Wed Oct  8 09:08:16 2025

vandermonde_approx_1d_test():
  python version: 3.10.12
  numpy version:  1.26.4
  Test vandermonde_approx_1d().

vandermonde_approx_1d_test01():
  Number of data points =  25

  Data array:
[[  0.          16.        ]
 [  0.04166667  -1.05551323]
 [  0.08333333   2.26104933]
 [  0.125       -1.79797683]
 [  0.16666667  -0.45145857]
 [  0.20833333   9.35015618]
 [  0.25       -10.11534458]
 [  0.29166667  -2.87127836]
 [  0.33333333 -10.9609897 ]
 [  0.375       -0.25866382]
 [  0.41666667   4.30258365]
 [  0.45833333  -8.19077715]
 [  0.5          3.41326062]
 [  0.54166667  -3.87577314]
 [  0.58333333  13.39554242]
 [  0.625        7.61085049]
 [  0.66666667  -1.704088  ]
 [  0.70833333   2.46931865]
 [  0.75        -7.76262782]
 [  0.79166667   7.69894974]
 [  0.83333333  -7.44390686]
 [  0.875       -8.32499608]
 [  0.91666667  -5.86531112]
 [  0.95833333  -5.44825645]
 [  1.          13.37906775]]
  Using polynomial approximant of degree 0

  L2 data interpolation error =  1.5122295212328338

  Normalized length of piecewise linear interpolant =  8.179701523574238
  Normalized length of polynomial approximant       =  1.0
  Graphics saved as "poly_0.png"

vandermonde_approx_1d_test01():
  Number of data points =  25

  Data array:
[[  0.          16.        ]
 [  0.04166667  -1.05551323]
 [  0.08333333   2.26104933]
 [  0.125       -1.79797683]
 [  0.16666667  -0.45145857]
 [  0.20833333   9.35015618]
 [  0.25       -10.11534458]
 [  0.29166667  -2.87127836]
 [  0.33333333 -10.9609897 ]
 [  0.375       -0.25866382]
 [  0.41666667   4.30258365]
 [  0.45833333  -8.19077715]
 [  0.5          3.41326062]
 [  0.54166667  -3.87577314]
 [  0.58333333  13.39554242]
 [  0.625        7.61085049]
 [  0.66666667  -1.704088  ]
 [  0.70833333   2.46931865]
 [  0.75        -7.76262782]
 [  0.79166667   7.69894974]
 [  0.83333333  -7.44390686]
 [  0.875       -8.32499608]
 [  0.91666667  -5.86531112]
 [  0.95833333  -5.44825645]
 [  1.          13.37906775]]
  Using polynomial approximant of degree 1

  L2 data interpolation error =  1.501335862431

  Normalized length of piecewise linear interpolant =  8.179701523574238
  Normalized length of polynomial approximant       =  1.0062339068501431
  Graphics saved as "data.png"
  Graphics saved as "poly_1.png"

vandermonde_approx_1d_test01():
  Number of data points =  25

  Data array:
[[  0.          16.        ]
 [  0.04166667  -1.05551323]
 [  0.08333333   2.26104933]
 [  0.125       -1.79797683]
 [  0.16666667  -0.45145857]
 [  0.20833333   9.35015618]
 [  0.25       -10.11534458]
 [  0.29166667  -2.87127836]
 [  0.33333333 -10.9609897 ]
 [  0.375       -0.25866382]
 [  0.41666667   4.30258365]
 [  0.45833333  -8.19077715]
 [  0.5          3.41326062]
 [  0.54166667  -3.87577314]
 [  0.58333333  13.39554242]
 [  0.625        7.61085049]
 [  0.66666667  -1.704088  ]
 [  0.70833333   2.46931865]
 [  0.75        -7.76262782]
 [  0.79166667   7.69894974]
 [  0.83333333  -7.44390686]
 [  0.875       -8.32499608]
 [  0.91666667  -5.86531112]
 [  0.95833333  -5.44825645]
 [  1.          13.37906775]]
  Using polynomial approximant of degree 2

