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1.10 bertrand 1: *> \brief \b ZTRTTF copies a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF).
1.7 bertrand 2: *
3: * =========== DOCUMENTATION ===========
1.1 bertrand 4: *
1.14 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.1 bertrand 7: *
1.7 bertrand 8: *> \htmlonly
1.14 bertrand 9: *> Download ZTRTTF + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztrttf.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztrttf.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztrttf.f">
1.7 bertrand 15: *> [TXT]</a>
1.14 bertrand 16: *> \endhtmlonly
1.7 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZTRTTF( TRANSR, UPLO, N, A, LDA, ARF, INFO )
1.14 bertrand 22: *
1.7 bertrand 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: * ..
1.14 bertrand 30: *
1.7 bertrand 31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> ZTRTTF copies a triangular matrix A from standard full format (TR)
38: *> to rectangular full packed format (TF) .
39: *> \endverbatim
40: *
41: * Arguments:
42: * ==========
43: *
44: *> \param[in] TRANSR
45: *> \verbatim
46: *> TRANSR is CHARACTER*1
47: *> = 'N': ARF in Normal mode is wanted;
48: *> = 'C': ARF in Conjugate Transpose mode is wanted;
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] A
65: *> \verbatim
66: *> A is COMPLEX*16 array, dimension ( LDA, N )
67: *> On entry, the triangular matrix A. If UPLO = 'U', the
68: *> leading N-by-N upper triangular part of the array A contains
69: *> the upper triangular matrix, and the strictly lower
70: *> triangular part of A is not referenced. If UPLO = 'L', the
71: *> leading N-by-N lower triangular part of the array A contains
72: *> the lower triangular matrix, and the strictly upper
73: *> triangular part of A is not referenced.
74: *> \endverbatim
75: *>
76: *> \param[in] LDA
77: *> \verbatim
78: *> LDA is INTEGER
79: *> The leading dimension of the matrix A. LDA >= max(1,N).
80: *> \endverbatim
81: *>
82: *> \param[out] ARF
83: *> \verbatim
84: *> ARF is COMPLEX*16 array, dimension ( N*(N+1)/2 ),
85: *> On exit, the upper or lower triangular matrix A stored in
86: *> RFP format. For a further discussion see Notes below.
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: *
1.14 bertrand 99: *> \author Univ. of Tennessee
100: *> \author Univ. of California Berkeley
101: *> \author Univ. of Colorado Denver
102: *> \author NAG Ltd.
1.7 bertrand 103: *
104: *> \ingroup complex16OTHERcomputational
105: *
106: *> \par Further Details:
107: * =====================
108: *>
109: *> \verbatim
110: *>
111: *> We first consider Standard Packed Format when N is even.
112: *> We give an example where N = 6.
113: *>
114: *> AP is Upper AP is Lower
115: *>
116: *> 00 01 02 03 04 05 00
117: *> 11 12 13 14 15 10 11
118: *> 22 23 24 25 20 21 22
119: *> 33 34 35 30 31 32 33
120: *> 44 45 40 41 42 43 44
121: *> 55 50 51 52 53 54 55
122: *>
123: *>
124: *> Let TRANSR = 'N'. RFP holds AP as follows:
125: *> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
126: *> three columns of AP upper. The lower triangle A(4:6,0:2) consists of
127: *> conjugate-transpose of the first three columns of AP upper.
128: *> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
129: *> three columns of AP lower. The upper triangle A(0:2,0:2) consists of
130: *> conjugate-transpose of the last three columns of AP lower.
131: *> To denote conjugate we place -- above the element. This covers the
132: *> case N even and TRANSR = 'N'.
133: *>
134: *> RFP A RFP A
135: *>
136: *> -- -- --
137: *> 03 04 05 33 43 53
138: *> -- --
139: *> 13 14 15 00 44 54
140: *> --
141: *> 23 24 25 10 11 55
142: *>
143: *> 33 34 35 20 21 22
144: *> --
145: *> 00 44 45 30 31 32
146: *> -- --
147: *> 01 11 55 40 41 42
148: *> -- -- --
149: *> 02 12 22 50 51 52
150: *>
151: *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
152: *> transpose of RFP A above. One therefore gets:
153: *>
154: *>
155: *> RFP A RFP A
156: *>
157: *> -- -- -- -- -- -- -- -- -- --
158: *> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
159: *> -- -- -- -- -- -- -- -- -- --
160: *> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
161: *> -- -- -- -- -- -- -- -- -- --
162: *> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
163: *>
164: *>
165: *> We next consider Standard Packed Format when N is odd.
