Introduction to MATLAB

R Introduction to MATLAB

Duancheng Ma

Department of Microstructure Physics and Alloy Design 40237 D¨ usseldorf, Germany [email protected]

Jan. 29th , 2015

Outline Get started Variable Operation Programming I/O Graphics Toolbox Before closing

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R What MATLAB can do, Installation and Get started

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Data type and Creating variables

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Operations and Manipulations Mathematical operations Relational and Logical operations Vectors and matrices manipulations

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Programming Scripts and Functions Control flows

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File I/O (Input and Output) Reading and Writing text files R Reading and Writing Microsoft Excel files

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Graphics

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Toolbox

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Before closing

Max-Planck-Institut f¨ ur Eisenforschung, D¨ usseldorf, Germany

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R can do What MATLAB

MATLAB, MAtrix LABoratory


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MATLAB, MAtrix LABoratory Basic functionality


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MATLAB, MAtrix LABoratory Basic functionality Numerical computation: Elementary math,linear algebra, statistics, numerical calculus, Fourier analysis, optimization, ...


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Programming: Control flows, scripts and functions.


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Visualization: 2D and 3D plots.


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Applications


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Applications Analyzing and manipulating data.


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Applications Analyzing and manipulating data. Developing algorithms.


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Applications Analyzing and manipulating data. Developing algorithms. Plotting data and functions.


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Applications Analyzing and manipulating data. Developing algorithms. Plotting data and functions. Creating GUI (Graphical User Interface).


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Applications Analyzing and manipulating data. Developing algorithms. Plotting data and functions. Creating GUI (Graphical User Interface). Interfacing with programs written in other languages, such as, C, C++, Java, Python, and FORTRAN. Max-Planck-Institut f¨ ur Eisenforschung, D¨ usseldorf, Germany

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Installation

Go to public(\\mafs1):\Install\MathWorks\ Follow the instructions on http://msusrv4/msuwiki/Matlab (credit goes to Dr. Claudio Zambaldi) Latest version: Matlab R2014b Number of licenses: 14


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Get started


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Get started

Command Window where you type your commands and see results


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Get started


Workspace where you see the existing variables


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Get started

Current Folder where you see the contents


in the current folder



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Get started Current directory






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Get started New Script


Current directory





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MATLAB editor

Write a script or a function The script or function file extension .m (m files)


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MATLAB editor

Write a script or a function The script or function file extension .m (m files) file name, * means not saved


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MATLAB editor


comment line, starting with %


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MATLAB editor


comment line, starting with % command lines


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MATLAB editor

Write a script or a function The script or function file extension .m (m files) real-time error check

file name, * means not saved

OK Warning Error



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Data types of variables No need to declare the data type of a variable.


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Data types of variables No need to declare the data type of a variable. Basic data types (you will use most of the time)


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Data types of variables No need to declare the data type of a variable. Basic data types (you will use most of the time) numeric types integer and floating-point data.


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Data types of variables No need to declare the data type of a variable. Basic data types (you will use most of the time) numeric types integer and floating-point data. characters and strings letters in single quotation marks, e.g. ’Hello world’


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Data types of variables No need to declare the data type of a variable. Basic data types (you will use most of the time) numeric types integer and floating-point data. characters and strings letters in single quotation marks, e.g. ’Hello world’ cell arrays contains different types and size, e.g. {’Hello’ 5 [1.1 3.0]}


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Other data types:


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Other data types: handle a reference to an object, such as, a function, or a figure


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Other data types: handle a reference to an object, such as, a function, or a figure structure group related data in fieldName, structName.fieldName Max-Planck-Institut f¨ ur Eisenforschung, D¨ usseldorf, Germany

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Other data types: handle a reference to an object, such as, a function, or a figure structure group related data in fieldName, structName.fieldName ... Max-Planck-Institut f¨ ur Eisenforschung, D¨ usseldorf, Germany

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Creating a variable Just assign a value to a name, e.g. (in command window) >> a=1 a= 1


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Creating a variable Just assign a value to a name, e.g. (in command window) >> a=1 a= 1 Variable name: must start with a letter,


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Creating a variable Just assign a value to a name, e.g. (in command window) >> a=1 a= 1 Variable name: must start with a letter, after that, letters, numbers and


(underscore), no others,

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Creating a variable Just assign a value to a name, e.g. (in command window) >> a=1 a= 1 Variable name: must start with a letter, after that, letters, numbers and (underscore), no others, case sensitive, e.g. a is different from A.


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Creating a variable Just assign a value to a name, e.g. (in command window) >> a=1 a= 1 Variable name: must start with a letter, after that, letters, numbers and (underscore), no others, case sensitive, e.g. a is different from A.

Avoid using the following names, as they are built-in variables i and j are imaginary unit Inf is positive infinity, -Inf is negative infinity pi is π, ratio of circle’s circumference to its diameter NaN means “Not a Number” ans the last value which is not assigned, like on a calculator Max-Planck-Institut f¨ ur Eisenforschung, D¨ usseldorf, Germany

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Creating scalar variables Explicitly assigned: >> a=1 a= 1 Function of existing variables and/or explicit values: >> b=1+a b= 2


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Creating scalar variables Explicitly assigned: >> a=1 a= 1 Function of existing variables and/or explicit values: >> b=1+a b= 2 End the command line with a semicolon to suppress output in the command window: >> b=1+a; >>


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Creating vector variables Row vector: in brackets, values are separated by comma or space. >> r=[1,2,3,4]; >> r=[1 2 3 4] r= 1234 Column vector: in brackets, values are separated by semicolon. >> c=[1;2;3;4] c= 1 2 3 4 Max-Planck-Institut f¨ ur Eisenforschung, D¨ usseldorf, Germany

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Creating matrix variables Similar to creating vectors, use semicolon to start a new row. >> A=[1 2;3 4] A= 1 2 3 4


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Creating matrix variables Similar to creating vectors, use semicolon to start a new row. >> A=[1 2;3 4] A= 1 2 3 4 Putting vectors and/or matrices together >> a=[1 2]; >> b=[3 4];


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Creating matrix variables Similar to creating vectors, use semicolon to start a new row. >> A=[1 2;3 4] A= 1 2 3 4 Putting vectors and/or matrices together >> a=[1 2]; >> b=[3 4]; >> A=[a;b] A= 1 2 3 4


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Creating matrix variables Similar to creating vectors, use semicolon to start a new row. >> A=[1 2;3 4] A= 1 2 3 4 Putting vectors and/or matrices together >> a=[1 2]; >> b=[3 4]; >> A=[a;b] A= 1 2 3 4 >> r=[a b] r= 1234 Max-Planck-Institut f¨ ur Eisenforschung, D¨ usseldorf, Germany

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Automatically creating vector and matrix variables Special matrices, zeros, ones, and eye


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Automatically creating vector and matrix variables Special matrices, zeros, ones, and eye >> A=zeros(3,2) A= 0 0 0 0 0 0


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Automatically creating vector and matrix variables Special matrices, zeros, ones, and eye >> A=zeros(3,2) >> A=ones(2,3) A= A= 0 0 1 1 1 0 0 1 1 1 0 0


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>> A=eye(3,3) A= 1 0 0 0 1 0 0 0 1




>> A=eye(3,3) A= 1 0 0 0 1 0 0 0 1

Random numbers between 0 and 1, rand >> A=rand(1,4) A= 0.9134 0.2785 0.9649 0.1576


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>> A=eye(3,3) A= 1 0 0 0 1 0 0 0 1

Random numbers between 0 and 1, rand >> A=rand(1,4) A= 0.9134 0.2785 0.9649 0.1576 linear spaced values, : (colon)


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>> A=eye(3,3) A= 1 0 0 0 1 0 0 0 1

Random numbers between 0 and 1, rand >> A=rand(1,4) A= 0.9134 0.2785 0.9649 0.1576 linear spaced values, : (colon) >> a=1:1:4 a= 1 2 3 4 Max-Planck-Institut f¨ ur Eisenforschung, D¨ usseldorf, Germany

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>> A=eye(3,3) A= 1 0 0 0 1 0 0 0 1

Random numbers between 0 and 1, rand >> A=rand(1,4) A= 0.9134 0.2785 0.9649 0.1576 linear spaced values, : (colon) >> a=1:1:4 a= 1 2 3 4 Max-Planck-Institut f¨ ur Eisenforschung, D¨ usseldorf, Germany

>> a=1:4 a= 1 2 3 Duancheng Ma,

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Creating character and string variables Similar to creating numeric variables, assign a value to a name, must be in single quotation marks >> s=’Hello world’ s= Hello world


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Creating character and string variables Similar to creating numeric variables, assign a value to a name, must be in single quotation marks >> s=’Hello world’ s= Hello world Use sprintf(format,variable),


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Creating character and string variables Similar to creating numeric variables, assign a value to a name, must be in single quotation marks >> s=’Hello world’ s= Hello world Use sprintf(format,variable), >> s=sprintf(’Base of the natural logarithm is %f’,exp(1)) s= Base of the natural logarithm is 2.718282


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Creating character and string variables Similar to creating numeric variables, assign a value to a name, must be in single quotation marks >> s=’Hello world’ s= Hello world Use sprintf(format,variable), >> s=sprintf(’Base of the natural logarithm is %f’,exp(1)) s= Base of the natural logarithm is 2.718282 >> s=sprintf(’In Excel the index starts with %s%d’,65,1) s= In Excel the index starts with A1 Max-Planck-Institut f¨ ur Eisenforschung, D¨ usseldorf, Germany

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Save and Load variables

>> save saved file a b save variables a b in saved file.mat in the current folder

>> load saved file load variables stored in saved file.mat stored variables a and b appear in the workspace


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Outline Get started Variable Operation Programming I/O Graphics Toolbox Before closing Mathematical operations Relational and Logical operations Vectors and matrices manipulations

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Operations on scalars Arithmetic operations: + Exponentiation:

