MATLAB code for Linear Algebra and Probability for Computer
Science Applications
Ernest Davis
Examples discussed in the text
Chapter 1: Matlab
- hailstone.m Hailstone procedure, p. 6.
- p35.m Script to compute x^{35}, p. 6.
- fib.m Recursive definition of Fibonacci numbers,
p. 8.
- quadform.m Solve the quadratic equation, p. 8.
- t1.m Local and global variables, p. 9.
Chapter 2: Vectors
- correlation.m Compute the correlation
of two vectors (p. 35).
- GetStopwords.m List of stop words for
Assignment 2.1, p. 43.
- hash.m Hash function for assignment 2.1, p. 43.
Chapter 3: Matrices
Chapter 5: Algorithms
- sampleRandomSings.m
sampleRandomSings(n,k) calls testRandomSings(n) k times and find the
frequency with which LU decomposition generates a zero vector in the
last row and the frequency with which the rank is measured at n-1.
See section 5.2.3, p. 122.
Chapter 6: Geometry
- TransformImage.m Coordinate
transformation on image arrays. p. 174.
- EulerRotation.m. Computes the
3x3 rotation matrix for the Z-X-Z Eulerian angles. Useful subroutine
in testing Assignment 6.3 (p. 178).
- polyhedra.m Script to constructs 5 polyhedra
as cellular arrays of faces. Useful for testing Assignmment 6.3 (p. 178).
Chapter 7: Change of Basis, DFT, and SVD
- getimage.m . Converts an image file to
an array. Used in exercise 7.3. Credit: Pascal Getreuer.
- dft.m Uses FFT to convert time-domain to
frequency domain (real DFT). Section 7.10.2, p. 213.
- idft.m Uses FFT to convert frequency domain
to time-domain (real DFT). Section 7.10.2, p. 213.
- trigBasis.m . Matrix whose columns are
the trigonometric Fourier components of size 2K. Section 7.10.2, p. 213.
Chapter 12: Monte Carlo Methods
- MCCircle.m Estimate the area of a circle, and
create a plot. Section 12.1.
- MCPrimes.m Estimate the number of integer
solutions to
"x^{2} +
y^{2} +
z^{2}" is prime where x, y, and z are between 0 and N.
- RelabellingSig.m
Use resampling to determine whether the difference in mean between
data sets V and W is significant. Discussed section 12.7, p. 368.
Chapter 14: Maximum Likelihood Estimate
Code used to generate figures in the text
The code to generate figure 6.19 is not included here, as that is the answer
to Programming Assignment 6.3.
- DrawFig31.m Smoothing. Figure 3.1, p. 52.
- DrawFig34.m Polynomial and
sinusoidal interpolation. Figure 3.4, p. 61.
- FourierA.m and
FourierB.m. Discrete Fourier vectors. p. 195.
- DrawFig96.m Distribution and density for
a step function. Figure 9.6 p. 280.
- DrawFig97.m Probability density as the limit
of histograms. Figure 9.7 p. 282.
- DrawSigmoid.m Distribution and density for
a bell-shaped curve. Figure 9.8, p. 283
- probStairs.m Subroutine for figure 9.7.
- DrawFig910.m Approximating the binomial
distribution with the Gaussian. Figure 9.10, p. 288.
- MCCircle1.m Monte Carlo estimate of the area
of a circle, Figure 12.1, p. 340.
- BoundingBoxFig1.m "Bounding box"
Figure 14.2, p. 395.
- BoundingBoxFig.m Code to generate
a random figure similar to Figure 14.2.