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# Java example source code file (RectangularCholeskyDecompositionTest.java)

This example Java source code file (RectangularCholeskyDecompositionTest.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

## Java - Java tags/keywords

realmatrix, rectangularcholeskydecomposition, rectangularcholeskydecompositiontest, test

## The RectangularCholeskyDecompositionTest.java Java example source code

```/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements.  See the NOTICE file distributed with
* 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
*
*
* Unless required by applicable law or agreed to in writing, software
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
*/

package org.apache.commons.math3.linear;

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);
}

}
```

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