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: *> \date December 2016
170: *
171: *> \ingroup complex16_blas_level3
172: *
173: *> \par Further Details:
174: * =====================
175: *>
176: *> \verbatim
177: *>
178: *> Level 3 Blas routine.
179: *>
180: *> -- Written on 8-February-1989.
181: *> Jack Dongarra, Argonne National Laboratory.
182: *> Iain Duff, AERE Harwell.
183: *> Jeremy Du Croz, Numerical Algorithms Group Ltd.
184: *> Sven Hammarling, Numerical Algorithms Group Ltd.
185: *> \endverbatim
186: *>
187: * =====================================================================
188: SUBROUTINE ZGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
189: *
190: * -- Reference BLAS level3 routine (version 3.7.0) --
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: * December 2016
194: *
195: * .. Scalar Arguments ..
196: COMPLEX*16 ALPHA,BETA
197: INTEGER K,LDA,LDB,LDC,M,N
198: CHARACTER TRANSA,TRANSB
199: * ..
200: * .. Array Arguments ..
201: COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*)
202: * ..
203: *
204: * =====================================================================
205: *
206: * .. External Functions ..
207: LOGICAL LSAME
208: EXTERNAL LSAME
209: * ..
210: * .. External Subroutines ..
211: EXTERNAL XERBLA
212: * ..
213: * .. Intrinsic Functions ..
214: INTRINSIC DCONJG,MAX
215: * ..
216: * .. Local Scalars ..
217: COMPLEX*16 TEMP
218: INTEGER I,INFO,J,L,NCOLA,NROWA,NROWB
219: LOGICAL CONJA,CONJB,NOTA,NOTB
220: * ..
221: * .. Parameters ..
222: COMPLEX*16 ONE
223: PARAMETER (ONE= (1.0D+0,0.0D+0))
224: COMPLEX*16 ZERO
225: PARAMETER (ZERO= (0.0D+0,0.0D+0))
226: * ..
227: *
228: * Set NOTA and NOTB as true if A and B respectively are not
229: * conjugated or transposed, set CONJA and CONJB as true if A and
230: * B respectively are to be transposed but not conjugated and set
231: * NROWA, NCOLA and NROWB as the number of rows and columns of A
232: * and the number of rows of B respectively.
233: *
234: NOTA = LSAME(TRANSA,'N')
235: NOTB = LSAME(TRANSB,'N')
236: CONJA = LSAME(TRANSA,'C')
237: CONJB = LSAME(TRANSB,'C')
238: IF (NOTA) THEN
239: NROWA = M
240: NCOLA = K
241: ELSE
242: NROWA = K
243: NCOLA = M
244: END IF
245: IF (NOTB) THEN
246: NROWB = K
247: ELSE
248: NROWB = N
249: END IF
250: *
251: * Test the input parameters.
252: *
253: INFO = 0
254: IF ((.NOT.NOTA) .AND. (.NOT.CONJA) .AND.
255: + (.NOT.LSAME(TRANSA,'T'))) THEN
256: INFO = 1
257: ELSE IF ((.NOT.NOTB) .AND. (.NOT.CONJB) .AND.
258: + (.NOT.LSAME(TRANSB,'T'))) THEN
259: INFO = 2
260: ELSE IF (M.LT.0) THEN
261: INFO = 3
262: ELSE IF (N.LT.0) THEN
263: INFO = 4
264: ELSE IF (K.LT.0) THEN
265: INFO = 5
266: ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
267: INFO = 8
268: ELSE IF (LDB.LT.MAX(1,NROWB)) THEN
269: INFO = 10
270: ELSE IF (LDC.LT.MAX(1,M)) THEN
271: INFO = 13
272: END IF
273: IF (INFO.NE.0) THEN
274: CALL XERBLA('ZGEMM ',INFO)
275: RETURN
276: END IF
277: *
278: * Quick return if possible.
279: *
280: IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
281: + (((ALPHA.EQ.ZERO).OR. (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN
282: *
283: * And when alpha.eq.zero.
284: *
285: IF (ALPHA.EQ.ZERO) THEN
286: IF (BETA.EQ.ZERO) THEN
287: DO 20 J = 1,N
288: DO 10 I = 1,M
289: C(I,J) = ZERO
290: 10 CONTINUE
291: 20 CONTINUE
292: ELSE
293: DO 40 J = 1,N
294: DO 30 I = 1,M
295: C(I,J) = BETA*C(I,J)
296: 30 CONTINUE
297: 40 CONTINUE
298: END IF
299: RETURN
300: END IF
301: *
302: * Start the operations.
303: *
304: IF (NOTB) THEN
305: IF (NOTA) THEN
306: *
307: * Form C := alpha*A*B + beta*C.
308: *
309: DO 90 J = 1,N
310: IF (BETA.EQ.ZERO) THEN
311: DO 50 I = 1,M
312: C(I,J) = ZERO
313: 50 CONTINUE
314: ELSE IF (BETA.NE.ONE) THEN
315: DO 60 I = 1,M
316: C(I,J) = BETA*C(I,J)
317: 60 CONTINUE
318: END IF
319: DO 80 L = 1,K
320: TEMP = ALPHA*B(L,J)
321: DO 70 I = 1,M
322: C(I,J) = C(I,J) + TEMP*A(I,L)
323: 70 CONTINUE
324: 80 CONTINUE
325: 90 CONTINUE
326: ELSE IF (CONJA) THEN
327: *
328: * Form C := alpha*A**H*B + beta*C.
