LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine zhemm ( character SIDE, character UPLO, integer M, integer N, complex*16 ALPHA, complex*16, dimension(lda,*) A, integer LDA, complex*16, dimension(ldb,*) B, integer LDB, complex*16 BETA, complex*16, dimension(ldc,*) C, integer LDC )

ZHEMM

Purpose:
``` ZHEMM  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*16 On entry, ALPHA specifies the scalar alpha.``` [in] A ``` A is COMPLEX*16 array of 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*16 array of 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*16 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*16 array of 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
November 2011
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 193 of file zhemm.f.

193 *
194 * -- Reference BLAS level3 routine (version 3.4.0) --
195 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
196 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
197 * November 2011
198 *
199 * .. Scalar Arguments ..
200  COMPLEX*16 alpha,beta
201  INTEGER lda,ldb,ldc,m,n
202  CHARACTER side,uplo
203 * ..
204 * .. Array Arguments ..
205  COMPLEX*16 a(lda,*),b(ldb,*),c(ldc,*)
206 * ..
207 *
208 * =====================================================================
209 *
210 * .. External Functions ..
211  LOGICAL lsame
212  EXTERNAL lsame
213 * ..
214 * .. External Subroutines ..
215  EXTERNAL xerbla
216 * ..
217 * .. Intrinsic Functions ..
218  INTRINSIC dble,dconjg,max
219 * ..
220 * .. Local Scalars ..
221  COMPLEX*16 temp1,temp2
222  INTEGER i,info,j,k,nrowa
223  LOGICAL upper
224 * ..
225 * .. Parameters ..
226  COMPLEX*16 one
227  parameter(one= (1.0d+0,0.0d+0))
228  COMPLEX*16 zero
229  parameter(zero= (0.0d+0,0.0d+0))
230 * ..
231 *
232 * Set NROWA as the number of rows of A.
233 *
234  IF (lsame(side,'L')) THEN
235  nrowa = m
236  ELSE
237  nrowa = n
238  END IF
239  upper = lsame(uplo,'U')
240 *
241 * Test the input parameters.
242 *
243  info = 0
244  IF ((.NOT.lsame(side,'L')) .AND. (.NOT.lsame(side,'R'))) THEN
245  info = 1
246  ELSE IF ((.NOT.upper) .AND. (.NOT.lsame(uplo,'L'))) THEN
247  info = 2
248  ELSE IF (m.LT.0) THEN
249  info = 3
250  ELSE IF (n.LT.0) THEN
251  info = 4
252  ELSE IF (lda.LT.max(1,nrowa)) THEN
253  info = 7
254  ELSE IF (ldb.LT.max(1,m)) THEN
255  info = 9
256  ELSE IF (ldc.LT.max(1,m)) THEN
257  info = 12
258  END IF
259  IF (info.NE.0) THEN
260  CALL xerbla('ZHEMM ',info)
261  RETURN
262  END IF
263 *
264 * Quick return if possible.
265 *
266  IF ((m.EQ.0) .OR. (n.EQ.0) .OR.
267  + ((alpha.EQ.zero).AND. (beta.EQ.one))) RETURN
268 *
269 * And when alpha.eq.zero.
270 *
271  IF (alpha.EQ.zero) THEN
272  IF (beta.EQ.zero) THEN
273  DO 20 j = 1,n
274  DO 10 i = 1,m
275  c(i,j) = zero
276  10 CONTINUE
277  20 CONTINUE
278  ELSE
279  DO 40 j = 1,n
280  DO 30 i = 1,m
281  c(i,j) = beta*c(i,j)
282  30 CONTINUE
283  40 CONTINUE
284  END IF
285  RETURN
286  END IF
287 *
288 * Start the operations.
289 *
290  IF (lsame(side,'L')) THEN
291 *
292 * Form C := alpha*A*B + beta*C.
293 *
294  IF (upper) THEN
295  DO 70 j = 1,n
296  DO 60 i = 1,m
297  temp1 = alpha*b(i,j)
298  temp2 = zero
299  DO 50 k = 1,i - 1
300  c(k,j) = c(k,j) + temp1*a(k,i)
301  temp2 = temp2 + b(k,j)*dconjg(a(k,i))
302  50 CONTINUE
303  IF (beta.EQ.zero) THEN
304  c(i,j) = temp1*dble(a(i,i)) + alpha*temp2
305  ELSE
306  c(i,j) = beta*c(i,j) + temp1*dble(a(i,i)) +
307  + alpha*temp2
308  END IF
309  60 CONTINUE
310  70 CONTINUE
311  ELSE
312  DO 100 j = 1,n
313  DO 90 i = m,1,-1
314  temp1 = alpha*b(i,j)
315  temp2 = zero
316  DO 80 k = i + 1,m
317  c(k,j) = c(k,j) + temp1*a(k,i)
318  temp2 = temp2 + b(k,j)*dconjg(a(k,i))
319  80 CONTINUE
320  IF (beta.EQ.zero) THEN
321  c(i,j) = temp1*dble(a(i,i)) + alpha*temp2
322  ELSE
323  c(i,j) = beta*c(i,j) + temp1*dble(a(i,i)) +
324  + alpha*temp2
325  END IF
326  90 CONTINUE
327  100 CONTINUE
328  END IF
329  ELSE
330 *
331 * Form C := alpha*B*A + beta*C.
332 *
333  DO 170 j = 1,n
334  temp1 = alpha*dble(a(j,j))
335  IF (beta.EQ.zero) THEN
336  DO 110 i = 1,m
337  c(i,j) = temp1*b(i,j)
338  110 CONTINUE
339  ELSE
340  DO 120 i = 1,m
341  c(i,j) = beta*c(i,j) + temp1*b(i,j)
342  120 CONTINUE
343  END IF
344  DO 140 k = 1,j - 1
345  IF (upper) THEN
346  temp1 = alpha*a(k,j)
347  ELSE
348  temp1 = alpha*dconjg(a(j,k))
349  END IF
350  DO 130 i = 1,m
351  c(i,j) = c(i,j) + temp1*b(i,k)
352  130 CONTINUE
353  140 CONTINUE
354  DO 160 k = j + 1,n
355  IF (upper) THEN
356  temp1 = alpha*dconjg(a(j,k))
357  ELSE
358  temp1 = alpha*a(k,j)
359  END IF
360  DO 150 i = 1,m
361  c(i,j) = c(i,j) + temp1*b(i,k)
362  150 CONTINUE
363  160 CONTINUE
364  170 CONTINUE
365  END IF
366 *
367  RETURN
368 *
369 * End of ZHEMM .
370 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

Here is the call graph for this function:

Here is the caller graph for this function: