1ZSPMV(1)            LAPACK auxiliary routine (version 3.2)            ZSPMV(1)
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NAME

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

25       UPLO     (input) CHARACTER*1
26                On entry, UPLO specifies whether the upper or lower triangular
27                part of the matrix A is supplied in the  packed  array  AP  as
28                follows: UPLO = 'U' or 'u'   The upper triangular part of A is
29                supplied in AP.  UPLO = 'L' or 'l'   The lower triangular part
30                of A is supplied in AP.  Unchanged on exit.
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32       N        (input) INTEGER
33                On entry, N specifies the order of the matrix A.  N must be at
34                least zero.  Unchanged on exit.
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36       ALPHA    (input) COMPLEX*16
37                On entry, ALPHA specifies  the  scalar  alpha.   Unchanged  on
38                exit.
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40       AP       (input) COMPLEX*16 array, dimension at least
41                (  ( N*( N + 1 ) )/2 ).  Before entry, with UPLO = 'U' or 'u',
42                the array AP must contain the upper  triangular  part  of  the
43                symmetric  matrix  packed  sequentially,  column by column, so
44                that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3  )  contain
45                a(  1,  2  )  and  a(  2, 2 ) respectively, and so on.  Before
46                entry, with UPLO = 'L' or 'l', the array AP must  contain  the
47                lower  triangular  part of the symmetric matrix packed sequen‐
48                tially, column by column, so that AP( 1 ) contains a( 1, 1  ),
49                AP(  2  )  and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respec‐
50                tively, and so on.  Unchanged on exit.
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52       X        (input) COMPLEX*16 array, dimension at least
53                ( 1 + ( N - 1 )*abs( INCX ) ).  Before entry, the  incremented
54                array  X  must  contain the N- element vector x.  Unchanged on
55                exit.
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57       INCX     (input) INTEGER
58                On entry, INCX specifies the increment for the elements of  X.
59                INCX must not be zero.  Unchanged on exit.
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61       BETA     (input) COMPLEX*16
62                On  entry,  BETA  specifies the scalar beta. When BETA is sup‐
63                plied as zero then Y need not be set on input.   Unchanged  on
64                exit.
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66       Y        (input/output) COMPLEX*16 array, dimension at least
67                (  1 + ( N - 1 )*abs( INCY ) ).  Before entry, the incremented
68                array Y must contain the n element vector y.  On  exit,  Y  is
69                overwritten by the updated vector y.
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71       INCY     (input) INTEGER
72                On  entry, INCY specifies the increment for the elements of Y.
73                INCY must not be zero.  Unchanged on exit.
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77 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                        ZSPMV(1)
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