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

 subroutine cher ( character uplo, integer n, real alpha, complex, dimension(*) x, integer incx, complex, dimension(lda,*) a, integer lda )

CHER

Purpose:
``` CHER   performs the hermitian rank 1 operation

A := alpha*x*x**H + A,

where alpha is a real scalar, x is an n element vector 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 REAL On entry, ALPHA specifies the scalar alpha.``` [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,out] A ``` A is COMPLEX 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 134 of file cher.f.

135*
136* -- Reference BLAS level2 routine --
137* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
138* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
139*
140* .. Scalar Arguments ..
141 REAL ALPHA
142 INTEGER INCX,LDA,N
143 CHARACTER UPLO
144* ..
145* .. Array Arguments ..
146 COMPLEX A(LDA,*),X(*)
147* ..
148*
149* =====================================================================
150*
151* .. Parameters ..
152 COMPLEX ZERO
153 parameter(zero= (0.0e+0,0.0e+0))
154* ..
155* .. Local Scalars ..
156 COMPLEX TEMP
157 INTEGER I,INFO,IX,J,JX,KX
158* ..
159* .. External Functions ..
160 LOGICAL LSAME
161 EXTERNAL lsame
162* ..
163* .. External Subroutines ..
164 EXTERNAL xerbla
165* ..
166* .. Intrinsic Functions ..
167 INTRINSIC conjg,max,real
168* ..
169*
170* Test the input parameters.
171*
172 info = 0
173 IF (.NOT.lsame(uplo,'U') .AND. .NOT.lsame(uplo,'L')) THEN
174 info = 1
175 ELSE IF (n.LT.0) THEN
176 info = 2
177 ELSE IF (incx.EQ.0) THEN
178 info = 5
179 ELSE IF (lda.LT.max(1,n)) THEN
180 info = 7
181 END IF
182 IF (info.NE.0) THEN
183 CALL xerbla('CHER ',info)
184 RETURN
185 END IF
186*
187* Quick return if possible.
188*
189 IF ((n.EQ.0) .OR. (alpha.EQ.real(zero))) RETURN
190*
191* Set the start point in X if the increment is not unity.
192*
193 IF (incx.LE.0) THEN
194 kx = 1 - (n-1)*incx
195 ELSE IF (incx.NE.1) THEN
196 kx = 1
197 END IF
198*
199* Start the operations. In this version the elements of A are
200* accessed sequentially with one pass through the triangular part
201* of A.
202*
203 IF (lsame(uplo,'U')) THEN
204*
205* Form A when A is stored in upper triangle.
206*
207 IF (incx.EQ.1) THEN
208 DO 20 j = 1,n
209 IF (x(j).NE.zero) THEN
210 temp = alpha*conjg(x(j))
211 DO 10 i = 1,j - 1
212 a(i,j) = a(i,j) + x(i)*temp
213 10 CONTINUE
214 a(j,j) = real(a(j,j)) + real(x(j)*temp)
215 ELSE
216 a(j,j) = real(a(j,j))
217 END IF
218 20 CONTINUE
219 ELSE
220 jx = kx
221 DO 40 j = 1,n
222 IF (x(jx).NE.zero) THEN
223 temp = alpha*conjg(x(jx))
224 ix = kx
225 DO 30 i = 1,j - 1
226 a(i,j) = a(i,j) + x(ix)*temp
227 ix = ix + incx
228 30 CONTINUE
229 a(j,j) = real(a(j,j)) + real(x(jx)*temp)
230 ELSE
231 a(j,j) = real(a(j,j))
232 END IF
233 jx = jx + incx
234 40 CONTINUE
235 END IF
236 ELSE
237*
238* Form A when A is stored in lower triangle.
239*
240 IF (incx.EQ.1) THEN
241 DO 60 j = 1,n
242 IF (x(j).NE.zero) THEN
243 temp = alpha*conjg(x(j))
244 a(j,j) = real(a(j,j)) + real(temp*x(j))
245 DO 50 i = j + 1,n
246 a(i,j) = a(i,j) + x(i)*temp
247 50 CONTINUE
248 ELSE
249 a(j,j) = real(a(j,j))
250 END IF
251 60 CONTINUE
252 ELSE
253 jx = kx
254 DO 80 j = 1,n
255 IF (x(jx).NE.zero) THEN
256 temp = alpha*conjg(x(jx))
257 a(j,j) = real(a(j,j)) + real(temp*x(jx))
258 ix = jx
259 DO 70 i = j + 1,n
260 ix = ix + incx
261 a(i,j) = a(i,j) + x(ix)*temp
262 70 CONTINUE
263 ELSE
264 a(j,j) = real(a(j,j))
265 END IF
266 jx = jx + incx
267 80 CONTINUE
268 END IF
269 END IF
270*
271 RETURN
272*
273* End of CHER
274*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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