LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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ztfttp.f
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1*> \brief \b ZTFTTP copies a triangular matrix from the rectangular full packed format (TF) to the standard packed format (TP).
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download ZTFTTP + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztfttp.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztfttp.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztfttp.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE ZTFTTP( TRANSR, UPLO, N, ARF, AP, INFO )
22*
23* .. Scalar Arguments ..
24* CHARACTER TRANSR, UPLO
25* INTEGER INFO, N
26* ..
27* .. Array Arguments ..
28* COMPLEX*16 AP( 0: * ), ARF( 0: * )
29* ..
30*
31*
32*> \par Purpose:
33* =============
34*>
35*> \verbatim
36*>
37*> ZTFTTP copies a triangular matrix A from rectangular full packed
38*> format (TF) to standard packed format (TP).
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] AP
72*> \verbatim
73*> AP is COMPLEX*16 array, dimension ( N*(N+1)/2 ),
74*> On exit, the upper or lower triangular matrix A, packed
75*> columnwise in a linear array. The j-th column of A is stored
76*> in the array AP as follows:
77*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
78*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
79*> \endverbatim
80*>
81*> \param[out] INFO
82*> \verbatim
83*> INFO is INTEGER
84*> = 0: successful exit
85*> < 0: if INFO = -i, the i-th argument had an illegal value
86*> \endverbatim
87*
88* Authors:
89* ========
90*
91*> \author Univ. of Tennessee
92*> \author Univ. of California Berkeley
93*> \author Univ. of Colorado Denver
94*> \author NAG Ltd.
95*
96*> \ingroup complex16OTHERcomputational
97*
98*> \par Further Details:
99* =====================
100*>
101*> \verbatim
102*>
103*> We first consider Standard Packed Format when N is even.
104*> We give an example where N = 6.
105*>
106*> AP is Upper AP is Lower
107*>
108*> 00 01 02 03 04 05 00
109*> 11 12 13 14 15 10 11
110*> 22 23 24 25 20 21 22
111*> 33 34 35 30 31 32 33
112*> 44 45 40 41 42 43 44
113*> 55 50 51 52 53 54 55
114*>
115*>
116*> Let TRANSR = 'N'. RFP holds AP as follows:
117*> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
118*> three columns of AP upper. The lower triangle A(4:6,0:2) consists of
119*> conjugate-transpose of the first three columns of AP upper.
120*> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
121*> three columns of AP lower. The upper triangle A(0:2,0:2) consists of
122*> conjugate-transpose of the last three columns of AP lower.
123*> To denote conjugate we place -- above the element. This covers the
124*> case N even and TRANSR = 'N'.
125*>
126*> RFP A RFP A
127*>
128*> -- -- --
129*> 03 04 05 33 43 53
130*> -- --
131*> 13 14 15 00 44 54
132*> --
133*> 23 24 25 10 11 55
134*>
135*> 33 34 35 20 21 22
136*> --
137*> 00 44 45 30 31 32
138*> -- --
139*> 01 11 55 40 41 42
140*> -- -- --
141*> 02 12 22 50 51 52
142*>
143*> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
144*> transpose of RFP A above. One therefore gets:
145*>
146*>
147*> RFP A RFP A
148*>
149*> -- -- -- -- -- -- -- -- -- --
150*> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
151*> -- -- -- -- -- -- -- -- -- --
152*> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
153*> -- -- -- -- -- -- -- -- -- --
154*> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
155*>
156*>
157*> We next consider Standard Packed Format when N is odd.
158*> We give an example where N = 5.
159*>
160*> AP is Upper AP is Lower
161*>
162*> 00 01 02 03 04 00
163*> 11 12 13 14 10 11
164*> 22 23 24 20 21 22
165*> 33 34 30 31 32 33
166*> 44 40 41 42 43 44
167*>
168*>
169*> Let TRANSR = 'N'. RFP holds AP as follows:
170*> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
171*> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
172*> conjugate-transpose of the first two columns of AP upper.
173*> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
174*> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
175*> conjugate-transpose of the last two columns of AP lower.
176*> To denote conjugate we place -- above the element. This covers the
177*> case N odd and TRANSR = 'N'.
178*>
179*> RFP A RFP A
180*>
181*> -- --
182*> 02 03 04 00 33 43
183*> --
184*> 12 13 14 10 11 44
185*>
186*> 22 23 24 20 21 22
187*> --
188*> 00 33 34 30 31 32
189*> -- --
190*> 01 11 44 40 41 42
191*>
192*> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
193*> transpose of RFP A above. One therefore gets:
194*>
195*>
196*> RFP A RFP A
197*>
198*> -- -- -- -- -- -- -- -- --
199*> 02 12 22 00 01 00 10 20 30 40 50
200*> -- -- -- -- -- -- -- -- --
201*> 03 13 23 33 11 33 11 21 31 41 51
202*> -- -- -- -- -- -- -- -- --
203*> 04 14 24 34 44 43 44 22 32 42 52
204*> \endverbatim
205*>
206* =====================================================================
207 SUBROUTINE ztfttp( TRANSR, UPLO, N, ARF, AP, INFO )
208*
209* -- LAPACK computational routine --
210* -- LAPACK is a software package provided by Univ. of Tennessee, --
211* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
212*
213* .. Scalar Arguments ..
