private void stochasticUpdateStep(Pair<Integer, Set<Integer>> wordPlusContexts, int s) {
double eta = learningRateDecay(s);
int wordIndex = wordPlusContexts.getFirst(); // actual center word
// Set h vector equal to the kth row of weight matrix W1. h = x' * W = W[k,:] = v(input)
RealVector h = W1.getRowVector(wordIndex); // 1xN row vector
for (int contextWordIndex : wordPlusContexts.getSecond()) {
Set<Integer> negativeContexts;
if (sampleUnigram) {
negativeContexts = negativeSampleContexts(wordIndex, noiseSampler);
} else {
negativeContexts = negativeSampleContexts(wordIndex);
}
// wordIndex is the input word
// negativeContexts is the k negative contexts
// contextWordIndex is 1 positive context
// First update the output vectors for 1 positive context
RealVector vPrime_j = W2.getColumnVector(contextWordIndex); // Nx1 column vector
double u = h.dotProduct(vPrime_j); // u_j = vPrime(output) * v(input)
double t_j = 1.0; // t_j := 1{j == contextWordIndex}
double scale = sigmoid(u) - t_j;
scale = eta * scale;
RealVector gradientOut2Hidden = h.mapMultiply(scale);
vPrime_j = vPrime_j.subtract(gradientOut2Hidden);
W2.setColumnVector(contextWordIndex, vPrime_j);
// Next backpropagate the error to the hidden layer and update the input vectors
RealVector v_I = h;
u = h.dotProduct(vPrime_j);
scale = sigmoid(u) - t_j;
scale = eta * scale;
RealVector gradientHidden2In = vPrime_j.mapMultiply(scale);
v_I = v_I.subtract(gradientHidden2In);
h = v_I;
W1.setRowVector(wordIndex, v_I);
// Repeat update process for k negative contexts
t_j = 0.0; // t_j := 1{j == contextWordIndex}
for (int negContext : negativeContexts) {
vPrime_j = W2.getColumnVector(negContext);
u = h.dotProduct(vPrime_j);
scale = sigmoid(u) - t_j;
scale = eta * scale;
gradientOut2Hidden = h.mapMultiply(scale);
vPrime_j = vPrime_j.subtract(gradientOut2Hidden);
W2.setColumnVector(negContext, vPrime_j);
// Backpropagate the error to the hidden layer and update the input vectors
v_I = h;
u = h.dotProduct(vPrime_j);
scale = sigmoid(u) - t_j;
scale = eta * scale;
gradientHidden2In = vPrime_j.mapMultiply(scale);
v_I = v_I.subtract(gradientHidden2In);
h = v_I;
W1.setRowVector(wordIndex, v_I);
}
}
}
private static Intersection getIntersection(Ray ray, SphereObject obj, Model model) {
RealMatrix transform = obj.getTransform();
final RealMatrix transformInverse = obj.getTransformInverse();
ray = ray.transform(transformInverse);
Vector3D c = VectorUtils.toVector3D(obj.getCenter());
Vector3D p0 = VectorUtils.toVector3D(ray.getP0());
Vector3D p1 = VectorUtils.toVector3D(ray.getP1());
float a = (float) p1.dotProduct(p1);
Vector3D p0c = p0.subtract(c);
float b = (float) p1.dotProduct(p0c) * 2.0f;
float cc = (float) (p0c.dotProduct(p0c)) - obj.getSize() * obj.getSize();
Double t = quadraticEquationRoot1(a, b, cc);
if (t == null || t < EPSILON) {
return new Intersection(false);
}
Intersection result = new Intersection(true);
result.setObject(obj);
final Vector3D p = p0.add(p1.scalarMultiply(t));
RealVector pv = VectorUtils.toRealVector(p);
pv.setEntry(3, 1.0);
RealVector pt = transform.preMultiply(pv);
result.setP(VectorUtils.toVector3D(pt));
RealVector nv = pv.subtract(obj.getCenter());
final RealVector nvt = transformInverse.transpose().preMultiply(nv);
result.setN(VectorUtils.toVector3D(nvt).normalize());
result.setDistance(t);
return result;
}