LAPACK 3.12.1
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 ).
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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