LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ cgemm()

 subroutine cgemm ( character TRANSA, character TRANSB, integer M, integer N, integer K, complex ALPHA, complex, dimension(lda,*) A, integer LDA, complex, dimension(ldb,*) B, integer LDB, complex BETA, complex, dimension(ldc,*) C, integer LDC )

CGEMM

Purpose:
``` CGEMM  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   or   op( X ) = X**H,

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**H.``` [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**H.``` [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 COMPLEX On entry, ALPHA specifies the scalar alpha.``` [in] A ``` A is COMPLEX 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 COMPLEX 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 COMPLEX 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 COMPLEX 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 ).```
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 cgemm.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  COMPLEX ALPHA,BETA
194  INTEGER K,LDA,LDB,LDC,M,N
195  CHARACTER TRANSA,TRANSB
196 * ..
197 * .. Array Arguments ..
198  COMPLEX 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 conjg,max
212 * ..
213 * .. Local Scalars ..
214  COMPLEX TEMP
215  INTEGER I,INFO,J,L,NROWA,NROWB
216  LOGICAL CONJA,CONJB,NOTA,NOTB
217 * ..
218 * .. Parameters ..
219  COMPLEX ONE
220  parameter(one= (1.0e+0,0.0e+0))
221  COMPLEX ZERO
222  parameter(zero= (0.0e+0,0.0e+0))
223 * ..
224 *
225 * Set NOTA and NOTB as true if A and B respectively are not
226 * conjugated or transposed, set CONJA and CONJB as true if A and
227 * B respectively are to be transposed but not conjugated and set
228 * NROWA and NROWB as the number of rows of A and B respectively.
229 *
230  nota = lsame(transa,'N')
231  notb = lsame(transb,'N')
232  conja = lsame(transa,'C')
233  conjb = lsame(transb,'C')
234  IF (nota) THEN
235  nrowa = m
236  ELSE
237  nrowa = k
238  END IF
239  IF (notb) THEN
240  nrowb = k
241  ELSE
242  nrowb = n
243  END IF
244 *
245 * Test the input parameters.
246 *
247  info = 0
248  IF ((.NOT.nota) .AND. (.NOT.conja) .AND.
249  + (.NOT.lsame(transa,'T'))) THEN
250  info = 1
251  ELSE IF ((.NOT.notb) .AND. (.NOT.conjb) .AND.
252  + (.NOT.lsame(transb,'T'))) THEN
253  info = 2
254  ELSE IF (m.LT.0) THEN
255  info = 3
256  ELSE IF (n.LT.0) THEN
257  info = 4
258  ELSE IF (k.LT.0) THEN
259  info = 5
260  ELSE IF (lda.LT.max(1,nrowa)) THEN
261  info = 8
262  ELSE IF (ldb.LT.max(1,nrowb)) THEN
263  info = 10
264  ELSE IF (ldc.LT.max(1,m)) THEN
265  info = 13
266  END IF
267  IF (info.NE.0) THEN
268  CALL xerbla('CGEMM ',info)
269  RETURN
270  END IF
271 *
272 * Quick return if possible.
273 *
274  IF ((m.EQ.0) .OR. (n.EQ.0) .OR.
275  + (((alpha.EQ.zero).OR. (k.EQ.0)).AND. (beta.EQ.one))) RETURN
276 *
277 * And when alpha.eq.zero.
278 *
279  IF (alpha.EQ.zero) THEN
280  IF (beta.EQ.zero) THEN
281  DO 20 j = 1,n
282  DO 10 i = 1,m
283  c(i,j) = zero
284  10 CONTINUE
285  20 CONTINUE
286  ELSE
287  DO 40 j = 1,n
288  DO 30 i = 1,m
289  c(i,j) = beta*c(i,j)
290  30 CONTINUE
291  40 CONTINUE
292  END IF
293  RETURN
294  END IF
295 *
296 * Start the operations.
297 *
298  IF (notb) THEN
299  IF (nota) THEN
300 *
301 * Form C := alpha*A*B + beta*C.
302 *
303  DO 90 j = 1,n
304  IF (beta.EQ.zero) THEN
305  DO 50 i = 1,m
306  c(i,j) = zero
307  50 CONTINUE
308  ELSE IF (beta.NE.one) THEN
309  DO 60 i = 1,m
