1ZSPMV(1)            LAPACK auxiliary routine (version 3.1)            ZSPMV(1)
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NAME

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

9       SUBROUTINE ZSPMV( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY )
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11           CHARACTER     UPLO
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13           INTEGER       INCX, INCY, N
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15           COMPLEX*16    ALPHA, BETA
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17           COMPLEX*16    AP( * ), X( * ), Y( * )
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PURPOSE

20       ZSPMV  performs the matrix-vector operation
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22       where  alpha  and beta are scalars, x and y are n element vectors and A
23       is an n by n symmetric matrix, supplied in packed form.
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ARGUMENTS

27       UPLO     (input) 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
30                follows:
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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        (input) 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    (input) COMPLEX*16
45                On  entry,  ALPHA  specifies  the  scalar alpha.  Unchanged on
46                exit.
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48       AP       (input) COMPLEX*16 array, dimension at least
49                ( ( N*( N + 1 ) )/2 ).  Before entry, with UPLO = 'U' or  'u',
50                the  array  AP  must  contain the upper triangular part of the
51                symmetric matrix packed sequentially,  column  by  column,  so
52                that  AP(  1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain
53                a( 1, 2 ) and a( 2, 2  )  respectively,  and  so  on.   Before
54                entry,  with  UPLO = 'L' or 'l', the array AP must contain the
55                lower triangular part of the symmetric matrix  packed  sequen‐
56                tially,  column by column, so that AP( 1 ) contains a( 1, 1 ),
57                AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3,  1  )  respec‐
58                tively, and so on.  Unchanged on exit.
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60       X        (input) COMPLEX*16 array, dimension at least
61                (  1 + ( N - 1 )*abs( INCX ) ).  Before entry, the incremented
62                array X must contain the N- element vector  x.   Unchanged  on
63                exit.
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65       INCX     (input) 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     (input) COMPLEX*16
70                On entry, BETA specifies the scalar beta. When  BETA  is  sup‐
71                plied  as  zero then Y need not be set on input.  Unchanged on
72                exit.
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74       Y        (input/output) COMPLEX*16 array, dimension at least
75                ( 1 + ( N - 1 )*abs( INCY ) ).  Before entry, the  incremented
76                array  Y  must  contain  the n element vector y. On exit, Y is
77                overwritten by the updated vector y.
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79       INCY     (input) INTEGER
80                On entry, INCY specifies the increment for the elements of  Y.
81                INCY must not be zero.  Unchanged on exit.
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85 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                        ZSPMV(1)