MATLAB Historical Overview Historical Overview

MATLAB

Adapted from various sources, with main origin MathWorks

Historical Overview

• Short for “matrix laboratory”.

• Invented in 1970’s by Cleve Moler, chairman of CS dept. at University of New Mexico.

• Originally designed to provide students access to LINPACK and EISPACK without learning to LINPACK and EISPACK without learning Fortran

• Numerical computing environment and programming language.

• Spread to other universities and found a strong audience within the applied mathematics community.

Historical Overview (cont.)

• Jack Little joined Cleve and Steve Bangert to found The MathWorks in 1984 and a developed C rewrite of MATLAB.

• MATLAB was first adopted by control design engineers, Little's specialty, but quickly spread to many other domains.domains.

• It is now also used in education, in particular the teaching of linear algebra and numerical analysis, and is popular amongst scientists involved with image processing.

• MATLAB origins video by Cleve:• http://www.mathworks.com/company/newsletters/news_notes/clevescorner/dec04.html

Overview

• MATLAB began with 80 functions – simple matrix calculator, portable machine graphics

• NOW it has over 8000 functions• NOW it has over 8000 functions

• MATLAB engines incorporated the LAPACK and BLAS libraries, embedding the state of the art software for matrix computation.

Overview

• MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation. Typical uses include

• Math and computation• Math and computation

• Algorithm development

• Data acquisition

• Modeling, simulation, and prototyping

• Data analysis, exploration, and visualization

• Scientific and engineering graphics

• Application development, including graphical user interface building

Overview (cont.)

• MATLAB is an interactive system whose basic data element is an array that does not require dimensioning. This allows you to solve many technical computing problems, especially those with matrix and vector formulations, in a fraction of the time it would take to write a program in a scalar noninteractive language such write a program in a scalar noninteractive language such as C or Fortran.

• MATLAB has evolved over a period of years with input from many users. In university environments, it is the standard instructional tool for introductory and advanced courses in mathematics, engineering, and science. In industry, MATLAB is the tool of choice for high-productivity research, development, and analysis.

Overview (cont.)

• MATLAB features a family of add-on application-specific solutions called toolboxes. Very important to most users of MATLAB, toolboxes allow you to learn and apply specialized technology. Toolboxes are comprehensive collections of MATLAB functions (M-files) that collections of MATLAB functions (M-files) that extend the MATLAB environment to solve particular classes of problems. Areas in which toolboxes are available include signal processing, control systems, neural networks, fuzzy logic, wavelets, simulation, and many others.

The Main Parts

• Desktop Tools and Development Environment

• The MATLAB Mathematical Function LibraryLibrary

• The MATLAB Language

• Graphics

• MATLAB External Interfaces

Desktop Tools and Development Environment

• This is the set of tools and facilities that help you use MATLAB functions and files. Many of these tools are graphical user interfaces. It includes the MATLAB interfaces. It includes the MATLAB desktop and Command Window, a command history, an editor and debugger, a code analyzer and other reports, and browsers for viewing help, the workspace, files, and the search path.

The MATLAB Mathematical Function Library

• This is a vast collection of computational algorithms ranging from elementary functions, like sum, sine, cosine, and complex arithmetic, to more sophisticated complex arithmetic, to more sophisticated functions like matrix inverse, matrix eigenvalues, Bessel functions, and fast Fourier transforms.

The MATLAB Language

• This is a high-level matrix/array language with control flow statements, functions, data structures, input/output, and object-oriented programming features. It allows oriented programming features. It allows both "programming in the small" to rapidly create quick and dirty throw-away programs, and "programming in the large" to create large and complex application programs.

Graphics

• MATLAB has extensive facilities for displaying

vectors and matrices as graphs, as well as

annotating and printing these graphs. It includes

high-level functions for two-dimensional and

three-dimensional data visualization, image three-dimensional data visualization, image

processing, animation, and presentation

graphics. It also includes low-level functions that

allow you to fully customize the appearance of

graphics as well as to build complete graphical

user interfaces on your MATLAB applications.

Line Graphs

Bar Graphs

Area Graphs

Direction Graphs

Radial Graphsplot bar (grouped) area feather polar

plotyy barh (grouped) pie quiver roseLine Graphs Surface Graphs Direction Graphs Volumetric Graphsplot3 surf quiver3 scatter3contour3 surfl comet3 coneplot

MATLAB External Interfaces

• This is a library that allows you to write C and Fortran programs that interact with MATLAB. It includes facilities for calling routines from MATLAB (dynamic linking), routines from MATLAB (dynamic linking), calling MATLAB as a computational engine, and for reading and writing MAT-files.

Limitations

• Proprietary product subject users to a vendor lock-in

• The language has a mixed heritage which can cause erratic syntax.– MATLAB uses parentheses, e.g. y = f (x), for both – MATLAB uses parentheses, e.g. y = f (x), for both

indexing into an array and calling a function.

• Doesn’t support references. Makes it difficult to implement data structures that contain indirections, such as open hash tables, linked lists, trees, and various other common computer science data structures.

Now, for some work…

Using Matlab

Working with Matrices

• Matlab works with essentially only one kind of object, a rectangular numerical matrix

• A matrix is a collection of numerical values that are organized into a specific configuration of rows and columns. into a specific configuration of rows and columns.

• The number of rows and columns can be any number

Example

3 rows and 4 columns define a 3 x 4 matrix having 12 elements

• A scalar is a single number and is represented by a 1 x 1 matrix in matlab.

• A vector is a one dimensional array of numbers and is represented by an n x 1 column vector or a 1 x n row vector of n elements

Using Matlab


c = 5.66 or c = [5.66] c is a scalar or a 1 x 1 matrix

Using Matlab



x = [ 3.5, 33.22, 24.5 ] x is a row vector or a 1 x 3 matrix

Using Matlab




x1 = [ 2

55

3

-1] x1 is column vector or a 4 x 1 matrix

Using Matlab




x1 = [ 2

55

3

-1] x1 is column vector or a 4 x 1 matrix

A = [ 1 2 4

2 -2 2

0 3 5

5 4 9 ] A is a 4 x 3 matrix

Using Matlab


• Spaces, commas, and semicolons are used to separate elements of a matrix

Using Matlab



• Spaces or commas separate elements of a row• Spaces or commas separate elements of a row

[1 2 3 4] or [1,2,3,4]

Using Matlab



• Spaces or commas separate elements of a row• Spaces or commas separate elements of a row

[1 2 3 4] or [1,2,3,4]

• Semicolons separate columns

[1,2,3,4;5,6,7,8;9,8,7,6] = [1 2 3 4

5 6 7 8

9 8 7 6]

Using Matlab

Indexing Matrices

• A m x n matrix is defined by the number of m rows and number of n columns

• An individual element of a matrix can be specified with the notation An individual element of a matrix can be specified with the notation An individual element of a matrix can be specified with the notation An individual element of a matrix can be specified with the notation A(i,j) or Ai,j for the generalized element, or by A(4,1)=5 for a specific A(i,j) or Ai,j for the generalized element, or by A(4,1)=5 for a specific A(i,j) or Ai,j for the generalized element, or by A(4,1)=5 for a specific A(i,j) or Ai,j for the generalized element, or by A(4,1)=5 for a specific A(i,j) or Ai,j for the generalized element, or by A(4,1)=5 for a specific A(i,j) or Ai,j for the generalized element, or by A(4,1)=5 for a specific A(i,j) or Ai,j for the generalized element, or by A(4,1)=5 for a specific A(i,j) or Ai,j for the generalized element, or by A(4,1)=5 for a specific element.element.element.element.

Using Matlab

Indexing Matrices

• A m x n matrix is defined by the number of m rows and number of n columns

• An individual element of a matrix can be specified with the notation An individual element of a matrix can be specified with the notation An individual element of a matrix can be specified with the notation An individual element of a matrix can be specified with the notation A(i,j) or Ai,j for the generalized element, or by A(4,1)=5 for a specific A(i,j) or Ai,j for the generalized element, or by A(4,1)=5 for a specific A(i,j) or Ai,j for the generalized element, or by A(4,1)=5 for a specific A(i,j) or Ai,j for the generalized element, or by A(4,1)=5 for a specific A(i,j) or Ai,j for the generalized element, or by A(4,1)=5 for a specific A(i,j) or Ai,j for the generalized element, or by A(4,1)=5 for a specific A(i,j) or Ai,j for the generalized element, or by A(4,1)=5 for a specific A(i,j) or Ai,j for the generalized element, or by A(4,1)=5 for a specific element.element.element.element.

Example:

>> A = [1 2 4 5;6 3 8 2] A is a 4 x 2 matrix

>> A(1,2)

Ans 6

• The colon operator can be used to index a range of elements

>> A(1:3,2)

Ans 1 2 4

Using Matlab

Indexing Matrices

• Specific elements of any matrix can be overwritten using the matrix index

Example:

A = [1 2 4 5A = [1 2 4 5

6 3 8 2]

>> A(1,2) = 9

Ans

A = [1 2 4 5

9 3 8 2]

Using Matlab

Matrix Shortcuts

• The ones and zeros functions can be used to create any m x n matrices composed entirely of ones or zeros

ExampleExample

a = ones(2,3)

a = [1 1

1 1

1 1]

b = zeros(1,5)

b = [0 0 0 0 0]

Using MatlabData Types and Formats

• The semicolon operator determines whether the result of an expression is displayed

• whowhowhowho lists all of the variables in your matlab workspacelists all of the variables in your matlab workspacelists all of the variables in your matlab workspacelists all of the variables in your matlab workspace

• whos list the variables and describes their matrix size

Using Matlab

Saving your WorkTo save data to a *.mat file:

Typing ‘save filename’ at the >> prompt and the file ‘filename.mat’ will be saved to the working directorySelect Save from the file pull down menu

To reload a *.mat file

1. Type ‘load filename’ at the >> prompt to load ‘filename.mat’(ensure the filename is located in the current working directory)2. Select Open from the file pull down menu and manually find the datafile

Exercises

Enter the following Matrices in matlab using spaces,

commas, and semicolons to separate rows and

columns:

9175

6211

[ ]553878122641A = B =

7231

9175 [ ]553878122641

160

16

22

4

A = B =

C =

19246525

12100

2162855

42166418

D =

[ ]65D =

E = a 5 x 9 matrix of 1’s

Exercises

Use the who and whos functions to confirm all of the

variables and matrices in the work space are

present and correct

9175

6211

[ ]553878122641A = B =

7231

9175 [ ]553878122641

160

16

22

4

A = B =

C =

19246525

12100

2162855

42166418

D =

[ ]65D =

E = a 5 x 9 matrix of 1’s

Exercises

Change the following elements in each matrix:

7231

9175

661

[ ]553878122641A = B =76

76 0

0 7231

160

16

22

4

C =

19246525

12100

2162855

42166418

D =

[ ]65D =

E = a 5 x 9 matrix of 1’s76

76

76

0

0

B. Matrix Operations

Indexing Matrices• An empty or null matrix can be created using square brackets

>> A = [ ]

** TIP: The size and length functions can quickly return the number

Matrix Operations

** TIP: The size and length functions can quickly return the number of elements and dimensions of a matrix variable

Indexing MatricesA = [1 2 4 5

6 3 8 2]

• The colon operator can can be used to remove entire rows or columns

Matrix Operations

columns

>> A(:,3) = [ ]

A = [1 2 5

6 3 2]

>> A(2,:) = [ ]

A = [1 2 5]

Indexing MatricesA = [1 2 4 5

6 3 8 2]

• However individual elements within a matrix cannot be assigned an empty value

Matrix Operations

an empty value

>> A(1,3) = [ ]

??? Subscripted assignment dimension mismatch.

A = [1 2 4 5 B = [5 3 7 9

6 3 8 2] 1 9 9 8]

• Multidimensional matrices can be created by concatenating 2-D matrices together

• The cat function concatenates matrices of compatible

N – Dimensional Matrices

• The cat function concatenates matrices of compatible dimensions together:

Usage: cat(dimensions, Matrix1, Matrix2)

ExamplesA = [1 2 4 5 B = [5 3 7 9

6 3 8 2] 1 9 9 8]

>> C = cat(3,[1,2,4,5;6,3,8,2],[5,3,7,9;1,9,9,8])

N – Dimensional Matrices

>> C = cat(3,A,B)

CAT(2,A,B) is the same as [A,B]. (i.e. concatenate rows)

CAT(1,A,B) is the same as [A;B]. (i.e. concatenate columns)

Scalar Operations• Scalar (single value) calculations can be can performed on

matrices and arrays

Basic Calculation Operators

+ Addition

Matrix Operations

+ Addition

- Subtraction

* Multiplication

/ Division

^ Exponentiation

Scalar Operations• Scalar (single value) calculations can be performed on matrices

and arrays

A = [1 2 4 5 B = [1 C = 5

6 3 8 2] 7

Matrix Operations

6 3 8 2] 7

3

3]

Try:

A + 10

A * 5

B / 2

A^C

Scalar Operations• Scalar (single value) calculations can be performed on matrices

and arrays

A = [1 2 4 5 B = [1 C = 5

6 3 8 2] 7

Matrix Operations

6 3 8 2] 7

3

3]

Try:

A + 10

A * 5

B / 2

A^C What is happening here?

