LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ dgemm()

 subroutine dgemm ( character TRANSA, character TRANSB, integer M, integer N, integer K, double precision ALPHA, double precision, dimension(lda,*) A, integer LDA, double precision, dimension(ldb,*) B, integer LDB, double precision BETA, double precision, dimension(ldc,*) C, integer LDC )

DGEMM

Purpose:
``` DGEMM  performs one of the matrix-matrix operations

C := alpha*op( A )*op( B ) + beta*C,

where  op( X ) is one of

op( X ) = X   or   op( X ) = X**T,

alpha and beta are scalars, and A, B and C are matrices, with op( A )
an m by k matrix,  op( B )  a  k by n matrix and  C an m by n matrix.```
Parameters
 [in] TRANSA ``` TRANSA is CHARACTER*1 On entry, TRANSA specifies the form of op( A ) to be used in the matrix multiplication as follows: TRANSA = 'N' or 'n', op( A ) = A. TRANSA = 'T' or 't', op( A ) = A**T. TRANSA = 'C' or 'c', op( A ) = A**T.``` [in] TRANSB ``` TRANSB is CHARACTER*1 On entry, TRANSB specifies the form of op( B ) to be used in the matrix multiplication as follows: TRANSB = 'N' or 'n', op( B ) = B. TRANSB = 'T' or 't', op( B ) = B**T. TRANSB = 'C' or 'c', op( B ) = B**T.``` [in] M ``` M is INTEGER On entry, M specifies the number of rows of the matrix op( A ) and of the matrix C. M must be at least zero.``` [in] N ``` N is INTEGER On entry, N specifies the number of columns of the matrix op( B ) and the number of columns of the matrix C. N must be at least zero.``` [in] K ``` K is INTEGER On entry, K specifies the number of columns of the matrix op( A ) and the number of rows of the matrix op( B ). K must be at least zero.``` [in] ALPHA ``` ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha.``` [in] A ``` A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is k when TRANSA = 'N' or 'n', and is m otherwise. Before entry with TRANSA = 'N' or 'n', the leading m by k part of the array A must contain the matrix A, otherwise the leading k by m part of the array A must contain the matrix A.``` [in] LDA ``` LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When TRANSA = 'N' or 'n' then LDA must be at least max( 1, m ), otherwise LDA must be at least max( 1, k ).``` [in] B ``` B is DOUBLE PRECISION array, dimension ( LDB, kb ), where kb is n when TRANSB = 'N' or 'n', and is k otherwise. Before entry with TRANSB = 'N' or 'n', the leading k by n part of the array B must contain the matrix B, otherwise the leading n by k part of the array B must contain the matrix B.``` [in] LDB ``` LDB is INTEGER On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. When TRANSB = 'N' or 'n' then LDB must be at least max( 1, k ), otherwise LDB must be at least max( 1, n ).``` [in] BETA ``` BETA is DOUBLE PRECISION. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input.``` [in,out] C ``` C is DOUBLE PRECISION array, dimension ( LDC, N ) Before entry, the leading m by n part of the array C must contain the matrix C, except when beta is zero, in which case C need not be set on entry. On exit, the array C is overwritten by the m by n matrix ( alpha*op( A )*op( B ) + beta*C ).``` [in] LDC ``` LDC is INTEGER On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC must be at least max( 1, m ).```
Further Details:
```  Level 3 Blas routine.

-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.```

Definition at line 186 of file dgemm.f.

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 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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