LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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chfrk.f
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1*> \brief \b CHFRK performs a Hermitian rank-k operation for matrix in RFP format.
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download CHFRK + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chfrk.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chfrk.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chfrk.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE CHFRK( TRANSR, UPLO, TRANS, N, K, ALPHA, A, LDA, BETA,
22* C )
23*
24* .. Scalar Arguments ..
25* REAL ALPHA, BETA
26* INTEGER K, LDA, N
27* CHARACTER TRANS, TRANSR, UPLO
28* ..
29* .. Array Arguments ..
30* COMPLEX A( LDA, * ), C( * )
31* ..
32*
33*
34*> \par Purpose:
35* =============
36*>
37*> \verbatim
38*>
39*> Level 3 BLAS like routine for C in RFP Format.
40*>
41*> CHFRK performs one of the Hermitian rank--k operations
42*>
43*> C := alpha*A*A**H + beta*C,
44*>
45*> or
46*>
47*> C := alpha*A**H*A + beta*C,
48*>
49*> where alpha and beta are real scalars, C is an n--by--n Hermitian
50*> matrix and A is an n--by--k matrix in the first case and a k--by--n
51*> matrix in the second case.
52*> \endverbatim
53*
54* Arguments:
55* ==========
56*
57*> \param[in] TRANSR
58*> \verbatim
59*> TRANSR is CHARACTER*1
60*> = 'N': The Normal Form of RFP A is stored;
61*> = 'C': The Conjugate-transpose Form of RFP A is stored.
62*> \endverbatim
63*>
64*> \param[in] UPLO
65*> \verbatim
66*> UPLO is CHARACTER*1
67*> On entry, UPLO specifies whether the upper or lower
68*> triangular part of the array C is to be referenced as
69*> follows:
70*>
71*> UPLO = 'U' or 'u' Only the upper triangular part of C
72*> is to be referenced.
73*>
74*> UPLO = 'L' or 'l' Only the lower triangular part of C
75*> is to be referenced.
76*>
77*> Unchanged on exit.
78*> \endverbatim
79*>
80*> \param[in] TRANS
81*> \verbatim
82*> TRANS is CHARACTER*1
83*> On entry, TRANS specifies the operation to be performed as
84*> follows:
85*>
86*> TRANS = 'N' or 'n' C := alpha*A*A**H + beta*C.
87*>
88*> TRANS = 'C' or 'c' C := alpha*A**H*A + beta*C.
89*>
90*> Unchanged on exit.
91*> \endverbatim
92*>
93*> \param[in] N
94*> \verbatim
95*> N is INTEGER
96*> On entry, N specifies the order of the matrix C. N must be
97*> at least zero.
98*> Unchanged on exit.
99*> \endverbatim
100*>
101*> \param[in] K
102*> \verbatim
103*> K is INTEGER
104*> On entry with TRANS = 'N' or 'n', K specifies the number
105*> of columns of the matrix A, and on entry with
106*> TRANS = 'C' or 'c', K specifies the number of rows of the
107*> matrix A. K must be at least zero.
108*> Unchanged on exit.
109*> \endverbatim
110*>
111*> \param[in] ALPHA
112*> \verbatim
113*> ALPHA is REAL
114*> On entry, ALPHA specifies the scalar alpha.
115*> Unchanged on exit.
116*> \endverbatim
117*>
118*> \param[in] A
119*> \verbatim
120*> A is COMPLEX array, dimension (LDA,ka)
121*> where KA
122*> is K when TRANS = 'N' or 'n', and is N otherwise. Before
123*> entry with TRANS = 'N' or 'n', the leading N--by--K part of
124*> the array A must contain the matrix A, otherwise the leading
125*> K--by--N part of the array A must contain the matrix A.
126*> Unchanged on exit.
127*> \endverbatim
128*>
129*> \param[in] LDA
130*> \verbatim
131*> LDA is INTEGER
132*> On entry, LDA specifies the first dimension of A as declared
133*> in the calling (sub) program. When TRANS = 'N' or 'n'
134*> then LDA must be at least max( 1, n ), otherwise LDA must
135*> be at least max( 1, k ).
136*> Unchanged on exit.
137*> \endverbatim
138*>
139*> \param[in] BETA
140*> \verbatim
141*> BETA is REAL
142*> On entry, BETA specifies the scalar beta.
