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function test_kernel_pre()
kerneltype = 'rbf';
rand('state', 123456);
n = 10;
m = 5;
cutoff = 5e-3;
X = rand(n, m);
Z = [ones(n, 1), X];
set_matrix(Z, "data->Z", "data->m+1");
K = zeros(n, n);
if strcmp(kerneltype, 'poly')
# Polynomial kernel
# (gamma * <x_1, x_2> + c)^d
gamma = 1.5;
c = 3.0;
d = 1.78;
for ii=1:n
for jj=1:n
K(ii, jj) = (gamma * (X(ii, :) * X(jj, :)') + c)^d;
end
end
elseif strcmp(kerneltype, 'rbf')
# RBF kernel
# exp(-gamma * norm(x1 - x2)^2)
gamma = 0.348
for ii=1:n
for jj=1:n
K(ii, jj) = exp(-gamma * sum((X(ii, :) - X(jj, :)).^2));
end
end
elseif strcmp(kerneltype, 'sigmoid')
# Sigmoid kernel
# tanh(gamma * <x_1, x_2> + c)
gamma = 1.23;
c = 1.6;
for ii=1:n
for jj=1:n
K(ii, jj) = tanh(gamma * (X(ii, :) * X(jj, :)') + c);
end
end
end
K(1, 2)
[P, Sigma] = eig(K);
eigenvalues = diag(Sigma);
ratios = eigenvalues ./ eigenvalues(end, end);
realP = fliplr(P(:, ratios > cutoff));
realSigma = flipud(eigenvalues(ratios > cutoff));
assert_matrix(realSigma, "data->Sigma", "1");
r = sum(ratios > cutoff);
fprintf("mu_assert(data->r == %i);\n", r);
M = realP * diag(realSigma);
newZ = [ones(n, 1) M];
assert_matrix_abs(newZ, "data->Z", "data->r+1");
assert_matrix(Z, "data->RAW", "data->m+1");
end
function set_matrix(A, name, cols)
for ii=1:size(A, 1)
for jj=1:size(A, 2)
fprintf("matrix_set(%s, %s, %i, %i, %.16f);\n", name, cols, ii-1, jj-1, A(ii, jj));
end
end
fprintf("\n");
end
function assert_matrix(A, name, cols)
for ii=1:size(A, 1)
for jj=1:size(A, 2)
fprintf(["mu_assert(fabs(matrix_get(%s, %s, %i, %i) -\n%.16f) <", ...
" eps,\n\"Incorrect %s at %i, %i\");\n"], name, cols, ...
ii-1, jj-1, A(ii, jj), name, ii-1, jj-1);
end
end
fprintf("\n");
end
function assert_matrix_abs(A, name, cols)
for ii=1:size(A, 1)
for jj=1:size(A, 2)
fprintf(["mu_assert(fabs(fabs(matrix_get(%s, %s, %i, %i)) -\nfabs(%.16f)) <", ...
" eps,\n\"Incorrect %s at %i, %i\");\n"], name, cols, ...
ii-1, jj-1, A(ii, jj), name, ii-1, jj-1);
end
end
fprintf("\n");
end
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