LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine chemv ( character UPLO, integer N, complex ALPHA, complex, dimension(lda,*) A, integer LDA, complex, dimension(*) X, integer INCX, complex BETA, complex, dimension(*) Y, integer INCY )

CHEMV

Purpose:
``` CHEMV  performs the matrix-vector  operation

y := alpha*A*x + beta*y,

where alpha and beta are scalars, x and y are n element vectors and
A is an n by n hermitian matrix.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of A is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of A is to be referenced.``` [in] N ``` N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero.``` [in] ALPHA ``` ALPHA is COMPLEX On entry, ALPHA specifies the scalar alpha.``` [in] A ``` A is COMPLEX array of DIMENSION ( LDA, n ). Before entry with 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. Before entry with 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 and 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. LDA must be at least max( 1, n ).``` [in] X ``` X is COMPLEX array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x.``` [in] INCX ``` INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero.``` [in] BETA ``` BETA is COMPLEX On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input.``` [in,out] Y ``` Y is COMPLEX array of dimension at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. On exit, Y is overwritten by the updated vector y.``` [in] INCY ``` INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero.```
Date
November 2011
Further Details:
```  Level 2 Blas routine.
The vector and matrix arguments are not referenced when N = 0, or M = 0

-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.```

Definition at line 156 of file chemv.f.

156 *
157 * -- Reference BLAS level2 routine (version 3.4.0) --
158 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
159 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
160 * November 2011
161 *
162 * .. Scalar Arguments ..
163  COMPLEX alpha,beta
164  INTEGER incx,incy,lda,n
165  CHARACTER uplo
166 * ..
167 * .. Array Arguments ..
168  COMPLEX a(lda,*),x(*),y(*)
169 * ..
170 *
171 * =====================================================================
172 *
173 * .. Parameters ..
174  COMPLEX one
175  parameter(one= (1.0e+0,0.0e+0))
176  COMPLEX zero
177  parameter(zero= (0.0e+0,0.0e+0))
178 * ..
179 * .. Local Scalars ..
180  COMPLEX temp1,temp2
181  INTEGER i,info,ix,iy,j,jx,jy,kx,ky
182 * ..
183 * .. External Functions ..
184  LOGICAL lsame
185  EXTERNAL lsame
186 * ..
187 * .. External Subroutines ..
188  EXTERNAL xerbla
189 * ..
190 * .. Intrinsic Functions ..
191  INTRINSIC conjg,max,real
192 * ..
193 *
194 * Test the input parameters.
195 *
196  info = 0
197  IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
198  info = 1
199  ELSE IF (n.LT.0) THEN
200  info = 2
201  ELSE IF (lda.LT.max(1,n)) THEN
202  info = 5
203  ELSE IF (incx.EQ.0) THEN
204  info = 7
205  ELSE IF (incy.EQ.0) THEN
206  info = 10
207  END IF
208  IF (info.NE.0) THEN
209  CALL xerbla('CHEMV ',info)
210  RETURN
211  END IF
212 *
213 * Quick return if possible.
214 *
215  IF ((n.EQ.0) .OR. ((alpha.EQ.zero).AND. (beta.EQ.one))) RETURN
216 *
217 * Set up the start points in X and Y.
218 *
219  IF (incx.GT.0) THEN
220  kx = 1
221  ELSE
222  kx = 1 - (n-1)*incx
223  END IF
224  IF (incy.GT.0) THEN
225  ky = 1
226  ELSE
227  ky = 1 - (n-1)*incy
228  END IF
229 *
230 * Start the operations. In this version the elements of A are
231 * accessed sequentially with one pass through the triangular part
232 * of A.
233 *
234 * First form y := beta*y.
235 *
236  IF (beta.NE.one) THEN
237  IF (incy.EQ.1) THEN
238  IF (beta.EQ.zero) THEN
239  DO 10 i = 1,n
240  y(i) = zero
241  10 CONTINUE
242  ELSE
243  DO 20 i = 1,n
244  y(i) = beta*y(i)
245  20 CONTINUE
246  END IF
247  ELSE
248  iy = ky
249  IF (beta.EQ.zero) THEN
250  DO 30 i = 1,n
251  y(iy) = zero
252  iy = iy + incy
253  30 CONTINUE
254  ELSE
255  DO 40 i = 1,n
256  y(iy) = beta*y(iy)
257  iy = iy + incy
258  40 CONTINUE
259  END IF
260  END IF
261  END IF
262  IF (alpha.EQ.zero) RETURN
263  IF (lsame(uplo,'U')) THEN
264 *
265 * Form y when A is stored in upper triangle.
266 *
267  IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
268  DO 60 j = 1,n
269  temp1 = alpha*x(j)
270  temp2 = zero
271  DO 50 i = 1,j - 1
272  y(i) = y(i) + temp1*a(i,j)
273  temp2 = temp2 + conjg(a(i,j))*x(i)
274  50 CONTINUE
275  y(j) = y(j) + temp1*REAL(A(J,J)) + alpha*temp2
276  60 CONTINUE
277  ELSE
278  jx = kx
279  jy = ky
280  DO 80 j = 1,n
281  temp1 = alpha*x(jx)
282  temp2 = zero
283  ix = kx
284  iy = ky
285  DO 70 i = 1,j - 1
286  y(iy) = y(iy) + temp1*a(i,j)
287  temp2 = temp2 + conjg(a(i,j))*x(ix)
288  ix = ix + incx
289  iy = iy + incy
290  70 CONTINUE
291  y(jy) = y(jy) + temp1*REAL(A(J,J)) + alpha*temp2
292  jx = jx + incx
293  jy = jy + incy
294  80 CONTINUE
295  END IF
296  ELSE
297 *
298 * Form y when A is stored in lower triangle.
299 *
300  IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
301  DO 100 j = 1,n
302  temp1 = alpha*x(j)
303  temp2 = zero
304  y(j) = y(j) + temp1*REAL(a(j,j))
305  DO 90 i = j + 1,n
306  y(i) = y(i) + temp1*a(i,j)
307  temp2 = temp2 + conjg(a(i,j))*x(i)
308  90 CONTINUE
309  y(j) = y(j) + alpha*temp2
310  100 CONTINUE
311  ELSE
312  jx = kx
313  jy = ky
314  DO 120 j = 1,n
315  temp1 = alpha*x(jx)
316  temp2 = zero
317  y(jy) = y(jy) + temp1*REAL(a(j,j))
318  ix = jx
319  iy = jy
320  DO 110 i = j + 1,n
321  ix = ix + incx
322  iy = iy + incy
323  y(iy) = y(iy) + temp1*a(i,j)
324  temp2 = temp2 + conjg(a(i,j))*x(ix)
325  110 CONTINUE
326  y(jy) = y(jy) + alpha*temp2
327  jx = jx + incx
328  jy = jy + incy
329  120 CONTINUE
330  END IF
331  END IF
332 *
333  RETURN
334 *
335 * End of CHEMV .
336 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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