Matrix Operations• Matrix to matrix calculations can be performed on matrices and

arrays

Addition and Subtraction• Matrix dimensions must be the same or the added/subtracted

value must be scalar

Matrix Operations

value must be scalar

A = [1 2 4 5 B = [1 C = 5 D = [2 4 6 8

6 3 8 2] 7 1 3 5 7]

3

3]

Try:

>>A + B >>A + C >>A + D

Matrix Multiplication

• Built in matrix multiplication in Matlab is either:

1. Algebraic dot product

Matrix Operations

1. Algebraic dot product

2. Element by element multiplication

The Dot Product

• The dot product for two matrices A and B is defined whenever the number of columns of A are equal to the number of rows of b

Matrix Operations

• A(x1,y1) * B(x2,y2)

The Dot Product


Matrix Operations

• A(x1,y1) * B(x2,y2)

The Dot Product


Matrix Operations

• A(x1,y1) * B(x2,y2)

The Dot Product


Matrix Operations

• A(x1,y1) * B(x2,y2) = C(x1,y2)

The Dot Product

• A(x1,y1) * B(x2,y2) = C(x1,y2)

A = [1 2 B = [1 D = [2 2 E = [2 4 3 6]

6 3] 7 2 2]

Matrix Operations

6 3] 7 2 2]

3

3]

Try:

>>A * D

>>B * E

>>A * B

Element by Element Multiplication• Element by element multiplication of matrices is performed with

the .* operator

• Matrices must have identical dimensions

A = [1 2 B = [1 D = [2 2 E = [2 4 3 6]

Matrix Operations

A = [1 2 B = [1 D = [2 2 E = [2 4 3 6]

6 3 ] 7 2 2 ]

3

3]

>>A .* D

Ans = [ 2 4

12 6]

Matrix Division

• Built in matrix division in Matlab is either:

1. Left or right matrix division

2. Element by element division

Matrix Operations

2. Element by element division

Left and Right Division

• Left and Right division utilizes the / and \ operators

• Left (\) division:

X = A\B is a solution to A*X = B

Matrix Operations

X = A\B is a solution to A*X = B

• Right (/) division:

X = B/A is a solution to X*A = B

• Left division requires A and B have the same number of rows

• Right division requires A and B have the same number of columns

Element by Element Division• Element by element division of matrices is performed with the ./

operator

• Matrices must have identical dimensions

A = [1 2 4 5 B = [1 D = [2 2 2 2 E = [2 4 3 6]

Matrix Operations

A = [1 2 4 5 B = [1 D = [2 2 2 2 E = [2 4 3 6]

6 3 8 2] 7 2 2 2 2]

3

3]

>>A ./ D

Ans = [ 0.5000 1.0000 2.0000 2.5000

3.0000 1.5000 4.0000 1.0000 ]

Element by Element Division

• Any division by zero will be returned as a NAN in matlab (not a number)

• Any subsequent operation with a NAN value will return NAN

Matrix Operations

Matrix Exponents

• Built in matrix Exponentiation in Matlab is either:

1. A series of Algebraic dot products

2. Element by element exponentiation

Matrix Operations

2. Element by element exponentiation

Examples:

• A^2 = A * A (Matrix must be square)

• A.^2 = A .* A

Shortcut: Transposing Matrices• The transpose of a matrix is the matrix formed by interchanging

the rows and columns of a given matrix

A = [1 2 4 5 B = [1

6 3 8 2] 7

Matrix Operations

6 3 8 2] 7

3

3]

>> transpose(A) >> B’

A = [1 6 B = [1 7 3 3]

2 3

4 8

5 2]

Other handy built in matrix functions Include:

inv() Matrix inverse

det() Matrix determinant

Matrix Operations

poly() Characteristic Polynomial

kron() Kronecker tensor product

C. Relational Operators

• Relational operators are used to compare two scaler values or matrices of equal dimensions

Relational Operators

< less than


<= less than or equal to

> Greater than

>= Greater than or equal to

== equal

~= not equal

• Comparison occurs between pairs of corresponding elements

• A 1 or 0 is returned for each comparison indicating TRUE or FALSE

• Matrix dimensions must be equal!


>> 5 == 5

Ans 1

>> 20 >= 15

Ans 1

A = [1 2 4 5 B = 7 C = [2 2 2 2

6 3 8 2] 2 2 2 2]

Try:

>>A > B

>> A < C


>> A < C

The Find Function• The ‘find’ function is extremely helpful with relational operators

for finding all matrix elements that fit some criteria

A = [1 2 4 5 B = 7 C = [2 2 2 2 D = [0 2 0 5 0 2]

6 3 8 2] 2 2 2 2]

• The positions of all elements that fit the given criteria are


• The positions of all elements that fit the given criteria are returned

>> find(D > 0)

• The resultant positions can be used as indexes to change these elements

>> D(find(D>0)) = 10 D = [10 2 10 5 10 2]

The Find Function

A = [1 2 4 5 B = 7 C = [2 2 2 2 D = [0 2 0 5 0 2]

6 3 8 2] 2 2 2 2]

• The ‘find’ function can also return the row and column indexes of


• The ‘find’ function can also return the row and column indexes of of matching elements by specifying row and column arguments

>> [x,y] = find(A == 5)

• The matching elements will be indexed by (x1,y1), (x2,y2), …

>> A(x,y) = 10

A = [ 1 2 4 10

6 3 8 2 ]

Embedding Functions• Functions may be embedded into other functions, i.e. the values

sent to a function can be the result from some other function

• Function embedding can be many levels deep

• Many lines of code can be condensed into one single command

Matrix Operations

A = [1 2 4 5 B = 2 C = [2 2 2 2 D = [0 2 0 3 0 2]

6 3 8 2] 2 2 2 2]

>> D(find(D>0))

Ans 2 3 2


sent to a function can be the result from some other function.



Matrix Operations

A = [1 2 4 5 B = 2 C = [2 2 2 2 D = [0 2 0 3 0 2]

6 3 8 2] 2 2 2 2]

>> D(find(D>0))

Ans 2 3 2

>>D(D(find(D>0)))

Ans 2 0 0


sent to a function can be the result from some other function.



Matrix Operations

A = [1 2 4 5 B = 2 C = [2 2 2 2 D = [0 2 0 3 0 2]

6 3 8 2] 2 2 2 2]

>> D(find(D>0))

Ans 2 3 2

>>D(D(find(D>0)))

Ans 2 0 0

>>A(B, D(find(D>0)) )

Ans 3 8 3

B. Multiple Command ExecutionExecution

Entering Long Lines of Code• If a matlab command contains many calculations, embedded functions

or long variable names, it may be necessary to split the command onto multiple lines so that it can be read more easily

• The ‘…’ command tells matlab to continue the current command onto the next line

Programming TricksEntering Long Lines of Code• If a matlab command contains many calculations, embedded functions



Programming Tricks

>> long_variable_name1 + long_variable_name2 + mean(long_variable_name3)

Entering Long Lines of Code• If a matlab command contains many calculations, embedded functions



Programming Tricks

>> long_variable_name1 + long_variable_name2 + mean(long_variable_name3)

>> long_variable_name1 + long_variable_name2 + …

mean(long_variable_name3)

Entering Multiple Lines Without Running Them• To enter multiple lines before running any of them, use Shift+Enter

or Shift+Return.

• The cursor moves down to the next line, where the next line can be written.

• to run all of the lines press Enter or Return .

Programming Tricks

• This allows the list of commands to be checked and edited before they are evaluated by matlab.

Entering Multiple Lines Without Running Them• Matlab can execute sequences of commands stored in files

• Files that contain matlab commands have the extension ‘*.m’

• *.m files are written and saved in the built in matlab m-file editor

• M-files are executed from the M-file editor or the command prompt

• M-files can call other M-files

Matlab Scripts

• M-files can call other M-files

**The location path of the M-file must be set in matlab

Advantages of M-files

• Easy editing and saving of work

• Undo changes

• Readability/Portability - non executable comments can be added using the ‘%’ symbol to make make commands easier to

Matlab Scripts

added using the ‘%’ symbol to make make commands easier to understand

• Saving M-files is far more memory efficient than saving a workspace

C. Control and Flow

• Logical operators are used to compare two boolean values

• A boolean value is a logical representation of true or false

• Conventionally 1 and 0 are used to represent true and false

Logical Operators

false

• In matlab when boolean comparisons are made, a value of ‘false’ or 0 represents false and any positive integer or ‘true’ represents true

Logical Operators

& AND

| OR

~ NOT

The & (AND) operator returns TRUE only if both A,B

Logical Operators

A & B = ?

• The & (AND) operator returns TRUE only if both A,B values are TRUE otherwise returns FALSE

& (AND) Truth Table: A B Result

1 1 1

1 0 0

0 1 0

0 0 0

Logical Operators

& AND

| OR

~ NOT

• The | (OR) operator returns TRUE if either A, B is

Logical Operators

A | B = ?

• The | (OR) operator returns TRUE if either A, B is TRUE, otherwise returns FALSE

| (OR) Truth Table: A B Result

1 1 1

1 0 1

0 1 1

0 0 0

Logical Operators

& AND

| OR

~ NOT

• The ~ (NOT) operator reverses the boolean

Logical Operators

~A = ?

~B = ?

• The ~ (NOT) operator reverses the boolean representation

~ (NOT) Truth Table: A ~A B ~B

1 0 1 0

0 1 0 1

Examples:

A = 0 B = false C = 1 D = 8 E = true

F = [ 0 1 0 2

0 3 0 1]

Logical Operators

Try:

>>A & B >>A & C >>A & D >>A & E >>A & F

>>A | B >>A | C >>A | D >>A | E >>A | F

>> ~A >> ~B >> ~C >> ~D >> ~E

>> ~F >> ~A&C >> ~C & F

Examples:

A = 0 B = false C = 1 D = 8 E = true

F = [ 0 1 0 2

0 3 0 1]

Logical Operators

>>A & B = 0 >>A & C = 0 >>A & D = 0 >>A & E = 0

>>A & F = [0 0 0 0 >>A | B = 0 >>A | C = 1

0 0 0 0] >>A | D = 1 >>A | E = 1

>>A | F = [0 1 0 1

0 1 0 1]

Examples:

A = 0 B = false C = 1 D = 8 E = true

F = [ 0 1 0 2

0 3 0 1]

Logical Operators

>> ~A = 1 >> ~B = 1 >> ~C = 0

>> ~D = 0 >> ~E = 0

>> ~F =[1 0 1 0 >> ~A&C = 1 >> ~C & F = [0 0 0 0

1 0 1 0] 0 0 0 0]

**When performing a boolean operation with a matrix, an element by element boolean comparison is made

Order of Precedence:

• When performing multiple logical operations without separating brackets, the ~ (NOT) operator is evaluated first, followed by the & (AND) operator and | (OR) operator

Logical Operators

operator

A&B|C = (A&B) | C

A|B&C = A | (B&C)

Order of Precedence:

• When performing multiple logical operations without separating brackets, the ~ (NOT) operator is evaluated first, followed by the & (AND) operator and | (OR) operator

Logical Operators

operator

A&B|C = (A&B) | C

A|B&C = A | (B&C)

A&~B|C = (A&(~B)) | C

A|~B&C = A | ((~B)&C)

• Control flow capability enables matlab to function beyond the level of a simple desk calculator

• With control flow statements, matlab can be used as a

Control and Flow

• With control flow statements, matlab can be used as a complete high-level matrix language

• Flow control in matlab is performed with condition statements and loops

• It is often necessary to only perform matlab operations when certain conditions are met

• Relational and Logical operators are used to define specific conditions

Condition Statements

• Simple flow control in matlab is performed with the ‘If’, ‘Else’, ‘Elseif’ and ‘Switch’ statements

If, Else, and Elseif

• An if statement evaluates a logical expression and evaluates a group of commands when the logical expression is true

• The list of conditional commands are terminated by the end statement


statement

• If the logical expression is false, all the conditional commands are skipped

• Execution of the script resumes after the end statement

Basic form:

if logical_expression

commands

end

Example

A = 6 B = 0

if A > 6


if A > 6

D = [1 2 6]

