Wed Oct  8 08:58:27 2025
Wed Oct  8 08:58:27 2025

test_interp_fun_test()
  python version: 3.10.12
  numpy version:  1.26.4
  Test test_interp_fun().

test_interp_fun_test01():
  p00_prob_num() returns the number of problems.
  p00_title() returns the problem title.
  p00_limit() returns the problem limits.

  Number of problems =  5

  Problem  1
Runge example, f(x) = 1 / ( x * x + 1 ), [-5,5]
  Range is [ -5.0 , 5.0 ]

  Problem  2
Bernstein example, f(x) = abs ( x ), [-1,1]
  Range is [ -1.0 , 1.0 ]

  Problem  3
Step function, f jumps from 0 to 1 at 0.
  Range is [ -1.0 , 1.0 ]

  Problem  4
The Doppler function, highly oscillatory near X = 0.
  Range is [ 0.0 , 1.0 ]

  Problem  5
Rabbit ears, f(x) = max(sin(x)+sin(x^2),1-abs(x-5)/5), [0,10].
  Range is [ 0.0 , 10.0 ]

test_interp_fun_test02():
  p00_story() prints the problem "story".

  The story for problem  1

  This is a famous example, due to Runge.  If equally spaced
  abscissas are used, the sequence of interpolating polynomials Pn(X)
  diverges, in the sense that the max norm of the difference
  between Pn(X) and F(X) becomes arbitrarily large as N increases.

  The story for problem  2

  This example is due to Bernstein.
  If equally spaced abscissas are used, the sequence of interpolating
  polynomials Pn(X) only converges to F(X) at -1, 0, and 1.

  The story for problem  3

  The step function is discontinuous.
  Attempts to approximate this function by high degree polynomials
  will rapidly diverge.

  The story for problem  4

  The Doppler function is continuous, but highly oscillatory
  near the value X = 0.

  The story for problem  5

  This example is very difficult to interpolate.
  It is essentially defined as a piecewise function,
  alternating between a straight line and a sinusoidal curve.

test_interp_fun_test03():
  Equally spaced polynomial interpolation.
  Evaluate the function at N equally spaced points.
  Determine the N-1 degre polynomial interpolant.
  Estimate the maximum difference between the function
  and the interpolant.

  Problem 1
  Runge example, f(x) = 1 / ( x * x + 1 ), [-5,5]

     N   Max |Error|

     1        0.961538
     5        0.438134
     9         1.04517
    13         3.60527
    17         14.0515
    21         58.2781

  Problem 2
  Bernstein example, f(x) = abs ( x ), [-1,1]

     N   Max |Error|

     1               1
     5          0.1472
     9        0.315753
    13         1.54906
    17         10.8772
    21         92.6992

  Problem 3
  Step function, f jumps from 0 to 1 at 0.

     N   Max |Error|

     1               1
     5        0.975672
     9          1.3314
    13         9.48697
    17         88.0671
    21         933.226

  Problem 4
  The Doppler function, highly oscillatory near X = 0.

     N   Max |Error|

     1          0.7614
     5        0.784056
     9        0.599198
    13         16.0925
    17         34.2374
    21         476.344

  Problem 5
  Rabbit ears, f(x) = max(sin(x)+sin(x^2),1-abs(x-5)/5), [0,10].

     N   Max |Error|

     1               1
     5          1.7313
     9         2.07062
    13         5.67344
    17         44.8345
    21         194.825

test_interp_fun_test():
  Normal end of execution.
Wed Oct  8 08:58:27 2025