LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ csymm()

 subroutine csymm ( character SIDE, character UPLO, integer M, integer N, complex ALPHA, complex, dimension(lda,*) A, integer LDA, complex, dimension(ldb,*) B, integer LDB, complex BETA, complex, dimension(ldc,*) C, integer LDC )

CSYMM

Purpose:
``` CSYMM  performs one of the matrix-matrix operations

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

or

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

where  alpha and beta are scalars, A is a symmetric matrix and  B and
C are m by n matrices.```
Parameters
 [in] SIDE ``` SIDE is CHARACTER*1 On entry, SIDE specifies whether the symmetric matrix A appears on the left or right in the operation as follows: SIDE = 'L' or 'l' C := alpha*A*B + beta*C, SIDE = 'R' or 'r' C := alpha*B*A + beta*C,``` [in] UPLO ``` UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the symmetric matrix A is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of the symmetric matrix is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of the symmetric matrix is to be referenced.``` [in] M ``` M is INTEGER On entry, M specifies the number of rows of the matrix C. M must be at least zero.``` [in] N ``` N is INTEGER On entry, N specifies the number of columns of the matrix C. N 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 m when SIDE = 'L' or 'l' and is n otherwise. Before entry with SIDE = 'L' or 'l', the m by m part of the array A must contain the symmetric matrix, such that when UPLO = 'U' or 'u', the leading m by m upper triangular part of the array A must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of A is not referenced, and when UPLO = 'L' or 'l', the leading m by m lower triangular part of the array A must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of A is not referenced. Before entry with SIDE = 'R' or 'r', the n by n part of the array A must contain the symmetric matrix, such that when UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of A is not referenced, and when UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of A is not referenced.``` [in] LDA ``` LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), otherwise LDA must be at least max( 1, n ).``` [in] B ``` B is COMPLEX array, dimension ( LDB, N ) Before entry, the leading m 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. LDB must be at least max( 1, m ).``` [in] BETA ``` BETA is COMPLEX On entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input.``` [in,out] C ``` C is COMPLEX array, dimension ( LDC, N ) Before entry, the leading m by n part of the array C must contain the matrix C, except when beta is zero, in which case C need not be set on entry. On exit, the array C is overwritten by the m by n 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, m ).```
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 191 of file csymm.f.

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