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--- courses:a4b33opt:cviceni3 [2009/10/06 19:16]
marz
+++ courses:a4b33opt:cviceni3 [2025/01/03 18:28] (aktuální)
@@ Řádek 1: / Řádek 1: @@
 ===== Cvičení 3 =====
-Tak už má někdo výsledek? Mně to vyšlo: 0.991 jak pro lambdu, tak pro epsilon. Jenom teď nevím, jak z toho nějak vykreslit graf jako funkci těch jednotlivých mezi-výpočtů. Jenom jsem tam narval body, ale víc nevím.
+Tak už má někdo výsledek? Mně to vyšlo pro lambdu i epsilon: 0.1000. Nějak se mi i podařilo vykreslit ten graf. (Třetí pokus :) )
-{{:courses:a4b33opt:opt3_funkcet.png|}}
+.100 mi taky vyšlo (a zimmermann neprotestoval) - mickapa1
---- //[[zacham3@fel.cvut.cz|Martin Zachar]] 2009/10/06 19:06//
+{{:courses:a4b33opt:funkcet3.png|}}
+Má to někdo podobně? Nebo i úplně jinak? --- //[[[email protected]|Martin Zachar]] 2009/10/06 19:06//
-=== Diskuze ===
+{{:courses:a4b33opt:opt21.jpg|}}
+ --- //mickapa1, ale nema to smysl porovnavat, zalezi asi i dost na inicializacni mnozine :-)//
+Ano, lambda a epsilon mi vyšly stejně. Ta lambda na 0 na začátku není špatný nápad ;)  --- //[[[email protected]|Roman Polášek]] 2009/10/07 12:04//
+=== Uloha 1 ===
+Vcetne animace, jak algoritmus funguje, snad to nekterym pomuze v pochopeni.  --- //[[[email protected]|Marek Sacha]] 2009/10/08 23:06//
+<code matlab>
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Author: Marek Sacha <[email protected]> %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+clear
+clc
+close all
+load data1.mat
+% Initialize random set of starting active edges
+% ix = vector of potential starting x-coordinates
+ix = x(1);
+% iy = vector of potential starting x-coordinates
+iy = y(1);
+% Initialize the point of maximum divergence (initial set contains only one point)
+ixm = x(1);
+iym = y(1);
+% Initialize at, bt, lt
+at = 0;
+bt = 0;
+lt = 0;
+% Initialize totlerance
+e = 0.0004;
+% Initialize distance
+dist = abs(at*ixm+bt-iym);
+[ xh xw ] = size(x);
+% Begin loop
+while dist - lt > e
+    test = dist - lt;
+    % Get height of reduced vector x = height of reduced vector y, to be able
+    % to constuct inequalities matrix for reduced problem
+    [ ixh ixw ] = size(ix);
+    % Construct inequalities matrix for reduced problem
+    %       | ix   1  -1 |
+    % A =   |-ix  -1  -1 |
+    %
+    A = [ ix ones(ixh,1) -1*ones(ixh,1); -1*ix -1*ones(ixh,1) -1*ones(ixh,1) ];
+    % Construct right side for reduced problem
+    %     |  iy |
+    % b = | -iy |
+    b = [ iy; -iy ];
+    % Construct function to be minimized
+    % f = 0x + 0y + lambda
+    f = [ 0; 0; 1];
+    % Run linprog
+    o = linprog(f,A,b);
+    % o = [ at bt lambdat ];
+    at = o(1);
+    bt = o(2);
+    lt = o(3);
+    % Search for points of maximum distance (ixm, iym) and finally the maximum
+    % distance
+    max_dist = 0;
+    for i=1:xh
+        actual_dist = abs(at*x(i)+bt-y(i));
+        max_point_x = [ x(i) ];
+        max_point_y = [ y(i) ];
+        if actual_dist > max_dist
+            max_dist = actual_dist;
+            imx = max_point_x;
+            imy = max_point_y;
+        elseif actual_dist == max_dist
+            imx = [ max_points_x ; max_point_x ];
+            imy = [ max_points_y ; max_point_y ];
+        end
+    end
+    dist = max_dist;
+    if dist - lt > e
+        ix = [ ix; imx ];
+        iy = [ iy; imy ];
+    end
+    clf;
+    hold on;
+    % Print separate points
+    plot(x,y,'y.');
+    % Print separate points
+    plot(ix,iy,'r.');
+    % Approximation line
+    plot(x,x*at+bt,'g');
+    % Top border
+    plot(x,x*at+bt+lt,'c');
+    % Bottom border
+    plot(x,x*at+bt-lt,'c');
+    hold off;
+    pause(2);
+end
+at
+bt
+lt
+</code>
+=== Uloha 2,3,4 ===
+Konverguje v 5 krocich.
