Code covered by the BSD License

# Chebfun V4

### Chebfun Team (view profile)

30 Apr 2009 (Updated )

Numerical computation with functions instead of numbers.

### Editor's Notes:

This file was selected as MATLAB Central Pick of the Week

guide2tests
function pass = guide2tests
% Perform various tests from chapter 2 of the Chebfun Guide.
% LNT 25 May 2008
splitting on

f = chebfun('log(1+tan(x))',[0 pi/4]);
I = sum(f); Iexact = pi*log(2)/8;
err1 = I-Iexact;
pass(1) = err1<chebfunpref('eps')*10;

f = chebfun('sin(sin(x))',[0 1]);
I = sum(f); Iexact = 0.4306061031206906049;
err2 = I-Iexact;
pass(2) = err2<chebfunpref('eps')*10;

t = chebfun('t',[0,1]);
f = 2*exp(-t.^2)/sqrt(pi);
I = sum(f); Iexact = erf(1);
err3 = I-Iexact;
pass(3) = err3<chebfunpref('eps')*10;

f = chebfun(@(x) abs(besselj(0,x)),[0 20]);
I = sum(f); Iexact = 4.4450316030016;
err4 = I-Iexact;
pass(4) = err4<chebfunpref('eps')*1e3;

% Commented out to save time

% x = chebfun('x');
% f = sech(3*sin(10*x));
% g = sin(9*x); h = min(f,g);
% I = sum(h); Iexact = -0.38155644885025;
% err5 = I-Iexact;
% pass(5) = err5<chebfunpref('eps')*10;

% splitting off
% x = chebfun('x',[0 1]);
% f = sech(10*(x-0.2)).^2 + sech(100*(x-0.4)).^4 + sech(1000*(x-0.6)).^6;
% I = sum(f); Iexact = 0.210802735500549;
% err6 = I-Iexact; pass6 = err6<chebfunpref('eps')*10;

% splitting on
% f = sech(10*(x-0.2)).^2 + sech(100*(x-0.4)).^4 + sech(1000*(x-0.6)).^6;
% I = sum(f);
% err7 = I-Iexact; pass7 = err7<1e2*chebfunpref('eps');