Introduction to Matlab 7 Lesson III

1
Introduction to Matlab 7Lesson III

• Marco Lattuada
• Swiss Federal Institute of Technology - ETH
• Institut für Chemie und Bioingenieurwissenschaften
  
• ETH Hönggerberg/ HCI F135 Zürich (Switzerland)
• E-mail lattuada_at_chem.ethz.ch
• http//www.morbidelli-group.ethz.ch/education/inde
  x

2
Short Resume

• Decisions
• Loops

if expression statements elseif
expression statements else expression statement
s end
switch test case result1 statements case
result2 statements otherwise statements end
for variable expression statements end
while expression statements end
3
M-Files

• What is an M-File?
• An M-File can be used to
• Types of M-Files

An M-File is a collection of commands. It is
equivalent of programs, functions, subroutines,
prodecures in other programming languages.

• Experiment an algorithm
• Create a perment record of an algorithm
• Built utilities

• Script M-File no input and no output. Operates
  on workspace variables.
• Function M-File contains a function command,
  accepts input variables and may delivers outputs.
  Other variables are local.

4
Example of Script

• How to run a script
• From the Matlab Command Window
• (Double-check the directory path...)
• From the Matlab Editor
• In Matlab Editor ? Debug ? run

5
Exercise

• Create a new M-File called 'solve_triangular'
• Write down the solution of the following
  triangular system
• Solution

6
A clarification about matrix operations

• Suppose that A is an NxN matrix, and b is an Nx1
  column vector
• The following divisions are allowed in Matlab
• XA\b Solution of AXb (X is Nx1)
• Yb/A gt Yb (A)-1 Solution of YAb (Y is
  1xN)
• ZA/b gt Best solution of ZbA There is no
  exact solution for this problem Matlab finds
  least square solution
• ZbA
• (Z is Nx1)

7
Functions in Matlab

• Function definition (in the M-File)
• Function handling from Matlab Command Window

By pressing fTAB, all the functions are
recalled
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Example of Function

• The M-File the "mysum" function (saved in
  mysum.m)
• The call

The workspace at the end
9
Exercise

• Create a new function called 'my_first_function'
• Scope of the function
• Compute the function f(x) 2x2-log(x)3
• Parameters of the function
• Input the x value for which the function must
  be evaluated
• Output the value of the function in x (that is,
  f(x))
• Run the function for different values of x
• Evaluate the function for x linspace(1,10,10)
• If x is less or equal than zero, then return the
  value f -1, otherwise compute the correct value
  f(x)
• Re-evaluate the function for x
  linspace(0,10,11)
• How would you rewrite the function so that it
  evaluates f(x) for all the components of a
  generic vector x?
• Plot f(x) versus x (use plot(x,y))

10
Exercise

• Create a new function called 'my_second_function'
• Scope of the function
• Compute the function f(x) 2x2-exp(x)3
• Parameters of the function
• Input a generic array x with n components
• Output an array n?1 with the values of the
  function in x
• Evaluate the function for 40 x values ranging
  from -5 to 5
• Plot f(x) versus x

11
View variables inside functions (debugging)

• Use the command keyboard
• Every time the function is called, it will stop
  the execution when reaching the keyboard command
• Type the name of the variables you want to see
• Use return to exit form the keyboard mode

12
Local vs. Global Variables

• All variables inside functions are local
  variables.
• This means that they exist only inside the
  function.
• If one wants to create a variable which is
  visible everywhere, it has to be declared as
  global
• The global declaration has to be done in the main
  program and in all functions where the variable
  should be visible

The value of alpha has changed!
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Exercise

• Plot the result of 'my_first_function' vs
  -50.55
• Type hold on
• Plot the result of 'my_second_function' vs
  -50.55 using the command plot(x,f,'ro')
• Check the actual axis interval by typing axis
• Define a new axis interval by typing axis(-3 3
  -10 20)
• Introduce the labels by xlabel('x'),
  ylabel('f(x)')
• Superimpose the function 3sin(x) plot(x,
  3sin(x),'g--')
• Create a new figure figure(2)
• Plot the function 2exp(x21)6 using the command
  semilogy instead of plot
• Place axis labels and rescale the plot to x
  -22 and y 10...1000

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More on 2D plots

• To plot data in a Cartesian plane, the command is
  plot(x,y)
• Try
• gtgtxlinspace(0,10,100)
• gtgtytanh(x).cos(x)
• gtgtplot(x,y)
• In order to specify line thickness, type of line,
  color, etc.
• gtgtplot(x,y,g,LineWidth,3)

Color
Line Width (default 0.5)
Line Style
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Plot Details

• Colors Line Styles

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Plots of data

• Try
• gtgtx110
• gtgtysin(x)
• gtgtplot(x,y)
• Plot by default draws a line between two
  successive points
• gtgtplot(x,y,k-d,MarkerSize,10,MarkerEdgeColor
  ,b,Marker
• FaceColor,y)

Color of Marker Edge (default line color)
Marker Size
Marker Type
Color of Marker Face (default white)
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Markers

18

• gtgtxlinspace(0,10,100)
• gtgtysin(x)
• gtgty2cos(x)
• To plot multiple data in the same figure
• gtgtplot(x,y,-o,x,y2,d)
• Alternatively
• gtgt plot(x,y,-o)
• gtgthold on
• gtgtplot(x,y2,--d)
• gtgthold off

Hold on keeps the graph open. Additional data
will be plotted in the same figure!
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Formatting a Plot

• gtgtxlabel(x)
• gtgtylabel(y)
• gtgttext(xt,yt,Text here) adds text at
  coordinates xt,yt
• gtgtlegend(this is a legend)
• gtgttext(xt,yt,Text here,PropertyName,PropertyValu
  e)
• gtgtaxis(xmin,xmax,ymin,ymax) specifies the
  interval where the plot should be visualized

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Text Properties
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Additional types of plot

• gtgtfplot(8xcos(x.2),1,10) plot a
  function in an interval
• gtgt x,yfplot(8xcos(x.2),1,10) no
  plot, just returns x,y
• gtgtsemilogx(x,y)
• gtgtsemilogy(x,y)
• gtgtloglog(x,y)
• gtgtthetalinspace(0,2pi,100)
• gtgtr1./(1theta.2)
• gtgtpolar(theta,r) plot in polar coordinates

Interval
Function
Like plot, but with either x, or y or both axes
in logarithmic scale
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Plots with Error Bars

• gtgtxlinspace(1,10,20)
• gtgty10./x
• gtgt errandn(20,1)
• gtgterrorbar(x,y,er)

er is the array containing the error on the
data The error bar is drawn from y-er to yer
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3D plots I- lines in space

• gtgttlinspace(0,2pi,100)
• gtgtxsqrt(t).cos(2t)
• gtgtysqrt(t).sin(2t)
• gtgtzt
• gtgtplot3(x,y,z)

Lines can be manipulated as done with plot
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3D-plots II

• gtgtxlinspace(-5,5,30)
• gtgtylinspace(-2,2,20)
• gtgtX,Ymeshgrid(x,y)
• gtgtZsin(X).cos(Y)
• gtgtmesh(X,Y,Z)
• gtgtsurf(X,Y,Z)
• gtgtshading interp
• gtgtcontour(X,Y,Z) like looking at mountain
  heights on a map
• gtgtcolorbar
• gtgtcontour3(X,Y,Z)
• gtgtcolorbar