Introduction to Matlab

1
Introduction to Matlab

• Matlab and toolboxes
• Matrices
• Built-in functions
• Plotting
• Matlab exercise

2
Matlab and Toolboxes

• Matlab
• A high-level language and interactive environment
  that enables you to perform computationally
  intensive tasks faster than with traditional
  programming languages such as C, C, and
  Fortran.
• Matlab toolboxes
• Optimization toolbox extends the Matlab
  technical computing environment with tools and
  widely used algorithms for standard and
  large-scale optimization.
• Statistics toolbox provides engineers,
  scientists, researchers, financial analysts, and
  statisticians with a comprehensive set of tools
  to assess and understand their data.
• From http//www.mathworks.com/

3
Matlab Workspace and Toolbar

• Variables are stored in the workspace
• who list current variables
• whos detailed list of variables
• clear removes all variables from the workspace
• Matlab files must be in either the working
  directory or in a directory listed in the search
  path
• pwd displays the current working directory
• what lists Matlab specific files in the working
  directory
• cd change current working directory
• path displays the current search path

Workspace Browser Path Browser Simulink Help
Window
4
Help

• Within Matlab
• Type help at the Matlab prompt or help followed
  by a function name for help on a specific
  function
• Online
• Online documentation for Matlab at the MathWorks
  website
• http//www.mathworks.com/access/helpdesk/help/tech
  doc/matlab.html
• There are also numerous tutorials online that are
  easily found with a web search.

5
Matrices

• Entering a matrix
• A -1 1 23,-1,1 -1, 3, 4
• A
• -1 1 2
• 3 -1 1
• -1 3 4
• Matrix operations
• AA
• A-A
• 3A
• AA
• ans
• 2 4 7
• -7 7 9

• Matrix referencing
• A(1,3)
• ans
• 2

• A(2,)
• ans
• 3 -1 1

• A.A
• ans
• 1 1 4
• 9 1 1
• 1 9 16

6
Built-in Functions

• Inverse
• inv(A)
• ans
• -0.7000 0.2000 0.3000
• -1.3000 -0.2000 0.7000
• 0.8000 0.2000 -0.2000
• Transpose
• A'
• ans
• -1 3 -1
• 1 -1 3
• 2 1 4

• Determinant
• det(A)
• ans
• 10
• Rank
• rank(A)
• ans
• 3

7
Linear Algebraic Systems

• Linear system of algebraic equations
• b 2 6 4
• rank(A)
• ans
• 3

• x inv(A)b
• x
• 1.0000
• -1.0000
• 2.0000

8
Eigenvalues

• eig(A)
• ans
• -1.3777 0.4526i
• -1.3777 - 0.4526i
• 4.7554

• p poly(A)
• p
• 1.0000 -2.0000 -11.0000 -10.0000
• roots(p)
• ans
• 4.7554
• -1.3777 0.4526i
• -1.3777 - 0.4526i

9
Eigenvalues cont.

• trace(A)
• ans
• 2
• det(A)
• ans
• 10

• sum(eig(A))
• ans
• 2.0000
• prod(eig(A))
• ans
• 10.0000

10
Plotting Commands

• Basic plots and graphs
• plot(X,Y) plot vectors or matrices
• hold hold current graph (for multiple plots on
  same graph)
• subplot(m,n,p) create axes in tiled positions
  (for multiple graphs in same figure)
• figure creates a new figure window (so a new
  plot does not replace a previous plot)
• Formatting axes
• xlim(0 1) sets the x-axis limits to 0 and 1
• ylim(0 1) sets the y-axis limits to 0 and 1
• Annotating plots
• title(Figure Title)
• xlabel(Label for X-axis)
• ylabel(Label for Y-axis)
• legend(Name of line 1,Name of line 2)

11
Plotting a Function
x 0.10.110 y1 7x./(0.6 x) y2
5x ./ (0.08x)
subplot(2,1,1) plot(x,y1) ylabel('y1')
subplot(2,1,2) plot(x,y2) ylabel('y2')
plot(x,y1,x,y2) xlabel('x') ylabel('y')
legend('y1','y2') figure
12
Matlab Exercise

• Problem Set 8.3, Problems 20c,d