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18 package org.apache.commons.math.linear;
19
20 import java.util.Arrays;
21
22 import org.apache.commons.math.linear.InvalidMatrixException;
23 import org.apache.commons.math.linear.MatrixUtils;
24 import org.apache.commons.math.linear.RealMatrix;
25 import org.apache.commons.math.linear.TriDiagonalTransformer;
26
27 import junit.framework.Test;
28 import junit.framework.TestCase;
29 import junit.framework.TestSuite;
30
31 public class TriDiagonalTransformerTest extends TestCase {
32
33 private double[][] testSquare5 = {
34 { 1, 2, 3, 1, 1 },
35 { 2, 1, 1, 3, 1 },
36 { 3, 1, 1, 1, 2 },
37 { 1, 3, 1, 2, 1 },
38 { 1, 1, 2, 1, 3 }
39 };
40
41 private double[][] testSquare3 = {
42 { 1, 3, 4 },
43 { 3, 2, 2 },
44 { 4, 2, 0 }
45 };
46
47 public TriDiagonalTransformerTest(String name) {
48 super(name);
49 }
50
51 public void testNonSquare() {
52 try {
53 new TriDiagonalTransformer(MatrixUtils.createRealMatrix(new double[3][2]));
54 fail("an exception should have been thrown");
55 } catch (InvalidMatrixException ime) {
56
57 } catch (Exception e) {
58 fail("wrong exception caught");
59 }
60 }
61
62 public void testAEqualQTQt() {
63 checkAEqualQTQt(MatrixUtils.createRealMatrix(testSquare5));
64 checkAEqualQTQt(MatrixUtils.createRealMatrix(testSquare3));
65 }
66
67 private void checkAEqualQTQt(RealMatrix matrix) {
68 TriDiagonalTransformer transformer = new TriDiagonalTransformer(matrix);
69 RealMatrix q = transformer.getQ();
70 RealMatrix qT = transformer.getQT();
71 RealMatrix t = transformer.getT();
72 double norm = q.multiply(t).multiply(qT).subtract(matrix).getNorm();
73 assertEquals(0, norm, 4.0e-15);
74 }
75
76 public void testNoAccessBelowDiagonal() {
77 checkNoAccessBelowDiagonal(testSquare5);
78 checkNoAccessBelowDiagonal(testSquare3);
79 }
80
81 private void checkNoAccessBelowDiagonal(double[][] data) {
82 double[][] modifiedData = new double[data.length][];
83 for (int i = 0; i < data.length; ++i) {
84 modifiedData[i] = data[i].clone();
85 Arrays.fill(modifiedData[i], 0, i, Double.NaN);
86 }
87 RealMatrix matrix = MatrixUtils.createRealMatrix(modifiedData);
88 TriDiagonalTransformer transformer = new TriDiagonalTransformer(matrix);
89 RealMatrix q = transformer.getQ();
90 RealMatrix qT = transformer.getQT();
91 RealMatrix t = transformer.getT();
92 double norm = q.multiply(t).multiply(qT).subtract(MatrixUtils.createRealMatrix(data)).getNorm();
93 assertEquals(0, norm, 4.0e-15);
94 }
95
96 public void testQOrthogonal() {
97 checkOrthogonal(new TriDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare5)).getQ());
98 checkOrthogonal(new TriDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare3)).getQ());
99 }
100
101 public void testQTOrthogonal() {
102 checkOrthogonal(new TriDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare5)).getQT());
103 checkOrthogonal(new TriDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare3)).getQT());
104 }
105
106 private void checkOrthogonal(RealMatrix m) {
107 RealMatrix mTm = m.transpose().multiply(m);
108 RealMatrix id = MatrixUtils.createRealIdentityMatrix(mTm.getRowDimension());
109 assertEquals(0, mTm.subtract(id).getNorm(), 1.0e-15);
110 }
111
112 public void testTTriDiagonal() {
113 checkTriDiagonal(new TriDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare5)).getT());
114 checkTriDiagonal(new TriDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare3)).getT());
115 }
116
117 private void checkTriDiagonal(RealMatrix m) {
118 final int rows = m.getRowDimension();
119 final int cols = m.getColumnDimension();
120 for (int i = 0; i < rows; ++i) {
121 for (int j = 0; j < cols; ++j) {
122 if ((i < j - 1) || (i > j + 1)) {
123 assertEquals(0, m.getEntry(i, j), 1.0e-16);
124 }
125 }
126 }
127 }
128
129 public void testMatricesValues5() {
130 checkMatricesValues(testSquare5,
131 new double[][] {
132 { 1.0, 0.0, 0.0, 0.0, 0.0 },
133 { 0.0, -0.5163977794943222, 0.016748280772542083, 0.839800693771262, 0.16669620021405473 },
134 { 0.0, -0.7745966692414833, -0.4354553000860955, -0.44989322880603355, -0.08930153582895772 },
135 { 0.0, -0.2581988897471611, 0.6364346693566014, -0.30263204032131164, 0.6608313651342882 },
136 { 0.0, -0.2581988897471611, 0.6364346693566009, -0.027289660803112598, -0.7263191580755246 }
137 },
138 new double[] { 1, 4.4, 1.433099579242636, -0.89537362758743, 2.062274048344794 },
139 new double[] { -Math.sqrt(15), -3.0832882879592476, 0.6082710842351517, 1.1786086405912128 });
140 }
141
142 public void testMatricesValues3() {
143 checkMatricesValues(testSquare3,
144 new double[][] {
145 { 1.0, 0.0, 0.0 },
146 { 0.0, -0.6, 0.8 },
147 { 0.0, -0.8, -0.6 },
148 },
149 new double[] { 1, 2.64, -0.64 },
150 new double[] { -5, -1.52 });
151 }
152
153 private void checkMatricesValues(double[][] matrix, double[][] qRef,
154 double[] mainDiagnonal,
155 double[] secondaryDiagonal) {
156 TriDiagonalTransformer transformer =
157 new TriDiagonalTransformer(MatrixUtils.createRealMatrix(matrix));
158
159
160 RealMatrix q = transformer.getQ();
161 assertEquals(0, q.subtract(MatrixUtils.createRealMatrix(qRef)).getNorm(), 1.0e-14);
162
163 RealMatrix t = transformer.getT();
164 double[][] tData = new double[mainDiagnonal.length][mainDiagnonal.length];
165 for (int i = 0; i < mainDiagnonal.length; ++i) {
166 tData[i][i] = mainDiagnonal[i];
167 if (i > 0) {
168 tData[i][i - 1] = secondaryDiagonal[i - 1];
169 }
170 if (i < secondaryDiagonal.length) {
171 tData[i][i + 1] = secondaryDiagonal[i];
172 }
173 }
174 assertEquals(0, t.subtract(MatrixUtils.createRealMatrix(tData)).getNorm(), 1.0e-14);
175
176
177 assertTrue(q == transformer.getQ());
178 assertTrue(t == transformer.getT());
179
180 }
181
182 public static Test suite() {
183 return new TestSuite(TriDiagonalTransformerTest.class);
184 }
185
186 }