circle.addPoint( 50, -6);
circle.addPoint(110, -20);
circle.addPoint( 35, 15);
circle.addPoint( 45, 97);
AbstractLeastSquaresOptimizer optimizer = createOptimizer();
PointVectorValuePair optimum
= optimizer.optimize(new MaxEval(100),
circle.getModelFunction(),
circle.getModelFunctionJacobian(),
new Target(new double[] { 0, 0, 0, 0, 0 }),
new Weight(new double[] { 1, 1, 1, 1, 1 }),
new InitialGuess(new double[] { 98.680, 47.345 }));
Assert.assertTrue(optimizer.getEvaluations() < 10);
double rms = optimizer.getRMS();
Assert.assertEquals(1.768262623567235, FastMath.sqrt(circle.getN()) * rms, 1e-10);
Vector2D center = new Vector2D(optimum.getPointRef()[0], optimum.getPointRef()[1]);
Assert.assertEquals(69.96016176931406, circle.getRadius(center), 1e-6);
Assert.assertEquals(96.07590211815305, center.getX(), 1e-6);
Assert.assertEquals(48.13516790438953, center.getY(), 1e-6);
double[][] cov = optimizer.computeCovariances(optimum.getPoint(), 1e-14);
Assert.assertEquals(1.839, cov[0][0], 0.001);
Assert.assertEquals(0.731, cov[0][1], 0.001);
Assert.assertEquals(cov[0][1], cov[1][0], 1e-14);
Assert.assertEquals(0.786, cov[1][1], 0.001);
// add perfect measurements and check errors are reduced
double r = circle.getRadius(center);
for (double d= 0; d < 2 * FastMath.PI; d += 0.01) {
circle.addPoint(center.getX() + r * FastMath.cos(d), center.getY() + r * FastMath.sin(d));
}
double[] target = new double[circle.getN()];
Arrays.fill(target, 0);
double[] weights = new double[circle.getN()];
Arrays.fill(weights, 2);
optimum = optimizer.optimize(new MaxEval(100),
circle.getModelFunction(),
circle.getModelFunctionJacobian(),
new Target(target),
new Weight(weights),
new InitialGuess(new double[] { 98.680, 47.345 }));
cov = optimizer.computeCovariances(optimum.getPoint(), 1e-14);
Assert.assertEquals(0.0016, cov[0][0], 0.001);
Assert.assertEquals(3.2e-7, cov[0][1], 1e-9);
Assert.assertEquals(cov[0][1], cov[1][0], 1e-14);
Assert.assertEquals(0.0016, cov[1][1], 0.001);
}