166: *> We give an example where N = 5.
167: *>
168: *> AP is Upper AP is Lower
169: *>
170: *> 00 01 02 03 04 00
171: *> 11 12 13 14 10 11
172: *> 22 23 24 20 21 22
173: *> 33 34 30 31 32 33
174: *> 44 40 41 42 43 44
175: *>
176: *>
177: *> Let TRANSR = 'N'. RFP holds AP as follows:
178: *> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
179: *> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
180: *> conjugate-transpose of the first two columns of AP upper.
181: *> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
182: *> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
183: *> conjugate-transpose of the last two columns of AP lower.
184: *> To denote conjugate we place -- above the element. This covers the
185: *> case N odd and TRANSR = 'N'.
186: *>
187: *> RFP A RFP A
188: *>
189: *> -- --
190: *> 02 03 04 00 33 43
191: *> --
192: *> 12 13 14 10 11 44
193: *>
194: *> 22 23 24 20 21 22
195: *> --
196: *> 00 33 34 30 31 32
197: *> -- --
198: *> 01 11 44 40 41 42
199: *>
200: *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
201: *> transpose of RFP A above. One therefore gets:
202: *>
203: *>
204: *> RFP A RFP A
205: *>
206: *> -- -- -- -- -- -- -- -- --
207: *> 02 12 22 00 01 00 10 20 30 40 50
208: *> -- -- -- -- -- -- -- -- --
209: *> 03 13 23 33 11 33 11 21 31 41 51
210: *> -- -- -- -- -- -- -- -- --
211: *> 04 14 24 34 44 43 44 22 32 42 52
212: *> \endverbatim
213: *>
214: * =====================================================================
215: SUBROUTINE ZTRTTF( TRANSR, UPLO, N, A, LDA, ARF, INFO )
1.1 bertrand 216: *
1.17 ! bertrand 217: * -- LAPACK computational routine --
1.1 bertrand 218: * -- LAPACK is a software package provided by Univ. of Tennessee, --
219: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
220: *
221: * .. Scalar Arguments ..
222: CHARACTER TRANSR, UPLO
223: INTEGER INFO, N, LDA
224: * ..
225: * .. Array Arguments ..
226: COMPLEX*16 A( 0: LDA-1, 0: * ), ARF( 0: * )
227: * ..
228: *
229: * =====================================================================
230: *
231: * .. Parameters ..
232: * ..
233: * .. Local Scalars ..
234: LOGICAL LOWER, NISODD, NORMALTRANSR
235: INTEGER I, IJ, J, K, L, N1, N2, NT, NX2, NP1X2
236: * ..
237: * .. External Functions ..
238: LOGICAL LSAME
239: EXTERNAL LSAME
240: * ..
241: * .. External Subroutines ..
242: EXTERNAL XERBLA
243: * ..
244: * .. Intrinsic Functions ..
245: INTRINSIC DCONJG, MAX, MOD
246: * ..
247: * .. Executable Statements ..
248: *
249: * Test the input parameters.
