSAME( UPLO, 'L' )
233: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN
234: INFO = -1
235: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
236: INFO = -2
237: ELSE IF( N.LT.0 ) THEN
238: INFO = -3
239: END IF
240: IF( INFO.NE.0 ) THEN
241: CALL XERBLA( 'DPFTRI', -INFO )
242: RETURN
243: END IF
244: *
245: * Quick return if possible
246: *
247: IF( N.EQ.0 )
1.6 bertrand 248: $ RETURN
1.1 bertrand 249: *
250: * Invert the triangular Cholesky factor U or L.
251: *
252: CALL DTFTRI( TRANSR, UPLO, 'N', N, A, INFO )
253: IF( INFO.GT.0 )
1.6 bertrand 254: $ RETURN
1.1 bertrand 255: *
256: * If N is odd, set NISODD = .TRUE.
257: * If N is even, set K = N/2 and NISODD = .FALSE.
258: *
259: IF( MOD( N, 2 ).EQ.0 ) THEN
260: K = N / 2
261: NISODD = .FALSE.
262: ELSE
263: NISODD = .TRUE.
264: END IF
265: *
266: * Set N1 and N2 depending on LOWER
267: *
268: IF( LOWER ) THEN
269: N2 = N / 2
270: N1 = N - N2
271: ELSE
272: N1 = N / 2
273: N2 = N - N1
274: END IF
275: *
276: * Start execution of triangular matrix multiply: inv(U)*inv(U)^C or
277: * inv(L)^C*inv(L). There are eight cases.
278: *
279: IF( NISODD ) THEN
280: *
281: * N is odd
282: *
283: IF( NORMALTRANSR ) THEN
284: *
285: * N is odd and TRANSR = 'N'
286: *
287: IF( LOWER ) THEN
288: *
289: * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:N1-1) )
290: * T1 -> a(0,0), T2 -> a(0,1), S -> a(N1,0)
291: * T1 -> a(0), T2 -> a(n), S -> a(N1)
292: *
293: CALL DLAUUM( 'L', N1, A( 0 ), N, INFO )
294: CALL DSYRK( 'L', 'T', N1, N2, ONE, A( N1 ), N, ONE,
1.6 bertrand 295: $ A( 0 ), N )
1.1 bertrand 296: CALL DTRMM( 'L', 'U', 'N', 'N', N2, N1, ONE, A( N ), N,
1.6 bertrand 297: $ A( N1 ), N )
1.1 bertrand 298: CALL DLAUUM( 'U', N2, A( N ), N, INFO )
299: *
300: ELSE
301: *
302: * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:N2-1)
303: * T1 -> a(N1+1,0), T2 -> a(N1,0), S -> a(0,0)
304: * T1 -> a(N2), T2 -> a(N1), S -> a(0)
305: *
306: CALL DLAUUM( 'L', N1, A( N2 ), N, INFO )
307: CALL DSYRK( 'L', 'N', N1, N2, ONE, A( 0 ), N, ONE,
1.6 bertrand 308: $ A( N2 ), N )
1.1 bertrand 309: CALL DTRMM( 'R', 'U', 'T', 'N', N1, N2, ONE, A( N1 ), N,
1.6 bertrand 310: $ A( 0 ), N )
1.1 bertrand 311: CALL DLAUUM( 'U', N2, A( N1 ), N, INFO )
312: *
313: END IF
314: *
315: ELSE
316: *
317: * N is odd and TRANSR = 'T'
318: *
319: IF( LOWER ) THEN
320: *
321: * SRPA for LOWER, TRANSPOSE, and N is odd
322: * T1 -> a(0), T2 -> a(1), S -> a(0+N1*N1)
323: *
324: CALL DLAUUM( 'U', N1, A( 0 ), N1, INFO )
325: CALL DSYRK( 'U', 'N', N1, N2, ONE, A( N1*N1 ), N1, ONE,
1.6 bertrand 326: $ A( 0 ), N1 )
1.1 bertrand 327: CALL DTRMM( 'R', 'L', 'N', 'N', N1, N2, ONE, A( 1 ), N1,
1.6 bertrand 328: $ A( N1*N1 ), N1 )
1.1 bertrand 329: CALL DLAUUM( 'L', N2, A( 1 ), N1, INFO )
330: *
331: ELSE
332: *
333: * SRPA for UPPER, TRANSPOSE, and N is odd
334: * T1 -> a(0+N2*N2), T2 -> a(0+N1*N2), S -> a(0)
335: *
336: CALL DLAUUM( 'U', N1, A( N2*N2 ), N2, INFO )
337: CALL DSYRK( 'U', 'T', N1, N2, ONE, A( 0 ), N2, ONE,
1.6 bertrand 338: $ A( N2*N2 ), N2 )
1.1 bertrand 339: CALL DTRMM( 'L', 'L', 'T', 'N', N2, N1, ONE, A( N1*N2 ),
1.6 bertrand 340: $ N2, A( 0 ), N2 )
1.1 bertrand 341: CALL DLAUUM( 'L', N2, A( N1*N2 ), N2, INFO )
342: *
343: END IF
344: *
345: END IF
346: *
347: ELSE
348: *
349: * N is even
350: *
351: IF( NORMALTRANSR ) THEN
352: *
353: * N is even and TRANSR = 'N'
354: *
355: IF( LOWER ) THEN
356: *
357: * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
358: * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
359: * T1 -> a(1), T2 -> a(0), S -> a(k+1)
360: *
361: CALL DLAUUM( 'L', K, A( 1 ), N+1, INFO )
362: CALL DSYRK( 'L', 'T', K, K, ONE, A( K+1 ), N+1, ONE,
1.6 bertrand 363: $ A( 1 ), N+1 )
1.1 bertrand 364: CALL DTRMM( 'L', 'U', 'N', 'N', K, K, ONE, A( 0 ), N+1,
1.6 bertrand 365: $ A( K+1 ), N+1 )
1.1 bertrand 366: CALL DLAUUM( 'U', K, A( 0 ), N+1, INFO )
367: *
368: ELSE
369: *
370: * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
371: * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
372: * T1 -> a(k+1), T2 -> a(k), S -> a(0)
373: *
374: CALL DLAUUM( 'L', K, A( K+1 ), N+1, INFO )
375: CALL DSYRK( 'L', 'N', K, K, ONE, A( 0 ), N+1, ONE,
1.6 bertrand 376: $ A( K+1 ), N+1 )
1.1 bertrand 377: CALL DTRMM( 'R', 'U', 'T', 'N', K, K, ONE, A( K ), N+1,
1.6 bertrand 378: $ A( 0 ), N+1 )
1.1 bertrand 379: CALL DLAUUM( 'U', K, A( K ), N+1, INFO )
380: *
381: END IF
382: *
383: ELSE
384: *
385: * N is even and TRANSR = 'T'
386: *
387: IF( LOWER ) THEN
388: *
389: * SRPA for LOWER, TRANSPOSE, and N is even (see paper)
390: * T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1),
391: * T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
392: *
393: CALL DLAUUM( 'U', K, A( K ), K, INFO )
394: CALL DSYRK( 'U', 'N', K, K, ONE, A( K*( K+1 ) ), K, ONE,
1.6 bertrand 395: $ A( K ), K )
1.1 bertrand 396: CALL DTRMM( 'R', 'L', 'N', 'N', K, K, ONE, A( 0 ), K,
1.6 bertrand 397: $ A( K*( K+1 ) ), K )
1.1 bertrand 398: CALL DLAUUM( 'L', K, A( 0 ), K, INFO )
399: *
400: ELSE
401: *
402: * SRPA for UPPER, TRANSPOSE, and N is even (see paper)
403: * T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0),
404: * T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
405: *
406: CALL DLAUUM( 'U', K, A( K*( K+1 ) ), K, INFO )
407: CALL DSYRK( 'U', 'T', K, K, ONE, A( 0 ), K, ONE,
1.6 bertrand 408: $ A( K*( K+1 ) ), K )
1.1 bertrand 409: CALL DTRMM( 'L', 'L', 'T', 'N', K, K, ONE, A( K*K ), K,
1.6 bertrand 410: $ A( 0 ), K )
1.1 bertrand 411: CALL DLAUUM( 'L', K, A( K*K ), K, INFO )
412: *
413: END IF
414: *
415: END IF
416: *
417: END IF
418: *
419: RETURN
420: *
421: * End of DPFTRI
422: *
423: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to dpftri.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack