optim-01

# filename: optim-01.m
# writer: won sunggyu
# date: 2025-05-09
# language: octave
# description: 선형 회귀 모델 추정 (OLS, Leasqr)

#------------------------------------------------------------------------------
# 초기화
#------------------------------------------------------------------------------

run("startup.m");
printf(fmt("{mfilename}\n", "#FF5733"));

#------------------------------------------------------------------------------
# 데이터 준비
#------------------------------------------------------------------------------

filename = "optim-01.mat";

data = load(filename);

x = data.x;
y = data.y;
a = data.a;
b = data.b;

#------------------------------------------------------------------------------
# 데이터 연산
#------------------------------------------------------------------------------

# Ordinary Least Squares Method
X = [x, ones(size(x))]; # [x 1] * [a; b] = y
Y = y;

theta = (X' * X) \ (X' * Y);

[a_r, b_r] = deal(theta(1), theta(2)); # y = ax + b_r
y_r = a_r * x + b_r;

# optim package (leasqr)
f = @(x, p) p(1)*x + p(2); % 모델 함수 (선형: y = a*x + b)

pin = [1; 0]; % 초기 추정값 [a, b]

[fopt, popt, cvg] = leasqr(x, y, pin, f);
# fopt 모델 함수의 예측값
# popt 최적화된 파라미터
# cvg 수렴 여부

#------------------------------------------------------------------------------
# 그래프 그리기
#------------------------------------------------------------------------------

figured("Size", [1280, 720], "Move", [-1280, 0], "Name", mfilename);
ax1 = subplots(1, 1);

plot(ax1, x, y);
plot(ax1, x, y_r, "LineWidth", 2);
plot(ax1, x, fopt, "LineStyle", "--", "LineWidth", 2);

param_t = {
    "Color", "#FF5733", ...
    "FontSize", 14, ...
    "FontWeight", "bold", ...
    "HorizontalAlignment", "left", ...
    "VerticalAlignment", "top", ...
    "Units", "Normalized"
};
text(ax1, 0.01, 0.99-0.05*0, sprintf("a_r = %f b_r = %f", a_r, b_r), param_t{:});
text(ax1, 0.01, 0.99-0.05*1, sprintf("a = %f b = %f", a, b), param_t{:});
text(ax1, 0.01, 0.99-0.05*2, sprintf("a_t = %f b_t = %f", popt(1), popt(2)), param_t{:});