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* 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,
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* See the License for the specific language governing permissions and
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*/
package org.apache.commons.math4.linear;
import org.apache.commons.math4.exception.MathIllegalArgumentException;
import org.apache.commons.math4.linear.Array2DRowRealMatrix;
import org.apache.commons.math4.linear.DecompositionSolver;
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.SingularValueDecomposition;
import org.junit.Assert;
import org.junit.Test;
public class SingularValueSolverTest {
private double[][] testSquare = {
{ 24.0 / 25.0, 43.0 / 25.0 },
{ 57.0 / 25.0, 24.0 / 25.0 }
};
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
private static final double normTolerance = 10e-14;
/** test solve dimension errors */
@Test
public void testSolveDimensionErrors() {
DecompositionSolver solver =
new SingularValueDecomposition(MatrixUtils.createRealMatrix(testSquare)).getSolver();
RealMatrix b = MatrixUtils.createRealMatrix(new double[3][2]);
try {
solver.solve(b);
Assert.fail("an exception should have been thrown");
} catch (MathIllegalArgumentException iae) {
// expected behavior
}
try {
solver.solve(b.getColumnVector(0));
Assert.fail("an exception should have been thrown");
} catch (MathIllegalArgumentException iae) {
// expected behavior
}
try {
solver.solve(new ArrayRealVectorTest.RealVectorTestImpl(b.getColumn(0)));
Assert.fail("an exception should have been thrown");
} catch (MathIllegalArgumentException iae) {
// expected behavior
}
}
/** test least square solve */
@Test
public void testLeastSquareSolve() {
RealMatrix m =
MatrixUtils.createRealMatrix(new double[][] {
{ 1.0, 0.0 },
{ 0.0, 0.0 }
});
DecompositionSolver solver = new SingularValueDecomposition(m).getSolver();
RealMatrix b = MatrixUtils.createRealMatrix(new double[][] {
{ 11, 12 }, { 21, 22 }
});
RealMatrix xMatrix = solver.solve(b);
Assert.assertEquals(11, xMatrix.getEntry(0, 0), 1.0e-15);
Assert.assertEquals(12, xMatrix.getEntry(0, 1), 1.0e-15);
Assert.assertEquals(0, xMatrix.getEntry(1, 0), 1.0e-15);
Assert.assertEquals(0, xMatrix.getEntry(1, 1), 1.0e-15);
RealVector xColVec = solver.solve(b.getColumnVector(0));
Assert.assertEquals(11, xColVec.getEntry(0), 1.0e-15);
Assert.assertEquals(0, xColVec.getEntry(1), 1.0e-15);
RealVector xColOtherVec = solver.solve(new ArrayRealVectorTest.RealVectorTestImpl(b.getColumn(0)));
Assert.assertEquals(11, xColOtherVec.getEntry(0), 1.0e-15);
Assert.assertEquals(0, xColOtherVec.getEntry(1), 1.0e-15);
}
/** test solve */
@Test
public void testSolve() {
DecompositionSolver solver =
new SingularValueDecomposition(MatrixUtils.createRealMatrix(testSquare)).getSolver();
RealMatrix b = MatrixUtils.createRealMatrix(new double[][] {
{ 1, 2, 3 }, { 0, -5, 1 }
});
RealMatrix xRef = MatrixUtils.createRealMatrix(new double[][] {
{ -8.0 / 25.0, -263.0 / 75.0, -29.0 / 75.0 },
{ 19.0 / 25.0, 78.0 / 25.0, 49.0 / 25.0 }
});
// using RealMatrix
Assert.assertEquals(0, solver.solve(b).subtract(xRef).getNorm(), normTolerance);
// using ArrayRealVector
for (int i = 0; i < b.getColumnDimension(); ++i) {
Assert.assertEquals(0,
solver.solve(b.getColumnVector(i)).subtract(xRef.getColumnVector(i)).getNorm(),
1.0e-13);
}
// 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,
solver.solve(v).subtract(xRef.getColumnVector(i)).getNorm(),
1.0e-13);
}
}
/** test condition number */
@Test
public void testConditionNumber() {
SingularValueDecomposition svd =
new SingularValueDecomposition(MatrixUtils.createRealMatrix(testSquare));
// replace 1.0e-15 with 1.5e-15
Assert.assertEquals(3.0, svd.getConditionNumber(), 1.5e-15);
}
@Test
public void testMath320B() {
RealMatrix rm = new Array2DRowRealMatrix(new double[][] {
{ 1.0, 2.0 }, { 1.0, 2.0 }
});
SingularValueDecomposition svd =
new SingularValueDecomposition(rm);
RealMatrix recomposed = svd.getU().multiply(svd.getS()).multiply(svd.getVT());
Assert.assertEquals(0.0, recomposed.subtract(rm).getNorm(), 2.0e-15);
}
@Test
public void testSingular() {
SingularValueDecomposition svd =
new SingularValueDecomposition(MatrixUtils.createRealMatrix(bigSingular));
RealMatrix pseudoInverse = svd.getSolver().getInverse();
RealMatrix expected = new Array2DRowRealMatrix(new double[][] {
{-0.0355022687,0.0512742236,-0.0001045523,0.0157719549},
{-0.3214992438,0.3162419255,0.0000348508,-0.0052573183},
{0.5437098346,-0.4107754586,-0.0008256918,0.132934376},
{-0.0714905202,0.053808742,0.0006279816,-0.0176817782}
});
Assert.assertEquals(0, expected.subtract(pseudoInverse).getNorm(), 1.0e-9);
}
}