LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ cher2k()

subroutine cher2k ( character uplo,
character trans,
integer n,
integer k,
complex alpha,
complex, dimension(lda,*) a,
integer lda,
complex, dimension(ldb,*) b,
integer ldb,
real beta,
complex, dimension(ldc,*) c,
integer ldc )

CHER2K

Purpose:
!>
!> CHER2K  performs one of the hermitian rank 2k operations
!>
!>    C := alpha*A*B**H + conjg( alpha )*B*A**H + beta*C,
!>
!> or
!>
!>    C := alpha*A**H*B + conjg( alpha )*B**H*A + beta*C,
!>
!> where  alpha and beta  are scalars with  beta  real,  C is an  n by n
!> hermitian matrix and  A and B  are  n by k matrices in the first case
!> and  k by n  matrices in the second case.
!>
Parameters
[in]UPLO
!>          UPLO is CHARACTER*1
!>           On  entry,   UPLO  specifies  whether  the  upper  or  lower
!>           triangular  part  of the  array  C  is to be  referenced  as
!>           follows:
!>
!>              UPLO = 'U' or 'u'   Only the  upper triangular part of  C
!>                                  is to be referenced.
!>
!>              UPLO = 'L' or 'l'   Only the  lower triangular part of  C
!>                                  is to be referenced.
!>
[in]TRANS
!>          TRANS is CHARACTER*1
!>           On entry,  TRANS  specifies the operation to be performed as
!>           follows:
!>
!>              TRANS = 'N' or 'n'    C := alpha*A*B**H          +
!>                                         conjg( alpha )*B*A**H +
!>                                         beta*C.
!>
!>              TRANS = 'C' or 'c'    C := alpha*A**H*B          +
!>                                         conjg( alpha )*B**H*A +
!>                                         beta*C.
!>
[in]N
!>          N is INTEGER
!>           On entry,  N specifies the order of the matrix C.  N must be
!>           at least zero.
!>
[in]K
!>          K is INTEGER
!>           On entry with  TRANS = 'N' or 'n',  K  specifies  the number
!>           of  columns  of the  matrices  A and B,  and on  entry  with
!>           TRANS = 'C' or 'c',  K  specifies  the number of rows of the
!>           matrices  A and B.  K must be at least zero.
!>
[in]ALPHA
!>          ALPHA is COMPLEX
!>           On entry, ALPHA specifies the scalar alpha.
!>
[in]A
!>          A is COMPLEX array, dimension ( LDA, ka ), where ka is
!>           k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
!>           Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
!>           part of the array  A  must contain the matrix  A,  otherwise
!>           the leading  k by n  part of the array  A  must contain  the
!>           matrix A.
!>
[in]LDA
!>          LDA is INTEGER
!>           On entry, LDA specifies the first dimension of A as declared
!>           in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
!>           then  LDA must be at least  max( 1, n ), otherwise  LDA must
!>           be at least  max( 1, k ).
!>
[in]B
!>          B is COMPLEX array, dimension ( LDB, kb ), where kb is
!>           k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
!>           Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
!>           part of the array  B  must contain the matrix  B,  otherwise
!>           the leading  k by n  part of the array  B  must contain  the
!>           matrix B.
!>
[in]LDB
!>          LDB is INTEGER
!>           On entry, LDB specifies the first dimension of B as declared
!>           in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
!>           then  LDB must be at least  max( 1, n ), otherwise  LDB must
!>           be at least  max( 1, k ).
!>
[in]BETA
!>          BETA is REAL
!>           On entry, BETA specifies the scalar beta.
!>
[in,out]C
!>          C is COMPLEX array, dimension ( LDC, N )
!>           Before entry  with  UPLO = 'U' or 'u',  the leading  n by n
!>           upper triangular part of the array C must contain the upper
!>           triangular part  of the  hermitian matrix  and the strictly
!>           lower triangular part of C is not referenced.  On exit, the
!>           upper triangular part of the array  C is overwritten by the
!>           upper triangular part of the updated matrix.
!>           Before entry  with  UPLO = 'L' or 'l',  the leading  n by n
!>           lower triangular part of the array C must contain the lower
!>           triangular part  of the  hermitian matrix  and the strictly
!>           upper triangular part of C is not referenced.  On exit, the
!>           lower triangular part of the array  C is overwritten by the
!>           lower triangular part of the updated matrix.
!>           Note that the imaginary parts of the diagonal elements need
!>           not be set,  they are assumed to be zero,  and on exit they
!>           are set to zero.
!>
[in]LDC
!>          LDC is INTEGER
!>           On entry, LDC specifies the first dimension of C as declared
!>           in  the  calling  (sub)  program.   LDC  must  be  at  least
!>           max( 1, n ).
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
!>
!>  Level 3 Blas routine.
!>
!>  -- Written on 8-February-1989.
!>     Jack Dongarra, Argonne National Laboratory.
!>     Iain Duff, AERE Harwell.
!>     Jeremy Du Croz, Numerical Algorithms Group Ltd.
!>     Sven Hammarling, Numerical Algorithms Group Ltd.
!>
!>  -- Modified 8-Nov-93 to set C(J,J) to REAL( C(J,J) ) when BETA = 1.
!>     Ed Anderson, Cray Research Inc.
!>

Definition at line 196 of file cher2k.f.

197*
198* -- Reference BLAS level3 routine --
199* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
200* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
201*
202* .. Scalar Arguments ..
203 COMPLEX ALPHA
204 REAL BETA
205 INTEGER K,LDA,LDB,LDC,N
206 CHARACTER TRANS,UPLO
207* ..
208* .. Array Arguments ..
209 COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
210* ..
211*
212* =====================================================================
213*
214* .. External Functions ..
215 LOGICAL LSAME
216 EXTERNAL lsame
217* ..
218* .. External Subroutines ..
219 EXTERNAL xerbla
220* ..
221* .. Intrinsic Functions ..
222 INTRINSIC conjg,max,real
223* ..
224* .. Local Scalars ..
225 COMPLEX TEMP1,TEMP2
226 INTEGER I,INFO,J,L,NROWA
227 LOGICAL UPPER
228* ..
229* .. Parameters ..
230 REAL ONE
231 parameter(one=1.0e+0)
232 COMPLEX ZERO
233 parameter(zero= (0.0e+0,0.0e+0))
234* ..
235*
236* Test the input parameters.
237*
238 IF (lsame(trans,'N')) THEN
239 nrowa = n
240 ELSE
241 nrowa = k
242 END IF
243 upper = lsame(uplo,'U')
244*
245 info = 0
246 IF ((.NOT.upper) .AND. (.NOT.lsame(uplo,'L'))) THEN
247 info = 1
248 ELSE IF ((.NOT.lsame(trans,'N')) .AND.
249 + (.NOT.lsame(trans,'C'))) THEN
250 info = 2
251 ELSE IF (n.LT.0) THEN
252 info = 3
253 ELSE IF (k.LT.0) THEN
254 info = 4
255 ELSE IF (lda.LT.max(1,nrowa)) THEN
256 info = 7
257 ELSE IF (ldb.LT.max(1,nrowa)) THEN
258 info = 9
259 ELSE IF (ldc.LT.max(1,n)) THEN
260 info = 12
261 END IF
262 IF (info.NE.0) THEN
263 CALL xerbla('CHER2K',info)
264 RETURN
265 END IF
266*
267* Quick return if possible.
268*
269 IF ((n.EQ.0) .OR. (((alpha.EQ.zero).OR.
270 + (k.EQ.0)).AND. (beta.EQ.one))) RETURN
271*
272* And when alpha.eq.zero.
273*
274 IF (alpha.EQ.zero) THEN
275 IF (upper) THEN
276 IF (beta.EQ.real(zero)) THEN
277 DO 20 j = 1,n
278 DO 10 i = 1,j
279 c(i,j) = zero
280 10 CONTINUE
281 20 CONTINUE
282 ELSE
283 DO 40 j = 1,n
284 DO 30 i = 1,j - 1
285 c(i,j) = beta*c(i,j)
286 30 CONTINUE
287 c(j,j) = beta*real(c(j,j))
288 40 CONTINUE
289 END IF
290 ELSE
291 IF (beta.EQ.real(zero)) THEN
292 DO 60 j = 1,n
293 DO 50 i = j,n
294 c(i,j) = zero
295 50 CONTINUE
296 60 CONTINUE
297 ELSE
298 DO 80 j = 1,n
299 c(j,j) = beta*real(c(j,j))
300 DO 70 i = j + 1,n
301 c(i,j) = beta*c(i,j)
302 70 CONTINUE
303 80 CONTINUE
304 END IF
305 END IF
306 RETURN
307 END IF
308*
309* Start the operations.
310*
311 IF (lsame(trans,'N')) THEN
312*
313* Form C := alpha*A*B**H + conjg( alpha )*B*A**H +
314* C.
315*
316 IF (upper) THEN
317 DO 130 j = 1,n
318 IF (beta.EQ.real(zero)) THEN
319 DO 90 i = 1,j
320 c(i,j) = zero
321 90 CONTINUE
322 ELSE IF (beta.NE.one) THEN