-

*

/

∧

Parentheses for complicated expressions: ( ) Built-in functions: e.g. (a is a scalar) √

a >> sqrt(a) ln (a) >> log(a) log10 (a) >> log10(a) exp (a) >> exp(a) cos (a) >> cos(a) % a in radians >> cosd(a) % a in degree ... ... all you can think of, but be careful, check the documentation to make sure Max-Planck-Institut f¨ ur Eisenforschung, D¨ usseldorf, Germany

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Transpose vectors and matrices Transpose: transpose(a), .0 , or >> a=[1 2 3]; >> transpose(a) ans= 1 2 3

0

>> a.0 ans= 1 2 3


>> a0 ans= 1 2 3

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Transpose vectors and matrices Transpose: transpose(a), .0 , or >> a=[1 2 3];

0

>> transpose(a) >> a.0 >> a0 ans= ans= ans= 1 1 1 2 2 2 3 3 3 Transpose complex numbers, be careful with 0 , it gives Hermitian-transpose >> a=[1 2 3+i]; >> transpose(a) ans= 1 2 3+i

>> a.0 ans= 1 2 3+i


>> a0 ans= 1 2 3-i Duancheng Ma,



Operations on vectors and matrices Standard operation and element-wise operation >> a=[a1 a2]; >> b=[b1 b2];


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Operations on vectors and matrices Standard operation and element-wise operation >> a=[a1 a2]; >> b=[b1 b2]; Standard >> a*b >> a*b0

⇒ a1 a2 · b1 b2 , wrong b1 ⇒ a1 a2 · =a1·b1+a2·b2, dot product b2


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Operations on vectors and matrices Standard operation and element-wise operation >> a=[a1 a2]; >> b=[b1 b2]; Standard >> a*b

⇒ a1 a2 · b1 b2 , wrong b1 ⇒ a1 a2 · =a1·b1+a2·b2, dot product >> a*b0 b2 Element-wise, use dot . >> a.*b ⇒ a1 · b1 a2 · b2 >> a./b ⇒ a1/b1 a2/b2 >> a.∧ 2 ⇒ a12 a22


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Operations on vectors and matrices Standard operation and element-wise operation >> a=[a1 a2]; >> b=[b1 b2]; Standard >> a*b

⇒ a1 a2 · b1 b2 , wrong b1 ⇒ a1 a2 · =a1·b1+a2·b2, dot product >> a*b0 b2 Element-wise, use dot . >> a.*b ⇒ a1 · b1 a2 · b2 >> a./b ⇒ a1/b1 a2/b2 >> a.∧ 2 ⇒ a12 a22

Built-in functions, if the function works for scalars, then it operates on vectors and matrices by element-wise >> sqrt(A) >> sqrtm(A)

⇒ square root of each element ⇒ square root of the matrix


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inverse and left side division

      A11 A12 A13 x1 b1 A21 A22 A23  · x2  = b2  A31 A32 A33 x3 b3

  A11 A12 A13 A = A21 A22 A23  A31 A32 A33

  x1 x = x2  x3

  b1 b = b2  b3

Use inverse of matrix A:

Use left side division:

>> x=inv(A)*b

>> x=A\b


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Relational and logical operations Relational operation less than < greater than > less or equal = equal == not equal ∼= Logical operation and & && (short circuit) or | || (short circuit) exclusive or xor not ∼ all all any any Boolean values: zero is false, non-zero is true. Max-Planck-Institut f¨ ur Eisenforschung, D¨ usseldorf, Germany

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Relational and logical operations

>> a=[3 2 8 5]; >> b=[7 1 4 5]; >> a>b ans= 0 1 1 0 >> a==b ans= 0 0 0 1


>> a=[2 0 3 0]; >> b=[4 1 0 0]; >> a&b ans= 1 0 0 0 >> a|b ans= 1 1 1 0

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Indexing the vectors

Indices must be real positive non-zero integers, e.g. 1, 2, 3, 4,...


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Indices must be real positive non-zero integers, e.g. 1, 2, 3, 4,... Accessing individual elements of a vector, a(n) returns nth element of the vector a. >> a=[1 2 3 4 5 6 7];

>> a(1) ans= 1


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>> a(1) ans= 1

use linear spaced value >> a(2:1:4) ans= 2 3 4


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>> a(1) ans= 1

use linear spaced value >> a(2:1:4) ans= 2 3 4


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use another vector >> a([2 4]) ans= 2 4



Indexing the matrices >> A=[1 2 3;4 5 6;7 8 9] A= 1 2 3 4 5 6 7 8 9


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Indexing the matrices >> A=[1 2 3;4 5 6;7 8 9] A= 1 2 3 4 5 6 7 8 9 A(n,m) returns element of the matrix A on nth row and mth column. >> A(2,3) >> A(2,2:1:3) >> A(:,2:1:3) ans= ans= ans= 6 5 6 2 3 5 6 8 9


