ue5

uebungen/factorio/funcApprox/P.m

@@ -1,9 +1,8 @@
 function [ p ] = P( b, xk, x )
-    b = b(1, :);
-    n = length(b);
+    n = size(b, 2);
     p = b(1, n);
     for k = (n-1) : -1 : 1
-        p = b(k) + p * (x - xk(k));
+        p = b(1, k) + p * (x - xk(k));
     end
 end
 

uebungen/factorio/funcApprox/findBestKnot.m

@@ -3,21 +3,58 @@
 format compact;
 format longg;
 
-calcKnot1 = 1847.7;
-calcKnot2 = 16350;
+%% calculate initial nodes
+% 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);
 
-KnotInterval = linspace(1, (calcKnot1+calcKnot2)/2);
-best = 22.8643526713838;
-window = .001;
-KnotInterval = linspace(best*(1-window), best*(1+window));
+n = 10; % amount of nodes
+
+% tschebyschow nodes:
+k = linspace(1, n, n)';
+% according to: https://en.wikipedia.org/wiki/Chebyshev_nodes#Definition
+x_i = sort(  (limit_start + limit_end)/2 + (limit_end -limit_start)/2 * cos( (2*k -1)/(2*n)*pi )  )
+
+minErr = 1e30;
+minTry = 9;
+maxTry = 10;
+
+%%
+for repeats = 1:1
+    for nodeNr = 1:n
+        window = 1;
+        nodeMinErr = 1e30;
+        for i=1:maxTry
+            window = window * .9;
+            KnotInterval = linspace(x_i(nodeNr)*(1-window), x_i(nodeNr)*(1+window), 10);
+
+            err = zeros(length(KnotInterval), 1);
+            for j=1:length(KnotInterval)
+                x_i(nodeNr) = KnotInterval(j);
+                err(j) = logbApproxNKnot(x_i, 1:n);
+            end
+            close;
+            plot(KnotInterval, err, '.r-');
+
+            [m,mi] = min(err);
+            fprintf('node%i, try%i, m%f, i%i\n', nodeNr, i, m, mi);
+
+            x_i(nodeNr) = KnotInterval(mi);
+            if minErr     > m; minErr     = m; end
+            if nodeMinErr > m; nodeMinErr = m; end
+            if nodeMinErr == minErr && i >= minTry
+                break;
+            end
+        end % i
+        fprintf('\n');
+    end % nodeNr
+    x_i
+%    pause
+end % repeats
 
-for i=1:length(KnotInterval)
-    err(i) = logbApproxNKnot(KnotInterval(i), 1);
-end
 
-plot(KnotInterval, err, '.r-');
 
-[m,i] =min(err)
 
-KnotInterval(i)
 

uebungen/factorio/funcApprox/logbApprox.m

@@ -16,7 +16,6 @@
 tk = cos( (2*k -1)/(2*n)*pi )
 % according to: https://en.wikipedia.org/wiki/Chebyshev_nodes#Definition
 x_i = sort(  (limit_start + limit_end)/2 + (limit_end -limit_start)/2 * cos( (2*k -1)/(2*n)*pi )  )
-x_i(1)=22.8643526713838;
 f_i = logb(x_i);
 
 %% berechne koeffizienten