1ZHPMV(1)                         BLAS routine                         ZHPMV(1)
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NAME

6       ZHPMV - performs the matrix-vector operation   y := alpha*A*x + beta*y,
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SYNOPSIS

9       SUBROUTINE ZHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
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11           DOUBLE                                           COMPLEX ALPHA,BETA
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13           INTEGER                                          INCX,INCY,N
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15           CHARACTER                                        UPLO
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17           DOUBLE                                           COMPLEX
18                                                            AP(*),X(*),Y(*)
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PURPOSE

21       ZHPMV  performs the matrix-vector operation
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23       where alpha and beta are scalars, x and y are n element vectors  and  A
24       is an n by 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  - COMPLEX*16      .
46              On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.
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48       AP     - COMPLEX*16       array of DIMENSION at least
49              ( ( n*( n + 1 ) )/2 ).  Before entry with UPLO = 'U' or 'u', the
50              array AP must contain the upper triangular part of the hermitian
51              matrix packed sequentially, column by column, so that  AP(  1  )
52              contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a(
53              2, 2 ) respectively, and so on.  Before entry with UPLO = 'L' or
54              'l',  the array AP must contain the lower triangular part of the
55              hermitian matrix packed sequentially, column by column, so  that
56              AP(  1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1
57              ) and a( 3, 1 ) respectively, and so on.  Note that  the  imagi‐
58              nary  parts  of  the  diagonal  elements need not be set and are
59              assumed to be zero.  Unchanged on exit.
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61       X      - COMPLEX*16       array of dimension at least
62              ( 1 + ( n - 1 )*abs( INCX ) ).  Before  entry,  the  incremented
63              array X must contain the n element vector x.  Unchanged on exit.
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65       INCX   - INTEGER.
66              On  entry,  INCX  specifies the increment for the elements of X.
67              INCX must not be zero.  Unchanged on exit.
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69       BETA   - COMPLEX*16      .
70              On entry, BETA specifies the scalar beta. When BETA is  supplied
71              as zero then Y need not be set on input.  Unchanged on exit.
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73       Y      - COMPLEX*16       array of dimension at least
74              (  1  +  ( n - 1 )*abs( INCY ) ).  Before entry, the incremented
75              array Y must contain the n element vector y. On exit, Y is over‐
76              written by the updated vector y.
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78       INCY   - INTEGER.
79              On  entry,  INCY  specifies the increment for the elements of Y.
80              INCY must not be zero.  Unchanged on exit.
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FURTHER DETAILS

83       Level 2 Blas routine.
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85       -- Written on 22-October-1986.
86          Jack Dongarra, Argonne National Lab.
87          Jeremy Du Croz, Nag Central Office.
88          Sven Hammarling, Nag Central Office.
89          Richard Hanson, Sandia National Labs.
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94BLAS routine                     November 2008                        ZHPMV(1)
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