1 SUBROUTINE SGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
2 * .. Scalar Arguments ..
3 REAL ALPHA,BETA
4 INTEGER K,LDA,LDB,LDC,M,N
5 CHARACTER TRANSA,TRANSB
6 * ..
7 * .. Array Arguments ..
8 REAL A(LDA,*),B(LDB,*),C(LDC,*)
9 * ..
10 *
11 * Purpose
12 * =======
13 *
14 * SGEMM 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**T,
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**T.
35 *
36 * TRANSA = 'C' or 'c', op( A ) = A**T.
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**T.
47 *
48 * TRANSB = 'C' or 'c', op( B ) = B**T.
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 - REAL .
70 * On entry, ALPHA specifies the scalar alpha.
71 * Unchanged on exit.
72 *
73 * A - REAL 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 - REAL 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 - REAL .
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 - REAL 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 MAX
143 * ..
144 * .. Local Scalars ..
145 REAL TEMP
146 INTEGER I,INFO,J,L,NCOLA,NROWA,NROWB
147 LOGICAL NOTA,NOTB
148 * ..
149 * .. Parameters ..
150 REAL ONE,ZERO
151 PARAMETER (ONE=1.0E+0,ZERO=0.0E+0)
152 * ..
153 *
154 * Set NOTA and NOTB as true if A and B respectively are not
155 * transposed and set NROWA, NCOLA and NROWB as the number of rows
156 * and columns of A and the number of rows of B respectively.
157 *
158 NOTA = LSAME(TRANSA,'N')
159 NOTB = LSAME(TRANSB,'N')
160 IF (NOTA) THEN
161 NROWA = M
162 NCOLA = K
163 ELSE
164 NROWA = K
165 NCOLA = M
166 END IF
167 IF (NOTB) THEN
168 NROWB = K
169 ELSE
170 NROWB = N
171 END IF
172 *
173 * Test the input parameters.
174 *
175 INFO = 0
176 IF ((.NOT.NOTA) .AND. (.NOT.LSAME(TRANSA,'C')) .AND.
177 + (.NOT.LSAME(TRANSA,'T'))) THEN
178 INFO = 1
179 ELSE IF ((.NOT.NOTB) .AND. (.NOT.LSAME(TRANSB,'C')) .AND.
180 + (.NOT.LSAME(TRANSB,'T'))) THEN
181 INFO = 2
182 ELSE IF (M.LT.0) THEN
183 INFO = 3
184 ELSE IF (N.LT.0) THEN
185 INFO = 4
186 ELSE IF (K.LT.0) THEN
187 INFO = 5
188 ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
189 INFO = 8
190 ELSE IF (LDB.LT.MAX(1,NROWB)) THEN
191 INFO = 10
192 ELSE IF (LDC.LT.MAX(1,M)) THEN
193 INFO = 13
194 END IF
195 IF (INFO.NE.0) THEN
196 CALL XERBLA('SGEMM ',INFO)
197 RETURN
198 END IF
199 *
200 * Quick return if possible.
201 *
202 IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
203 + (((ALPHA.EQ.ZERO).OR. (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN
204 *
205 * And if alpha.eq.zero.
206 *
207 IF (ALPHA.EQ.ZERO) THEN
208 IF (BETA.EQ.ZERO) THEN
209 DO 20 J = 1,N
210 DO 10 I = 1,M
211 C(I,J) = ZERO
212 10 CONTINUE
213 20 CONTINUE
214 ELSE
215 DO 40 J = 1,N
216 DO 30 I = 1,M
217 C(I,J) = BETA*C(I,J)
218 30 CONTINUE
219 40 CONTINUE
220 END IF
221 RETURN
222 END IF
223 *
224 * Start the operations.
225 *
226 IF (NOTB) THEN
227 IF (NOTA) THEN
228 *
229 * Form C := alpha*A*B + beta*C.
