demo-03b

# filename: demo-03b.m
# writer: won sunggyu
# date: 2025-04-22
# language: octave
# description: (번외) 베셀 함수 구경하기

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

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

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

dx = 0.1;
nx = 1000;
x = 0:dx:dx*(nx-1);

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

# 베셀 함수 (4종, 1-4차)
Jn = zeros(4, nx);  # Bessel function of the first kind (Jₙ(x))
Yn = zeros(4, nx);  # Bessel function of the second kind (Yₙ(x))
In = zeros(4, nx);  # Bessel function of the third kind (Iₙ(x))
Kn = zeros(4, nx);  # Bessel function of the fourth kind (Kₙ(x))

for i=1:4
    Jn(i, :) = besselj(i, x);
    Yn(i, :) = bessely(i, x);
    In(i, :) = besseli(i, x);
    Kn(i, :) = besselk(i, x);
end

Yn = Yn / max(max(abs(Yn)));
In = In / max(max(abs(In)));
Kn = Kn / max(max(abs(Kn)));

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

# 그래프
figured("Size", [1920, 960], "Move", [0, 0], "Name", mfilename);
ax = subplots(4, 4, "Xlabel", "Non-dimension");

for i=1:4
    plot(ax(i, 1), x, Jn(i, :));
    plot(ax(i, 2), x, Yn(i, :));
    plot(ax(i, 3), x, In(i, :));
    plot(ax(i, 4), x, Kn(i, :));
end

for i=1:4
    title(ax(i, 1), sprintf("Bessel Function of the First Kind (J_%d(x))", i-1));
    title(ax(i, 2), sprintf("Bessel Function of the Second Kind (Y_%d(x))", i-1));
    title(ax(i, 3), sprintf("Bessel Function of the Third Kind (I_%d(x))", i-1));
    title(ax(i, 4), sprintf("Bessel Function of the Fourth Kind (K_%d(x))", i-1));
end