143*> Unchanged on exit.
144*> \endverbatim
145*>
146*> \param[in,out] C
147*> \verbatim
148*> C is COMPLEX array, dimension (N*(N+1)/2)
149*> On entry, the matrix A in RFP Format. RFP Format is
150*> described by TRANSR, UPLO and N. Note that the imaginary
151*> parts of the diagonal elements need not be set, they are
152*> assumed to be zero, and on exit they are set to zero.
153*> \endverbatim
154*
155* Authors:
156* ========
157*
158*> \author Univ. of Tennessee
159*> \author Univ. of California Berkeley
160*> \author Univ. of Colorado Denver
161*> \author NAG Ltd.
162*
163*> \ingroup complexOTHERcomputational
164*
165* =====================================================================
166 SUBROUTINE chfrk( TRANSR, UPLO, TRANS, N, K, ALPHA, A, LDA, BETA,
167 $ C )
168*
169* -- LAPACK computational routine --
170* -- LAPACK is a software package provided by Univ. of Tennessee, --
171* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
172*
173* .. Scalar Arguments ..
174 REAL ALPHA, BETA
175 INTEGER K, LDA, N
176 CHARACTER TRANS, TRANSR, UPLO
177* ..
178* .. Array Arguments ..
179 COMPLEX A( LDA, * ), C( * )
180* ..
181*
182* =====================================================================
183*
184* ..
185* .. Parameters ..
186 REAL ONE, ZERO
187 COMPLEX CZERO
188 parameter( one = 1.0e+0, zero = 0.0e+0 )
189 parameter( czero = ( 0.0e+0, 0.0e+0 ) )
190* ..
191* .. Local Scalars ..
192 LOGICAL LOWER, NORMALTRANSR, NISODD, NOTRANS
193 INTEGER INFO, NROWA, J, NK, N1, N2
194 COMPLEX CALPHA, CBETA
195* ..
196* .. External Functions ..
197 LOGICAL LSAME
198 EXTERNAL lsame
199* ..
200* .. External Subroutines ..
201 EXTERNAL cgemm, cherk, xerbla
202* ..
203* .. Intrinsic Functions ..
204 INTRINSIC max, cmplx
205* ..
206* .. Executable Statements ..
207*
208*
209* Test the input parameters.
210*
211 info = 0
212 normaltransr = lsame( transr, 'N' )
213 lower = lsame( uplo, 'L' )
214 notrans = lsame( trans, 'N' )
215*
216 IF( notrans ) THEN
217 nrowa = n
218 ELSE
219 nrowa = k
220 END IF
221*
222 IF( .NOT.normaltransr .AND. .NOT.lsame( transr, 'C' ) ) THEN
223 info = -1
224 ELSE IF( .NOT.lower .AND. .NOT.lsame( uplo, 'U' ) ) THEN
225 info = -2
226 ELSE IF( .NOT.notrans .AND. .NOT.lsame( trans, 'C' ) ) THEN
227 info = -3
228 ELSE IF( n.LT.0 ) THEN
229 info = -4
230 ELSE IF( k.LT.0 ) THEN
231 info = -5
232 ELSE IF( lda.LT.max( 1, nrowa ) ) THEN
233 info = -8
234 END IF
235 IF( info.NE.0 ) THEN
236 CALL xerbla( 'CHFRK ', -info )
237 RETURN
238 END IF
239*
240* Quick return if possible.
241*
242* The quick return case: ((ALPHA.EQ.0).AND.(BETA.NE.ZERO)) is not
243* done (it is in CHERK for example) and left in the general case.
244*
245 IF( ( n.EQ.0 ) .OR. ( ( ( alpha.EQ.zero ) .OR. ( k.EQ.0 ) ) .AND.
246 $ ( beta.EQ.one ) ) )RETURN
247*
248 IF( ( alpha.EQ.zero ) .AND. ( beta.EQ.zero ) ) THEN
249 DO j = 1, ( ( n*( n+1 ) ) / 2 )
250 c( j ) = czero
251 END DO
252 RETURN
253 END IF
254*
255 calpha = cmplx( alpha, zero )
256 cbeta = cmplx( beta, zero )
257*
258* C is N-by-N.
259* If N is odd, set NISODD = .TRUE., and N1 and N2.
260* If N is even, NISODD = .FALSE., and NK.
261*
262 IF( mod( n, 2 ).EQ.0 ) THEN
263 nisodd = .false.
264 nk = n / 2
265 ELSE
266 nisodd = .true.
267 IF( lower ) THEN
268 n2 = n / 2
269 n1 = n - n2
270 ELSE
271 n1 = n / 2
272 n2 = n - n1
273 END IF
274 END IF
275*
276 IF( nisodd ) THEN
277*
278* N is odd
279*
280 IF( normaltransr ) THEN
281*
282* N is odd and TRANSR = 'N'
283*
284 IF( lower ) THEN
285*
286* N is odd, TRANSR = 'N', and UPLO = 'L'
287*
288 IF( notrans ) THEN
289*
290* N is odd, TRANSR = 'N', UPLO = 'L', and TRANS = 'N'
291*
292 CALL cherk( 'L', 'N', n1, k, alpha, a( 1, 1 ), lda,
293 $ beta, c( 1 ), n )
294 CALL cherk( 'U', 'N', n2, k, alpha, a( n1+1, 1 ), lda,
295 $ beta, c( n+1 ), n )
296 CALL cgemm( 'N', 'C', n2, n1, k, calpha, a( n1+1, 1 ),
297 $ lda, a( 1, 1 ), lda, cbeta, c( n1+1 ), n )
298*
299 ELSE
300*
301* N is odd, TRANSR = 'N', UPLO = 'L', and TRANS = 'C'
302*
303 CALL cherk( 'L', 'C', n1, k, alpha, a( 1, 1 ), lda,
304 $ beta, c( 1 ), n )
305 CALL cherk( 'U', 'C', n2, k, alpha, a( 1, n1+1 ), lda,
306 $ beta, c( n+1 ), n )
307 CALL cgemm( 'C', 'N', n2, n1, k, calpha, a( 1, n1+1 ),
308 $ lda, a( 1, 1 ), lda, cbeta, c( n1+1 ), n )
309*
310 END IF
311*
312 ELSE
313*
314* N is odd, TRANSR = 'N', and UPLO = 'U'
315*
316 IF( notrans ) THEN
317*
318* N is odd, TRANSR = 'N', UPLO = 'U', and TRANS = 'N'
319*
320 CALL cherk( 'L', 'N', n1, k, alpha, a( 1, 1 ), lda,
321 $ beta, c( n2+1 ), n )
322 CALL cherk( 'U', 'N', n2, k, alpha, a( n2, 1 ), lda,
323 $ beta, c( n1+1 ), n )
324 CALL cgemm( 'N', 'C', n1, n2, k, calpha, a( 1, 1 ),
325 $ lda, a( n2, 1 ), lda, cbeta, c( 1 ), n )
326*
327 ELSE
328*
329* N is odd, TRANSR = 'N', UPLO = 'U', and TRANS = 'C'
330*
331 CALL cherk( 'L', 'C', n1, k, alpha, a( 1, 1 ), lda,
332 $ beta, c( n2+1 ), n )
333 CALL cherk( 'U', 'C', n2, k, alpha, a( 1, n2 ), lda,
334 $ beta, c( n1+1 ), n )
335 CALL cgemm( 'C', 'N', n1, n2, k, calpha, a( 1, 1 ),
336 $ lda, a( 1, n2 ), lda, cbeta, c( 1 ), n )
337*
338 END IF
339*
340 END IF
341*
342 ELSE
343*
344* N is odd, and TRANSR = 'C'
345*
346 IF( lower ) THEN
347*
348* N is odd, TRANSR = 'C', and UPLO = 'L'
349*
350 IF( notrans ) THEN
351*
352* N is odd, TRANSR = 'C', UPLO = 'L', and TRANS = 'N'
353*
354 CALL cherk( 'U', 'N', n1, k, alpha, a( 1, 1 ), lda,
355 $ beta, c( 1 ), n1 )
356 CALL cherk( 'L', 'N', n2, k, alpha, a( n1+1, 1 ), lda,
357 $ beta, c( 2 ), n1 )
358 CALL cgemm( 'N', 'C', n1, n2, k, calpha, a( 1, 1 ),
359 $ lda, a( n1+1, 1 ), lda, cbeta,
360 $ c( n1*n1+1 ), n1 )
361*
362 ELSE
363*
364* N is odd, TRANSR = 'C', UPLO = 'L', and TRANS = 'C'
365*
366 CALL cherk( 'U', 'C', n1, k, alpha, a( 1, 1 ), lda,
367 $ beta, c( 1 ), n1 )
368 CALL cherk( 'L', 'C', n2, k, alpha, a( 1, n1+1 ), lda,
369 $ beta, c( 2 ), n1 )
370 CALL cgemm( 'C', 'N', n1, n2, k, calpha, a( 1, 1 ),
371 $ lda, a( 1, n1+1 ), lda, cbeta,
372 $ c( n1*n1+1 ), n1 )
373*
374 END IF
375*
376 ELSE
377*
378* N is odd, TRANSR = 'C', and UPLO = 'U'
379*
380 IF( notrans ) THEN
381*
382* N is odd, TRANSR = 'C', UPLO = 'U', and TRANS = 'N'
383*
384 CALL cherk( 'U', 'N', n1, k, alpha, a( 1, 1 ), lda,
385 $ beta, c( n2*n2+1 ), n2 )
386 CALL cherk( 'L', 'N', n2, k, alpha, a( n1+1, 1 ), lda,
387 $ beta, c( n1*n2+1 ), n2 )
388 CALL cgemm( 'N', 'C', n2, n1, k, calpha, a( n1+1, 1 ),
389 $ lda, a( 1, 1 ), lda, cbeta, c( 1 ), n2 )
390*
391 ELSE
392*
393* N is odd, TRANSR = 'C', UPLO = 'U', and TRANS = 'C'
394*
395 CALL cherk( 'U', 'C', n1, k, alpha, a( 1, 1 ), lda,
396 $ beta, c( n2*n2+1 ), n2 )
397 CALL cherk( 'L', 'C', n2, k, alpha, a( 1, n1+1 ), lda,
398 $ beta, c( n1*n2+1 ), n2 )
399 CALL cgemm( 'C', 'N', n2, n1, k, calpha, a( 1, n1+1 ),
400 $ lda, a( 1, 1 ), lda, cbeta, c( 1 ), n2 )
401*
402 END IF
403*
404 END IF
405*
406 END IF
407*
408 ELSE
409*
410* N is even
411*
412 IF( normaltransr ) THEN
413*
414* N is even and TRANSR = 'N'
415*
416 IF( lower ) THEN
417*
418* N is even, TRANSR = 'N', and UPLO = 'L'
419*
420 IF( notrans ) THEN
421*
422* N is even, TRANSR = 'N', UPLO = 'L', and TRANS = 'N'
423*
424 CALL cherk( 'L', 'N', nk, k, alpha, a( 1, 1 ), lda,
425 $ beta, c( 2 ), n+1 )
426 CALL cherk( 'U', 'N', nk, k, alpha, a( nk+1, 1 ), lda,
427 $ beta, c( 1 ), n+1 )
428 CALL cgemm( 'N', 'C', nk, nk, k, calpha, a( nk+1, 1 ),
429 $ lda, a( 1, 1 ), lda, cbeta, c( nk+2 ),
430 $ n+1 )
431*
432 ELSE
433*
434* N is even, TRANSR = 'N', UPLO = 'L', and TRANS = 'C'
435*
436 CALL cherk( 'L', 'C', nk, k, alpha, a( 1, 1 ), lda,
437 $ beta, c( 2 ), n+1 )
438 CALL cherk( 'U', 'C', nk, k, alpha, a( 1, nk+1 ), lda,
439 $ beta, c( 1 ), n+1 )
440 CALL cgemm( 'C', 'N', nk, nk, k, calpha, a( 1, nk+1 ),
441 $ lda, a( 1, 1 ), lda, cbeta, c( nk+2 ),
442 $ n+1 )
443*
444 END IF
445*
446 ELSE
447*
448* N is even, TRANSR = 'N', and UPLO = 'U'
449*
450 IF( notrans ) THEN
451*
452* N is even, TRANSR = 'N', UPLO = 'U', and TRANS = 'N'
453*
454 CALL cherk( 'L', 'N', nk, k, alpha, a( 1, 1 ), lda,
455 $ beta, c( nk+2 ), n+1 )
456 CALL cherk( 'U', 'N', nk, k, alpha, a( nk+1, 1 ), lda,
457 $ beta, c( nk+1 ), n+1 )
458 CALL cgemm( 'N', 'C', nk, nk, k, calpha, a( 1, 1 ),
459 $ lda, a( nk+1, 1 ), lda, cbeta, c( 1 ),
460 $ n+1 )
461*
462 ELSE
463*
464* N is even, TRANSR = 'N', UPLO = 'U', and TRANS = 'C'
465*
