RM Practical 05

clc;

clear;

clf;

sigma = 5.67e-8;

A = 0:0.01:1;

Fs = 1368;

T = ((1 - A) .* Fs ./ (4 * sigma)).^(1/4);

[a, b] = reglin(A, T);

T_linear = a*A + b;

X5 = [ones(A') A' (A'.^2) (A'.^3) (A'.^4) (A'.^5)];

coeff5 = X5 \ T';

T_poly5 = coeff5(1) + coeff5(2)*A + coeff5(3)*A.^2 + coeff5(4)*A.^3 +

coeff5(5)*A.^4 + coeff5(6)*A.^5;

X6 = [ones(A') A' (A'.^2) (A'.^3) (A'.^4) (A'.^5) (A'.^6)];

coeff6 = X6 \ T';

T_poly6 = coeff6(1) + coeff6(2)*A + coeff6(3)*A.^2 + coeff6(4)*A.^3 +

coeff6(5)*A.^4 + coeff6(6)*A.^5 + coeff6(7)*A.^6;

plot(A, T, 'black');

plot(A, T_linear, 'm');

plot(A, T_poly5, 'red');

plot(A, T_poly6, 'blue');

xlabel('Albedo');

ylabel('Temperature (K)');

title('Albedo vs Temperature with Fitting');

legend(['Original','Linear','Poly5','Poly6']);

xgrid();

disp('Linear Coefficients (a, b):');

disp([a b]);

disp('Polynomial Degree 5 Coefficients:');

disp(coeff5);

disp('Polynomial Degree 6 Coefficients:');

disp(coeff6);