/*
* 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.math.linear;
import static org.junit.Assert.assertEquals;
import static org.junit.Assert.assertTrue;
import org.apache.commons.math.MathException;
import org.apache.commons.math.linear.CholeskyDecomposition;
import org.apache.commons.math.linear.CholeskyDecompositionImpl;
import org.apache.commons.math.linear.MatrixUtils;
import org.apache.commons.math.linear.NonSquareMatrixException;
import org.apache.commons.math.linear.NotPositiveDefiniteMatrixException;
import org.apache.commons.math.linear.NotSymmetricMatrixException;
import org.apache.commons.math.linear.RealMatrix;
import org.junit.Test;
public class CholeskyDecompositionImplTest {
private double[][] testData = new double[][] {
{ 1, 2, 4, 7, 11 },
{ 2, 13, 23, 38, 58 },
{ 4, 23, 77, 122, 182 },
{ 7, 38, 122, 294, 430 },
{ 11, 58, 182, 430, 855 }
};
/** test dimensions */
@Test
public void testDimensions() throws MathException {
CholeskyDecomposition llt =
new CholeskyDecompositionImpl(MatrixUtils.createRealMatrix(testData));
assertEquals(testData.length, llt.getL().getRowDimension());
assertEquals(testData.length, llt.getL().getColumnDimension());
assertEquals(testData.length, llt.getLT().getRowDimension());
assertEquals(testData.length, llt.getLT().getColumnDimension());
}
/** test non-square matrix */
@Test(expected = NonSquareMatrixException.class)
public void testNonSquare() throws MathException {
new CholeskyDecompositionImpl(MatrixUtils.createRealMatrix(new double[3][2]));
}
/** test non-symmetric matrix */
@Test(expected = NotSymmetricMatrixException.class)
public void testNotSymmetricMatrixException() throws MathException {
double[][] changed = testData.clone();
changed[0][changed[0].length - 1] += 1.0e-5;
new CholeskyDecompositionImpl(MatrixUtils.createRealMatrix(changed));
}
/** test non positive definite matrix */
@Test(expected = NotPositiveDefiniteMatrixException.class)
public void testNotPositiveDefinite() throws MathException {
new CholeskyDecompositionImpl(MatrixUtils.createRealMatrix(new double[][] {
{ 14, 11, 13, 15, 24 },
{ 11, 34, 13, 8, 25 },
{ 13, 13, 14, 15, 21 },
{ 15, 8, 15, 18, 23 },
{ 24, 25, 21, 23, 45 }
}));
}
@Test(expected = NotPositiveDefiniteMatrixException.class)
public void testMath274() throws MathException {
new CholeskyDecompositionImpl(MatrixUtils.createRealMatrix(new double[][] {
{ 0.40434286, -0.09376327, 0.30328980, 0.04909388 },
{-0.09376327, 0.10400408, 0.07137959, 0.04762857 },
{ 0.30328980, 0.07137959, 0.30458776, 0.04882449 },
{ 0.04909388, 0.04762857, 0.04882449, 0.07543265 }
}));
}
/** test A = LLT */
@Test
public void testAEqualLLT() throws MathException {
RealMatrix matrix = MatrixUtils.createRealMatrix(testData);
CholeskyDecomposition llt = new CholeskyDecompositionImpl(matrix);
RealMatrix l = llt.getL();
RealMatrix lt = llt.getLT();
double norm = l.multiply(lt).subtract(matrix).getNorm();
assertEquals(0, norm, 1.0e-15);
}
/** test that L is lower triangular */
@Test
public void testLLowerTriangular() throws MathException {
RealMatrix matrix = MatrixUtils.createRealMatrix(testData);
RealMatrix l = new CholeskyDecompositionImpl(matrix).getL();
for (int i = 0; i < l.getRowDimension(); i++) {
for (int j = i + 1; j < l.getColumnDimension(); j++) {
assertEquals(0.0, l.getEntry(i, j), 0.0);
}
}
}
/** test that LT is transpose of L */
@Test
public void testLTTransposed() throws MathException {
RealMatrix matrix = MatrixUtils.createRealMatrix(testData);
CholeskyDecomposition llt = new CholeskyDecompositionImpl(matrix);
RealMatrix l = llt.getL();
RealMatrix lt = llt.getLT();
double norm = l.subtract(lt.transpose()).getNorm();
assertEquals(0, norm, 1.0e-15);
}
/** test matrices values */
@Test
public void testMatricesValues() throws MathException {
RealMatrix lRef = MatrixUtils.createRealMatrix(new double[][] {
{ 1, 0, 0, 0, 0 },
{ 2, 3, 0, 0, 0 },
{ 4, 5, 6, 0, 0 },
{ 7, 8, 9, 10, 0 },
{ 11, 12, 13, 14, 15 }
});
CholeskyDecomposition llt =
new CholeskyDecompositionImpl(MatrixUtils.createRealMatrix(testData));
// check values against known references
RealMatrix l = llt.getL();
assertEquals(0, l.subtract(lRef).getNorm(), 1.0e-13);
RealMatrix lt = llt.getLT();
assertEquals(0, lt.subtract(lRef.transpose()).getNorm(), 1.0e-13);
// check the same cached instance is returned the second time
assertTrue(l == llt.getL());
assertTrue(lt == llt.getLT());
}
}