1: SUBROUTINE ZGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
2: * .. Scalar Arguments ..
3: DOUBLE COMPLEX ALPHA,BETA
4: INTEGER K,LDA,LDB,LDC,M,N
5: CHARACTER TRANSA,TRANSB
6: * ..
7: * .. Array Arguments ..
8: DOUBLE COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
9: * ..
10: *
11: * Purpose
12: * =======
13: *
14: * ZGEMM performs one of the matrix-matrix operations
15: *
16: * C := alpha*op( A )*op( B ) + beta*C,
17: *
18: * where op( X ) is one of
19: *
20: * op( X ) = X or op( X ) = X' or op( X ) = conjg( X' ),
21: *
22: * alpha and beta are scalars, and A, B and C are matrices, with op( A )
23: * an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.
24: *
25: * Arguments
26: * ==========
27: *
28: * TRANSA - CHARACTER*1.
29: * On entry, TRANSA specifies the form of op( A ) to be used in
30: * the matrix multiplication as follows:
31: *
32: * TRANSA = 'N' or 'n', op( A ) = A.
33: *
34: * TRANSA = 'T' or 't', op( A ) = A'.
35: *
36: * TRANSA = 'C' or 'c', op( A ) = conjg( A' ).
37: *
38: * Unchanged on exit.
39: *
40: * TRANSB - CHARACTER*1.
41: * On entry, TRANSB specifies the form of op( B ) to be used in
42: * the matrix multiplication as follows:
43: *
44: * TRANSB = 'N' or 'n', op( B ) = B.
45: *
46: * TRANSB = 'T' or 't', op( B ) = B'.
47: *
48: * TRANSB = 'C' or 'c', op( B ) = conjg( B' ).
49: *
50: * Unchanged on exit.
51: *
52: * M - INTEGER.
53: * On entry, M specifies the number of rows of the matrix
54: * op( A ) and of the matrix C. M must be at least zero.
55: * Unchanged on exit.
56: *
57: * N - INTEGER.
58: * On entry, N specifies the number of columns of the matrix
59: * op( B ) and the number of columns of the matrix C. N must be
60: * at least zero.
61: * Unchanged on exit.
62: *
63: * K - INTEGER.
64: * On entry, K specifies the number of columns of the matrix
65: * op( A ) and the number of rows of the matrix op( B ). K must
66: * be at least zero.
67: * Unchanged on exit.
68: *
69: * ALPHA - COMPLEX*16 .
70: * On entry, ALPHA specifies the scalar alpha.
71: * Unchanged on exit.
72: *
73: * A - COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is
74: * k when TRANSA = 'N' or 'n', and is m otherwise.
75: * Before entry with TRANSA = 'N' or 'n', the leading m by k
76: * part of the array A must contain the matrix A, otherwise
77: * the leading k by m part of the array A must contain the
78: * matrix A.
79: * Unchanged on exit.
80: *
81: * LDA - INTEGER.
82: * On entry, LDA specifies the first dimension of A as declared
83: * in the calling (sub) program. When TRANSA = 'N' or 'n' then
84: * LDA must be at least max( 1, m ), otherwise LDA must be at
85: * least max( 1, k ).
86: * Unchanged on exit.
87: *
88: * B - COMPLEX*16 array of DIMENSION ( LDB, kb ), where kb is
89: * n when TRANSB = 'N' or 'n', and is k otherwise.
90: * Before entry with TRANSB = 'N' or 'n', the leading k by n
91: * part of the array B must contain the matrix B, otherwise
92: * the leading n by k part of the array B must contain the
93: * matrix B.
94: * Unchanged on exit.
95: *
96: * LDB - INTEGER.
97: * On entry, LDB specifies the first dimension of B as declared
98: * in the calling (sub) program. When TRANSB = 'N' or 'n' then
99: * LDB must be at least max( 1, k ), otherwise LDB must be at
100: * least max( 1, n ).
101: * Unchanged on exit.
102: *
103: * BETA - COMPLEX*16 .
104: * On entry, BETA specifies the scalar beta. When BETA is
105: * supplied as zero then C need not be set on input.
106: * Unchanged on exit.
107: *
108: * C - COMPLEX*16 array of DIMENSION ( LDC, n ).
109: * Before entry, the leading m by n part of the array C must
110: * contain the matrix C, except when beta is zero, in which
111: * case C need not be set on entry.
112: * On exit, the array C is overwritten by the m by n matrix
113: * ( alpha*op( A )*op( B ) + beta*C ).
114: *
115: * LDC - INTEGER.
116: * On entry, LDC specifies the first dimension of C as declared
117: * in the calling (sub) program. LDC must be at least
118: * max( 1, m ).
119: * Unchanged on exit.
120: *
121: * Further Details
122: * ===============
123: *
124: * Level 3 Blas routine.
125: *
126: * -- Written on 8-February-1989.
127: * Jack Dongarra, Argonne National Laboratory.
128: * Iain Duff, AERE Harwell.
129: * Jeremy Du Croz, Numerical Algorithms Group Ltd.
130: * Sven Hammarling, Numerical Algorithms Group Ltd.
131: *
132: * =====================================================================
133: *
134: * .. External Functions ..
135: LOGICAL LSAME
136: EXTERNAL LSAME
137: * ..
138: * .. External Subroutines ..
139: EXTERNAL XERBLA
140: * ..
141: * .. Intrinsic Functions ..
142: INTRINSIC DCONJG,MAX
143: * ..
144: * .. Local Scalars ..
145: DOUBLE COMPLEX TEMP
146: INTEGER I,INFO,J,L,NCOLA,NROWA,NROWB
147: LOGICAL CONJA,CONJB,NOTA,NOTB
148: * ..
149: * .. Parameters ..
150: DOUBLE COMPLEX ONE
151: PARAMETER (ONE= (1.0D+0,0.0D+0))
152: DOUBLE COMPLEX ZERO
153: PARAMETER (ZERO= (0.0D+0,0.0D+0))
154: * ..
155: *
156: * Set NOTA and NOTB as true if A and B respectively are not
157: * conjugated or transposed, set CONJA and CONJB as true if A and
158: * B respectively are to be transposed but not conjugated and set
159: * NROWA, NCOLA and NROWB as the number of rows and columns of A
160: * and the number of rows of B respectively.
161: *
162: NOTA = LSAME(TRANSA,'N')
163: NOTB = LSAME(TRANSB,'N')
164: CONJA = LSAME(TRANSA,'C')
165: CONJB = LSAME(TRANSB,'C')
166: IF (NOTA) THEN
167: NROWA = M
168: NCOLA = K
169: ELSE
170: NROWA = K
171: NCOLA = M
172: END IF
173: IF (NOTB) THEN
174: NROWB = K
175: ELSE
176: NROWB = N
177: END IF
178: *
179: * Test the input parameters.
180: *
181: INFO = 0
182: IF ((.NOT.NOTA) .AND. (.NOT.CONJA) .AND.
183: + (.NOT.LSAME(TRANSA,'T'))) THEN
184: INFO = 1
185: ELSE IF ((.NOT.NOTB) .AND. (.NOT.CONJB) .AND.
186: + (.NOT.LSAME(TRANSB,'T'))) THEN
187: INFO = 2
188: ELSE IF (M.LT.0) THEN
189: INFO = 3
190: ELSE IF (N.LT.0) THEN
191: INFO = 4
192: ELSE IF (K.LT.0) THEN
193: INFO = 5
194: ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
195: INFO = 8
196: ELSE IF (LDB.LT.MAX(1,NROWB)) THEN
197: INFO = 10
198: ELSE IF (LDC.LT.MAX(1,M)) THEN
199: INFO = 13
200: END IF
201: IF (INFO.NE.0) THEN
202: CALL XERBLA('ZGEMM ',INFO)
203: RETURN
204: END IF
205: *
206: * Quick return if possible.
207: *
208: IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
209: + (((ALPHA.EQ.ZERO).OR. (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN
210: *
211: * And when alpha.eq.zero.
212: *
213: IF (ALPHA.EQ.ZERO) THEN
214: IF (BETA.EQ.ZERO) THEN
215: DO 20 J = 1,N
216: DO 10 I = 1,M
217: C(I,J) = ZERO
218: 10 CONTINUE
219: 20 CONTINUE
220: ELSE
221: DO 40 J = 1,N
222: DO 30 I = 1,M
223: C(I,J) = BETA*C(I,J)
224: 30 CONTINUE
225: 40 CONTINUE
226: END IF
227: RETURN
228: END IF
229: *
230: * Start the operations.
231: *
232: IF (NOTB) THEN
233: IF (NOTA) THEN
234: *
235: * Form C := alpha*A*B + beta*C.
236: *
237: DO 90 J = 1,N
238: IF (BETA.EQ.ZERO) THEN
239: DO 50 I = 1,M
240: C(I,J) = ZERO
241: 50 CONTINUE
242: ELSE IF (BETA.NE.ONE) THEN
243: DO 60 I = 1,M
244: C(I,J) = BETA*C(I,J)
245: 60 CONTINUE
246: END IF
247: DO 80 L = 1,K
248: IF (B(L,J).NE.ZERO) THEN
249: TEMP = ALPHA*B(L,J)
250: DO 70 I = 1,M
251: C(I,J) = C(I,J) + TEMP*A(I,L)
252: 70 CONTINUE
253: END IF
254: 80 CONTINUE
255: 90 CONTINUE
256: ELSE IF (CONJA) THEN
257: *
258: * Form C := alpha*conjg( A' )*B + beta*C.
