 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ chpmv()

 subroutine chpmv ( character UPLO, integer N, complex ALPHA, complex, dimension(*) AP, complex, dimension(*) X, integer INCX, complex BETA, complex, dimension(*) Y, integer INCY )

CHPMV

Purpose:
``` CHPMV  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, supplied in packed form.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array AP as follows: UPLO = 'U' or 'u' The upper triangular part of A is supplied in AP. UPLO = 'L' or 'l' The lower triangular part of A is supplied in AP.``` [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] AP ``` AP is COMPLEX array, dimension at least ( ( n*( n + 1 ) )/2 ). Before entry with UPLO = 'U' or 'u', the array AP must contain the upper triangular part of the hermitian matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on. Before entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular part of the hermitian matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on. Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero.``` [in] X ``` X is COMPLEX array, 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, 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.```
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 148 of file chpmv.f.

149*
150* -- Reference BLAS level2 routine --
151* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
152* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
153*
154* .. Scalar Arguments ..
155 COMPLEX ALPHA,BETA
156 INTEGER INCX,INCY,N
157 CHARACTER UPLO
158* ..
159* .. Array Arguments ..
160 COMPLEX AP(*),X(*),Y(*)
161* ..
162*
163* =====================================================================
164*
165* .. Parameters ..
166 COMPLEX ONE
167 parameter(one= (1.0e+0,0.0e+0))
168 COMPLEX ZERO
169 parameter(zero= (0.0e+0,0.0e+0))
170* ..
171* .. Local Scalars ..
172 COMPLEX TEMP1,TEMP2
173 INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY
174* ..
175* .. External Functions ..
176 LOGICAL LSAME
177 EXTERNAL lsame
178* ..
179* .. External Subroutines ..
180 EXTERNAL xerbla
181* ..
182* .. Intrinsic Functions ..
183 INTRINSIC conjg,real
184* ..
185*
186* Test the input parameters.
187*
188 info = 0
189 IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
190 info = 1
191 ELSE IF (n.LT.0) THEN
192 info = 2
193 ELSE IF (incx.EQ.0) THEN
194 info = 6
195 ELSE IF (incy.EQ.0) THEN
196 info = 9
197 END IF
198 IF (info.NE.0) THEN
199 CALL xerbla('CHPMV ',info)
200 RETURN
201 END IF
202*
203* Quick return if possible.
204*
205 IF ((n.EQ.0) .OR. ((alpha.EQ.zero).AND. (beta.EQ.one))) RETURN
206*
207* Set up the start points in X and Y.
208*
209 IF (incx.GT.0) THEN
210 kx = 1
211 ELSE
212 kx = 1 - (n-1)*incx
213 END IF
214 IF (incy.GT.0) THEN
215 ky = 1
216 ELSE
217 ky = 1 - (n-1)*incy
218 END IF
219*
220* Start the operations. In this version the elements of the array AP
221* are accessed sequentially with one pass through AP.
222*
223* First form y := beta*y.
224*
225 IF (beta.NE.one) THEN
226 IF (incy.EQ.1) THEN
227 IF (beta.EQ.zero) THEN
228 DO 10 i = 1,n
229 y(i) = zero
230 10 CONTINUE
231 ELSE
232 DO 20 i = 1,n
233 y(i) = beta*y(i)
234 20 CONTINUE
235 END IF
236 ELSE
237 iy = ky
238 IF (beta.EQ.zero) THEN
239 DO 30 i = 1,n
240 y(iy) = zero
241 iy = iy + incy
242 30 CONTINUE
243 ELSE
244 DO 40 i = 1,n
245 y(iy) = beta*y(iy)
246 iy = iy + incy
247 40 CONTINUE
248 END IF
249 END IF
250 END IF
251 IF (alpha.EQ.zero) RETURN
252 kk = 1
253 IF (lsame(uplo,'U')) THEN
254*
255* Form y when AP contains the upper triangle.
256*
257 IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
258 DO 60 j = 1,n
259 temp1 = alpha*x(j)
260 temp2 = zero
261 k = kk
262 DO 50 i = 1,j - 1
263 y(i) = y(i) + temp1*ap(k)
264 temp2 = temp2 + conjg(ap(k))*x(i)
265 k = k + 1
266 50 CONTINUE
267 y(j) = y(j) + temp1*real(ap(kk+j-1)) + alpha*temp2
268 kk = kk + j
269 60 CONTINUE
270 ELSE
271 jx = kx
272 jy = ky
273 DO 80 j = 1,n
274 temp1 = alpha*x(jx)
275 temp2 = zero
276 ix = kx
277 iy = ky
278 DO 70 k = kk,kk + j - 2
279 y(iy) = y(iy) + temp1*ap(k)
280 temp2 = temp2 + conjg(ap(k))*x(ix)
281 ix = ix + incx
282 iy = iy + incy
283 70 CONTINUE
284 y(jy) = y(jy) + temp1*real(ap(kk+j-1)) + alpha*temp2
285 jx = jx + incx
286 jy = jy + incy
287 kk = kk + j
288 80 CONTINUE
289 END IF
290 ELSE
291*
292* Form y when AP contains the lower triangle.
293*
294 IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
295 DO 100 j = 1,n
296 temp1 = alpha*x(j)
297 temp2 = zero
298 y(j) = y(j) + temp1*real(ap(kk))
299 k = kk + 1
300 DO 90 i = j + 1,n
301 y(i) = y(i) + temp1*ap(k)
302 temp2 = temp2 + conjg(ap(k))*x(i)
303 k = k + 1
304 90 CONTINUE
305 y(j) = y(j) + alpha*temp2
306 kk = kk + (n-j+1)
307 100 CONTINUE
308 ELSE
309 jx = kx
310 jy = ky
311 DO 120 j = 1,n
312 temp1 = alpha*x(jx)
313 temp2 = zero
314 y(jy) = y(jy) + temp1*real(ap(kk))
315 ix = jx
316 iy = jy
317 DO 110 k = kk + 1,kk + n - j
318 ix = ix + incx
319 iy = iy + incy
320 y(iy) = y(iy) + temp1*ap(k)
321 temp2 = temp2 + conjg(ap(k))*x(ix)
322 110 CONTINUE
323 y(jy) = y(jy) + alpha*temp2
324 jx = jx + incx
325 jy = jy + incy
326 kk = kk + (n-j+1)
327 120 CONTINUE
328 END IF
329 END IF
330*
331 RETURN
332*
333* End of CHPMV
334*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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