+ --- //[[[email protected]|Marek Sacha]] 2009/10/08 23:06//
+<code matlab>
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Author: Marek Sacha <[email protected]> %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+clear
+clc
+close all
+load data2.mat
+% Initialize random set of starting active edges
+% ix = vector of potential starting x-coordinates
+ix = x(1);
+% iy = vector of potential starting x-coordinates
+iy = y(1);
+% Initialize the point of maximum divergence (initial set contains only one point and in fact, why not random number one ;-))
+ixm = x(1);
+iym = y(1);
+% Initialize at, bt, lt
+at = 0;
+bt = 0;
+lt = 0;
+% Initialize totlerance
+e = 0.0004;
+% Initialize distance
+dist = abs(at*ixm+bt-iym);
+% Initialize support vectors for final graph
+idist = [ dist ];
+il = [ 0 ];
+[ xh xw ] = size(x);
+% Begin loop
+while dist - lt > e
+    test = dist - lt;
+    % Get height of reduced vector x = height of reduced vector y, to be able
+    % to constuct inequalities matrix for reduced problem
+    [ ixh ixw ] = size(ix);
+    % Construct inequalities matrix for reduced problem
+    %       | ix   1  -1 |
+    % A =   |-ix  -1  -1 |
+    %
+    A = [ ix ones(ixh,1) -1*ones(ixh,1); -1*ix -1*ones(ixh,1) -1*ones(ixh,1) ];
+    % Construct right side for reduced problem
+    %     |  iy |
+    % b = | -iy |
+    b = [ iy; -iy ];
+    % Construct function to be minimized
+    % f = 0x + 0y + lambda
+    f = [ 0; 0; 1];
+    % Run linprog
+    o = linprog(f,A,b);
+    % o = [ at bt lambdat ];
+    at = o(1);
+    bt = o(2);
+    lt = o(3);
+    % Search for points of maximum distance (ixm, iym) and finally the maximum
+    % distance
+    max_dist = 0;
+    for i=1:xh
+        actual_dist = abs(at*x(i)+bt-y(i));
+        max_point_x = [ x(i) ];
+        max_point_y = [ y(i) ];
+        if actual_dist > max_dist
+            max_dist = actual_dist;
+            imx = max_point_x;
+            imy = max_point_y;
+        elseif actual_dist == max_dist
+            imx = [ max_points_x ; max_point_x ];
+            imy = [ max_points_y ; max_point_y ];
+        end
+    end
+    dist = max_dist;
+    if dist - lt > e
+        ix = [ ix; imx ];
+        iy = [ iy; imy ];
+        idist = [ idist; dist ];
+        il = [ il; lt ];
+    else
+        idist = [ idist; dist ];
+        il = [ il; lt ];
+        % Hurray, we are victorious %
+        clf;
+        hold on;
+        % Print actual distance
+        plot(1:(ixh+1),idist,'yo');
+        % Print lambda
+        plot(1:(ixh+1),il,'r+');
+        hold off;
+        % Print out requested results
+        dist
+        lt
+    end
+end
+</code>
 ~~DISCUSSION~~

courses/a4b33opt/cviceni3.1254849362.txt.gz · Poslední úprava: 2025/01/03 18:23 (upraveno mimo DokuWiki)

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