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