readme

Mathematical Methods by Moor n Stiling.

% Try some data for a rationally-interpolated filter


res.m
% 
% Computes <a^n>_m
%
% function d = res(a,n,m)
%
% a = value
% n = exponent
% m = modulo
%
% d = remainder(a^n,m0


schurcohn.m
% 
% Returns 1 if p is a Schur polynomial (all roots inside unit circle)
%
% function stable = schurcohn(p)
% 
% p = polynomial coefficients
%
% stable = 1 if stable polynomial


simppivot.m
% 
% Pivot a linear programming tableau about the p,q entry
% 
% function tableau = simppivot(intableau,p,q)
%
% intableau = tableau
% (p,q) = point about which to pivot
%
% tableau = pivoted tableau


solvlincong.m
% 
% Ddetermine the solution to the linear congruence
% a x equiv b (mod m), if it exists
%
% function x = solvlincong(a,m,b)


sreal.m
% sysreal.m
% data for the system identification example in the SVD stuff


sreal1.m
% SVD realization


sugiyama.m
% 
% Compute the GCD g = (b,c) using the Euclidean algorithm
% and return s,t such that bs+ct = g, where b and c are polynomials
% with real coefficients
%
% thresh = (optional) threshold argument used to truncate small remainders


sysidsvd2.m
% 
% given a sequence of impulse responses in h (a cell array)
% identify a system (A,B,C)
% This uses the tohankel method of finding a nearest hankel matrix
% of desired rank
%
% function [A,B,C] = sysidsvd(h,order)
%
% h = impulse response sequence (cell array)
% order = desired order of system
%
% (A,B,C) = system


taylorf.mm
(* example of a taylor series *)


tocrt.m
% 
% Compute the representation of the scalar x using the
% using the Chinese Remainder Theorem (CRT) with
% moduli m = [m1,m2,...,mr].  It is assumed (without checking)
% that the moduli are relatively prime
%
% function y = tocrt(x,m)
%
% x = number to convert
% m = set of moduli
%
% y = CRT representation of x


tocrtpoly.m
% 
% Compute the representation of the polynomial f using the
% using the Chinese Remainder Theorem (CRT) with
% moduli m = {m1,m2,...,mr}.  It is assumed (without checking)
% that the moduli are relatively prime.
% m is passed in as a cell array containing polynomial vectors
% and y is returned as a cell array containing polynomial vectors
%
% function y = tocrt(f,m)
%
% f = polynomial
% m = set of modulo polynomials
%
% y = CRT form of f


tohankelbig.m
% 
% Determine the matrix nearest to A which is (block) Hankel and has rank r
% using the composite mapping algorithm
%
% function A = tohankelbig(A,r)
%
% A = input matrix
% r = desired ranke
% d = (optional) block size (default=1)
%
% A = nearest rank r Hankel matrix
% diff = norm of difference between matrices


triginterp.m
% demonstrate trigonometric interpolation


vandsolve1.m
%
% Solves the equation Vx = fs, where V is the Vandermonde
% matrix determined from ts.
%
% function a = vandsolve1(ts,fs)
%
% ts = abscissa values
% fs = ordinate values
%
% a = solution


vitnop.m
% 
% Compute the norm of the difference between inputs
% This function may be feval'ed for use with the Viterbi algorithm
% In this case, the norm is simply taken as the branch number
%
% function d = vitnop(branch,input)
%


vitsqnorm.m
% 
% Compute the square norm of the difference between inputs
% This function may be feval'ed for use with the Viterbi algorithm
% (state and nextstate are not used here)
%
% function d = vitsqnorm(branch,input,state,nextstate)


wino3by3.m
% 
% Convolve the 3-sequence a with the 3-sequence b 
% a and b are both assumed to be column vectors
% using Winograd convolution
%
% function c = wino3by3(a,b) 


winotest.m
% Set up data for a Winograd convolution algorithm


winotest2.m
% Set up data for a Winograd convolution algorithm 


***************************************************************
Directory: mkpict
***************************************************************
attract1.m
% a plot showing an attractor


attract2.m
% a plot showing an attractor


bayes1.m
% Bayes decision tests


bayes2.m
% Bayes decision tests for Gaussian


bayes4.m
% show the decision regions for a 3-way test


binchan.m
% 
% Data for Bayesian detection on the binary channel


binchanex.m
% data for binary channel


chebyplot.m
% Plot Chebyshev polynomials


chi2plot.m
% 
% Plot the chi-squared r.v.


compmap3.m
% make figure comppos1


condhilb.m
% Plot the condition of the Hilbert matrix


drawtrellis.m
% 
% Draw a trellis in LaTeX picture mode
%
% function drawtrellis(fid,numbranch,r,p)
%
% fid = output file id
% numbranch = number of branches to draw
% r = path cost values
% p = flag
%
% Other values are contained in global variables.  See the file


drawtrelpiece.m
%
% Draw a piece of a trellis in LaTeX picture mode
%
% fname = file name
% trellis = trellis description
% branchweight = weights of branches


drawvit.m
% Program to draw the paths for the Viterbi algorithm using a LaTeX picture


duality1.m
% Make a plot illustrating duality


eigdir.m
% make a contour plot of eigenstuff


eigdir2.m
% make a contour plot of eigenstuff


eigdirex.m
% make a contour plot of eigenstuff


eigdist.m
% show the asymptotic equal distribution of eigenvalues


ellipse.m
% Plot contours of an ellipse with large eigenvalue disparity
% and the results of steepest descent


ellipsecg.m
% Plot contours of an ellipse with large eigenvalue disparity
% and the results of conjugate gradient.


