LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
Loading...
Searching...
No Matches

◆ 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.

187*
188* -- Reference BLAS level3 routine --
189* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
190* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
191*
192* .. Scalar Arguments ..
193 REAL ALPHA,BETA
194 INTEGER K,LDA,LDB,LDC,M,N
195 CHARACTER TRANSA,TRANSB
196* ..
197* .. Array Arguments ..
198 REAL A(LDA,*),B(LDB,*),C(LDC,*)
199* ..
200*
201* =====================================================================
202*
203* .. External Functions ..
204 LOGICAL LSAME
205 EXTERNAL lsame
206* ..
207* .. External Subroutines ..
208 EXTERNAL xerbla
209* ..
210* .. Intrinsic Functions ..
211 INTRINSIC max
212* ..
213* .. Local Scalars ..
214 REAL TEMP
215 INTEGER I,INFO,J,L,NROWA,NROWB
216 LOGICAL NOTA,NOTB
217* ..
218* .. Parameters ..
219 REAL ONE,ZERO
220 parameter(one=1.0e+0,zero=0.0e+0)
221* ..
222*
223* Set NOTA and NOTB as true if A and B respectively are not
224* transposed and set NROWA and NROWB as the number of rows of A
225* and B respectively.
226*
227 nota = lsame(transa,'N')
228 notb = lsame(transb,'N')
229 IF (nota) THEN
230 nrowa = m
231 ELSE
232 nrowa = k
233 END IF
234 IF (notb) THEN
235 nrowb = k
236 ELSE
237 nrowb = n
238 END IF
239*
240* Test the input parameters.
241*
242 info = 0
243 IF ((.NOT.nota) .AND. (.NOT.lsame(transa,'C')) .AND.
244 + (.NOT.lsame(transa,'T'))) THEN
245 info = 1
246 ELSE IF ((.NOT.notb) .AND. (.NOT.lsame(transb,'C')) .AND.
247 + (.NOT.lsame(transb,'T'))) THEN
248 info = 2
249 ELSE IF (m.LT.0) THEN
250 info = 3
251 ELSE IF (n.LT.0) THEN
252 info = 4
253 ELSE IF (k.LT.0) THEN
254 info = 5
255 ELSE IF (lda.LT.max(1,nrowa)) THEN
256 info = 8
257 ELSE IF (ldb.LT.max(1,nrowb)) THEN
258 info = 10
259 ELSE IF (ldc.LT.max(1,m)) THEN
260 info = 13
261 END IF
262 IF (info.NE.0) THEN
263 CALL xerbla('SGEMM ',info)
264 RETURN
265 END IF
266*
267* Quick return if possible.
268*
269 IF ((m.EQ.0) .OR. (n.EQ.0) .OR.
270 + (((alpha.EQ.zero).OR. (k.EQ.0)).AND. (beta.EQ.one))) RETURN
271*
272* And if alpha.eq.zero.
273*
274 IF (alpha.EQ.zero) THEN
275 IF (beta.EQ.zero) THEN
276 DO 20 j = 1,n
277 DO 10 i = 1,m
278 c(i,j) = zero
279 10 CONTINUE
280 20 CONTINUE
281 ELSE
282 DO 40 j = 1,n
283 DO 30 i = 1,m
284 c(i,j) = beta*c(i,j)
285 30 CONTINUE
286 40 CONTINUE
287 END IF
288 RETURN
289 END IF
290*
291* Start the operations.
292*
293 IF (notb) THEN
294 IF (nota) THEN
295*
296* Form C := alpha*A*B + beta*C.
297*
298 DO 90 j = 1,n
299 IF (beta.EQ.zero) THEN
300 DO 50 i = 1,m
301 c(i,j) = zero
302 50 CONTINUE
303 ELSE IF (beta.NE.one) THEN
304 DO 60 i = 1,m
305 c(i,j) = beta*c(i,j)
306 60 CONTINUE
307 END IF
308 DO 80 l = 1,k
309 temp = alpha*b(l,j)
310 DO 70 i = 1,m
311 c(i,j) = c(i,j) + temp*a(i,l)
312 70 CONTINUE
313 80 CONTINUE
314 90 CONTINUE
315 ELSE
316*
317* Form C := alpha*A**T*B + beta*C
318*
319 DO 120 j = 1,n
320 DO 110 i = 1,m
321 temp = zero
322 DO 100 l = 1,k
323 temp = temp + a(l,i)*b(l,j)
324 100 CONTINUE
325 IF (beta.EQ.zero) THEN
326 c(i,j) = alpha*temp
327 ELSE
328 c(i,j) = alpha*temp + beta*c(i,j)
329 END IF
330 110 CONTINUE
331 120 CONTINUE
332 END IF
333 ELSE
334 IF (nota) THEN
335*
336* Form C := alpha*A*B**T + beta*C
337*
338 DO 170 j = 1,n
339 IF (beta.EQ.zero) THEN
340 DO 130 i = 1,m
341 c(i,j) = zero
342 130 CONTINUE
343 ELSE IF (beta.NE.one) THEN
344 DO 140 i = 1,m
345 c(i,j) = beta*c(i,j)
346 140 CONTINUE
347 END IF
348 DO 160 l = 1,k
349 temp = alpha*b(j,l)
350 DO 150 i = 1,m
351 c(i,j) = c(i,j) + temp*a(i,l)
352 150 CONTINUE
353 160 CONTINUE
354 170 CONTINUE
355 ELSE
356*
357* Form C := alpha*A**T*B**T + beta*C
358*
359 DO 200 j = 1,n
360 DO 190 i = 1,m
361 temp = zero
362 DO 180 l = 1,k
363 temp = temp + a(l,i)*b(j,l)
364 180 CONTINUE
365 IF (beta.EQ.zero) THEN
366 c(i,j) = alpha*temp
367 ELSE
368 c(i,j) = alpha*temp + beta*c(i,j)
369 END IF
370 190 CONTINUE
371 200 CONTINUE
372 END IF
373 END IF
374*
375 RETURN
376*
377* End of SGEMM
378*
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
lsame
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
Here is the call graph for this function: