第1回 MATLAB seminar 2022年08月02日

%% 1 量
% scalar
1
2
3
a = 5;
​
% vector
% yoko
[1 2 3 4 5]
[1, 2, 3, 4, 5]
b = [1, 2, 3, 4, 5];
% tate
[1; 2; 3; 4; 5]
b = [1; 2; 3; 4; 5];
% sucsession
​
b = 1:10;
b = 1:2:10;
b = 1:0.1:10;
b = linspace(1, 10, 100);
​
% 行列
[1 2 3; 8 7 6; 9 7 5]
A = [1 2 3; 8 7 6; 9 7 5];
[1 2 3; 8 7 6; 9 7] % error
​
% 特殊な行列
zeros(4, 3)
ones(5, 3)
eye(5)
magic(5)
randn(5, 5)
​
% 多次元配列
zeros(3, 3, 3)
%% 2 量と量の演算
% a スカラ一つ
a = 5;
1/a
-a
​
% b ベクトル一つ
b = [1, 3, 7];
-b
1/b % error
1 ./ b % elementwise
b' % transpose
norm(b) % 絶対値
cumsum(b)
diff(b)
​
% c 行列だけ
A = magic(3);
-A % = -1 * A
det(A)
trace(A)
inv(A)
A' % transpose
eig(A) % 固有値
rank(A)
​
% 行列の抽出と代入
A = randi(6, 3, 10);
A(2, 1:2:10);
A(:, 1:2:end);
A(1:2, 1:2) = ones(2, 2);
​
%%
% d scalar vs scalar
a = 4; b = 3;
a + b
a * b
a - b
a / b
a^b
mod(a, b)
​
% e scalar * vector
a = 4;
b = [1, 2, 5, 7];
a + b
a - b
a * b
a ./ b
b / a
a .^ b
% f scalar vs matrix
a = 4;
A = magic(3);
a + A
a - A
a * A
a / A % error try
a ./ A % or
a * inv(A) % but
A / a % is ok
A .^ a
​
% g vector vs vector
v = [3, 4, 5, 1]
w = [2, 3, 1, 1]
v + w % v - w
v * w' % 内積 = dot()
v' * w
v .* w'
v = [3, 4, 5]
w = [2, 3, 1]
cross(v, w)
v .^ w
​
% h vector *
% skip
​
% i matrix * matrix
A = randi(10, 3, 3)
B = randi(10, 3, 3)
​
A + B % A - B
A * B
A .* B % Hadamard product
A/B
A .^ B
trace(A*B) == trace(B*A)
​
%% 特殊関数
a = 0.5;
sin(a)
cos(a)
tanh(a)
exp(a)
gamma(a)
pi
exp(1)
besseli
​
%% 乱数
randn % 正規分布
data = randn(1000, 1);
histogram(data)
​
data2 = data .^ 2; % 正規分布の自乗、つまりχ自乗
histogram(data2);
​
data = rand(1000, 1); % 一様分布
histogram(data)
​
randi([2, 4], 5, 5) % 整数
%% for, if
for I = 1:10
    disp(I)
end
​
for I = 1:3:10
    disp(I)
end
​
for I = 1:10
    if mod(I, 2) == 0
        disp(I)
    end
end
​
%% graph
% https://jp.mathworks.com/help/matlab/creating_plots/types-of-matlab-plots.html
load sunspot;
d = sunspot;
plot(d(:, 1), d(:, 2))
scatter(d(:, 1), d(:, 2))
​
%% sin(x)
N = 10000;
x = linspace(0, 4*pi, N);
y = sin(x);
plot(x, y)