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1.7 bertrand 1: *> \brief \b ZTFTTR
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 ZTFTTR + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztfttr.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztfttr.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztfttr.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZTFTTR( TRANSR, UPLO, N, ARF, A, LDA, INFO )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER TRANSR, UPLO
25: * INTEGER INFO, N, LDA
26: * ..
27: * .. Array Arguments ..
28: * COMPLEX*16 A( 0: LDA-1, 0: * ), ARF( 0: * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> ZTFTTR copies a triangular matrix A from rectangular full packed
38: *> format (TF) to standard full format (TR).
39: *> \endverbatim
40: *
41: * Arguments:
42: * ==========
43: *
44: *> \param[in] TRANSR
45: *> \verbatim
46: *> TRANSR is CHARACTER*1
47: *> = 'N': ARF is in Normal format;
48: *> = 'C': ARF is in Conjugate-transpose format;
49: *> \endverbatim
50: *>
51: *> \param[in] UPLO
52: *> \verbatim
53: *> UPLO is CHARACTER*1
54: *> = 'U': A is upper triangular;
55: *> = 'L': A is lower triangular.
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] ARF
65: *> \verbatim
66: *> ARF is COMPLEX*16 array, dimension ( N*(N+1)/2 ),
67: *> On entry, the upper or lower triangular matrix A stored in
68: *> RFP format. For a further discussion see Notes below.
69: *> \endverbatim
70: *>
71: *> \param[out] A
72: *> \verbatim
73: *> A is COMPLEX*16 array, dimension ( LDA, N )
74: *> On exit, the triangular matrix A. If UPLO = 'U', the
75: *> leading N-by-N upper triangular part of the array A contains
76: *> the upper triangular matrix, and the strictly lower
77: *> triangular part of A is not referenced. If UPLO = 'L', the
78: *> leading N-by-N lower triangular part of the array A contains
79: *> the lower triangular matrix, and the strictly upper
80: *> triangular part of A is not referenced.
81: *> \endverbatim
82: *>
83: *> \param[in] LDA
84: *> \verbatim
85: *> LDA is INTEGER
86: *> The leading dimension of the array A. LDA >= max(1,N).
87: *> \endverbatim
88: *>
89: *> \param[out] INFO
90: *> \verbatim
91: *> INFO is INTEGER
92: *> = 0: successful exit
93: *> < 0: if INFO = -i, the i-th argument had an illegal value
94: *> \endverbatim
95: *
96: * Authors:
97: * ========
98: *
99: *> \author Univ. of Tennessee
100: *> \author Univ. of California Berkeley
101: *> \author Univ. of Colorado Denver
102: *> \author NAG Ltd.
103: *
104: *> \date November 2011
105: *
106: *> \ingroup complex16OTHERcomputational
107: *
108: *> \par Further Details:
109: * =====================
110: *>
111: *> \verbatim
112: *>
113: *> We first consider Standard Packed Format when N is even.
114: *> We give an example where N = 6.
115: *>
116: *> AP is Upper AP is Lower
117: *>
118: *> 00 01 02 03 04 05 00
119: *> 11 12 13 14 15 10 11
120: *> 22 23 24 25 20 21 22
121: *> 33 34 35 30 31 32 33
122: *> 44 45 40 41 42 43 44
123: *> 55 50 51 52 53 54 55
124: *>
125: *>
126: *> Let TRANSR = 'N'. RFP holds AP as follows:
127: *> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
128: *> three columns of AP upper. The lower triangle A(4:6,0:2) consists of
129: *> conjugate-transpose of the first three columns of AP upper.
130: *> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
131: *> three columns of AP lower. The upper triangle A(0:2,0:2) consists of
132: *> conjugate-transpose of the last three columns of AP lower.
133: *> To denote conjugate we place -- above the element. This covers the
134: *> case N even and TRANSR = 'N'.