A = A + 1

end

if A | B

E = mean(B)

end


• The else statement forces execution of the commands below the else statement if the original logical expression evaluates to false

• Only one list of commands can be executed


Basic form:


commands 1

else

commands 2

end

Example

A = 6 B = 0


if A > 6

D = [1 2 6]

A = A + 1

else

D = [ 0 0 0]

A = A - 1

end

if A & B

E = mean(B)

else

E = 0

end


• The elseif statement forces execution of the commands below the else statement if the original logical expression evaluates to false




Basic form:


commands 1

elseif logical_expression_2

commands 2

elseif logical_expression_3

commands 3

end

Example

A = 6 B = 0

if A > 3

D = [1 2 6]


D = [1 2 6]

A = A + 1

elseif A > 2

D = D + 1

A = A + 2

end

** Both the if and elseif statements are evaluated

Switch• The switch statement can act as many elseif statements

• Only the one case statement who’s value satisfies the original expression is evaluated

Basic form:

switch expression (scalar or string)


switch expression (scalar or string)

case value 1

commands 1

case value 2

commands 2

case value n

commands n

end

Example

A = 6 B = 0

switch A

case 4

D = [ 0 0 0]

A = A - 1


A = A - 1

case 5

B = 1

case 6

D = [1 2 6]

A = A + 1

end

** Only case 6 is evaluated

• Loops are an important component of flow control that enables matlab to repeat multiple statements in specific and controllable ways

Loops

• Simple repetition in matlab is controlled by two types of loops:

1. For loops

2. While loops

For Loops

• The for loop executes a statement or group of statements a predetermined number of times

Loops

Basic Form:

for index = start:increment:end

statements

end

** If ‘increment’ is not specified, an increment of 1 is assumed by matlab

For Loops

Examples:

for i = 1:1:100

Loops

for i = 1:1:100

x(i) = 0

end

• Assigns 0 to the first 100 elements of vector x

• If x does not exist or has fewer than 100 elements, additional space will be automatically allocated

For Loops

• Loops can be nested in other loops

A = [ ]

Loops

for i = 1:m

for j = 1:n

A(i,j) = i + j

end

end

• Creates an m by n matrix A whose elements are the sum of their matrix position

While Loops

• The while loop executes a statement or group of statements repeatedly as long as the controlling expression is true

Loops

expression is true

Basic Form:

while expression

statements

end

While Loops

Examples:

A = 6 B = 15

while A > 0 & B < 10

A = A + 1

Loops

A = A + 1

B = B – 2

end

• Iteratively increase A and decrease B until the two conditions of the while loop are met

** Be very careful to ensure that your while loop will eventually reach its termination condition to prevent an infinite loop

While Loops

Examples:

A = 6 B = 15

while A > 0 & B < 10

if A < 0

Loops

if A < 0

A = A + 1

elseif B > 10

B = B – 2

end

end

• Conditional statements can be nested for specific internal control of variables

Breaking out of loops

• The ‘break’ command instantly terminates a for and while loop

• When a break is encountered by matlab, execution of the script continues outside and after the loop

Loops

the script continues outside and after the loop

Breaking out of loopsExample:

A = 6 B = 15

count = 1

while A > 0 & B < 10

A = A + 1

Loops

A = A + 1

B = B + 2

count = count + 1

if count > 100

break

end

end

• Break out of the loop after 100 repetitions if the while condition has not been met

Functions in Matlab

• In Matlab, each function is a .m file

– It is good protocol to name your .m file the same as

your function name, i.e. funcname.m

• function outargs=funcname(inargs);

Function outputinput

Simple Example

• Find the cube of a number -> (x3)

• Type the code below into an .m file and save it as cube.m

• Set the Matlab directory appropriately

• In Matlab window, type cube(3), is the result • In Matlab window, type cube(3), is the result correct?

• Now you have a reusable function that can calculate the cube of any number

function [y] = cube(x)y = x*x*x;

>> cube(3)Ans = 125>> cube 1.75Ans = 5.3594

Add Some Help

• Find the cube of a number -> (x3)

• Add commented text between the funciton declaration and the first line of code

• Now type help cube in Matlab window• Now type help cube in Matlab window

function [y] = cube(x)% Put some text herey = x*x*x;

>> help cubePut some text here

Find the cube of two numbers

• Any numbers of inputs and outputs can be handled in a function

• For a simple example, extend the cube function to accept two inputs and find the function to accept two inputs and find the cube of each

function [y1, y2] = cube(x1, x2)% Put some text herey1 = x1*x1*x1;y2 = x2*x2*x2;

>> cube(2,3)Ans = 8 ???>> [a b] = cube(2,3)a = 8b = 27

nargin

• Matlab will accept a function call with any number of inputs and outputs

• nargin can be used to find out how many inputs the user has providedinputs the user has provided

– It is automatically passed with the function

function [y1, y2] = cube(x1, x2)if nargin == 1

y1 = x1*x1*x1;y2 = nan;

elseif nargin == 2y1 = x1*x1*x1;

y2 = x2*x2*x2;

end

>> cube(2,3)Ans = 8>> [a b] = cube(2,3)a = 8b = 27

return

• return terminates computation of the function and returns whatever is calculated thus far

function [y1, y2] = cube(x1, x2)if nargin == 1

y1 = x1*x1*x1;y2 = nan;return

endy1 = x1*x1*x1;

y2 = x2*x2*x2;

>> cube(2,3)Ans = 8>> [a b] = cube(2,3)a = 8b = 27

Find the Cube of Any Number of

Numbers

• Any ideas on how to accomplish this?

• Lets further extend the function to cube a vector of numbers

• Before we thought of the variables as • Before we thought of the variables as scalars, now rethink the power of vectors

function [y] = cube(x)% Put some text herey = x.^3;

>> cube(2)

Ans = 8

>> cube([2 3])Ans = [8 27]

Mini-Project

• Lets combine what we have learned thus far in the course

– Loops, If Statements, Functions

– Basic Matlab Operators– Basic Matlab Operators

• Should finish this in class today

• If you get through this then you are doing well

Mini-Project

• Raising any number of numbers to the nth power

• Inputs:– A vector of numbers to be raised (N1…Nm)

– A vector of powers (P1…Pm)

• Outputs:• Outputs:– A vector of raised values (N1P1 … NmPm)

– An error flag: 1 if error in calculation, 0 if successful

• Caveats:– If only one input is provided, the function should square each

entry, so output = (N12…Nm2) and error flag is 0

– If the length of N and P are not the same, this is an error, return anything in the output vector and a 1 in the error flag

• Make sure to comment and document the function

Mini-Project

• Plan before you code

• Remember that xn=x*x*x*x … *x (n times)

• Hint: remember the built in functions ‘length’ and ‘size’ will return the dimensions of any given variable

• Ask questions and take your time

Solution 1

(simple)

function [y, e] = raise(x,n)

if nargin == 1

y = x.^2;

e = 0;

return

elseif nargin == 2

if length(x)~=length(n)

y = nan;

e = 1;

returnreturn

end

for i=1:length(x)

y(i) = x(i)^n(i);

end

e = 0;

return

end

Solution 2 function [y, e] = raise(x,n)

y = ones(1,length(x));

if nargin == 1

[y e] = raise(x,2*ones(1,length(x)));

return

elseif nargin == 2

if length(x)~=length(n)

y = NaN;

e = 1;e = 1;

return

end

for i=1:length(x)

for j=1:n(i)

y(i) = y(i)*x(i);

end

end

e = 0;

return

end

Importing Data

• Basic issue:

– How do we get data from other sources into

Matlab so that we can play with it?

• Other Issues:• Other Issues:

– Where do we get the data?

– What types of data can we import

• Easily or Not

load

• Command opens and imports data from a standard ASCII file into a matlab variable

• Restrictions

– Data must be constantly sized– Data must be constantly sized

– Data must be ASCII

– No other characters

load

• Consider the simple file below

• Create in notepad and save as test1.txt and

text2.txt

• In matlab, set the path to the correct place (ie.

where the file is) and type load(‘test1.txt’)where the file is) and type load(‘test1.txt’)

• Now, type x = load(‘test1.txt’)

1 2

3 4

5 2

4 8

16 32

test1

load

• Now the file is no longer simple because not

every row has the same amount of characters

• Create in notepad and save as test2.txt and

text2.txt

• type y = load(‘test2.txt’)• type y = load(‘test2.txt’)

– Error!

1 2

3 4

5

4 8

16 32

test2

load

• Now type in the same thing from test1.txt into

Excel and save the workbook as test1.xls

• type y = load(‘test1.xls’)

– What happens?

• Forcing the issue with Excel data• Forcing the issue with Excel data

test11 2

3 4

5 2

4 8

16 32

load

• Works for simple and unstructured code

• Powerful and easy to use but limited

• Will likely force you to manually handle

simplifying data which is prone to error

• More complex functions are more flexible

File Handling

• f* functions are associated with file opening,

reading, manipulating, writing, …

• Basic Functions of Interest for opening and

reading generic files in matlab

– fopen– fopen

– fclose

– fseek/ftell/frewind

– fscanf

– fgetl

fopen

• Opens a file object in matlab that points to the file of interest

• fid = fopen(‘filepath’)– absolute directory + filename

• If file of interest is C:\Andrew\Project_1\file.dat• If file of interest is C:\Andrew\Project_1\file.dat

• fid = fopen(‘C:\Andrew\Project_1\file.dat’)

– relative path + filename• If your matlab path is set to c:\Andrew\Project_1

• fid = fopen(‘file.dat’)

• fid is an integer that represents the file– Can open multiple files and matlab will assign unique

fids

fclose

• When you are done with a file, it is a good idea

to close it especially if you are opening many

files

• fclose(fid)

What is a File?

• A specific organization of data

• In matlab it is identified with a fid

• Location is specified with a pointer that can be

moved aroundfid

file_name

fid

Pointer

Moving the Pointer

• We already know how to assign a fid (fopen)

• To find where the file is pointing:

– x = ftell(fid)

• To point somewhere else

– fseek(fid,offset,origin)

• Move pointer in file fid by offset relative to origin

– Move pointer by a fixed number of bytes

– Origin can be beginning, current, end of file

• To point to the beginning

– frewind(fid)

Getting Data

• Why move the pointer around?– Get somewhere in the file from where you want data

• [data] = fscanf(fid,format,size)• Format

– You have to tell matlab the type of data it should be – You have to tell matlab the type of data it should be expecting in the text file so that it can convert it

• ‘%d’, ‘%f’, ‘%c’, ‘%s’

• Size– You can specify how to organize the imported data

• [m,n] – import the data as m by n, n can be infinite

• Be careful because matlab will mangle your data and not tell you

Lets Try It• Open text1.txt using the fopen command

– Remember to save the fid, we will need it

• Create a variable with the data of text1.txt

• Now create another variable y with the data of text1.txt in it by using fscanf (do not simply copy x)

– What happens here?– What happens here?

– Need to set file pointer to beginning using rewind(fid)

• Now use the size option to import the data with 5 rows and 2 columns

• Try the same thing with test2.txt

– It works and fills in the blanks. This is powerful but dangerous

Lets Try It• Open text1.txt using the fopen command

– Remember to save the fid, we will need it

fid = fopen('test1.txt)

• Create a variable with the data of text1.txt

[x] = fscanf(fid,'%f%f')[x] = fscanf(fid,'%f%f')

• Now create another variable y with the data of text1.txt in it by using fscanf (do not simply copy x)

[y] = fscanf(fid,'%f%f')

– What happens here?

– Need to set file pointer to beginning using frewind(fid)

Lets Try It• Now use the size option to import the data with 5 rows and 2

columns

[data2] = fscanf(fid,'%f%f',[5,2])

- Careful this is the same format as the original data but not the same organization!!

frewind(fid)

[data3] = fscanf(fid,'%f%f',[2,5])

data3’

- now the data is formatted correctly

• Try the same thing with test2.txt

– It works and fills in the blanks. This is powerful but dangerous

Getting Data

• fgetl returns the next line of the file as a

character array

• You may need to convert these to numbers

>> fid1 = fopen(‘test1.txt’);>> fid1 = fopen(‘test1.txt’);

>> a_str = fgetl(fid1)

a_str = 1 2

>> a_num = str2num(a_str)

a_num = [1 2]

Realistic File

• A realistic file of data will have header information,

labeled columns and other information embedded within

it.

• Option 1: Manually go through deleting this information

and import using load of fopen commands.and import using load of fopen commands.

