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1 SUBROUTINE DGEMM ( TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB,
2 $ BETA, C, LDC )
3 * .. Scalar Arguments ..
4 CHARACTER*1 TRANSA, TRANSB
5 INTEGER M, N, K, LDA, LDB, LDC
6 DOUBLE PRECISION ALPHA, BETA
7 * .. Array Arguments ..
8 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * )
9 * ..
10 *
11 * Purpose
12 * =======
13 *
14 * DGEMM 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',
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 * Parameters
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 ) = 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 ) = 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 - DOUBLE PRECISION.
70 * On entry, ALPHA specifies the scalar alpha.
71 * Unchanged on exit.
72 *
73 * A - DOUBLE PRECISION 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 - DOUBLE PRECISION 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 - DOUBLE PRECISION.
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 - DOUBLE PRECISION 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 *
122 * Level 3 Blas routine.
123 *
124 * -- Written on 8-February-1989.
125 * Jack Dongarra, Argonne National Laboratory.
126 * Iain Duff, AERE Harwell.
127 * Jeremy Du Croz, Numerical Algorithms Group Ltd.
128 * Sven Hammarling, Numerical Algorithms Group Ltd.
129 *
130 *
131 * .. External Functions ..
132 LOGICAL LSAME
133 EXTERNAL LSAME
134 * .. External Subroutines ..
135 EXTERNAL XERBLA
136 * .. Intrinsic Functions ..
137 INTRINSIC MAX
138 * .. Local Scalars ..
139 LOGICAL NOTA, NOTB
140 INTEGER I, INFO, J, L, NCOLA, NROWA, NROWB
141 DOUBLE PRECISION TEMP
142 * .. Parameters ..
143 DOUBLE PRECISION ONE , ZERO
144 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
145 * ..
146 * .. Executable Statements ..
147 *
148 * Set NOTA and NOTB as true if A and B respectively are not
149 * transposed and set NROWA, NCOLA and NROWB as the number of rows
150 * and columns of A and the number of rows of B respectively.
151 *
152 NOTA = LSAME( TRANSA, 'N' )
153 NOTB = LSAME( TRANSB, 'N' )
154 IF( NOTA )THEN
155 NROWA = M
156 NCOLA = K
157 ELSE
158 NROWA = K
159 NCOLA = M
160 END IF
161 IF( NOTB )THEN
162 NROWB = K
163 ELSE
164 NROWB = N
165 END IF
166 *
167 * Test the input parameters.
168 *
169 INFO = 0
170 IF( ( .NOT.NOTA ).AND.
171 $ ( .NOT.LSAME( TRANSA, 'C' ) ).AND.
172 $ ( .NOT.LSAME( TRANSA, 'T' ) ) )THEN
173 INFO = 1
174 ELSE IF( ( .NOT.NOTB ).AND.
175 $ ( .NOT.LSAME( TRANSB, 'C' ) ).AND.
176 $ ( .NOT.LSAME( TRANSB, 'T' ) ) )THEN
177 INFO = 2
178 ELSE IF( M .LT.0 )THEN
179 INFO = 3
180 ELSE IF( N .LT.0 )THEN
181 INFO = 4
182 ELSE IF( K .LT.0 )THEN
183 INFO = 5
184 ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN
185 INFO = 8
186 ELSE IF( LDB.LT.MAX( 1, NROWB ) )THEN
187 INFO = 10
188 ELSE IF( LDC.LT.MAX( 1, M ) )THEN
189 INFO = 13
190 END IF
191 IF( INFO.NE.0 )THEN
192 CALL XERBLA( 'DGEMM ', INFO )
193 RETURN
194 END IF
195 *
196 * Quick return if possible.
197 *
198 IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.
199 $ ( ( ( ALPHA.EQ.ZERO ).OR.( K.EQ.0 ) ).AND.( BETA.EQ.ONE ) ) )
200 $ RETURN
201 *
202 * And if alpha.eq.zero.
203 *
204 IF( ALPHA.EQ.ZERO )THEN
205 IF( BETA.EQ.ZERO )THEN
206 DO 20, J = 1, N
207 DO 10, I = 1, M
208 C( I, J ) = ZERO
209 10 CONTINUE
210 20 CONTINUE
211 ELSE
212 DO 40, J = 1, N
213 DO 30, I = 1, M
214 C( I, J ) = BETA*C( I, J )
215 30 CONTINUE
216 40 CONTINUE
217 END IF
218 RETURN
219 END IF
220 *
221 * Start the operations.
222 *
223 IF( NOTB )THEN
224 IF( NOTA )THEN
225 *
226 * Form C := alpha*A*B + beta*C.
227 *
228 DO 90, J = 1, N
229 IF( BETA.EQ.ZERO )THEN
230 DO 50, I = 1, M
231 C( I, J ) = ZERO
232 50 CONTINUE
233 ELSE IF( BETA.NE.ONE )THEN
234 DO 60, I = 1, M
235 C( I, J ) = BETA*C( I, J )
236 60 CONTINUE
237 END IF
238 DO 80, L = 1, K
239 IF( B( L, J ).NE.ZERO )THEN
240 TEMP = ALPHA*B( L, J )
241 DO 70, I = 1, M
242 C( I, J ) = C( I, J ) + TEMP*A( I, L )
243 70 CONTINUE
244 END IF
245 80 CONTINUE
246 90 CONTINUE
247 ELSE
248 *
249 * Form C := alpha*A'*B + beta*C
250 *
251 DO 120, J = 1, N
252 DO 110, I = 1, M
253 TEMP = ZERO
254 DO 100, L = 1, K
255 TEMP = TEMP + A( L, I )*B( L, J )
256 100 CONTINUE
257 IF( BETA.EQ.ZERO )THEN
258 C( I, J ) = ALPHA*TEMP
259 ELSE
260 C( I, J ) = ALPHA*TEMP + BETA*C( I, J )
261 END IF
262 110 CONTINUE
263 120 CONTINUE
264 END IF
265 ELSE
266 IF( NOTA )THEN
267 *
268 * Form C := alpha*A*B' + beta*C
269 *
270 DO 170, J = 1, N
271 IF( BETA.EQ.ZERO )THEN
272 DO 130, I = 1, M
273 C( I, J ) = ZERO
274 130 CONTINUE
275 ELSE IF( BETA.NE.ONE )THEN
276 DO 140, I = 1, M
277 C( I, J ) = BETA*C( I, J )
278 140 CONTINUE
279 END IF
280 DO 160, L = 1, K
281 IF( B( J, L ).NE.ZERO )THEN
282 TEMP = ALPHA*B( J, L )
283 DO 150, I = 1, M
284 C( I, J ) = C( I, J ) + TEMP*A( I, L )
285 150 CONTINUE
286 END IF
287 160 CONTINUE
288 170 CONTINUE
289 ELSE
290 *
291 * Form C := alpha*A'*B' + beta*C
292 *
293 DO 200, J = 1, N
294 DO 190, I = 1, M
295 TEMP = ZERO
296 DO 180, L = 1, K
297 TEMP = TEMP + A( L, I )*B( J, L )
298 180 CONTINUE
299 IF( BETA.EQ.ZERO )THEN
300 C( I, J ) = ALPHA*TEMP
301 ELSE
302 C( I, J ) = ALPHA*TEMP + BETA*C( I, J )
303 END IF
304 190 CONTINUE
305 200 CONTINUE
306 END IF
307 END IF
308 *
309 RETURN
310 *
311 * End of DGEMM .
312 *
313 END
314

john.pye@anu.edu.au
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