1: *> \brief \b ZTRTTF
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZTRTTF + dependencies
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16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZTRTTF( TRANSR, UPLO, N, A, LDA, ARF, 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: *> 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: *
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 ZTRTTF( TRANSR, UPLO, N, A, LDA, ARF, INFO )
218: *
219: * -- LAPACK computational routine (version 3.4.0) --
220: * -- LAPACK is a software package provided by Univ. of Tennessee, --
221: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
222: * November 2011
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 I, IJ, J, K, L, N1, N2, NT, NX2, NP1X2
239: * ..
240: * .. External Functions ..
241: LOGICAL LSAME
242: EXTERNAL LSAME
243: * ..
244: * .. External Subroutines ..
245: EXTERNAL XERBLA
246: * ..
247: * .. Intrinsic Functions ..
248: INTRINSIC DCONJG, MAX, MOD
249: * ..
250: * .. Executable Statements ..
251: *
252: * Test the input parameters.
253: *
254: INFO = 0
255: NORMALTRANSR = LSAME( TRANSR, 'N' )
256: LOWER = LSAME( UPLO, 'L' )
257: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
258: INFO = -1
259: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
260: INFO = -2
261: ELSE IF( N.LT.0 ) THEN
262: INFO = -3
263: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
264: INFO = -5
265: END IF
266: IF( INFO.NE.0 ) THEN
267: CALL XERBLA( 'ZTRTTF', -INFO )
268: RETURN
269: END IF
270: *
271: * Quick return if possible
272: *
273: IF( N.LE.1 ) THEN
274: IF( N.EQ.1 ) THEN
275: IF( NORMALTRANSR ) THEN
276: ARF( 0 ) = A( 0, 0 )
277: ELSE
278: ARF( 0 ) = DCONJG( A( 0, 0 ) )
279: END IF
280: END IF
281: RETURN
282: END IF
283: *
284: * Size of array ARF(1:2,0:nt-1)
285: *
286: NT = N*( N+1 ) / 2
287: *
288: * set N1 and N2 depending on LOWER: for N even N1=N2=K
289: *
290: IF( LOWER ) THEN
291: N2 = N / 2
292: N1 = N - N2
293: ELSE
294: N1 = N / 2
295: N2 = N - N1
296: END IF
297: *
298: * If N is odd, set NISODD = .TRUE., LDA=N+1 and A is (N+1)--by--K2.
299: * If N is even, set K = N/2 and NISODD = .FALSE., LDA=N and A is
300: * N--by--(N+1)/2.
301: *
302: IF( MOD( N, 2 ).EQ.0 ) THEN
303: K = N / 2
304: NISODD = .FALSE.
305: IF( .NOT.LOWER )
306: $ NP1X2 = N + N + 2
307: ELSE
308: NISODD = .TRUE.
309: IF( .NOT.LOWER )
310: $ NX2 = N + N
311: END IF
312: *
313: IF( NISODD ) THEN
314: *
315: * N is odd
316: *
317: IF( NORMALTRANSR ) THEN
318: *
319: * N is odd and TRANSR = 'N'
320: *
321: IF( LOWER ) THEN
322: *
323: * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
324: * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
325: * T1 -> a(0), T2 -> a(n), S -> a(n1); lda=n
326: *
327: IJ = 0
328: DO J = 0, N2
329: DO I = N1, N2 + J
330: ARF( IJ ) = DCONJG( A( N2+J, I ) )
331: IJ = IJ + 1
332: END DO
333: DO I = J, N - 1
334: ARF( IJ ) = A( I, J )
335: IJ = IJ + 1
336: END DO
337: END DO
338: *
339: ELSE
340: *
341: * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
342: * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
343: * T1 -> a(n2), T2 -> a(n1), S -> a(0); lda=n
344: *
345: IJ = NT - N
346: DO J = N - 1, N1, -1
347: DO I = 0, J
348: ARF( IJ ) = A( I, J )
349: IJ = IJ + 1
350: END DO
351: DO L = J - N1, N1 - 1
352: ARF( IJ ) = DCONJG( A( J-N1, L ) )
353: IJ = IJ + 1
354: END DO
355: IJ = IJ - NX2
356: END DO
357: *
358: END IF
359: *
360: ELSE
361: *
362: * N is odd and TRANSR = 'C'
363: *
364: IF( LOWER ) THEN
365: *
366: * SRPA for LOWER, TRANSPOSE and N is odd
367: * T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
368: * T1 -> A(0+0) , T2 -> A(1+0) , S -> A(0+n1*n1); lda=n1
369: *
370: IJ = 0
371: DO J = 0, N2 - 1
372: DO I = 0, J
373: ARF( IJ ) = DCONJG( A( J, I ) )
374: IJ = IJ + 1
375: END DO
376: DO I = N1 + J, N - 1
377: ARF( IJ ) = A( I, N1+J )
378: IJ = IJ + 1
379: END DO
380: END DO
381: DO J = N2, N - 1
382: DO I = 0, N1 - 1
383: ARF( IJ ) = DCONJG( A( J, I ) )
384: IJ = IJ + 1
385: END DO
386: END DO
387: *
388: ELSE
389: *
390: * SRPA for UPPER, TRANSPOSE and N is odd
391: * T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
392: * T1 -> A(n2*n2), T2 -> A(n1*n2), S -> A(0); lda=n2
393: *
394: IJ = 0
395: DO J = 0, N1
396: DO I = N1, N - 1
397: ARF( IJ ) = DCONJG( A( J, I ) )
398: IJ = IJ + 1
399: END DO
400: END DO
401: DO J = 0, N1 - 1
402: DO I = 0, J
403: ARF( IJ ) = A( I, J )
404: IJ = IJ + 1
405: END DO
406: DO L = N2 + J, N - 1
407: ARF( IJ ) = DCONJG( A( N2+J, L ) )
408: IJ = IJ + 1
409: END DO
410: END DO
411: *
412: END IF
413: *
414: END IF
415: *
416: ELSE
417: *
418: * N is even
419: *
420: IF( NORMALTRANSR ) THEN
421: *
422: * N is even and TRANSR = 'N'
423: *
424: IF( LOWER ) THEN
425: *
426: * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
427: * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
428: * T1 -> a(1), T2 -> a(0), S -> a(k+1); lda=n+1
429: *
430: IJ = 0
431: DO J = 0, K - 1
432: DO I = K, K + J
433: ARF( IJ ) = DCONJG( A( K+J, I ) )
434: IJ = IJ + 1
435: END DO
436: DO I = J, N - 1
437: ARF( IJ ) = A( I, J )
438: IJ = IJ + 1
439: END DO
440: END DO
441: *
442: ELSE
443: *
444: * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
445: * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
446: * T1 -> a(k+1), T2 -> a(k), S -> a(0); lda=n+1
447: *
448: IJ = NT - N - 1
449: DO J = N - 1, K, -1
450: DO I = 0, J
451: ARF( IJ ) = A( I, J )
452: IJ = IJ + 1
453: END DO
454: DO L = J - K, K - 1
455: ARF( IJ ) = DCONJG( A( J-K, L ) )
456: IJ = IJ + 1
457: END DO
458: IJ = IJ - NP1X2
459: END DO
460: *
461: END IF
462: *
463: ELSE
464: *
465: * N is even and TRANSR = 'C'
466: *
467: IF( LOWER ) THEN
468: *
469: * SRPA for LOWER, TRANSPOSE and N is even (see paper, A=B)
470: * T1 -> A(0,1) , T2 -> A(0,0) , S -> A(0,k+1) :
471: * T1 -> A(0+k) , T2 -> A(0+0) , S -> A(0+k*(k+1)); lda=k
472: *
473: IJ = 0
474: J = K
475: DO I = K, N - 1
476: ARF( IJ ) = A( I, J )
477: IJ = IJ + 1
478: END DO
479: DO J = 0, K - 2
480: DO I = 0, J
481: ARF( IJ ) = DCONJG( A( J, I ) )
482: IJ = IJ + 1
483: END DO
484: DO I = K + 1 + J, N - 1
485: ARF( IJ ) = A( I, K+1+J )
486: IJ = IJ + 1
487: END DO
488: END DO
489: DO J = K - 1, N - 1
490: DO I = 0, K - 1
491: ARF( IJ ) = DCONJG( A( J, I ) )
492: IJ = IJ + 1
493: END DO
494: END DO
495: *
496: ELSE
497: *
498: * SRPA for UPPER, TRANSPOSE and N is even (see paper, A=B)
499: * T1 -> A(0,k+1) , T2 -> A(0,k) , S -> A(0,0)
500: * T1 -> A(0+k*(k+1)) , T2 -> A(0+k*k) , S -> A(0+0)); lda=k
501: *
502: IJ = 0
503: DO J = 0, K
504: DO I = K, N - 1
505: ARF( IJ ) = DCONJG( A( J, I ) )
506: IJ = IJ + 1
507: END DO
508: END DO
509: DO J = 0, K - 2
510: DO I = 0, J
511: ARF( IJ ) = A( I, J )
512: IJ = IJ + 1
513: END DO
514: DO L = K + 1 + J, N - 1
515: ARF( IJ ) = DCONJG( A( K+1+J, L ) )
516: IJ = IJ + 1
517: END DO
518: END DO
519: *
520: * Note that here J = K-1
521: *
522: DO I = 0, J
523: ARF( IJ ) = A( I, J )
524: IJ = IJ + 1
525: END DO
526: *
527: END IF
528: *
529: END IF
530: *
531: END IF
532: *
533: RETURN
534: *
535: * End of ZTRTTF
536: *
537: END
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