• Option 2: Have matlab delete and format available data

on the fly

Realistic File

• Powerful function textread can be used to input almost any text file

• Handles (input variables):

– Opening the file– Opening the file

– Ignoring Header Information

– Accepting Column Labels

• Will work for most applications

Realistic File

• Powerful function textread can be used to input almost any text file

Usage:Usage:

[var1 varN] = textread(‘filename’,’format’,args)

Summary

• Lots of options to load files

– load for basics

– fscanf for complex

– textread for most things– textread for most things

– xlsread for Excel worksheets

• Also saving Excel sheets as tab delimitted

Week 5 Lecture Outline

Plotting Data

A. Basics

B. Generating dataB. Generating data

C. 2D Plots (Line, Scatter, Bar)

D. Plot Features

Basics• Matlab has a powerful plotting engine that can

generate a wide variety of plots.

Generating Data• Matlab does not understand functions, it can

only use arrays of numbers.

– a=t2

– b=sin(2*pi*t)

– c=e-10*t note: matlab command is exp()– c=e-10*t note: matlab command is exp()

– d=cos(4*pi*t)

– e=2t3-4t2+t

• Generate it numerically over specific range

• Try and generate a-e over the interval 0:0.01:2

t=0:0.01:10; %make x vector

y=t.^2; %now we have the appropriate y

% but only over the specified range

Line/Scatter

• Simplest plot function is plot()

• Try typing plot(y)– Matlab automatically generates a figure and draws the data and

connects its lines

– Looks right, but the x axis units are incorrect

• Type plot(x,y), will look identical but have correct x-axis • Type plot(x,y), will look identical but have correct x-axis units

• Plot(x1,y1,s1,x2,y2,s2, …) many plots in one command

• Plot(x) where x is a matrix, will result in plotting each column as a separate trace

Line/Scatter

• Plot a and then plot b

– What do you see?

– Only b

• Matlab will replace the current plot with any new one

unless you specifically tell it not tounless you specifically tell it not to

• To have both plots on one figure use the hold on

command

• To make multiple plots use the figure command

plot(t,a)

plot(t,b)

% Put a and b on one plot

plot(t,a);

hold on;

plot(t,b);

% Make two plots

plot(t,a);

figure;

plot(t,b);

Hold On / Hold Off

• Hold on command only needs to be issued once per

figure, thus calling hold on will result in all subsequent

plot commands going to one figure unless a new figure

command is issued or hold off is used.

plot(a);

Hold on;

plot(b);

plot(c);

Hold off;

Figure;

plot(d);

plot(a);

Hold on;

plot(b);

plot(c);

Hold off;

plot(d);

plot(a);

Hold on;

plot(b);

plot(c);

Figure;

plot(d);

Linespec• Currently, all the plots were done in the Matlab

default color … blue

• This and many other features can be changed by selecting a different option within the plotcommand

% red line% red line

Plot(t,a,’r’);

Hold on;

% black line

Plot(t,b,’k’);

% green dots

Plot(t,c,’g.’);

% cyan x’s

Plot(t,d,’cx’)

% dashed magenta

% line with o’s

Plot(t,e,’--om’)

Linespec• Now we have added color, line style and markers to the data

• We can also modify line width, marker edge and fill color and marker size

% dashed magenta % line with o’s, …

Plot(t,e,’--om’, ‘LineWidth’,3,'MarkerEdgeColor',‘k‘, 'MarkerFaceColor',‘y‘, MarkerSize,9)Plot(t,e,’--om’, ‘LineWidth’,3,'MarkerEdgeColor',‘k‘, 'MarkerFaceColor',‘y‘, MarkerSize,9)

Labels, Title and Legend• To add labels to the x and y axes, we can use the xlabel and ylabel

commands

• To add a title, use the title command

• To add a legend, use the legend command

plot(t,a,t,b,’r’,t,c,’--om’); %generate all plots in one shot

title(‘Random Plots’)

xlabel(‘time(ms)’);

ylabel(‘f(t)’)

legend(‘Function 1’,’Function 2’,’Function 3’);

Quick Assignment 1

• Plot a as a thick black line

• Plot b as a series of red circles.

• Label each axis, add a title and a legend

4Mini Assignment #1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

Time (ms)

f(t)

t2

sin(2*pi*t)

Quick Assignment 1

1

1.5

2

2.5

3

3.5

4

f(t)

Mini Assignment #1

t2

sin(2*pi*t)

figure

plot(t,a,'k','LineWidth',3); hold on;

plot(t,b,'ro')

xlabel('Time (ms)');

ylabel('f(t)');

legend('t^2','sin(2*pi*t)');

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-1

-0.5

0

0.5

Time (ms)

legend('t^2','sin(2*pi*t)');

title('Mini Assignment #1')

Axis commands• We can alter the displayed range and other parameters of the plot by

using the axis command– Axis([xmin xmax ymin ymax])

– Axis equal;

– Axis square;

2

Figure;

Plot(t,a,’r’);

Axis([-2 2 -2 2]);

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Error Bars• In addition to markers, matlab can generate error bars for each

datapoint using the errorbar command– errorbar(x,y,e) or errorbar(x,y,ll,lu);

– Will generate line plus error bars at y+/-e or (y-ll,y+lu)

t2 = 0:1:10;

f = t2+(rand(1,length(t2))-0.5);

12

14

f = t2+(rand(1,length(t2))-0.5);

err1 = 0.1*f;

err2_l = 0.1*f;

err2_u = 0.25*f;

errorbar(t2,f,err1);

figure;

errorbar(t2,f,err2_l, err2_u);

-2 0 2 4 6 8 10 120

2

4

6

8

10

12

-2 0 2 4 6 8 10 120

2

4

6

8

10

Subplots• So far we have only been generating individual plots

• Matlab can also generate a matrix of plots using the subplot command

figure;

subplot(2,2,1) 2

2.5

3

3.5

4

0

0.5

1

subplot(2,2,1)

plot(t,a);

subplot(2,2,2)

plot(t,b);

subplot(2,2,3)

plot(t,c);

subplot(2,2,4)

plot(t,d);

0 0.5 1 1.5 20

0.5

1

1.5

2

0 0.5 1 1.5 2-1

-0.5

0

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2-1

-0.5

0

0.5

1

Quick Assignment 2

• Generate a 3x1 array of figures, each with a title

• Axis range of plots 1 and 2 should be 0 to 1 on x and y

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1Functions a and b

1Functions c and d

• Plot 1 should include function a and b (color code)

• Plot 2 should include c and d (color code)

• Plot 3 should include f with error bars of your liking

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

-2 0 2 4 6 8 10 120

10

20function f with errorbars

Quick Assignment 2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1Functions a and b

1Functions c and d

figure

subplot(3,1,1)

plot(t,a,t,b,'r');

axis([0 1 0 1]);

title('Functions a and b')

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

-2 0 2 4 6 8 10 120

10

20function f with errorbars

title('Functions a and b')

subplot(3,1,2)

plot(t,c,t,d,'m');

axis([0 1 0 1]);

title('Functions c and d')

subplot(3,1,3)

errorbar(t2,f,err1);

title('function f with errorbars')

Bar Graphs• So far we have focused on line/scatter plots, the other most common

plot type is a bar graph

• Matlab bar(x,y,width) command will generate a bar graph that is related to the underlying functions where the width of each bar is specified by width (default = 1);

• Can be used with subplot and all the other features we have discussed so fardiscussed so far

t3 = 0:1:25;

f = sqrt(t3);

bar(t3,f);

-5 0 5 10 15 20 25 300

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Histograms• Matlab hist(y,m) command will generate a frequency histogram of

vector y distributed among m bins

• Also can use hist(y,x) where x is a vector defining the bin centers

– Note you can use histc function if you want to define bin edges instead

• Can be used with subplot and all the other features we have discussed so far

hist(b,10);

Figure;

Hist(b,[-1 -0.75 0 0.25 0.5 0.75 1]);

-1.5 -1 -0.5 0 0.5 1 1.50

5

10

15

20

25

30

35

40

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

35

40

45

Quick Assignment 3

• Generate the following data set

– It results in multiple noisy repeats of some trial

• Create mean_x to be the mean of all the trials at each

point of x

• Create std_x to be the standard deviation of all trials at • Create std_x to be the standard deviation of all trials at

each point of x

• Add labels and titles

t = 0:0.1:1

for(i=1:25)

x(i,:) = exp(-10.*t) + 0.5*(rand(1,length(t))-0.5);

end

Quick Assignment 3

• Make a plot that is to include 2 subplots

• Plot #1:– Plot each individual trial (25 lines) in thin dotted black lines,

• tip: remember about how matlab interprets matricies for the plot command.

– Plot the mean of the trials with a thick, red, dashed line and error – Plot the mean of the trials with a thick, red, dashed line and error lines surrounding each datapoint that correspond to the standard deviation of each of the points

• Plot #2:– A histogram that expresses the distribution of the signal at the

end of each trial (last sample)

Quick Assignment 3

-0.2 0 0.2 0.4 0.6 0.8 1 1.2-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4Repeats of a Given Task

Repeat

Err

or

Rate

t = 0:0.1:1

for(i=1:25)

x(i,:) = exp(-10.*t) + 0.5*(rand(1,length(t))-0.5);

end

mean_x = mean(x);

std_x = std(x);

figure

subplot(2,1,1)

plot(t,x,'k'); hold on;Repeat

-0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.250

1

2

3

4

5Distribution of Endpoint Position

Deviation (mm)

Occura

nces

plot(t,x,'k'); hold on;

errorbar(t,mean_x,std_x,'--r','LineWidth', 3);

title('Repeats of a Given Task')

xlabel('Repeat');

ylabel('Error Rate');

subplot(2,1,2)

hist(x(:,11),10)

title('Distribution of Endpoint Position');

xlabel('Deviation (mm)')

ylabel('Occurances')

Quick Assignment 3

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4Repeats of a Given Task

Err

or

Rate

-0.2 0 0.2 0.4 0.6 0.8 1 1.2-0.4

Repeat

-0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.250

1

2

3

4

5Distribution of Endpoint Position

Deviation (mm)

Occura

nces

Recap

• Learned about basic 2D plot functions

– plot,bar,hist

• Dealing with multiple plots and graphs

– Hold, figure, subplot– Hold, figure, subplot

• Discussed adding features to graphs

– Xlabel,title,legend,…

3D Plots

• Matlab provides a wide range of 3D plot options, we will talk about 3 different plot types.– Mesh, Surf, Contour

Dataset

• Try [x,y,z] = peaks(25)– Does this work?

• If not, lets create an arbitrary dataset

– x=-10:10; y = -10:10; z=x.^2’*y.^2;

Mesh

• Connects a series of discrete data points with a mesh– mesh(x,y,z) where X(i) and Y(j) are the intersections of

the mesh and Z(i,j) is the height at that intersection

– mesh(Z) assumes X and Y are simple 1..N and 1..M– mesh(Z) assumes X and Y are simple 1..N and 1..M

Surf

• Very similar to mesh, with filled grid

Contour

• Projection of equal heights of 3D plot onto a 2D plane

• Use like surf or mesh – contour(x,y,z)

Meshc,surfc

• Combination surface/mesh and contour plot

• Use like surf or mesh – meshc(x,y,z)

Plot3• Plots lines and points in space, just like plot but now for an

(x,y,z) triple

• Plot3(x,y,z), each a vector of equal length

• Use all the same specfiers to generate colors, line-types, etc.

Plot commands

• Note that almost all 2D plotting commands such as xlabel, ylabel, title will still work in 3D plots

• 3D plots can be added as subplots just like • 3D plots can be added as subplots just like any other plot type

• Some other special features and functions exist…

View

• Changes the view of the current 3D plot– view(az,el)

– Az = azimuth (rotation around z-axis)

– El = Elevation (rotation around xy-plane)

• Useful rotations (0,0),(90,0)• Useful rotations (0,0),(90,0)

Colorbar

• For the 3D plots, it is useful to add a colorbar to the figure to indicate height.

• Colorbar(‘vert’) adds a vertical colorbar

• Colorbar(‘horiz) adds a horizontal colorbar• Colorbar(‘horiz) adds a horizontal colorbar

caxis

• Allows you to set the range of colors in the plot.

• Caxis([min max]) will choose the range of colors

from the current color map to assign to the plot.

Values outside this range will use the min/max

availableavailable

Colormap

• Plenty of other controls to personalize the plot– colormap colormap_name sets to new map

– Colormap (sets the types of colors that appear in 3D

plot). These can be custom of one of several premadeplot). These can be custom of one of several premade

– bone Hsv, jet, autumn, vga, summer, …

– See help graph3D for more

– Use colormapeditor function for graphical selection of

color map

Research

• http://www.ifs.tuwien.ac.at/~silvia/research-tips/

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