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* licenses this file to You under the Apache License, Version 2.0 (the
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* You may obtain a copy of the License at
* http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law
* or agreed to in writing, software distributed under the License is
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package org.apache.commons.math4.fitting.leastsquares;
import org.apache.commons.math4.TestUtils;
import org.apache.commons.math4.analysis.MultivariateMatrixFunction;
import org.apache.commons.math4.analysis.MultivariateVectorFunction;
import org.apache.commons.math4.exception.MathIllegalStateException;
import org.apache.commons.math4.fitting.leastsquares.LeastSquaresBuilder;
import org.apache.commons.math4.fitting.leastsquares.LeastSquaresFactory;
import org.apache.commons.math4.fitting.leastsquares.LeastSquaresProblem;
import org.apache.commons.math4.fitting.leastsquares.MultivariateJacobianFunction;
import org.apache.commons.math4.fitting.leastsquares.ValueAndJacobianFunction;
import org.apache.commons.math4.fitting.leastsquares.LeastSquaresProblem.Evaluation;
import org.apache.commons.math4.linear.ArrayRealVector;
import org.apache.commons.math4.linear.DiagonalMatrix;
import org.apache.commons.math4.linear.MatrixUtils;
import org.apache.commons.math4.linear.RealMatrix;
import org.apache.commons.math4.linear.RealVector;
import org.apache.commons.math4.linear.SingularMatrixException;
import org.apache.commons.math4.util.FastMath;
import org.apache.commons.math4.util.Pair;
import org.apache.commons.numbers.core.Precision;
import org.junit.Assert;
import org.junit.Test;
import java.io.IOException;
import java.util.Arrays;
/**
* The only features tested here are utility methods defined
* in {@link LeastSquaresProblem.Evaluation} that compute the
* chi-square and parameters standard-deviations.
*/
public class EvaluationTest {
/**
* Create a {@link LeastSquaresBuilder} from a {@link StatisticalReferenceDataset}.
*
* @param dataset the source data
* @return a builder for further customization.
*/
public LeastSquaresBuilder builder(StatisticalReferenceDataset dataset) {
StatisticalReferenceDataset.LeastSquaresProblem problem
= dataset.getLeastSquaresProblem();
final double[] start = dataset.getParameters();
final double[] observed = dataset.getData()[1];
final double[] weights = new double[observed.length];
Arrays.fill(weights, 1d);
return new LeastSquaresBuilder()
.model(problem.getModelFunction(), problem.getModelFunctionJacobian())
.target(observed)
.weight(new DiagonalMatrix(weights))
.start(start);
}
@Test
public void testComputeResiduals() {
//setup
RealVector point = new ArrayRealVector(2);
Evaluation evaluation = new LeastSquaresBuilder()
.target(new ArrayRealVector(new double[]{3,-1}))
.model(new MultivariateJacobianFunction() {
@Override
public Pair<RealVector, RealMatrix> value(RealVector point) {
return new Pair<RealVector, RealMatrix>(
new ArrayRealVector(new double[]{1, 2}),
MatrixUtils.createRealIdentityMatrix(2)
);
}
})
.weight(MatrixUtils.createRealIdentityMatrix(2))
.build()
.evaluate(point);
//action + verify
Assert.assertArrayEquals(
evaluation.getResiduals().toArray(),
new double[]{2, -3},
Precision.EPSILON);
}
@Test
public void testComputeCovariance() throws IOException {
//setup
RealVector point = new ArrayRealVector(2);
Evaluation evaluation = new LeastSquaresBuilder()
.model(new MultivariateJacobianFunction() {
@Override
public Pair<RealVector, RealMatrix> value(RealVector point) {
return new Pair<RealVector, RealMatrix>(
new ArrayRealVector(2),
MatrixUtils.createRealDiagonalMatrix(new double[]{1, 1e-2})
);
}
})
.weight(MatrixUtils.createRealDiagonalMatrix(new double[]{1, 1}))
.target(new ArrayRealVector(2))
.build()
.evaluate(point);
//action
TestUtils.assertEquals(
"covariance",
evaluation.getCovariances(FastMath.nextAfter(1e-4, 0.0)),
MatrixUtils.createRealMatrix(new double[][]{{1, 0}, {0, 1e4}}),
Precision.EPSILON
);
//singularity fail
try {
evaluation.getCovariances(FastMath.nextAfter(1e-4, 1.0));
Assert.fail("Expected Exception");
} catch (SingularMatrixException e) {
//expected
}
}
@Test
public void testComputeValueAndJacobian() {
//setup
final RealVector point = new ArrayRealVector(new double[]{1, 2});
Evaluation evaluation = new LeastSquaresBuilder()
.weight(new DiagonalMatrix(new double[]{16, 4}))
.model(new MultivariateJacobianFunction() {
@Override
public Pair<RealVector, RealMatrix> value(RealVector actualPoint) {
//verify correct values passed in
Assert.assertArrayEquals(
point.toArray(), actualPoint.toArray(), Precision.EPSILON);
//return values
return new Pair<RealVector, RealMatrix>(
new ArrayRealVector(new double[]{3, 4}),
MatrixUtils.createRealMatrix(new double[][]{{5, 6}, {7, 8}})
);
}
})
.target(new double[2])
.build()
.evaluate(point);
//action
RealVector residuals = evaluation.getResiduals();
RealMatrix jacobian = evaluation.getJacobian();
//verify
Assert.assertArrayEquals(evaluation.getPoint().toArray(), point.toArray(), 0);
Assert.assertArrayEquals(new double[]{-12, -8}, residuals.toArray(), Precision.EPSILON);
