antiderivcheb.m

function ps = antiderivcheb(pa,qs,ab)
%ANTIDERIVCHEB   Antiderivative on a Chebyshev grid.
%
%   PS = ANTIDERIVCHEB(PA,QS,[A B]) computes the antiderivative P of a
%   polynomial Q with initial value P(A) = PA.
%
%   Inputs:
%
%     PA: initial value for the antiderivative
%
%     QS: sample of the integrand Q on a Chebyshev grid of degree M over
%     [A,B]
%
%     AB = [A B]: interval endpoints
%
%   Outputs:
%
%     PS: sample of the antiderivative on the Chebyshev grid of degree M+1
%     over [A,B]
%
%   If Q is a polynomial of degree at most M, then the antiderivative is
%   exact, up to roundoff error.
%
%   Example:
%
%     g = @(x) cos(x); a = 0; b = 4*pi;
%     fa = 5;
%     m = 30;
%     qs = samplecheb(g,[a b],m);
%     ps = antiderivcheb(fa,qs,[a b]);
%     p = interpcheb(ps,[a b]);
%     f = @(x) 5+sin(x);
%     newfig;
%     plotfun(f,[a b]);
%     plotfun(p,[a b]);
%
%   Copyright 2019 Brian Sutton

narginchk(3,3);
natecheck('antiderivcheb',pa,qs,ab);
a = ab(1);
b = ab(2);
m = length(qs)-1;
K = (b-a)/2*intmatrixcheb(m);
ps = pa*ones(m+2,1)+K*qs;