octave 擬合線性方程式範例

參考影片: https://www.youtube.com/watch?v=osh80YCg_GM&list=PLE7DDD91010BC51F8&index=17

% 假設實驗數據 (x̂,ŷ) 計算最小誤差線性方程式 ŷ = c1 + c2*x̂ + c3*x̂² + c4*x̂³ 的解

samples = 64; % 測量樣本數

c1 = 10;

c2 = 0.8;

c3 = 0.5;

c4 = 0.3;

f = @(t) c1 + c2*t + c3*(t^2)+ c4*(t^3);

y = [];

x1 = [];

x2 = [];

x3 = [];

for (t = 1 : samples) % 取樣, Δt

s = f(t);

err = rand - 0.5; % 誤差訊號

noise = s * err; % max +- 50% signal

y = [y, s + noise]; % 讀取測量訊號組成向量

x1 = [x1, t];

x2 = [x2, t^2];

x3 = [x3, t^3];

end

P = [ones(1, samples); x1; x2; x3]'; % 測量矩陣

v = P' * y'; % 測量樣本線性轉換

A = P' * P; % 矩陣變換

elements = numel(v);

lastone = elements + 1;

R = []; % to be solve by Reduce Row Echelon Form

for (t = 1 : elements)

R = [R; A(t,:), v(t,:)];% combine together

end

M = rref(R); % 解方程式 Ax = v

g = [];

for (t = 1 : samples)

z = 0;

for (el = 1 : elements)

z = z + M(el, lastone) * (t^(el-1));

end

g = [g, z];

end

plot(x1, y, 'g:x', x1, g ,'r-');