#! /usr/bin/env python
#
def vandermonde_matrix_1d ( n, x ):

#*****************************************************************************80
#
## VANDERMONDE_MATRIX_1D computes a Vandermonde 1D interpolation matrix.
#
#  Discussion:
#
#    We assume the interpolant has the form
#
#      p(x) = c1 + c2 * x + c3 * x^2 + ... + cn * x^(n-1).
#
#    We have n data values (x(i),y(i)) which must be interpolated:
#
#      p(x(i)) = c1 + c2 * x(i) + c3 * x(i)^2 + ... + cn * x(i)^(n-1) = y(i)
#
#    This can be cast as an NxN linear system for the polynomial
#    coefficients:
#
#      [ 1 x1 x1^2 ... x1^(n-1) ] [  c1 ] = [  y1 ]
#      [ 1 x2 x2^2 ... x2^(n-1) ] [  c2 ] = [  y2 ]
#      [ ...................... ] [ ... ] = [ ... ]
#      [ 1 xn xn^2 ... xn^(n-1) ] [  cn ] = [  yn ]
#
#    and if the x values are distinct, the matrix A is theoretically
#    invertible (though in fact, generally badly conditioned).
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    03 July 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer N, the number of data points.
#
#    Input, real X(N,1), the data values.
#
#    Output, real A(N,N), the Vandermonde matrix for X.
#
  import numpy as np

  a = np.zeros ( [ n, n ] )

  for i in range ( 0, n ):
    a[i,0] = 1.0

  for j in range ( 1, n ):
    for i in range ( 0, n ):
      a[i,j] = a[i,j-1] * x[i]

  return a

def vandermonde_matrix_1d_test ( ):

#*****************************************************************************80
#
## VANDERMONDE_MATRIX_1D_TEST tests VANDERMONDE_MATRIX_1D.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    04 July 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform
  from r8mat_print import r8mat_print

  print ( '' )
  print ( 'VANDERMONDE_MATRIX_1D_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  VANDERMONDE_MATRIX_1D sets the Vandermonde matrix for 1D interpolation.' )

  nd = 4
  xd = np.array ( [ -1.0, 2.0, 3.0, 5.0 ] )

  ad = vandermonde_matrix_1d ( nd, xd )

  r8mat_print ( nd, nd, ad, '  Vandermonde matrix:' )
#
#  Terminate.
#
  print ( '' )
  print ( 'VANDERMONDE_MATRIX_1D_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  vandermonde_matrix_1d_test ( )
  timestamp ( )