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courses:a4b33opt:cviceni4 [2009/10/12 14:42] petul.ka created |
courses:a4b33opt:cviceni4 [2025/01/03 18:28] (aktuální) |
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| Řádek 1: | Řádek 1: | ||
| ===== Cvičení 4 ===== | ===== Cvičení 4 ===== | ||
| + | ==== Uloha 1 ==== | ||
| + | Soubor pal3_H.m (samostatne definova H(x,e)) | ||
| + | --- //[[[email protected]|Marek Sacha]] 2009/10/13 01:06// | ||
| + | <code matlab> | ||
| + | function [ h ] = pal3_H( x , e ) | ||
| + | % [ h ] = pal3_H( x , e ) | ||
| + | % | ||
| + | % Computes value of function H(x,e) | ||
| + | % x is a column vector | ||
| + | % e is a constant | ||
| + | % | ||
| + | % Author: Marek Sacha [email protected] | ||
| + | % Date: 12.10.2009 | ||
| + | [ xw xh ] = size(x); | ||
| + | temp_e = e*-1*ones(xw,xh); | ||
| + | temp = [ zeros(xw,xh) (x+temp_e) ((-1*x)+temp_e) ]; | ||
| + | % do not forget to count max in second dimension | ||
| + | h = max(temp,[],2); | ||
| + | </code> | ||
| + | |||
| + | Uloha 1 | ||
| + | --- //[[[email protected]|Marek Sacha]] 2009/10/13 01:06// | ||
| + | <code matlab> | ||
| + | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | ||
| + | % Author: Marek Sacha <[email protected]> % | ||
| + | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | ||
| + | |||
| + | clear | ||
| + | clc | ||
| + | close all | ||
| + | |||
| + | % initialize e | ||
| + | e = 0.3; | ||
| + | % initialize x | ||
| + | x = -1 : 0.01 : 1; | ||
| + | % function works vith column vector only | ||
| + | x = x'; | ||
| + | y = pal3_H(x,e); | ||
| + | plot(x,y,'r'); | ||
| + | xlabel('x ') | ||
| + | ylabel('H(x,e)'); | ||
| + | |||
| + | </code> | ||
| + | |||
| + | |||
| + | ==== Uloha 2 ==== | ||
| + | Vykresli i graf s ruznymivysledky aproximacnich primkek pro ruzne tolerance chyby e (0.001, 0.01, 0.1 0.5 ) | ||
| + | |||
| + | Odvozeni prevodu ulohy na LP viz scan (trik lambda = lambda1 + lambda2 + .... + lambda n): | ||
| + | |||
| + | {{:courses:a4b33opt:opt_cv3_odvozeni_uloha_2_opravene.jpg|}} | ||
| + | |||
| + | --- //[[[email protected]|Marek Sacha]] 2009/10/13 00:48// | ||
| + | <code> | ||
| + | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | ||
| + | % Author: Marek Sacha <[email protected]> % | ||
| + | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | ||
| + | |||
| + | clear all | ||
| + | clc | ||
| + | load data1.mat | ||
| + | |||
| + | % initialize e, test various cases | ||
| + | E = [ 0.001 0.01 0.1 0.5 ]; | ||
| + | |||
| + | % Colours for different cases | ||
| + | C = [ 'r' 'g' 'b' 'c' ]; | ||
| + | |||
| + | hold on; | ||
| + | |||
| + | for j=1:4 | ||
| + | |||
| + | % Initialize e | ||
| + | | ||
| + | e=E(j); | ||
| + | |||
| + | [ xh xw ] = size(x); | ||
| + | % Construct inequalities matrix | ||
| + | % a b l1 l2 ... ln | ||
| + | % ++++++++++++++++++++++++ | ||
| + | % | x1 1 -1 0 ... 0 | | ||
| + | % | x2 1 0 -1 ... 0 | | ||
| + | % ... | ||
| + | % | xn 1 0 0 ... -1 | | ||
| + | % A = |-x1 -1 -1 0 ... 0 | | ||
| + | % |-x2 -1 0 -1 ... 0 | | ||
| + | % ... | ||
| + | % |-xn -1 0 0 ... -1 | | ||
| + | % | 0 0 -1 0 ... 0 | | ||
| + | % | 0 0 0 -1 ... 0 | | ||
| + | % ... | ||
| + | % | 0 0 0 0 ... -1 | | ||
| + | % ++++++++++++++++++++++++ | ||
| + | % | ||
| + | A = [ x ones(xh,1) -1*eye(xh); -1*x -1*ones(xh,1) -1*eye(xh); zeros(xh,1) zeros(xh,1) -1*eye(xh) ]; | ||
| + | % Construct right side | ||
| + | % | e + y | | ||
| + | % b = | e - y | | ||
| + | % | 0 | | ||
| + | b = [ (e*ones(xh,1))+y; (e*ones(xh,1))-y; zeros(xh,1) ]; | ||
| + | % Construct function to be minimized | ||
| + | % f = 0a + 0b + lambda1 + lambda2 + lambda3 + ... + lambdan | ||
| + | f = [ 0 ; 0; ones(xh,1)]; | ||
| + | % Run linprog | ||
| + | o = linprog(f,A,b); | ||
| + | % o = [ a b lambda1 lambda2 ... lambdan ]; | ||
| + | % Print separate points | ||
| + | plot(x,y,'y.'); | ||
| + | % Approximation line | ||
| + | plot(x,x*o(1)+o(2),C(j)); | ||
| + | | ||
| + | |||
| + | end | ||
| + | |||
| + | hold off; | ||
| + | </code> | ||
| + | |||
| + | |||
| + | |||
