/*
* Copyright (c) 2014 Oculus Info Inc.
* http://www.oculusinfo.com/
*
* Released under the MIT License.
*
* Permission is hereby granted, free of charge, to any person obtaining a copy of
* this software and associated documentation files (the "Software"), to deal in
* the Software without restriction, including without limitation the rights to
* use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
* of the Software, and to permit persons to whom the Software is furnished to do
* so, subject to the following conditions:
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*/
package com.oculusinfo.math.linearalgebra;
import junit.framework.Assert;
import org.junit.Test;
public class TestTriDiagonalMatrix {
private static final double EPSILON = 1E-12;
@Test
public void testMultiplication () {
TriDiagonalMatrix M = new TriDiagonalMatrix(1, 1,
1, 1, 1,
1, 1, 1,
1, 1);
Vector X = new Vector(1, 2, 3, 4);
Vector Y = M.times(X);
Assert.assertEquals(4, Y.size());
Assert.assertEquals(3, Y.coord(0), EPSILON);
Assert.assertEquals(6, Y.coord(1), EPSILON);
Assert.assertEquals(9, Y.coord(2), EPSILON);
Assert.assertEquals(7, Y.coord(3), EPSILON);
M = new TriDiagonalMatrix(1, 2,
3, 4, 5,
6, 7, 8,
9, 8, 7,
6, 5, 4,
3, 2);
X = new Vector(1, 2, 3, 4, 5, 6);
Y = M.times(X);
Assert.assertEquals(6, Y.size());
Assert.assertEquals(5, Y.coord(0), EPSILON);
Assert.assertEquals(26, Y.coord(1), EPSILON);
Assert.assertEquals(65, Y.coord(2), EPSILON);
Assert.assertEquals(94, Y.coord(3), EPSILON);
Assert.assertEquals(73, Y.coord(4), EPSILON);
Assert.assertEquals(27, Y.coord(5), EPSILON);
M = new TriDiagonalMatrix(1, 2,
1, 2);
X = new Vector(3, 4);
Y = M.times(X);
Assert.assertEquals(2, Y.size());
Assert.assertEquals(11, Y.coord(0), EPSILON);
Assert.assertEquals(11, Y.coord(1), EPSILON);
}
@Test
public void test1DSolving () {
TriDiagonalMatrix M = new TriDiagonalMatrix(0);
Vector D = new Vector(0);
Vector X = M.solve(D);
Assert.assertEquals(new Vector(1), X);
D = new Vector(1);
X = M.solve(D);
Assert.assertEquals(new Vector(Double.NaN), X);
M = new TriDiagonalMatrix(1);
D = new Vector(0);
X = M.solve(D);
Assert.assertEquals(new Vector(0), X);
D = new Vector(1);
X = M.solve(D);
Assert.assertEquals(new Vector(1), X);
}
@Test
public void test2DSolving () {
Vector vNaN = new Vector(Double.NaN, Double.NaN);
TriDiagonalMatrix M;
Vector D;
Vector X;
M = new TriDiagonalMatrix(0, 0, 0, 0);
D = new Vector(0, 0);
X = M.solve(D);
Assert.assertEquals(2, X.size());
Assert.assertFalse(Double.isNaN(X.coord(0)));
Assert.assertFalse(Double.isNaN(X.coord(1)));
D = new Vector(1, 0);
X = M.solve(D);
Assert.assertEquals(vNaN, X);
D = new Vector(0, 1);
X = M.solve(D);
Assert.assertEquals(vNaN, X);
M = new TriDiagonalMatrix(0, 1, 0, 1);
D = new Vector(1, 0);
X = M.solve(D);
Assert.assertEquals(vNaN, X);
