LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
zhemv.f
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1 *> \brief \b ZHEMV
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 ZHEMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
12 *
13 * .. Scalar Arguments ..
14 * COMPLEX*16 ALPHA,BETA
15 * INTEGER INCX,INCY,LDA,N
16 * CHARACTER UPLO
17 * ..
18 * .. Array Arguments ..
19 * COMPLEX*16 A(LDA,*),X(*),Y(*)
20 * ..
21 *
22 *
23 *> \par Purpose:
24 * =============
25 *>
26 *> \verbatim
27 *>
28 *> ZHEMV 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.
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 array A is to be referenced as
44 *> follows:
45 *>
46 *> UPLO = 'U' or 'u' Only the upper triangular part of A
47 *> is to be referenced.
48 *>
49 *> UPLO = 'L' or 'l' Only the lower triangular part of A
50 *> is to be referenced.
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] A
67 *> \verbatim
68 *> A is COMPLEX*16 array, dimension ( LDA, N )
69 *> Before entry with UPLO = 'U' or 'u', the leading n by n
70 *> upper triangular part of the array A must contain the upper
71 *> triangular part of the hermitian matrix and the strictly
72 *> lower triangular part of A is not referenced.
73 *> Before entry with UPLO = 'L' or 'l', the leading n by n
74 *> lower triangular part of the array A must contain the lower
75 *> triangular part of the hermitian matrix and the strictly
76 *> upper triangular part of A is not referenced.
77 *> Note that the imaginary parts of the diagonal elements need
78 *> not be set and are assumed to be zero.
79 *> \endverbatim
80 *>
81 *> \param[in] LDA
82 *> \verbatim
83 *> LDA is INTEGER
84 *> On entry, LDA specifies the first dimension of A as declared
85 *> in the calling (sub) program. LDA must be at least
86 *> max( 1, n ).
87 *> \endverbatim
88 *>
89 *> \param[in] X
90 *> \verbatim
91 *> X is COMPLEX*16 array, dimension at least
92 *> ( 1 + ( n - 1 )*abs( INCX ) ).
93 *> Before entry, the incremented array X must contain the n
94 *> element vector x.
95 *> \endverbatim
96 *>
97 *> \param[in] INCX
98 *> \verbatim
99 *> INCX is INTEGER
100 *> On entry, INCX specifies the increment for the elements of
101 *> X. INCX must not be zero.
102 *> \endverbatim
103 *>
104 *> \param[in] BETA
105 *> \verbatim
106 *> BETA is COMPLEX*16
107 *> On entry, BETA specifies the scalar beta. When BETA is
108 *> supplied as zero then Y need not be set on input.
109 *> \endverbatim
110 *>
111 *> \param[in,out] Y
112 *> \verbatim
113 *> Y is COMPLEX*16 array, dimension at least
114 *> ( 1 + ( n - 1 )*abs( INCY ) ).
115 *> Before entry, the incremented array Y must contain the n
116 *> element vector y. On exit, Y is overwritten by the updated
117 *> vector y.
118 *> \endverbatim
119 *>
120 *> \param[in] INCY
121 *> \verbatim
122 *> INCY is INTEGER
123 *> On entry, INCY specifies the increment for the elements of
124 *> Y. INCY must not be zero.
125 *> \endverbatim
126 *
127 * Authors:
128 * ========
129 *
130 *> \author Univ. of Tennessee
131 *> \author Univ. of California Berkeley
132 *> \author Univ. of Colorado Denver
133 *> \author NAG Ltd.
134 *
135 *> \ingroup complex16_blas_level2
136 *
137 *> \par Further Details:
138 * =====================
139 *>
140 *> \verbatim
141 *>
142 *> Level 2 Blas routine.
143 *> The vector and matrix arguments are not referenced when N = 0, or M = 0
144 *>
145 *> -- Written on 22-October-1986.
146 *> Jack Dongarra, Argonne National Lab.
147 *> Jeremy Du Croz, Nag Central Office.
148 *> Sven Hammarling, Nag Central Office.
149 *> Richard Hanson, Sandia National Labs.
150 *> \endverbatim
151 *>
152 * =====================================================================
153  SUBROUTINE zhemv(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
154 *
155 * -- Reference BLAS level2 routine --
156 * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
157 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
158 *
159 * .. Scalar Arguments ..
160  COMPLEX*16 ALPHA,BETA
161  INTEGER INCX,INCY,LDA,N
162  CHARACTER UPLO
163 * ..
164 * .. Array Arguments ..
165  COMPLEX*16 A(LDA,*),X(*),Y(*)
166 * ..
167 *
168 * =====================================================================
169 *
170 * .. Parameters ..
171  COMPLEX*16 ONE
172  parameter(one= (1.0d+0,0.0d+0))
173  COMPLEX*16 ZERO
174  parameter(zero= (0.0d+0,0.0d+0))
175 * ..
