LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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stpttf.f
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1*> \brief \b STPTTF copies a triangular matrix from the standard packed format (TP) to the rectangular full packed format (TF).
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download STPTTF + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/stpttf.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/stpttf.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/stpttf.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE STPTTF( TRANSR, UPLO, N, AP, ARF, INFO )
22*
23* .. Scalar Arguments ..
24* CHARACTER TRANSR, UPLO
25* INTEGER INFO, N
26* ..
27* .. Array Arguments ..
28* REAL AP( 0: * ), ARF( 0: * )
29*
30*
31*> \par Purpose:
32* =============
33*>
34*> \verbatim
35*>
36*> STPTTF copies a triangular matrix A from standard packed format (TP)
37*> to rectangular full packed format (TF).
38*> \endverbatim
39*
40* Arguments:
41* ==========
42*
43*> \param[in] TRANSR
44*> \verbatim
45*> TRANSR is CHARACTER*1
46*> = 'N': ARF in Normal format is wanted;
47*> = 'T': ARF in Conjugate-transpose format is wanted.
48*> \endverbatim
49*>
50*> \param[in] UPLO
51*> \verbatim
52*> UPLO is CHARACTER*1
53*> = 'U': A is upper triangular;
54*> = 'L': A is lower triangular.
55*> \endverbatim
56*>
57*> \param[in] N
58*> \verbatim
59*> N is INTEGER
60*> The order of the matrix A. N >= 0.
61*> \endverbatim
62*>
63*> \param[in] AP
64*> \verbatim
65*> AP is REAL array, dimension ( N*(N+1)/2 ),
66*> On entry, the upper or lower triangular matrix A, packed
67*> columnwise in a linear array. The j-th column of A is stored
68*> in the array AP as follows:
69*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
70*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
71*> \endverbatim
72*>
73*> \param[out] ARF
74*> \verbatim
75*> ARF is REAL array, dimension ( N*(N+1)/2 ),
76*> On exit, the upper or lower triangular matrix A stored in
77*> RFP format. For a further discussion see Notes below.
78*> \endverbatim
79*>
80*> \param[out] INFO
81*> \verbatim
82*> INFO is INTEGER
83*> = 0: successful exit
84*> < 0: if INFO = -i, the i-th argument had an illegal value
85*> \endverbatim
86*
87* Authors:
88* ========
89*
90*> \author Univ. of Tennessee
91*> \author Univ. of California Berkeley
92*> \author Univ. of Colorado Denver
93*> \author NAG Ltd.
94*
95*> \ingroup realOTHERcomputational
96*
97*> \par Further Details:
98* =====================
99*>
100*> \verbatim
101*>
102*> We first consider Rectangular Full Packed (RFP) Format when N is
103*> even. We give an example where N = 6.
104*>
105*> AP is Upper AP is Lower
106*>
107*> 00 01 02 03 04 05 00
108*> 11 12 13 14 15 10 11
109*> 22 23 24 25 20 21 22
110*> 33 34 35 30 31 32 33
111*> 44 45 40 41 42 43 44
112*> 55 50 51 52 53 54 55
113*>
114*>
115*> Let TRANSR = 'N'. RFP holds AP as follows:
116*> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
117*> three columns of AP upper. The lower triangle A(4:6,0:2) consists of
118*> the transpose of the first three columns of AP upper.
119*> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
120*> three columns of AP lower. The upper triangle A(0:2,0:2) consists of
121*> the transpose of the last three columns of AP lower.
122*> This covers the case N even and TRANSR = 'N'.
123*>
124*> RFP A RFP A
125*>
126*> 03 04 05 33 43 53
127*> 13 14 15 00 44 54
128*> 23 24 25 10 11 55
129*> 33 34 35 20 21 22
130*> 00 44 45 30 31 32
131*> 01 11 55 40 41 42
132*> 02 12 22 50 51 52
133*>
134*> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
135*> transpose of RFP A above. One therefore gets:
136*>
137*>
138*> RFP A RFP A
139*>
140*> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
141*> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
142*> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
143*>
144*>
145*> We then consider Rectangular Full Packed (RFP) Format when N is
146*> odd. We give an example where N = 5.
147*>
148*> AP is Upper AP is Lower
149*>
150*> 00 01 02 03 04 00
151*> 11 12 13 14 10 11
152*> 22 23 24 20 21 22
153*> 33 34 30 31 32 33
154*> 44 40 41 42 43 44
155*>
156*>
157*> Let TRANSR = 'N'. RFP holds AP as follows:
158*> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
159*> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
160*> the transpose of the first two columns of AP upper.
161*> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
162*> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
163*> the transpose of the last two columns of AP lower.
164*> This covers the case N odd and TRANSR = 'N'.
