 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
Searching...
No Matches

## ◆ csyrk()

 subroutine csyrk ( character UPLO, character TRANS, integer N, integer K, complex ALPHA, complex, dimension(lda,*) A, integer LDA, complex BETA, complex, dimension(ldc,*) C, integer LDC )

CSYRK

Purpose:
``` CSYRK  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 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] BETA ``` BETA is COMPLEX 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 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 csyrk.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 ALPHA,BETA
174 INTEGER K,LDA,LDC,N
175 CHARACTER TRANS,UPLO
176* ..
177* .. Array Arguments ..
178 COMPLEX 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 TEMP
195 INTEGER I,INFO,J,L,NROWA
196 LOGICAL UPPER
197* ..
198* .. Parameters ..
199 COMPLEX ONE
200 parameter(one= (1.0e+0,0.0e+0))
201 COMPLEX ZERO
202 parameter(zero= (0.0e+0,0.0e+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('CSYRK ',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 CSYRK
359*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
Here is the call graph for this function:
Here is the caller graph for this function: