LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ sgemm()

subroutine sgemm ( character transa,
character transb,
integer m,
integer n,
integer k,
real alpha,
real, dimension(lda,*) a,
integer lda,
real, dimension(ldb,*) b,
integer ldb,
real beta,
real, dimension(ldc,*) c,
integer ldc )

SGEMM

Purpose:
!>
!> SGEMM  performs one of the matrix-matrix operations
!>
!>    C := alpha*op( A )*op( B ) + beta*C,
!>
!> where  op( X ) is one of
!>
!>    op( X ) = X   or   op( X ) = X**T,
!>
!> alpha and beta are scalars, and A, B and C are matrices, with op( A )
!> an m by k matrix,  op( B )  a  k by n matrix and  C an m by n matrix.
!>
Parameters
[in]TRANSA
!>          TRANSA is CHARACTER*1
!>           On entry, TRANSA specifies the form of op( A ) to be used in
!>           the matrix multiplication as follows:
!>
!>              TRANSA = 'N' or 'n',  op( A ) = A.
!>
!>              TRANSA = 'T' or 't',  op( A ) = A**T.
!>
!>              TRANSA = 'C' or 'c',  op( A ) = A**T.
!>
[in]TRANSB
!>          TRANSB is CHARACTER*1
!>           On entry, TRANSB specifies the form of op( B ) to be used in
!>           the matrix multiplication as follows:
!>
!>              TRANSB = 'N' or 'n',  op( B ) = B.
!>
!>              TRANSB = 'T' or 't',  op( B ) = B**T.
!>
!>              TRANSB = 'C' or 'c',  op( B ) = B**T.
!>
[in]M
!>          M is INTEGER
!>           On entry,  M  specifies  the number  of rows  of the  matrix
!>           op( A )  and 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
!>           op( B ) and the number of columns of the matrix C. N must be
!>           at least zero.
!>
[in]K
!>          K is INTEGER
!>           On entry,  K  specifies  the number of columns of the matrix
!>           op( A ) and the number of rows of the matrix op( B ). K 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
!>           k  when  TRANSA = 'N' or 'n',  and is  m  otherwise.
!>           Before entry with  TRANSA = 'N' or 'n',  the leading  m by k
!>           part of the array  A  must contain the matrix  A,  otherwise
!>           the leading  k by m  part of the array  A  must contain  the
!>           matrix A.
!>
[in]LDA
!>          LDA is INTEGER
!>           On entry, LDA specifies the first dimension of A as declared
!>           in the calling (sub) program. When  TRANSA = 'N' or 'n' then
!>           LDA must be at least  max( 1, m ), otherwise  LDA must be at
!>           least  max( 1, k ).
!>
[in]B
!>          B is REAL array, dimension ( LDB, kb ), where kb is
!>           n  when  TRANSB = 'N' or 'n',  and is  k  otherwise.
!>           Before entry with  TRANSB = 'N' or 'n',  the leading  k by n
!>           part of the array  B  must contain the matrix  B,  otherwise
!>           the leading  n by k  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. When  TRANSB = 'N' or 'n' then
!>           LDB must be at least  max( 1, k ), otherwise  LDB must be at
!>           least  max( 1, n ).
!>
[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  matrix
!>           ( alpha*op( A )*op( B ) + beta*C ).
!>
[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 186 of file sgemm.f.

