1ZHER(1)                          BLAS routine                          ZHER(1)
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NAME

6       ZHER - performs the hermitian rank 1 operation   A := alpha*x*conjg( x'
7       ) + A,
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SYNOPSIS

10       SUBROUTINE ZHER(UPLO,N,ALPHA,X,INCX,A,LDA)
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12           DOUBLE                                 PRECISION ALPHA
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14           INTEGER                                INCX,LDA,N
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16           CHARACTER                              UPLO
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18           DOUBLE                                 COMPLEX A(LDA,*),X(*)
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PURPOSE

21       ZHER   performs the hermitian rank 1 operation
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23       where alpha is a real scalar, x is an n element vector and A is an n by
24       n hermitian matrix.
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ARGUMENTS

28       UPLO   - CHARACTER*1.
29              On  entry,  UPLO specifies whether the upper or lower triangular
30              part of the array A is to be referenced as follows:
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32              UPLO = 'U' or 'u'   Only the upper triangular part of A is to be
33              referenced.
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35              UPLO = 'L' or 'l'   Only the lower triangular part of A is to be
36              referenced.
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38              Unchanged on exit.
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40       N      - INTEGER.
41              On entry, N specifies the order of the matrix A.  N must  be  at
42              least zero.  Unchanged on exit.
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44       ALPHA  - DOUBLE PRECISION.
45              On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.
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47       X      - COMPLEX*16       array of dimension at least
48              (  1  +  ( n - 1 )*abs( INCX ) ).  Before entry, the incremented
49              array X must contain the n element vector x.  Unchanged on exit.
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51       INCX   - INTEGER.
52              On entry, INCX specifies the increment for the  elements  of  X.
53              INCX must not be zero.  Unchanged on exit.
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55       A      - COMPLEX*16       array of DIMENSION ( LDA, n ).
56              Before  entry  with  UPLO = 'U' or 'u', the leading n by n upper
57              triangular part of the array A must contain the upper triangular
58              part  of  the hermitian matrix and the strictly lower triangular
59              part of A is not referenced. On exit, the upper triangular  part
60              of  the  array  A is overwritten by the upper triangular part of
61              the updated matrix.  Before entry with UPLO = 'L'  or  'l',  the
62              leading n by n lower triangular part of the array A must contain
63              the lower triangular  part  of  the  hermitian  matrix  and  the
64              strictly  upper triangular part of A is not referenced. On exit,
65              the lower triangular part of the array A is overwritten  by  the
66              lower  triangular  part  of  the  updated matrix.  Note that the
67              imaginary parts of the diagonal elements need not be  set,  they
68              are assumed to be zero, and on exit they are set to zero.
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70       LDA    - INTEGER.
71              On  entry, LDA specifies the first dimension of A as declared in
72              the calling (sub) program. LDA must be at least  max(  1,  n  ).
73              Unchanged on exit.
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FURTHER DETAILS

76       Level 2 Blas routine.
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78       -- Written on 22-October-1986.
79          Jack Dongarra, Argonne National Lab.
80          Jeremy Du Croz, Nag Central Office.
81          Sven Hammarling, Nag Central Office.
82          Richard Hanson, Sandia National Labs.
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87BLAS routine                     November 2008                         ZHER(1)
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