1ZHPMV(1)                         BLAS routine                         ZHPMV(1)
2
3
4

NAME

6       ZHPMV - the matrix-vector operation   y := alpha*A*x + beta*y,
7

SYNOPSIS

9       SUBROUTINE ZHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
10
11           DOUBLE                                           COMPLEX ALPHA,BETA
12
13           INTEGER                                          INCX,INCY,N
14
15           CHARACTER                                        UPLO
16
17           DOUBLE                                           COMPLEX
18                                                            AP(*),X(*),Y(*)
19

PURPOSE

21       ZHPMV  performs the matrix-vector operation
22
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.
25
26

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:
32
33              UPLO  =  'U' or 'u'   The upper triangular part of A is supplied
34              in AP.
35
36              UPLO = 'L' or 'l'   The lower triangular part of A  is  supplied
37              in AP.
38
39              Unchanged on exit.
40
41       N      - INTEGER.
42              On  entry,  N specifies the order of the matrix A.  N must be at
43              least zero.  Unchanged on exit.
44
45       ALPHA  - COMPLEX*16      .
46              On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.
47
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.
60
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.
64
65       INCX   - INTEGER.
66              On  entry,  INCX  specifies the increment for the elements of X.
67              INCX must not be zero.  Unchanged on exit.
68
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.
72
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.
77
78       INCY   - INTEGER.
79              On  entry,  INCY  specifies the increment for the elements of Y.
80              INCY must not be zero.  Unchanged on exit.
81
82              Level 2 Blas routine.
83
84              -- Written on 22-October-1986.  Jack Dongarra, Argonne  National
85              Lab.   Jeremy Du Croz, Nag Central Office.  Sven Hammarling, Nag
86              Central Office.  Richard Hanson, Sandia National Labs.
87
88
89
90BLAS routine                     November 2006                        ZHPMV(1)