188*
189* -- Reference BLAS level3 routine --
190* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
191* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
192*
193* .. Scalar Arguments ..
194 REAL ALPHA,BETA
195 INTEGER K,LDA,LDB,LDC,M,N
196 CHARACTER TRANSA,TRANSB
197* ..
198* .. Array Arguments ..
199 REAL A(LDA,*),B(LDB,*),C(LDC,*)
200* ..
201*
202* =====================================================================
203*
204* .. External Functions ..
205 LOGICAL LSAME
206 EXTERNAL lsame
207* ..
208* .. External Subroutines ..
209 EXTERNAL xerbla
210* ..
211* .. Intrinsic Functions ..
212 INTRINSIC max
213* ..
214* .. Local Scalars ..
215 REAL TEMP
216 INTEGER I,INFO,J,L,NROWA,NROWB
217 LOGICAL NOTA,NOTB
218* ..
219* .. Parameters ..
220 REAL ONE,ZERO
221 parameter(one=1.0e+0,zero=0.0e+0)
222* ..
223*
224* Set NOTA and NOTB as true if A and B respectively are not
225* transposed and set NROWA and NROWB as the number of rows of A
226* and B respectively.
227*
228 nota = lsame(transa,'N')
229 notb = lsame(transb,'N')
230 IF (nota) THEN
231 nrowa = m
232 ELSE
233 nrowa = k
234 END IF
235 IF (notb) THEN
236 nrowb = k
237 ELSE
238 nrowb = n
239 END IF
240*
241* Test the input parameters.
242*
243 info = 0
244 IF ((.NOT.nota) .AND. (.NOT.lsame(transa,'C')) .AND.
245 + (.NOT.lsame(transa,'T'))) THEN
246 info = 1
247 ELSE IF ((.NOT.notb) .AND. (.NOT.lsame(transb,'C')) .AND.
248 + (.NOT.lsame(transb,'T'))) THEN
249 info = 2
250 ELSE IF (m.LT.0) THEN
251 info = 3
252 ELSE IF (n.LT.0) THEN
253 info = 4
254 ELSE IF (k.LT.0) THEN
255 info = 5
256 ELSE IF (lda.LT.max(1,nrowa)) THEN
257 info = 8
258 ELSE IF (ldb.LT.max(1,nrowb)) THEN
259 info = 10
260 ELSE IF (ldc.LT.max(1,m)) THEN
261 info = 13
262 END IF
263 IF (info.NE.0) THEN
264 CALL xerbla('SGEMM ',info)
265 RETURN
266 END IF
267*
268* Quick return if possible.
269*
270 IF ((m.EQ.0) .OR. (n.EQ.0) .OR.
271 + (((alpha.EQ.zero).OR. (k.EQ.0)).AND. (beta.EQ.one))) RETURN
272*
273* And if alpha.eq.zero.
274*
275 IF (alpha.EQ.zero) THEN
276 IF (beta.EQ.zero) THEN
277 DO 20 j = 1,n
278 DO 10 i = 1,m
279 c(i,j) = zero
280 10 CONTINUE
281 20 CONTINUE
282 ELSE
283 DO 40 j = 1,n
284 DO 30 i = 1,m
285 c(i,j) = beta*c(i,j)
286 30 CONTINUE
287 40 CONTINUE
288 END IF
289 RETURN
290 END IF
291*
292* Start the operations.
293*
294 IF (notb) THEN
295 IF (nota) THEN
296*
297* Form C := alpha*A*B + beta*C.
298*
299 DO 90 j = 1,n
300 IF (beta.EQ.zero) THEN
301 DO 50 i = 1,m
302 c(i,j) = zero
303 50 CONTINUE
304 ELSE IF (beta.NE.one) THEN
305 DO 60 i = 1,m
306 c(i,j) = beta*c(i,j)
307 60 CONTINUE
308 END IF
309 DO 80 l = 1,k
310 temp = alpha*b(l,j)
311 DO 70 i = 1,m
312 c(i,j) = c(i,j) + temp*a(i,l)
313 70 CONTINUE
314 80 CONTINUE
315 90 CONTINUE
316 ELSE
317*
318* Form C := alpha*A**T*B + beta*C
319*
320 DO 120 j = 1,n
321 DO 110 i = 1,m
322 temp = zero
323 DO 100 l = 1,k
324 temp = temp + a(l,i)*b(l,j)
325 100 CONTINUE
326 IF (beta.EQ.zero) THEN
327 c(i,j) = alpha*temp
328 ELSE
329 c(i,j) = alpha*temp + beta*c(i,j)
330 END IF
331 110 CONTINUE
332 120 CONTINUE
333 END IF
334 ELSE
335 IF (nota) THEN
336*
337* Form C := alpha*A*B**T + beta*C
338*
339 DO 170 j = 1,n
340 IF (beta.EQ.zero) THEN
341 DO 130 i = 1,m
342 c(i,j) = zero
343 130 CONTINUE
344 ELSE IF (beta.NE.one) THEN
345 DO 140 i = 1,m
346 c(i,j) = beta*c(i,j)
347 140 CONTINUE
348 END IF
349 DO 160 l = 1,k
350 temp = alpha*b(j,l)
351 DO 150 i = 1,m
352 c(i,j) = c(i,j) + temp*a(i,l)
353 150 CONTINUE
354 160 CONTINUE
355 170 CONTINUE
356 ELSE
357*
358* Form C := alpha*A**T*B**T + beta*C
359*
360 DO 200 j = 1,n
361 DO 190 i = 1,m
362 temp = zero
363 DO 180 l = 1,k
364 temp = temp + a(l,i)*b(j,l)
365 180 CONTINUE
366 IF (beta.EQ.zero) THEN
367 c(i,j) = alpha*temp
368 ELSE
369 c(i,j) = alpha*temp + beta*c(i,j)
370 END IF
371 190 CONTINUE
372 200 CONTINUE
373 END IF
374 END IF
375*
376 RETURN
377*
378* End of SGEMM
379*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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