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23 package org.hipparchus.linear;
24
25 import java.util.Random;
26
27 import org.hipparchus.exception.LocalizedCoreFormats;
28 import org.hipparchus.exception.MathIllegalArgumentException;
29 import org.hipparchus.random.RandomDataGenerator;
30 import org.junit.Assert;
31 import org.junit.Test;
32
33 public class SchurTransformerTest {
34
35 private double[][] testSquare5 = {
36 { 5, 4, 3, 2, 1 },
37 { 1, 4, 0, 3, 3 },
38 { 2, 0, 3, 0, 0 },
39 { 3, 2, 1, 2, 5 },
40 { 4, 2, 1, 4, 1 }
41 };
42
43 private double[][] testSquare3 = {
44 { 2, -1, 1 },
45 { -1, 2, 1 },
46 { 1, -1, 2 }
47 };
48
49
50 private double[][] testRandom = {
51 { 0.680, -0.3300, -0.2700, -0.717, -0.687, 0.0259 },
52 { -0.211, 0.5360, 0.0268, 0.214, -0.198, 0.6780 },
53 { 0.566, -0.4440, 0.9040, -0.967, -0.740, 0.2250 },
54 { 0.597, 0.1080, 0.8320, -0.514, -0.782, -0.4080 },
55 { 0.823, -0.0452, 0.2710, -0.726, 0.998, 0.2750 },
56 { -0.605, 0.2580, 0.4350, 0.608, -0.563, 0.0486 }
57 };
58
59 @Test
60 public void testNonSquare() {
61 try {
62 new SchurTransformer(MatrixUtils.createRealMatrix(new double[3][2]));
63 Assert.fail("an exception should have been thrown");
64 } catch (MathIllegalArgumentException ime) {
65 Assert.assertEquals(LocalizedCoreFormats.NON_SQUARE_MATRIX, ime.getSpecifier());
66 }
67 }
68
69 @Test
70 public void testAEqualPTPt() {
71 checkAEqualPTPt(MatrixUtils.createRealMatrix(testSquare5));
72 checkAEqualPTPt(MatrixUtils.createRealMatrix(testSquare3));
73 checkAEqualPTPt(MatrixUtils.createRealMatrix(testRandom));
74 }
75
76 @Test
77 public void testPOrthogonal() {
78 checkOrthogonal(new SchurTransformer(MatrixUtils.createRealMatrix(testSquare5)).getP());
79 checkOrthogonal(new SchurTransformer(MatrixUtils.createRealMatrix(testSquare3)).getP());
80 checkOrthogonal(new SchurTransformer(MatrixUtils.createRealMatrix(testRandom)).getP());
81 }
82
83 @Test
84 public void testPTOrthogonal() {
85 checkOrthogonal(new SchurTransformer(MatrixUtils.createRealMatrix(testSquare5)).getPT());
86 checkOrthogonal(new SchurTransformer(MatrixUtils.createRealMatrix(testSquare3)).getPT());
87 checkOrthogonal(new SchurTransformer(MatrixUtils.createRealMatrix(testRandom)).getPT());
88 }
89
90 @Test
91 public void testSchurForm() {
92 checkSchurForm(new SchurTransformer(MatrixUtils.createRealMatrix(testSquare5)).getT());
93 checkSchurForm(new SchurTransformer(MatrixUtils.createRealMatrix(testSquare3)).getT());
94 checkSchurForm(new SchurTransformer(MatrixUtils.createRealMatrix(testRandom)).getT());
95 }
96
97 @Test
98 public void testRandomData() {
99 for (int run = 0; run < 100; run++) {
100 Random r = new Random(System.currentTimeMillis());
101
102
103 int size = r.nextInt(20) + 4;
104
105 double[][] data = new double[size][size];
106 for (int i = 0; i < size; i++) {
107 for (int j = 0; j < size; j++) {
108 data[i][j] = r.nextInt(100);
109 }
110 }
111
112 RealMatrix m = MatrixUtils.createRealMatrix(data);
113 RealMatrix s = checkAEqualPTPt(m);
114 checkSchurForm(s);
115 }
116 }
117
118 @Test
119 public void testRandomDataNormalDistribution() {
120 for (int run = 0; run < 100; run++) {
121 Random r = new Random(System.currentTimeMillis());
