LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ zher2()

 subroutine zher2 ( character uplo, integer n, complex*16 alpha, complex*16, dimension(*) x, integer incx, complex*16, dimension(*) y, integer incy, complex*16, dimension(lda,*) a, integer lda )

ZHER2

Purpose:
``` ZHER2  performs the hermitian rank 2 operation

A := alpha*x*y**H + conjg( alpha )*y*x**H + A,

where alpha is a scalar, x and y are n element vectors and A is an n
by n hermitian matrix.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of A is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of A is to be referenced.``` [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*16 On entry, ALPHA specifies the scalar alpha.``` [in] X ``` X is COMPLEX*16 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] Y ``` Y is COMPLEX*16 array, dimension at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y.``` [in] INCY ``` INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero.``` [in,out] A ``` A is COMPLEX*16 array, dimension ( LDA, N ) Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular part of the hermitian matrix and the strictly lower triangular part of A is not referenced. On exit, the upper triangular part of the array A is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the hermitian matrix and the strictly upper triangular part of A is not referenced. On exit, the lower triangular part of the array A is overwritten by the lower triangular part of the updated matrix. Note that the imaginary parts of the diagonal elements need not be set, they are assumed to be zero, and on exit they are set to zero.``` [in] LDA ``` LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ).```
Further Details:
```  Level 2 Blas routine.

-- 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 149 of file zher2.f.

150*
151* -- Reference BLAS level2 routine --
152* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
153* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
154*
155* .. Scalar Arguments ..
156 COMPLEX*16 ALPHA
157 INTEGER INCX,INCY,LDA,N
158 CHARACTER UPLO
159* ..
160* .. Array Arguments ..
161 COMPLEX*16 A(LDA,*),X(*),Y(*)
162* ..
163*
164* =====================================================================
165*
166* .. Parameters ..
167 COMPLEX*16 ZERO
168 parameter(zero= (0.0d+0,0.0d+0))
169* ..
170* .. Local Scalars ..
171 COMPLEX*16 TEMP1,TEMP2
172 INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY
173* ..
174* .. External Functions ..
175 LOGICAL LSAME
176 EXTERNAL lsame
177* ..
178* .. External Subroutines ..
179 EXTERNAL xerbla
180* ..
181* .. Intrinsic Functions ..
182 INTRINSIC dble,dconjg,max
183* ..
184*
185* Test the input parameters.
186*
187 info = 0
188 IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
189 info = 1
190 ELSE IF (n.LT.0) THEN
191 info = 2
192 ELSE IF (incx.EQ.0) THEN
193 info = 5
194 ELSE IF (incy.EQ.0) THEN
195 info = 7
196 ELSE IF (lda.LT.max(1,n)) THEN
197 info = 9
198 END IF
199 IF (info.NE.0) THEN
200 CALL xerbla('ZHER2 ',info)
201 RETURN
202 END IF
203*
204* Quick return if possible.
205*
206 IF ((n.EQ.0) .OR. (alpha.EQ.zero)) RETURN
207*
208* Set up the start points in X and Y if the increments are not both
209* unity.
210*
211 IF ((incx.NE.1) .OR. (incy.NE.1)) THEN
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 jx = kx
223 jy = ky
224 END IF
225*
226* Start the operations. In this version the elements of A are
227* accessed sequentially with one pass through the triangular part
228* of A.
229*
230 IF (lsame(uplo,'U')) THEN
231*
232* Form A when A is stored in the upper triangle.
233*
234 IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
235 DO 20 j = 1,n
236 IF ((x(j).NE.zero) .OR. (y(j).NE.zero)) THEN
237 temp1 = alpha*dconjg(y(j))
238 temp2 = dconjg(alpha*x(j))
239 DO 10 i = 1,j - 1
240 a(i,j) = a(i,j) + x(i)*temp1 + y(i)*temp2
241 10 CONTINUE
242 a(j,j) = dble(a(j,j)) +
243 + dble(x(j)*temp1+y(j)*temp2)
244 ELSE
245 a(j,j) = dble(a(j,j))
246 END IF
247 20 CONTINUE
248 ELSE
249 DO 40 j = 1,n
250 IF ((x(jx).NE.zero) .OR. (y(jy).NE.zero)) THEN
251 temp1 = alpha*dconjg(y(jy))
252 temp2 = dconjg(alpha*x(jx))
253 ix = kx
254 iy = ky
255 DO 30 i = 1,j - 1
256 a(i,j) = a(i,j) + x(ix)*temp1 + y(iy)*temp2
257 ix = ix + incx
258 iy = iy + incy
259 30 CONTINUE
260 a(j,j) = dble(a(j,j)) +
261 + dble(x(jx)*temp1+y(jy)*temp2)
262 ELSE
263 a(j,j) = dble(a(j,j))
264 END IF
265 jx = jx + incx
266 jy = jy + incy
267 40 CONTINUE
268 END IF
269 ELSE
270*
271* Form A when A is stored in the lower triangle.
272*
273 IF ((incx.EQ.1) .AND. (incy.EQ.1)) THEN
274 DO 60 j = 1,n
275 IF ((x(j).NE.zero) .OR. (y(j).NE.zero)) THEN
276 temp1 = alpha*dconjg(y(j))
277 temp2 = dconjg(alpha*x(j))
278 a(j,j) = dble(a(j,j)) +
279 + dble(x(j)*temp1+y(j)*temp2)
280 DO 50 i = j + 1,n
281 a(i,j) = a(i,j) + x(i)*temp1 + y(i)*temp2
282 50 CONTINUE
283 ELSE
284 a(j,j) = dble(a(j,j))
285 END IF
286 60 CONTINUE
287 ELSE
288 DO 80 j = 1,n
289 IF ((x(jx).NE.zero) .OR. (y(jy).NE.zero)) THEN
290 temp1 = alpha*dconjg(y(jy))
291 temp2 = dconjg(alpha*x(jx))
292 a(j,j) = dble(a(j,j)) +
293 + dble(x(jx)*temp1+y(jy)*temp2)
294 ix = jx
295 iy = jy
296 DO 70 i = j + 1,n
297 ix = ix + incx
298 iy = iy + incy
299 a(i,j) = a(i,j) + x(ix)*temp1 + y(iy)*temp2
300 70 CONTINUE
301 ELSE
302 a(j,j) = dble(a(j,j))
303 END IF
304 jx = jx + incx
305 jy = jy + incy
306 80 CONTINUE
307 END IF
308 END IF
309*
310 RETURN
311*
312* End of ZHER2
313*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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