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 ).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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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