function [ n_data, n, k, x, b ] = bernstein_poly_01_values ( n_data )

%*****************************************************************************80
%
%% BERNSTEIN_POLY_01_VALUES returns some values of the Bernstein polynomials.
%
%  Discussion:
%
%    The Bernstein polynomials are assumed to be based on [0,1].
%
%    The formula for the Bernstein polynomials is
%
%      B(N,I)(X) = [N!/(I!*(N-I)!)] * (1-X)^(N-I) * X^I
%
%    In Mathematica, the function can be evaluated by:
%
%      Binomial[n,i] * (1-x)^(n-i) * x^i
%
%  First values:
%
%    B(0,0)(X) = 1
%
%    B(1,0)(X) =      1-X
%    B(1,1)(X) =               X
%
%    B(2,0)(X) =     (1-X)^2
%    B(2,1)(X) = 2 * (1-X)   * X
%    B(2,2)(X) =               X^2
%
%    B(3,0)(X) =     (1-X)^3
%    B(3,1)(X) = 3 * (1-X)^2 * X
%    B(3,2)(X) = 3 * (1-X)   * X^2
%    B(3,3)(X) =               X^3
%
%    B(4,0)(X) =     (1-X)^4
%    B(4,1)(X) = 4 * (1-X)^3 * X
%    B(4,2)(X) = 6 * (1-X)^2 * X^2
%    B(4,3)(X) = 4 * (1-X)   * X^3
%    B(4,4)(X) =               X^4
%
%  Special values:
%
%    B(N,I)(X) has a unique maximum value at X = I/N.
%
%    B(N,I)(X) has an I-fold zero at 0 and and N-I fold zero at 1.
%
%    B(N,I)(1/2) = C(N,K) / 2^N
%
%    For a fixed X and N, the polynomials add up to 1:
%
%      Sum ( 0 <= I <= N ) B(N,I)(X) = 1
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    15 September 2004
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Stephen Wolfram,
%    The Mathematica Book,
%    Fourth Edition,
%    Wolfram Media / Cambridge University Press, 1999.
%
%  Parameters:
%
%    Input/output, integer N_DATA.  The user sets N_DATA to 0 before the
%    first call.  On each call, the routine increments N_DATA by 1, and
%    returns the corresponding data; when there is no more data, the
%    output value of N_DATA will be 0 again.
%
%    Output, integer N, the degree of the polynomial.
%
%    Output, integer K, the index of the polynomial.
%
%    Output, real X, the argument of the polynomial.
%
%    Output, real B, the value of the polynomial B(N,K)(X).
%
  n_max = 15;

  b_vec = [ ...
     0.1000000000000000E+01, ...
     0.7500000000000000E+00, ...
     0.2500000000000000E+00, ...
     0.5625000000000000E+00, ...
     0.3750000000000000E+00, ...
     0.6250000000000000E-01, ...
     0.4218750000000000E+00, ...
     0.4218750000000000E+00, ...
     0.1406250000000000E+00, ...
     0.1562500000000000E-01, ...
     0.3164062500000000E+00, ...
     0.4218750000000000E+00, ...
     0.2109375000000000E+00, ...
     0.4687500000000000E-01, ...
     0.3906250000000000E-02 ];

  k_vec = [ ...
    0, ...
    0, 1, ...
    0, 1, 2, ...
    0, 1, 2, 3, ...
    0, 1, 2, 3, 4 ];

  n_vec = [ ...
    0, ...
    1, 1, ...
    2, 2, 2, ...
    3, 3, 3, 3, ...
    4, 4, 4, 4, 4 ];

  x_vec = [ ...
     0.25E+00, ...
     0.25E+00, ...
     0.25E+00, ...
     0.25E+00, ...
     0.25E+00, ...
     0.25E+00, ...
     0.25E+00, ...
     0.25E+00, ...
     0.25E+00, ...
     0.25E+00, ...
     0.25E+00, ...
     0.25E+00, ...
     0.25E+00, ...
     0.25E+00, ...
     0.25E+00 ];

  if ( n_data < 0 )
    n_data = 0;
  end

  n_data = n_data + 1;

  if ( n_max < n_data )
    n_data = 0;
    n = 0;
    k = 0;
    x = 0.0;
    b = 0.0;
  else
    n = n_vec(n_data);
    k = k_vec(n_data);
    x = x_vec(n_data);
    b = b_vec(n_data);
  end

  return
end

johannesgerer
github-repos/MATLAB/johannesgerer-jburkardt-m/jburkardt-m-1726deb4a34dd08a49c26359d44ef47253f006c1/polpak/bernstein_poly_01_values.m
jburkardt-m
github-repos/MATLAB/johannesgerer-jburkardt-m
1726deb4a34dd08a49c26359d44ef47253f006c1