 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ ztrttf()

 subroutine ztrttf ( character TRANSR, character UPLO, integer N, complex*16, dimension( 0: lda-1, 0: * ) A, integer LDA, complex*16, dimension( 0: * ) ARF, integer INFO )

ZTRTTF copies a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF).

Purpose:
``` ZTRTTF copies a triangular matrix A from standard full format (TR)
to rectangular full packed format (TF) .```
Parameters
 [in] TRANSR ``` TRANSR is CHARACTER*1 = 'N': ARF in Normal mode is wanted; = 'C': ARF in Conjugate Transpose mode is wanted;``` [in] UPLO ``` UPLO is CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular.``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] A ``` A is COMPLEX*16 array, dimension ( LDA, N ) On entry, the triangular matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced.``` [in] LDA ``` LDA is INTEGER The leading dimension of the matrix A. LDA >= max(1,N).``` [out] ARF ``` ARF is COMPLEX*16 array, dimension ( N*(N+1)/2 ), On exit, the upper or lower triangular matrix A stored in RFP format. For a further discussion see Notes below.``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```
Further Details:
```  We first consider Standard Packed Format when N is even.
We give an example where N = 6.

AP is Upper             AP is Lower

00 01 02 03 04 05       00
11 12 13 14 15       10 11
22 23 24 25       20 21 22
33 34 35       30 31 32 33
44 45       40 41 42 43 44
55       50 51 52 53 54 55

Let TRANSR = 'N'. RFP holds AP as follows:
For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
three columns of AP upper. The lower triangle A(4:6,0:2) consists of
conjugate-transpose of the first three columns of AP upper.
For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
three columns of AP lower. The upper triangle A(0:2,0:2) consists of
conjugate-transpose of the last three columns of AP lower.
To denote conjugate we place -- above the element. This covers the
case N even and TRANSR = 'N'.

RFP A                   RFP A

-- -- --
03 04 05                33 43 53
-- --
13 14 15                00 44 54
--
23 24 25                10 11 55

33 34 35                20 21 22
--
00 44 45                30 31 32
-- --
01 11 55                40 41 42
-- -- --
02 12 22                50 51 52

Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
transpose of RFP A above. One therefore gets:

RFP A                   RFP A

-- -- -- --                -- -- -- -- -- --
03 13 23 33 00 01 02    33 00 10 20 30 40 50
-- -- -- -- --                -- -- -- -- --
04 14 24 34 44 11 12    43 44 11 21 31 41 51
-- -- -- -- -- --                -- -- -- --
05 15 25 35 45 55 22    53 54 55 22 32 42 52

We next  consider Standard Packed Format when N is odd.
We give an example where N = 5.

AP is Upper                 AP is Lower

00 01 02 03 04              00
11 12 13 14              10 11
22 23 24              20 21 22
33 34              30 31 32 33
44              40 41 42 43 44

Let TRANSR = 'N'. RFP holds AP as follows:
For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
three columns of AP upper. The lower triangle A(3:4,0:1) consists of
conjugate-transpose of the first two   columns of AP upper.
For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
three columns of AP lower. The upper triangle A(0:1,1:2) consists of
conjugate-transpose of the last two   columns of AP lower.
To denote conjugate we place -- above the element. This covers the
case N odd  and TRANSR = 'N'.

RFP A                   RFP A

-- --
02 03 04                00 33 43
--
12 13 14                10 11 44

22 23 24                20 21 22
--
00 33 34                30 31 32
-- --
01 11 44                40 41 42

Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
transpose of RFP A above. One therefore gets:

RFP A                   RFP A

-- -- --                   -- -- -- -- -- --
02 12 22 00 01             00 10 20 30 40 50
-- -- -- --                   -- -- -- -- --
03 13 23 33 11             33 11 21 31 41 51
-- -- -- -- --                   -- -- -- --
04 14 24 34 44             43 44 22 32 42 52```

Definition at line 215 of file ztrttf.f.

