 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ csyr2k()

 subroutine csyr2k ( character UPLO, character TRANS, integer N, integer K, complex ALPHA, complex, dimension(lda,*) A, integer LDA, complex, dimension(ldb,*) B, integer LDB, complex BETA, complex, dimension(ldc,*) C, integer LDC )

CSYR2K

Purpose:
``` CSYR2K  performs one of the symmetric rank 2k operations

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

or

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

where  alpha and beta  are scalars,  C is an  n by n symmetric 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**T + alpha*B*A**T + beta*C. TRANS = 'T' or 't' C := alpha*A**T*B + alpha*B**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 matrices A and B, and on entry with TRANS = 'T' or 't', 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 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 ).```
Date
December 2016
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 190 of file csyr2k.f.

190 *
191 * -- Reference BLAS level3 routine (version 3.7.0) --
192 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
193 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
194 * December 2016
195 *
196 * .. Scalar Arguments ..
197  COMPLEX alpha,beta
198  INTEGER k,lda,ldb,ldc,n
199  CHARACTER trans,uplo
200 * ..
201 * .. Array Arguments ..
202  COMPLEX a(lda,*),b(ldb,*),c(ldc,*)
203 * ..
204 *
205 * =====================================================================
206 *
207 * .. External Functions ..
208  LOGICAL lsame
209  EXTERNAL lsame
210 * ..
211 * .. External Subroutines ..
212  EXTERNAL xerbla
213 * ..
214 * .. Intrinsic Functions ..
215  INTRINSIC max
216 * ..
217 * .. Local Scalars ..
218  COMPLEX temp1,temp2
219  INTEGER i,info,j,l,nrowa
220  LOGICAL upper
221 * ..
222 * .. Parameters ..
223  COMPLEX one
224  parameter(one= (1.0e+0,0.0e+0))
225  COMPLEX zero
226  parameter(zero= (0.0e+0,0.0e+0))
227 * ..
228 *
229 * Test the input parameters.
230 *
231  IF (lsame(trans,'N')) THEN
232  nrowa = n
233  ELSE
234  nrowa = k
235  END IF
236  upper = lsame(uplo,'U')
237 *
238  info = 0
239  IF ((.NOT.upper) .AND. (.NOT.lsame(uplo,'L'))) THEN
240  info = 1
241  ELSE IF ((.NOT.lsame(trans,'N')) .AND.
242  + (.NOT.lsame(trans,'T'))) THEN
243  info = 2
244  ELSE IF (n.LT.0) THEN
245  info = 3
246  ELSE IF (k.LT.0) THEN
247  info = 4
248  ELSE IF (lda.LT.max(1,nrowa)) THEN
249  info = 7
250  ELSE IF (ldb.LT.max(1,nrowa)) THEN
251  info = 9
252  ELSE IF (ldc.LT.max(1,n)) THEN
253  info = 12
254  END IF
255  IF (info.NE.0) THEN
256  CALL xerbla('CSYR2K',info)
257  RETURN
258  END IF
259 *
260 * Quick return if possible.
261 *
262  IF ((n.EQ.0) .OR. (((alpha.EQ.zero).OR.
263  + (k.EQ.0)).AND. (beta.EQ.one))) RETURN
264 *
265 * And when alpha.eq.zero.
266 *
267  IF (alpha.EQ.zero) THEN
268  IF (upper) THEN
269  IF (beta.EQ.zero) THEN
270  DO 20 j = 1,n
271  DO 10 i = 1,j
272  c(i,j) = zero
273  10 CONTINUE
274  20 CONTINUE
275  ELSE
276  DO 40 j = 1,n
277  DO 30 i = 1,j
278  c(i,j) = beta*c(i,j)
279  30 CONTINUE
280  40 CONTINUE
281  END IF
282  ELSE
283  IF (beta.EQ.zero) THEN
284  DO 60 j = 1,n
285  DO 50 i = j,n
286  c(i,j) = zero
287  50 CONTINUE
288  60 CONTINUE
289  ELSE
290  DO 80 j = 1,n
291  DO 70 i = j,n
292  c(i,j) = beta*c(i,j)
293  70 CONTINUE
294  80 CONTINUE
295  END IF
296  END IF
297  RETURN
298  END IF
299 *
300 * Start the operations.
301 *
302  IF (lsame(trans,'N')) THEN
303 *
304 * Form C := alpha*A*B**T + alpha*B*A**T + C.
305 *
306  IF (upper) THEN
307  DO 130 j = 1,n
308  IF (beta.EQ.zero) THEN
309  DO 90 i = 1,j
310  c(i,j) = zero
311  90 CONTINUE
312  ELSE IF (beta.NE.one) THEN
313  DO 100 i = 1,j
314  c(i,j) = beta*c(i,j)
315  100 CONTINUE
316  END IF
317  DO 120 l = 1,k
318  IF ((a(j,l).NE.zero) .OR. (b(j,l).NE.zero)) THEN
319  temp1 = alpha*b(j,l)
320  temp2 = alpha*a(j,l)
321  DO 110 i = 1,j
322  c(i,j) = c(i,j) + a(i,l)*temp1 +
323  + b(i,l)*temp2
324  110 CONTINUE
325  END IF
326  120 CONTINUE
327  130 CONTINUE
328  ELSE
329  DO 180 j = 1,n
330  IF (beta.EQ.zero) THEN
331  DO 140 i = j,n
332  c(i,j) = zero
333  140 CONTINUE
334  ELSE IF (beta.NE.one) THEN
335  DO 150 i = j,n
336  c(i,j) = beta*c(i,j)
337  150 CONTINUE
338  END IF
339  DO 170 l = 1,k
340  IF ((a(j,l).NE.zero) .OR. (b(j,l).NE.zero)) THEN
341  temp1 = alpha*b(j,l)
342  temp2 = alpha*a(j,l)
343  DO 160 i = j,n
344  c(i,j) = c(i,j) + a(i,l)*temp1 +
345  + b(i,l)*temp2
346  160 CONTINUE
347  END IF
348  170 CONTINUE
349  180 CONTINUE
350  END IF
351  ELSE
352 *
353 * Form C := alpha*A**T*B + alpha*B**T*A + C.
354 *
355  IF (upper) THEN
356  DO 210 j = 1,n
357  DO 200 i = 1,j
358  temp1 = zero
359  temp2 = zero
360  DO 190 l = 1,k
361  temp1 = temp1 + a(l,i)*b(l,j)
362  temp2 = temp2 + b(l,i)*a(l,j)
363  190 CONTINUE
364  IF (beta.EQ.zero) THEN
365  c(i,j) = alpha*temp1 + alpha*temp2
366  ELSE
367  c(i,j) = beta*c(i,j) + alpha*temp1 +
368  + alpha*temp2
369  END IF
370  200 CONTINUE
371  210 CONTINUE
372  ELSE
373  DO 240 j = 1,n
374  DO 230 i = j,n
375  temp1 = zero
376  temp2 = zero
377  DO 220 l = 1,k
378  temp1 = temp1 + a(l,i)*b(l,j)
379  temp2 = temp2 + b(l,i)*a(l,j)
380  220 CONTINUE
381  IF (beta.EQ.zero) THEN
382  c(i,j) = alpha*temp1 + alpha*temp2
383  ELSE
384  c(i,j) = beta*c(i,j) + alpha*temp1 +
385  + alpha*temp2
386  END IF
387  230 CONTINUE
388  240 CONTINUE
389  END IF
390  END IF
391 *
392  RETURN
393 *
394 * End of CSYR2K.
395 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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