176 * .. Local Scalars ..
177  COMPLEX*16 TEMP1,TEMP2
178  INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY
179 * ..
180 * .. External Functions ..
181  LOGICAL LSAME
182  EXTERNAL lsame
183 * ..
184 * .. External Subroutines ..
185  EXTERNAL xerbla
186 * ..
187 * .. Intrinsic Functions ..
188  INTRINSIC dble,dconjg,max
189 * ..
190 *
191 * Test the input parameters.
192 *
193  info = 0
194  IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
195  info = 1
196  ELSE IF (n.LT.0) THEN
197  info = 2
198  ELSE IF (lda.LT.max(1,n)) THEN
199  info = 5
200  ELSE IF (incx.EQ.0) THEN
201  info = 7
202  ELSE IF (incy.EQ.0) THEN
203  info = 10
204  END IF
205  IF (info.NE.0) THEN
206  CALL xerbla('ZHEMV ',info)
207  RETURN
208  END IF
209 *
210 * Quick return if possible.
211 *
212  IF ((n.EQ.0) .OR. ((alpha.EQ.zero).AND. (beta.EQ.one))) RETURN
213 *
214 * Set up the start points in X and Y.
215 *
216  IF (incx.GT.0) THEN
217  kx = 1
218  ELSE
219  kx = 1 - (n-1)*incx
220  END IF
221  IF (incy.GT.0) THEN
222  ky = 1
223  ELSE
224  ky = 1 - (n-1)*incy
225  END IF
226 *
227 * Start the operations. In this version the elements of A are
228 * accessed sequentially with one pass through the triangular part
229 * of A.
230 *
231 * First form y := beta*y.
232 *
233  IF (beta.NE.one) THEN
234  IF (incy.EQ.1) THEN
235  IF (beta.EQ.zero) THEN
236  DO 10 i = 1,n
237  y(i) = zero
238  10 CONTINUE
239  ELSE
240  DO 20 i = 1,n
241  y(i) = beta*y(i)
242  20 CONTINUE
243  END IF
244  ELSE
245  iy = ky
246  IF (beta.EQ.zero) THEN
247  DO 30 i = 1,n
248  y(iy) = zero
249  iy = iy + incy
250  30 CONTINUE
251  ELSE
252  DO 40 i = 1,n
253  y(iy) = beta*y(iy)
254  iy = iy + incy
255  40 CONTINUE
256  END IF
257  END IF
258  END IF
259  IF (alpha.EQ.zero) RETURN
260  IF (lsame(uplo,'U')) THEN
261 *
262 * Form y when A is stored in upper triangle.
263 *
264  IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
265  DO 60 j = 1,n
266  temp1 = alpha*x(j)
267  temp2 = zero
268  DO 50 i = 1,j - 1
269  y(i) = y(i) + temp1*a(i,j)
270  temp2 = temp2 + dconjg(a(i,j))*x(i)
271  50 CONTINUE
272  y(j) = y(j) + temp1*dble(a(j,j)) + alpha*temp2
273  60 CONTINUE
274  ELSE
275  jx = kx
276  jy = ky
277  DO 80 j = 1,n
278  temp1 = alpha*x(jx)
279  temp2 = zero
280  ix = kx
281  iy = ky
282  DO 70 i = 1,j - 1
283  y(iy) = y(iy) + temp1*a(i,j)
284  temp2 = temp2 + dconjg(a(i,j))*x(ix)
285  ix = ix + incx
286  iy = iy + incy
287  70 CONTINUE
288  y(jy) = y(jy) + temp1*dble(a(j,j)) + alpha*temp2
289  jx = jx + incx
290  jy = jy + incy
291  80 CONTINUE
292  END IF
293  ELSE
294 *
295 * Form y when A is stored in 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*dble(a(j,j))
302  DO 90 i = j + 1,n
303  y(i) = y(i) + temp1*a(i,j)
304  temp2 = temp2 + dconjg(a(i,j))*x(i)
305  90 CONTINUE
306  y(j) = y(j) + alpha*temp2
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(a(j,j))
315  ix = jx
316  iy = jy
317  DO 110 i = j + 1,n
318  ix = ix + incx
319  iy = iy + incy
320  y(iy) = y(iy) + temp1*a(i,j)
321  temp2 = temp2 + dconjg(a(i,j))*x(ix)
322  110 CONTINUE
323  y(jy) = y(jy) + alpha*temp2
324  jx = jx + incx
325  jy = jy + incy
326  120 CONTINUE
327  END IF
328  END IF
329 *
330  RETURN
331 *
332 * End of ZHEMV
333 *
334  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zhemv(UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZHEMV
Definition: zhemv.f:154