323 DO 100 i = 1,j - 1
324 c(i,j) = beta*c(i,j)
325 100 CONTINUE
326 c(j,j) = beta*real(c(j,j))
327 ELSE
328 c(j,j) = real(c(j,j))
329 END IF
330 DO 120 l = 1,k
331 IF ((a(j,l).NE.zero) .OR. (b(j,l).NE.zero)) THEN
332 temp1 = alpha*conjg(b(j,l))
333 temp2 = conjg(alpha*a(j,l))
334 DO 110 i = 1,j - 1
335 c(i,j) = c(i,j) + a(i,l)*temp1 +
336 + b(i,l)*temp2
337 110 CONTINUE
338 c(j,j) = real(c(j,j)) +
339 + real(a(j,l)*temp1+b(j,l)*temp2)
340 END IF
341 120 CONTINUE
342 130 CONTINUE
343 ELSE
344 DO 180 j = 1,n
345 IF (beta.EQ.real(zero)) THEN
346 DO 140 i = j,n
347 c(i,j) = zero
348 140 CONTINUE
349 ELSE IF (beta.NE.one) THEN
350 DO 150 i = j + 1,n
351 c(i,j) = beta*c(i,j)
352 150 CONTINUE
353 c(j,j) = beta*real(c(j,j))
354 ELSE
355 c(j,j) = real(c(j,j))
356 END IF
357 DO 170 l = 1,k
358 IF ((a(j,l).NE.zero) .OR. (b(j,l).NE.zero)) THEN
359 temp1 = alpha*conjg(b(j,l))
360 temp2 = conjg(alpha*a(j,l))
361 DO 160 i = j + 1,n
362 c(i,j) = c(i,j) + a(i,l)*temp1 +
363 + b(i,l)*temp2
364 160 CONTINUE
365 c(j,j) = real(c(j,j)) +
366 + real(a(j,l)*temp1+b(j,l)*temp2)
367 END IF
368 170 CONTINUE
369 180 CONTINUE
370 END IF
371 ELSE
372*
373* Form C := alpha*A**H*B + conjg( alpha )*B**H*A +
374* C.
375*
376 IF (upper) THEN
377 DO 210 j = 1,n
378 DO 200 i = 1,j
379 temp1 = zero
380 temp2 = zero
381 DO 190 l = 1,k
382 temp1 = temp1 + conjg(a(l,i))*b(l,j)
383 temp2 = temp2 + conjg(b(l,i))*a(l,j)
384 190 CONTINUE
385 IF (i.EQ.j) THEN
386 IF (beta.EQ.real(zero)) THEN
387 c(j,j) = real(alpha*temp1+
388 + conjg(alpha)*temp2)
389 ELSE
390 c(j,j) = beta*real(c(j,j)) +
391 + real(alpha*temp1+
392 + conjg(alpha)*temp2)
393 END IF
394 ELSE
395 IF (beta.EQ.real(zero)) THEN
396 c(i,j) = alpha*temp1 + conjg(alpha)*temp2
397 ELSE
398 c(i,j) = beta*c(i,j) + alpha*temp1 +
399 + conjg(alpha)*temp2
400 END IF
401 END IF
402 200 CONTINUE
403 210 CONTINUE
404 ELSE
405 DO 240 j = 1,n
406 DO 230 i = j,n
407 temp1 = zero
408 temp2 = zero
409 DO 220 l = 1,k
410 temp1 = temp1 + conjg(a(l,i))*b(l,j)
411 temp2 = temp2 + conjg(b(l,i))*a(l,j)
412 220 CONTINUE
413 IF (i.EQ.j) THEN
414 IF (beta.EQ.real(zero)) THEN
415 c(j,j) = real(alpha*temp1+
416 + conjg(alpha)*temp2)
417 ELSE
418 c(j,j) = beta*real(c(j,j)) +
419 + real(alpha*temp1+
420 + conjg(alpha)*temp2)
421 END IF
422 ELSE
423 IF (beta.EQ.real(zero)) THEN
424 c(i,j) = alpha*temp1 + conjg(alpha)*temp2
425 ELSE
426 c(i,j) = beta*c(i,j) + alpha*temp1 +
427 + conjg(alpha)*temp2
428 END IF
429 END IF
430 230 CONTINUE
431 240 CONTINUE
432 END IF
433 END IF
434*
435 RETURN
436*
437* End of CHER2K
438*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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