[NumericalAnalysis] Matlab - 2

1. M-Files

Script file

% Implement scriptdemo.m script file
% Get all variables/formulas too
scriptdemo

Function file

% Implement freefall.m function file
freefall(12,68.1,0.25)
>> 53.1878

freefall.m

function v = freefall(t, m, c)

g = 9.81
v = sqrt(g*m/c)*tanh(sqrt(g*c/m)*t)

function in MATLAB can return more than one value.

y = [8 5 10 12 6 7.5 4];
[m, s] = stats(y)

stats.m

function [mean, stdev] = stats(x)
n = length(x);
mean = sum(x)/n;
stdev = sqrt(sum((x-mean).^2/(n-1)));

Subfunction

함수 파일에 여러 개의 subfunciton 정의 가능.

다만 파일명과 같은 함수만 호출 가능.

freefallsubfunc(t,m,c) % Can execute
vel(t,m,c) % Can't execute

freefuncsubfunc.m

function v = freefallsubfunc(t,m,c)
v = vel(t,m,c);
end

function v = vel(t,m,c)
g = 9.81;
v = sqrt(g*m/c)*tanh(sqrt(g*c/m)*t);
end

2. Input / Output

Input and Output

% input
m = input('Mass (kg): ');
% output
velocity = 50.6175;
fprintf('The velocity is %8.4f m/s\n', velocity)
>> 'The velocity is 50.6175 m/s'

Format Code

Format Code	Description
%d	integer
%e	scientific format with lowercase e
%E	scientific format with uppercase E
%f	decimal
%g	the more compact of %e or %f

Control Code

Control Code	Description
\n	Start new line
\t	tab

Save and Load

계산된 변수들을 읽거나 쓰기 가능

save veldrag v c
>> save variable v, c in 'veldrag.mat' file 
load veldrag
>> load variable v, c in 'veldrag.mat' file 

3. Structured Programming

### 분기문

% if
if grade >= 60
		disp('passing grade')
end
% same as
if grade >= 60, disp('passing grade'), end
% if - elseif - else
if x > 0
		sign = 1;
elseif x < 0
		sign = -1;
else
		sgn = 0;
end
% switch
switch grade
		case 'A'
				disp('Excellent')
		case 'B'
		...
		case 'F'
				disp('Would like fries with with your order?')
		otherwise
				disp('Huh!')
end

✋ Tip

nargin은 함수가 전달받은 파라미터 개수를 나타낸다.

freefall2.m

function v = freefall2(t, m, cd)

switch nargin
		case 0
				error('Must enter time ans mass')
		case 1
				error('Must enter mass')
		case 2
				cd = 0.27;
end
g = 9.81;
v = sqrt(g*m/c)*tanh(sqrt(g*c/m)*t);

반복문

% for
for i = 1:5
		disp(i)
end
>> 1 2 3 4 5
% while
x = 8;
while x > 0
		x = x - 3
		disp(x)
end
>> 5 2

Vectorization

MATLAB에서 for문은 상당히 비효율적이다. 따라서 for문을 사용하는 대신 Vectorization을 사용할 수 있다.

% vectorization: Replace the unefficient 'for' loop
i = 0;
for t = 0:0.02:50 % unefficient for loop
		i = i + 1
		y(i) = cos(t);
end
% same as
t = 0:0.02:50
y = cos(t) % 각 원소에 cos 매핑 적용

Preallocation of Memory

MATLAB은 배열에 새로운 원소를 추가하게 되면 자동으로 배열의 크기를 증가시킨다.

이는 코드의 유연성을 증가시켜 주지만, 매우 비효율적이다(특히 느리다).

clear y
t = 0:.01:5;
for i = 1:length(t)
		if t(i) > 1
				y(i) = 1/t(i);
		else
				y(i) = 1;
		end
end
% Instead, preallocate y array
clear y
t = 0:.01:5;
y = ones(size(t)); % Preallocation
for i = 1:length(t)
		if t(i) > 1
				y(i) = 1/t(i);
		else
				y(i) = 1;
		end
end

3. Pass functions to M-files

Anonymous Functions

% f1 is function
% parameters are x and y, it return value of x^2 + y^2
f1 = @(x,y) x^2 + y^2
f1(3,4)
>> 25
% anonymous function can contain variable that exists in the workspace. 
a = 4;
b = 2;
f2 = @(x) a*x^b;
f2(3)
>> 36
% The variable value of created funciton doesn't changes. 
a = 3;
f2(3);
>> 36 % not 27
% But below code works. 
f2 = @(x) a*x^b;
f2(3)
>> 27

Function Functions

vel = @(t) sqrt(9.81 * 68.1 / 0.25) * tanh(sqrt(9.81 * 0.25 / 68.1)*t);
% fplot is function that plots the value of function
fplot(vel, [0 12]) 

vel = @(t) sqrt(9.81 * 68.1 / 0.25) * tanh(sqrt(9.81 * 0.25 / 68.1)*t);
funcavg(vel, 0, 12, 60)

funcavg.m

function favg = funcavg(f, a, b, n)

x = linspace(a, b, n);
y = f(x);
favg = mean(y);

Passing Parameters

Anonymous function의 파라미터를 어떻게 바꿀 수 있을까?

MATLAB은 varargin 이라는 파라미터를 function function 의 마지막 파라미터로 추가할 수 있다.

전달된 함수가 function function 내에서 호출될 때마다 varargin{:}을 이용해 마지막 인수로 전달되었던 함수 파라미터들을 전달해야 합니다.

vel = @(t,m,cd) sqrt(9.81*m/cd) * tanh(aqrt(9.81*cd/m)*t);
funcavg2(vel, 0, 12, 60, 68.1, 0.25)
funcavg2(vel, 0, 12, 60, 100, 0.28)

funcavg2.m

function favg = funcavg(f, a, b, n, varargin)

x = linspace(a, b, n)
y = f(x, varargin{:});
favg = mean(y)

4. Others

Pause

pause stops until there is a keyboard input.

for n = 3:10
		% magic: 마방진 행렬, mesh: 3차원 visualization
		mesh(magic(n))
		% stop
		pause
end

Tic and Toc

tic and toc work together to measure elaped time.

beep causes the computer to emit a beep sound.

tic
beep
pause(5)
beep
toc

animation

projectile animates the code.