135: *>
136: *> RFP A RFP A
137: *>
138: *> -- -- --
139: *> 03 04 05 33 43 53
140: *> -- --
141: *> 13 14 15 00 44 54
142: *> --
143: *> 23 24 25 10 11 55
144: *>
145: *> 33 34 35 20 21 22
146: *> --
147: *> 00 44 45 30 31 32
148: *> -- --
149: *> 01 11 55 40 41 42
150: *> -- -- --
151: *> 02 12 22 50 51 52
152: *>
153: *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
154: *> transpose of RFP A above. One therefore gets:
155: *>
156: *>
157: *> RFP A RFP A
158: *>
159: *> -- -- -- -- -- -- -- -- -- --
160: *> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
161: *> -- -- -- -- -- -- -- -- -- --
162: *> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
163: *> -- -- -- -- -- -- -- -- -- --
164: *> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
165: *>
166: *>
167: *> We next consider Standard Packed Format when N is odd.
168: *> We give an example where N = 5.
169: *>
170: *> AP is Upper AP is Lower
171: *>
172: *> 00 01 02 03 04 00
173: *> 11 12 13 14 10 11
174: *> 22 23 24 20 21 22
175: *> 33 34 30 31 32 33
176: *> 44 40 41 42 43 44
177: *>
178: *>
179: *> Let TRANSR = 'N'. RFP holds AP as follows:
180: *> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
181: *> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
182: *> conjugate-transpose of the first two columns of AP upper.
183: *> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
184: *> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
185: *> conjugate-transpose of the last two columns of AP lower.
186: *> To denote conjugate we place -- above the element. This covers the
187: *> case N odd and TRANSR = 'N'.
188: *>
189: *> RFP A RFP A
190: *>
191: *> -- --
192: *> 02 03 04 00 33 43
193: *> --
194: *> 12 13 14 10 11 44
195: *>
196: *> 22 23 24 20 21 22
197: *> --
198: *> 00 33 34 30 31 32
199: *> -- --
200: *> 01 11 44 40 41 42
201: *>
202: *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
203: *> transpose of RFP A above. One therefore gets:
204: *>
205: *>
206: *> RFP A RFP A
207: *>
208: *> -- -- -- -- -- -- -- -- --
209: *> 02 12 22 00 01 00 10 20 30 40 50
210: *> -- -- -- -- -- -- -- -- --
211: *> 03 13 23 33 11 33 11 21 31 41 51
212: *> -- -- -- -- -- -- -- -- --
213: *> 04 14 24 34 44 43 44 22 32 42 52
214: *> \endverbatim
215: *>
216: * =====================================================================
217: SUBROUTINE ZTFTTR( TRANSR, UPLO, N, ARF, A, LDA, INFO )
1.1 bertrand 218: *
1.7 bertrand 219: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 220: * -- LAPACK is a software package provided by Univ. of Tennessee, --
221: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.7 bertrand 222: * November 2011
1.1 bertrand 223: *
224: * .. Scalar Arguments ..
225: CHARACTER TRANSR, UPLO
226: INTEGER INFO, N, LDA
227: * ..
228: * .. Array Arguments ..
229: COMPLEX*16 A( 0: LDA-1, 0: * ), ARF( 0: * )
230: * ..
231: *
232: * =====================================================================
233: *
234: * .. Parameters ..
235: * ..
236: * .. Local Scalars ..
237: LOGICAL LOWER, NISODD, NORMALTRANSR
238: INTEGER N1, N2, K, NT, NX2, NP1X2
239: INTEGER I, J, L, IJ
240: * ..
241: * .. External Functions ..
242: LOGICAL LSAME
243: EXTERNAL LSAME
244: * ..
245: * .. External Subroutines ..
246: EXTERNAL XERBLA
247: * ..
248: * .. Intrinsic Functions ..
249: INTRINSIC DCONJG, MAX, MOD
250: * ..
251: * .. Executable Statements ..
252: *
253: * Test the input parameters.
