LAPACK  3.10.0 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 ).```
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 188 of file csymm.f.

189 *
190 * -- Reference BLAS level3 routine --
191 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
192 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
193 *
194 * .. Scalar Arguments ..
195  COMPLEX ALPHA,BETA
196  INTEGER LDA,LDB,LDC,M,N
197  CHARACTER SIDE,UPLO
198 * ..
199 * .. Array Arguments ..
200  COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
201 * ..
202 *
203 * =====================================================================
204 *
205 * .. External Functions ..
206  LOGICAL LSAME
207  EXTERNAL lsame
208 * ..
209 * .. External Subroutines ..
210  EXTERNAL xerbla
211 * ..
212 * .. Intrinsic Functions ..
213  INTRINSIC max
214 * ..
215 * .. Local Scalars ..
216  COMPLEX TEMP1,TEMP2
217  INTEGER I,INFO,J,K,NROWA
218  LOGICAL UPPER
219 * ..
220 * .. Parameters ..
221  COMPLEX ONE
222  parameter(one= (1.0e+0,0.0e+0))
223  COMPLEX ZERO
224  parameter(zero= (0.0e+0,0.0e+0))
225 * ..
226 *
227 * Set NROWA as the number of rows of A.
228 *
229  IF (lsame(side,'L')) THEN
230  nrowa = m
231  ELSE
232  nrowa = n
233  END IF
234  upper = lsame(uplo,'U')
235 *
236 * Test the input parameters.
237 *
238  info = 0
239  IF ((.NOT.lsame(side,'L')) .AND. (.NOT.lsame(side,'R'))) THEN
240  info = 1
241  ELSE IF ((.NOT.upper) .AND. (.NOT.lsame(uplo,'L'))) THEN
242  info = 2
243  ELSE IF (m.LT.0) THEN
244  info = 3
245  ELSE IF (n.LT.0) THEN
246  info = 4
247  ELSE IF (lda.LT.max(1,nrowa)) THEN
248  info = 7
249  ELSE IF (ldb.LT.max(1,m)) THEN
250  info = 9
251  ELSE IF (ldc.LT.max(1,m)) THEN
252  info = 12
253  END IF
254  IF (info.NE.0) THEN
255  CALL xerbla('CSYMM ',info)
256  RETURN
257  END IF
258 *
259 * Quick return if possible.
260 *
261  IF ((m.EQ.0) .OR. (n.EQ.0) .OR.
262  + ((alpha.EQ.zero).AND. (beta.EQ.one))) RETURN
263 *
264 * And when alpha.eq.zero.
265 *
266  IF (alpha.EQ.zero) THEN
267  IF (beta.EQ.zero) THEN
268  DO 20 j = 1,n
269  DO 10 i = 1,m
270  c(i,j) = zero
271  10 CONTINUE
272  20 CONTINUE
273  ELSE
274  DO 40 j = 1,n
275  DO 30 i = 1,m
276  c(i,j) = beta*c(i,j)
277  30 CONTINUE
278  40 CONTINUE
279  END IF
280  RETURN
281  END IF
282 *
283 * Start the operations.
284 *
285  IF (lsame(side,'L')) THEN
286 *
287 * Form C := alpha*A*B + beta*C.
288 *
289  IF (upper) THEN
290  DO 70 j = 1,n
291  DO 60 i = 1,m
292  temp1 = alpha*b(i,j)
293  temp2 = zero
294  DO 50 k = 1,i - 1
295  c(k,j) = c(k,j) + temp1*a(k,i)
296  temp2 = temp2 + b(k,j)*a(k,i)
297  50 CONTINUE
298  IF (beta.EQ.zero) THEN
299  c(i,j) = temp1*a(i,i) + alpha*temp2
300  ELSE
301  c(i,j) = beta*c(i,j) + temp1*a(i,i) +
302  + alpha*temp2
303  END IF
304  60 CONTINUE
305  70 CONTINUE
306  ELSE
307  DO 100 j = 1,n
308  DO 90 i = m,1,-1
309  temp1 = alpha*b(i,j)
310  temp2 = zero
311  DO 80 k = i + 1,m
312  c(k,j) = c(k,j) + temp1*a(k,i)
313  temp2 = temp2 + b(k,j)*a(k,i)
314  80 CONTINUE
315  IF (beta.EQ.zero) THEN
316  c(i,j) = temp1*a(i,i) + alpha*temp2
317  ELSE
318  c(i,j) = beta*c(i,j) + temp1*a(i,i) +
319  + alpha*temp2
320  END IF
321  90 CONTINUE
322  100 CONTINUE
323  END IF
324  ELSE
325 *
326 * Form C := alpha*B*A + beta*C.
327 *
328  DO 170 j = 1,n
329  temp1 = alpha*a(j,j)
330  IF (beta.EQ.zero) THEN
331  DO 110 i = 1,m
332  c(i,j) = temp1*b(i,j)
333  110 CONTINUE
334  ELSE
335  DO 120 i = 1,m
336  c(i,j) = beta*c(i,j) + temp1*b(i,j)
337  120 CONTINUE
338  END IF
339  DO 140 k = 1,j - 1
340  IF (upper) THEN
341  temp1 = alpha*a(k,j)
342  ELSE
343  temp1 = alpha*a(j,k)
344  END IF
345  DO 130 i = 1,m
346  c(i,j) = c(i,j) + temp1*b(i,k)
347  130 CONTINUE
348  140 CONTINUE
349  DO 160 k = j + 1,n
350  IF (upper) THEN
351  temp1 = alpha*a(j,k)
352  ELSE
353  temp1 = alpha*a(k,j)
354  END IF
355  DO 150 i = 1,m
356  c(i,j) = c(i,j) + temp1*b(i,k)
357  150 CONTINUE
358  160 CONTINUE
359  170 CONTINUE
360  END IF
361 *
362  RETURN
363 *
364 * End of CSYMM
365 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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