230 *
231 DO 90 J = 1,N
232 IF (BETA.EQ.ZERO) THEN
233 DO 50 I = 1,M
234 C(I,J) = ZERO
235 50 CONTINUE
236 ELSE IF (BETA.NE.ONE) THEN
237 DO 60 I = 1,M
238 C(I,J) = BETA*C(I,J)
239 60 CONTINUE
240 END IF
241 DO 80 L = 1,K
242 IF (B(L,J).NE.ZERO) THEN
243 TEMP = ALPHA*B(L,J)
244 DO 70 I = 1,M
245 C(I,J) = C(I,J) + TEMP*A(I,L)
246 70 CONTINUE
247 END IF
248 80 CONTINUE
249 90 CONTINUE
250 ELSE
251 *
252 * Form C := alpha*A**T*B + beta*C
253 *
254 DO 120 J = 1,N
255 DO 110 I = 1,M
256 TEMP = ZERO
257 DO 100 L = 1,K
258 TEMP = TEMP + A(L,I)*B(L,J)
259 100 CONTINUE
260 IF (BETA.EQ.ZERO) THEN
261 C(I,J) = ALPHA*TEMP
262 ELSE
263 C(I,J) = ALPHA*TEMP + BETA*C(I,J)
264 END IF
265 110 CONTINUE
266 120 CONTINUE
267 END IF
268 ELSE
269 IF (NOTA) THEN
270 *
271 * Form C := alpha*A*B**T + beta*C
272 *
273 DO 170 J = 1,N
274 IF (BETA.EQ.ZERO) THEN
275 DO 130 I = 1,M
276 C(I,J) = ZERO
277 130 CONTINUE
278 ELSE IF (BETA.NE.ONE) THEN
279 DO 140 I = 1,M
280 C(I,J) = BETA*C(I,J)
281 140 CONTINUE
282 END IF
283 DO 160 L = 1,K
284 IF (B(J,L).NE.ZERO) THEN
285 TEMP = ALPHA*B(J,L)
286 DO 150 I = 1,M
287 C(I,J) = C(I,J) + TEMP*A(I,L)
288 150 CONTINUE
289 END IF
290 160 CONTINUE
291 170 CONTINUE
292 ELSE
293 *
294 * Form C := alpha*A**T*B**T + beta*C
295 *
296 DO 200 J = 1,N
297 DO 190 I = 1,M
298 TEMP = ZERO
299 DO 180 L = 1,K
300 TEMP = TEMP + A(L,I)*B(J,L)
301 180 CONTINUE
302 IF (BETA.EQ.ZERO) THEN
303 C(I,J) = ALPHA*TEMP
304 ELSE
305 C(I,J) = ALPHA*TEMP + BETA*C(I,J)
306 END IF
307 190 CONTINUE
308 200 CONTINUE
309 END IF
310 END IF
311 *
312 RETURN
313 *
314 * End of SGEMM .
315 *
316 END
2 * .. Scalar Arguments ..
3 REAL ALPHA,BETA
4 INTEGER K,LDA,LDB,LDC,M,N
5 CHARACTER TRANSA,TRANSB
6 * ..
7 * .. Array Arguments ..
8 REAL A(LDA,*),B(LDB,*),C(LDC,*)
9 * ..
10 *
11 * Purpose
12 * =======
13 *
14 * SGEMM 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**T,
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**T.
35 *
36 * TRANSA = 'C' or 'c', op( A ) = A**T.
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**T.
47 *
48 * TRANSB = 'C' or 'c', op( B ) = B**T.
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 - REAL .
70 * On entry, ALPHA specifies the scalar alpha.
71 * Unchanged on exit.
72 *
73 * A - REAL 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 - REAL 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 - REAL .
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 - REAL 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 MAX
143 * ..
144 * .. Local Scalars ..
145 REAL TEMP
146 INTEGER I,INFO,J,L,NCOLA,NROWA,NROWB
147 LOGICAL NOTA,NOTB
148 * ..
149 * .. Parameters ..
150 REAL ONE,ZERO
151 PARAMETER (ONE=1.0E+0,ZERO=0.0E+0)
152 * ..
153 *
154 * Set NOTA and NOTB as true if A and B respectively are not
155 * transposed and set NROWA, NCOLA and NROWB as the number of rows
156 * and columns of A and the number of rows of B respectively.
157 *
158 NOTA = LSAME(TRANSA,'N')
159 NOTB = LSAME(TRANSB,'N')
160 IF (NOTA) THEN
161 NROWA = M
162 NCOLA = K
163 ELSE
164 NROWA = K
165 NCOLA = M
166 END IF
167 IF (NOTB) THEN
168 NROWB = K
169 ELSE
170 NROWB = N
171 END IF
172 *
173 * Test the input parameters.
