LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ 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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