Matlab Notes

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Matlab 小记

BASIC

frequent use:

  • arithmetrc
    trigonometry
    exponents and logarithms
    complex numbers
    cartesian coordinate

embedding functions:
sin(cos(pi))
cos(pi) %储存到ans里面
sin(ans)

LHS = RHS
不可换左右
variables 不可以开头为数字
logical;char;numbic
defult:double

>> whos%问变量的详细资料
>>who
  • Keyword
    ans%keyword
    i,j%complex numbers
    inf:indefintlly
    1/0=inf
    eps: 很小
    NaN：非数值
    inf/inf
    pi: Π
    sqrt() or ()^0.5
    ln is log
    exp
    log10() log2()%base 10,2
    >>iskeyword %查看哪个是keyword

Array

vector

row vector
    `>>a=[1 2 3 4]`
column vector
    `>>b=[1;2;3;4]%分号代表换行`
a*b
b*a
A=[1 2 3 ;4 5 6;7 8 9]

array indexing

A(8)%找特定位置的值
    索引方式:
    ```
    A    [1 4 7]
        [2 5 8]
        [3 6 9]
    ```
A(row,column)
    A(1,2)==2
    A([1 3 5])%第一第三第五
    A([1 3;1 3])%一个矩阵
    A(3,2)
    A([1 3],[1 3])==
    A([row row],[col col])
    行与列的交集

Replacing Entries

A(1,2) = 76
  • Colon Operator:
    用来做等差级数
  A=[1:100]%[first:last]
  A=1:2:99%等差为2
  B=[1:5;2:3:15;-2:0.5:0]
  str='a':2:'z'
  A(3,:)%第三行
  A(3,:)=[]%delete第三行
  delete rows of columns of A

Array Concatenation

A=[1 2 ;3 4]
B=[9 9 ;9 9]
F=[A B];F[A;B]

Array Manipulation

+ - * / ^ . '
A*B%矩阵相乘
A.*B%点乘各个元素对应相乘
A/B==A*inv(B)
A./B

A+a%矩阵＋实数，每个元素加標量
A^a=A*A
A.^a=个别取两次方
C=A’%转置对角线转置

Some Special Matrix

linspace();
eye(n);nXn identity matrix
zeros(n1,n2)n1Xn2zero matrix
ones(m,n)every entry as 1
diag();diagonal matrix对角线矩阵
diag([2 3 4])对角线234
rand

Functions:

max(A)%每列的最大项
max(max(a))%全部最大项
min(A)
sum(A)
mean(a)%每列平均值
sort()%每个column大小排序
    从小排到大
sortrows()%第一列的大小排序
行
size(A)%row col
length(A)%vector 的
find(A==5)%返回一个数的位置

Script

script

(F5) run
fx按钮找公式
%百分比符号
右键command
%%section,用来分节，可以运行节
run section
断点点行前面

快捷键

ctrl+R注释
Ctrl+T取消注释
Ctrl+I智能排版

Structured programming techniques

sum

if,elseif,else
for switch case ot herwise
try catch
while
break
continue
endpause
return

relational logical

if(condition) rational operation

< less than <= less than or equal to
> greater than
== equal to
~= not equal to 
&& and
|| or

if elseif else

if condition 1
statement1
elseif condition2
statement2
else
statement3
end

for instance

a=3;
if rem(a,2)==0  %a除以2余数为0
    disp('a is even')%偶数
else
    disp('a is odd')
end

switch

switch expression
case value1
statement1
case value2
statement2
.
.
otherwise
statement
end

for instance

input_num = 1;
switch input_num
case -1
    disp('negative 1');
case 0
    disp('zeros')
case 1

while

while expression
    statement
end

for instance

n=1;
while prod(1:n)<1e100 %product阶乘 n！<10^100
    n=n+1;
end

for

for variable=start:increment :end
    commands
end

for instance

for n=1:10
    a(n)=2^n;
end
disp(a)
clear a

for n=1:2:10
    a(n)=2^n;
end
%n在变在改变array的大小

not pre-allocating

tic
for ii = 1:2000
    for jj = 1:2000
        A(ii,jj) = ii+jj;
    end
end
toc

pre-allocating提前扩展空间

A=zeros(2000,2000);
tic%时间开始
for ii = 1:2000
    for jj = 1:2000
        A(ii,jj) = ii+jj;
    end
end
toc%计时结束

#inclue<stdio.h>
int main(void)
{
int count;
for(count=1;count<=500;count++)
    print("I wei");
return 0;
}

break

>break%调出一次循环

    while error > error_threshold
        if k>100
            break
        end
        clc        
    end

Tips for Script Writing

  1. clear all %remove previous variable
  2. close all %to close all fig
  3. use semicolon; at the end of commands to inhibit unwanted output
  4. Use ellipsis… to make scripts more readable
  5. A = [1 2 3 4 5 6 ;…%用来连接两行
    6 5 6 1 5 1];

  6. 宕机时ctrl + c强行终止

    Variables:string ,structure,cell

    Multidimensional Array

    • logical逻辑
      • 0，1
    • char
      • a,b..
    • numeric数值
      • int8 8bit,uint8 nsigned,single,double defult
        int16,uint16,
        int64,uint64
    • cell
    • struct

Scalar
function handle(@)

A=20
B=int8(20)
B=int8(A)

Character (char)

s1 = 'h'
whos %显示多少个变数
uint16(s1) %结果是ascii码的decimal

String

An array collects characters:

s1 = 'Example';
s2 = 'String';

String concatenation

s3 = [s1 s2]; %output：s3 ='ExampleString'
s4 = [s1 ; s2]; %error：串联的矩阵的维度不一致
s5 = [s1 ;s1 ]

Logical Operations and Assignments

str = 'adsfdsf'; %str(3)='s'
'a' == str 
%output: ans = 1   0   0   0   0   0   0

str(str == 'a') = 'z'
%等同于str(1   0   0   0   0   0   0) = 'z'
%output: str ='zdsfdsf'; 遂a替换成z

Exercise:write a script that inverts any given string

Structure

  • A method of storing heterogeneous data
  • Structure contain arrays called fields

Student assignment grades:
student
.name -> JohnDoe
.id -> id2@sfu.ca
.number -> 524264
.grade -> 56

student.name  = 'JohnDoe';
student.id = 'id2@sfu';
student.number = 524264;
student.grade = [100,75,73;95,91,85.5;100,98,72];
student

student(2).name  = 'Ann Lane';
student(2).id = 'id22@sfu';
student(2).number = 5242646;
student(2).grade = [98,75,73;45,91,85.5;100,98,72];

Exercise:Retrieve the 3rd grade for Ann Lane

​ Structure Functions

  • rmfield %Remove fields from structure
    rmfield(student,'id')
  • fieldnames %Field names of structure
    fieldnames(student)%回传成string

​ Nesting Structures

A = struct('data',[1 5 3 5 6],'nest',...
    struct('testnum','Test 1',...
    'xdata',[4 2 3],'ydata', [7 1 6])); %一共4个field
A(2).data = [5 2 3 5 8];
A(2).nest.testnum = 'Test 2';
A(2).nest.xdata = [3 5 4];
A(2).nest.ydata = [5 0 9];
A.nest

Cell Array

  • Another method of storing heterogeneous data
  • Similar to matrix but each entry contains different type of data
  • Declared using{}
clear A
%像存放不同元素的分块矩阵
A(1,1) = {[1 4 3;0 5 8;7 2 9]};
A(1,2) = {'Anne Smith'};
A(2,1) = {3 + 7i};
A(2,2) = {-pi:pi:pi};
A

A{1,1} = [1 4 3;0 5 8;7 2 9];
A{1,2} = 'Anne Smith';
A{2,1} = 3 + 7i;
A{2,2} = -pi:pi:pi;
A

How Does Matlab Do It?

  • Each entry in a cell array holds a pointer to a data structure
  • Defferent cells of the same cell array can point to different types of data structure

Accessing Cell Array

  • Curly braces,{},are used to access the “content” of cell arrays

  • C = A(1,1)% pointer 指向指针output: ans = [3x3 double]

  • C = A{1,1}%访问内容 output: ans = [1 4 3;0 5 8;7 2 9]

  • A{1,1}(1,1) %output: ans = 1

Cell Array Functions

  • cell2mat %Convert cell array to numeric array

  • cell2struct %Convert cell array to structure array

  • num2cell() and mat2cell()
    Transform a matrix into a cell variable 

      a=magic(3) %3*3matrix
  %output: 
       a =
       8     1     6
       3     5     7
       4     9     2
  b=num2cell(a)
  %output
      b =3×3 cell 数组
      [8]    [1]    [6]
      [3]    [5]    [7]
      [4]    [9]    [2]
  c=mat2cell(a,[1 1 1],3)%(mtrix,row,col)
  %output
      c =3×1 cell 数组
      [1×3 double]
      [1×3 double]
      [1×3 double]

  c=mat2cell(a,[2 1],3)%a3*3矩阵，row分为2行一组和最后行一组（两行），列分为三合一（一列）
  %output:
      c =  2×1 cell 数组
      [2×3 double]
      [1×3 double]

Multidimensional Array

  • vector row + column row + column + layer
    eg.三个维度cell: row(down) column(right) layer(back)

cat()

%A{1,2,2} = 1 
A = [1 2 ;3 4];B=[5 6 ; 7 8]
C = cat(1,A,B) %row方向向下（-z轴）
C = cat(2,A,B) %column 方向右（y轴）
C = cat(3,A,B) %layer 向后（-x轴）

clear A B C
A{1,1} = {[1 4 3;0 5 8;7 2 9]};
A{1,2} = {'Anne Smith'};
A{2,1} = {3 + 7i};
A{2,2} = {-pi:pi:pi};
B{1,1} = [1 4 3;0 5 8;7 2 9];
B{1,2} = 'Anne Smith';
B{2,1} = 3 + 7i;
B{2,2} = -pi:pi:pi;
C = cat(3,A,B)

reshape()

  • Returns a new array with assigned rows and columns
    r1*c1 -> r2*c2
    `matlab
    A{1,1} = [1 4 3;0 5 8;7 2 9];
    A{1,2} = ‘Anne Smith’;
    A{2,1} = 3 + 7i;
    A{2,2} = -pi:pi:pi;
    C = reshape(A,1,4)

%output:
C =
1×4 cell 数组
[3×3 double] [3.0000 + 7.0000i] ‘Anne Smith’ [1×3 double]
A =
2×2 cell 数组
[3×3 double] ‘Anne Smith’
[3.0000 + 7.0000i] [1×3 double]


**Checking Variables And Variable Status**

* isnan %Detect an element that isnot a number(NaN)
* isreal %Determine if all array elements are real numbers
* iscell %Determine if input is cell array
* ischar %Determine if input is character array
* islogical ...

# Data access
存档读取
## File Access
- File sys to work Space

| File content |  extension    |   Description   | ImportFunction     |  Export Function    |
| ------------ | ---- | ---- | ---- | ---- |
| Matlab formatted  data | MAT | Saved matlab workspace | load | save |
| Text |      | Space delimited numbers | load | save |
| Spreadsheet | XLS,XLSX | EXCEL | xlsread | xlswrite |