254: *
255: INFO = 0
256: NORMALTRANSR = LSAME( TRANSR, 'N' )
257: LOWER = LSAME( UPLO, 'L' )
258: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
259: INFO = -1
260: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
261: INFO = -2
262: ELSE IF( N.LT.0 ) THEN
263: INFO = -3
264: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
265: INFO = -6
266: END IF
267: IF( INFO.NE.0 ) THEN
268: CALL XERBLA( 'ZTFTTR', -INFO )
269: RETURN
270: END IF
271: *
272: * Quick return if possible
273: *
274: IF( N.LE.1 ) THEN
275: IF( N.EQ.1 ) THEN
276: IF( NORMALTRANSR ) THEN
277: A( 0, 0 ) = ARF( 0 )
278: ELSE
279: A( 0, 0 ) = DCONJG( ARF( 0 ) )
280: END IF
281: END IF
282: RETURN
283: END IF
284: *
285: * Size of array ARF(1:2,0:nt-1)
286: *
287: NT = N*( N+1 ) / 2
288: *
289: * set N1 and N2 depending on LOWER: for N even N1=N2=K
290: *
291: IF( LOWER ) THEN
292: N2 = N / 2
293: N1 = N - N2
294: ELSE
295: N1 = N / 2
296: N2 = N - N1
297: END IF
298: *
299: * If N is odd, set NISODD = .TRUE., LDA=N+1 and A is (N+1)--by--K2.
300: * If N is even, set K = N/2 and NISODD = .FALSE., LDA=N and A is
301: * N--by--(N+1)/2.
302: *
303: IF( MOD( N, 2 ).EQ.0 ) THEN
304: K = N / 2
305: NISODD = .FALSE.
306: IF( .NOT.LOWER )
1.6 bertrand 307: $ NP1X2 = N + N + 2
1.1 bertrand 308: ELSE
309: NISODD = .TRUE.
310: IF( .NOT.LOWER )
1.6 bertrand 311: $ NX2 = N + N
1.1 bertrand 312: END IF
313: *
314: IF( NISODD ) THEN
315: *
316: * N is odd
317: *
318: IF( NORMALTRANSR ) THEN
319: *
320: * N is odd and TRANSR = 'N'
321: *
322: IF( LOWER ) THEN
323: *
324: * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
325: * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
326: * T1 -> a(0), T2 -> a(n), S -> a(n1); lda=n
327: *
328: IJ = 0
329: DO J = 0, N2
330: DO I = N1, N2 + J
331: A( N2+J, I ) = DCONJG( ARF( IJ ) )
332: IJ = IJ + 1
333: END DO
334: DO I = J, N - 1
335: A( I, J ) = ARF( IJ )
336: IJ = IJ + 1
337: END DO
338: END DO
339: *
340: ELSE
341: *
342: * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
343: * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
344: * T1 -> a(n2), T2 -> a(n1), S -> a(0); lda=n
345: *
346: IJ = NT - N
347: DO J = N - 1, N1, -1
348: DO I = 0, J
349: A( I, J ) = ARF( IJ )
350: IJ = IJ + 1
351: END DO
352: DO L = J - N1, N1 - 1
353: A( J-N1, L ) = DCONJG( ARF( IJ ) )
354: IJ = IJ + 1
355: END DO
356: IJ = IJ - NX2
357: END DO
358: *
359: END IF
360: *
361: ELSE
362: *
363: * N is odd and TRANSR = 'C'
364: *
365: IF( LOWER ) THEN
366: *
367: * SRPA for LOWER, TRANSPOSE and N is odd
368: * T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
369: * T1 -> A(0+0) , T2 -> A(1+0) , S -> A(0+n1*n1); lda=n1
370: *
371: IJ = 0
372: DO J = 0, N2 - 1
373: DO I = 0, J
374: A( J, I ) = DCONJG( ARF( IJ ) )
375: IJ = IJ + 1
376: END DO
377: DO I = N1 + J, N - 1
378: A( I, N1+J ) = ARF( IJ )
379: IJ = IJ + 1
380: END DO
381: END DO
382: DO J = N2, N - 1
383: DO I = 0, N1 - 1
384: A( J, I ) = DCONJG( ARF( IJ ) )
385: IJ = IJ + 1
386: END DO
387: END DO
388: *
389: ELSE
390: *
