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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,
* 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 org.apache.commons.math4.exception.MathIllegalArgumentException;
import org.apache.commons.math4.linear.DecompositionSolver;
import org.apache.commons.math4.linear.LUDecomposition;
import org.apache.commons.math4.linear.MatrixUtils;
import org.apache.commons.math4.linear.RealMatrix;
import org.apache.commons.math4.linear.SingularMatrixException;
import org.junit.Test;
import org.junit.Assert;
public class LUSolverTest {
private double[][] testData = {
{ 1.0, 2.0, 3.0},
{ 2.0, 5.0, 3.0},
{ 1.0, 0.0, 8.0}
};
private double[][] luData = {
{ 2.0, 3.0, 3.0 },
{ 0.0, 5.0, 7.0 },
{ 6.0, 9.0, 8.0 }
};
// singular matrices
private double[][] singular = {
{ 2.0, 3.0 },
{ 2.0, 3.0 }
};
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
/** test threshold impact */
@Test
public void testThreshold() {
final RealMatrix matrix = MatrixUtils.createRealMatrix(new double[][] {
{ 1.0, 2.0, 3.0},
{ 2.0, 5.0, 3.0},
{ 4.000001, 9.0, 9.0}
});
Assert.assertFalse(new LUDecomposition(matrix, 1.0e-5).getSolver().isNonSingular());
Assert.assertTrue(new LUDecomposition(matrix, 1.0e-10).getSolver().isNonSingular());
}
/** test singular */
@Test
public void testSingular() {
DecompositionSolver solver =
new LUDecomposition(MatrixUtils.createRealMatrix(testData)).getSolver();
Assert.assertTrue(solver.isNonSingular());
solver = new LUDecomposition(MatrixUtils.createRealMatrix(singular)).getSolver();
Assert.assertFalse(solver.isNonSingular());
solver = new LUDecomposition(MatrixUtils.createRealMatrix(bigSingular)).getSolver();
Assert.assertFalse(solver.isNonSingular());
}
/** test solve dimension errors */
@Test
public void testSolveDimensionErrors() {
DecompositionSolver solver =
new LUDecomposition(MatrixUtils.createRealMatrix(testData)).getSolver();
RealMatrix b = MatrixUtils.createRealMatrix(new double[2][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 solve singularity errors */
@Test
public void testSolveSingularityErrors() {
DecompositionSolver solver =
new LUDecomposition(MatrixUtils.createRealMatrix(singular)).getSolver();
RealMatrix b = MatrixUtils.createRealMatrix(new double[2][2]);
try {
solver.solve(b);
Assert.fail("an exception should have been thrown");
} catch (SingularMatrixException ime) {
// expected behavior
}
try {
solver.solve(b.getColumnVector(0));
Assert.fail("an exception should have been thrown");
} catch (SingularMatrixException ime) {
// expected behavior
}
try {
solver.solve(new ArrayRealVectorTest.RealVectorTestImpl(b.getColumn(0)));
Assert.fail("an exception should have been thrown");
} catch (SingularMatrixException ime) {
// expected behavior
}
}
/** test solve */
@Test
public void testSolve() {
DecompositionSolver solver =
new LUDecomposition(MatrixUtils.createRealMatrix(testData)).getSolver();
RealMatrix b = MatrixUtils.createRealMatrix(new double[][] {
{ 1, 0 }, { 2, -5 }, { 3, 1 }
});
RealMatrix xRef = MatrixUtils.createRealMatrix(new double[][] {
{ 19, -71 }, { -6, 22 }, { -2, 9 }
});
// using RealMatrix
Assert.assertEquals(0, solver.solve(b).subtract(xRef).getNorm(), 1.0e-13);
// 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 determinant */
@Test
public void testDeterminant() {
Assert.assertEquals( -1, getDeterminant(MatrixUtils.createRealMatrix(testData)), 1.0e-15);
Assert.assertEquals(-10, getDeterminant(MatrixUtils.createRealMatrix(luData)), 1.0e-14);
Assert.assertEquals( 0, getDeterminant(MatrixUtils.createRealMatrix(singular)), 1.0e-17);
Assert.assertEquals( 0, getDeterminant(MatrixUtils.createRealMatrix(bigSingular)), 1.0e-10);
}
private double getDeterminant(RealMatrix m) {
return new LUDecomposition(m).getDeterminant();
}
}