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Indexing the matrices >> A=[1 2 3;4 5 6;7 8 9] A= 1 2 3 4 5 6 7 8 9 A(n,m) returns element of the matrix A on nth row and mth column. >> A(2,3) >> A(2,2:1:3) >> A(:,2:1:3) ans= ans= ans= 6 5 6 2 3 5 6 8 9 th A(n) returns n element of the matrix A. >> A(2) >> A(1:1:3) ans= ans= 4 1 4 7 Max-Planck-Institut f¨ ur Eisenforschung, D¨ usseldorf, Germany

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Command sort to sort vectors and matrices >> a=[2 4 1 5 6 3] a= 2 4 1 5

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Sorting the vector a in the ascending order, >> sort(a) ans= 1 2 3 4 5 6


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Sorting the vector a in the ascending order, >> sort(a) ans= 1 2 3 4 5 6 Getting the arrangement, i.e. indices in the sorted vector, >> [as, as ix]=sort(a) as= 1 2 3 4 5 6 as ix= 3 1 6 2 4 5


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Sorting the vector a in the ascending order, >> sort(a) ans= 1 2 3 4 5 6 Getting the arrangement, i.e. indices in the sorted vector, >> [as, as ix]=sort(a) as= 1 2 3 4 5 6 as ix= 3 1 6 2 4 5 Sorting the vector a in the descending order, sort(a,’descend’), Max-Planck-Institut f¨ ur Eisenforschung, D¨ usseldorf, Germany

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Sorting the vector a in the ascending order, >> sort(a) ans= 1 2 3 4 5 6 Getting the arrangement, i.e. indices in the sorted vector, >> [as, as ix]=sort(a) as= 1 2 3 4 5 6 as ix= 3 1 6 2 4 5 Sorting the vector a in the descending order, sort(a,’descend’), For matrices, sort is to sort each column. Max-Planck-Institut f¨ ur Eisenforschung, D¨ usseldorf, Germany

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Command find >> a=[2 4 1 5 6 3 1] a= 2 4 1 5

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Finding the value 1 in vector a, >> find(a==1) ans= 3 7 =⇒the 3rd and 7th element in vector a are 1.


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Command find >> a=[2 4 1 5 6 3 1] a= 2 4 1 5

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Finding the value 1 in vector a, >> find(a==1) ans= 3 7 =⇒the 3rd and 7th element in vector a are 1. Finding the value 4 or 5 in vector a, >> find(a==4 | a==5) ans= 2 4 =⇒the 2nd and 4th element in vector a is 4 or 5.


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Command find >> A=[5 4 1 ;2 6 3] A= 5 4 1 2 6 3 Finding the value 4 in matrix A, >> find(A==4) ans= 3 =⇒the 3rd element in matrix A is 4.


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Command find >> A=[5 4 1 ;2 6 3] A= 5 4 1 2 6 3 Finding the value 4 in matrix A, >> find(A==4) ans= 3 =⇒the 3rd element in matrix A is 4. >> [r, c]=find(A==4) r= 1 =⇒on 1st row c= 2 =⇒on 2rd column. Max-Planck-Institut f¨ ur Eisenforschung, D¨ usseldorf, Germany

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Outline Get started Variable Operation Programming I/O Graphics Toolbox Before closing Scripts and Functions Control flows R MATLAB

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What

can do, Installation and Get started

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Graphics

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Toolbox

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Before closing


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Outline Get started Variable Operation Programming I/O Graphics Toolbox Before closing Scripts and Functions Control flows

Starting MATLAB editor Current directory






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Starting MATLAB editor New Script


Current directory





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MATLAB script

A script is a collection of commands which executed in sequence real-time error check

file name, * means not saved

OK Warning Error



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MATLAB script

A script is a collection of commands which executed in sequence real-time error check

file name, * means not saved Press to run

OK Warning Error

?



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MATLAB function

A function can be called in a script, another function, or in the Command windows. Max-Planck-Institut f¨ ur Eisenforschung, D¨ usseldorf, Germany

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MATLAB function

it starts with function


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MATLAB function

declare the function

[output arg1,output arg2,...]=function name(input arg1,input arg2,...) Max-Planck-Institut f¨ ur Eisenforschung, D¨ usseldorf, Germany

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MATLAB function

file name function name

The file name and the function name should be the same. Max-Planck-Institut f¨ ur Eisenforschung, D¨ usseldorf, Germany

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MATLAB function

help contents

>> help data =⇒ help contents appear in command window. Max-Planck-Institut f¨ ur Eisenforschung, D¨ usseldorf, Germany

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MATLAB function

code


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Call MATLAB function

If you want to call your MATLAB functions, make sure, The function file is in the Current directory.

OR The folder where the function file is is in the search path. Home tab⇒Environment section⇒Set Path


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Set Path Set Path


Current directory





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Control flow: if/elseif/else

if conditional command end

if conditional command else conditional command end

if conditional command elseif conditional command else conditional command end

conditional is evaluated to be true or false, execute when true,


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Control flow: for and while loop for Index=initVal:step:endVal command end


while conditional command end

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e.g. to calculate 5! i.e. 1×2×3×4×5=120


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e.g. to calculate 5! i.e. 1×2×3×4×5=120 a=1; for n=1:1:5 a=a*n; end


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e.g. to calculate 5! i.e. 1×2×3×4×5=120 a=1; for n=1:1:5 a=a*n; end


a=1;n=1; while n class(c) =⇒ check data type of c ans= cell


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Outline Get started Variable Operation Programming I/O Graphics Toolbox Before closing R Reading and Writing text files Reading and Writing Microsoft Excel files

data.txt Reading Y=X∧ 2 X Y 1 1 2 4 3 9 4 16 5 25 6 36 7 49 8 64 9 81 10 100 11 121 12 144

>> class(c) =⇒ check data type of c ans= cell >> size(c) ans= 1 2 =⇒ c has one row and two columns


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>> class(c) =⇒ check data type of c ans= cell >> size(c) ans= 1 2 =⇒ c has one row and two columns >> c(1) =⇒ use () to access the 1st element in c


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>> class(c) ans= cell >> size(c) ans= 1 2 >> c(1) ans= [12x1 int32]

=⇒ check data type of c

=⇒ c has one row and two columns =⇒ use () to access the 1st element in c =⇒ the 1st element in c is a vector, it has 12 rows and 1 column, its data type is 32-bit signed integer.


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>> class(c) ans= cell >> size(c) ans= 1 2 >> c(1) ans= [12x1 int32] >> c{1} ans= 1 2 .. . 11 12

=⇒ check data type of c

=⇒ c has one row and two columns =⇒ use () to access the 1st element in c =⇒ the 1st element in c is a vector, it has 12 rows and 1 column, its data type is 32-bit signed integer. =⇒ use {} to access the 1st element in c


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data.txt Writing


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data.txt Writing Y=X∧ 2 X Y 1 1 2 4 3 9 4 16 5 25 6 36 7 49 8 64 9 81 10 100 11 121 12 144 Max-Planck-Institut f¨ ur Eisenforschung, D¨ usseldorf, Germany

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data.txt Writing Y=X∧ 2 X Y 1 1 2 4 3 9 4 16 5 25 6 36 7 49 8 64 9 81 10 100 11 121 12 144

fid=fopen(’data.txt’,’w’);


=⇒ open the file to write - permission, ’w’ is to write - file name, in single quotation marks - file ID

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X=1:1:12=⇒ prepare X data, linear spaced Y=X.∧ 2 =⇒ prepare Y data, element-wise operation


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X=1:1:12=⇒ prepare X data, linear spaced Y=X.∧ 2 =⇒ prepare Y data, element-wise operation fprintf(fid,’Y=X.∧ 2\n’); =⇒ write the first line


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X=1:1:12=⇒ prepare X data, linear spaced Y=X.∧ 2 =⇒ prepare Y data, element-wise operation fprintf(fid,’Y=X.∧ 2\n’); =⇒ write the first line


-format, in single quotation marks -file ID \n is to switch to a new line

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X=1:1:12=⇒ prepare X data, linear spaced Y=X.∧ 2 =⇒ prepare Y data, element-wise operation fprintf(fid,’Y=X.∧ 2\n’); =⇒ write the first line -format, in single quotation marks -file ID \n is to switch to a new line

fprintf(fid,’X Y\n’);


=⇒ write the second line

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for n=1:1:length(X) fprintf(fid,’%d %d\n’,X(n),Y(n)); end


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for n=1:1:length(X) fprintf(fid,’%d %d\n’,X(n),Y(n)); end


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for n=1:1:length(X) fprintf(fid,’%d %d\n’,X(n),Y(n)); end fclose(fid);


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R Excel files Reading and Writing Microsoft

data=xlsread(file name,sheet name,data range) data, numeric type, file name and sheet name, string, e.g. ’data.xlsx’ and ’Sheet1’, data range, string, e.g. ’A1:C10’.

xlswrite(file name,M,sheet name,data range) M, a matrix.


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R graphics overview MATLAB

2D plots Line graphs Bar graphs Area graphs Direction graphs Radial graphs Scatter graphs

3D plots Line Graphs Mesh Graphs and Bar Graphs Area Graphs and Constructive Objects Surface Graphs Direction Graphs Volumetric Graphs


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R graphics overview MATLAB

2D plots Line graphs: plot and plotyy Bar graphs: bar and hist Area graphs Direction graphs Radial graphs Scatter graphs

3D plots Line Graphs Mesh Graphs and Bar Graphs Area Graphs and Constructive Objects Surface Graphs: surf Direction Graphs Volumetric Graphs


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Line plot: plot >>x=1:1:12; >>y=x.∧ 2;


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Line plot: plot >>x=1:1:12; >>y=x.∧ 2; >>plot(x,y);


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Line plot: plot >>x=1:1:12; >>y=x.∧ 2; >>plot(x,y); >>plot(x,y,’Color’,’red’);


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Line plot: plot >>x=1:1:12; >>y=x.∧ 2; >>plot(x,y); >>plot(x,y,’Color’,’red’); >>plot(x,y,’Color’,’red’,’Marker’,’o’);


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Line plot: plot >>x=1:1:12; >>y=x.∧ 2; >>plot(x,y); >>plot(x,y,’Color’,’red’); >>plot(x,y,’Color’,’red’,’Marker’,’o’); >>xlabel(’x’);


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Line plot: plot >>x=1:1:12; >>y=x.∧ 2; >>plot(x,y); >>plot(x,y,’Color’,’red’); >>plot(x,y,’Color’,’red’,’Marker’,’o’); >>xlabel(’x’); >>ylabel(’y’);


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Line plot: plot >>x=1:1:12; >>y=x.∧ 2; >>plot(x,y); >>plot(x,y,’Color’,’red’); >>plot(x,y,’Color’,’red’,’Marker’,’o’); >>xlabel(’x’); >>ylabel(’y’); >>y1=x.∧ 3;


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Line plot: plot >>x=1:1:12; >>y=x.∧ 2; >>plot(x,y); >>plot(x,y,’Color’,’red’); >>plot(x,y,’Color’,’red’,’Marker’,’o’); >>xlabel(’x’); >>ylabel(’y’); >>y1=x.∧ 3; >>hold on;=⇒new plot on existing plot


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Line plot: plot >>x=1:1:12; >>y=x.∧ 2; >>plot(x,y); >>plot(x,y,’Color’,’red’); >>plot(x,y,’Color’,’red’,’Marker’,’o’); >>xlabel(’x’); >>ylabel(’y’); >>y1=x.∧ 3; >>hold on;=⇒new plot on existing plot >>plot(x,y1,’Color’,’black’,’Marker’,’s’);


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Line plot: plot >>x=1:1:12; >>y=x.∧ 2; >>plot(x,y); >>plot(x,y,’Color’,’red’); >>plot(x,y,’Color’,’red’,’Marker’,’o’); >>xlabel(’x’); >>ylabel(’y’); >>y1=x.∧ 3; >>hold on;=⇒new plot on existing plot >>plot(x,y1,’Color’,’black’,’Marker’,’s’); >>legend({’x∧ 2’ ’x∧ 3’});


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Line plot: plot >>x=1:1:12; >>y=x.∧ 2; >>plot(x,y); >>plot(x,y,’Color’,’red’); >>plot(x,y,’Color’,’red’,’Marker’,’o’); >>xlabel(’x’); >>ylabel(’y’); >>y1=x.∧ 3; >>hold on;=⇒new plot on existing plot >>plot(x,y1,’Color’,’black’,’Marker’,’s’); >>legend({’x∧ 2’ ’x∧ 3’}); >>legend({’x∧ 2’ ’x∧ 3’},’Location’,’NorthWest’);


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Line plot: plot >>x=1:1:12; >>y=x.∧ 2; 1800

>>plot(x,y);

x2 x3

1600

>>plot(x,y,’Color’,’red’);

1400

>>plot(x,y,’Color’,’red’,’Marker’,’o’);

1200

1000

y

>>xlabel(’x’); >>ylabel(’y’); >>y1=x.∧ 3;

800

600

400

>>hold on;=⇒new plot on existing plot >>plot(x,y1,’Color’,’black’,’Marker’,’s’);

200

0 0

2

4

6

8

10

x

>>legend({’x∧ 2’ ’x∧ 3’}); >>legend({’x∧ 2’ ’x∧ 3’},’Location’,’NorthWest’); >>print(’-dpdf’,’-r1000’,’plot.pdf’)=⇒print the figure to pdf


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Line plot: plotyy (y on both left and right) >>x=1:1:12; >>y=x.∧ 2; >>y1=x.∧ 3;


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Line plot: plotyy (y on both left and right) >>x=1:1:12; >>y=x.∧ 2; >>y1=x.∧ 3; >>[ax,h1,h2]=plotyy(x,y1,x,y); get two axes handles (ax) and two graphic objects handles (h1 and h2)


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What are in these handles? >>get(h1)=⇒properties of the blue curve


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6 property

6 value


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What are in these handles? >>get(h1)=⇒properties of the blue curve >>get(h1,’Marker’) >>ans = none


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What are in these handles? >>get(h1)=⇒properties of the blue curve >>get(h1,’Marker’) >>ans = none >>set(h1,’Marker’,’o’);


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What are in these handles? >>get(h1)=⇒properties of the blue curve >>get(h1,’Marker’) >>ans = none >>set(h1,’Marker’,’o’); >>set(h1,’LineStyle’,’–’);


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What are in these handles? >>get(h1)=⇒properties of the blue curve >>get(h1,’Marker’) >>ans = none >>set(h1,’Marker’,’o’); >>set(h1,’LineStyle’,’–’); >>set(h1,’Color’,’black’);


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What are in these handles? >>get(h1)=⇒properties of the blue curve >>get(h1,’Marker’) >>ans = none >>set(h1,’Marker’,’o’); >>set(h1,’LineStyle’,’–’); >>set(h1,’Color’,’black’); >>set(ax(1),’YColor’,’black’);


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Bar plot: bar

>>a=rand(1,5); =⇒get 5 random numbers


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Bar plot: bar

>>a=rand(1,5); =⇒get 5 random numbers >>h=bar(a); get the graphic object handle (h)


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Bar plot: bar

>>a=rand(1,5); =⇒get 5 random numbers >>h=bar(a); get the graphic object handle (h) >>set(h,’FaceColor’,’white’);


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Bar plot: bar

>>a=rand(1,5); =⇒get 5 random numbers >>h=bar(a); get the graphic object handle (h) >>set(h,’FaceColor’,’white’); >>set(h,’EdgeColor’,’blue’);


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Bar plot: bar

>>a=rand(1,5); =⇒get 5 random numbers >>h=bar(a); get the graphic object handle (h) >>set(h,’FaceColor’,’white’); >>set(h,’EdgeColor’,’blue’); >>XTL={’1st’ ’2nd’ ’3rd’ ’4th’ ’5th’}; >>set(gca,’XTickLabel’,XTL); get the current axes handle (gca)


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Bar plot: hist for probability and statistics >>a=randn(1,1e4); =⇒get 104 random numbers following normal distribution


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Bar plot: hist for probability and statistics >>a=randn(1,1e4); =⇒get 104 random numbers following normal distribution >>subplot(1,2,1);=⇒ multiple plots


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Bar plot: hist for probability and statistics >>a=randn(1,1e4); =⇒get 104 random numbers following normal distribution >>subplot(1,2,1);=⇒ multiple plots >>hist(a);


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Bar plot: hist for probability and statistics >>a=randn(1,1e4); =⇒get 104 random numbers following normal distribution >>subplot(1,2,1);=⇒ multiple plots >>hist(a); >>hist(a,100);=⇒ 100 bins


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Bar plot: hist for probability and statistics >>a=randn(1,1e4); =⇒get 104 random numbers following normal distribution >>subplot(1,2,1);=⇒ multiple plots >>hist(a); >>hist(a,100);=⇒ 100 bins >>subplot(1,2,2);


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Bar plot: hist for probability and statistics >>a=randn(1,1e4); =⇒get 104 random numbers following normal distribution >>subplot(1,2,1);=⇒ multiple plots >>hist(a); >>hist(a,100);=⇒ 100 bins >>subplot(1,2,2); >>[c,x]=hist(a,100);=⇒ no figure is plotted c, counts, x, center of bins.


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Bar plot: hist for probability and statistics >>a=randn(1,1e4); =⇒get 104 random numbers following normal distribution >>subplot(1,2,1);=⇒ multiple plots >>hist(a); >>hist(a,100);=⇒ 100 bins >>subplot(1,2,2); >>[c,x]=hist(a,100);=⇒ no figure is plotted c, counts, x, center of bins. >>plot(x,c);=⇒ line graph


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Surface plot: surf

>>x=0:0.01:2*pi; >>y=0:0.01:2*pi; >>for n=1:1:length(x) >> >> >>

for m=1:1:length(y) z(n,m)=cos(x(n))+sin(y(m)); end

>>end=⇒get z=cos(x)+sin(y)


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Surface plot: surf



>>end=⇒get z=cos(x)+sin(y) >>hs=surf(x,y,z);=⇒ get surface handle (hs)


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Surface plot: surf



>>end=⇒get z=cos(x)+sin(y) >>hs=surf(x,y,z);=⇒ get surface handle (hs) >>set(hs,’LineStyle’,’none’);


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Surface plot: surf



>>end=⇒get z=cos(x)+sin(y) >>hs=surf(x,y,z);=⇒ get surface handle (hs) >>set(hs,’LineStyle’,’none’); >>colorbar


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Surface plot: surf

>>x=0:0.01:2*pi; >>y=0:0.01:2*pi; >>for n=1:1:length(x) >>

for m=1:1:length(y)

>> >>

z(n,m)=cos(x(n))+sin(y(m)); end

>>end=⇒get z=cos(x)+sin(y) >>hs=surf(x,y,z);=⇒ get surface handle (hs) >>set(hs,’LineStyle’,’none’); >>colorbar >>light


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Surface plot: surf

>>x=0:0.01:2*pi; >>y=0:0.01:2*pi; >>for n=1:1:length(x) >>

for m=1:1:length(y)

>> >>

z(n,m)=cos(x(n))+sin(y(m)); end

>>end=⇒get z=cos(x)+sin(y) >>hs=surf(x,y,z);=⇒ get surface handle (hs) >>set(hs,’LineStyle’,’none’); >>colorbar >>light >>colormap hsv


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Graphics

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Toolbox

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Before closing


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What are the toolboxes?


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Toolboxes are additions to MATLAB, which means you need to pay extra for them.


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Toolboxes are additions to MATLAB, which means you need to pay extra for them. Each toolbox is for a specific purpose,


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Toolboxes are additions to MATLAB, which means you need to pay extra for them. Each toolbox is for a specific purpose, Each toolbox contains a collection (library) of functions, and usually a graphical user interface.


