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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.linear.MatrixUtils;
import org.apache.commons.math4.linear.RealMatrix;
import org.apache.commons.math4.linear.RectangularCholeskyDecomposition;
import org.junit.Test;
import org.junit.Assert;
public class RectangularCholeskyDecompositionTest {
@Test
public void testDecomposition3x3() {
RealMatrix m = MatrixUtils.createRealMatrix(new double[][] {
{ 1, 9, 9 },
{ 9, 225, 225 },
{ 9, 225, 625 }
});
RectangularCholeskyDecomposition d =
new RectangularCholeskyDecomposition(m, 1.0e-6);
// as this decomposition permutes lines and columns, the root is NOT triangular
// (in fact here it is the lower right part of the matrix which is zero and
// the upper left non-zero)
Assert.assertEquals(0.8, d.getRootMatrix().getEntry(0, 2), 1.0e-15);
Assert.assertEquals(25.0, d.getRootMatrix().getEntry(2, 0), 1.0e-15);
Assert.assertEquals(0.0, d.getRootMatrix().getEntry(2, 2), 1.0e-15);
RealMatrix root = d.getRootMatrix();
RealMatrix rebuiltM = root.multiply(root.transpose());
Assert.assertEquals(0.0, m.subtract(rebuiltM).getNorm(), 1.0e-15);
}
@Test
public void testFullRank() {
RealMatrix base = MatrixUtils.createRealMatrix(new double[][] {
{ 0.1159548705, 0., 0., 0. },
{ 0.0896442724, 0.1223540781, 0., 0. },
{ 0.0852155322, 4.558668e-3, 0.1083577299, 0. },
{ 0.0905486674, 0.0213768077, 0.0128878333, 0.1014155693 }
});
RealMatrix m = base.multiply(base.transpose());
RectangularCholeskyDecomposition d =
new RectangularCholeskyDecomposition(m, 1.0e-10);
RealMatrix root = d.getRootMatrix();
RealMatrix rebuiltM = root.multiply(root.transpose());
Assert.assertEquals(0.0, m.subtract(rebuiltM).getNorm(), 1.0e-15);
// the pivoted Cholesky decomposition is *not* unique. Here, the root is
// not equal to the original trianbular base matrix
Assert.assertTrue(root.subtract(base).getNorm() > 0.3);
}
@Test
public void testMath789() {
final RealMatrix m1 = MatrixUtils.createRealMatrix(new double[][]{
{0.013445532, 0.010394690, 0.009881156, 0.010499559},
{0.010394690, 0.023006616, 0.008196856, 0.010732709},
{0.009881156, 0.008196856, 0.019023866, 0.009210099},
{0.010499559, 0.010732709, 0.009210099, 0.019107243}
});
composeAndTest(m1, 4);
final RealMatrix m2 = MatrixUtils.createRealMatrix(new double[][]{
{0.0, 0.0, 0.0, 0.0, 0.0},
{0.0, 0.013445532, 0.010394690, 0.009881156, 0.010499559},
{0.0, 0.010394690, 0.023006616, 0.008196856, 0.010732709},
{0.0, 0.009881156, 0.008196856, 0.019023866, 0.009210099},
{0.0, 0.010499559, 0.010732709, 0.009210099, 0.019107243}
});
composeAndTest(m2, 4);
final RealMatrix m3 = MatrixUtils.createRealMatrix(new double[][]{
{0.013445532, 0.010394690, 0.0, 0.009881156, 0.010499559},
{0.010394690, 0.023006616, 0.0, 0.008196856, 0.010732709},
{0.0, 0.0, 0.0, 0.0, 0.0},
{0.009881156, 0.008196856, 0.0, 0.019023866, 0.009210099},
{0.010499559, 0.010732709, 0.0, 0.009210099, 0.019107243}
});
composeAndTest(m3, 4);
}
private void composeAndTest(RealMatrix m, int expectedRank) {
RectangularCholeskyDecomposition r = new RectangularCholeskyDecomposition(m);
Assert.assertEquals(expectedRank, r.getRank());
RealMatrix root = r.getRootMatrix();
RealMatrix rebuiltMatrix = root.multiply(root.transpose());
Assert.assertEquals(0.0, m.subtract(rebuiltMatrix).getNorm(), 1.0e-16);
}
}