216*
217* -- LAPACK computational routine --
218* -- LAPACK is a software package provided by Univ. of Tennessee, --
219* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
220*
221* .. Scalar Arguments ..
222 CHARACTER TRANSR, UPLO
223 INTEGER INFO, N, LDA
224* ..
225* .. Array Arguments ..
226 COMPLEX*16 A( 0: LDA-1, 0: * ), ARF( 0: * )
227* ..
228*
229* =====================================================================
230*
231* .. Parameters ..
232* ..
233* .. Local Scalars ..
234 LOGICAL LOWER, NISODD, NORMALTRANSR
235 INTEGER I, IJ, J, K, L, N1, N2, NT, NX2, NP1X2
236* ..
237* .. External Functions ..
238 LOGICAL LSAME
239 EXTERNAL lsame
240* ..
241* .. External Subroutines ..
242 EXTERNAL xerbla
243* ..
244* .. Intrinsic Functions ..
245 INTRINSIC dconjg, max, mod
246* ..
247* .. Executable Statements ..
248*
249* Test the input parameters.
250*
251 info = 0
252 normaltransr = lsame( transr, 'N' )
253 lower = lsame( uplo, 'L' )
254 IF( .NOT.normaltransr .AND. .NOT.lsame( transr, 'C' ) ) THEN
255 info = -1
256 ELSE IF( .NOT.lower .AND. .NOT.lsame( uplo, 'U' ) ) THEN
257 info = -2
258 ELSE IF( n.LT.0 ) THEN
259 info = -3
260 ELSE IF( lda.LT.max( 1, n ) ) THEN
261 info = -5
262 END IF
263 IF( info.NE.0 ) THEN
264 CALL xerbla( 'ZTRTTF', -info )
265 RETURN
266 END IF
267*
268* Quick return if possible
269*
270 IF( n.LE.1 ) THEN
271 IF( n.EQ.1 ) THEN
272 IF( normaltransr ) THEN
273 arf( 0 ) = a( 0, 0 )
274 ELSE
275 arf( 0 ) = dconjg( a( 0, 0 ) )
276 END IF
277 END IF
278 RETURN
279 END IF
280*
281* Size of array ARF(1:2,0:nt-1)
282*
283 nt = n*( n+1 ) / 2
284*
285* set N1 and N2 depending on LOWER: for N even N1=N2=K
286*
287 IF( lower ) THEN
288 n2 = n / 2
289 n1 = n - n2
290 ELSE
291 n1 = n / 2
292 n2 = n - n1
293 END IF
294*
295* If N is odd, set NISODD = .TRUE., LDA=N+1 and A is (N+1)--by--K2.
296* If N is even, set K = N/2 and NISODD = .FALSE., LDA=N and A is
297* N--by--(N+1)/2.
298*
299 IF( mod( n, 2 ).EQ.0 ) THEN
300 k = n / 2
301 nisodd = .false.
302 IF( .NOT.lower )
303 \$ np1x2 = n + n + 2
304 ELSE
305 nisodd = .true.
306 IF( .NOT.lower )
307 \$ nx2 = n + n
308 END IF
309*
310 IF( nisodd ) THEN
311*
312* N is odd
313*
314 IF( normaltransr ) THEN
315*
316* N is odd and TRANSR = 'N'
317*
318 IF( lower ) THEN
319*
320* SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
321* T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
322* T1 -> a(0), T2 -> a(n), S -> a(n1); lda=n
323*
324 ij = 0
325 DO j = 0, n2
326 DO i = n1, n2 + j
327 arf( ij ) = dconjg( a( n2+j, i ) )
328 ij = ij + 1
329 END DO
330 DO i = j, n - 1
331 arf( ij ) = a( i, j )
332 ij = ij + 1
333 END DO
334 END DO
335*
336 ELSE
337*
338* SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
339* T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
340* T1 -> a(n2), T2 -> a(n1), S -> a(0); lda=n
341*
342 ij = nt - n
343 DO j = n - 1, n1, -1
344 DO i = 0, j
345 arf( ij ) = a( i, j )
346 ij = ij + 1
347 END DO
348 DO l = j - n1, n1 - 1
349 arf( ij ) = dconjg( a( j-n1, l ) )
350 ij = ij + 1
351 END DO
352 ij = ij - nx2
353 END DO
354*
355 END IF
356*
357 ELSE
358*
359* N is odd and TRANSR = 'C'
360*
361 IF( lower ) THEN
362*
363* SRPA for LOWER, TRANSPOSE and N is odd
364* T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
365* T1 -> A(0+0) , T2 -> A(1+0) , S -> A(0+n1*n1); lda=n1
