/* Check that the operations do not throw an exception (cf. MATH-645). */
@Test
public void testConcurrentModification() {
final RealVector u = new OpenMapRealVector(3, 1e-6);
u.setEntry(0, 1);
u.setEntry(1, 0);
u.setEntry(2, 2);
final RealVector v1 = new OpenMapRealVector(3, 1e-6);
v1.setEntry(0, 0);
v1.setEntry(1, 3);
v1.setEntry(2, 0);
u.ebeMultiply(v1);
u.ebeDivide(v1);
}
@Override
public Label predict(Instance instance) {
Label l = null;
if (instance.getLabel() instanceof ClassificationLabel || instance.getLabel() == null) {
// ----------------- declare variables ------------------
double lambda = 0.0;
RealVector x_instance = new ArrayRealVector(matrixX.getColumnDimension(), 0);
double result = 0.0;
// -------------------------- initialize xi -------------------------
for (int idx = 0; idx < matrixX.getColumnDimension(); idx++) {
x_instance.setEntry(idx, instance.getFeatureVector().get(idx + 1));
}
// ------------------ get lambda -----------------------
for (int j = 0; j < alpha.getDimension(); j++) {
lambda += alpha.getEntry(j) * kernelFunction(matrixX.getRowVector(j), x_instance);
}
// ----------------- make prediction -----------------
Sigmoid g = new Sigmoid(); // helper function
result = g.value(lambda);
l = new ClassificationLabel(result < 0.5 ? 0 : 1);
} else {
System.out.println("label type error!");
}
return l;
}
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;
}
@Override
public void train(List<Instance> instances) {
// ------------------------ initialize rows and columns ---------------------
int rows = instances.size();
int columns = 0;
// get max columns
for (Instance i : instances) {
int localColumns = Collections.max(i.getFeatureVector().getFeatureMap().keySet());
if (localColumns > columns) columns = localColumns;
}
// ------------------------ initialize alpha vector -----------------------
alpha = new ArrayRealVector(rows, 0);
// ------------------------ initialize base X and Y for use --------------------------
double[][] X = new double[rows][columns];
double[] Y = new double[rows];
for (int i = 0; i < rows; i++) {
Y[i] = ((ClassificationLabel) instances.get(i).getLabel()).getLabelValue();
for (int j = 0; j < columns; j++) {
X[i][j] = instances.get(i).getFeatureVector().get(j + 1);
}
}
// ---------------------- gram matrix -------------------
matrixX = new Array2DRowRealMatrix(X);
RealMatrix gram = new Array2DRowRealMatrix(rows, rows);
for (int i = 0; i < rows; i++) {
for (int j = 0; j < rows; j++) {
gram.setEntry(i, j, kernelFunction(matrixX.getRowVector(i), matrixX.getRowVector(j)));
}
}
// ---------------------- gradient ascent --------------------------
Sigmoid g = new Sigmoid(); // helper function
System.out.println("Training start...");
System.out.println(
"Learning rate: " + _learning_rate + " Training times: " + _training_iterations);
for (int idx = 0; idx < _training_iterations; idx++) {
System.out.println("Training iteration: " + (idx + 1));
for (int k = 0; k < rows; k++) {
double gradient_ascent = 0.0;
RealVector alpha_gram = gram.operate(alpha);
for (int i = 0; i < rows; i++) {
double lambda = alpha_gram.getEntry(i);
double kernel = gram.getEntry(i, k);
gradient_ascent =
gradient_ascent
+ Y[i] * g.value(-lambda) * kernel
+ (1 - Y[i]) * g.value(lambda) * (-kernel);
}
alpha.setEntry(k, alpha.getEntry(k) + _learning_rate * gradient_ascent);
}
}
System.out.println("Training done!");
}
/**
* Solve the linear equation A × X = B in least square sense.
*
* <p>The m×n matrix A may not be square, the solution X is such that ||A × X - B||
* is minimal.
*
* @param b right-hand side of the equation A × X = B
* @return a vector X that minimizes the two norm of A × X - B
* @exception IllegalArgumentException if matrices dimensions don't match
* @exception InvalidMatrixException if decomposed matrix is singular
*/
public RealVector solve(final RealVector b)
throws IllegalArgumentException, InvalidMatrixException {
if (b.getDimension() != uT.getColumnDimension()) {
throw MathRuntimeException.createIllegalArgumentException(
"vector length mismatch: got {0} but expected {1}",
b.getDimension(), uT.getColumnDimension());
}
final RealVector w = uT.operate(b);
for (int i = 0; i < singularValues.length; ++i) {
final double si = singularValues[i];
if (si == 0) {
throw new SingularMatrixException();
}
w.setEntry(i, w.getEntry(i) / si);
}
return v.operate(w);
}
