 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ ztpttf()

 subroutine ztpttf ( character TRANSR, character UPLO, integer N, complex*16, dimension( 0: * ) AP, complex*16, dimension( 0: * ) ARF, integer INFO )

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

Purpose:
``` ZTPTTF copies a triangular matrix A from standard packed format (TP)
to rectangular full packed format (TF).```
Parameters
 [in] TRANSR ``` TRANSR is CHARACTER*1 = 'N': ARF in Normal format is wanted; = 'C': ARF in Conjugate-transpose format 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] AP ``` AP is COMPLEX*16 array, dimension ( N*(N+1)/2 ), On entry, the upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=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 206 of file ztpttf.f.

207 *
208 * -- LAPACK computational routine --
209 * -- LAPACK is a software package provided by Univ. of Tennessee, --
210 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
211 *
212 * .. Scalar Arguments ..
213  CHARACTER TRANSR, UPLO
214  INTEGER INFO, N
215 * ..
216 * .. Array Arguments ..
217  COMPLEX*16 AP( 0: * ), ARF( 0: * )
218 *
219 * =====================================================================
220 *
221 * .. Parameters ..
222 * ..
223 * .. Local Scalars ..
224  LOGICAL LOWER, NISODD, NORMALTRANSR
225  INTEGER N1, N2, K, NT
226  INTEGER I, J, IJ
227  INTEGER IJP, JP, LDA, JS
228 * ..
229 * .. External Functions ..
230  LOGICAL LSAME
231  EXTERNAL lsame
232 * ..
233 * .. External Subroutines ..
234  EXTERNAL xerbla
235 * ..
236 * .. Intrinsic Functions ..
237  INTRINSIC dconjg, mod
238 * ..
239 * .. Executable Statements ..
240 *
241 * Test the input parameters.
242 *
243  info = 0
244  normaltransr = lsame( transr, 'N' )
245  lower = lsame( uplo, 'L' )
246  IF( .NOT.normaltransr .AND. .NOT.lsame( transr, 'C' ) ) THEN
247  info = -1
248  ELSE IF( .NOT.lower .AND. .NOT.lsame( uplo, 'U' ) ) THEN
249  info = -2
250  ELSE IF( n.LT.0 ) THEN
251  info = -3
252  END IF
253  IF( info.NE.0 ) THEN
254  CALL xerbla( 'ZTPTTF', -info )
255  RETURN
256  END IF
257 *
258 * Quick return if possible
259 *
260  IF( n.EQ.0 )
261  \$ RETURN
262 *
263  IF( n.EQ.1 ) THEN
264  IF( normaltransr ) THEN
265  arf( 0 ) = ap( 0 )
266  ELSE
267  arf( 0 ) = dconjg( ap( 0 ) )
268  END IF
269  RETURN
270  END IF
271 *
272 * Size of array ARF(0:NT-1)
273 *
274  nt = n*( n+1 ) / 2
275 *
276 * Set N1 and N2 depending on LOWER
277 *
278  IF( lower ) THEN
279  n2 = n / 2
280  n1 = n - n2
281  ELSE
282  n1 = n / 2
283  n2 = n - n1
284  END IF
285 *
286 * If N is odd, set NISODD = .TRUE.
287 * If N is even, set K = N/2 and NISODD = .FALSE.
288 *
289 * set lda of ARF^C; ARF^C is (0:(N+1)/2-1,0:N-noe)
290 * where noe = 0 if n is even, noe = 1 if n is odd
291 *
292  IF( mod( n, 2 ).EQ.0 ) THEN
293  k = n / 2
294  nisodd = .false.
295  lda = n + 1
296  ELSE
297  nisodd = .true.
298  lda = n
299  END IF
300 *
301 * ARF^C has lda rows and n+1-noe cols
302 *
303  IF( .NOT.normaltransr )
304  \$ lda = ( n+1 ) / 2
305 *
306 * start execution: there are eight cases
307 *
308  IF( nisodd ) THEN
309 *
310 * N is odd
311 *
312  IF( normaltransr ) THEN
313 *
314 * N is odd and TRANSR = 'N'
315 *
316  IF( lower ) THEN
317 *
318 * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
319 * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
320 * T1 -> a(0), T2 -> a(n), S -> a(n1); lda = n
321 *
322  ijp = 0
323  jp = 0
324  DO j = 0, n2
325  DO i = j, n - 1
326  ij = i + jp
327  arf( ij ) = ap( ijp )
328  ijp = ijp + 1
329  END DO
330  jp = jp + lda
331  END DO
332  DO i = 0, n2 - 1
333  DO j = 1 + i, n2
334  ij = i + j*lda
335  arf( ij ) = dconjg( ap( ijp ) )
336  ijp = ijp + 1
337  END DO
338  END DO
339 *
340  ELSE
341 *
342 * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
343 * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
344 * T1 -> a(n2), T2 -> a(n1), S -> a(0)
345 *
346  ijp = 0
