1CHPR(1)                          BLAS routine                          CHPR(1)
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NAME

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

10       SUBROUTINE CHPR(UPLO,N,ALPHA,X,INCX,AP)
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12           REAL                                ALPHA
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14           INTEGER                             INCX,N
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16           CHARACTER                           UPLO
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18           COMPLEX                             AP(*),X(*)
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PURPOSE

21       CHPR    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, supplied in packed form.
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ARGUMENTS

28       UPLO   - CHARACTER*1.
29              On  entry,  UPLO specifies whether the upper or lower triangular
30              part of the matrix A is supplied in the packed array AP as  fol‐
31              lows:
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33              UPLO  =  'U' or 'u'   The upper triangular part of A is supplied
34              in AP.
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36              UPLO = 'L' or 'l'   The lower triangular part of A  is  supplied
37              in AP.
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39              Unchanged on exit.
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41       N      - INTEGER.
42              On  entry,  N specifies the order of the matrix A.  N must be at
43              least zero.  Unchanged on exit.
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45       ALPHA  - REAL            .
46              On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.
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48       X      - COMPLEX          array of dimension at least
49              ( 1 + ( n - 1 )*abs( INCX ) ).  Before  entry,  the  incremented
50              array X must contain the n element vector x.  Unchanged on exit.
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52       INCX   - INTEGER.
53              On  entry,  INCX  specifies the increment for the elements of X.
54              INCX must not be zero.  Unchanged on exit.
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56       AP     - COMPLEX          array of DIMENSION at least
57              ( ( n*( n + 1 ) )/2 ).  Before entry with  UPLO =  'U'  or  'u',
58              the  array AP must contain the upper triangular part of the her‐
59              mitian matrix packed sequentially, column by column, so that AP(
60              1  )  contains  a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
61              and a( 2, 2 ) respectively, and so on. On exit, the array AP  is
62              overwritten  by the upper triangular part of the updated matrix.
63              Before entry with UPLO = 'L' or 'l', the array AP  must  contain
64              the lower triangular part of the hermitian matrix packed sequen‐
65              tially, column by column, so that AP( 1 ) contains a(  1,  1  ),
66              AP(  2  )  and  AP(  3 ) contain a( 2, 1 ) and a( 3, 1 ) respec‐
67              tively, and so on. On exit, the array AP is overwritten  by  the
68              lower  triangular  part  of  the  updated matrix.  Note that the
69              imaginary parts of the diagonal elements need not be  set,  they
70              are assumed to be zero, and on exit they are set to zero.
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FURTHER DETAILS

73       Level 2 Blas routine.
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75       -- Written on 22-October-1986.
76          Jack Dongarra, Argonne National Lab.
77          Jeremy Du Croz, Nag Central Office.
78          Sven Hammarling, Nag Central Office.
79          Richard Hanson, Sandia National Labs.
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84BLAS routine                     November 2008                         CHPR(1)