LAPACK  3.10.0
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 *> \ingroup complexOTHERcomputational
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 ctfttp( 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 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 conjg
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( 'CTFTTP', -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 ) = conjg( 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 ) = conjg( 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 ) = conjg( 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 ) = conjg( 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 ) = conjg( 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 ) = conjg( 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 ) = conjg( 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 ) = conjg( 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 ) = conjg( 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 CTFTTP
539 *
540  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
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:208