public static boolean testCostAndGradient(Minimizable.ByGradient minable) {
Matrix parameters = minable.getNewMatrix();
parameters.setAll(0.0);
minable.setParameters(parameters);
testCostAndGradientCurrentParameters(minable);
parameters.setAll(0.0);
Matrix delta = minable.getNewMatrix();
minable.getCostGradient(delta);
delta.timesEquals(-0.0001);
parameters.plusEquals(delta);
minable.setParameters(parameters);
testCostAndGradientCurrentParameters(minable);
return true;
}
public static double testCostAndGradientCurrentParameters(Minimizable.ByGradient minable) {
Matrix parameters = minable.getParameters(minable.getNewMatrix());
double cost = minable.getCost();
// the gradient from the minimizable function
Matrix analyticGradient = minable.getCostGradient(minable.getNewMatrix());
// the gradient calculate from the slope of the cost
Matrix empiricalGradient = (Matrix) analyticGradient.cloneMatrix();
// This setting of epsilon should make the individual elements of
// the analytical gradient and the empirical gradient equal. This
// simplifies the comparison of the individual dimensions of the
// gradient and thus makes debugging easier.
double epsilon = 0.1 / analyticGradient.twoNorm();
double tolerance = epsilon * 5;
System.out.println("epsilon = " + epsilon + " tolerance=" + tolerance);
// Check each direction, perturb it, measure new cost,
// and make sure it agrees with the gradient from minable.getCostGradient()
for (int i = 0; i < parameters.singleSize(); i++) {
double param = parameters.singleValue(i);
parameters.setSingleValue(i, param + epsilon);
// logger.fine ("Parameters:"); parameters.print();
minable.setParameters(parameters);
double epsCost = minable.getCost();
double slope = (epsCost - cost) / epsilon;
System.out.println(
"cost="
+ cost
+ " epsCost="
+ epsCost
+ " slope["
+ i
+ "] = "
+ slope
+ " gradient[]="
+ analyticGradient.singleValue(i));
assert (!Double.isNaN(slope));
logger.fine(
"TestMinimizable checking singleIndex "
+ i
+ ": gradient slope = "
+ analyticGradient.singleValue(i)
+ ", cost+epsilon slope = "
+ slope
+ ": slope difference = "
+ Math.abs(slope - analyticGradient.singleValue(i)));
// No negative below because the gradient points in the direction
// of maximizing the function.
empiricalGradient.setSingleValue(i, slope);
parameters.setSingleValue(i, param);
}
// Normalize the matrices to have the same L2 length
System.out.println("empiricalGradient.twoNorm = " + empiricalGradient.twoNorm());
analyticGradient.timesEquals(1.0 / analyticGradient.twoNorm());
empiricalGradient.timesEquals(1.0 / empiricalGradient.twoNorm());
// logger.info ("AnalyticGradient:"); analyticGradient.print();
// logger.info ("EmpiricalGradient:"); empiricalGradient.print();
// Return the angle between the two vectors, in radians
double angle = Math.acos(analyticGradient.dotProduct(empiricalGradient));
logger.info("TestMinimizable angle = " + angle);
if (Math.abs(angle) > tolerance)
throw new IllegalStateException("Gradient/Cost mismatch: angle=" + angle);
if (Double.isNaN(angle)) throw new IllegalStateException("Gradient/Cost error: angle is NaN!");
return angle;
}