1: *> \brief \b DGEMM
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 DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
12: *
13: * .. Scalar Arguments ..
14: * DOUBLE PRECISION ALPHA,BETA
15: * INTEGER K,LDA,LDB,LDC,M,N
16: * CHARACTER TRANSA,TRANSB
17: * ..
18: * .. Array Arguments ..
19: * DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*)
20: * ..
21: *
22: *
23: *> \par Purpose:
24: * =============
25: *>
26: *> \verbatim
27: *>
28: *> DGEMM 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,
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**T.
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**T.
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 DOUBLE PRECISION.
95: *> On entry, ALPHA specifies the scalar alpha.
96: *> \endverbatim
97: *>
98: *> \param[in] A
99: *> \verbatim
100: *> A is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION.
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 DOUBLE PRECISION 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 double_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 DGEMM(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: DOUBLE PRECISION ALPHA,BETA
194: INTEGER K,LDA,LDB,LDC,M,N
195: CHARACTER TRANSA,TRANSB
196: * ..
197: * .. Array Arguments ..
198: DOUBLE PRECISION 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: DOUBLE PRECISION TEMP
215: INTEGER I,INFO,J,L,NROWA,NROWB
216: LOGICAL NOTA,NOTB
217: * ..
218: * .. Parameters ..
219: DOUBLE PRECISION ONE,ZERO
220: PARAMETER (ONE=1.0D+0,ZERO=0.0D+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('DGEMM ',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 DGEMM
378: *
379: END
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