250: *
251: INFO = 0
252: NORMALTRANSR = LSAME( TRANSR, 'N' )
253: LOWER = LSAME( UPLO, 'L' )
254: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
255: INFO = -1
256: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
257: INFO = -2
258: ELSE IF( N.LT.0 ) THEN
259: INFO = -3
260: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
261: INFO = -5
262: END IF
263: IF( INFO.NE.0 ) THEN
264: CALL XERBLA( 'ZTRTTF', -INFO )
265: RETURN
266: END IF
267: *
268: * Quick return if possible
269: *
270: IF( N.LE.1 ) THEN
271: IF( N.EQ.1 ) THEN
272: IF( NORMALTRANSR ) THEN
273: ARF( 0 ) = A( 0, 0 )
274: ELSE
275: ARF( 0 ) = DCONJG( A( 0, 0 ) )
276: END IF
277: END IF
278: RETURN
279: END IF
280: *
281: * Size of array ARF(1:2,0:nt-1)
282: *
283: NT = N*( N+1 ) / 2
284: *
285: * set N1 and N2 depending on LOWER: for N even N1=N2=K
286: *
287: IF( LOWER ) THEN
288: N2 = N / 2
289: N1 = N - N2
290: ELSE
291: N1 = N / 2
292: N2 = N - N1
293: END IF
294: *
295: * If N is odd, set NISODD = .TRUE., LDA=N+1 and A is (N+1)--by--K2.
296: * If N is even, set K = N/2 and NISODD = .FALSE., LDA=N and A is
297: * N--by--(N+1)/2.
298: *
299: IF( MOD( N, 2 ).EQ.0 ) THEN
300: K = N / 2
301: NISODD = .FALSE.
302: IF( .NOT.LOWER )
1.6 bertrand 303: $ NP1X2 = N + N + 2
1.1 bertrand 304: ELSE
305: NISODD = .TRUE.
306: IF( .NOT.LOWER )
1.6 bertrand 307: $ NX2 = N + N
1.1 bertrand 308: END IF
309: *
310: IF( NISODD ) THEN
311: *
312: * N is odd
313: *
314: IF( NORMALTRANSR ) THEN
315: *
316: * N is odd and TRANSR = 'N'
317: *
318: IF( LOWER ) THEN
319: *
320: * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
321: * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
322: * T1 -> a(0), T2 -> a(n), S -> a(n1); lda=n
323: *
324: IJ = 0
325: DO J = 0, N2
326: DO I = N1, N2 + J
327: ARF( IJ ) = DCONJG( A( N2+J, I ) )
328: IJ = IJ + 1
329: END DO
330: DO I = J, N - 1
331: ARF( IJ ) = A( I, J )
332: IJ = IJ + 1
333: END DO
334: END DO
335: *
336: ELSE
337: *
338: * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
339: * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
340: * T1 -> a(n2), T2 -> a(n1), S -> a(0); lda=n
341: *
342: IJ = NT - N
343: DO J = N - 1, N1, -1
344: DO I = 0, J
345: ARF( IJ ) = A( I, J )
346: IJ = IJ + 1
347: END DO
348: DO L = J - N1, N1 - 1
349: ARF( IJ ) = DCONJG( A( J-N1, L ) )
350: IJ = IJ + 1
351: END DO
352: IJ = IJ - NX2
353: END DO
354: *
355: END IF
356: *
357: ELSE
358: *
359: * N is odd and TRANSR = 'C'
360: *
361: IF( LOWER ) THEN
362: *
363: * SRPA for LOWER, TRANSPOSE and N is odd
364: * T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
365: * T1 -> A(0+0) , T2 -> A(1+0) , S -> A(0+n1*n1); lda=n1
366: *
367: IJ = 0
368: DO J = 0, N2 - 1
369: DO I = 0, J
370: ARF( IJ ) = DCONJG( A( J, I ) )
371: IJ = IJ + 1
372: END DO
373: DO I = N1 + J, N - 1
374: ARF( IJ ) = A( I, N1+J )
375: IJ = IJ + 1
376: END DO
377: END DO
378: DO J = N2, N - 1
379: DO I = 0, N1 - 1
380: ARF( IJ ) = DCONJG( A( J, I ) )
381: IJ = IJ + 1
382: END DO
383: END DO
384: *
385: ELSE
386: *