entplot.m
% plot the binary entropy function


expmod.m
% Test Cadzow's results on the sinusoidal modeling


fourser.m
% example Fourier series


hilb1.m
% Program to generate the data for the hilbert approximation to
% the exponential function


ifs3.m
% Plot the logistic map and the orbit of a point


ifs3b.m
% Plot the logistic map and the orbit of a point
% do not specify lambda and x0 here: it is done by an upper script


ifs4.m
% Demonstrate the logistic map


ifsex3.m
% find an affine transformation Ax + b that transforms from
% {x00,x10,x20} to {x01,x11,x21}


ifsfig1.m
% Make side-by-side figures


legendreplot.m
% Plot legendre polynomials


makeim.m
% make a test image for tomography example


matcond.m
% Make an ill-conditioned matrix of sinusoids.


matcond2.m
% Set up an ill-conditioned matrix of sinusoids


min1.m
% make the contour plot for wftest


min2.m
% make the contour plot for wftest


moveiter.m
% test the solution of a moving RHS in the equation Ax=b


newt1.m
% Demonstrate newton's stuff


newt2.m
% Demonstrate newton's stuff on Rosenbrocks function


oddeven.m
% data for odd/even game


orthog.mma
(* sample file for orthogonalization *)


patrec1.m
% generate some simple pattern recognition example data


plotI0.m
% Plot the Bessel function


plotJsurf.m
% plot a quadratice error surface


plotbpsk.m
% Plot the probability of error for BPSK


plotgauss.m
% Plot the Gaussian function


plotgauss2.m
% Plot approximations to the central limit theorem


plotgauss3.m
% plot a Gauss surface plot


plotwavelet.m
% plot the wavelet data


roc1.m
% plot the roc for a gaussian r.v.


roc2.m
% plot the roc for a a xi^2


roc3.m
% plot the roc for a gaussian r.v. and its conjugate


rosenbrock.m
% Plot the Rosenbrock function contours


rosengrad.m
% 
% compute the gradient of the rosenbrock function for test purposes
% function grad = rosengrad(x)


saddle1.m
% make a saddle plot 


scatter.m
% create a scatter plot to demonstrate principal component


scatterex.m
% create a scatter plot to demonstrate principal component


sigmoid.m
% plot the sigmoid function


steeperr.m
% Plot errors of the steepest descent


steeperrplot.m
% Make plots of error for steepest descent


steepest1.m
% Demonstrate steepest descent on Rosenbrocks function


sugitest.m
% test the Sugiyama algorithm


surf1.m
% make a surface plot


test2regress.m
% Test the formulas for regression in two dimensions
% input: x and y vectors


test2regress2.m
% Test the formulas for regression in two dimensions
% input: x and y vectors


testeigfil.m
% Test the eigenfilter stuff


testeigfil2.m
% Test the eigenfilter stuff


testeigfil3.m
% test the eigenfilter stuff


testexlms.m
% Test the lms in a system identification setting
% Assume a Gaussian input


testlms.m
% test the lms in an equalizer setting
% Assume a binary +/- 1 input.


testmusic.m
% Test the music algorithm


testnn1.m
% test the neural network stuff


testnn2.m
% test the neural network stuff
% (run testnn1.m first to get the network trained)
%
% does some plots after the initial training is finished


testnn3.m
% test the neural network stuff
% try different values of mu and alpha
% run testnn1 first to get the training data


testrls.m
% test the rls in an equalizer setting
% Assume a binary +/- 1 input.


testrls2.m
% test the rls in a system identification setting
% Assume a binary +/- 1 input.


testrls2ex.m
% test the rls in a system identification setting
% Assume a binary +/- 1 input.


testrlsex.m
% test the rls in an equalizer setting
% Assume a binary +/- 1 input.


testrot.m
% test the procrustes rotation


testtls.m
% Test tls stuff


vq1.m
% Generate random Gaussian data, determine a codebook for it, and plot


wftestcont.m
% make the contour plot for wftest


***************************************************************
Directory: solutions
***************************************************************
ator2.m
% 
% Given the coefficients from a 2nd-order AR model
% y[t+2] + a1 y[t+1] + a2 y[t] = f[t+2],
% where f has variance sigmaf2, compute sigma_y^2, r[1], and r[2].
% 
% function [sigma2,r1,r2] = ator2(a1,a2,sigmaf2)
%
% a1, a2 -- AR model coefficients
% sigmaf2 -- input noise variance
%
% sigma2 -- output noise variance
% r1, r2 -- covariance values


backdyn.m
%
% Backward dynamic programming
%
% function [pathlist,cost] = backdyn(H,W)
%
% H = graph
% W = costs
%
% pathlist = list of paths
% cost = cost of paths


backsub.m
% 
% solve Ux = b, where U is upper triangular
%
% function x = backsub(U,b)
% U = upper triangular matrix
% b = right and side
%
% x = solution


bayesest1.m
% Example of non-Gaussian Bayes estimate


correst.m
% 
% Estimate the autocorrelation function
% the returned values are offset (by Matlab requirements) so that
% r(1) = r[0], etc.
% Only correlations for positive lags are returned.  For other values,
% use the fact that r[k] = conj(r[-k])
%
% function r = correst