LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ ctftri()

subroutine ctftri ( character transr,
character uplo,
character diag,
integer n,
complex, dimension( 0: * ) a,
integer info )

CTFTRI

Download CTFTRI + dependencies [TGZ] [ZIP] [TXT]

Purpose:
!>
!> CTFTRI computes the inverse of a triangular matrix A stored in RFP
!> format.
!>
!> This is a Level 3 BLAS version of the algorithm.
!>
Parameters
[in]TRANSR
!>          TRANSR is CHARACTER*1
!>          = 'N':  The Normal TRANSR of RFP A is stored;
!>          = 'C':  The Conjugate-transpose TRANSR of RFP A is stored.
!>
[in]UPLO
!>          UPLO is CHARACTER*1
!>          = 'U':  A is upper triangular;
!>          = 'L':  A is lower triangular.
!>
[in]DIAG
!>          DIAG is CHARACTER*1
!>          = 'N':  A is non-unit triangular;
!>          = 'U':  A is unit triangular.
!>
[in]N
!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>
[in,out]A
!>          A is COMPLEX array, dimension ( N*(N+1)/2 );
!>          On entry, the triangular matrix A in RFP format. RFP format
!>          is described by TRANSR, UPLO, and N as follows: If TRANSR =
!>          'N' then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is
!>          (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'C' then RFP is
!>          the Conjugate-transpose of RFP A as defined when
!>          TRANSR = 'N'. The contents of RFP A are defined by UPLO as
!>          follows: If UPLO = 'U' the RFP A contains the nt elements of
!>          upper packed A; If UPLO = 'L' the RFP A contains the nt
!>          elements of lower packed A. The LDA of RFP A is (N+1)/2 when
!>          TRANSR = 'C'. When TRANSR is 'N' the LDA is N+1 when N is
!>          even and N is odd. See the Note below for more details.
!>
!>          On exit, the (triangular) inverse of the original matrix, in
!>          the same storage format.
!>
[out]INFO
!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -i, the i-th argument had an illegal value
!>          > 0: if INFO = i, A(i,i) is exactly zero.  The triangular
!>               matrix is singular and its inverse can not be computed.
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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 218 of file ctftri.f.