  L2 data interpolation error =  1.4735744915962923

  Normalized length of piecewise linear interpolant =  8.179701523574238
  Normalized length of polynomial approximant       =  1.0739954897958253
  Graphics saved as "poly_2.png"

vandermonde_approx_1d_test01():
  Number of data points =  25

  Data array:
[[  0.          16.        ]
 [  0.04166667  -1.05551323]
 [  0.08333333   2.26104933]
 [  0.125       -1.79797683]
 [  0.16666667  -0.45145857]
 [  0.20833333   9.35015618]
 [  0.25       -10.11534458]
 [  0.29166667  -2.87127836]
 [  0.33333333 -10.9609897 ]
 [  0.375       -0.25866382]
 [  0.41666667   4.30258365]
 [  0.45833333  -8.19077715]
 [  0.5          3.41326062]
 [  0.54166667  -3.87577314]
 [  0.58333333  13.39554242]
 [  0.625        7.61085049]
 [  0.66666667  -1.704088  ]
 [  0.70833333   2.46931865]
 [  0.75        -7.76262782]
 [  0.79166667   7.69894974]
 [  0.83333333  -7.44390686]
 [  0.875       -8.32499608]
 [  0.91666667  -5.86531112]
 [  0.95833333  -5.44825645]
 [  1.          13.37906775]]
  Using polynomial approximant of degree 3

  L2 data interpolation error =  1.4473827182445052

  Normalized length of piecewise linear interpolant =  8.179701523574238
  Normalized length of polynomial approximant       =  1.1998427372874463
  Graphics saved as "poly_3.png"

vandermonde_approx_1d_test01():
  Number of data points =  25

  Data array:
[[  0.          16.        ]
 [  0.04166667  -1.05551323]
 [  0.08333333   2.26104933]
 [  0.125       -1.79797683]
 [  0.16666667  -0.45145857]
 [  0.20833333   9.35015618]
 [  0.25       -10.11534458]
 [  0.29166667  -2.87127836]
 [  0.33333333 -10.9609897 ]
 [  0.375       -0.25866382]
 [  0.41666667   4.30258365]
 [  0.45833333  -8.19077715]
 [  0.5          3.41326062]
 [  0.54166667  -3.87577314]
 [  0.58333333  13.39554242]
 [  0.625        7.61085049]
 [  0.66666667  -1.704088  ]
 [  0.70833333   2.46931865]
 [  0.75        -7.76262782]
 [  0.79166667   7.69894974]
 [  0.83333333  -7.44390686]
 [  0.875       -8.32499608]
 [  0.91666667  -5.86531112]
 [  0.95833333  -5.44825645]
 [  1.          13.37906775]]
  Using polynomial approximant of degree 4

  L2 data interpolation error =  1.2774929503953896

  Normalized length of piecewise linear interpolant =  8.179701523574238
  Normalized length of polynomial approximant       =  1.9703625718283106
  Graphics saved as "poly_4.png"

vandermonde_approx_1d_test01():
  Number of data points =  25

  Data array:
[[  0.          16.        ]
 [  0.04166667  -1.05551323]
 [  0.08333333   2.26104933]
 [  0.125       -1.79797683]
 [  0.16666667  -0.45145857]
 [  0.20833333   9.35015618]
 [  0.25       -10.11534458]
 [  0.29166667  -2.87127836]
 [  0.33333333 -10.9609897 ]
 [  0.375       -0.25866382]
 [  0.41666667   4.30258365]
 [  0.45833333  -8.19077715]
 [  0.5          3.41326062]
 [  0.54166667  -3.87577314]
 [  0.58333333  13.39554242]
 [  0.625        7.61085049]
 [  0.66666667  -1.704088  ]
 [  0.70833333   2.46931865]
 [  0.75        -7.76262782]
 [  0.79166667   7.69894974]
 [  0.83333333  -7.44390686]
 [  0.875       -8.32499608]
 [  0.91666667  -5.86531112]
 [  0.95833333  -5.44825645]
 [  1.          13.37906775]]
  Using polynomial approximant of degree 5

  L2 data interpolation error =  1.1875859978878671

  Normalized length of piecewise linear interpolant =  8.179701523574238
  Normalized length of polynomial approximant       =  2.2758275540106463
  Graphics saved as "poly_5.png"

vandermonde_approx_1d_test01():
  Number of data points =  25

  Data array:
[[  0.          16.        ]
 [  0.04166667  -1.05551323]
 [  0.08333333   2.26104933]
 [  0.125       -1.79797683]
 [  0.16666667  -0.45145857]
 [  0.20833333   9.35015618]
 [  0.25       -10.11534458]
 [  0.29166667  -2.87127836]
 [  0.33333333 -10.9609897 ]
 [  0.375       -0.25866382]
 [  0.41666667   4.30258365]
 [  0.45833333  -8.19077715]
 [  0.5          3.41326062]
 [  0.54166667  -3.87577314]
 [  0.58333333  13.39554242]
 [  0.625        7.61085049]
 [  0.66666667  -1.704088  ]
 [  0.70833333   2.46931865]
 [  0.75        -7.76262782]
 [  0.79166667   7.69894974]
 [  0.83333333  -7.44390686]
 [  0.875       -8.32499608]
 [  0.91666667  -5.86531112]
 [  0.95833333  -5.44825645]
 [  1.          13.37906775]]
  Using polynomial approximant of degree 9

