LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
Loading...
Searching...
No Matches
zhpmv.f
Go to the documentation of this file.
1*> \brief \b ZHPMV
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8* Definition:
9* ===========
10*
11* SUBROUTINE ZHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
12*
13* .. Scalar Arguments ..
14* COMPLEX*16 ALPHA,BETA
15* INTEGER INCX,INCY,N
16* CHARACTER UPLO
17* ..
18* .. Array Arguments ..
19* COMPLEX*16 AP(*),X(*),Y(*)
20* ..
21*
22*
23*> \par Purpose:
24* =============
25*>
26*> \verbatim
27*>
28*> ZHPMV performs the matrix-vector operation
29*>
30*> y := alpha*A*x + beta*y,
31*>
32*> where alpha and beta are scalars, x and y are n element vectors and
33*> A is an n by n hermitian matrix, supplied in packed form.
34*> \endverbatim
35*
36* Arguments:
37* ==========
38*
39*> \param[in] UPLO
40*> \verbatim
41*> UPLO is CHARACTER*1
42*> On entry, UPLO specifies whether the upper or lower
43*> triangular part of the matrix A is supplied in the packed
44*> array AP as follows:
45*>
46*> UPLO = 'U' or 'u' The upper triangular part of A is
47*> supplied in AP.
48*>
49*> UPLO = 'L' or 'l' The lower triangular part of A is
50*> supplied in AP.
51*> \endverbatim
52*>
53*> \param[in] N
54*> \verbatim
55*> N is INTEGER
56*> On entry, N specifies the order of the matrix A.
57*> N must be at least zero.
58*> \endverbatim
59*>
60*> \param[in] ALPHA
61*> \verbatim
62*> ALPHA is COMPLEX*16
63*> On entry, ALPHA specifies the scalar alpha.
64*> \endverbatim
65*>
66*> \param[in] AP
67*> \verbatim
68*> AP is COMPLEX*16 array, dimension at least
69*> ( ( n*( n + 1 ) )/2 ).
70*> Before entry with UPLO = 'U' or 'u', the array AP must
71*> contain the upper triangular part of the hermitian matrix
72*> packed sequentially, column by column, so that AP( 1 )
73*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
74*> and a( 2, 2 ) respectively, and so on.
75*> Before entry with UPLO = 'L' or 'l', the array AP must
76*> contain the lower triangular part of the hermitian matrix
77*> packed sequentially, column by column, so that AP( 1 )
78*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
79*> and a( 3, 1 ) respectively, and so on.
80*> Note that the imaginary parts of the diagonal elements need
81*> not be set and are assumed to be zero.
82*> \endverbatim
83*>
84*> \param[in] X
85*> \verbatim
86*> X is COMPLEX*16 array, dimension at least
87*> ( 1 + ( n - 1 )*abs( INCX ) ).
88*> Before entry, the incremented array X must contain the n
89*> element vector x.
90*> \endverbatim
91*>
92*> \param[in] INCX
93*> \verbatim
94*> INCX is INTEGER
95*> On entry, INCX specifies the increment for the elements of
96*> X. INCX must not be zero.
97*> \endverbatim
98*>
99*> \param[in] BETA
100*> \verbatim
101*> BETA is COMPLEX*16
102*> On entry, BETA specifies the scalar beta. When BETA is
103*> supplied as zero then Y need not be set on input.
104*> \endverbatim
105*>
106*> \param[in,out] Y
107*> \verbatim
108*> Y is COMPLEX*16 array, dimension at least
109*> ( 1 + ( n - 1 )*abs( INCY ) ).
110*> Before entry, the incremented array Y must contain the n
111*> element vector y. On exit, Y is overwritten by the updated
112*> vector y.
113*> \endverbatim
114*>
115*> \param[in] INCY
116*> \verbatim
117*> INCY is INTEGER
118*> On entry, INCY specifies the increment for the elements of
119*> Y. INCY must not be zero.
120*> \endverbatim
121*
122* Authors:
123* ========
124*
125*> \author Univ. of Tennessee
126*> \author Univ. of California Berkeley
127*> \author Univ. of Colorado Denver
128*> \author NAG Ltd.
129*
130*> \ingroup complex16_blas_level2
131*
132*> \par Further Details:
133* =====================
134*>
135*> \verbatim
136*>
137*> Level 2 Blas routine.
138*> The vector and matrix arguments are not referenced when N = 0, or M = 0
139*>
140*> -- Written on 22-October-1986.
141*> Jack Dongarra, Argonne National Lab.
142*> Jeremy Du Croz, Nag Central Office.
143*> Sven Hammarling, Nag Central Office.
144*> Richard Hanson, Sandia National Labs.
145*> \endverbatim
146*>
147* =====================================================================
148 SUBROUTINE zhpmv(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
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*16 ALPHA,BETA
156 INTEGER INCX,INCY,N
157 CHARACTER UPLO
158* ..
159* .. Array Arguments ..
160 COMPLEX*16 AP(*),X(*),Y(*)
161* ..
162*
163* =====================================================================
164*
165* .. Parameters ..
166 COMPLEX*16 ONE
167 parameter(one= (1.0d+0,0.0d+0))
168 COMPLEX*16 ZERO
169 parameter(zero= (0.0d+0,0.0d+0))
170* ..
171* .. Local Scalars ..
172 COMPLEX*16 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 dble,dconjg
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('ZHPMV ',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 + dconjg(ap(k))*x(i)
265 k = k + 1
266 50 CONTINUE
267 y(j) = y(j) + temp1*dble(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 + dconjg(ap(k))*x(ix)
281 ix = ix + incx
282 iy = iy + incy
283 70 CONTINUE
284 y(jy) = y(jy) + temp1*dble(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*dble(ap(kk))
299 k = kk + 1
300 DO 90 i = j + 1,n
301 y(i) = y(i) + temp1*ap(k)
302 temp2 = temp2 + dconjg(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*dble(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 + dconjg(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 ZHPMV
334*
335 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zhpmv(UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
ZHPMV
Definition: zhpmv.f:149