LAPACK  3.6.1
LAPACK: Linear Algebra PACKage
ctfttp.f
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1 *> \brief \b CTFTTP 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 CTFTTP + dependencies
10 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ctfttp.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ctfttp.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ctfttp.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CTFTTP( TRANSR, UPLO, N, ARF, AP, INFO )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER TRANSR, UPLO
25 * INTEGER INFO, N
26 * ..
27 * .. Array Arguments ..
28 * COMPLEX AP( 0: * ), ARF( 0: * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> CTFTTP 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 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 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 *> \date September 2012
97 *
98 *> \ingroup complexOTHERcomputational
99 *
100 *> \par Further Details:
101 * =====================
102 *>
103 *> \verbatim
104 *>
105 *> We first consider Standard Packed Format when N is even.
106 *> We give an example where N = 6.
107 *>
108 *> AP is Upper AP is Lower
109 *>
110 *> 00 01 02 03 04 05 00
111 *> 11 12 13 14 15 10 11
112 *> 22 23 24 25 20 21 22
113 *> 33 34 35 30 31 32 33
114 *> 44 45 40 41 42 43 44
115 *> 55 50 51 52 53 54 55
116 *>
117 *>
118 *> Let TRANSR = 'N'. RFP holds AP as follows:
119 *> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
120 *> three columns of AP upper. The lower triangle A(4:6,0:2) consists of
121 *> conjugate-transpose of the first three columns of AP upper.
122 *> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
123 *> three columns of AP lower. The upper triangle A(0:2,0:2) consists of
124 *> conjugate-transpose of the last three columns of AP lower.
125 *> To denote conjugate we place -- above the element. This covers the
126 *> case N even and TRANSR = 'N'.
127 *>
128 *> RFP A RFP A
129 *>
130 *> -- -- --
131 *> 03 04 05 33 43 53
132 *> -- --
133 *> 13 14 15 00 44 54
134 *> --
135 *> 23 24 25 10 11 55
136 *>
137 *> 33 34 35 20 21 22
138 *> --
139 *> 00 44 45 30 31 32
140 *> -- --
141 *> 01 11 55 40 41 42
142 *> -- -- --
143 *> 02 12 22 50 51 52
144 *>
145 *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
146 *> transpose of RFP A above. One therefore gets:
147 *>
148 *>
149 *> RFP A RFP A
150 *>
151 *> -- -- -- -- -- -- -- -- -- --
152 *> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
153 *> -- -- -- -- -- -- -- -- -- --
154 *> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
155 *> -- -- -- -- -- -- -- -- -- --
156 *> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
157 *>
158 *>
159 *> We next consider Standard Packed Format when N is odd.
160 *> We give an example where N = 5.
161 *>
162 *> AP is Upper AP is Lower
163 *>
164 *> 00 01 02 03 04 00
165 *> 11 12 13 14 10 11
166 *> 22 23 24 20 21 22
167 *> 33 34 30 31 32 33
168 *> 44 40 41 42 43 44
169 *>
170 *>
171 *> Let TRANSR = 'N'. RFP holds AP as follows:
172 *> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
173 *> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
174 *> conjugate-transpose of the first two columns of AP upper.
175 *> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
176 *> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
177 *> conjugate-transpose of the last two columns of AP lower.
178 *> To denote conjugate we place -- above the element. This covers the
179 *> case N odd and TRANSR = 'N'.
180 *>
181 *> RFP A RFP A
182 *>
183 *> -- --
184 *> 02 03 04 00 33 43
185 *> --
186 *> 12 13 14 10 11 44
187 *>
188 *> 22 23 24 20 21 22
189 *> --
190 *> 00 33 34 30 31 32
191 *> -- --
192 *> 01 11 44 40 41 42
193 *>
194 *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
195 *> transpose of RFP A above. One therefore gets:
196 *>
197 *>
198 *> RFP A RFP A
199 *>
200 *> -- -- -- -- -- -- -- -- --
201 *> 02 12 22 00 01 00 10 20 30 40 50
202 *> -- -- -- -- -- -- -- -- --
203 *> 03 13 23 33 11 33 11 21 31 41 51
204 *> -- -- -- -- -- -- -- -- --
205 *> 04 14 24 34 44 43 44 22 32 42 52
206 *> \endverbatim
207 *>
208 * =====================================================================
209  SUBROUTINE ctfttp( TRANSR, UPLO, N, ARF, AP, INFO )
210 *
211 * -- LAPACK computational routine (version 3.4.2) --
212 * -- LAPACK is a software package provided by Univ. of Tennessee, --
213 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
214 * September 2012
215 *
216 * .. Scalar Arguments ..
217  CHARACTER TRANSR, UPLO
218  INTEGER INFO, N
219 * ..
220 * .. Array Arguments ..
221  COMPLEX AP( 0: * ), ARF( 0: * )
222 * ..
223 *
224 * =====================================================================
225 *
226 * .. Parameters ..
227 * ..
228 * .. Local Scalars ..
229  LOGICAL LOWER, NISODD, NORMALTRANSR
230  INTEGER N1, N2, K, NT
231  INTEGER I, J, IJ
232  INTEGER IJP, JP, LDA, JS
233 * ..
234 * .. External Functions ..
235  LOGICAL LSAME
236  EXTERNAL lsame
237 * ..
238 * .. External Subroutines ..
239  EXTERNAL xerbla
240 * ..
241 * .. Intrinsic Functions ..
242  INTRINSIC conjg
243 * ..
244 * .. Intrinsic Functions ..
245 * ..
246 * .. Executable Statements ..
247 *
248 * Test the input parameters.
249 *
250  info = 0
251  normaltransr = lsame( transr, 'N' )
252  lower = lsame( uplo, 'L' )
253  IF( .NOT.normaltransr .AND. .NOT.lsame( transr, 'C' ) ) THEN
254  info = -1
255  ELSE IF( .NOT.lower .AND. .NOT.lsame( uplo, 'U' ) ) THEN
256  info = -2
257  ELSE IF( n.LT.0 ) THEN
258  info = -3
259  END IF
260  IF( info.NE.0 ) THEN
261  CALL xerbla( 'CTFTTP', -info )
262  RETURN
263  END IF
264 *
265 * Quick return if possible
266 *
267  IF( n.EQ.0 )
268  $ RETURN
269 *
270  IF( n.EQ.1 ) THEN
271  IF( normaltransr ) THEN
272  ap( 0 ) = arf( 0 )
273  ELSE
274  ap( 0 ) = conjg( arf( 0 ) )
275  END IF
276  RETURN
277  END IF
278 *
279 * Size of array ARF(0:NT-1)
280 *
281  nt = n*( n+1 ) / 2
282 *
283 * Set N1 and N2 depending on LOWER
284 *
285  IF( lower ) THEN
286  n2 = n / 2
287  n1 = n - n2
288  ELSE
289  n1 = n / 2
290  n2 = n - n1
291  END IF
292 *
293 * If N is odd, set NISODD = .TRUE.
294 * If N is even, set K = N/2 and NISODD = .FALSE.
295 *
296 * set lda of ARF^C; ARF^C is (0:(N+1)/2-1,0:N-noe)
297 * where noe = 0 if n is even, noe = 1 if n is odd
298 *
299  IF( mod( n, 2 ).EQ.0 ) THEN
300  k = n / 2
301  nisodd = .false.
302  lda = n + 1
303  ELSE
304  nisodd = .true.
305  lda = n
306  END IF
307 *
308 * ARF^C has lda rows and n+1-noe cols
309 *
310  IF( .NOT.normaltransr )
311  $ lda = ( n+1 ) / 2
312 *
313 * start execution: there are eight cases
314 *
315  IF( nisodd ) THEN
316 *
317 * N is odd
318 *
319  IF( normaltransr ) THEN
320 *
321 * N is odd and TRANSR = 'N'
322 *
323  IF( lower ) THEN
324 *
325 * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
326 * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
327 * T1 -> a(0), T2 -> a(n), S -> a(n1); lda = n
328 *
329  ijp = 0
330  jp = 0
331  DO j = 0, n2
332  DO i = j, n - 1
333  ij = i + jp
334  ap( ijp ) = arf( ij )
335  ijp = ijp + 1
336  END DO
337  jp = jp + lda
338  END DO
339  DO i = 0, n2 - 1
340  DO j = 1 + i, n2
341  ij = i + j*lda
342  ap( ijp ) = conjg( arf( ij ) )
343  ijp = ijp + 1
344  END DO
345  END DO
346 *
347  ELSE
348 *
349 * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
350 * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
351 * T1 -> a(n2), T2 -> a(n1), S -> a(0)
352 *
353  ijp = 0
354  DO j = 0, n1 - 1
355  ij = n2 + j
356  DO i = 0, j
357  ap( ijp ) = conjg( arf( ij ) )
358  ijp = ijp + 1
359  ij = ij + lda
360  END DO
361  END DO
362  js = 0
363  DO j = n1, n - 1
364  ij = js
365  DO ij = js, js + j
366  ap( ijp ) = arf( ij )
367  ijp = ijp + 1
368  END DO
369  js = js + lda
370  END DO
371 *
372  END IF
373 *
374  ELSE
375 *
376 * N is odd and TRANSR = 'C'
377 *
378  IF( lower ) THEN
379 *
380 * SRPA for LOWER, TRANSPOSE and N is odd
381 * T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
382 * T1 -> a(0+0) , T2 -> a(1+0) , S -> a(0+n1*n1); lda=n1
383 *
384  ijp = 0
385  DO i = 0, n2
386  DO ij = i*( lda+1 ), n*lda - 1, lda
387  ap( ijp ) = conjg( arf( ij ) )
388  ijp = ijp + 1
389  END DO
390  END DO
391  js = 1
392  DO j = 0, n2 - 1
393  DO ij = js, js + n2 - j - 1
394  ap( ijp ) = arf( ij )
395  ijp = ijp + 1
396  END DO
397  js = js + lda + 1
398  END DO
399 *
400  ELSE
401 *
402 * SRPA for UPPER, TRANSPOSE and N is odd
403 * T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
404 * T1 -> a(n2*n2), T2 -> a(n1*n2), S -> a(0); lda = n2
405 *
406  ijp = 0
407  js = n2*lda
408  DO j = 0, n1 - 1
409  DO ij = js, js + j
410  ap( ijp ) = arf( ij )
411  ijp = ijp + 1
412  END DO
413  js = js + lda
414  END DO
415  DO i = 0, n1
416  DO ij = i, i + ( n1+i )*lda, lda
417  ap( ijp ) = conjg( arf( ij ) )
418  ijp = ijp + 1
419  END DO
420  END DO
421 *
422  END IF
423 *
424  END IF
425 *
426  ELSE
427 *
428 * N is even
429 *
430  IF( normaltransr ) THEN
431 *
432 * N is even and TRANSR = 'N'
433 *
434  IF( lower ) THEN
435 *
436 * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
437 * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
438 * T1 -> a(1), T2 -> a(0), S -> a(k+1)
439 *
440  ijp = 0
441  jp = 0
442  DO j = 0, k - 1
443  DO i = j, n - 1
444  ij = 1 + i + jp
445  ap( ijp ) = arf( ij )
446  ijp = ijp + 1
447  END DO
448  jp = jp + lda
449  END DO
450  DO i = 0, k - 1
451  DO j = i, k - 1
452  ij = i + j*lda
453  ap( ijp ) = conjg( arf( ij ) )
454  ijp = ijp + 1
455  END DO
456  END DO
457 *
458  ELSE
459 *
460 * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
461 * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
462 * T1 -> a(k+1), T2 -> a(k), S -> a(0)
463 *
464  ijp = 0
465  DO j = 0, k - 1
466  ij = k + 1 + j
467  DO i = 0, j
468  ap( ijp ) = conjg( arf( ij ) )
469  ijp = ijp + 1
470  ij = ij + lda
471  END DO
472  END DO
473  js = 0
474  DO j = k, n - 1
475  ij = js
476  DO ij = js, js + j
477  ap( ijp ) = arf( ij )
478  ijp = ijp + 1
479  END DO
480  js = js + lda
481  END DO
482 *
483  END IF
484 *
485  ELSE
486 *
487 * N is even and TRANSR = 'C'
488 *
489  IF( lower ) THEN
490 *
491 * SRPA for LOWER, TRANSPOSE and N is even (see paper)
492 * T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
493 * T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
494 *
495  ijp = 0
496  DO i = 0, k - 1
497  DO ij = i + ( i+1 )*lda, ( n+1 )*lda - 1, lda
498  ap( ijp ) = conjg( arf( ij ) )
499  ijp = ijp + 1
500  END DO
501  END DO
502  js = 0
503  DO j = 0, k - 1
504  DO ij = js, js + k - j - 1
505  ap( ijp ) = arf( ij )
506  ijp = ijp + 1
507  END DO
508  js = js + lda + 1
509  END DO
510 *
511  ELSE
512 *
513 * SRPA for UPPER, TRANSPOSE and N is even (see paper)
514 * T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0)
515 * T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
516 *
517  ijp = 0
518  js = ( k+1 )*lda
519  DO j = 0, k - 1
520  DO ij = js, js + j
521  ap( ijp ) = arf( ij )
522  ijp = ijp + 1
523  END DO
524  js = js + lda
525  END DO
526  DO i = 0, k - 1
527  DO ij = i, i + ( k+i )*lda, lda
528  ap( ijp ) = conjg( arf( ij ) )
529  ijp = ijp + 1
530  END DO
531  END DO
532 *
533  END IF
534 *
535  END IF
536 *
537  END IF
538 *
539  RETURN
540 *
541 * End of CTFTTP
542 *
543  END
ctfttp
subroutine ctfttp(TRANSR, UPLO, N, ARF, AP, INFO)
CTFTTP copies a triangular matrix from the rectangular full packed format (TF) to the standard packed...
Definition: ctfttp.f:210
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62