1DSPMV(1)                         BLAS routine                         DSPMV(1)
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NAME

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

9       SUBROUTINE DSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
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11           DOUBLE                                           PRECISION
12                                                            ALPHA,BETA
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14           INTEGER                                          INCX,INCY,N
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16           CHARACTER                                        UPLO
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18           DOUBLE                                           PRECISION
19                                                            AP(*),X(*),Y(*)
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PURPOSE

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

29       UPLO   - CHARACTER*1.
30              On entry, UPLO specifies whether the upper or  lower  triangular
31              part  of the matrix A is supplied in the packed array AP as fol‐
32              lows:
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34              UPLO = 'U' or 'u'   The upper triangular part of A  is  supplied
35              in AP.
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37              UPLO  =  'L' or 'l'   The lower triangular part of A is supplied
38              in AP.
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40              Unchanged on exit.
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42       N      - INTEGER.
43              On entry, N specifies the order of the matrix A.  N must  be  at
44              least zero.  Unchanged on exit.
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46       ALPHA  - DOUBLE PRECISION.
47              On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.
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49       AP     - DOUBLE PRECISION array of DIMENSION at least
50              ( ( n*( n + 1 ) )/2 ).  Before entry with UPLO = 'U' or 'u', the
51              array AP must contain the upper triangular part of the symmetric
52              matrix  packed  sequentially,  column by column, so that AP( 1 )
53              contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a(
54              2, 2 ) respectively, and so on.  Before entry with UPLO = 'L' or
55              'l', the array AP must contain the lower triangular part of  the
56              symmetric  matrix packed sequentially, column by column, so that
57              AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2,  1
58              ) and a( 3, 1 ) respectively, and so on.  Unchanged on exit.
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60       X      - DOUBLE PRECISION array of 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 exit.
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64       INCX   - INTEGER.
65              On entry, INCX specifies the increment for the  elements  of  X.
66              INCX must not be zero.  Unchanged on exit.
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68       BETA   - DOUBLE PRECISION.
69              On  entry, BETA specifies the scalar beta. When BETA is supplied
70              as zero then Y need not be set on input.  Unchanged on exit.
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72       Y      - DOUBLE PRECISION array of dimension at least
73              ( 1 + ( n - 1 )*abs( INCY ) ).  Before  entry,  the  incremented
74              array Y must contain the n element vector y. On exit, Y is over‐
75              written by the updated vector y.
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77       INCY   - INTEGER.
78              On entry, INCY specifies the increment for the  elements  of  Y.
79              INCY must not be zero.  Unchanged on exit.
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81              Level 2 Blas routine.
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83              --  Written on 22-October-1986.  Jack Dongarra, Argonne National
84              Lab.  Jeremy Du Croz, Nag Central Office.  Sven Hammarling,  Nag
85              Central Office.  Richard Hanson, Sandia National Labs.
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89BLAS routine                     November 2006                        DSPMV(1)