LAPACK  3.5.0
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sgemm.f
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1 *> \brief \b SGEMM
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 SGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
12 *
13 * .. Scalar Arguments ..
14 * REAL ALPHA,BETA
15 * INTEGER K,LDA,LDB,LDC,M,N
16 * CHARACTER TRANSA,TRANSB
17 * ..
18 * .. Array Arguments ..
19 * REAL A(LDA,*),B(LDB,*),C(LDC,*)
20 * ..
21 *
22 *
23 *> \par Purpose:
24 * =============
25 *>
26 *> \verbatim
27 *>
28 *> SGEMM 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 REAL
95 *> On entry, ALPHA specifies the scalar alpha.
96 *> \endverbatim
97 *>
98 *> \param[in] A
99 *> \verbatim
100 *> A is REAL 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 REAL 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 REAL
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 REAL 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 2011
170 *
171 *> \ingroup single_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 sgemm(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
189 *
190 * -- Reference BLAS level3 routine (version 3.4.0) --
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 2011
194 *
195 * .. Scalar Arguments ..
196  REAL alpha,beta
197  INTEGER k,lda,ldb,ldc,m,n
198  CHARACTER transa,transb
199 * ..
200 * .. Array Arguments ..
201  REAL 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  REAL temp
218  INTEGER i,info,j,l,ncola,nrowa,nrowb
219  LOGICAL nota,notb
220 * ..
221 * .. Parameters ..
222  REAL one,zero
223  parameter(one=1.0e+0,zero=0.0e+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('SGEMM ',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  IF (b(l,j).NE.zero) THEN
315  temp = alpha*b(l,j)
316  DO 70 i = 1,m
317  c(i,j) = c(i,j) + temp*a(i,l)
318  70 CONTINUE
319  END IF
320  80 CONTINUE
321  90 CONTINUE
322  ELSE
323 *
324 * Form C := alpha*A**T*B + beta*C
325 *
326  DO 120 j = 1,n
327  DO 110 i = 1,m
328  temp = zero
329  DO 100 l = 1,k
330  temp = temp + a(l,i)*b(l,j)
331  100 CONTINUE
332  IF (beta.EQ.zero) THEN
333  c(i,j) = alpha*temp
334  ELSE
335  c(i,j) = alpha*temp + beta*c(i,j)
336  END IF
337  110 CONTINUE
338  120 CONTINUE
339  END IF
340  ELSE
341  IF (nota) THEN
342 *
343 * Form C := alpha*A*B**T + beta*C
344 *
345  DO 170 j = 1,n
346  IF (beta.EQ.zero) THEN
347  DO 130 i = 1,m
348  c(i,j) = zero
349  130 CONTINUE
350  ELSE IF (beta.NE.one) THEN
351  DO 140 i = 1,m
352  c(i,j) = beta*c(i,j)
353  140 CONTINUE
354  END IF
355  DO 160 l = 1,k
356  IF (b(j,l).NE.zero) THEN
357  temp = alpha*b(j,l)
358  DO 150 i = 1,m
359  c(i,j) = c(i,j) + temp*a(i,l)
360  150 CONTINUE
361  END IF
362  160 CONTINUE
363  170 CONTINUE
364  ELSE
365 *
366 * Form C := alpha*A**T*B**T + beta*C
367 *
368  DO 200 j = 1,n
369  DO 190 i = 1,m
370  temp = zero
371  DO 180 l = 1,k
372  temp = temp + a(l,i)*b(j,l)
373  180 CONTINUE
374  IF (beta.EQ.zero) THEN
375  c(i,j) = alpha*temp
376  ELSE
377  c(i,j) = alpha*temp + beta*c(i,j)
378  END IF
379  190 CONTINUE
380  200 CONTINUE
381  END IF
382  END IF
383 *
384  RETURN
385 *
386 * End of SGEMM .
387 *
388  END