demo_spline.m

Interpolation routines in matlab

%
% Cubic Spline Interpolation
%

clear;
%
%  interpolation of Runge's function (1+x^2)^(-1)
%  on the interval [-5, 5]
%

clear;


% Interval on which Runge's function is to be approximated
A = -5;
B =  5;


% evaluate Runge's function at z
m = 1000;
h = (B-A)/(m-1);
z = (A:h:B);
r = 1 ./(1+z.^2);

plot(z, r, 'k'); hold on  % plot Runge's function

n = input(' number of interpolation points  n = ')

%   compute equidistant interpolation points
%   and function values to be interpolated

    h = (B-A)/(n-1);
    x = (A:h:B);
    f = 1 ./ (1+x.^2);

    fpa = -2*A/(1+A^2)^2;  % derivative of Runge's function at -5
    fpb = -2*B/(1+B^2)^2;  % derivative of Runge's function at +5

 



% Compute free cubic spline

[a, b, c, d, iflag] = cfspline( x, f );

s = csplineeval( x, a, b, c, d, z );

plot(z, s, 'r:'); hold on   % plot free cubic spline



% Compute clamped cubic spline

[a, b, c, d, iflag] = ccspline( x, f, fpa, fpb );

s = csplineeval( x, a, b, c, d, z );
plot(z, s, 'g--'); hold off   % plot clamped cubic spline
legend('Runge''s fctn.', 'free cubic spline', 'clamped cubic spline')