Flash Gordon and the Mud Men of Matlab

1
Flash Gordon and the Mud Men of Matlab

2
Quick Exercise (!)

• Consider Polynomial Addition again
• how would you write a program that takes in
  two polynomials and irrespective of their sizes
  it adds the polynomials together ? Given that the
  function length(A) returns the length of a
  vector.
• Answers on a postcard to dgordon_at_maths.kst.dit.i
  e
• oh, and while youre here anyhow, if you have a
  browser open, please go to the following sites
• http//www.the
  hungersite.com
• http//www.hitsagainsthunger.c
  om

3
Creating Programs

• Title Program.m

C
function out program(inputs) PROGRAM ltcodegt
4
Know Thyself

• Where am I ?
• pwd
• Get me onto the hard disk
• cd C
• Where am I now ?
• pwd
• Get me to where I know
• cd ..

5
Quick Answer (!)
function c mypoly(a,b) MYPOLY Add two
polynomials of variable lengths
mypoly(a,b) add the polynomial A to the
polynomial B, even if they are of
different length Author Damian Gordon
Date 3/5/2001 Mod'd x/x/2001 c
zeros(1,length(b) - length(a)) a zeros(1,
length(a) - length(b)) b
6
Recursion

• function b bart(a)
• BART The Bart Simpson program writes on the
  blackboard
• program, Bart writes the message a few
  times
• and then goes home to see the Simpsons
• if a 1
• disp('I will not....')
• else
• disp('I will not skateboard in the halls')
• bart(a - 1)
• end

7
Curve Fitting

• What is the best fit ?
• In this case least squares curve fit
• What curve should be used ?
• It depends...

8
POLYFIT Curve Fitting

• polyfit(x,y,n) - fit a polynomial
• x,y - data points describing the curve
• n - polynomial order
• n 1 -- linear regression
• n 2 -- quadratic regression

9
Curve Fitting Example

• x 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
• y -.447 1.978 3.28 6.16 7.08 7.34 7.66 9.56
  9.48 9.30 11.2
• polyfit(x,y,n)
• n 1
• p 10.3185 1.4400
• n 2
• p -9.8108 20.1293 -0.0317
• y -9.8108x2 20.1293x - 0.0317

10
Curve Fitting Example

• xi linspace(0,1,100)
• z polyval(p,xi)
• plot(x,y,'o',x,y,xi,z,'')

11
Interpolation - 1D

• t interp1(x,y,.75)
• t
• 9.5200
• also
• interp1(x,y,.75,spline)
• interp1(x,y,.75,cubic)

12
Interpolation - 2D

• interp2(x,y,Z,xi,yi,TYPE)

TYPE 'nearest' - nearest neighbor
interpolation 'linear' - bilinear
interpolation 'cubic' - bicubic
interpolation 'spline' - spline
interpolation
13
Fourier Functions

• fft
• fft2
• ifft
• ifft2
• filter
• filter2
• fftshift

• Fast fourier transform
• 2-D fft
• Inverse fft
• 2-D Inverse fft
• Discrete time filter
• 2-D discrete tf
• shift FFT results so -ve freqs appear first

14
Tensors

• See Programs
• Tensors
• Tensors.html

15
3D Graphics

• T 0pi/5010pi
• plot3(sin(t), cos(t), t)

16
3D Graphics

• title('Helix'), xlabel('sin(t)'),
• ylabel('cos(t)'), zlabel('t')
• grid

17
3D Graphics

• Rotate view by elevation and azimuth
• view(az, el)
• view(-37.5, 60)