% fun_integral_norm.m — Integrals, means and norms of a surfacefun.
%
% These reductions integrate over the surface using the on-surface
% measure. No plot here — just printed quantities.

mip load --install flatironinstitute/flatironinstitute/surfacefun

p = 16;
nref = 2;
dom = surfacemesh.sphere(p + 1, nref);

f = surfacefun(@(x, y, z) cos(6*x) .* y + exp(z), dom);

fprintf('integral(f) = %.6f\n', integral(f));     % definite integral over the surface
fprintf('mean(f)     = %.6f\n', mean(f));          % integral / surface area
fprintf('L2 norm     = %.6f\n', norm(f));          % sqrt(integral of f^2)
fprintf('Linf norm   = %.6f\n', norm(f, inf));     % max |f|