foo tschebyschow

uebungen/factorio/funcApprox/P.m

@@ -0,0 +1,9 @@
+function [ p ] = P( b, xk, x )
+    b = b(1, :);
+    n = length(b);
+    p = b(1, n);
+    for k = (n-1) : -1 : 1
+        p = b(k) + p * (x - xk(k));
+    end
+end
+

uebungen/factorio/funcApprox/foo.m

@@ -0,0 +1,81 @@
+clear all;
+close all;
+format compact;
+format shortg;
+
+% intervall in which to approximate
+limit_start = 1;
+limit_end = 3e5;
+base = (limit_end)^(1/100); % of the log, meaning logb(limit_end) := 100 
+logb = @(x) log(x)/log(base);
+
+n = 10; % amount of nodes
+
+% tschebyschow nodes:
+k = linspace(1, n, n)';
+x_i = sort(  (limit_start + limit_end)/2 + (limit_end -limit_start)/2 * cos( (2*k -1)/(2*n)*pi )  );
+f_i = logb(x_i);
+
+%% berechne koeffizienten
+
+%x_i = [1,2,3,4];
+%f_i = [1,2,7,9];
+
+f = zeros(length(f_i));
+f(:,1) = f_i;
+for s = 2:length(f_i)
+    for z = 1:(length(f_i)-s+1)
+%        fprintf('\nz%d, s%d ', z, s);
+        f(z,s) = (f(z+1,s-1) - f(z,s-1) ) / ( x_i(z+s-1) - x_i(z) );
+%        x_i(z)
+%        x_i(z+s-1)
+%        x_i(z+s-1) - x_i(z)
+    end
+%    fprintf('\n');
+end
+
+%% Plot P and points
+
+subplot(2,1,1);
+plot(x_i, f_i, 'ob', 'HandleVisibility', 'off');
+hold on;
+xP = logspace(log10(1),log10(limit_end), 1e4);
+yP = zeros(length(xP),1);
+for fehlerIndex=1:length(xP)
+    yP(fehlerIndex) = P(f, x_i, xP(fehlerIndex));
+end
+plot(xP, yP, 'b-', 'DisplayName', 'P(f)(x)');
+hold on;
+%f_interp = interp1(x_i, f_i, xP)';
+%plot(xP, f_interp, '.r-');
+
+%%original function
+funcX = logspace(log10(min(xP)), log10(max(xP)), length(xP));
+funcY = logb(funcX)';
+plot(funcX, funcY, 'g-', 'DisplayName', 'f(x) = logb');
+
+legend('Location','SouthEast');
+xlabel('x');
+ylabel('y');
+
+
+%% plot error
+
+subplot(2,1,2);
+err = abs(funcY - yP);
+plot(xP, err, '.r-');
+xlabel('x');
+ylabel('fehler');
+legend('|f-P(f)| = error');
+
+[max_fehler, fehlerIndex] = max(err)
+worstApproxX = xP(fehlerIndex)
+
+
+
+
+
+
+
+
+