 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ chemm()

 subroutine chemm ( character SIDE, character UPLO, integer M, integer N, complex ALPHA, complex, dimension(lda,*) A, integer LDA, complex, dimension(ldb,*) B, integer LDB, complex BETA, complex, dimension(ldc,*) C, integer LDC )

CHEMM

Purpose:
``` CHEMM  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 an hermitian matrix and  B and
C are m by n matrices.```
Parameters
 [in] SIDE ``` SIDE is CHARACTER*1 On entry, SIDE specifies whether the hermitian 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 hermitian matrix A is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of the hermitian matrix is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of the hermitian 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 COMPLEX On entry, ALPHA specifies the scalar alpha.``` [in] A ``` A is COMPLEX 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 hermitian 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 hermitian 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 hermitian 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 hermitian 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 hermitian 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 hermitian matrix and the strictly upper triangular part of A is not referenced. Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero.``` [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 COMPLEX 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 COMPLEX 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 COMPLEX 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 ).```
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 190 of file chemm.f.

191 *
192 * -- Reference BLAS level3 routine --
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 *
196 * .. Scalar Arguments ..
197  COMPLEX ALPHA,BETA
198  INTEGER LDA,LDB,LDC,M,N
199  CHARACTER SIDE,UPLO
200 * ..
201 * .. Array Arguments ..
202  COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
203 * ..
204 *
205 * =====================================================================
206 *
207 * .. External Functions ..
208  LOGICAL LSAME
209  EXTERNAL lsame
210 * ..
211 * .. External Subroutines ..
212  EXTERNAL xerbla
213 * ..
214 * .. Intrinsic Functions ..
215  INTRINSIC conjg,max,real
216 * ..
217 * .. Local Scalars ..
218  COMPLEX TEMP1,TEMP2
219  INTEGER I,INFO,J,K,NROWA
220  LOGICAL UPPER
221 * ..
222 * .. Parameters ..
223  COMPLEX ONE
224  parameter(one= (1.0e+0,0.0e+0))
225  COMPLEX ZERO
226  parameter(zero= (0.0e+0,0.0e+0))
227 * ..
228 *
229 * Set NROWA as the number of rows of A.
230 *
231  IF (lsame(side,'L')) THEN
232  nrowa = m
233  ELSE
234  nrowa = n
235  END IF
236  upper = lsame(uplo,'U')
237 *
238 * Test the input parameters.
239 *
240  info = 0
241  IF ((.NOT.lsame(side,'L')) .AND. (.NOT.lsame(side,'R'))) THEN
242  info = 1
243  ELSE IF ((.NOT.upper) .AND. (.NOT.lsame(uplo,'L'))) THEN
244  info = 2
245  ELSE IF (m.LT.0) THEN
246  info = 3
247  ELSE IF (n.LT.0) THEN
248  info = 4
249  ELSE IF (lda.LT.max(1,nrowa)) THEN
250  info = 7
251  ELSE IF (ldb.LT.max(1,m)) THEN
252  info = 9
253  ELSE IF (ldc.LT.max(1,m)) THEN
254  info = 12
255  END IF
256  IF (info.NE.0) THEN
257  CALL xerbla('CHEMM ',info)
258  RETURN
259  END IF
260 *
261 * Quick return if possible.
262 *
263  IF ((m.EQ.0) .OR. (n.EQ.0) .OR.
264  + ((alpha.EQ.zero).AND. (beta.EQ.one))) RETURN
265 *
266 * And when alpha.eq.zero.
267 *
268  IF (alpha.EQ.zero) THEN
269  IF (beta.EQ.zero) THEN
270  DO 20 j = 1,n
271  DO 10 i = 1,m
272  c(i,j) = zero
273  10 CONTINUE
274  20 CONTINUE
275  ELSE
276  DO 40 j = 1,n
277  DO 30 i = 1,m
278  c(i,j) = beta*c(i,j)
279  30 CONTINUE
280  40 CONTINUE
281  END IF
282  RETURN
283  END IF
284 *
285 * Start the operations.
286 *
287  IF (lsame(side,'L')) THEN
288 *
289 * Form C := alpha*A*B + beta*C.
290 *
291  IF (upper) THEN
292  DO 70 j = 1,n
293  DO 60 i = 1,m
294  temp1 = alpha*b(i,j)
295  temp2 = zero
296  DO 50 k = 1,i - 1
297  c(k,j) = c(k,j) + temp1*a(k,i)
298  temp2 = temp2 + b(k,j)*conjg(a(k,i))
299  50 CONTINUE
300  IF (beta.EQ.zero) THEN
301  c(i,j) = temp1*real(a(i,i)) + alpha*temp2
302  ELSE
303  c(i,j) = beta*c(i,j) + temp1*real(a(i,i)) +
304  + alpha*temp2
305  END IF
306  60 CONTINUE
307  70 CONTINUE
308  ELSE
309  DO 100 j = 1,n
310  DO 90 i = m,1,-1
311  temp1 = alpha*b(i,j)
312  temp2 = zero
313  DO 80 k = i + 1,m
314  c(k,j) = c(k,j) + temp1*a(k,i)
315  temp2 = temp2 + b(k,j)*conjg(a(k,i))
316  80 CONTINUE
317  IF (beta.EQ.zero) THEN
318  c(i,j) = temp1*real(a(i,i)) + alpha*temp2
319  ELSE
320  c(i,j) = beta*c(i,j) + temp1*real(a(i,i)) +
321  + alpha*temp2
322  END IF
323  90 CONTINUE
324  100 CONTINUE
325  END IF
326  ELSE
327 *
328 * Form C := alpha*B*A + beta*C.
329 *
330  DO 170 j = 1,n
331  temp1 = alpha*real(a(j,j))
332  IF (beta.EQ.zero) THEN
333  DO 110 i = 1,m
334  c(i,j) = temp1*b(i,j)
335  110 CONTINUE
336  ELSE
337  DO 120 i = 1,m
338  c(i,j) = beta*c(i,j) + temp1*b(i,j)
339  120 CONTINUE
340  END IF
341  DO 140 k = 1,j - 1
342  IF (upper) THEN
343  temp1 = alpha*a(k,j)
344  ELSE
345  temp1 = alpha*conjg(a(j,k))
346  END IF
347  DO 130 i = 1,m
348  c(i,j) = c(i,j) + temp1*b(i,k)
349  130 CONTINUE
350  140 CONTINUE
351  DO 160 k = j + 1,n
352  IF (upper) THEN
353  temp1 = alpha*conjg(a(j,k))
354  ELSE
355  temp1 = alpha*a(k,j)
356  END IF
357  DO 150 i = 1,m
358  c(i,j) = c(i,j) + temp1*b(i,k)
359  150 CONTINUE
360  160 CONTINUE
361  170 CONTINUE
362  END IF
363 *
364  RETURN
365 *
366 * End of CHEMM
367 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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