**save() and load()**

* Save(all) workspace data to a file
```matlab
clear; a = magic(4);
save mydatal.mat %压缩不可编辑阅读
save mydata2.mat -ascii %可编辑和阅读

  • Load data store in a file:

    load('mydatal.mat')
load('mydata2.mat','-ascii')

    Excel File Reading : xlsread()

  • Read from Excel spreadsheet

    Score = xlsread('xxx.xlsx')
Score = xlsread('xxx.xlsx','B2:D4') %excel 的表格位置
%两个结果相同

Excel File Writing:xlswrite()

  • Calculate the means and write into Excel spreadsheet
M = mean(Score')'; %算平均值
xlswrite('04Score.xlsx',M,1,'E2:E4'); 
%xlswrite(filename,variable,sheet,location)
xlswrite('04Score.xlsx',{'Mean'},1,'E1');

Getting Text in Excel Spreadsheet

  • Getting both the text and numbers
    [Score Header]=xlsread('04Score.xlsx')

Low-level File Input/Output

  • Read and write file at the byte or character level
  • A file has an ID fid
  • Location in the file is specified by a pointer that can be moved around
Function Decription
fopen Open file,or obtain info about open files
fclose close one or all open files
fscanf read data from text file
fprintf write data to text file
feof Test for end-of-file
  • Open and close a file:
    fid = fopen('[filename]', '[permission]')
  • permission : r r+ w w+ a a+
    status = fclose(fid);
  1. Generate x ,y
  2. Open a file
  3. write x,y into file
  4. Close the file
x = 0:pi/10:pi; y=sin(x); fid=fopen('sinx.txt','w');
for i=1:11
    fprintf(fid,'%5.3f %8.4f\n',x(i),y(i));%总共数值是5个，有三个小数
end
fclose(fid); type sinx.txt

Read and write through Formatted I/O

  • Read:A = fscanf(fid,format,size);

    • Data read = Format specifier[format] Amount of data to read[size]

  • Write:fprintf(fid,format,x,y...)

  • Format specifier: %-12.5e

SPECIFIER DESCRIPTION
%c Single character
%d Decimal notation
%e Exponential notation
%f Fixed-point notation
%g The more compact of %o or%f
%o Octal notation (unsigned)
%s String of characters
%u Decimal notation(unsigned)
%x Hexadecimal notation

Reading from Files

  • Check if it is the end of file: feof(fid)
    fid = fopen('asciiData.txt','r'); i = 1;
while ~feof(fid)
  name(i,:) = fscanf(fid,'%5c',1);
  year(i) = fscanf(fid,'%d',1);
  no1(i) = fscanf(fid,'%d',1);
  no2(i) = fscanf(fid,'%d',1);
  no3(i) = fscanf(fid,'%g',1);
  no4(i) = fscanf(fid,'%g\n',1);
  i+=1;
end
fclose(fid);

Basic plotting

Basics

  • Matlab has a powerful plotting enfine that can generate a wide variety of plots

Plot from Data

  • Matlab does not understand functions
    f(t) = sin(2pit)
  • Strategies
    1. Generate the numeric values of a function over a spectfic range
    2. Display the data “points” in a graphical way

plot()

  • plot(x,y) plots each vector pairs(x,y)
  • plot(y) plots each vector pairs(x,y),where x=[1…n],n=length(y)
  • Example:
    • plot(cos(0:pi/20:2*pi))
    • plot(cos(0:pi/20:2*pi))
      plot(sin(0:pi/20:2*pi))%会刷新，把之前的图刷新掉

  • hold on/off

    • Use hold on to have both plots in one figure
      hold on
plot(cos(0:pi/20:2*pi));
plot(sin(0:pi/20:2*pi))
hold off

Plot Style

  • plot(x,y,’str’) plots each vector pairs(x,y) using the format defined in str (check linespec)
DATA MARKERS LINETYPES COLORS
Dot . solid line - Black k
Asterisk * Dashed line – Blue b
cross X Dash-dotted line -. Cyan c
circle o Dotted line : Green g
plus sign + Magenta m
square s Red r
diamond d White w
Five-pointed star p Yellow y
Traangle(down) v
Triangle(up) ^
Triangle(left)<
Triangle(right) >
Hexagram H 
```matlab