TestUtils.assertEquals(
"jacobian",
jacobian,
MatrixUtils.createRealMatrix(new double[][]{{20, 24},{14, 16}}),
Precision.EPSILON);
}
@Test
public void testComputeCost() throws IOException {
final StatisticalReferenceDataset dataset
= StatisticalReferenceDatasetFactory.createKirby2();
final LeastSquaresProblem lsp = builder(dataset).build();
final double expected = dataset.getResidualSumOfSquares();
final double cost = lsp.evaluate(lsp.getStart()).getCost();
final double actual = cost * cost;
Assert.assertEquals(dataset.getName(), expected, actual, 1e-11 * expected);
}
@Test
public void testComputeRMS() throws IOException {
final StatisticalReferenceDataset dataset
= StatisticalReferenceDatasetFactory.createKirby2();
final LeastSquaresProblem lsp = builder(dataset).build();
final double expected = FastMath.sqrt(dataset.getResidualSumOfSquares() /
dataset.getNumObservations());
final double actual = lsp.evaluate(lsp.getStart()).getRMS();
Assert.assertEquals(dataset.getName(), expected, actual, 1e-11 * expected);
}
@Test
public void testComputeSigma() throws IOException {
final StatisticalReferenceDataset dataset
= StatisticalReferenceDatasetFactory.createKirby2();
final LeastSquaresProblem lsp = builder(dataset).build();
final double[] expected = dataset.getParametersStandardDeviations();
final Evaluation evaluation = lsp.evaluate(lsp.getStart());
final double cost = evaluation.getCost();
final RealVector sig = evaluation.getSigma(1e-14);
final int dof = lsp.getObservationSize() - lsp.getParameterSize();
for (int i = 0; i < sig.getDimension(); i++) {
final double actual = FastMath.sqrt(cost * cost / dof) * sig.getEntry(i);
Assert.assertEquals(dataset.getName() + ", parameter #" + i,
expected[i], actual, 1e-6 * expected[i]);
}
}
@Test
public void testEvaluateCopiesPoint() throws IOException {
//setup
StatisticalReferenceDataset dataset
= StatisticalReferenceDatasetFactory.createKirby2();
LeastSquaresProblem lsp = builder(dataset).build();
RealVector point = new ArrayRealVector(lsp.getParameterSize());
//action
Evaluation evaluation = lsp.evaluate(point);
//verify
Assert.assertNotSame(point, evaluation.getPoint());
point.setEntry(0, 1);
Assert.assertEquals(evaluation.getPoint().getEntry(0), 0, 0);
}
@Test
public void testLazyEvaluation() {
final RealVector dummy = new ArrayRealVector(new double[] { 0 });
final LeastSquaresProblem p
= LeastSquaresFactory.create(LeastSquaresFactory.model(dummyModel(), dummyJacobian()),
dummy, dummy, null, null, 0, 0, true, null);
// Should not throw because actual evaluation is deferred.
final Evaluation eval = p.evaluate(dummy);
try {
eval.getResiduals();
Assert.fail("Exception expected");
} catch (RuntimeException e) {
// Expecting exception.
Assert.assertEquals("dummyModel", e.getMessage());
}
try {
eval.getJacobian();
Assert.fail("Exception expected");
} catch (RuntimeException e) {
// Expecting exception.
Assert.assertEquals("dummyJacobian", e.getMessage());
}
}
// MATH-1151
@Test
public void testLazyEvaluationPrecondition() {
final RealVector dummy = new ArrayRealVector(new double[] { 0 });
// "ValueAndJacobianFunction" is required but we implement only
// "MultivariateJacobianFunction".
final MultivariateJacobianFunction m1 = new MultivariateJacobianFunction() {
@Override
public Pair<RealVector, RealMatrix> value(RealVector notUsed) {
return new Pair<>(null, null);
}
};
try {
// Should throw.
LeastSquaresFactory.create(m1, dummy, dummy, null, null, 0, 0, true, null);
Assert.fail("Expecting MathIllegalStateException");
} catch (MathIllegalStateException e) {
// Expected.
}
final MultivariateJacobianFunction m2 = new ValueAndJacobianFunction() {
@Override
public Pair<RealVector, RealMatrix> value(RealVector notUsed) {
return new Pair<>(null, null);
}
@Override
public RealVector computeValue(final double[] params) {
return null;
}
@Override
public RealMatrix computeJacobian(final double[] params) {
return null;
}
};
// Should pass.
LeastSquaresFactory.create(m2, dummy, dummy, null, null, 0, 0, true, null);
}
@Test
public void testDirectEvaluation() {
final RealVector dummy = new ArrayRealVector(new double[] { 0 });
final LeastSquaresProblem p
= LeastSquaresFactory.create(LeastSquaresFactory.model(dummyModel(), dummyJacobian()),
dummy, dummy, null, null, 0, 0, false, null);
try {
// Should throw.
p.evaluate(dummy);
Assert.fail("Exception expected");
} catch (RuntimeException e) {
// Expecting exception.
// Whether it is model or Jacobian that caused it is not significant.
final String msg = e.getMessage();
Assert.assertTrue(msg.equals("dummyModel") ||
msg.equals("dummyJacobian"));
}
}
/** Used for testing direct vs lazy evaluation. */
private MultivariateVectorFunction dummyModel() {
return new MultivariateVectorFunction() {
@Override
public double[] value(double[] p) {
throw new RuntimeException("dummyModel");
}
};
}
/** Used for testing direct vs lazy evaluation. */
private MultivariateMatrixFunction dummyJacobian() {
return new MultivariateMatrixFunction() {
@Override
public double[][] value(double[] p) {
throw new RuntimeException("dummyJacobian");
}
};
}
}