LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ zherk()

subroutine zherk ( character uplo,
character trans,
integer n,
integer k,
double precision alpha,
complex*16, dimension(lda,*) a,
integer lda,
double precision beta,
complex*16, dimension(ldc,*) c,
integer ldc )

ZHERK

Purpose:
!>
!> ZHERK  performs one of the hermitian rank k operations
!>
!>    C := alpha*A*A**H + beta*C,
!>
!> or
!>
!>    C := alpha*A**H*A + beta*C,
!>
!> where  alpha and beta  are  real scalars,  C is an  n by n  hermitian
!> matrix and  A  is an  n by k  matrix in the  first case and a  k by n
!> matrix 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*A**H + beta*C.
!>
!>              TRANS = 'C' or 'c'   C := alpha*A**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   matrix   A,   and  on   entry   with
!>           TRANS = 'C' or 'c',  K  specifies  the number of rows of the
!>           matrix A.  K must be at least zero.
!>
[in]ALPHA
!>          ALPHA is DOUBLE PRECISION .
!>           On entry, ALPHA specifies the scalar alpha.
!>
[in]A
!>          A is COMPLEX*16 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]BETA
!>          BETA is DOUBLE PRECISION.
!>           On entry, BETA specifies the scalar beta.
!>
[in,out]C
!>          C is COMPLEX*16 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 DBLE( C(J,J) ) when BETA = 1.
!>     Ed Anderson, Cray Research Inc.
!>

Definition at line 172 of file zherk.f.

173*
174* -- Reference BLAS level3 routine --
175* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
176* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
177*
178* .. Scalar Arguments ..
179 DOUBLE PRECISION ALPHA,BETA
180 INTEGER K,LDA,LDC,N
181 CHARACTER TRANS,UPLO
182* ..
183* .. Array Arguments ..
184 COMPLEX*16 A(LDA,*),C(LDC,*)
185* ..
186*
187* =====================================================================
188*
189* .. External Functions ..
190 LOGICAL LSAME
191 EXTERNAL lsame
192* ..
193* .. External Subroutines ..
194 EXTERNAL xerbla
195* ..
196* .. Intrinsic Functions ..
197 INTRINSIC dble,dcmplx,dconjg,max
198* ..
199* .. Local Scalars ..
200 COMPLEX*16 TEMP
201 DOUBLE PRECISION RTEMP
202 INTEGER I,INFO,J,L,NROWA
203 LOGICAL UPPER
204* ..
205* .. Parameters ..
206 DOUBLE PRECISION ONE,ZERO
207 parameter(one=1.0d+0,zero=0.0d+0)
208* ..
209*
210* Test the input parameters.
211*
212 IF (lsame(trans,'N')) THEN
213 nrowa = n
214 ELSE
215 nrowa = k
216 END IF
217 upper = lsame(uplo,'U')
218*
219 info = 0
220 IF ((.NOT.upper) .AND. (.NOT.lsame(uplo,'L'))) THEN
221 info = 1
222 ELSE IF ((.NOT.lsame(trans,'N')) .AND.
223 + (.NOT.lsame(trans,'C'))) THEN
224 info = 2
225 ELSE IF (n.LT.0) THEN
226 info = 3
227 ELSE IF (k.LT.0) THEN
228 info = 4
229 ELSE IF (lda.LT.max(1,nrowa)) THEN
230 info = 7
231 ELSE IF (ldc.LT.max(1,n)) THEN
232 info = 10
233 END IF
234 IF (info.NE.0) THEN
235 CALL xerbla('ZHERK ',info)
236 RETURN
237 END IF
238*
239* Quick return if possible.
240*
241 IF ((n.EQ.0) .OR. (((alpha.EQ.zero).OR.
242 + (k.EQ.0)).AND. (beta.EQ.one))) RETURN
243*
244* And when alpha.eq.zero.
245*
246 IF (alpha.EQ.zero) THEN
247 IF (upper) THEN
248 IF (beta.EQ.zero) THEN
249 DO 20 j = 1,n
250 DO 10 i = 1,j
251 c(i,j) = zero
252 10 CONTINUE
253 20 CONTINUE
254 ELSE
255 DO 40 j = 1,n
256 DO 30 i = 1,j - 1
257 c(i,j) = beta*c(i,j)
258 30 CONTINUE
259 c(j,j) = beta*dble(c(j,j))
260 40 CONTINUE
261 END IF
262 ELSE
263 IF (beta.EQ.zero) THEN
264 DO 60 j = 1,n
265 DO 50 i = j,n
266 c(i,j) = zero
267 50 CONTINUE
268 60 CONTINUE
269 ELSE
270 DO 80 j = 1,n
271 c(j,j) = beta*dble(c(j,j))
272 DO 70 i = j + 1,n
273 c(i,j) = beta*c(i,j)
274 70 CONTINUE
275 80 CONTINUE
276 END IF
277 END IF
278 RETURN
279 END IF
280*
281* Start the operations.
282*
283 IF (lsame(trans,'N')) THEN
284*
285* Form C := alpha*A*A**H + beta*C.
286*
287 IF (upper) THEN
288 DO 130 j = 1,n
289 IF (beta.EQ.zero) THEN
290 DO 90 i = 1,j
291 c(i,j) = zero
292 90 CONTINUE
293 ELSE IF (beta.NE.one) THEN
294 DO 100 i = 1,j - 1
295 c(i,j) = beta*c(i,j)
296 100 CONTINUE
297 c(j,j) = beta*dble(c(j,j))
298 ELSE
299 c(j,j) = dble(c(j,j))
300 END IF
301 DO 120 l = 1,k
302 IF (a(j,l).NE.dcmplx(zero)) THEN
303 temp = alpha*dconjg(a(j,l))
304 DO 110 i = 1,j - 1
305 c(i,j) = c(i,j) + temp*a(i,l)
306 110 CONTINUE
307 c(j,j) = dble(c(j,j)) + dble(temp*a(i,l))
308 END IF
309 120 CONTINUE
310 130 CONTINUE
311 ELSE
312 DO 180 j = 1,n
313 IF (beta.EQ.zero) THEN
314 DO 140 i = j,n
315 c(i,j) = zero
316 140 CONTINUE
317 ELSE IF (beta.NE.one) THEN
318 c(j,j) = beta*dble(c(j,j))
319 DO 150 i = j + 1,n
320 c(i,j) = beta*c(i,j)
321 150 CONTINUE
322 ELSE
323 c(j,j) = dble(c(j,j))
324 END IF
325 DO 170 l = 1,k
326 IF (a(j,l).NE.dcmplx(zero)) THEN
327 temp = alpha*dconjg(a(j,l))
328 c(j,j) = dble(c(j,j)) + dble(temp*a(j,l))
329 DO 160 i = j + 1,n
330 c(i,j) = c(i,j) + temp*a(i,l)
331 160 CONTINUE
332 END IF
333 170 CONTINUE
334 180 CONTINUE
335 END IF
336 ELSE
337*
338* Form C := alpha*A**H*A + beta*C.
339*
340 IF (upper) THEN
341 DO 220 j = 1,n
342 DO 200 i = 1,j - 1
343 temp = zero
344 DO 190 l = 1,k
345 temp = temp + dconjg(a(l,i))*a(l,j)
346 190 CONTINUE
347 IF (beta.EQ.zero) THEN
348 c(i,j) = alpha*temp
349 ELSE
350 c(i,j) = alpha*temp + beta*c(i,j)
351 END IF
352 200 CONTINUE
353 rtemp = zero
354 DO 210 l = 1,k
355 rtemp = rtemp + dble(dconjg(a(l,j))*a(l,j))
356 210 CONTINUE
357 IF (beta.EQ.zero) THEN
358 c(j,j) = alpha*rtemp
359 ELSE
360 c(j,j) = alpha*rtemp + beta*dble(c(j,j))
361 END IF
362 220 CONTINUE
363 ELSE
364 DO 260 j = 1,n
365 rtemp = zero
366 DO 230 l = 1,k
367 rtemp = rtemp + dble(dconjg(a(l,j))*a(l,j))
368 230 CONTINUE
369 IF (beta.EQ.zero) THEN
370 c(j,j) = alpha*rtemp
371 ELSE
372 c(j,j) = alpha*rtemp + beta*dble(c(j,j))
373 END IF
374 DO 250 i = j + 1,n
375 temp = zero
376 DO 240 l = 1,k
377 temp = temp + dconjg(a(l,i))*a(l,j)
378 240 CONTINUE
379 IF (beta.EQ.zero) THEN
380 c(i,j) = alpha*temp
381 ELSE
382 c(i,j) = alpha*temp + beta*c(i,j)
383 END IF
384 250 CONTINUE
385 260 CONTINUE
386 END IF
387 END IF
388*
389 RETURN
390*
391* End of ZHERK
392*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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