LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
Searching...
No Matches

## ◆ zsymm()

 subroutine zsymm ( character side, character uplo, integer m, integer n, complex*16 alpha, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(ldb,*) b, integer ldb, complex*16 beta, complex*16, dimension(ldc,*) c, integer ldc )

ZSYMM

Purpose:
``` ZSYMM  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*16 On entry, ALPHA specifies the scalar alpha.``` [in] A ``` A is COMPLEX*16 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*16 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*16 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*16 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 zsymm.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*16 ALPHA,BETA
196 INTEGER LDA,LDB,LDC,M,N
197 CHARACTER SIDE,UPLO
198* ..
199* .. Array Arguments ..
200 COMPLEX*16 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*16 TEMP1,TEMP2
217 INTEGER I,INFO,J,K,NROWA
218 LOGICAL UPPER
219* ..
220* .. Parameters ..
221 COMPLEX*16 ONE
222 parameter(one= (1.0d+0,0.0d+0))
223 COMPLEX*16 ZERO
224 parameter(zero= (0.0d+0,0.0d+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.
240 + (.NOT.lsame(side,'R'))) THEN
241 info = 1
242 ELSE IF ((.NOT.upper) .AND.
243 + (.NOT.lsame(uplo,'L'))) THEN
244 info = 2
245 ELSE IF (m.LT.0) THEN
246 info = 3
247 ELSE IF (n.LT.0) THEN
248 info = 4
249 ELSE IF (lda.LT.max(1,nrowa)) THEN
250 info = 7
251 ELSE IF (ldb.LT.max(1,m)) THEN
252 info = 9
253 ELSE IF (ldc.LT.max(1,m)) THEN
254 info = 12
255 END IF
256 IF (info.NE.0) THEN
257 CALL xerbla('ZSYMM ',info)
258 RETURN
259 END IF
260*
261* Quick return if possible.
262*
263 IF ((m.EQ.0) .OR. (n.EQ.0) .OR.
264 + ((alpha.EQ.zero).AND. (beta.EQ.one))) RETURN
265*
266* And when alpha.eq.zero.
267*
268 IF (alpha.EQ.zero) THEN
269 IF (beta.EQ.zero) THEN
270 DO 20 j = 1,n
271 DO 10 i = 1,m
272 c(i,j) = zero
273 10 CONTINUE
274 20 CONTINUE
275 ELSE
276 DO 40 j = 1,n
277 DO 30 i = 1,m
278 c(i,j) = beta*c(i,j)
279 30 CONTINUE
280 40 CONTINUE
281 END IF
282 RETURN
283 END IF
284*
285* Start the operations.
286*
287 IF (lsame(side,'L')) THEN
288*
289* Form C := alpha*A*B + beta*C.
290*
291 IF (upper) THEN
292 DO 70 j = 1,n
293 DO 60 i = 1,m
294 temp1 = alpha*b(i,j)
295 temp2 = zero
296 DO 50 k = 1,i - 1
297 c(k,j) = c(k,j) + temp1*a(k,i)
298 temp2 = temp2 + b(k,j)*a(k,i)
299 50 CONTINUE
300 IF (beta.EQ.zero) THEN
301 c(i,j) = temp1*a(i,i) + alpha*temp2
302 ELSE
303 c(i,j) = beta*c(i,j) + temp1*a(i,i) +
304 + alpha*temp2
305 END IF
306 60 CONTINUE
307 70 CONTINUE
308 ELSE
309 DO 100 j = 1,n
310 DO 90 i = m,1,-1
311 temp1 = alpha*b(i,j)
312 temp2 = zero
313 DO 80 k = i + 1,m
314 c(k,j) = c(k,j) + temp1*a(k,i)
315 temp2 = temp2 + b(k,j)*a(k,i)
316 80 CONTINUE
317 IF (beta.EQ.zero) THEN
318 c(i,j) = temp1*a(i,i) + alpha*temp2
319 ELSE
320 c(i,j) = beta*c(i,j) + temp1*a(i,i) +
321 + alpha*temp2
322 END IF
323 90 CONTINUE
324 100 CONTINUE
325 END IF
326 ELSE
327*
328* Form C := alpha*B*A + beta*C.
329*
330 DO 170 j = 1,n
331 temp1 = alpha*a(j,j)
332 IF (beta.EQ.zero) THEN
333 DO 110 i = 1,m
334 c(i,j) = temp1*b(i,j)
335 110 CONTINUE
336 ELSE
337 DO 120 i = 1,m
338 c(i,j) = beta*c(i,j) + temp1*b(i,j)
339 120 CONTINUE
340 END IF
341 DO 140 k = 1,j - 1
342 IF (upper) THEN
343 temp1 = alpha*a(k,j)
344 ELSE
345 temp1 = alpha*a(j,k)
346 END IF
347 DO 130 i = 1,m
348 c(i,j) = c(i,j) + temp1*b(i,k)
349 130 CONTINUE
350 140 CONTINUE
351 DO 160 k = j + 1,n
352 IF (upper) THEN
353 temp1 = alpha*a(j,k)
354 ELSE
355 temp1 = alpha*a(k,j)
356 END IF
357 DO 150 i = 1,m
358 c(i,j) = c(i,j) + temp1*b(i,k)
359 150 CONTINUE
360 160 CONTINUE
361 170 CONTINUE
362 END IF
363*
364 RETURN
365*
366* End of ZSYMM
367*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
Here is the call graph for this function:
Here is the caller graph for this function: