LAPACK 3.12.0
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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