LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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zgemm.f
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1*> \brief \b ZGEMM
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8* Definition:
9* ===========
10*
11* SUBROUTINE ZGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
12*
13* .. Scalar Arguments ..
14* COMPLEX*16 ALPHA,BETA
15* INTEGER K,LDA,LDB,LDC,M,N
16* CHARACTER TRANSA,TRANSB
17* ..
18* .. Array Arguments ..
19* COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*)
20* ..
21*
22*
23*> \par Purpose:
24* =============
25*>
26*> \verbatim
27*>
28*> ZGEMM performs one of the matrix-matrix operations
29*>
30*> C := alpha*op( A )*op( B ) + beta*C,
31*>
32*> where op( X ) is one of
33*>
34*> op( X ) = X or op( X ) = X**T or op( X ) = X**H,
35*>
36*> alpha and beta are scalars, and A, B and C are matrices, with op( A )
37*> an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.
38*> \endverbatim
39*
40* Arguments:
41* ==========
42*
43*> \param[in] TRANSA
44*> \verbatim
45*> TRANSA is CHARACTER*1
46*> On entry, TRANSA specifies the form of op( A ) to be used in
47*> the matrix multiplication as follows:
48*>
49*> TRANSA = 'N' or 'n', op( A ) = A.
50*>
51*> TRANSA = 'T' or 't', op( A ) = A**T.
52*>
53*> TRANSA = 'C' or 'c', op( A ) = A**H.
54*> \endverbatim
55*>
56*> \param[in] TRANSB
57*> \verbatim
58*> TRANSB is CHARACTER*1
59*> On entry, TRANSB specifies the form of op( B ) to be used in
60*> the matrix multiplication as follows:
61*>
62*> TRANSB = 'N' or 'n', op( B ) = B.
63*>
64*> TRANSB = 'T' or 't', op( B ) = B**T.
65*>
66*> TRANSB = 'C' or 'c', op( B ) = B**H.
67*> \endverbatim
68*>
69*> \param[in] M
70*> \verbatim
71*> M is INTEGER
72*> On entry, M specifies the number of rows of the matrix
73*> op( A ) and of the matrix C. M must be at least zero.
74*> \endverbatim
75*>
76*> \param[in] N
77*> \verbatim
78*> N is INTEGER
79*> On entry, N specifies the number of columns of the matrix
80*> op( B ) and the number of columns of the matrix C. N must be
81*> at least zero.
82*> \endverbatim
83*>
84*> \param[in] K
85*> \verbatim
86*> K is INTEGER
87*> On entry, K specifies the number of columns of the matrix
88*> op( A ) and the number of rows of the matrix op( B ). K must
89*> be at least zero.
90*> \endverbatim
91*>
92*> \param[in] ALPHA
93*> \verbatim
94*> ALPHA is COMPLEX*16
95*> On entry, ALPHA specifies the scalar alpha.
96*> \endverbatim
97*>
98*> \param[in] A
99*> \verbatim
100*> A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is
101*> k when TRANSA = 'N' or 'n', and is m otherwise.
102*> Before entry with TRANSA = 'N' or 'n', the leading m by k
103*> part of the array A must contain the matrix A, otherwise
104*> the leading k by m part of the array A must contain the
105*> matrix A.
106*> \endverbatim
107*>
108*> \param[in] LDA
109*> \verbatim
110*> LDA is INTEGER
111*> On entry, LDA specifies the first dimension of A as declared
112*> in the calling (sub) program. When TRANSA = 'N' or 'n' then
113*> LDA must be at least max( 1, m ), otherwise LDA must be at
114*> least max( 1, k ).
115*> \endverbatim
116*>
117*> \param[in] B
118*> \verbatim
119*> B is COMPLEX*16 array, dimension ( LDB, kb ), where kb is
120*> n when TRANSB = 'N' or 'n', and is k otherwise.
121*> Before entry with TRANSB = 'N' or 'n', the leading k by n
122*> part of the array B must contain the matrix B, otherwise
123*> the leading n by k part of the array B must contain the
124*> matrix B.
125*> \endverbatim
126*>
127*> \param[in] LDB
128*> \verbatim
129*> LDB is INTEGER
130*> On entry, LDB specifies the first dimension of B as declared
131*> in the calling (sub) program. When TRANSB = 'N' or 'n' then
132*> LDB must be at least max( 1, k ), otherwise LDB must be at
133*> least max( 1, n ).
134*> \endverbatim
135*>
136*> \param[in] BETA
137*> \verbatim
138*> BETA is COMPLEX*16
139*> On entry, BETA specifies the scalar beta. When BETA is
140*> supplied as zero then C need not be set on input.
141*> \endverbatim
142*>
143*> \param[in,out] C
144*> \verbatim
145*> C is COMPLEX*16 array, dimension ( LDC, N )
146*> Before entry, the leading m by n part of the array C must
147*> contain the matrix C, except when beta is zero, in which
148*> case C need not be set on entry.
149*> On exit, the array C is overwritten by the m by n matrix
150*> ( alpha*op( A )*op( B ) + beta*C ).
151*> \endverbatim
152*>
153*> \param[in] LDC
154*> \verbatim
155*> LDC is INTEGER
156*> On entry, LDC specifies the first dimension of C as declared
157*> in the calling (sub) program. LDC must be at least
158*> max( 1, m ).
159*> \endverbatim
160*
161* Authors:
162* ========
163*
164*> \author Univ. of Tennessee
165*> \author Univ. of California Berkeley
166*> \author Univ. of Colorado Denver
167*> \author NAG Ltd.
168*
169*> \ingroup complex16_blas_level3
170*
171*> \par Further Details:
172* =====================
173*>
174*> \verbatim
175*>
176*> Level 3 Blas routine.
177*>
178*> -- Written on 8-February-1989.
179*> Jack Dongarra, Argonne National Laboratory.
180*> Iain Duff, AERE Harwell.
181*> Jeremy Du Croz, Numerical Algorithms Group Ltd.
182*> Sven Hammarling, Numerical Algorithms Group Ltd.
183*> \endverbatim
184*>
185* =====================================================================
186 SUBROUTINE zgemm(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
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*16 ALPHA,BETA
194 INTEGER K,LDA,LDB,LDC,M,N
195 CHARACTER TRANSA,TRANSB
196* ..
197* .. Array Arguments ..
198 COMPLEX*16 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 dconjg,max
212* ..
213* .. Local Scalars ..
214 COMPLEX*16 TEMP
215 INTEGER I,INFO,J,L,NROWA,NROWB
216 LOGICAL CONJA,CONJB,NOTA,NOTB
217* ..
218* .. Parameters ..
219 COMPLEX*16 ONE
220 parameter(one= (1.0d+0,0.0d+0))
221 COMPLEX*16 ZERO
222 parameter(zero= (0.0d+0,0.0d+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('ZGEMM ',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 + dconjg(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*dconjg(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 + dconjg(a(l,i))*dconjg(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 + dconjg(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)*dconjg(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 ZGEMM
476*
477 END
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
zgemm
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:187