 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ dsymm()

 subroutine dsymm ( character SIDE, character UPLO, integer M, integer N, 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 )

DSYMM

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

C := alpha*A*B + beta*C,

or

C := alpha*B*A + beta*C,

where alpha and beta are scalars,  A is a symmetric matrix and  B and
C are  m by n matrices.```
Parameters
 [in] SIDE ``` SIDE is CHARACTER*1 On entry, SIDE specifies whether the symmetric matrix A appears on the left or right in the operation as follows: SIDE = 'L' or 'l' C := alpha*A*B + beta*C, SIDE = 'R' or 'r' C := alpha*B*A + beta*C,``` [in] UPLO ``` UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the symmetric matrix A is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of the symmetric matrix is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of the symmetric matrix is to be referenced.``` [in] M ``` M is INTEGER On entry, M specifies the number of rows 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 C. N 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 m when SIDE = 'L' or 'l' and is n otherwise. Before entry with SIDE = 'L' or 'l', the m by m part of the array A must contain the symmetric matrix, such that when UPLO = 'U' or 'u', the leading m by m upper triangular part of the array A must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of A is not referenced, and when UPLO = 'L' or 'l', the leading m by m lower triangular part of the array A must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of A is not referenced. Before entry with SIDE = 'R' or 'r', the n by n part of the array A must contain the symmetric matrix, such that when UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of A is not referenced, and when UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of A is not referenced.``` [in] LDA ``` LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), otherwise LDA must be at least max( 1, n ).``` [in] B ``` B is DOUBLE PRECISION array, dimension ( LDB, N ) Before entry, the leading m by n 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. LDB must be at least max( 1, m ).``` [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 updated matrix.``` [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 ).```
Date
December 2016
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 191 of file dsymm.f.

191 *
192 * -- Reference BLAS level3 routine (version 3.7.0) --
193 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
194 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
195 * December 2016
196 *
197 * .. Scalar Arguments ..
198  DOUBLE PRECISION alpha,beta
199  INTEGER lda,ldb,ldc,m,n
200  CHARACTER side,uplo
201 * ..
202 * .. Array Arguments ..
203  DOUBLE PRECISION a(lda,*),b(ldb,*),c(ldc,*)
204 * ..
205 *
206 * =====================================================================
207 *
208 * .. External Functions ..
209  LOGICAL lsame
210  EXTERNAL lsame
211 * ..
212 * .. External Subroutines ..
213  EXTERNAL xerbla
214 * ..
215 * .. Intrinsic Functions ..
216  INTRINSIC max
217 * ..
218 * .. Local Scalars ..
219  DOUBLE PRECISION temp1,temp2
220  INTEGER i,info,j,k,nrowa
221  LOGICAL upper
222 * ..
223 * .. Parameters ..
224  DOUBLE PRECISION one,zero
225  parameter(one=1.0d+0,zero=0.0d+0)
226 * ..
227 *
228 * Set NROWA as the number of rows of A.
229 *
230  IF (lsame(side,'L')) THEN
231  nrowa = m
232  ELSE
233  nrowa = n
234  END IF
235  upper = lsame(uplo,'U')
236 *
237 * Test the input parameters.
238 *
239  info = 0
240  IF ((.NOT.lsame(side,'L')) .AND. (.NOT.lsame(side,'R'))) THEN
241  info = 1
242  ELSE IF ((.NOT.upper) .AND. (.NOT.lsame(uplo,'L'))) THEN
243  info = 2
244  ELSE IF (m.LT.0) THEN
245  info = 3
246  ELSE IF (n.LT.0) THEN
247  info = 4
248  ELSE IF (lda.LT.max(1,nrowa)) THEN
249  info = 7
250  ELSE IF (ldb.LT.max(1,m)) THEN
251  info = 9
252  ELSE IF (ldc.LT.max(1,m)) THEN
253  info = 12
254  END IF
255  IF (info.NE.0) THEN
256  CALL xerbla('DSYMM ',info)
257  RETURN
258  END IF
259 *
260 * Quick return if possible.
261 *
262  IF ((m.EQ.0) .OR. (n.EQ.0) .OR.
263  + ((alpha.EQ.zero).AND. (beta.EQ.one))) RETURN
264 *
265 * And when alpha.eq.zero.
266 *
267  IF (alpha.EQ.zero) THEN
268  IF (beta.EQ.zero) THEN
269  DO 20 j = 1,n
270  DO 10 i = 1,m
271  c(i,j) = zero
272  10 CONTINUE
273  20 CONTINUE
274  ELSE
275  DO 40 j = 1,n
276  DO 30 i = 1,m
277  c(i,j) = beta*c(i,j)
278  30 CONTINUE
279  40 CONTINUE
280  END IF
281  RETURN
282  END IF
283 *
284 * Start the operations.
285 *
286  IF (lsame(side,'L')) THEN
287 *
288 * Form C := alpha*A*B + beta*C.
289 *
290  IF (upper) THEN
291  DO 70 j = 1,n
292  DO 60 i = 1,m
293  temp1 = alpha*b(i,j)
294  temp2 = zero
295  DO 50 k = 1,i - 1
296  c(k,j) = c(k,j) + temp1*a(k,i)
297  temp2 = temp2 + b(k,j)*a(k,i)
298  50 CONTINUE
299  IF (beta.EQ.zero) THEN
300  c(i,j) = temp1*a(i,i) + alpha*temp2
301  ELSE
302  c(i,j) = beta*c(i,j) + temp1*a(i,i) +
303  + alpha*temp2
304  END IF
305  60 CONTINUE
306  70 CONTINUE
307  ELSE
308  DO 100 j = 1,n
309  DO 90 i = m,1,-1
310  temp1 = alpha*b(i,j)
311  temp2 = zero
312  DO 80 k = i + 1,m
313  c(k,j) = c(k,j) + temp1*a(k,i)
314  temp2 = temp2 + b(k,j)*a(k,i)
315  80 CONTINUE
316  IF (beta.EQ.zero) THEN
317  c(i,j) = temp1*a(i,i) + alpha*temp2
318  ELSE
319  c(i,j) = beta*c(i,j) + temp1*a(i,i) +
320  + alpha*temp2
321  END IF
322  90 CONTINUE
323  100 CONTINUE
324  END IF
325  ELSE
326 *
327 * Form C := alpha*B*A + beta*C.
328 *
329  DO 170 j = 1,n
330  temp1 = alpha*a(j,j)
331  IF (beta.EQ.zero) THEN
332  DO 110 i = 1,m
333  c(i,j) = temp1*b(i,j)
334  110 CONTINUE
335  ELSE
336  DO 120 i = 1,m
337  c(i,j) = beta*c(i,j) + temp1*b(i,j)
338  120 CONTINUE
339  END IF
340  DO 140 k = 1,j - 1
341  IF (upper) THEN
342  temp1 = alpha*a(k,j)
343  ELSE
344  temp1 = alpha*a(j,k)
345  END IF
346  DO 130 i = 1,m
347  c(i,j) = c(i,j) + temp1*b(i,k)
348  130 CONTINUE
349  140 CONTINUE
350  DO 160 k = j + 1,n
351  IF (upper) THEN
352  temp1 = alpha*a(j,k)
353  ELSE
354  temp1 = alpha*a(k,j)
355  END IF
356  DO 150 i = 1,m
357  c(i,j) = c(i,j) + temp1*b(i,k)
358  150 CONTINUE
359  160 CONTINUE
360  170 CONTINUE
361  END IF
362 *
363  RETURN
364 *
365 * End of DSYMM .
366 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
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