demo-02

# filename: demo-02.m
# writer: won sunggyu
# date: 2025-04-22
# language: octave
# description: 연산자, 행렬 연산자, 행렬 연산 함수

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

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

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

x = [1 2 3];
y = [4 5 6];
A = [1, 2; 3, 4];
B = [5, 6; 7, 8];

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

# pointwise multiplication
r_pointwise_add = x + y  # (1,3) + (1,3) = (1,3)
r_pointwise_sub = x - y  # (1,3) - (1,3) = (1,3)
r_pointwise_mul = x .* y  # (1,3) .* (1,3) = (1,3)
r_pointwise_div = x ./ y  # (1,3) ./ (1,3) = (1,3)

# implicit expansion applize automatically while operating
r_pointwise_add_w = x + y'  # (1,3) + (3,1) = (3,3)
r_pointwise_sub_w = x - y'  # (1,3) - (3,1) = (3,3)

# inner product
r_inner1 = x * y'  # (1,3) * (3,1) = (1,1)
r_inner2 = dot(x, y)

# cross product: 2D or 3D geometry
r_cross = cross(x, y)

# outer product with  (pointwise multiplication)
r_outer_w = x .* y'  # (1,3) .* (3,1) = (3,3)

# dyadic product (no good for big size data)
r_dyadic_w = x' .* y  # (3,1) .* (1,3) = (3,3)

# matrix operation
m_add = A + B  # (2,2) + (2,2) = (2,2)
m_sub = A - B  # (2,2) - (2,2) = (2,2)
m_mul = A .* B  # (2,2) .* (2,2) = (2,2)
m_div = A ./ B  # (2,2) ./ (2,2) = (2,2)
m_mmul = A * B  # (2,2) * (2,2) = (2,2)

# matrix solve A * x = B
m_sol1 = A \ B  # (2,2) * (2,2) = (2,2)
m_sol2 = inv(A) * B  # (2,2) * (2,2) = (2,2)
m_sol3 = linsolve(A, B)  # (2,2) * (2,2) = (2,2)

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