174 *
175 INFO = 0
176 IF ((.NOT.NOTA) .AND. (.NOT.LSAME(TRANSA,'C')) .AND.
177 + (.NOT.LSAME(TRANSA,'T'))) THEN
178 INFO = 1
179 ELSE IF ((.NOT.NOTB) .AND. (.NOT.LSAME(TRANSB,'C')) .AND.
180 + (.NOT.LSAME(TRANSB,'T'))) THEN
181 INFO = 2
182 ELSE IF (M.LT.0) THEN
183 INFO = 3
184 ELSE IF (N.LT.0) THEN
185 INFO = 4
186 ELSE IF (K.LT.0) THEN
187 INFO = 5
188 ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
189 INFO = 8
190 ELSE IF (LDB.LT.MAX(1,NROWB)) THEN
191 INFO = 10
192 ELSE IF (LDC.LT.MAX(1,M)) THEN
193 INFO = 13
194 END IF
195 IF (INFO.NE.0) THEN
196 CALL XERBLA('SGEMM ',INFO)
197 RETURN
198 END IF
199 *
200 * Quick return if possible.
201 *
202 IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
203 + (((ALPHA.EQ.ZERO).OR. (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN
204 *
205 * And if alpha.eq.zero.
206 *
207 IF (ALPHA.EQ.ZERO) THEN
208 IF (BETA.EQ.ZERO) THEN
209 DO 20 J = 1,N
210 DO 10 I = 1,M
211 C(I,J) = ZERO
212 10 CONTINUE
213 20 CONTINUE
214 ELSE
215 DO 40 J = 1,N
216 DO 30 I = 1,M
217 C(I,J) = BETA*C(I,J)
218 30 CONTINUE
219 40 CONTINUE
220 END IF
221 RETURN
222 END IF
223 *
224 * Start the operations.
225 *
226 IF (NOTB) THEN
227 IF (NOTA) THEN
228 *
229 * Form C := alpha*A*B + beta*C.
230 *
231 DO 90 J = 1,N
232 IF (BETA.EQ.ZERO) THEN
233 DO 50 I = 1,M
234 C(I,J) = ZERO
235 50 CONTINUE
236 ELSE IF (BETA.NE.ONE) THEN
237 DO 60 I = 1,M
238 C(I,J) = BETA*C(I,J)
239 60 CONTINUE
240 END IF
241 DO 80 L = 1,K
242 IF (B(L,J).NE.ZERO) THEN
243 TEMP = ALPHA*B(L,J)
244 DO 70 I = 1,M
245 C(I,J) = C(I,J) + TEMP*A(I,L)
246 70 CONTINUE
247 END IF
248 80 CONTINUE
249 90 CONTINUE
250 ELSE
251 *
252 * Form C := alpha*A**T*B + beta*C
253 *
254 DO 120 J = 1,N
255 DO 110 I = 1,M
256 TEMP = ZERO
257 DO 100 L = 1,K
258 TEMP = TEMP + A(L,I)*B(L,J)
259 100 CONTINUE
260 IF (BETA.EQ.ZERO) THEN
261 C(I,J) = ALPHA*TEMP
262 ELSE
263 C(I,J) = ALPHA*TEMP + BETA*C(I,J)
264 END IF
265 110 CONTINUE
266 120 CONTINUE
267 END IF
268 ELSE
269 IF (NOTA) THEN
270 *
271 * Form C := alpha*A*B**T + beta*C
272 *
273 DO 170 J = 1,N
274 IF (BETA.EQ.ZERO) THEN
275 DO 130 I = 1,M
276 C(I,J) = ZERO
277 130 CONTINUE
278 ELSE IF (BETA.NE.ONE) THEN
279 DO 140 I = 1,M
280 C(I,J) = BETA*C(I,J)
281 140 CONTINUE
282 END IF
283 DO 160 L = 1,K
284 IF (B(J,L).NE.ZERO) THEN
285 TEMP = ALPHA*B(J,L)
286 DO 150 I = 1,M
287 C(I,J) = C(I,J) + TEMP*A(I,L)
288 150 CONTINUE
289 END IF
290 160 CONTINUE
291 170 CONTINUE
292 ELSE
293 *
294 * Form C := alpha*A**T*B**T + beta*C
295 *
296 DO 200 J = 1,N
297 DO 190 I = 1,M
298 TEMP = ZERO
299 DO 180 L = 1,K
300 TEMP = TEMP + A(L,I)*B(J,L)
301 180 CONTINUE
302 IF (BETA.EQ.ZERO) THEN
303 C(I,J) = ALPHA*TEMP
304 ELSE
305 C(I,J) = ALPHA*TEMP + BETA*C(I,J)
306 END IF
307 190 CONTINUE
308 200 CONTINUE
309 END IF
310 END IF
311 *
312 RETURN
313 *
314 * End of SGEMM .
315 *
316 END