214 CHARACTER TRANSR, UPLO
215 INTEGER INFO, N
216* ..
217* .. Array Arguments ..
218 COMPLEX*16 AP( 0: * ), ARF( 0: * )
219* ..
220*
221* =====================================================================
222*
223* .. Parameters ..
224* ..
225* .. Local Scalars ..
226 LOGICAL LOWER, NISODD, NORMALTRANSR
227 INTEGER N1, N2, K, NT
228 INTEGER I, J, IJ
229 INTEGER IJP, JP, LDA, JS
230* ..
231* .. External Functions ..
232 LOGICAL LSAME
233 EXTERNAL lsame
234* ..
235* .. External Subroutines ..
236 EXTERNAL xerbla
237* ..
238* .. Intrinsic Functions ..
239 INTRINSIC dconjg
240* ..
241* .. Intrinsic Functions ..
242* ..
243* .. Executable Statements ..
244*
245* Test the input parameters.
246*
247 info = 0
248 normaltransr = lsame( transr, 'N' )
249 lower = lsame( uplo, 'L' )
250 IF( .NOT.normaltransr .AND. .NOT.lsame( transr, 'C' ) ) THEN
251 info = -1
252 ELSE IF( .NOT.lower .AND. .NOT.lsame( uplo, 'U' ) ) THEN
253 info = -2
254 ELSE IF( n.LT.0 ) THEN
255 info = -3
256 END IF
257 IF( info.NE.0 ) THEN
258 CALL xerbla( 'ZTFTTP', -info )
259 RETURN
260 END IF
261*
262* Quick return if possible
263*
264 IF( n.EQ.0 )
265 $ RETURN
266*
267 IF( n.EQ.1 ) THEN
268 IF( normaltransr ) THEN
269 ap( 0 ) = arf( 0 )
270 ELSE
271 ap( 0 ) = dconjg( arf( 0 ) )
272 END IF
273 RETURN
274 END IF
275*
276* Size of array ARF(0:NT-1)
277*
278 nt = n*( n+1 ) / 2
279*
280* Set N1 and N2 depending on LOWER
281*
282 IF( lower ) THEN
283 n2 = n / 2
284 n1 = n - n2
285 ELSE
286 n1 = n / 2
287 n2 = n - n1
288 END IF
289*
290* If N is odd, set NISODD = .TRUE.
291* If N is even, set K = N/2 and NISODD = .FALSE.
292*
293* set lda of ARF^C; ARF^C is (0:(N+1)/2-1,0:N-noe)
294* where noe = 0 if n is even, noe = 1 if n is odd
295*
296 IF( mod( n, 2 ).EQ.0 ) THEN
297 k = n / 2
298 nisodd = .false.
299 lda = n + 1
300 ELSE
301 nisodd = .true.
302 lda = n
303 END IF
304*
305* ARF^C has lda rows and n+1-noe cols
306*
307 IF( .NOT.normaltransr )
308 $ lda = ( n+1 ) / 2
309*
310* start execution: there are eight cases
311*
312 IF( nisodd ) THEN
313*
314* N is odd
315*
316 IF( normaltransr ) THEN
317*
318* N is odd and TRANSR = 'N'
319*
320 IF( lower ) THEN
321*
322* SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
323* T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
324* T1 -> a(0), T2 -> a(n), S -> a(n1); lda = n
325*
326 ijp = 0
327 jp = 0
328 DO j = 0, n2
329 DO i = j, n - 1
330 ij = i + jp
331 ap( ijp ) = arf( ij )
332 ijp = ijp + 1
333 END DO
334 jp = jp + lda
335 END DO
336 DO i = 0, n2 - 1
337 DO j = 1 + i, n2
338 ij = i + j*lda
339 ap( ijp ) = dconjg( arf( ij ) )
340 ijp = ijp + 1
341 END DO
342 END DO
343*
344 ELSE
345*
346* SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
347* T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
348* T1 -> a(n2), T2 -> a(n1), S -> a(0)
349*
350 ijp = 0
351 DO j = 0, n1 - 1
352 ij = n2 + j
353 DO i = 0, j
354 ap( ijp ) = dconjg( arf( ij ) )
355 ijp = ijp + 1
356 ij = ij + lda
357 END DO
358 END DO
359 js = 0
360 DO j = n1, n - 1
361 ij = js
362 DO ij = js, js + j
363 ap( ijp ) = arf( ij )
364 ijp = ijp + 1
365 END DO
366 js = js + lda
367 END DO
368*
369 END IF
370*
371 ELSE
372*
373* N is odd and TRANSR = 'C'
374*
375 IF( lower ) THEN
376*
377* SRPA for LOWER, TRANSPOSE and N is odd
378* T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
379* T1 -> a(0+0) , T2 -> a(1+0) , S -> a(0+n1*n1); lda=n1
380*
381 ijp = 0
382 DO i = 0, n2
383 DO ij = i*( lda+1 ), n*lda - 1, lda
384 ap( ijp ) = dconjg( arf( ij ) )
385 ijp = ijp + 1
386 END DO
387 END DO
388 js = 1
389 DO j = 0, n2 - 1
390 DO ij = js, js + n2 - j - 1
391 ap( ijp ) = arf( ij )
392 ijp = ijp + 1
393 END DO
394 js = js + lda + 1
395 END DO
396*
397 ELSE
398*
399* SRPA for UPPER, TRANSPOSE and N is odd
400* T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
401* T1 -> a(n2*n2), T2 -> a(n1*n2), S -> a(0); lda = n2
402*
403 ijp = 0
404 js = n2*lda
405 DO j = 0, n1 - 1
406 DO ij = js, js + j
407 ap( ijp ) = arf( ij )
408 ijp = ijp + 1
409 END DO
410 js = js + lda
411 END DO
412 DO i = 0, n1
413 DO ij = i, i + ( n1+i )*lda, lda
414 ap( ijp ) = dconjg( arf( ij ) )
415 ijp = ijp + 1
416 END DO
417 END DO
418*
419 END IF
420*
421 END IF
422*
423 ELSE
424*
425* N is even
426*
427 IF( normaltransr ) THEN
428*
429* N is even and TRANSR = 'N'
430*
431 IF( lower ) THEN
432*
433* SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
434* T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
435* T1 -> a(1), T2 -> a(0), S -> a(k+1)
436*
437 ijp = 0
438 jp = 0
439 DO j = 0, k - 1
440 DO i = j, n - 1
441 ij = 1 + i + jp
442 ap( ijp ) = arf( ij )
443 ijp = ijp + 1
444 END DO
445 jp = jp + lda
446 END DO
447 DO i = 0, k - 1
448 DO j = i, k - 1
449 ij = i + j*lda
450 ap( ijp ) = dconjg( arf( ij ) )
451 ijp = ijp + 1
452 END DO
453 END DO
454*
455 ELSE
456*
457* SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
458* T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
459* T1 -> a(k+1), T2 -> a(k), S -> a(0)
460*
461 ijp = 0
462 DO j = 0, k - 1
463 ij = k + 1 + j
464 DO i = 0, j
465 ap( ijp ) = dconjg( arf( ij ) )
466 ijp = ijp + 1
467 ij = ij + lda
468 END DO
469 END DO
470 js = 0
471 DO j = k, n - 1
472 ij = js
473 DO ij = js, js + j
474 ap( ijp ) = arf( ij )
475 ijp = ijp + 1
476 END DO
477 js = js + lda
478 END DO
479*
480 END IF
481*
482 ELSE
483*
484* N is even and TRANSR = 'C'
485*
486 IF( lower ) THEN
487*
488* SRPA for LOWER, TRANSPOSE and N is even (see paper)
489* T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
490* T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
491*
492 ijp = 0
493 DO i = 0, k - 1
494 DO ij = i + ( i+1 )*lda, ( n+1 )*lda - 1, lda
495 ap( ijp ) = dconjg( arf( ij ) )
496 ijp = ijp + 1
497 END DO
498 END DO
499 js = 0
500 DO j = 0, k - 1
501 DO ij = js, js + k - j - 1
502 ap( ijp ) = arf( ij )
503 ijp = ijp + 1
504 END DO
505 js = js + lda + 1
506 END DO
507*
508 ELSE
509*
510* SRPA for UPPER, TRANSPOSE and N is even (see paper)
511* T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0)
512* T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
513*
514 ijp = 0
515 js = ( k+1 )*lda
516 DO j = 0, k - 1
517 DO ij = js, js + j
518 ap( ijp ) = arf( ij )
519 ijp = ijp + 1
520 END DO
521 js = js + lda
522 END DO
523 DO i = 0, k - 1
524 DO ij = i, i + ( k+i )*lda, lda
525 ap( ijp ) = dconjg( arf( ij ) )
526 ijp = ijp + 1
527 END DO
528 END DO
529*
530 END IF
531*
532 END IF
533*
534 END IF
535*
536 RETURN
537*
538* End of ZTFTTP
539*
540 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ztfttp(TRANSR, UPLO, N, ARF, AP, INFO)
ZTFTTP copies a triangular matrix from the rectangular full packed format (TF) to the standard packed...
Definition: ztfttp.f:208