  L2 data interpolation error =  1.044866193667195

  Normalized length of piecewise linear interpolant =  8.179701523574238
  Normalized length of polynomial approximant       =  3.0012956357036096
  Graphics saved as "poly_9.png"

vandermonde_approx_1d_test01():
  Number of data points =  25

  Data array:
[[  0.          16.        ]
 [  0.04166667  -1.05551323]
 [  0.08333333   2.26104933]
 [  0.125       -1.79797683]
 [  0.16666667  -0.45145857]
 [  0.20833333   9.35015618]
 [  0.25       -10.11534458]
 [  0.29166667  -2.87127836]
 [  0.33333333 -10.9609897 ]
 [  0.375       -0.25866382]
 [  0.41666667   4.30258365]
 [  0.45833333  -8.19077715]
 [  0.5          3.41326062]
 [  0.54166667  -3.87577314]
 [  0.58333333  13.39554242]
 [  0.625        7.61085049]
 [  0.66666667  -1.704088  ]
 [  0.70833333   2.46931865]
 [  0.75        -7.76262782]
 [  0.79166667   7.69894974]
 [  0.83333333  -7.44390686]
 [  0.875       -8.32499608]
 [  0.91666667  -5.86531112]
 [  0.95833333  -5.44825645]
 [  1.          13.37906775]]
  Using polynomial approximant of degree 12

  L2 data interpolation error =  1.0347441286644508

  Normalized length of piecewise linear interpolant =  8.179701523574238
  Normalized length of polynomial approximant       =  3.237385167169268
  Graphics saved as "poly_12.png"

vandermonde_approx_1d_test01():
  Number of data points =  25

  Data array:
[[  0.          16.        ]
 [  0.04166667  -1.05551323]
 [  0.08333333   2.26104933]
 [  0.125       -1.79797683]
 [  0.16666667  -0.45145857]
 [  0.20833333   9.35015618]
 [  0.25       -10.11534458]
 [  0.29166667  -2.87127836]
 [  0.33333333 -10.9609897 ]
 [  0.375       -0.25866382]
 [  0.41666667   4.30258365]
 [  0.45833333  -8.19077715]
 [  0.5          3.41326062]
 [  0.54166667  -3.87577314]
 [  0.58333333  13.39554242]
 [  0.625        7.61085049]
 [  0.66666667  -1.704088  ]
 [  0.70833333   2.46931865]
 [  0.75        -7.76262782]
 [  0.79166667   7.69894974]
 [  0.83333333  -7.44390686]
 [  0.875       -8.32499608]
 [  0.91666667  -5.86531112]
 [  0.95833333  -5.44825645]
 [  1.          13.37906775]]
  Using polynomial approximant of degree 15

  L2 data interpolation error =  0.8433420426574753

  Normalized length of piecewise linear interpolant =  8.179701523574238
  Normalized length of polynomial approximant       =  8.023584187842285
  Graphics saved as "poly_15.png"

vandermonde_approx_1d_test01():
  Number of data points =  25

  Data array:
[[  0.          16.        ]
 [  0.04166667  -1.05551323]
 [  0.08333333   2.26104933]
 [  0.125       -1.79797683]
 [  0.16666667  -0.45145857]
 [  0.20833333   9.35015618]
 [  0.25       -10.11534458]
 [  0.29166667  -2.87127836]
 [  0.33333333 -10.9609897 ]
 [  0.375       -0.25866382]
 [  0.41666667   4.30258365]
 [  0.45833333  -8.19077715]
 [  0.5          3.41326062]
 [  0.54166667  -3.87577314]
 [  0.58333333  13.39554242]
 [  0.625        7.61085049]
 [  0.66666667  -1.704088  ]
 [  0.70833333   2.46931865]
 [  0.75        -7.76262782]
 [  0.79166667   7.69894974]
 [  0.83333333  -7.44390686]
 [  0.875       -8.32499608]
 [  0.91666667  -5.86531112]
 [  0.95833333  -5.44825645]
 [  1.          13.37906775]]
  Using polynomial approximant of degree 18

  L2 data interpolation error =  0.819528575812682

  Normalized length of piecewise linear interpolant =  8.179701523574238
  Normalized length of polynomial approximant       =  16.81301332807605
  Graphics saved as "poly_18.png"

vandermonde_approx_1d_test():
  Normal end of execution.
Wed Oct  8 09:08:17 2025