function sheet3_public

%DRIVER_7p1
DRIVER_7p6

return

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function DRIVER_7p1

f = chebfun('sin(100*x)./(1+x.^2)');
fprintf(1,'Total varation of f = %0.8f\n',norm(diff(f),1))

plot(f)
grid on
keyboard

return

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function DRIVER_7p6

flag_option = 1;

s       = linspace(-1,1,10);
f       = @(x) exp(x);
%f       = @(x) sin(23*x);
fspline = @(x) spline(s,f(s),x);
p       = chebfun(fspline); 

figure(1)
hold off
tt = linspace(-1,1,1000);
plot(tt,f(tt),'b',...
     tt,fspline(tt),'r',...
     s,f(s),'kx',...
     'LineWidth',2)
legend('f','spline')

figure(2)
hold off
aa = chebcoeffs(p);
nn = 1:length(aa);
loglog(nn,abs(aa),'b.',...
       nn,nn.^(-4),'r--',...
       'LineWidth',2,...
       'MarkerSize',20)
xlabel('n')
legend('|a_n|','n^{-4}')
title('Decay of Chebyshev coefficients for a spline.')

keyboard

return

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