387: * SRPA for UPPER, TRANSPOSE and N is odd
388: * T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
389: * T1 -> A(n2*n2), T2 -> A(n1*n2), S -> A(0); lda=n2
390: *
391: IJ = 0
392: DO J = 0, N1
393: DO I = N1, N - 1
394: ARF( IJ ) = DCONJG( A( J, I ) )
395: IJ = IJ + 1
396: END DO
397: END DO
398: DO J = 0, N1 - 1
399: DO I = 0, J
400: ARF( IJ ) = A( I, J )
401: IJ = IJ + 1
402: END DO
403: DO L = N2 + J, N - 1
404: ARF( IJ ) = DCONJG( A( N2+J, L ) )
405: IJ = IJ + 1
406: END DO
407: END DO
408: *
409: END IF
410: *
411: END IF
412: *
413: ELSE
414: *
415: * N is even
416: *
417: IF( NORMALTRANSR ) THEN
418: *
419: * N is even and TRANSR = 'N'
420: *
421: IF( LOWER ) THEN
422: *
423: * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
424: * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
425: * T1 -> a(1), T2 -> a(0), S -> a(k+1); lda=n+1
426: *
427: IJ = 0
428: DO J = 0, K - 1
429: DO I = K, K + J
430: ARF( IJ ) = DCONJG( A( K+J, I ) )
431: IJ = IJ + 1
432: END DO
433: DO I = J, N - 1
434: ARF( IJ ) = A( I, J )
435: IJ = IJ + 1
436: END DO
437: END DO
438: *
439: ELSE
440: *
441: * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
442: * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
443: * T1 -> a(k+1), T2 -> a(k), S -> a(0); lda=n+1
444: *
445: IJ = NT - N - 1
446: DO J = N - 1, K, -1
447: DO I = 0, J
448: ARF( IJ ) = A( I, J )
449: IJ = IJ + 1
450: END DO
451: DO L = J - K, K - 1
452: ARF( IJ ) = DCONJG( A( J-K, L ) )
453: IJ = IJ + 1
454: END DO
455: IJ = IJ - NP1X2
456: END DO
457: *
458: END IF
459: *
460: ELSE
461: *
462: * N is even and TRANSR = 'C'
463: *
464: IF( LOWER ) THEN
465: *
466: * SRPA for LOWER, TRANSPOSE and N is even (see paper, A=B)
467: * T1 -> A(0,1) , T2 -> A(0,0) , S -> A(0,k+1) :
468: * T1 -> A(0+k) , T2 -> A(0+0) , S -> A(0+k*(k+1)); lda=k
469: *
470: IJ = 0
471: J = K
472: DO I = K, N - 1
473: ARF( IJ ) = A( I, J )
474: IJ = IJ + 1
475: END DO
476: DO J = 0, K - 2
477: DO I = 0, J
478: ARF( IJ ) = DCONJG( A( J, I ) )
479: IJ = IJ + 1
480: END DO
481: DO I = K + 1 + J, N - 1
482: ARF( IJ ) = A( I, K+1+J )
483: IJ = IJ + 1
484: END DO
485: END DO
486: DO J = K - 1, N - 1
487: DO I = 0, K - 1
488: ARF( IJ ) = DCONJG( A( J, I ) )
489: IJ = IJ + 1
490: END DO
491: END DO
492: *
493: ELSE
494: *
495: * SRPA for UPPER, TRANSPOSE and N is even (see paper, A=B)
496: * T1 -> A(0,k+1) , T2 -> A(0,k) , S -> A(0,0)
497: * T1 -> A(0+k*(k+1)) , T2 -> A(0+k*k) , S -> A(0+0)); lda=k
498: *
499: IJ = 0
500: DO J = 0, K
501: DO I = K, N - 1
502: ARF( IJ ) = DCONJG( A( J, I ) )
503: IJ = IJ + 1
504: END DO
505: END DO
506: DO J = 0, K - 2
507: DO I = 0, J
508: ARF( IJ ) = A( I, J )
509: IJ = IJ + 1
510: END DO
511: DO L = K + 1 + J, N - 1
512: ARF( IJ ) = DCONJG( A( K+1+J, L ) )
513: IJ = IJ + 1
514: END DO
515: END DO
516: *
517: * Note that here J = K-1
518: *
519: DO I = 0, J
520: ARF( IJ ) = A( I, J )
521: IJ = IJ + 1
522: END DO
523: *
524: END IF
525: *
526: END IF
527: *
528: END IF
529: *
530: RETURN
531: *
532: * End of ZTRTTF
533: *
534: END