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 of 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 of 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 of 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 November 2015
170: *
171: *> \ingroup double_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 DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
189: *
190: * -- Reference BLAS level3 routine (version 3.6.0) --
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: * November 2015
194: *
195: * .. Scalar Arguments ..
196: DOUBLE PRECISION ALPHA,BETA
197: INTEGER K,LDA,LDB,LDC,M,N
198: CHARACTER TRANSA,TRANSB
199: * ..
200: * .. Array Arguments ..
201: DOUBLE PRECISION 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 MAX
215: * ..
216: * .. Local Scalars ..
217: DOUBLE PRECISION TEMP
218: INTEGER I,INFO,J,L,NCOLA,NROWA,NROWB
219: LOGICAL NOTA,NOTB
220: * ..
221: * .. Parameters ..
222: DOUBLE PRECISION ONE,ZERO
223: PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
224: * ..
225: *
226: * Set NOTA and NOTB as true if A and B respectively are not
227: * transposed and set NROWA, NCOLA and NROWB as the number of rows
228: * and columns of A and the number of rows of B respectively.
229: *
230: NOTA = LSAME(TRANSA,'N')
231: NOTB = LSAME(TRANSB,'N')
232: IF (NOTA) THEN
233: NROWA = M
234: NCOLA = K
235: ELSE
236: NROWA = K
237: NCOLA = M
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.LSAME(TRANSA,'C')) .AND.
249: + (.NOT.LSAME(TRANSA,'T'))) THEN
250: INFO = 1
251: ELSE IF ((.NOT.NOTB) .AND. (.NOT.LSAME(TRANSB,'C')) .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('DGEMM ',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 if 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
321: *
322: * Form C := alpha*A**T*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 + 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: END IF
338: ELSE
339: IF (NOTA) THEN
340: *
341: * Form C := alpha*A*B**T + beta*C
342: *
343: DO 170 J = 1,N
344: IF (BETA.EQ.ZERO) THEN
345: DO 130 I = 1,M
346: C(I,J) = ZERO
347: 130 CONTINUE
348: ELSE IF (BETA.NE.ONE) THEN
349: DO 140 I = 1,M
350: C(I,J) = BETA*C(I,J)
351: 140 CONTINUE
352: END IF
353: DO 160 L = 1,K
354: TEMP = ALPHA*B(J,L)
355: DO 150 I = 1,M
356: C(I,J) = C(I,J) + TEMP*A(I,L)
357: 150 CONTINUE
358: 160 CONTINUE
359: 170 CONTINUE
360: ELSE
361: *
362: * Form C := alpha*A**T*B**T + beta*C
363: *
364: DO 200 J = 1,N
365: DO 190 I = 1,M
366: TEMP = ZERO
367: DO 180 L = 1,K
368: TEMP = TEMP + A(L,I)*B(J,L)
369: 180 CONTINUE
370: IF (BETA.EQ.ZERO) THEN
371: C(I,J) = ALPHA*TEMP
372: ELSE
373: C(I,J) = ALPHA*TEMP + BETA*C(I,J)
374: END IF
375: 190 CONTINUE
376: 200 CONTINUE
377: END IF
378: END IF
379: *
380: RETURN
381: *
382: * End of DGEMM .
383: *
384: END
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