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* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. 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 distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math4.linear;
import java.util.Random;
import org.apache.commons.math4.exception.MathIllegalArgumentException;
import org.apache.commons.math4.linear.DecompositionSolver;
import org.apache.commons.math4.linear.EigenDecomposition;
import org.apache.commons.math4.linear.MatrixUtils;
import org.apache.commons.math4.linear.RealMatrix;
import org.apache.commons.math4.linear.SingularMatrixException;
import org.apache.commons.numbers.core.Precision;
import org.junit.Test;
import org.junit.Assert;
public class EigenSolverTest {
private double[][] bigSingular = {
{ 1.0, 2.0, 3.0, 4.0 },
{ 2.0, 5.0, 3.0, 4.0 },
{ 7.0, 3.0, 256.0, 1930.0 },
{ 3.0, 7.0, 6.0, 8.0 }
}; // 4th row = 1st + 2nd
/** test non invertible matrix */
@Test
public void testNonInvertible() {
Random r = new Random(9994100315209l);
RealMatrix m =
EigenDecompositionTest.createTestMatrix(r, new double[] { 1.0, 0.0, -1.0, -2.0, -3.0 });
DecompositionSolver es = new EigenDecomposition(m).getSolver();
Assert.assertFalse(es.isNonSingular());
try {
es.getInverse();
Assert.fail("an exception should have been thrown");
} catch (SingularMatrixException ime) {
// expected behavior
}
}
/** test invertible matrix */
@Test
public void testInvertible() {
Random r = new Random(9994100315209l);
RealMatrix m =
EigenDecompositionTest.createTestMatrix(r, new double[] { 1.0, 0.5, -1.0, -2.0, -3.0 });
DecompositionSolver es = new EigenDecomposition(m).getSolver();
Assert.assertTrue(es.isNonSingular());
RealMatrix inverse = es.getInverse();
RealMatrix error =
m.multiply(inverse).subtract(MatrixUtils.createRealIdentityMatrix(m.getRowDimension()));
Assert.assertEquals(0, error.getNorm(), 4.0e-15);
}
/**
* Verifies operation on very small values.
* Matrix with eigenvalues {8e-100, -1e-100, -1e-100}
*/
@Test
public void testInvertibleTinyValues() {
final double tiny = 1e-100;
RealMatrix m = MatrixUtils.createRealMatrix(new double[][] {
{3, 2, 4},
{2, 0, 2},
{4, 2, 3}
});
m = m.scalarMultiply(tiny);
final EigenDecomposition ed = new EigenDecomposition(m);
RealMatrix inv = ed.getSolver().getInverse();
final RealMatrix id = m.multiply(inv);
for (int i = 0; i < m.getRowDimension(); i++) {
for (int j = 0; j < m.getColumnDimension(); j++) {
if (i == j) {
Assert.assertTrue(Precision.equals(1, id.getEntry(i, j), 1e-15));
} else {
Assert.assertTrue(Precision.equals(0, id.getEntry(i, j), 1e-15));
}
}
}
}
@Test(expected=SingularMatrixException.class)
public void testNonInvertibleMath1045() {
EigenDecomposition eigen =
new EigenDecomposition(MatrixUtils.createRealMatrix(bigSingular));
eigen.getSolver().getInverse();
}
@Test(expected=SingularMatrixException.class)
public void testZeroMatrix() {
EigenDecomposition eigen =
new EigenDecomposition(MatrixUtils.createRealMatrix(new double[][] {{0}}));
eigen.getSolver().getInverse();
}
@Test
public void testIsNonSingularTinyOutOfOrderEigenvalue() {
final EigenDecomposition eigen
= new EigenDecomposition(MatrixUtils.createRealMatrix(new double[][] {
{ 1e-13, 0 },
{ 1, 1 },
}));
Assert.assertFalse("Singular matrix not detected",
eigen.getSolver().isNonSingular());
}
/** test solve dimension errors */
@Test
public void testSolveDimensionErrors() {
final double[] refValues = new double[] {
2.003, 2.002, 2.001, 1.001, 1.000, 0.001
};
final RealMatrix matrix = EigenDecompositionTest.createTestMatrix(new Random(35992629946426l), refValues);
DecompositionSolver es = new EigenDecomposition(matrix).getSolver();
RealMatrix b = MatrixUtils.createRealMatrix(new double[2][2]);
try {
es.solve(b);
Assert.fail("an exception should have been thrown");
} catch (MathIllegalArgumentException iae) {
// expected behavior
}
try {
es.solve(b.getColumnVector(0));
Assert.fail("an exception should have been thrown");
} catch (MathIllegalArgumentException iae) {
// expected behavior
}
try {
es.solve(new ArrayRealVectorTest.RealVectorTestImpl(b.getColumn(0)));
Assert.fail("an exception should have been thrown");
} catch (MathIllegalArgumentException iae) {
// expected behavior
}
}
/** test solve */
@Test
public void testSolve() {
RealMatrix m = MatrixUtils.createRealMatrix(new double[][] {
{ 91, 5, 29, 32, 40, 14 },
{ 5, 34, -1, 0, 2, -1 },
{ 29, -1, 12, 9, 21, 8 },
{ 32, 0, 9, 14, 9, 0 },
{ 40, 2, 21, 9, 51, 19 },
{ 14, -1, 8, 0, 19, 14 }
});
DecompositionSolver es = new EigenDecomposition(m).getSolver();
RealMatrix b = MatrixUtils.createRealMatrix(new double[][] {
{ 1561, 269, 188 },
{ 69, -21, 70 },
{ 739, 108, 63 },
{ 324, 86, 59 },
{ 1624, 194, 107 },
{ 796, 69, 36 }
});
RealMatrix xRef = MatrixUtils.createRealMatrix(new double[][] {
{ 1, 2, 1 },
{ 2, -1, 2 },
{ 4, 2, 3 },
{ 8, -1, 0 },
{ 16, 2, 0 },
{ 32, -1, 0 }
});
// using RealMatrix
RealMatrix solution=es.solve(b);
Assert.assertEquals(0, solution.subtract(xRef).getNorm(), 2.5e-12);
// using RealVector
for (int i = 0; i < b.getColumnDimension(); ++i) {
Assert.assertEquals(0,
es.solve(b.getColumnVector(i)).subtract(xRef.getColumnVector(i)).getNorm(),
2.0e-11);
}
// using RealVector with an alternate implementation
for (int i = 0; i < b.getColumnDimension(); ++i) {
ArrayRealVectorTest.RealVectorTestImpl v =
new ArrayRealVectorTest.RealVectorTestImpl(b.getColumn(i));
Assert.assertEquals(0,
es.solve(v).subtract(xRef.getColumnVector(i)).getNorm(),
2.0e-11);
}
}
}