219*
220* -- LAPACK computational routine --
221* -- LAPACK is a software package provided by Univ. of Tennessee, --
222* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
223*
224* .. Scalar Arguments ..
225 CHARACTER TRANSR, UPLO, DIAG
226 INTEGER INFO, N
227* ..
228* .. Array Arguments ..
229 COMPLEX A( 0: * )
230* ..
231*
232* =====================================================================
233*
234* .. Parameters ..
235 COMPLEX CONE
236 parameter( cone = ( 1.0e+0, 0.0e+0 ) )
237* ..
238* .. Local Scalars ..
239 LOGICAL LOWER, NISODD, NORMALTRANSR
240 INTEGER N1, N2, K
241* ..
242* .. External Functions ..
243 LOGICAL LSAME
244 EXTERNAL lsame
245* ..
246* .. External Subroutines ..
247 EXTERNAL xerbla, ctrmm, ctrtri
248* ..
249* .. Intrinsic Functions ..
250 INTRINSIC mod
251* ..
252* .. Executable Statements ..
253*
254* Test the input parameters.
255*
256 info = 0
257 normaltransr = lsame( transr, 'N' )
258 lower = lsame( uplo, 'L' )
259 IF( .NOT.normaltransr .AND. .NOT.lsame( transr, 'C' ) ) THEN
260 info = -1
261 ELSE IF( .NOT.lower .AND. .NOT.lsame( uplo, 'U' ) ) THEN
262 info = -2
263 ELSE IF( .NOT.lsame( diag, 'N' ) .AND.
264 $ .NOT.lsame( diag, 'U' ) )
265 $ THEN
266 info = -3
267 ELSE IF( n.LT.0 ) THEN
268 info = -4
269 END IF
270 IF( info.NE.0 ) THEN
271 CALL xerbla( 'CTFTRI', -info )
272 RETURN
273 END IF
274*
275* Quick return if possible
276*
277 IF( n.EQ.0 )
278 $ RETURN
279*
280* If N is odd, set NISODD = .TRUE.
281* If N is even, set K = N/2 and NISODD = .FALSE.
282*
283 IF( mod( n, 2 ).EQ.0 ) THEN
284 k = n / 2
285 nisodd = .false.
286 ELSE
287 nisodd = .true.
288 END IF
289*
290* Set N1 and N2 depending on LOWER
291*
292 IF( lower ) THEN
293 n2 = n / 2
294 n1 = n - n2
295 ELSE
296 n1 = n / 2
297 n2 = n - n1
298 END IF
299*
300*
301* start execution: there are eight cases
302*
303 IF( nisodd ) THEN
304*
305* N is odd
306*
307 IF( normaltransr ) THEN
308*
309* N is odd and TRANSR = 'N'
310*
311 IF( lower ) THEN
312*
313* SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
314* T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
315* T1 -> a(0), T2 -> a(n), S -> a(n1)
316*
317 CALL ctrtri( 'L', diag, n1, a( 0 ), n, info )
318 IF( info.GT.0 )
319 $ RETURN
320 CALL ctrmm( 'R', 'L', 'N', diag, n2, n1, -cone,
321 $ a( 0 ),
322 $ n, a( n1 ), n )
323 CALL ctrtri( 'U', diag, n2, a( n ), n, info )
324 IF( info.GT.0 )
325 $ info = info + n1
326 IF( info.GT.0 )
327 $ RETURN
328 CALL ctrmm( 'L', 'U', 'C', diag, n2, n1, cone, a( n ),
329 $ n,
330 $ a( n1 ), n )
331*
332 ELSE
333*
334* SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
335* T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
336* T1 -> a(n2), T2 -> a(n1), S -> a(0)
337*
338 CALL ctrtri( 'L', diag, n1, a( n2 ), n, info )
339 IF( info.GT.0 )
340 $ RETURN
341 CALL ctrmm( 'L', 'L', 'C', diag, n1, n2, -cone,
342 $ a( n2 ),
343 $ n, a( 0 ), n )
344 CALL ctrtri( 'U', diag, n2, a( n1 ), n, info )
345 IF( info.GT.0 )
346 $ info = info + n1
347 IF( info.GT.0 )
348 $ RETURN
349 CALL ctrmm( 'R', 'U', 'N', diag, n1, n2, cone,
350 $ a( n1 ),
351 $ n, a( 0 ), n )
352*
353 END IF
354*
355 ELSE
356*
357* N is odd and TRANSR = 'C'
358*
359 IF( lower ) THEN
360*
361* SRPA for LOWER, TRANSPOSE and N is odd
362* T1 -> a(0), T2 -> a(1), S -> a(0+n1*n1)
363*
364 CALL ctrtri( 'U', diag, n1, a( 0 ), n1, info )
365 IF( info.GT.0 )
366 $ RETURN
367 CALL ctrmm( 'L', 'U', 'N', diag, n1, n2, -cone,
368 $ a( 0 ),
369 $ n1, a( n1*n1 ), n1 )
370 CALL ctrtri( 'L', diag, n2, a( 1 ), n1, info )
371 IF( info.GT.0 )
372 $ info = info + n1