310  c(i,j) = beta*c(i,j)
311  60 CONTINUE
312  END IF
313  DO 80 l = 1,k
314  temp = alpha*b(l,j)
315  DO 70 i = 1,m
316  c(i,j) = c(i,j) + temp*a(i,l)
317  70 CONTINUE
318  80 CONTINUE
319  90 CONTINUE
320  ELSE IF (conja) THEN
321 *
322 * Form C := alpha*A**H*B + beta*C.
323 *
324  DO 120 j = 1,n
325  DO 110 i = 1,m
326  temp = zero
327  DO 100 l = 1,k
328  temp = temp + conjg(a(l,i))*b(l,j)
329  100 CONTINUE
330  IF (beta.EQ.zero) THEN
331  c(i,j) = alpha*temp
332  ELSE
333  c(i,j) = alpha*temp + beta*c(i,j)
334  END IF
335  110 CONTINUE
336  120 CONTINUE
337  ELSE
338 *
339 * Form C := alpha*A**T*B + beta*C
340 *
341  DO 150 j = 1,n
342  DO 140 i = 1,m
343  temp = zero
344  DO 130 l = 1,k
345  temp = temp + a(l,i)*b(l,j)
346  130 CONTINUE
347  IF (beta.EQ.zero) THEN
348  c(i,j) = alpha*temp
349  ELSE
350  c(i,j) = alpha*temp + beta*c(i,j)
351  END IF
352  140 CONTINUE
353  150 CONTINUE
354  END IF
355  ELSE IF (nota) THEN
356  IF (conjb) THEN
357 *
358 * Form C := alpha*A*B**H + beta*C.
359 *
360  DO 200 j = 1,n
361  IF (beta.EQ.zero) THEN
362  DO 160 i = 1,m
363  c(i,j) = zero
364  160 CONTINUE
365  ELSE IF (beta.NE.one) THEN
366  DO 170 i = 1,m
367  c(i,j) = beta*c(i,j)
368  170 CONTINUE
369  END IF
370  DO 190 l = 1,k
371  temp = alpha*conjg(b(j,l))
372  DO 180 i = 1,m
373  c(i,j) = c(i,j) + temp*a(i,l)
374  180 CONTINUE
375  190 CONTINUE
376  200 CONTINUE
377  ELSE
378 *
379 * Form C := alpha*A*B**T + beta*C
380 *
381  DO 250 j = 1,n
382  IF (beta.EQ.zero) THEN
383  DO 210 i = 1,m
384  c(i,j) = zero
385  210 CONTINUE
386  ELSE IF (beta.NE.one) THEN
387  DO 220 i = 1,m
388  c(i,j) = beta*c(i,j)
389  220 CONTINUE
390  END IF
391  DO 240 l = 1,k
392  temp = alpha*b(j,l)
393  DO 230 i = 1,m
394  c(i,j) = c(i,j) + temp*a(i,l)
395  230 CONTINUE
396  240 CONTINUE
397  250 CONTINUE
398  END IF
399  ELSE IF (conja) THEN
400  IF (conjb) THEN
401 *
402 * Form C := alpha*A**H*B**H + beta*C.
403 *
404  DO 280 j = 1,n
405  DO 270 i = 1,m
406  temp = zero
407  DO 260 l = 1,k
408  temp = temp + conjg(a(l,i))*conjg(b(j,l))
409  260 CONTINUE
410  IF (beta.EQ.zero) THEN
411  c(i,j) = alpha*temp
412  ELSE
413  c(i,j) = alpha*temp + beta*c(i,j)
414  END IF
415  270 CONTINUE
416  280 CONTINUE
417  ELSE
418 *
419 * Form C := alpha*A**H*B**T + beta*C
420 *
421  DO 310 j = 1,n
422  DO 300 i = 1,m
423  temp = zero
424  DO 290 l = 1,k
425  temp = temp + conjg(a(l,i))*b(j,l)
426  290 CONTINUE
427  IF (beta.EQ.zero) THEN
428  c(i,j) = alpha*temp
429  ELSE
430  c(i,j) = alpha*temp + beta*c(i,j)
431  END IF
432  300 CONTINUE
433  310 CONTINUE
434  END IF
435  ELSE
436  IF (conjb) THEN
437 *
438 * Form C := alpha*A**T*B**H + beta*C
439 *
440  DO 340 j = 1,n
441  DO 330 i = 1,m
442  temp = zero
443  DO 320 l = 1,k
444  temp = temp + a(l,i)*conjg(b(j,l))
445  320 CONTINUE
446  IF (beta.EQ.zero) THEN
447  c(i,j) = alpha*temp
448  ELSE
449  c(i,j) = alpha*temp + beta*c(i,j)
450  END IF
451  330 CONTINUE
452  340 CONTINUE
453  ELSE
454 *
455 * Form C := alpha*A**T*B**T + beta*C
456 *
457  DO 370 j = 1,n
458  DO 360 i = 1,m
459  temp = zero
460  DO 350 l = 1,k
461  temp = temp + a(l,i)*b(j,l)
462  350 CONTINUE
463  IF (beta.EQ.zero) THEN
464  c(i,j) = alpha*temp
465  ELSE
466  c(i,j) = alpha*temp + beta*c(i,j)
467  END IF
468  360 CONTINUE
469  370 CONTINUE
470  END IF
471  END IF
472 *
473  RETURN
474 *
475 * End of CGEMM
476 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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