hold on
plot(cos(0:pi/20:2pi),’or–’);
plot(sin(0:pi/20:2pi),’xg:’)
hold off

```

legend()

  • Add legend to graphical
    legend('L1',...)
  • Plsition adjustment
    x=0:0.5:4*pi;
y=sin(x); h = cos(x);w=1./(1+exp(-x));
g=(1/(2*pi*2)^0.5).*exp((-1.*(x-2*pi).^2)./(2*2^2));
plot(x,y,'bd-',x,h,'gp:',x,w,'ro-',x,g,'c^-');

    legend('sin(x)','cos(x)','Sigmoid','Gauss function')

title() and ?label()

  • title() xlabel() ylabel() zlabel()
    x=0:0.1:2*pi;y1=sin(x);y2=exp(-x);
plot(x,y1,'--*',x,y2,':o');
xlabel('t=0 to 2\pi');
ylabel('values of sin(t) and e^{x}');
legend('sin(t)','e^{x}');
title('Function Plots of sin(t) and e^{x}');

text() and annotation

  • Text with mathematical expression using LaTex
    `matlab
    x = linspace(0,3); y=x.^2.sin(x); plot(x,y);
    line([2,2],[0,2^2    sin(2)]);
    str = ‘$$ \int_{0}^{2} x^2\sin(x) dx $$’;%\int为积分
    text(0.25,2.5,str,’Interpreter’,’latex’);
    %0.25,2.5为位置，str为显示字符串，后面为固定格式latex显示

annotation(‘arrow’,’X’,[0.32,0.5],’Y’,[0.6,0.4]);
%（箭头，从某点到某点）


**Figure Adjustment**
* Several properties
  * Font
  * Font size
  * Line width
  * Axis limit
  * Tick position
  * Tick label

**Graphical Object**
* A fig is composed of many objects
Figure object         Axes object            Line object
* Edit->Figure properties->more properties

**Modifying Properties of An object**
* Strategy
  1. Identify the "handle" of an object
    * Upon creation:
        `h = plot(x,y);`

| Function | Purpose                                   |
| -------- | ----------------------------------------- |
| gca      | Return the handle of the "current" axes   |
| gcf      | Return the handle of the "current" figure |
| allchild | Find all children of specified objects    |
| ancestor | Find ancestor of graphics object          |
| delete   | Delete an object                          |
| findall  | Find all graphics objects                 |

  2. Fetch or modify the object's properties

    * To fech properties ,use `get()`
    ```matlab
    x = linspace(0,2*pi,1000);
    y = sin(x); plot(x,y);
    h = plot(x,y); get(h)

```matlab
get(gca) %handle of axes
```
* To modify properties use `set()`

  • For example ,to change the lim of the x-axis

    1. Find the handle of the x-axis
    2. Modify the limits
      `matlab
      set(gca,’XLim’,[0,2*pi]);
      set(gca,’YLim’,[-1.2,1.2]);
      %xlim([1,20])

    set(gca, ‘FontSize’,20);
    set(gca,’XTick’,0:pi/2:2*pi);
    set(gca,’XTickLabel’,0:90:360);%坐标可自设

    set(gca, ‘FontName’,’symbol’);
    set(gca,’XTickLabel’{‘0’,’p/2’,’p’,’3p/2’,’2p’});
    `
    Line Specification

    • Line style and width
      set(h,'LineStyle','-.'LineWidth',7.0,'Color,'g')
      Alternative plot(x,y,'-.g','LineWidth',7.0)
    • Face and edge colors of the marker
      plot(x,'-md','LineWith',2,'MarkerEdgeColor','k','MarkerFaceColor','g','MarkerSize',10);

Multiple Figures

  • Create a figure window by calling figure
    x = -10:0.1:10;
y1 = x.^2 - 8;
y2 = exp(x);
figure,plot(x,y1);
figure,plot(x,y2);
  • Be careful when using the gcf handle where thre exists multple fig
    • Figure Position and Size
      figure('Position',[left,bottom,width,height])
  • Several Plots in One Figure
    subplot(m,n,1);
    t = 0:0.1:2*pi; x = 3*cos(t);y=sin(t);
subplot(2,2,1);plot(x,y); axis normal
subplot(2,2,2);plot(x,y); axis square %x total = y total
subplot(2,2,3);plot(x,y); axis equal %xunit和yunit一格大小同
subplot(2,2,4);plot(x,y); axis equal tight %Tight
    | Control of Grid,box,and axis | |
    | ——————————– | —————- |
    | grid on/off | axis equal |
    | axis on/off | axis equal tight |
    | axis normal | axis image |
    | axis square | azis ij /xy |

Saving Figures into Files

saveas(gcf,'<filename>','<formattype>');
  • Bitmap Image Format
    • jpeg 24-bit
    • png 24-bit
    • tiff 24-bit
    • bmpmono BMP Monochrome
    • bmp
    • bmp256 8-bit(256color,uses a fixed colormap)
  • Vector Graphics Format √
    • pdf
    • meta
    • eps
    • epsc
    • svg
    • ps
    • psc

Advanced 2D plots

  • What would you like to show?
    • Comparison
    • Relationship
    • Composition
    • Distribution

Logarithm Plots

x = logspace(-1,1,100); %x=10^(-1) ... 10^1[一共100个]
y = x.^2;
plot(x,y);
title('plot');
subplot(2,2,2);



# Color space


# 3D plots
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