347  DO j = 0, n1 - 1
348  ij = n2 + j
349  DO i = 0, j
350  arf( ij ) = dconjg( ap( ijp ) )
351  ijp = ijp + 1
352  ij = ij + lda
353  END DO
354  END DO
355  js = 0
356  DO j = n1, n - 1
357  ij = js
358  DO ij = js, js + j
359  arf( ij ) = ap( ijp )
360  ijp = ijp + 1
361  END DO
362  js = js + lda
363  END DO
364 *
365  END IF
366 *
367  ELSE
368 *
369 * N is odd and TRANSR = 'C'
370 *
371  IF( lower ) THEN
372 *
373 * SRPA for LOWER, TRANSPOSE and N is odd
374 * T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
375 * T1 -> a(0+0) , T2 -> a(1+0) , S -> a(0+n1*n1); lda=n1
376 *
377  ijp = 0
378  DO i = 0, n2
379  DO ij = i*( lda+1 ), n*lda - 1, lda
380  arf( ij ) = dconjg( ap( ijp ) )
381  ijp = ijp + 1
382  END DO
383  END DO
384  js = 1
385  DO j = 0, n2 - 1
386  DO ij = js, js + n2 - j - 1
387  arf( ij ) = ap( ijp )
388  ijp = ijp + 1
389  END DO
390  js = js + lda + 1
391  END DO
392 *
393  ELSE
394 *
395 * SRPA for UPPER, TRANSPOSE and N is odd
396 * T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
397 * T1 -> a(n2*n2), T2 -> a(n1*n2), S -> a(0); lda = n2
398 *
399  ijp = 0
400  js = n2*lda
401  DO j = 0, n1 - 1
402  DO ij = js, js + j
403  arf( ij ) = ap( ijp )
404  ijp = ijp + 1
405  END DO
406  js = js + lda
407  END DO
408  DO i = 0, n1
409  DO ij = i, i + ( n1+i )*lda, lda
410  arf( ij ) = dconjg( ap( ijp ) )
411  ijp = ijp + 1
412  END DO
413  END DO
414 *
415  END IF
416 *
417  END IF
418 *
419  ELSE
420 *
421 * N is even
422 *
423  IF( normaltransr ) THEN
424 *
425 * N is even and TRANSR = 'N'
426 *
427  IF( lower ) THEN
428 *
429 * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
430 * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
431 * T1 -> a(1), T2 -> a(0), S -> a(k+1)
432 *
433  ijp = 0
434  jp = 0
435  DO j = 0, k - 1
436  DO i = j, n - 1
437  ij = 1 + i + jp
438  arf( ij ) = ap( ijp )
439  ijp = ijp + 1
440  END DO
441  jp = jp + lda
442  END DO
443  DO i = 0, k - 1
444  DO j = i, k - 1
445  ij = i + j*lda
446  arf( ij ) = dconjg( ap( ijp ) )
447  ijp = ijp + 1
448  END DO
449  END DO
450 *
451  ELSE
452 *
453 * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
454 * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
455 * T1 -> a(k+1), T2 -> a(k), S -> a(0)
456 *
457  ijp = 0
458  DO j = 0, k - 1
459  ij = k + 1 + j
460  DO i = 0, j
461  arf( ij ) = dconjg( ap( ijp ) )
462  ijp = ijp + 1
463  ij = ij + lda
464  END DO
465  END DO
466  js = 0
467  DO j = k, n - 1
468  ij = js
469  DO ij = js, js + j
470  arf( ij ) = ap( ijp )
471  ijp = ijp + 1
472  END DO
473  js = js + lda
474  END DO
475 *
476  END IF
477 *
478  ELSE
479 *
480 * N is even and TRANSR = 'C'
481 *
482  IF( lower ) THEN
483 *
484 * SRPA for LOWER, TRANSPOSE and N is even (see paper)
485 * T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
486 * T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
487 *
488  ijp = 0
489  DO i = 0, k - 1
490  DO ij = i + ( i+1 )*lda, ( n+1 )*lda - 1, lda
491  arf( ij ) = dconjg( ap( ijp ) )
492  ijp = ijp + 1
493  END DO
494  END DO
495  js = 0
496  DO j = 0, k - 1
497  DO ij = js, js + k - j - 1
498  arf( ij ) = ap( ijp )
499  ijp = ijp + 1
500  END DO
501  js = js + lda + 1
502  END DO
503 *
504  ELSE
505 *
506 * SRPA for UPPER, TRANSPOSE and N is even (see paper)
507 * T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0)
508 * T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
509 *
510  ijp = 0
511  js = ( k+1 )*lda
512  DO j = 0, k - 1
513  DO ij = js, js + j
514  arf( ij ) = ap( ijp )
515  ijp = ijp + 1
516  END DO
517  js = js + lda
518  END DO
519  DO i = 0, k - 1
520  DO ij = i, i + ( k+i )*lda, lda
521  arf( ij ) = dconjg( ap( ijp ) )
522  ijp = ijp + 1
523  END DO
524  END DO
525 *
526  END IF
527 *
528  END IF
529 *
530  END IF
531 *
532  RETURN
533 *
534 * End of ZTPTTF
535 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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