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function M = sampleUniformInts(N, r, c) % M is an rxc matrix of integers in 1..N prob = normalize(ones(N,1)); M = sample_discrete(prob, r, c);

function m = sqdist(p, q, A) % SQDIST Squared Euclidean or Mahalanobis distance. % SQDIST(p,q) returns m(i,j) = (p(:,i) - q(:,j))'*(p(:,i) - q(:,j)). % SQDIST(p,q,A) returns m(i,j) = (p(:,i)

function b = positive_semidefinite(M) % % Return true iff v M v' >= 0 for any vector v. % We do this by checking that all the eigenvalues are non-negative. E = eig(M); if length(find(E>=0)) ==

function [M, z] = normalise(A, dim) % NORMALISE Make the entries of a (multidimensional) array sum to 1 % [M, c] = normalise(A) % c is the normalizing constant % % [M, c] = normalise(A, dim) % I

colors = ['r' 'b' 'k' 'g' 'c' 'y' 'm' ... 'r' 'b' 'k' 'g' 'c' 'y' 'm']; symbols = ['o' 'x' 's' '>' '

function M = setdiag(M, v) % SETDIAG Set the diagonal of a matrix to a specified scalar/vector. % M = set_diag(M, v) n = length(M); if length(v)==1 v = repmat(v, 1, n); end % e.g., for 3x

function M = rand_psd(d, d2, k) % Create a random positive definite matrix of size d by d by k (k defaults to 1) % M = rand_psd(d, d2, k) default: d2 = d, k = 1 if nargin

function M = sample_discrete(prob, r, c) % SAMPLE_DISCRETE Like the built in 'rand', except we draw from a non-uniform discrete distrib. % M = sample_discrete(prob, r, c) % % Example: sample_discr

function M = assign_cols(cols, vals, M) % ASSIGN_COLS Assign values to columns of a matrix % function M = assign_cols(M, cols, vals, M) % % Example: % M = assign_cols(data, ones(1,N)) % will con

function [M, z] = normalise(A, dim) % NORMALISE Make the entries of a (multidimensional) array sum to 1 % [M, c] = normalise(A) % c is the normalizing constant % % [M, c] = normalise(A, dim) % I