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Where are the toolboxes?






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Where are the toolboxes? APPS






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Where are the toolboxes?






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Where are the toolboxes? list of toolboxes






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Available licensed toolboxes number of licenses Mathematics, statistics and optimization Optimization Global Optimization Neural Network Partial Differential Equation Statistics Curve Fitting Symbolic Math Image Processing and Computer Vision Image Processing Signal Processing and Communications Signal Processing DSP System Communications Max-Planck-Institut f¨ ur Eisenforschung, D¨ usseldorf, Germany

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3 N/A N/A 1 2 3 1 4 1 1 1 R Introduction to MATLAB


Available licensed toolboxes number of licenses Mathematics, statistics and optimization Optimization Global Optimization Neural Network Partial Differential Equation Statistics Curve Fitting Symbolic Math Image Processing and Computer Vision Image Processing Signal Processing and Communications Signal Processing DSP System Communications Max-Planck-Institut f¨ ur Eisenforschung, D¨ usseldorf, Germany

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3 N/A N/A 1 2 3 1 4 1 1 1 R Introduction to MATLAB


Click Curve Fitting icon Curve Fitting






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Curve fitting toolbox graphic interface


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Data for fitting

must be in workspace


Fitting function

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Data for fitting

Fitting function


Fitted coefficients Goodness‐of‐fit

Figure plotting fitting data and function


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Data for fitting x=1:1:12; y=x.∧ 2;

Fitting function


f(x)=p1*x+p2

Fitted coefficients Goodness‐of‐fit Goodness of fit SSE=1335 P SSE= i (yi − f (xi ))2



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Data for fitting x=1:1:12; y=x.∧ 2;


Fitting function

f(x)=p1*x∧ 3+p2*x∧ 2+p3*x+p4

Fitted coefficients Goodness‐of‐fit Goodness of fit SSE=1.314e-27 P SSE= i (yi − f (xi ))2



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Curve fitting toolbox graphic interface FileGenerateCode

Data for fitting

Fitting function


Fitted coefficients Goodness‐of‐fit



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Generated code


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Generated code

function [fitresult,gof]=createFit(x,y)


-

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Generated code


-

fitresult: Curve fit object data type gof: structure data type


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Generated code


-

fitresult: Curve fit object data type gof: structure data type >>coeffvalues(fitresult) =⇒get the fitted coefficients type “help cfit” in command window for a complete list of methods


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Generated code


-

fitresult: Curve fit object data type gof: structure data type >>coeffvalues(fitresult) =⇒get the fitted coefficients type “help cfit” in command window for a complete list of methods >>gof.sse =⇒get SSE of goodness of fit


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Graphics

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Toolbox

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Before closing


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Before closing R MATLAB documentation is very well written, and you can learn most of the functions by yourself.


Duancheng Ma,



Before closing R MATLAB documentation is very well written, and you can learn most of the functions by yourself. R The library of the built-in functions of MATLAB is very large, which meets most of your requirements.


Duancheng Ma,



Before closing R MATLAB documentation is very well written, and you can learn most of the functions by yourself. R The library of the built-in functions of MATLAB is very large, which meets most of your requirements. In case what you need is missing in the built-in function library, try your luck at http://mathworks.com/matlabcentral/fileexchange/.


Duancheng Ma,



Before closing R MATLAB documentation is very well written, and you can learn most of the functions by yourself. R The library of the built-in functions of MATLAB is very large, which meets most of your requirements. In case what you need is missing in the built-in function library, try your luck at http://mathworks.com/matlabcentral/fileexchange/. R MATLAB now has the capability of handling symbolic math R through Symbolic Math Toolbox . It seems, however, it is R

not as powerful as Mathematica (http://en.wikipedia.org/wiki/List of computer algebra systems).


Duancheng Ma,



Before closing R MATLAB documentation is very well written, and you can learn most of the functions by yourself. R The library of the built-in functions of MATLAB is very large, which meets most of your requirements. In case what you need is missing in the built-in function library, try your luck at http://mathworks.com/matlabcentral/fileexchange/. R MATLAB now has the capability of handling symbolic math R through Symbolic Math Toolbox . It seems, however, it is R

not as powerful as Mathematica (http://en.wikipedia.org/wiki/List of computer algebra systems). R “An Introduction to MATLAB Programming and Numerical Methods for Engineers” (2015) by Timmy Siauw and Alexandre Bayen, http://www.sciencedirect.com/science/book/9780124202283 Max-Planck-Institut f¨ ur Eisenforschung, D¨ usseldorf, Germany

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R Open sources: alternatives to MATLAB

Some open sources for scientific computing: IPython http://ipython.org/notebook.html Sage http://www.sagemath.org/ https://cloud.sagemath.com/ Pyzo http://www.pyzo.org/index.html Julia http://julialang.org/ SciPy http://wiki.scipy.org/SciPy GUN Octave https://www.gnu.org/software/octave/


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Thank you for your attention and have fun R ! with MATLAB


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