初階 Matlab

作者:蔡承佑

https://matlab.mathworks.com (IDE)
https://drive.matlab.com (folder)

介面操作

command history

儲存之前寫過的指令

search

看指令如何使用

快捷鍵

停止執行

ctrl + c

命名

一般變數 : Capital letter is lower case
Matrix : Capital letter is upper case

Function

Debug

設立紅色個flag，F10可以執行下一步

• Syntax Error (語法錯誤)
• Semantic Error (語義錯誤)

語法

Precedence

版面

make stronger code

Scripts

script (.m)
有點像是(.py)一次執行scripts內的全部指令

help

help [command]

showing how to use that command

輸出 command 超過一行

加上…

儲存 Command Window

save

會產生.mat檔案
儲存包括變數

叫回 .mat

load

調整format

format compact

log out

quit

清除上面的指令

clc

delete variable

1. clear [variable name]
   (without variable name would clear all variables)
2. click delete in workspace

command

%

;,

; 執行但不會輸出
, 執行且輸出(不terminate)

figure

產生新的圖表

edit(產生檔案)

edit

section(%%)

點選section -> 按 Run Section 就會執行 section 的 code

%% Examples of skipping remainder of iterations

%% Example 1
% Skipping is accomplished in the while condition.
ii = 1;
while ii < length(readings) && readings(ii) <= 100
    readings(ii) = 0;
    ii = ii + 1;
end

%% Example 2
% Skipping is acomplished with a break statement.
for ii = 1:length(readings)
    if readings(ii) > 100
        break;
    else
        readings(ii) = 0;
    end
end

%% Example 3
% Shows that for-loop index retains is last value
% after the loop is exited. It's similar to Example 2,
% but omits the setting of values to 0 and prints the
% index of the first reading above 100.
for ii = 1:length(readings)
    if readings(ii) > 100
        break;
    end
end
fprintf('First reading above 100 is at index %d.\n', ii);

可以點擊publish

variable

number

x = 9.65e12
y = 23e-2

function

可以寫在.m檔內

function pretty_picture(N)
%command

t = 0:(.99*pi/2):N;
x = t.*sin(t);
y = t.*cos(t);
plot(x, y, 'k')
axis square

function [m,s] = stat(x)
    n = length(x);
    m = sum(x)/n;
    s = sqrt(sum((x-m).^2/n));
end

image

show image

• method 1

imshow('[image path]')

-method 2

pretty_picture = imread('[image path]');
image(pretty_picture)

關掉 x 軸 y 軸

axis off

math

無窮大

inf
-inf

更號

sqrt(2)

sin

• 依照弳(rad): sin(30)
• 依照度(deg): sind(30)

plus

plus(number1, number2)

次方

^

虛數i

0.0000 + 1.0000i

指令時間

tic toc

tic;
…
toc

cputime

t0 = cputime; f(8); cputime - t0

open webpage

function open_webpage
url = input('Enter the url: ','s');
if isempty(url)
    fprintf("No url entered, so quitting.\n");
    return;
end
search_time = datetime; % same as datetime("now")
status = web(url);
if status == 0 % started web browser
    fprintf("At %s, you opened the web page at\n",search_time);
fprintf("%s\n",url);
else
    fprint("Could not start web browser\n");
end
[~,weekday_name] = weekday(search_time,'long');
fprintf("Have a great %s!\n", weekday_name);

Matrix

*scalars also known as number

key word:

• end最後一行或最後一列
• : 所有row或column

Definition

• 2D array = "matrix"
• 1D array = "vector"
• Empty matrix: 1-by-0

Matrix宣告

• 2D array
  空白分割為column 分號分割為row

x = [1 4 7]

x = 1 4 7

y = [1; 4; 7]

y =
1
4
7

z = [1 4 7; 2 8 6]

z =
1 4 7
2 8 6

• Empty matrix
  x = []

• 初始化某一列某一行
  matlab 第一個是1不是0
  X(row_id, coloumn_id)

X = [1:4; 5:8; 9:12]

X =
1 2 3 4
5 6 7 8
9 10 11 12

X(2, 3)

ans = 7

• Extend array
  超過行列值的部分補0

X(4, 5)

Index exceeds matrix dimensions

X(4, 5) = 456

X =
1 2 3 4 0
5 6 7 8 0
9 10 11 12 0
0 0 0 0 456

• subarray
  X(row_id, column_id)

X(2, [1 3])

ans = 5 7

: operator

array_name = begin : 遞增多少(沒有這個欄位就是1) : end(包括)

x = 1:3:10

x = 1 4 7 10

x = 1:4

x = 1 2 3 4

colon function

colon(1, 7)

ans = 1 2 3 4 5 6 7

查看 matrix 的維度長

X = [0 1 -1; 2.5 pi 100]
size(X)

ans = 2 3

Combining Matrices

Definition

宣告

Transforming Matrices

Definition

宣告'

H = [1 2 3; 4 5 6]
G = H'

H =
1 2 3
4 5 6

G =
1 4
2 5
3 6

(1:2:5)'

ans =
1
3
5

Arithmetics of Matrices

如果有常數 則是每個元素都跟這個常數進行四則運算

Add

• sum(vector)
  1. 將column的所有元素加起來
  2. 若為 1Xn 則將vector所有元素相加

Multiplication

1. Array Multiplication .*

2. Matrix Multiplication *

矩陣乘法

Division

• Array Division (斜線下面篇哪裡 哪裡就是分子)

1. X./Y (over)

2. X.\Y (under)
   
   

次方

• Array (.^)

• Matrix (^)

餘數

rem(x, y), x 為被除數 y 為除數

repmat

Matrix初始化技巧

Matrix 初始化技巧(善用zeros跟ones)

function M = sparse2matrix(cellvec)
    sz = cellvec{1};
    val = cellvec{2};
    M = val*ones(sz);
    for i = 3:length(cellvec)
        el = cellvec{i};
        M(el(1), el(2)) = el(3);
    end
end

Function

Robustness

1. 用%加上註解在函式內容的最上面，當用help時會顯示
2. 用error function
3. 判斷可能的nargin跟nargout
4. 多用isscalar判斷是否為純量

function [table summa] = multable(n, m)

%MULTABLE multiplication table.
% T = MULTABLE(N) returns an N-by-N matrix
% containing the multiplication table for
% the integers 1 through N.
% MULTABLE(N,M) returns an N-by-M matrix.
% Both input arguments must be positive
% integers.
% [T SM] = MULTABLE(...) returns the matrix
% containing the multiplication table in T
% and the sum of all its elements in SM.

if nargin < 1
    error('must have at least one input argument');
end

if nargin < 2
    m = n;
end

table = (1:n)' * (1:m);

if nargout == 2
    summa = sum(table(:));
end

Polymorphism

輸入形式或數量不同但名稱相同的function
利用 nargin 跟 nargout 達成

function [table summa] = multable(n, m)

if nargin < 2
    m = n;
end

table = (1:n)' * (1:m);

if nargout == 2
    summa = sum(table(:));
end

varargin 無限多輸入
放在最後一個input

varargout 無限多輸出

Definition

function <回傳值> = <function_name>(<input>)
…
end

function a = myRand
a = 1 + rand(3, 4)*9;
end

function a = myRand(low, high)
a = low + rand(3, 4)*(high - low);
end

function [a, s] = myRand(low, high)
a = low + rand(3, 4)*(high - low);
v = a(:);
s = sum(v);
end

Subfunction

全域變數

global <variable_name>
宣告跟初始化要分開

Persistent variable

是一種local variable在呼叫第二次函式時不會改變，除非使用clear <function_name>

return

可以中斷function藉由return

Tool Box

Matrix Building Function

diag([7 3 9 1])

ans =
7 0 0 0
0 3 0 0
0 0 9 0
0 0 0 1

rand(m, n)

範圍是 0 到 1

randi(imax, m, n)

用途: 生成均勻分布的隨機整數。
imax: 指定生成的隨機整數的最大值，隨機整數將在 1 到 imax 之間（包括 imax）。
m 和 n: 指定生成的隨機整數矩陣的尺寸。

randn(m, n)

用途: 生成服從標準正態分布（均值為 0，標準差為 1）的隨機實數。
m 和 n: 指定生成的隨機數矩陣的尺寸。

判斷function
isscalar()
isempty()

Nested Function

function 內還有一個 function
inner function 的 variable, outer function不會有 (local scope)
outer function 的 variable, inner function會有 (non-local scope)

Function Handles

可以用在cell但不行用在array

variables

plot

自訂義

也可以多個變數
xfn = @(x, y) x+y

Return Multiple (deal)

Random

random 的生成跟 rng的值有關
所以每次重新打開輸入rand的值會是一樣的

想要更改可以改動rng => rng('shuffle')

Input Output

input

<variable_name> = input('<statement>');

function a = one_more
x = input('Gimme a number, buddy: ');
a = x + 1

fprintf

用法像是 C 的 printf 包刮 %d %5.2f 特別的是可以為矩陣

fprintf('This concludes Lesson 3\n')

如果輸出的為特殊字符，例如: ' 、 % 、
則打兩次 '' 、 %% 、 \

sprintf

sprintf()將element 指定給變數

plot

不要刷新表格(hold)

如果在一個表格輸入plot會蓋掉原本的圖，如果不想要蓋掉可以用hold

hold on
…
hold off

help plot
doc plot

新增及切換下一個表格

figure(表格名稱)

關閉表格

close [表格名稱]
close all

表格新增方格線 (grid)

grid on
grid off

新增 x 軸 y 軸名稱 title

xlabel('[label name]')
ylabel('[label name]')
title('[tile of plot]')

改變 x 軸 y 軸範圍

axis([[x軸開頭], [x軸結束], [y軸開頭], [y軸結束]])

length 顯示 vector 長度

x_coordinates = [1, 3, 10];
length(x_coordinates)

ans = 3

legend

type

2D

1. plot([x vector], [y vector])
   plot(x1, y1, x2, y2)

x_coordinates = [1, 3, 10]; %element vector
y_coordinates = [2, -4.2, 12.3];
plot(x_coordinates, y_coordinates); %plot function

2. plot([x vector], [y vector], [LineSpec])
   plot(x1, y1, LineSpec1, x2, y2, LineSpec2)

plot(x_coordinates, y_coordinates, '*')

bar

bar([x vector], [y vector])

pie

pie([4 2 7 4 7])

hist 分布圖

hist(<vector_name>)

Conditional Statement

Logical values

Non-zero: true
Zero: false
MATLAB returns 1 for true

if

function guess_my_number(x)
if x == 42
    fprintf('Congrats! You guessed my number!\n');
elseif x < 42
    fprintf('Too small. Try again\n');
else 
    fprintf('Too big. Try again.\n')
end

Relation Operator

可以用在matrix上

[4 -1 7 5 3] > [5 -9 6 5 -3]

ans =
0 1 1 0 1

[4 -1 7 5 3] <= 4

ans =
1 1 0 0 1

sum([14 9 3 14 8 3] == 14)
% 計算有幾個14

ans = 2

Combine Logical values

Array (& | )

Nested if-statements(記得加end)

function ultimate_question_nested2(x)
if x <= 42
    if x == 42
        fprintf('Wow! You answered the question.\n');
    else
        fprintf('Too small. Try again.\n');
    end
else 
    fprintf('Too big. Try again.\n');
end

Switch Case

switch month
    case {1, 3, 5, 7, 8, 10, 12}
        day_in_month = 31;
    case {4, 6, 9, 11}
        day_in_month = 30;
    case 2
        if (mod(year, 4) == 0 && mod(year, 100) ~= 0) || mod(year, 400) == 0
            day_in_month = 29;
        else
            day_in_month = 28;
        end
    otherwise
        valid = false;
end