329: *
330: DO 120 J = 1,N
331: DO 110 I = 1,M
332: TEMP = ZERO
333: DO 100 L = 1,K
334: TEMP = TEMP + DCONJG(A(L,I))*B(L,J)
335: 100 CONTINUE
336: IF (BETA.EQ.ZERO) THEN
337: C(I,J) = ALPHA*TEMP
338: ELSE
339: C(I,J) = ALPHA*TEMP + BETA*C(I,J)
340: END IF
341: 110 CONTINUE
342: 120 CONTINUE
343: ELSE
344: *
345: * Form C := alpha*A**T*B + beta*C
346: *
347: DO 150 J = 1,N
348: DO 140 I = 1,M
349: TEMP = ZERO
350: DO 130 L = 1,K
351: TEMP = TEMP + A(L,I)*B(L,J)
352: 130 CONTINUE
353: IF (BETA.EQ.ZERO) THEN
354: C(I,J) = ALPHA*TEMP
355: ELSE
356: C(I,J) = ALPHA*TEMP + BETA*C(I,J)
357: END IF
358: 140 CONTINUE
359: 150 CONTINUE
360: END IF
361: ELSE IF (NOTA) THEN
362: IF (CONJB) THEN
363: *
364: * Form C := alpha*A*B**H + beta*C.
365: *
366: DO 200 J = 1,N
367: IF (BETA.EQ.ZERO) THEN
368: DO 160 I = 1,M
369: C(I,J) = ZERO
370: 160 CONTINUE
371: ELSE IF (BETA.NE.ONE) THEN
372: DO 170 I = 1,M
373: C(I,J) = BETA*C(I,J)
374: 170 CONTINUE
375: END IF
376: DO 190 L = 1,K
377: TEMP = ALPHA*DCONJG(B(J,L))
378: DO 180 I = 1,M
379: C(I,J) = C(I,J) + TEMP*A(I,L)
380: 180 CONTINUE
381: 190 CONTINUE
382: 200 CONTINUE
383: ELSE
384: *
385: * Form C := alpha*A*B**T + beta*C
386: *
387: DO 250 J = 1,N
388: IF (BETA.EQ.ZERO) THEN
389: DO 210 I = 1,M
390: C(I,J) = ZERO
391: 210 CONTINUE
392: ELSE IF (BETA.NE.ONE) THEN
393: DO 220 I = 1,M
394: C(I,J) = BETA*C(I,J)
395: 220 CONTINUE
396: END IF
397: DO 240 L = 1,K
398: TEMP = ALPHA*B(J,L)
399: DO 230 I = 1,M
400: C(I,J) = C(I,J) + TEMP*A(I,L)
401: 230 CONTINUE
402: 240 CONTINUE
403: 250 CONTINUE
404: END IF
405: ELSE IF (CONJA) THEN
406: IF (CONJB) THEN
407: *
408: * Form C := alpha*A**H*B**H + beta*C.
409: *
410: DO 280 J = 1,N
411: DO 270 I = 1,M
412: TEMP = ZERO
413: DO 260 L = 1,K
414: TEMP = TEMP + DCONJG(A(L,I))*DCONJG(B(J,L))
415: 260 CONTINUE
416: IF (BETA.EQ.ZERO) THEN
417: C(I,J) = ALPHA*TEMP
418: ELSE
419: C(I,J) = ALPHA*TEMP + BETA*C(I,J)
420: END IF
421: 270 CONTINUE
422: 280 CONTINUE
423: ELSE
424: *
425: * Form C := alpha*A**H*B**T + beta*C
426: *
427: DO 310 J = 1,N
428: DO 300 I = 1,M
429: TEMP = ZERO
430: DO 290 L = 1,K
431: TEMP = TEMP + DCONJG(A(L,I))*B(J,L)
432: 290 CONTINUE
433: IF (BETA.EQ.ZERO) THEN
434: C(I,J) = ALPHA*TEMP
435: ELSE
436: C(I,J) = ALPHA*TEMP + BETA*C(I,J)
437: END IF
438: 300 CONTINUE
439: 310 CONTINUE
440: END IF
441: ELSE
442: IF (CONJB) THEN
443: *
444: * Form C := alpha*A**T*B**H + beta*C
445: *
446: DO 340 J = 1,N
447: DO 330 I = 1,M
448: TEMP = ZERO
449: DO 320 L = 1,K
450: TEMP = TEMP + A(L,I)*DCONJG(B(J,L))
451: 320 CONTINUE
452: IF (BETA.EQ.ZERO) THEN
453: C(I,J) = ALPHA*TEMP
454: ELSE
455: C(I,J) = ALPHA*TEMP + BETA*C(I,J)
456: END IF
457: 330 CONTINUE
458: 340 CONTINUE
459: ELSE
460: *
461: * Form C := alpha*A**T*B**T + beta*C
462: *
463: DO 370 J = 1,N
464: DO 360 I = 1,M
465: TEMP = ZERO
466: DO 350 L = 1,K
467: TEMP = TEMP + A(L,I)*B(J,L)
468: 350 CONTINUE
469: IF (BETA.EQ.ZERO) THEN
470: C(I,J) = ALPHA*TEMP
471: ELSE
472: C(I,J) = ALPHA*TEMP + BETA*C(I,J)
473: END IF
474: 360 CONTINUE
475: 370 CONTINUE
476: END IF
477: END IF
478: *
479: RETURN
480: *
481: * End of ZGEMM .
482: *
483: END
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