391: * SRPA for UPPER, TRANSPOSE and N is odd
392: * T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
393: * T1 -> A(n2*n2), T2 -> A(n1*n2), S -> A(0); lda = n2
394: *
395: IJ = 0
396: DO J = 0, N1
397: DO I = N1, N - 1
398: A( J, I ) = DCONJG( ARF( IJ ) )
399: IJ = IJ + 1
400: END DO
401: END DO
402: DO J = 0, N1 - 1
403: DO I = 0, J
404: A( I, J ) = ARF( IJ )
405: IJ = IJ + 1
406: END DO
407: DO L = N2 + J, N - 1
408: A( N2+J, L ) = DCONJG( ARF( IJ ) )
409: IJ = IJ + 1
410: END DO
411: END DO
412: *
413: END IF
414: *
415: END IF
416: *
417: ELSE
418: *
419: * N is even
420: *
421: IF( NORMALTRANSR ) THEN
422: *
423: * N is even and TRANSR = 'N'
424: *
425: IF( LOWER ) THEN
426: *
427: * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
428: * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
429: * T1 -> a(1), T2 -> a(0), S -> a(k+1); lda=n+1
430: *
431: IJ = 0
432: DO J = 0, K - 1
433: DO I = K, K + J
434: A( K+J, I ) = DCONJG( ARF( IJ ) )
435: IJ = IJ + 1
436: END DO
437: DO I = J, N - 1
438: A( I, J ) = ARF( IJ )
439: IJ = IJ + 1
440: END DO
441: END DO
442: *
443: ELSE
444: *
445: * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
446: * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
447: * T1 -> a(k+1), T2 -> a(k), S -> a(0); lda=n+1
448: *
449: IJ = NT - N - 1
450: DO J = N - 1, K, -1
451: DO I = 0, J
452: A( I, J ) = ARF( IJ )
453: IJ = IJ + 1
454: END DO
455: DO L = J - K, K - 1
456: A( J-K, L ) = DCONJG( ARF( IJ ) )
457: IJ = IJ + 1
458: END DO
459: IJ = IJ - NP1X2
460: END DO
461: *
462: END IF
463: *
464: ELSE
465: *
466: * N is even and TRANSR = 'C'
467: *
468: IF( LOWER ) THEN
469: *
470: * SRPA for LOWER, TRANSPOSE and N is even (see paper, A=B)
471: * T1 -> A(0,1) , T2 -> A(0,0) , S -> A(0,k+1) :
472: * T1 -> A(0+k) , T2 -> A(0+0) , S -> A(0+k*(k+1)); lda=k
473: *
474: IJ = 0
475: J = K
476: DO I = K, N - 1
477: A( I, J ) = ARF( IJ )
478: IJ = IJ + 1
479: END DO
480: DO J = 0, K - 2
481: DO I = 0, J
482: A( J, I ) = DCONJG( ARF( IJ ) )
483: IJ = IJ + 1
484: END DO
485: DO I = K + 1 + J, N - 1
486: A( I, K+1+J ) = ARF( IJ )
487: IJ = IJ + 1
488: END DO
489: END DO
490: DO J = K - 1, N - 1
491: DO I = 0, K - 1
492: A( J, I ) = DCONJG( ARF( IJ ) )
493: IJ = IJ + 1
494: END DO
495: END DO
496: *
497: ELSE
498: *
499: * SRPA for UPPER, TRANSPOSE and N is even (see paper, A=B)
500: * T1 -> A(0,k+1) , T2 -> A(0,k) , S -> A(0,0)
501: * T1 -> A(0+k*(k+1)) , T2 -> A(0+k*k) , S -> A(0+0)); lda=k
502: *
503: IJ = 0
504: DO J = 0, K
505: DO I = K, N - 1
506: A( J, I ) = DCONJG( ARF( IJ ) )
507: IJ = IJ + 1
508: END DO
509: END DO
510: DO J = 0, K - 2
511: DO I = 0, J
512: A( I, J ) = ARF( IJ )
513: IJ = IJ + 1
514: END DO
515: DO L = K + 1 + J, N - 1
516: A( K+1+J, L ) = DCONJG( ARF( IJ ) )
517: IJ = IJ + 1
518: END DO
519: END DO
520: *
521: * Note that here J = K-1
522: *
523: DO I = 0, J
524: A( I, J ) = ARF( IJ )
525: IJ = IJ + 1
526: END DO
527: *
528: END IF
529: *
530: END IF
531: *
532: END IF
533: *
534: RETURN
535: *
536: * End of ZTFTTR
537: *
538: END