165*>
166*> RFP A RFP A
167*>
168*> 02 03 04 00 33 43
169*> 12 13 14 10 11 44
170*> 22 23 24 20 21 22
171*> 00 33 34 30 31 32
172*> 01 11 44 40 41 42
173*>
174*> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
175*> transpose of RFP A above. One therefore gets:
176*>
177*> RFP A RFP A
178*>
179*> 02 12 22 00 01 00 10 20 30 40 50
180*> 03 13 23 33 11 33 11 21 31 41 51
181*> 04 14 24 34 44 43 44 22 32 42 52
182*> \endverbatim
183*>
184* =====================================================================
185 SUBROUTINE stpttf( TRANSR, UPLO, N, AP, ARF, INFO )
186*
187* -- LAPACK computational routine --
188* -- LAPACK is a software package provided by Univ. of Tennessee, --
189* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
190*
191* .. Scalar Arguments ..
192 CHARACTER TRANSR, UPLO
193 INTEGER INFO, N
194* ..
195* .. Array Arguments ..
196 REAL AP( 0: * ), ARF( 0: * )
197*
198* =====================================================================
199*
200* .. Parameters ..
201* ..
202* .. Local Scalars ..
203 LOGICAL LOWER, NISODD, NORMALTRANSR
204 INTEGER N1, N2, K, NT
205 INTEGER I, J, IJ
206 INTEGER IJP, JP, LDA, JS
207* ..
208* .. External Functions ..
209 LOGICAL LSAME
210 EXTERNAL lsame
211* ..
212* .. External Subroutines ..
213 EXTERNAL xerbla
214* ..
215* .. Intrinsic Functions ..
216 INTRINSIC mod
217* ..
218* .. Executable Statements ..
219*
220* Test the input parameters.
221*
222 info = 0
223 normaltransr = lsame( transr, 'N' )
224 lower = lsame( uplo, 'L' )
225 IF( .NOT.normaltransr .AND. .NOT.lsame( transr, 'T' ) ) THEN
226 info = -1
227 ELSE IF( .NOT.lower .AND. .NOT.lsame( uplo, 'U' ) ) THEN
228 info = -2
229 ELSE IF( n.LT.0 ) THEN
230 info = -3
231 END IF
232 IF( info.NE.0 ) THEN
233 CALL xerbla( 'STPTTF', -info )
234 RETURN
235 END IF
236*
237* Quick return if possible
238*
239 IF( n.EQ.0 )
240 $ RETURN
241*
242 IF( n.EQ.1 ) THEN
243 IF( normaltransr ) THEN
244 arf( 0 ) = ap( 0 )
245 ELSE
246 arf( 0 ) = ap( 0 )
247 END IF
248 RETURN
249 END IF
250*
251* Size of array ARF(0:NT-1)
252*
253 nt = n*( n+1 ) / 2
254*
255* Set N1 and N2 depending on LOWER
256*
257 IF( lower ) THEN
258 n2 = n / 2
259 n1 = n - n2
260 ELSE
261 n1 = n / 2
262 n2 = n - n1
263 END IF
264*
265* If N is odd, set NISODD = .TRUE.
266* If N is even, set K = N/2 and NISODD = .FALSE.
267*
268* set lda of ARF^C; ARF^C is (0:(N+1)/2-1,0:N-noe)
269* where noe = 0 if n is even, noe = 1 if n is odd
270*
271 IF( mod( n, 2 ).EQ.0 ) THEN
272 k = n / 2
273 nisodd = .false.
274 lda = n + 1
275 ELSE
276 nisodd = .true.
