LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ ssymm()

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

SSYMM

Purpose:
``` SSYMM  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 REAL On entry, ALPHA specifies the scalar alpha.``` [in] A ``` A is REAL 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 REAL 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 REAL 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 REAL 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 ssymm.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 REAL ALPHA,BETA
196 INTEGER LDA,LDB,LDC,M,N
197 CHARACTER SIDE,UPLO
198* ..
199* .. Array Arguments ..
200 REAL 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 REAL TEMP1,TEMP2
217 INTEGER I,INFO,J,K,NROWA
218 LOGICAL UPPER
219* ..
220* .. Parameters ..
221 REAL ONE,ZERO
222 parameter(one=1.0e+0,zero=0.0e+0)
223* ..
224*
225* Set NROWA as the number of rows of A.
226*
227 IF (lsame(side,'L')) THEN
228 nrowa = m
229 ELSE
230 nrowa = n
231 END IF
232 upper = lsame(uplo,'U')
233*
234* Test the input parameters.
235*
236 info = 0
237 IF ((.NOT.lsame(side,'L')) .AND.
238 + (.NOT.lsame(side,'R'))) THEN
239 info = 1
240 ELSE IF ((.NOT.upper) .AND.
241 + (.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('SSYMM ',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 SSYMM
365*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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