LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ zsyrk()

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

ZSYRK

Purpose:
 ZSYRK  performs one of the symmetric rank k operations

    C := alpha*A*A**T + beta*C,

 or

    C := alpha*A**T*A + beta*C,

 where  alpha and beta  are scalars,  C is an  n by n symmetric 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**T + beta*C.

              TRANS = 'T' or 't'   C := alpha*A**T*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 = 'T' or 't',  K  specifies  the number of rows of the
           matrix A.  K must be at least zero.
[in]ALPHA
          ALPHA is COMPLEX*16
           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 COMPLEX*16
           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  symmetric 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  symmetric 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.
[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.

Definition at line 166 of file zsyrk.f.

167*
168* -- Reference BLAS level3 routine --
169* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
170* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
171*
172* .. Scalar Arguments ..
173 COMPLEX*16 ALPHA,BETA
174 INTEGER K,LDA,LDC,N
175 CHARACTER TRANS,UPLO
176* ..
177* .. Array Arguments ..
178 COMPLEX*16 A(LDA,*),C(LDC,*)
179* ..
180*
181* =====================================================================
182*
183* .. External Functions ..
184 LOGICAL LSAME
185 EXTERNAL lsame
186* ..
187* .. External Subroutines ..
188 EXTERNAL xerbla
189* ..
190* .. Intrinsic Functions ..
191 INTRINSIC max
192* ..
193* .. Local Scalars ..
194 COMPLEX*16 TEMP
195 INTEGER I,INFO,J,L,NROWA
196 LOGICAL UPPER
197* ..
198* .. Parameters ..
199 COMPLEX*16 ONE
200 parameter(one= (1.0d+0,0.0d+0))
201 COMPLEX*16 ZERO
202 parameter(zero= (0.0d+0,0.0d+0))
203* ..
204*
205* Test the input parameters.
206*
207 IF (lsame(trans,'N')) THEN
208 nrowa = n
209 ELSE
210 nrowa = k
211 END IF
212 upper = lsame(uplo,'U')
213*
214 info = 0
215 IF ((.NOT.upper) .AND. (.NOT.lsame(uplo,'L'))) THEN
216 info = 1
217 ELSE IF ((.NOT.lsame(trans,'N')) .AND.
218 + (.NOT.lsame(trans,'T'))) THEN
219 info = 2
220 ELSE IF (n.LT.0) THEN
221 info = 3
222 ELSE IF (k.LT.0) THEN
223 info = 4
224 ELSE IF (lda.LT.max(1,nrowa)) THEN
225 info = 7
226 ELSE IF (ldc.LT.max(1,n)) THEN
227 info = 10
228 END IF
229 IF (info.NE.0) THEN
230 CALL xerbla('ZSYRK ',info)
231 RETURN
232 END IF
233*
234* Quick return if possible.
235*
236 IF ((n.EQ.0) .OR. (((alpha.EQ.zero).OR.
237 + (k.EQ.0)).AND. (beta.EQ.one))) RETURN
238*
239* And when alpha.eq.zero.
240*
241 IF (alpha.EQ.zero) THEN
242 IF (upper) THEN
243 IF (beta.EQ.zero) THEN
244 DO 20 j = 1,n
245 DO 10 i = 1,j
246 c(i,j) = zero
247 10 CONTINUE
248 20 CONTINUE
249 ELSE
250 DO 40 j = 1,n
251 DO 30 i = 1,j
252 c(i,j) = beta*c(i,j)
253 30 CONTINUE
254 40 CONTINUE
255 END IF
256 ELSE
257 IF (beta.EQ.zero) THEN
258 DO 60 j = 1,n
259 DO 50 i = j,n
260 c(i,j) = zero
261 50 CONTINUE
262 60 CONTINUE
263 ELSE
264 DO 80 j = 1,n
265 DO 70 i = j,n
266 c(i,j) = beta*c(i,j)
267 70 CONTINUE
268 80 CONTINUE
269 END IF
270 END IF
271 RETURN
272 END IF
273*
274* Start the operations.
275*
276 IF (lsame(trans,'N')) THEN
277*
278* Form C := alpha*A*A**T + beta*C.
279*
280 IF (upper) THEN
281 DO 130 j = 1,n
282 IF (beta.EQ.zero) THEN
283 DO 90 i = 1,j
284 c(i,j) = zero
285 90 CONTINUE
286 ELSE IF (beta.NE.one) THEN
287 DO 100 i = 1,j
288 c(i,j) = beta*c(i,j)
289 100 CONTINUE
290 END IF
291 DO 120 l = 1,k
292 IF (a(j,l).NE.zero) THEN
293 temp = alpha*a(j,l)
294 DO 110 i = 1,j
295 c(i,j) = c(i,j) + temp*a(i,l)
296 110 CONTINUE
297 END IF
298 120 CONTINUE
299 130 CONTINUE
300 ELSE
301 DO 180 j = 1,n
302 IF (beta.EQ.zero) THEN
303 DO 140 i = j,n
304 c(i,j) = zero
305 140 CONTINUE
306 ELSE IF (beta.NE.one) THEN
307 DO 150 i = j,n
308 c(i,j) = beta*c(i,j)
309 150 CONTINUE
310 END IF
311 DO 170 l = 1,k
312 IF (a(j,l).NE.zero) THEN
313 temp = alpha*a(j,l)
314 DO 160 i = j,n
315 c(i,j) = c(i,j) + temp*a(i,l)
316 160 CONTINUE
317 END IF
318 170 CONTINUE
319 180 CONTINUE
320 END IF
321 ELSE
322*
323* Form C := alpha*A**T*A + beta*C.
324*
325 IF (upper) THEN
326 DO 210 j = 1,n
327 DO 200 i = 1,j
328 temp = zero
329 DO 190 l = 1,k
330 temp = temp + a(l,i)*a(l,j)
331 190 CONTINUE
332 IF (beta.EQ.zero) THEN
333 c(i,j) = alpha*temp
334 ELSE
335 c(i,j) = alpha*temp + beta*c(i,j)
336 END IF
337 200 CONTINUE
338 210 CONTINUE
339 ELSE
340 DO 240 j = 1,n
341 DO 230 i = j,n
342 temp = zero
343 DO 220 l = 1,k
344 temp = temp + a(l,i)*a(l,j)
345 220 CONTINUE
346 IF (beta.EQ.zero) THEN
347 c(i,j) = alpha*temp
348 ELSE
349 c(i,j) = alpha*temp + beta*c(i,j)
350 END IF
351 230 CONTINUE
352 240 CONTINUE
353 END IF
354 END IF
355*
356 RETURN
357*
358* End of ZSYRK
359*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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