122 RandomDataGenerator randomDataGenerator = new RandomDataGenerator(100);
123
124
125 int size = r.nextInt(20) + 4;
126
127 double[][] data = new double[size][size];
128 for (int i = 0; i < size; i++) {
129 for (int j = 0; j < size; j++) {
130 data[i][j] = randomDataGenerator.nextNormal(0.0, r.nextDouble() * 5);
131 }
132 }
133
134 RealMatrix m = MatrixUtils.createRealMatrix(data);
135 RealMatrix s = checkAEqualPTPt(m);
136 checkSchurForm(s);
137 }
138 }
139
140 @Test
141 public void testMath848() {
142 double[][] data = {
143 { 0.1849449280, -0.0646971046, 0.0774755812, -0.0969651755, -0.0692648806, 0.3282344352, -0.0177423074, 0.2063136340},
144 {-0.0742700134, -0.0289063030, -0.0017269460, -0.0375550146, -0.0487737922, -0.2616837868, -0.0821201295, -0.2530000167},
145 { 0.2549910127, 0.0995733692, -0.0009718388, 0.0149282808, 0.1791878897, -0.0823182816, 0.0582629256, 0.3219545182},
146 {-0.0694747557, -0.1880649148, -0.2740630911, 0.0720096468, -0.1800836914, -0.3518996425, 0.2486747833, 0.6257938167},
147 { 0.0536360918, -0.1339297778, 0.2241579764, -0.0195327484, -0.0054103808, 0.0347564518, 0.5120802482, -0.0329902864},
148 {-0.5933332356, -0.2488721082, 0.2357173629, 0.0177285473, 0.0856630593, -0.3567126300, -0.1600668126, -0.1010899621},
149 {-0.0514349819, -0.0854319435, 0.1125050061, 0.0063453560, -0.2250000688, -0.2209343090, 0.1964623477, -0.1512329924},
150 { 0.0197395947, -0.1997170581, -0.1425959019, -0.2749477910, -0.0969467073, 0.0603688520, -0.2826905192, 0.1794315473}};
151 RealMatrix m = MatrixUtils.createRealMatrix(data);
152 RealMatrix s = checkAEqualPTPt(m);
153 checkSchurForm(s);
154 }
155
156
157
158
159
160 private RealMatrix checkAEqualPTPt(RealMatrix matrix) {
161 SchurTransformer transformer = new SchurTransformer(matrix);
162 RealMatrix p = transformer.getP();
163 RealMatrix t = transformer.getT();
164 RealMatrix pT = transformer.getPT();
165
166 RealMatrix result = p.multiply(t).multiply(pT);
167
168 double norm = result.subtract(matrix).getNorm1();
169 Assert.assertEquals(0, norm, 1.0e-9);
170
171 return t;
172 }
173
174 private void checkOrthogonal(RealMatrix m) {
175 RealMatrix mTm = m.transposeMultiply(m);
176 RealMatrix id = MatrixUtils.createRealIdentityMatrix(mTm.getRowDimension());
177 Assert.assertEquals(0, mTm.subtract(id).getNorm1(), 1.0e-14);
178 }
179
180 private void checkSchurForm(final RealMatrix m) {
181 final int rows = m.getRowDimension();
182 final int cols = m.getColumnDimension();
183 for (int i = 0; i < rows; ++i) {
184 for (int j = 0; j < cols; ++j) {
185 if (i > j + 1) {
186 Assert.assertEquals(0, m.getEntry(i, j), 1.0e-16);
187 }
188 }
189 }
190 }
191
192 @SuppressWarnings("unused")
193 private void checkMatricesValues(double[][] matrix, double[][] pRef, double[][] hRef) {
194
195 SchurTransformer transformer =
196 new SchurTransformer(MatrixUtils.createRealMatrix(matrix));
197
198
199 RealMatrix p = transformer.getP();
200 Assert.assertEquals(0, p.subtract(MatrixUtils.createRealMatrix(pRef)).getNorm1(), 1.0e-14);
201
202 RealMatrix t = transformer.getT();
203 Assert.assertEquals(0, t.subtract(MatrixUtils.createRealMatrix(hRef)).getNorm1(), 1.0e-14);
204
205
206 Assert.assertTrue(p == transformer.getP());
207 Assert.assertTrue(t == transformer.getT());
208 }
209 }