polyinterp <- function ( x, y )

#*****************************************************************************80
#
## polyinterp carries out Vandermonde polynomial interpolation.
#
#  Licensing:
#
#    Copyright 2016 James P. Howard, II
#
#    The computer code and data files on this web page are distributed under
#    https://opensource.org/licenses/BSD-2-Clause, the BSD-2-Clause license.
#
#  Modified:
#
#    21 February 2020
#
#  Author:
#
#    Original R code by James Howard;
#    Modifications by John Burkardt.
#
#  Reference:
#
#    James Howard,
#    Computational Methods for Numerical Analysis with R,
#    CRC Press, 2017,
#    ISBN13: 978-1-4987-2363-3.
#
{
  if ( length ( x ) != length ( y ) )
  {
    stop ( "Length of x and y vectors must be the same!" )
  }

  n <- length ( x ) - 1
  vandermonde <- rep ( 1, length ( x ) )
  for ( i in 1 : n )
  {
    xi <- x^i
    vandermonde <- cbind ( vandermonde, xi )
  }
  beta <- solve ( vandermonde, y )
  names(beta) <- NULL

  return ( beta )
}