D = new Vector(0, 1);
X = M.solve(D);
Assert.assertEquals(vNaN, X);
D = new Vector(2, 2);
X = M.solve(D);
Assert.assertEquals(2, X.size());
Assert.assertFalse(Double.isNaN(X.coord(0)));
Assert.assertEquals(2.0, X.coord(1), EPSILON);
M = new TriDiagonalMatrix(1, 1, 0, 0);
D = new Vector(4, 0);
X = M.solve(D);
Assert.assertEquals(2, X.size());
Assert.assertEquals(4.0, X.coord(0) + X.coord(1), EPSILON);
D = new Vector(1, 0);
X = M.solve(D);
Assert.assertEquals(2, X.size());
Assert.assertEquals(1.0, X.coord(0) + X.coord(1), EPSILON);
D = new Vector(0, 1);
X = M.solve(D);
Assert.assertEquals(vNaN, X);
D = new Vector(1, 1);
X = M.solve(D);
Assert.assertEquals(vNaN, X);
M = new TriDiagonalMatrix(1, 0, 1, 0);
D = new Vector(1, 0);
X = M.solve(D);
Assert.assertEquals(vNaN, X);
D = new Vector(0, 1);
X = M.solve(D);
Assert.assertEquals(vNaN, X);
D = new Vector(2, 2);
X = M.solve(D);
Assert.assertEquals(2, X.size());
Assert.assertEquals(2.0, X.coord(0), EPSILON);
Assert.assertFalse(Double.isNaN(X.coord(1)));
M = new TriDiagonalMatrix(0, 0, 1, 1);
D = new Vector(1, 0);
X = M.solve(D);
Assert.assertEquals(vNaN, X);
D = new Vector(0, 4);
X = M.solve(D);
Assert.assertEquals(2, X.size());
Assert.assertEquals(4.0, X.coord(0) + X.coord(1), EPSILON);
D = new Vector(1, 1);
X = M.solve(D);
Assert.assertEquals(vNaN, X);
M = new TriDiagonalMatrix(0, 1, 2, 3);
D = new Vector(2, 12);
X = M.solve(D);
Assert.assertEquals(new Vector(3, 2), X);
M = new TriDiagonalMatrix(1, 0, 2, 3);
D = new Vector(3, 12);
X = M.solve(D);
Assert.assertEquals(new Vector(3, 2), X);
M = new TriDiagonalMatrix(2, 1, 0, 3);
D = new Vector(8, 6);
X = M.solve(D);
Assert.assertEquals(new Vector(3, 2), X);
M = new TriDiagonalMatrix(3, 1, 2, 0);
D = new Vector(11, 6);
X = M.solve(D);
Assert.assertEquals(new Vector(3, 2), X);
M = new TriDiagonalMatrix(1, 2, 3, 4);
D = new Vector(7, 17);
X = M.solve(D);
Assert.assertEquals(new Vector(3, 2), X);
}
@Test
public void test3DSolving () {
Vector vNaN = new Vector(Double.NaN, Double.NaN, Double.NaN);
TriDiagonalMatrix M;
Vector D;
Vector X, X0, X1;
M = new TriDiagonalMatrix(0, 1,
0, 1, 2,
3, 4);
D = new Vector(4, 7, 17);
X = M.solve(D);
Assert.assertEquals(vNaN, X);
D = new Vector(3, 7, 17);
X = M.solve(D);
Assert.assertEquals(3, X.size());
Assert.assertFalse(Double.isNaN(X.coord(0)));
Assert.assertEquals(3.0, X.coord(1), EPSILON);
Assert.assertEquals(2.0, X.coord(2), EPSILON);
M = new TriDiagonalMatrix(0, 1,
2, 3, 4,
5, 6);
X0 = new Vector(1, 2, 3);
D = M.times(X0);
X1 = M.solve(D);
Assert.assertEquals(X0, X1);
M = new TriDiagonalMatrix(1, 2,
0, 3, 4,
5, 6);
X0 = new Vector(1, 2, 3);
D = M.times(X0);
X1 = M.solve(D);
Assert.assertEquals(X0, X1);
M = new TriDiagonalMatrix(1, 2,
3, 4, 5,
6, 7);
X0 = new Vector(1, 2, 3);
D = M.times(X0);
X1 = M.solve(D);
Assert.assertEquals(X0, X1);
}
}