466 CALL cherk( 'L', 'C', nk, k, alpha, a( 1, 1 ), lda,
467 $ beta, c( nk+2 ), n+1 )
468 CALL cherk( 'U', 'C', nk, k, alpha, a( 1, nk+1 ), lda,
469 $ beta, c( nk+1 ), n+1 )
470 CALL cgemm( 'C', 'N', nk, nk, k, calpha, a( 1, 1 ),
471 $ lda, a( 1, nk+1 ), lda, cbeta, c( 1 ),
472 $ n+1 )
473*
474 END IF
475*
476 END IF
477*
478 ELSE
479*
480* N is even, and TRANSR = 'C'
481*
482 IF( lower ) THEN
483*
484* N is even, TRANSR = 'C', and UPLO = 'L'
485*
486 IF( notrans ) THEN
487*
488* N is even, TRANSR = 'C', UPLO = 'L', and TRANS = 'N'
489*
490 CALL cherk( 'U', 'N', nk, k, alpha, a( 1, 1 ), lda,
491 $ beta, c( nk+1 ), nk )
492 CALL cherk( 'L', 'N', nk, k, alpha, a( nk+1, 1 ), lda,
493 $ beta, c( 1 ), nk )
494 CALL cgemm( 'N', 'C', nk, nk, k, calpha, a( 1, 1 ),
495 $ lda, a( nk+1, 1 ), lda, cbeta,
496 $ c( ( ( nk+1 )*nk )+1 ), nk )
497*
498 ELSE
499*
500* N is even, TRANSR = 'C', UPLO = 'L', and TRANS = 'C'
501*
502 CALL cherk( 'U', 'C', nk, k, alpha, a( 1, 1 ), lda,
503 $ beta, c( nk+1 ), nk )
504 CALL cherk( 'L', 'C', nk, k, alpha, a( 1, nk+1 ), lda,
505 $ beta, c( 1 ), nk )
506 CALL cgemm( 'C', 'N', nk, nk, k, calpha, a( 1, 1 ),
507 $ lda, a( 1, nk+1 ), lda, cbeta,
508 $ c( ( ( nk+1 )*nk )+1 ), nk )
509*
510 END IF
511*
512 ELSE
513*
514* N is even, TRANSR = 'C', and UPLO = 'U'
515*
516 IF( notrans ) THEN
517*
518* N is even, TRANSR = 'C', UPLO = 'U', and TRANS = 'N'
519*
520 CALL cherk( 'U', 'N', nk, k, alpha, a( 1, 1 ), lda,
521 $ beta, c( nk*( nk+1 )+1 ), nk )
522 CALL cherk( 'L', 'N', nk, k, alpha, a( nk+1, 1 ), lda,
523 $ beta, c( nk*nk+1 ), nk )
524 CALL cgemm( 'N', 'C', nk, nk, k, calpha, a( nk+1, 1 ),
525 $ lda, a( 1, 1 ), lda, cbeta, c( 1 ), nk )
526*
527 ELSE
528*
529* N is even, TRANSR = 'C', UPLO = 'U', and TRANS = 'C'
530*
531 CALL cherk( 'U', 'C', nk, k, alpha, a( 1, 1 ), lda,
532 $ beta, c( nk*( nk+1 )+1 ), nk )
533 CALL cherk( 'L', 'C', nk, k, alpha, a( 1, nk+1 ), lda,
534 $ beta, c( nk*nk+1 ), nk )
535 CALL cgemm( 'C', 'N', nk, nk, k, calpha, a( 1, nk+1 ),
536 $ lda, a( 1, 1 ), lda, cbeta, c( 1 ), nk )
537*
538 END IF
539*
540 END IF
541*
542 END IF
543*
544 END IF
545*
546 RETURN
547*
548* End of CHFRK
549*
550 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine cgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
CGEMM
Definition: cgemm.f:187
subroutine cherk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
CHERK
Definition: cherk.f:173
subroutine chfrk(TRANSR, UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C)
CHFRK performs a Hermitian rank-k operation for matrix in RFP format.
Definition: chfrk.f:168