LAPACK 3.11.0
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 ).
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. (.NOT.lsame(side,'R'))) THEN
238 info = 1
239 ELSE IF ((.NOT.upper) .AND. (.NOT.lsame(uplo,'L'))) THEN
240 info = 2
241 ELSE IF (m.LT.0) THEN
242 info = 3
243 ELSE IF (n.LT.0) THEN
244 info = 4
245 ELSE IF (lda.LT.max(1,nrowa)) THEN
246 info = 7
247 ELSE IF (ldb.LT.max(1,m)) THEN
248 info = 9
249 ELSE IF (ldc.LT.max(1,m)) THEN
250 info = 12
251 END IF
252 IF (info.NE.0) THEN
253 CALL xerbla('SSYMM ',info)
254 RETURN
255 END IF
256*
257* Quick return if possible.
258*
259 IF ((m.EQ.0) .OR. (n.EQ.0) .OR.
260 + ((alpha.EQ.zero).AND. (beta.EQ.one))) RETURN
261*
262* And when alpha.eq.zero.
263*
264 IF (alpha.EQ.zero) THEN
265 IF (beta.EQ.zero) THEN
266 DO 20 j = 1,n
267 DO 10 i = 1,m
268 c(i,j) = zero
269 10 CONTINUE
270 20 CONTINUE
271 ELSE
272 DO 40 j = 1,n
273 DO 30 i = 1,m
274 c(i,j) = beta*c(i,j)
275 30 CONTINUE
276 40 CONTINUE
277 END IF
278 RETURN
279 END IF
280*
281* Start the operations.
282*
283 IF (lsame(side,'L')) THEN
284*
285* Form C := alpha*A*B + beta*C.
286*
287 IF (upper) THEN
288 DO 70 j = 1,n
289 DO 60 i = 1,m
290 temp1 = alpha*b(i,j)
291 temp2 = zero
292 DO 50 k = 1,i - 1
293 c(k,j) = c(k,j) + temp1*a(k,i)
294 temp2 = temp2 + b(k,j)*a(k,i)
295 50 CONTINUE
296 IF (beta.EQ.zero) THEN
297 c(i,j) = temp1*a(i,i) + alpha*temp2
298 ELSE
299 c(i,j) = beta*c(i,j) + temp1*a(i,i) +
300 + alpha*temp2
301 END IF
302 60 CONTINUE
303 70 CONTINUE
304 ELSE
305 DO 100 j = 1,n
306 DO 90 i = m,1,-1
307 temp1 = alpha*b(i,j)
308 temp2 = zero
309 DO 80 k = i + 1,m
310 c(k,j) = c(k,j) + temp1*a(k,i)
311 temp2 = temp2 + b(k,j)*a(k,i)
312 80 CONTINUE
313 IF (beta.EQ.zero) THEN
314 c(i,j) = temp1*a(i,i) + alpha*temp2
315 ELSE
316 c(i,j) = beta*c(i,j) + temp1*a(i,i) +
317 + alpha*temp2
318 END IF
319 90 CONTINUE
320 100 CONTINUE
321 END IF
322 ELSE
323*
324* Form C := alpha*B*A + beta*C.
325*
326 DO 170 j = 1,n
327 temp1 = alpha*a(j,j)
328 IF (beta.EQ.zero) THEN
329 DO 110 i = 1,m
330 c(i,j) = temp1*b(i,j)
331 110 CONTINUE
332 ELSE
333 DO 120 i = 1,m
334 c(i,j) = beta*c(i,j) + temp1*b(i,j)
335 120 CONTINUE
336 END IF
337 DO 140 k = 1,j - 1
338 IF (upper) THEN
339 temp1 = alpha*a(k,j)
340 ELSE
341 temp1 = alpha*a(j,k)
342 END IF
343 DO 130 i = 1,m
344 c(i,j) = c(i,j) + temp1*b(i,k)
345 130 CONTINUE
346 140 CONTINUE
347 DO 160 k = j + 1,n
348 IF (upper) THEN
349 temp1 = alpha*a(j,k)
350 ELSE
351 temp1 = alpha*a(k,j)
352 END IF
353 DO 150 i = 1,m
354 c(i,j) = c(i,j) + temp1*b(i,k)
355 150 CONTINUE
356 160 CONTINUE
357 170 CONTINUE
358 END IF
359*
360 RETURN
361*
362* End of SSYMM
363*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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