277 lda = n
278 END IF
279*
280* ARF^C has lda rows and n+1-noe cols
281*
282 IF( .NOT.normaltransr )
283 $ lda = ( n+1 ) / 2
284*
285* start execution: there are eight cases
286*
287 IF( nisodd ) THEN
288*
289* N is odd
290*
291 IF( normaltransr ) THEN
292*
293* N is odd and TRANSR = 'N'
294*
295 IF( lower ) THEN
296*
297* N is odd, TRANSR = 'N', and UPLO = 'L'
298*
299 ijp = 0
300 jp = 0
301 DO j = 0, n2
302 DO i = j, n - 1
303 ij = i + jp
304 arf( ij ) = ap( ijp )
305 ijp = ijp + 1
306 END DO
307 jp = jp + lda
308 END DO
309 DO i = 0, n2 - 1
310 DO j = 1 + i, n2
311 ij = i + j*lda
312 arf( ij ) = ap( ijp )
313 ijp = ijp + 1
314 END DO
315 END DO
316*
317 ELSE
318*
319* N is odd, TRANSR = 'N', and UPLO = 'U'
320*
321 ijp = 0
322 DO j = 0, n1 - 1
323 ij = n2 + j
324 DO i = 0, j
325 arf( ij ) = ap( ijp )
326 ijp = ijp + 1
327 ij = ij + lda
328 END DO
329 END DO
330 js = 0
331 DO j = n1, n - 1
332 ij = js
333 DO ij = js, js + j
334 arf( ij ) = ap( ijp )
335 ijp = ijp + 1
336 END DO
337 js = js + lda
338 END DO
339*
340 END IF
341*
342 ELSE
343*
344* N is odd and TRANSR = 'T'
345*
346 IF( lower ) THEN
347*
348* N is odd, TRANSR = 'T', and UPLO = 'L'
349*
350 ijp = 0
351 DO i = 0, n2
352 DO ij = i*( lda+1 ), n*lda - 1, lda
353 arf( ij ) = ap( ijp )
354 ijp = ijp + 1
355 END DO
356 END DO
357 js = 1
358 DO j = 0, n2 - 1
359 DO ij = js, js + n2 - j - 1
360 arf( ij ) = ap( ijp )
361 ijp = ijp + 1
362 END DO
363 js = js + lda + 1
364 END DO
365*
366 ELSE
367*
368* N is odd, TRANSR = 'T', and UPLO = 'U'
369*
370 ijp = 0
371 js = n2*lda
372 DO j = 0, n1 - 1
373 DO ij = js, js + j
374 arf( ij ) = ap( ijp )
375 ijp = ijp + 1
376 END DO
377 js = js + lda
378 END DO
379 DO i = 0, n1
380 DO ij = i, i + ( n1+i )*lda, lda
381 arf( ij ) = ap( ijp )
382 ijp = ijp + 1
383 END DO
384 END DO
385*
386 END IF
387*
388 END IF
389*
390 ELSE
391*
392* N is even
393*
394 IF( normaltransr ) THEN
395*
396* N is even and TRANSR = 'N'
397*
398 IF( lower ) THEN
399*
400* N is even, TRANSR = 'N', and UPLO = 'L'
401*
402 ijp = 0
403 jp = 0
404 DO j = 0, k - 1
405 DO i = j, n - 1
406 ij = 1 + i + jp
407 arf( ij ) = ap( ijp )
408 ijp = ijp + 1
409 END DO
410 jp = jp + lda
411 END DO
412 DO i = 0, k - 1
413 DO j = i, k - 1
414 ij = i + j*lda
415 arf( ij ) = ap( ijp )
416 ijp = ijp + 1
417 END DO
418 END DO
419*
420 ELSE
421*
422* N is even, TRANSR = 'N', and UPLO = 'U'
423*
424 ijp = 0
425 DO j = 0, k - 1
426 ij = k + 1 + j
427 DO i = 0, j
428 arf( ij ) = ap( ijp )
429 ijp = ijp + 1
430 ij = ij + lda
431 END DO
432 END DO
433 js = 0
434 DO j = k, n - 1
435 ij = js
436 DO ij = js, js + j
437 arf( ij ) = ap( ijp )
438 ijp = ijp + 1
439 END DO
440 js = js + lda
441 END DO
442*
443 END IF
444*
445 ELSE
446*
447* N is even and TRANSR = 'T'
448*
449 IF( lower ) THEN
450*
451* N is even, TRANSR = 'T', and UPLO = 'L'
452*
453 ijp = 0
454 DO i = 0, k - 1
455 DO ij = i + ( i+1 )*lda, ( n+1 )*lda - 1, lda
456 arf( ij ) = ap( ijp )
457 ijp = ijp + 1
458 END DO
459 END DO
460 js = 0
461 DO j = 0, k - 1
462 DO ij = js, js + k - j - 1
463 arf( ij ) = ap( ijp )
464 ijp = ijp + 1
465 END DO
466 js = js + lda + 1
467 END DO
468*
469 ELSE
470*
471* N is even, TRANSR = 'T', and UPLO = 'U'
472*
473 ijp = 0
474 js = ( k+1 )*lda
475 DO j = 0, k - 1
476 DO ij = js, js + j
477 arf( ij ) = ap( ijp )
478 ijp = ijp + 1
479 END DO
480 js = js + lda
481 END DO
482 DO i = 0, k - 1
483 DO ij = i, i + ( k+i )*lda, lda
484 arf( ij ) = ap( ijp )
485 ijp = ijp + 1
486 END DO
487 END DO
488*
489 END IF
490*
491 END IF
492*
493 END IF
494*
495 RETURN
496*
497* End of STPTTF
498*
499 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine stpttf(TRANSR, UPLO, N, AP, ARF, INFO)
STPTTF copies a triangular matrix from the standard packed format (TP) to the rectangular full packed...
Definition: stpttf.f:186