Loops

1:5可以是任何array

for

for n = 1:5
    fprintf("%d\n", n)
end

function f = fibo(n)
if ( ~isscalar(n) || n < 1 || n ~= fix(n))
    error('n must be a positive integer!');
end
 
f(1) = 1;
f(2) = 1;
for ii = 3:n
    f(ii) = f(ii-2) + f(ii-1);
end

雙重迴圈 (matrix 遍歷)

[row col] = size(A);
for r = 1:row
    fprintf('Working on row %d...\n',r);
    for c = 1:col
        P(r,c) = A(r,c) * A(r,c);
        fprintf('(%d %d)\n',r,c);
    end
end

while

function [n total] = possum(limit)
total = 0;
n = 0;
while total <= limit
    n = n + 1;
    total = total + n;
end
fprintf('sum: %d count: %d\n', total, n);  

break

quit loop immediately
只會break inner loop 可善用flag

Logical Indexing (Special)

index 的地方由 true/false 的 array 判斷

logical

判斷array的元素是否為true

holmes = logical([1 -2 0 0 9.12 -2])

holmes =
1 1 0 0 1 1

二維陣列

如果是二維陣列呢?

因為陣列是column major

因為是column major改是由上往下 再由左往右

Preallocation

提前 allocate ，使的初始化時，不會重複宣告

function prealloc
N = 5000;
A = zeros(N,N);
for ii = 1:N
    for jj = 1:N
        A(ii,jj) = ii*jj;
    end
end

zeros(N, N) 就是在preallocate

Data Type

查看變數type

1. class(<variable_name)
2. whos 查看目前所有type

useful function (type check、range check、conversion)

out of range

Numbers

range of numbers

String

1. char array ('')
2. string ("")

string

視為double/char array
char => %s

如果要用 == 比較 : char matrix 的 dimension 必須相同

如果要創建string 的 matrix 長度必須相同，否則會遇到vercat(內建函式比較string)

string function

findstr(string, <want_to_find_what_string>)

strcmp(str1, str2), 1 is true, 0 is false

strcmpi(str1, str2), i means ignoring case

str2num(string)

num2str(number)

sprintf()將element 指定給變數

strrep(string, char1, char2)把string中的char1改成char2

circshift
Caesear 加密法

extractBetween(s, 3, 8) 對付當s為string而非char array
extractBetween(s, str1, str2) 取str1 str2之間的string

注意char string

若要像 array 一樣對 string 操作，那他必須採用 char array 的方式表示('') 而不是 string ("")

可以用 string() 、 char() 做切換

其他type轉string容易 => string()
但string轉其他type難 => 除了double() => 先轉double再轉其他type

string(pi)
ans = 3.14

double("pi")
ans = NaN

double("17")
ans = 17
double('17')
ans = 49 55

Struct

rule

1. homogeneity rule

每個struct內的元素擁有相同field，但也僅限於第一層

account(2)的owner內可能有不同元素

struct can be an array

account(2).number = 1
account(2).name = 'Charlie'
account %查看所有的field

struct function

isfield(struct, 'field')

struct = rmfield(struct, 'field')

struct = struct(…)

Cells

pointer
()可以視為指標的值
{row, col}可以視為指標指向的值

跟 char matrix 不同，每個元素不用等長了

%% The Ultimate Legend of Big John
page{1} = 'You could find him on the field almost any day.';
page{2} = 'Tall, dark hair, and eyes of steel gray.';
page{3} = 'They say he pulled a Frisbee ''bout half a mile,';
page{4} = 'And when he''d stick in the corner, you could almost catch a smile';
page{5} = 'On Big John.';
%% Print it
fprintf('\n');
for ii = 1:length(page)
    fprintf('%s\n',page{ii});
end
fprintf('\n');