259: *
260: DO 120 J = 1,N
261: DO 110 I = 1,M
262: TEMP = ZERO
263: DO 100 L = 1,K
264: TEMP = TEMP + DCONJG(A(L,I))*B(L,J)
265: 100 CONTINUE
266: IF (BETA.EQ.ZERO) THEN
267: C(I,J) = ALPHA*TEMP
268: ELSE
269: C(I,J) = ALPHA*TEMP + BETA*C(I,J)
270: END IF
271: 110 CONTINUE
272: 120 CONTINUE
273: ELSE
274: *
275: * Form C := alpha*A'*B + beta*C
276: *
277: DO 150 J = 1,N
278: DO 140 I = 1,M
279: TEMP = ZERO
280: DO 130 L = 1,K
281: TEMP = TEMP + A(L,I)*B(L,J)
282: 130 CONTINUE
283: IF (BETA.EQ.ZERO) THEN
284: C(I,J) = ALPHA*TEMP
285: ELSE
286: C(I,J) = ALPHA*TEMP + BETA*C(I,J)
287: END IF
288: 140 CONTINUE
289: 150 CONTINUE
290: END IF
291: ELSE IF (NOTA) THEN
292: IF (CONJB) THEN
293: *
294: * Form C := alpha*A*conjg( B' ) + beta*C.
295: *
296: DO 200 J = 1,N
297: IF (BETA.EQ.ZERO) THEN
298: DO 160 I = 1,M
299: C(I,J) = ZERO
300: 160 CONTINUE
301: ELSE IF (BETA.NE.ONE) THEN
302: DO 170 I = 1,M
303: C(I,J) = BETA*C(I,J)
304: 170 CONTINUE
305: END IF
306: DO 190 L = 1,K
307: IF (B(J,L).NE.ZERO) THEN
308: TEMP = ALPHA*DCONJG(B(J,L))
309: DO 180 I = 1,M
310: C(I,J) = C(I,J) + TEMP*A(I,L)
311: 180 CONTINUE
312: END IF
313: 190 CONTINUE
314: 200 CONTINUE
315: ELSE
316: *
317: * Form C := alpha*A*B' + beta*C
318: *
319: DO 250 J = 1,N
320: IF (BETA.EQ.ZERO) THEN
321: DO 210 I = 1,M
322: C(I,J) = ZERO
323: 210 CONTINUE
324: ELSE IF (BETA.NE.ONE) THEN
325: DO 220 I = 1,M
326: C(I,J) = BETA*C(I,J)
327: 220 CONTINUE
328: END IF
329: DO 240 L = 1,K
330: IF (B(J,L).NE.ZERO) THEN
331: TEMP = ALPHA*B(J,L)
332: DO 230 I = 1,M
333: C(I,J) = C(I,J) + TEMP*A(I,L)
334: 230 CONTINUE
335: END IF
336: 240 CONTINUE
337: 250 CONTINUE
338: END IF
339: ELSE IF (CONJA) THEN
340: IF (CONJB) THEN
341: *
342: * Form C := alpha*conjg( A' )*conjg( B' ) + beta*C.
343: *
344: DO 280 J = 1,N
345: DO 270 I = 1,M
346: TEMP = ZERO
347: DO 260 L = 1,K
348: TEMP = TEMP + DCONJG(A(L,I))*DCONJG(B(J,L))
349: 260 CONTINUE
350: IF (BETA.EQ.ZERO) THEN
351: C(I,J) = ALPHA*TEMP
352: ELSE
353: C(I,J) = ALPHA*TEMP + BETA*C(I,J)
354: END IF
355: 270 CONTINUE
356: 280 CONTINUE
357: ELSE
358: *
359: * Form C := alpha*conjg( A' )*B' + beta*C
360: *
361: DO 310 J = 1,N
362: DO 300 I = 1,M
363: TEMP = ZERO
364: DO 290 L = 1,K
365: TEMP = TEMP + DCONJG(A(L,I))*B(J,L)
366: 290 CONTINUE
367: IF (BETA.EQ.ZERO) THEN
368: C(I,J) = ALPHA*TEMP
369: ELSE
370: C(I,J) = ALPHA*TEMP + BETA*C(I,J)
371: END IF
372: 300 CONTINUE
373: 310 CONTINUE
374: END IF
375: ELSE
376: IF (CONJB) THEN
377: *
378: * Form C := alpha*A'*conjg( B' ) + beta*C
379: *
380: DO 340 J = 1,N
381: DO 330 I = 1,M
382: TEMP = ZERO
383: DO 320 L = 1,K
384: TEMP = TEMP + A(L,I)*DCONJG(B(J,L))
385: 320 CONTINUE
386: IF (BETA.EQ.ZERO) THEN
387: C(I,J) = ALPHA*TEMP
388: ELSE
389: C(I,J) = ALPHA*TEMP + BETA*C(I,J)
390: END IF
391: 330 CONTINUE
392: 340 CONTINUE
393: ELSE
394: *
395: * Form C := alpha*A'*B' + beta*C
396: *
397: DO 370 J = 1,N
398: DO 360 I = 1,M
399: TEMP = ZERO
400: DO 350 L = 1,K
401: TEMP = TEMP + A(L,I)*B(J,L)
402: 350 CONTINUE
403: IF (BETA.EQ.ZERO) THEN
404: C(I,J) = ALPHA*TEMP
405: ELSE
406: C(I,J) = ALPHA*TEMP + BETA*C(I,J)
407: END IF
408: 360 CONTINUE
409: 370 CONTINUE
410: END IF
411: END IF
412: *
413: RETURN
414: *
415: * End of ZGEMM .
416: *
417: END
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