366*
367 ij = 0
368 DO j = 0, n2 - 1
369 DO i = 0, j
370 arf( ij ) = dconjg( a( j, i ) )
371 ij = ij + 1
372 END DO
373 DO i = n1 + j, n - 1
374 arf( ij ) = a( i, n1+j )
375 ij = ij + 1
376 END DO
377 END DO
378 DO j = n2, n - 1
379 DO i = 0, n1 - 1
380 arf( ij ) = dconjg( a( j, i ) )
381 ij = ij + 1
382 END DO
383 END DO
384*
385 ELSE
386*
387* SRPA for UPPER, TRANSPOSE and N is odd
388* T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
389* T1 -> A(n2*n2), T2 -> A(n1*n2), S -> A(0); lda=n2
390*
391 ij = 0
392 DO j = 0, n1
393 DO i = n1, n - 1
394 arf( ij ) = dconjg( a( j, i ) )
395 ij = ij + 1
396 END DO
397 END DO
398 DO j = 0, n1 - 1
399 DO i = 0, j
400 arf( ij ) = a( i, j )
401 ij = ij + 1
402 END DO
403 DO l = n2 + j, n - 1
404 arf( ij ) = dconjg( a( n2+j, l ) )
405 ij = ij + 1
406 END DO
407 END DO
408*
409 END IF
410*
411 END IF
412*
413 ELSE
414*
415* N is even
416*
417 IF( normaltransr ) THEN
418*
419* N is even and TRANSR = 'N'
420*
421 IF( lower ) THEN
422*
423* SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
424* T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
425* T1 -> a(1), T2 -> a(0), S -> a(k+1); lda=n+1
426*
427 ij = 0
428 DO j = 0, k - 1
429 DO i = k, k + j
430 arf( ij ) = dconjg( a( k+j, i ) )
431 ij = ij + 1
432 END DO
433 DO i = j, n - 1
434 arf( ij ) = a( i, j )
435 ij = ij + 1
436 END DO
437 END DO
438*
439 ELSE
440*
441* SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
442* T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
443* T1 -> a(k+1), T2 -> a(k), S -> a(0); lda=n+1
444*
445 ij = nt - n - 1
446 DO j = n - 1, k, -1
447 DO i = 0, j
448 arf( ij ) = a( i, j )
449 ij = ij + 1
450 END DO
451 DO l = j - k, k - 1
452 arf( ij ) = dconjg( a( j-k, l ) )
453 ij = ij + 1
454 END DO
455 ij = ij - np1x2
456 END DO
457*
458 END IF
459*
460 ELSE
461*
462* N is even and TRANSR = 'C'
463*
464 IF( lower ) THEN
465*
466* SRPA for LOWER, TRANSPOSE and N is even (see paper, A=B)
467* T1 -> A(0,1) , T2 -> A(0,0) , S -> A(0,k+1) :
468* T1 -> A(0+k) , T2 -> A(0+0) , S -> A(0+k*(k+1)); lda=k
469*
470 ij = 0
471 j = k
472 DO i = k, n - 1
473 arf( ij ) = a( i, j )
474 ij = ij + 1
475 END DO
476 DO j = 0, k - 2
477 DO i = 0, j
478 arf( ij ) = dconjg( a( j, i ) )
479 ij = ij + 1
480 END DO
481 DO i = k + 1 + j, n - 1
482 arf( ij ) = a( i, k+1+j )
483 ij = ij + 1
484 END DO
485 END DO
486 DO j = k - 1, n - 1
487 DO i = 0, k - 1
488 arf( ij ) = dconjg( a( j, i ) )
489 ij = ij + 1
490 END DO
491 END DO
492*
493 ELSE
494*
495* SRPA for UPPER, TRANSPOSE and N is even (see paper, A=B)
496* T1 -> A(0,k+1) , T2 -> A(0,k) , S -> A(0,0)
497* T1 -> A(0+k*(k+1)) , T2 -> A(0+k*k) , S -> A(0+0)); lda=k
498*
499 ij = 0
500 DO j = 0, k
501 DO i = k, n - 1
502 arf( ij ) = dconjg( a( j, i ) )
503 ij = ij + 1
504 END DO
505 END DO
506 DO j = 0, k - 2
507 DO i = 0, j
508 arf( ij ) = a( i, j )
509 ij = ij + 1
510 END DO
511 DO l = k + 1 + j, n - 1
512 arf( ij ) = dconjg( a( k+1+j, l ) )
513 ij = ij + 1
514 END DO
515 END DO
516*
517* Note that here J = K-1
518*
519 DO i = 0, j
520 arf( ij ) = a( i, j )
521 ij = ij + 1
522 END DO
523*
524 END IF
525*
526 END IF
527*
528 END IF
529*
530 RETURN
531*
532* End of ZTRTTF
533*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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