Cell array

c{1} is number c(1) is cell

cell function

Datatime

setting

HOME -> Preferences -> Command Window

datetime(year, month, day)
datetime(year, month, day, hour, month, second)

timezones 看時區

format

Duration

• hours(2.5)、years(3)、days(3)、months()、seconds()、duration(hours, minutes, seconds)

calyears(整數)=>直接加一年，years()=>事實上是加365.2425天
所以+calyears(1)還會是同一天，但+years(1)就不一定了

right_now = datetime("now")
three_years_from_now = right_now + years(3)

• .years year()

• arrithmetic

missing_days = days(datetime(1764, 5, 17) - datetime(1764, 2, 15))

Function Handles

可以用在cell但不行用在array

variables

plot

File I/O (like wsl)

pwd

show current path (linux format)

Windows format => ['C:', strrep(pwd, '/', '')]

ls

cd

get into directory

mkdir

mkdir(file_name)

rmdir

rmdir(file_name)

save

儲存目前變數於.mat

load

load .mat檔

可以決定load哪些
loat .mat檔的名稱 變數名 變數名

讀取excel檔案

[num, text, raw] = xlsread("path")
class(num) = double
class(text) = string
class(raw) = cell
他們都可以用 pointer 或 array 的方式處理

[num, string] = xlsread("path")
[~, ~, everything] = xlsread("path")

tmep 可以用 ~ 代替指讀取string

Text file

• Opening: fid = fopen(filename, permission)
  • 如果沒有成功開啟fid<0
• Closing: fclose(fid)
• File identifier (fid): a handle to refer to the file once open
• Permission: what we want to do with the file
  • read, write, overwrite, append

• 輸入file
  • fid = fopen(filename, 'w+t');
  • fprintf(fid, '%s\n', Title_1);

function write_temp_precip_txt(filename)
Title_1 = 'Climate Data for Nashville, TN';
Title_2 = '(Average highs (F), lows (F), and precip (in)';
Label_1 = ' High ';
Label_2 = ' Low  ';
Label_3 = 'Precip';
Mo_1 = {'Jan','Feb','March','April','May','June'};
Mo_2 = {'July','Aug','Sep','Oct','Nov','Dec'};  
Data_1 = [
   46	28	3.98
   51	31	3.7
   61	39	4.88
   70	47	3.94
   78	57	5.08
   85	65	4.09];
Data_2 = [
   89	69	3.78
   88	68	3.27
   82	61	3.58
   71	49	2.87
   59	40	4.45
   49	31	4.53];
fid = fopen(filename,'w+t');
if fid < 0
   fprintf('error opening file\n');
   return;
end
fprintf(fid,'%s\n',Title_1);
fprintf(fid,'%s\n',Title_2);
fprintf(fid,'\n');
fprintf(fid,'       %s%s%s\n',Label_1,Label_2,Label_3);
for ii = 1:6
   fprintf(fid,'%5s: ',Mo_1{ii});
   fprintf(fid,'%5.2f,%5.2f,%5.2f\n',Data_1(ii,:));  
end
fprintf(fid,'\n');
fprintf(fid,'       %s%s%s\n',Label_1,Label_2,Label_3);
for ii = 1:6
   fprintf(fid,'%5s: ',Mo_2{ii});
   fprintf(fid,'%5.2f,%5.2f,%5.2f\n',Data_2(ii,:));  
end
fclose(fid);

• read file
  • one line at a time

function view_text_file(filename)
fid = fopen(filename, 'rt');
if fid < 0
    error('error opening file %s\n\n', filename);
end

% Read file as a set of strings, one string per line:
oneline = fgets(fid);
while ischar(oneline)
    fprintf('%s', oneline) % display one line
    oneline = fgets(fid);
end
fprintf('\n');
fclose(fid);

• Reading lines into string variables is easy
• Parsing these strings to get numerical data is much harder
• Not covered
• Binary files (.dat) are more suited for numerical data

Writing binary files

Reading binary files

binary files (dimension one)