373 IF( info.GT.0 )
374 $ RETURN
375 CALL ctrmm( 'R', 'L', 'C', diag, n1, n2, cone, a( 1 ),
376 $ n1, a( n1*n1 ), n1 )
377*
378 ELSE
379*
380* SRPA for UPPER, TRANSPOSE and N is odd
381* T1 -> a(0+n2*n2), T2 -> a(0+n1*n2), S -> a(0)
382*
383 CALL ctrtri( 'U', diag, n1, a( n2*n2 ), n2, info )
384 IF( info.GT.0 )
385 $ RETURN
386 CALL ctrmm( 'R', 'U', 'C', diag, n2, n1, -cone,
387 $ a( n2*n2 ), n2, a( 0 ), n2 )
388 CALL ctrtri( 'L', diag, n2, a( n1*n2 ), n2, info )
389 IF( info.GT.0 )
390 $ info = info + n1
391 IF( info.GT.0 )
392 $ RETURN
393 CALL ctrmm( 'L', 'L', 'N', diag, n2, n1, cone,
394 $ a( n1*n2 ), n2, a( 0 ), n2 )
395 END IF
396*
397 END IF
398*
399 ELSE
400*
401* N is even
402*
403 IF( normaltransr ) THEN
404*
405* N is even and TRANSR = 'N'
406*
407 IF( lower ) THEN
408*
409* SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
410* T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
411* T1 -> a(1), T2 -> a(0), S -> a(k+1)
412*
413 CALL ctrtri( 'L', diag, k, a( 1 ), n+1, info )
414 IF( info.GT.0 )
415 $ RETURN
416 CALL ctrmm( 'R', 'L', 'N', diag, k, k, -cone, a( 1 ),
417 $ n+1, a( k+1 ), n+1 )
418 CALL ctrtri( 'U', diag, k, a( 0 ), n+1, info )
419 IF( info.GT.0 )
420 $ info = info + k
421 IF( info.GT.0 )
422 $ RETURN
423 CALL ctrmm( 'L', 'U', 'C', diag, k, k, cone, a( 0 ),
424 $ n+1,
425 $ a( k+1 ), n+1 )
426*
427 ELSE
428*
429* SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
430* T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
431* T1 -> a(k+1), T2 -> a(k), S -> a(0)
432*
433 CALL ctrtri( 'L', diag, k, a( k+1 ), n+1, info )
434 IF( info.GT.0 )
435 $ RETURN
436 CALL ctrmm( 'L', 'L', 'C', diag, k, k, -cone,
437 $ a( k+1 ),
438 $ n+1, a( 0 ), n+1 )
439 CALL ctrtri( 'U', diag, k, a( k ), n+1, info )
440 IF( info.GT.0 )
441 $ info = info + k
442 IF( info.GT.0 )
443 $ RETURN
444 CALL ctrmm( 'R', 'U', 'N', diag, k, k, cone, a( k ),
445 $ n+1,
446 $ a( 0 ), n+1 )
447 END IF
448 ELSE
449*
450* N is even and TRANSR = 'C'
451*
452 IF( lower ) THEN
453*
454* SRPA for LOWER, TRANSPOSE and N is even (see paper)
455* T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
456* T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
457*
458 CALL ctrtri( 'U', diag, k, a( k ), k, info )
459 IF( info.GT.0 )
460 $ RETURN
461 CALL ctrmm( 'L', 'U', 'N', diag, k, k, -cone, a( k ),
462 $ k,
463 $ a( k*( k+1 ) ), k )
464 CALL ctrtri( 'L', diag, k, a( 0 ), k, info )
465 IF( info.GT.0 )
466 $ info = info + k
467 IF( info.GT.0 )
468 $ RETURN
469 CALL ctrmm( 'R', 'L', 'C', diag, k, k, cone, a( 0 ),
470 $ k,
471 $ a( k*( k+1 ) ), k )
472 ELSE
473*
474* SRPA for UPPER, TRANSPOSE and N is even (see paper)
475* T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0)
476* T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
477*
478 CALL ctrtri( 'U', diag, k, a( k*( k+1 ) ), k, info )
479 IF( info.GT.0 )
480 $ RETURN
481 CALL ctrmm( 'R', 'U', 'C', diag, k, k, -cone,
482 $ a( k*( k+1 ) ), k, a( 0 ), k )
483 CALL ctrtri( 'L', diag, k, a( k*k ), k, info )
484 IF( info.GT.0 )
485 $ info = info + k
486 IF( info.GT.0 )
487 $ RETURN
488 CALL ctrmm( 'L', 'L', 'N', diag, k, k, cone, a( k*k ),
489 $ k,
490 $ a( 0 ), k )
491 END IF
492 END IF
493 END IF
494*
495 RETURN
496*
497* End of CTFTRI
498*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
ctrmm
subroutine ctrmm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
CTRMM
Definition ctrmm.f:177
ctrtri
subroutine ctrtri(uplo, diag, n, a, lda, info)
CTRTRI
Definition ctrtri.f:107
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