optim-01

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

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

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

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

dx = 0.01; # x의 간격
x = (0:dx:10-dx)'; # x의 범위
noise = 0.1 * randn(size(x)); # Gaussian noise

[a, b] = deal(0.5, 1.0); # y = ax + b
y = a * exp(-b * x) + noise;

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

# optim package (leasqr)
f1 = @(x, p) p(1)*exp(-p(2)*x); % 모델 함수 (비선형: y = a*exp(-b*x))
pin1 = [1; 0]; % 초기 추정값 [a, b]
[fopt1, popt1, cvg1] = leasqr(x, y, pin1, f1);

f2 = @(x, p) p(1)*x.^2 + p(2)*x + p(3); % 모델 함수 (다항식: y = a*x^2 + b*x + c)
pin2 = [1; 1; 1]; % 초기 추정값 [a, b, c]
[fopt2, popt2, cvg2] = leasqr(x, y, pin2, f2);

# for c=[cvg1, cvg2]
#     if c == 0
#         printf(fmt("converged\n", "#FF5733"));
#     else
#         printf(fmt("not converged\n", "#FF5733"));
#     end
# end

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

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

plot(ax1, x, y);
plot(ax1, x, fopt1, "LineStyle", "-", "LineWidth", 2);
plot(ax1, x, fopt2, "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 = %f b = %f", a, b), param_t{:});
text(ax1, 0.01, 0.99-0.05*1, sprintf("a_t = %f b_t = %f", popt1(1), popt1(2)), param_t{:});
text(ax1, 0.01, 0.99-0.05*2, sprintf("p = %f, %f, %f", popt2(1), popt2(2), popt2(3)), param_t{:});