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

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

9       SUBROUTINE CHPR(UPLO,N,ALPHA,X,INCX,AP)
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11           REAL                                ALPHA
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13           INTEGER                             INCX,N
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15           CHARACTER                           UPLO
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17           COMPLEX                             AP(*),X(*)
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PURPOSE

20       CHPR    performs the hermitian rank 1 operation
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22       where alpha is a real scalar, x is an n element vector and A is an n by
23       n hermitian matrix, supplied in packed form.
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ARGUMENTS

27       UPLO   - CHARACTER*1.
28              On entry, UPLO specifies whether the upper or  lower  triangular
29              part  of the matrix A is supplied in the packed array AP as fol‐
30              lows:
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32              UPLO = 'U' or 'u'   The upper triangular part of A  is  supplied
33              in AP.
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35              UPLO  =  'L' or 'l'   The lower triangular part of A is supplied
36              in AP.
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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  - REAL            .
45              On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.
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47       X      - COMPLEX          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       AP     - COMPLEX          array of DIMENSION at least
56              (  (  n*(  n + 1 ) )/2 ).  Before entry with  UPLO = 'U' or 'u',
57              the array AP must contain the upper triangular part of the  her‐
58              mitian matrix packed sequentially, column by column, so that AP(
59              1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a(  1,  2  )
60              and  a( 2, 2 ) respectively, and so on. On exit, the array AP is
61              overwritten by the upper triangular part of the updated  matrix.
62              Before  entry  with UPLO = 'L' or 'l', the array AP must contain
63              the lower triangular part of the hermitian matrix packed sequen‐
64              tially,  column  by  column, so that AP( 1 ) contains a( 1, 1 ),
65              AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and  a(  3,  1  )  respec‐
66              tively,  and  so on. On exit, the array AP is overwritten by the
67              lower triangular part of the  updated  matrix.   Note  that  the
68              imaginary  parts  of the diagonal elements need not be set, they
69              are assumed to be zero, and on exit they are set to zero.
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71              Level 2 Blas routine.
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73              -- Written on 22-October-1986.  Jack Dongarra, Argonne  National
74              Lab.   Jeremy Du Croz, Nag Central Office.  Sven Hammarling, Nag
75              Central Office.  Richard Hanson, Sandia National Labs.
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79BLAS routine                     November 2006                         CHPR(1)