LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

◆ 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 ).```
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 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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