 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ 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)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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