Data-Helper/inner_prod_rbf.m at master · Jobenland/Data-Helper · GitHub

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function out_IP = inner_prod_rbf(freq_n, freq_m, epsilon)

a = epsilon*log(freq_n/freq_m);
out_IP = -epsilon*(-1+a^2)*exp(-(a^2/2))*sqrt(pi/2);

% % begin integrate test:
% y_n = -log(freq_n);
% y_m = -log(freq_m);
%
% switch rbf_type
%     case 'gaussian'
%         rbf_n = @(y) exp(-(epsilon*(y-y_n)).^2);
%         rbf_m = @(y) exp(-(epsilon*(y-y_m)).^2);
%
%     case 'C0_matern'
%         rbf_n = @(y)  exp(-abs(epsilon*(y-y_n)));
%         rbf_m = @(y)  exp(-abs(epsilon*(y-y_m)));
%
%     case 'C2_matern'
%         rbf_n = @(y)  exp(-abs(epsilon*(y-y_n))).*(1+abs(epsilon*(y-y_n)));
%         rbf_m = @(y)  exp(-abs(epsilon*(y-y_m))).*(1+abs(epsilon*(y-y_m)));
%
%     case 'C4_matern'
%         rbf_n = @(y)  exp(-abs(epsilon*(y-y_n))).*(3+3*abs(epsilon*(y-y_n))+abs(epsilon*(y-y_n)).^2);
%         rbf_m = @(y)  exp(-abs(epsilon*(y-y_m))).*(3+3*abs(epsilon*(y-y_m))+abs(epsilon*(y-y_m)).^2);
%
%     case 'C6_matern'
%         rbf_n = @(y)  exp(-abs(epsilon*(y-y_n))).*(15+15*abs(epsilon*(y-y_n))+6*abs(epsilon*(y-y_n)).^2+abs(epsilon*(y-y_n)).^3);
%         rbf_m = @(y)  exp(-abs(epsilon*(y-y_m))).*(15+15*abs(epsilon*(y-y_m))+6*abs(epsilon*(y-y_m)).^2+abs(epsilon*(y-y_m)).^3);
%
%     case 'inverse_quadratic'
%         rbf_n = @(y) 1./(1+(epsilon*(y-y_n)).^2);
%         rbf_m = @(y) 1./(1+(epsilon*(y-y_m)).^2);
%
%     case 'inverse_quadric'
%         rbf_n = @(y) 1./sqrt(1+(epsilon*(y-y_n)).^2);
%         rbf_m = @(y) 1./sqrt(1+(epsilon*(y-y_m)).^2);
%
%     case 'cauchy'
%         rbf_n = @(y) 1./(1+abs(epsilon*(y-y_n)));
%         rbf_m = @(y) 1./(1+abs(epsilon*(y-y_m)));
%
%     otherwise
%         warning('Unexpected RBF input');
%
% end
% % end of switch
%
% % compute derivative
% delta = 1E-8;
% sqr_drbf_dy = @(y) 1/(2*delta).*(rbf_n(y+delta)-rbf_n(y-delta)).*1/(2*delta).*(rbf_m(y+delta)-rbf_m(y-delta));
% out_IP2 = integral(@(y) sqr_drbf_dy(y),-Inf,Inf);
%
% fprintf('absolute error = %e \n', abs(out_IP- out_IP2));
% % end test


end