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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 org.apache.commons.math4.exception.MathIllegalArgumentException;
import org.apache.commons.math4.fraction.Fraction;
import org.apache.commons.math4.fraction.FractionField;
import org.apache.commons.math4.linear.Array2DRowFieldMatrix;
import org.apache.commons.math4.linear.FieldDecompositionSolver;
import org.apache.commons.math4.linear.FieldLUDecomposition;
import org.apache.commons.math4.linear.FieldMatrix;
import org.apache.commons.math4.linear.FieldVector;
import org.apache.commons.math4.linear.SingularMatrixException;
import org.apache.commons.math4.linear.SparseFieldVector;
import org.junit.Assert;
import org.junit.Test;
public class FieldLUSolverTest {
private int[][] testData = {
{ 1, 2, 3},
{ 2, 5, 3},
{ 1, 0, 8}
};
private int[][] luData = {
{ 2, 3, 3 },
{ 0, 5, 7 },
{ 6, 9, 8 }
};
// singular matrices
private int[][] singular = {
{ 2, 3 },
{ 2, 3 }
};
private int[][] bigSingular = {
{ 1, 2, 3, 4 },
{ 2, 5, 3, 4 },
{ 7, 3, 256, 1930 },
{ 3, 7, 6, 8 }
}; // 4th row = 1st + 2nd
public static FieldMatrix<Fraction> createFractionMatrix(final int[][] data) {
final int numRows = data.length;
final int numCols = data[0].length;
final Array2DRowFieldMatrix<Fraction> m;
m = new Array2DRowFieldMatrix<>(FractionField.getInstance(),
numRows, numCols);
for (int i = 0; i < numRows; i++) {
for (int j = 0; j < numCols; j++) {
m.setEntry(i, j, new Fraction(data[i][j], 1));
}
}
return m;
}
/** test singular */
@Test
public void testSingular() {
FieldDecompositionSolver<Fraction> solver;
solver = new FieldLUDecomposition<>(createFractionMatrix(testData))
.getSolver();
Assert.assertTrue(solver.isNonSingular());
solver = new FieldLUDecomposition<>(createFractionMatrix(singular))
.getSolver();
Assert.assertFalse(solver.isNonSingular());
solver = new FieldLUDecomposition<>(createFractionMatrix(bigSingular))
.getSolver();
Assert.assertFalse(solver.isNonSingular());
}
/** test solve dimension errors */
@Test
public void testSolveDimensionErrors() {
FieldDecompositionSolver<Fraction> solver;
solver = new FieldLUDecomposition<>(createFractionMatrix(testData))
.getSolver();
FieldMatrix<Fraction> b = createFractionMatrix(new int[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
}
}
/** test solve singularity errors */
@Test
public void testSolveSingularityErrors() {
FieldDecompositionSolver<Fraction> solver;
solver = new FieldLUDecomposition<>(createFractionMatrix(singular))
.getSolver();
FieldMatrix<Fraction> b = createFractionMatrix(new int[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
}
}
/** test solve */
@Test
public void testSolve() {
FieldDecompositionSolver<Fraction> solver;
solver = new FieldLUDecomposition<>(createFractionMatrix(testData))
.getSolver();
FieldMatrix<Fraction> b = createFractionMatrix(new int[][] {
{ 1, 0 }, { 2, -5 }, { 3, 1 }
});
FieldMatrix<Fraction> xRef = createFractionMatrix(new int[][] {
{ 19, -71 }, { -6, 22 }, { -2, 9 }
});
// using FieldMatrix
FieldMatrix<Fraction> x = solver.solve(b);
for (int i = 0; i < x.getRowDimension(); i++){
for (int j = 0; j < x.getColumnDimension(); j++){
Assert.assertEquals("(" + i + ", " + j + ")",
xRef.getEntry(i, j), x.getEntry(i, j));
}
}
// using ArrayFieldVector
for (int j = 0; j < b.getColumnDimension(); j++) {
final FieldVector<Fraction> xj = solver.solve(b.getColumnVector(j));
for (int i = 0; i < xj.getDimension(); i++){
Assert.assertEquals("(" + i + ", " + j + ")",
xRef.getEntry(i, j), xj.getEntry(i));
}
}
// using SparseFieldVector
for (int j = 0; j < b.getColumnDimension(); j++) {
final SparseFieldVector<Fraction> bj;
bj = new SparseFieldVector<>(FractionField.getInstance(),
b.getColumn(j));
final FieldVector<Fraction> xj = solver.solve(bj);
for (int i = 0; i < xj.getDimension(); i++) {
Assert.assertEquals("(" + i + ", " + j + ")",
xRef.getEntry(i, j), xj.getEntry(i));
}
}
}
/** test determinant */
@Test
public void testDeterminant() {
Assert.assertEquals( -1, getDeterminant(createFractionMatrix(testData)), 1E-15);
Assert.assertEquals(-10, getDeterminant(createFractionMatrix(luData)), 1E-14);
Assert.assertEquals( 0, getDeterminant(createFractionMatrix(singular)), 1E-15);
Assert.assertEquals( 0, getDeterminant(createFractionMatrix(bigSingular)), 1E-15);
}
private double getDeterminant(final FieldMatrix<Fraction> m) {
return new FieldLUDecomposition<>(m).getDeterminant().doubleValue();
}
}