LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 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 of 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 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 151 of file chpmv.f.

151 *
152 * -- Reference BLAS level2 routine (version 3.4.0) --
153 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
154 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
155 * November 2011
156 *
157 * .. Scalar Arguments ..
158  COMPLEX alpha,beta
159  INTEGER incx,incy,n
160  CHARACTER uplo
161 * ..
162 * .. Array Arguments ..
163  COMPLEX ap(*),x(*),y(*)
164 * ..
165 *
166 * =====================================================================
167 *
168 * .. Parameters ..
169  COMPLEX one
170  parameter(one= (1.0e+0,0.0e+0))
171  COMPLEX zero
172  parameter(zero= (0.0e+0,0.0e+0))
173 * ..
174 * .. Local Scalars ..
175  COMPLEX temp1,temp2
176  INTEGER i,info,ix,iy,j,jx,jy,k,kk,kx,ky
177 * ..
178 * .. External Functions ..
179  LOGICAL lsame
180  EXTERNAL lsame
181 * ..
182 * .. External Subroutines ..
183  EXTERNAL xerbla
184 * ..
185 * .. Intrinsic Functions ..
186  INTRINSIC conjg,real
187 * ..
188 *
189 * Test the input parameters.
190 *
191  info = 0
192  IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
193  info = 1
194  ELSE IF (n.LT.0) THEN
195  info = 2
196  ELSE IF (incx.EQ.0) THEN
197  info = 6
198  ELSE IF (incy.EQ.0) THEN
199  info = 9
200  END IF
201  IF (info.NE.0) THEN
202  CALL xerbla('CHPMV ',info)
203  RETURN
204  END IF
205 *
206 * Quick return if possible.
207 *
208  IF ((n.EQ.0) .OR. ((alpha.EQ.zero).AND. (beta.EQ.one))) RETURN
209 *
210 * Set up the start points in X and Y.
211 *
212  IF (incx.GT.0) THEN
213  kx = 1
214  ELSE
215  kx = 1 - (n-1)*incx
216  END IF
217  IF (incy.GT.0) THEN
218  ky = 1
219  ELSE
220  ky = 1 - (n-1)*incy
221  END IF
222 *
223 * Start the operations. In this version the elements of the array AP
224 * are accessed sequentially with one pass through AP.
225 *
226 * First form y := beta*y.
227 *
228  IF (beta.NE.one) THEN
229  IF (incy.EQ.1) THEN
230  IF (beta.EQ.zero) THEN
231  DO 10 i = 1,n
232  y(i) = zero
233  10 CONTINUE
234  ELSE
235  DO 20 i = 1,n
236  y(i) = beta*y(i)
237  20 CONTINUE
238  END IF
239  ELSE
240  iy = ky
241  IF (beta.EQ.zero) THEN
242  DO 30 i = 1,n
243  y(iy) = zero
244  iy = iy + incy
245  30 CONTINUE
246  ELSE
247  DO 40 i = 1,n
248  y(iy) = beta*y(iy)
249  iy = iy + incy
250  40 CONTINUE
251  END IF
252  END IF
253  END IF
254  IF (alpha.EQ.zero) RETURN
255  kk = 1
256  IF (lsame(uplo,'U')) THEN
257 *
258 * Form y when AP contains the upper triangle.
259 *
260  IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
261  DO 60 j = 1,n
262  temp1 = alpha*x(j)
263  temp2 = zero
264  k = kk
265  DO 50 i = 1,j - 1
266  y(i) = y(i) + temp1*ap(k)
267  temp2 = temp2 + conjg(ap(k))*x(i)
268  k = k + 1
269  50 CONTINUE
270  y(j) = y(j) + temp1*REAL(AP(KK+J-1)) + alpha*temp2
271  kk = kk + j
272  60 CONTINUE
273  ELSE
274  jx = kx
275  jy = ky
276  DO 80 j = 1,n
277  temp1 = alpha*x(jx)
278  temp2 = zero
279  ix = kx
280  iy = ky
281  DO 70 k = kk,kk + j - 2
282  y(iy) = y(iy) + temp1*ap(k)
283  temp2 = temp2 + conjg(ap(k))*x(ix)
284  ix = ix + incx
285  iy = iy + incy
286  70 CONTINUE
287  y(jy) = y(jy) + temp1*REAL(AP(KK+J-1)) + alpha*temp2
288  jx = jx + incx
289  jy = jy + incy
290  kk = kk + j
291  80 CONTINUE
292  END IF
293  ELSE
294 *
295 * Form y when AP contains the lower triangle.
296 *
297  IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
298  DO 100 j = 1,n
299  temp1 = alpha*x(j)
300  temp2 = zero
301  y(j) = y(j) + temp1*REAL(ap(kk))
302  k = kk + 1
303  DO 90 i = j + 1,n
304  y(i) = y(i) + temp1*ap(k)
305  temp2 = temp2 + conjg(ap(k))*x(i)
306  k = k + 1
307  90 CONTINUE
308  y(j) = y(j) + alpha*temp2
309  kk = kk + (n-j+1)
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(ap(kk))
318  ix = jx
319  iy = jy
320  DO 110 k = kk + 1,kk + n - j
321  ix = ix + incx
322  iy = iy + incy
323  y(iy) = y(iy) + temp1*ap(k)
324  temp2 = temp2 + conjg(ap(k))*x(ix)
325  110 CONTINUE
326  y(jy) = y(jy) + alpha*temp2
327  jx = jx + incx
328  jy = jy + incy
329  kk = kk + (n-j+1)
330  120 CONTINUE
331  END IF
332  END IF
333 *
334  RETURN
335 *
336 * End of CHPMV .
337 *
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: