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3    * contributor license agreements.  See the NOTICE file distributed with
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7    * the License.  You may obtain a copy of the License at
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9    *      http://www.apache.org/licenses/LICENSE-2.0
10   * 
11   * Unless required by applicable law or agreed to in writing, software
12   * distributed under the License is distributed on an "AS IS" BASIS,
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14   * See the License for the specific language governing permissions and
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16   */
17  package org.apache.commons.math.linear;
18  
19  import org.apache.commons.math.Field;
20  import org.apache.commons.math.fraction.Fraction;
21  import org.apache.commons.math.fraction.FractionConversionException;
22  import org.apache.commons.math.fraction.FractionField;
23  
24  import junit.framework.Test;
25  import junit.framework.TestCase;
26  import junit.framework.TestSuite;
27  
28  /**
29   * Test cases for the {@link SparseFieldMatrix} class.
30   *
31   * @version $Revision: 799857 $ $Date: 2009-08-01 09:07:12 -0400 (Sat, 01 Aug 2009) $
32   */
33  public class SparseFieldMatrixTest extends TestCase {
34      // 3 x 3 identity matrix
35      protected Fraction[][] id = { {new Fraction(1), new Fraction(0), new Fraction(0) }, { new Fraction(0), new Fraction(1), new Fraction(0) }, { new Fraction(0), new Fraction(0), new Fraction(1) } };
36      // Test data for group operations
37      protected Fraction[][] testData = { { new Fraction(1), new Fraction(2), new Fraction(3) }, { new Fraction(2), new Fraction(5), new Fraction(3) },
38              { new Fraction(1), new Fraction(0), new Fraction(8) } };
39      protected Fraction[][] testDataLU = null;
40      protected Fraction[][] testDataPlus2 = { { new Fraction(3), new Fraction(4), new Fraction(5) }, { new Fraction(4), new Fraction(7), new Fraction(5) },
41              { new Fraction(3), new Fraction(2), new Fraction(10) } };
42      protected Fraction[][] testDataMinus = { { new Fraction(-1), new Fraction(-2), new Fraction(-3) },
43              { new Fraction(-2), new Fraction(-5), new Fraction(-3) }, { new Fraction(-1), new Fraction(0), new Fraction(-8) } };
44      protected Fraction[] testDataRow1 = { new Fraction(1), new Fraction(2), new Fraction(3) };
45      protected Fraction[] testDataCol3 = { new Fraction(3), new Fraction(3), new Fraction(8) };
46      protected Fraction[][] testDataInv = { { new Fraction(-40), new Fraction(16), new Fraction(9) }, { new Fraction(13), new Fraction(-5), new Fraction(-3) },
47              { new Fraction(5), new Fraction(-2), new Fraction(-1) } };
48      protected Fraction[] preMultTest = { new Fraction(8), new Fraction(12), new Fraction(33) };
49      protected Fraction[][] testData2 = { { new Fraction(1), new Fraction(2), new Fraction(3) }, { new Fraction(2), new Fraction(5), new Fraction(3) } };
50      protected Fraction[][] testData2T = { { new Fraction(1), new Fraction(2) }, { new Fraction(2), new Fraction(5) }, { new Fraction(3), new Fraction(3) } };
51      protected Fraction[][] testDataPlusInv = { { new Fraction(-39), new Fraction(18), new Fraction(12) },
52              { new Fraction(15), new Fraction(0), new Fraction(0) }, { new Fraction(6), new Fraction(-2), new Fraction(7) } };
53  
54      // lu decomposition tests
55      protected Fraction[][] luData = { { new Fraction(2), new Fraction(3), new Fraction(3) }, { new Fraction(0), new Fraction(5), new Fraction(7) }, { new Fraction(6), new Fraction(9), new Fraction(8) } };
56      protected Fraction[][] luDataLUDecomposition = null;
57  
58      // singular matrices
59      protected Fraction[][] singular = { { new Fraction(2), new Fraction(3) }, { new Fraction(2), new Fraction(3) } };
60      protected Fraction[][] bigSingular = { { new Fraction(1), new Fraction(2), new Fraction(3), new Fraction(4) },
61              { new Fraction(2), new Fraction(5), new Fraction(3), new Fraction(4) }, { new Fraction(7), new Fraction(3), new Fraction(256), new Fraction(1930) }, { new Fraction(3), new Fraction(7), new Fraction(6), new Fraction(8) } }; // 4th
62  
63      // row
64      // =
65      // 1st
66      // +
67      // 2nd
68      protected Fraction[][] detData = { { new Fraction(1), new Fraction(2), new Fraction(3) }, { new Fraction(4), new Fraction(5), new Fraction(6) },
69              { new Fraction(7), new Fraction(8), new Fraction(10) } };
70      protected Fraction[][] detData2 = { { new Fraction(1), new Fraction(3) }, { new Fraction(2), new Fraction(4) } };
71  
72      // vectors
73      protected Fraction[] testVector = { new Fraction(1), new Fraction(2), new Fraction(3) };
74      protected Fraction[] testVector2 = { new Fraction(1), new Fraction(2), new Fraction(3), new Fraction(4) };
75  
76      // submatrix accessor tests
77      protected Fraction[][] subTestData = null;
78  
79      // array selections
80      protected Fraction[][] subRows02Cols13 = { {new Fraction(2), new Fraction(4) }, { new Fraction(4), new Fraction(8) } };
81      protected Fraction[][] subRows03Cols12 = { { new Fraction(2), new Fraction(3) }, { new Fraction(5), new Fraction(6) } };
82      protected Fraction[][] subRows03Cols123 = { { new Fraction(2), new Fraction(3), new Fraction(4) }, { new Fraction(5), new Fraction(6), new Fraction(7) } };
83  
84      // effective permutations
85      protected Fraction[][] subRows20Cols123 = { { new Fraction(4), new Fraction(6), new Fraction(8) }, { new Fraction(2), new Fraction(3), new Fraction(4) } };
86      protected Fraction[][] subRows31Cols31 = null;
87  
88      // contiguous ranges
89      protected Fraction[][] subRows01Cols23 = null;
90      protected Fraction[][] subRows23Cols00 = { { new Fraction(2) }, { new Fraction(4) } };
91      protected Fraction[][] subRows00Cols33 = { { new Fraction(4) } };
92  
93      // row matrices
94      protected Fraction[][] subRow0 = { { new Fraction(1), new Fraction(2), new Fraction(3), new Fraction(4) } };
95      protected Fraction[][] subRow3 = { { new Fraction(4), new Fraction(5), new Fraction(6), new Fraction(7) } };
96  
97      // column matrices
98      protected Fraction[][] subColumn1 = null;
99      protected Fraction[][] subColumn3 = null;
100 
101     // tolerances
102     protected double entryTolerance = 10E-16;
103     protected double normTolerance = 10E-14;
104     protected Field<Fraction> field = FractionField.getInstance();
105 
106     public SparseFieldMatrixTest(String name) {
107         super(name);
108         setupFractionArrays();
109     }
110 
111     private void setupFractionArrays() {
112         try {
113             testDataLU = new Fraction[][]{ { new Fraction(2), new Fraction(5), new Fraction(3) }, { new Fraction(.5d), new Fraction(-2.5d), new Fraction(6.5d) },
114                     { new Fraction(0.5d), new Fraction(0.2d), new Fraction(.2d) } };
115             luDataLUDecomposition = new Fraction[][]{ { new Fraction(6), new Fraction(9), new Fraction(8) },
116                 { new Fraction(0), new Fraction(5), new Fraction(7) }, { new Fraction(0.33333333333333), new Fraction(0), new Fraction(0.33333333333333) } };
117             subTestData = new Fraction [][]{ { new Fraction(1), new Fraction(2), new Fraction(3), new Fraction(4) },
118                     { new Fraction(1.5), new Fraction(2.5), new Fraction(3.5), new Fraction(4.5) }, { new Fraction(2), new Fraction(4), new Fraction(6), new Fraction(8) }, { new Fraction(4), new Fraction(5), new Fraction(6), new Fraction(7) } };
119             subRows31Cols31 = new Fraction[][]{ { new Fraction(7), new Fraction(5) }, { new Fraction(4.5), new Fraction(2.5) } };
120             subRows01Cols23 = new Fraction[][]{ { new Fraction(3), new Fraction(4) }, { new Fraction(3.5), new Fraction(4.5) } };
121             subColumn1 = new Fraction [][]{ { new Fraction(2) }, { new Fraction(2.5) }, { new Fraction(4) }, { new Fraction(5) } };
122             subColumn3 = new Fraction[][]{ { new Fraction(4) }, { new Fraction(4.5) }, { new Fraction(8) }, { new Fraction(7) } };
123         } catch (FractionConversionException e) {
124             // ignore, can't happen
125         }
126         
127                 
128     }
129 
130     public static Test suite() {
131         TestSuite suite = new TestSuite(SparseFieldMatrixTest.class);
132         suite.setName("SparseFieldMatrix<Fraction> Tests");
133         return suite;
134     }
135 
136     /** test dimensions */
137     public void testDimensions() {
138         SparseFieldMatrix<Fraction> m = createSparseMatrix(testData);
139         SparseFieldMatrix<Fraction> m2 = createSparseMatrix(testData2);
140         assertEquals("testData row dimension", 3, m.getRowDimension());
141         assertEquals("testData column dimension", 3, m.getColumnDimension());
142         assertTrue("testData is square", m.isSquare());
143         assertEquals("testData2 row dimension", m2.getRowDimension(), 2);
144         assertEquals("testData2 column dimension", m2.getColumnDimension(), 3);
145         assertTrue("testData2 is not square", !m2.isSquare());
146     }
147 
148     /** test copy functions */
149     public void testCopyFunctions() {
150         SparseFieldMatrix<Fraction> m1 = createSparseMatrix(testData);
151         FieldMatrix<Fraction> m2 = m1.copy();
152         assertEquals(m1.getClass(), m2.getClass());
153         assertEquals((m2), m1);
154         SparseFieldMatrix<Fraction> m3 = createSparseMatrix(testData);
155         FieldMatrix<Fraction> m4 = m3.copy();
156         assertEquals(m3.getClass(), m4.getClass());
157         assertEquals((m4), m3);
158     }
159 
160     /** test add */
161     public void testAdd() {
162         SparseFieldMatrix<Fraction> m = createSparseMatrix(testData);
163         SparseFieldMatrix<Fraction> mInv = createSparseMatrix(testDataInv);
164         SparseFieldMatrix<Fraction> mDataPlusInv = createSparseMatrix(testDataPlusInv);
165         FieldMatrix<Fraction> mPlusMInv = m.add(mInv);
166         for (int row = 0; row < m.getRowDimension(); row++) {
167             for (int col = 0; col < m.getColumnDimension(); col++) {
168                 assertEquals("sum entry entry", 
169                     mDataPlusInv.getEntry(row, col).doubleValue(), mPlusMInv.getEntry(row, col).doubleValue(), 
170                     entryTolerance);
171             }
172         }
173     }
174 
175     /** test add failure */
176     public void testAddFail() {
177         SparseFieldMatrix<Fraction> m = createSparseMatrix(testData);
178         SparseFieldMatrix<Fraction> m2 = createSparseMatrix(testData2);
179         try {
180             m.add(m2);
181             fail("IllegalArgumentException expected");
182         } catch (IllegalArgumentException ex) {
183             // ignored
184         }
185     }
186 
187     
188     /** test m-n = m + -n */
189     public void testPlusMinus() {
190         SparseFieldMatrix<Fraction> m = createSparseMatrix(testData);
191         SparseFieldMatrix<Fraction> n = createSparseMatrix(testDataInv);
192         assertClose("m-n = m + -n", m.subtract(n),
193             n.scalarMultiply(new Fraction(-1)).add(m), entryTolerance);
194         try {
195             m.subtract(createSparseMatrix(testData2));
196             fail("Expecting illegalArgumentException");
197         } catch (IllegalArgumentException ex) {
198             // ignored
199         }
200     }
201 
202     /** test multiply */
203     public void testMultiply() {
204         SparseFieldMatrix<Fraction> m = createSparseMatrix(testData);
205         SparseFieldMatrix<Fraction> mInv = createSparseMatrix(testDataInv);
206         SparseFieldMatrix<Fraction> identity = createSparseMatrix(id);
207         SparseFieldMatrix<Fraction> m2 = createSparseMatrix(testData2);
208         assertClose("inverse multiply", m.multiply(mInv), identity,
209                 entryTolerance);
210         assertClose("inverse multiply", m.multiply(new Array2DRowFieldMatrix<Fraction>(testDataInv)), identity,
211                     entryTolerance);
212         assertClose("inverse multiply", mInv.multiply(m), identity,
213                 entryTolerance);
214         assertClose("identity multiply", m.multiply(identity), m,
215                 entryTolerance);
216         assertClose("identity multiply", identity.multiply(mInv), mInv,
217                 entryTolerance);
218         assertClose("identity multiply", m2.multiply(identity), m2,
219                 entryTolerance);
220         try {
221             m.multiply(createSparseMatrix(bigSingular));
222             fail("Expecting illegalArgumentException");
223         } catch (IllegalArgumentException ex) {
224             // ignored
225         }
226     }
227 
228     // Additional Test for Array2DRowRealMatrixTest.testMultiply
229 
230     private Fraction[][] d3 = new Fraction[][] { { new Fraction(1), new Fraction(2), new Fraction(3), new Fraction(4) }, { new Fraction(5), new Fraction(6), new Fraction(7), new Fraction(8) } };
231     private Fraction[][] d4 = new Fraction[][] { { new Fraction(1) }, { new Fraction(2) }, { new Fraction(3) }, { new Fraction(4) } };
232     private Fraction[][] d5 = new Fraction[][] { { new Fraction(30) }, { new Fraction(70) } };
233 
234     public void testMultiply2() {
235         FieldMatrix<Fraction> m3 = createSparseMatrix(d3);
236         FieldMatrix<Fraction> m4 = createSparseMatrix(d4);
237         FieldMatrix<Fraction> m5 = createSparseMatrix(d5);
238         assertClose("m3*m4=m5", m3.multiply(m4), m5, entryTolerance);
239     }
240 
241     /** test trace */
242     public void testTrace() {
243         FieldMatrix<Fraction> m = createSparseMatrix(id);
244         assertEquals("identity trace", 3d, m.getTrace().doubleValue(), entryTolerance);
245         m = createSparseMatrix(testData2);
246         try {
247             m.getTrace();
248             fail("Expecting NonSquareMatrixException");
249         } catch (NonSquareMatrixException ex) {
250             // ignored
251         }
252     }
253 
254     /** test sclarAdd */
255     public void testScalarAdd() {
256         FieldMatrix<Fraction> m = createSparseMatrix(testData);
257         assertClose("scalar add", createSparseMatrix(testDataPlus2), 
258             m.scalarAdd(new Fraction(2)), entryTolerance);
259     }
260 
261     /** test operate */
262     public void testOperate() {
263         FieldMatrix<Fraction> m = createSparseMatrix(id);
264         assertClose("identity operate", testVector, m.operate(testVector),
265                 entryTolerance);
266         assertClose("identity operate", testVector, m.operate(
267                 new ArrayFieldVector<Fraction>(testVector)).getData(), entryTolerance);
268         m = createSparseMatrix(bigSingular);
269         try {
270             m.operate(testVector);
271             fail("Expecting illegalArgumentException");
272         } catch (IllegalArgumentException ex) {
273             // ignored
274         }
275     }
276 
277     /** test issue MATH-209 */
278     public void testMath209() {
279         FieldMatrix<Fraction> a = createSparseMatrix(new Fraction[][] {
280                 { new Fraction(1), new Fraction(2) }, { new Fraction(3), new Fraction(4) }, { new Fraction(5), new Fraction(6) } });
281         Fraction[] b = a.operate(new Fraction[] { new Fraction(1), new Fraction(1) });
282         assertEquals(a.getRowDimension(), b.length);
283         assertEquals(3.0, b[0].doubleValue(), 1.0e-12);
284         assertEquals(7.0, b[1].doubleValue(), 1.0e-12);
285         assertEquals(11.0, b[2].doubleValue(), 1.0e-12);
286     }
287 
288     /** test transpose */
289     public void testTranspose() {
290         
291         FieldMatrix<Fraction> m = createSparseMatrix(testData); 
292         FieldMatrix<Fraction> mIT = new FieldLUDecompositionImpl<Fraction>(m).getSolver().getInverse().transpose();
293         FieldMatrix<Fraction> mTI = new FieldLUDecompositionImpl<Fraction>(m.transpose()).getSolver().getInverse();
294         assertClose("inverse-transpose", mIT, mTI, normTolerance);
295         m = createSparseMatrix(testData2);
296         FieldMatrix<Fraction> mt = createSparseMatrix(testData2T);
297         assertClose("transpose",mt,m.transpose(),normTolerance);
298     }
299 
300     /** test preMultiply by vector */
301     public void testPremultiplyVector() {
302         FieldMatrix<Fraction> m = createSparseMatrix(testData);
303         assertClose("premultiply", m.preMultiply(testVector), preMultTest,
304             normTolerance);
305         assertClose("premultiply", m.preMultiply(
306             new ArrayFieldVector<Fraction>(testVector).getData()), preMultTest, normTolerance);
307         m = createSparseMatrix(bigSingular);
308         try {
309             m.preMultiply(testVector);
310             fail("expecting IllegalArgumentException");
311         } catch (IllegalArgumentException ex) {
312             // ignored
313         }
314     }
315 
316     public void testPremultiply() {
317         FieldMatrix<Fraction> m3 = createSparseMatrix(d3);
318         FieldMatrix<Fraction> m4 = createSparseMatrix(d4);
319         FieldMatrix<Fraction> m5 = createSparseMatrix(d5);
320         assertClose("m3*m4=m5", m4.preMultiply(m3), m5, entryTolerance);
321 
322         SparseFieldMatrix<Fraction> m = createSparseMatrix(testData);
323         SparseFieldMatrix<Fraction> mInv = createSparseMatrix(testDataInv);
324         SparseFieldMatrix<Fraction> identity = createSparseMatrix(id);
325         assertClose("inverse multiply", m.preMultiply(mInv), identity,
326                 entryTolerance);
327         assertClose("inverse multiply", mInv.preMultiply(m), identity,
328                 entryTolerance);
329         assertClose("identity multiply", m.preMultiply(identity), m,
330                 entryTolerance);
331         assertClose("identity multiply", identity.preMultiply(mInv), mInv,
332                 entryTolerance);
333         try {
334             m.preMultiply(createSparseMatrix(bigSingular));
335             fail("Expecting illegalArgumentException");
336         } catch (IllegalArgumentException ex) {
337             // ignored
338         }
339     }
340 
341     public void testGetVectors() {
342         FieldMatrix<Fraction> m = createSparseMatrix(testData);
343         assertClose("get row", m.getRow(0), testDataRow1, entryTolerance);
344         assertClose("get col", m.getColumn(2), testDataCol3, entryTolerance);
345         try {
346             m.getRow(10);
347             fail("expecting MatrixIndexException");
348         } catch (MatrixIndexException ex) {
349             // ignored
350         }
351         try {
352             m.getColumn(-1);
353             fail("expecting MatrixIndexException");
354         } catch (MatrixIndexException ex) {
355             // ignored
356         }
357     }
358 
359     public void testGetEntry() {
360         FieldMatrix<Fraction> m = createSparseMatrix(testData);
361         assertEquals("get entry", m.getEntry(0, 1).doubleValue(), 2d, entryTolerance);
362         try {
363             m.getEntry(10, 4);
364             fail("Expecting MatrixIndexException");
365         } catch (MatrixIndexException ex) {
366             // expected
367         }
368     }
369 
370     /** test examples in user guide */
371     public void testExamples() {
372         // Create a real matrix with two rows and three columns
373         Fraction[][] matrixData = { { new Fraction(1), new Fraction(2), new Fraction(3) }, { new Fraction(2), new Fraction(5), new Fraction(3) } };
374         FieldMatrix<Fraction> m = createSparseMatrix(matrixData);
375         // One more with three rows, two columns
376         Fraction[][] matrixData2 = { { new Fraction(1), new Fraction(2) }, { new Fraction(2), new Fraction(5) }, { new Fraction(1), new Fraction(7) } };
377         FieldMatrix<Fraction> n = createSparseMatrix(matrixData2);
378         // Now multiply m by n
379         FieldMatrix<Fraction> p = m.multiply(n);
380         assertEquals(2, p.getRowDimension());
381         assertEquals(2, p.getColumnDimension());
382         // Invert p
383         FieldMatrix<Fraction> pInverse = new FieldLUDecompositionImpl<Fraction>(p).getSolver().getInverse(); 
384         assertEquals(2, pInverse.getRowDimension());
385         assertEquals(2, pInverse.getColumnDimension());
386 
387         // Solve example
388         Fraction[][] coefficientsData = { { new Fraction(2), new Fraction(3), new Fraction(-2) }, { new Fraction(-1), new Fraction(7), new Fraction(6) },
389                 { new Fraction(4), new Fraction(-3), new Fraction(-5) } };
390         FieldMatrix<Fraction> coefficients = createSparseMatrix(coefficientsData);
391         Fraction[] constants = { new Fraction(1), new Fraction(-2), new Fraction(1) };
392         Fraction[] solution = new FieldLUDecompositionImpl<Fraction>(coefficients).getSolver().solve(constants);
393         assertEquals((new Fraction(2).multiply((solution[0])).add(new Fraction(3).multiply(solution[1])).subtract(new Fraction(2).multiply(solution[2]))).doubleValue(),
394                 constants[0].doubleValue(), 1E-12);
395         assertEquals(((new Fraction(-1).multiply(solution[0])).add(new Fraction(7).multiply(solution[1])).add(new Fraction(6).multiply(solution[2]))).doubleValue(),
396                 constants[1].doubleValue(), 1E-12);
397         assertEquals(((new Fraction(4).multiply(solution[0])).subtract(new Fraction(3).multiply( solution[1])).subtract(new Fraction(5).multiply(solution[2]))).doubleValue(),
398                 constants[2].doubleValue(), 1E-12);
399 
400     }
401 
402     // test submatrix accessors
403     public void testSubMatrix() {
404         FieldMatrix<Fraction> m = createSparseMatrix(subTestData);
405         FieldMatrix<Fraction> mRows23Cols00 = createSparseMatrix(subRows23Cols00);
406         FieldMatrix<Fraction> mRows00Cols33 = createSparseMatrix(subRows00Cols33);
407         FieldMatrix<Fraction> mRows01Cols23 = createSparseMatrix(subRows01Cols23);
408         FieldMatrix<Fraction> mRows02Cols13 = createSparseMatrix(subRows02Cols13);
409         FieldMatrix<Fraction> mRows03Cols12 = createSparseMatrix(subRows03Cols12);
410         FieldMatrix<Fraction> mRows03Cols123 = createSparseMatrix(subRows03Cols123);
411         FieldMatrix<Fraction> mRows20Cols123 = createSparseMatrix(subRows20Cols123);
412         FieldMatrix<Fraction> mRows31Cols31 = createSparseMatrix(subRows31Cols31);
413         assertEquals("Rows23Cols00", mRows23Cols00, m.getSubMatrix(2, 3, 0, 0));
414         assertEquals("Rows00Cols33", mRows00Cols33, m.getSubMatrix(0, 0, 3, 3));
415         assertEquals("Rows01Cols23", mRows01Cols23, m.getSubMatrix(0, 1, 2, 3));
416         assertEquals("Rows02Cols13", mRows02Cols13, 
417             m.getSubMatrix(new int[] { 0, 2 }, new int[] { 1, 3 }));
418         assertEquals("Rows03Cols12", mRows03Cols12, 
419             m.getSubMatrix(new int[] { 0, 3 }, new int[] { 1, 2 }));
420         assertEquals("Rows03Cols123", mRows03Cols123, 
421             m.getSubMatrix(new int[] { 0, 3 }, new int[] { 1, 2, 3 }));
422         assertEquals("Rows20Cols123", mRows20Cols123, 
423             m.getSubMatrix(new int[] { 2, 0 }, new int[] { 1, 2, 3 }));
424         assertEquals("Rows31Cols31", mRows31Cols31, 
425             m.getSubMatrix(new int[] { 3, 1 }, new int[] { 3, 1 }));
426         assertEquals("Rows31Cols31", mRows31Cols31, 
427             m.getSubMatrix(new int[] { 3, 1 }, new int[] { 3, 1 }));
428 
429         try {
430             m.getSubMatrix(1, 0, 2, 4);
431             fail("Expecting MatrixIndexException");
432         } catch (MatrixIndexException ex) {
433             // expected
434         }
435         try {
436             m.getSubMatrix(-1, 1, 2, 2);
437             fail("Expecting MatrixIndexException");
438         } catch (MatrixIndexException ex) {
439             // expected
440         }
441         try {
442             m.getSubMatrix(1, 0, 2, 2);
443             fail("Expecting MatrixIndexException");
444         } catch (MatrixIndexException ex) {
445             // expected
446         }
447         try {
448             m.getSubMatrix(1, 0, 2, 4);
449             fail("Expecting MatrixIndexException");
450         } catch (MatrixIndexException ex) {
451             // expected
452         }
453         try {
454             m.getSubMatrix(new int[] {}, new int[] { 0 });
455             fail("Expecting MatrixIndexException");
456         } catch (MatrixIndexException ex) {
457             // expected
458         }
459         try {
460             m.getSubMatrix(new int[] { 0 }, new int[] { 4 });
461             fail("Expecting MatrixIndexException");
462         } catch (MatrixIndexException ex) {
463             // expected
464         }
465     }
466 
467     public void testGetRowMatrix() {
468         FieldMatrix<Fraction> m = createSparseMatrix(subTestData);
469         FieldMatrix<Fraction> mRow0 = createSparseMatrix(subRow0);
470         FieldMatrix<Fraction> mRow3 = createSparseMatrix(subRow3);
471         assertEquals("Row0", mRow0, m.getRowMatrix(0));
472         assertEquals("Row3", mRow3, m.getRowMatrix(3));
473         try {
474             m.getRowMatrix(-1);
475             fail("Expecting MatrixIndexException");
476         } catch (MatrixIndexException ex) {
477             // expected
478         }
479         try {
480             m.getRowMatrix(4);
481             fail("Expecting MatrixIndexException");
482         } catch (MatrixIndexException ex) {
483             // expected
484         }
485     }
486 
487     public void testGetColumnMatrix() {
488         FieldMatrix<Fraction> m = createSparseMatrix(subTestData);
489         FieldMatrix<Fraction> mColumn1 = createSparseMatrix(subColumn1);
490         FieldMatrix<Fraction> mColumn3 = createSparseMatrix(subColumn3);
491         assertEquals("Column1", mColumn1, m.getColumnMatrix(1));
492         assertEquals("Column3", mColumn3, m.getColumnMatrix(3));
493         try {
494             m.getColumnMatrix(-1);
495             fail("Expecting MatrixIndexException");
496         } catch (MatrixIndexException ex) {
497             // expected
498         }
499         try {
500             m.getColumnMatrix(4);
501             fail("Expecting MatrixIndexException");
502         } catch (MatrixIndexException ex) {
503             // expected
504         }
505     }
506 
507     public void testGetRowVector() {
508         FieldMatrix<Fraction> m = createSparseMatrix(subTestData);
509         FieldVector<Fraction> mRow0 = new ArrayFieldVector<Fraction>(subRow0[0]);
510         FieldVector<Fraction> mRow3 = new ArrayFieldVector<Fraction>(subRow3[0]);
511         assertEquals("Row0", mRow0, m.getRowVector(0));
512         assertEquals("Row3", mRow3, m.getRowVector(3));
513         try {
514             m.getRowVector(-1);
515             fail("Expecting MatrixIndexException");
516         } catch (MatrixIndexException ex) {
517             // expected
518         }
519         try {
520             m.getRowVector(4);
521             fail("Expecting MatrixIndexException");
522         } catch (MatrixIndexException ex) {
523             // expected
524         }
525     }
526 
527     public void testGetColumnVector() {
528         FieldMatrix<Fraction> m = createSparseMatrix(subTestData);
529         FieldVector<Fraction> mColumn1 = columnToVector(subColumn1);
530         FieldVector<Fraction> mColumn3 = columnToVector(subColumn3);
531         assertEquals("Column1", mColumn1, m.getColumnVector(1));
532         assertEquals("Column3", mColumn3, m.getColumnVector(3));
533         try {
534             m.getColumnVector(-1);
535             fail("Expecting MatrixIndexException");
536         } catch (MatrixIndexException ex) {
537             // expected
538         }
539         try {
540             m.getColumnVector(4);
541             fail("Expecting MatrixIndexException");
542         } catch (MatrixIndexException ex) {
543             // expected
544         }
545     }
546 
547     private FieldVector<Fraction> columnToVector(Fraction[][] column) {
548         Fraction[] data = new Fraction[column.length];
549         for (int i = 0; i < data.length; ++i) {
550             data[i] = column[i][0];
551         }
552         return new ArrayFieldVector<Fraction>(data, false);
553     }
554 
555     public void testEqualsAndHashCode() {
556         SparseFieldMatrix<Fraction> m = createSparseMatrix(testData);
557         SparseFieldMatrix<Fraction> m1 = (SparseFieldMatrix<Fraction>) m.copy();
558         SparseFieldMatrix<Fraction> mt = (SparseFieldMatrix<Fraction>) m.transpose();
559         assertTrue(m.hashCode() != mt.hashCode());
560         assertEquals(m.hashCode(), m1.hashCode());
561         assertEquals(m, m);
562         assertEquals(m, m1);
563         assertFalse(m.equals(null));
564         assertFalse(m.equals(mt));
565         assertFalse(m.equals(createSparseMatrix(bigSingular)));
566     }
567 
568     /* Disable for now
569     public void testToString() {
570         SparseFieldMatrix<Fraction> m = createSparseMatrix(testData);
571         assertEquals("SparseFieldMatrix<Fraction>{{1.0,2.0,3.0},{2.0,5.0,3.0},{1.0,0.0,8.0}}", 
572             m.toString());
573         m = new SparseFieldMatrix<Fraction>(field, 1, 1);
574         assertEquals("SparseFieldMatrix<Fraction>{{0.0}}", m.toString());
575     }
576     */
577 
578     public void testSetSubMatrix() throws Exception {
579         SparseFieldMatrix<Fraction> m = createSparseMatrix(testData);
580         m.setSubMatrix(detData2, 1, 1);
581         FieldMatrix<Fraction> expected = createSparseMatrix(new Fraction[][] {
582                 { new Fraction(1), new Fraction(2), new Fraction(3) }, { new Fraction(2), new Fraction(1), new Fraction(3) }, { new Fraction(1), new Fraction(2), new Fraction(4) } });
583         assertEquals(expected, m);
584 
585         m.setSubMatrix(detData2, 0, 0);
586         expected = createSparseMatrix(new Fraction[][] {
587                 { new Fraction(1), new Fraction(3), new Fraction(3) }, { new Fraction(2), new Fraction(4), new Fraction(3) }, { new Fraction(1), new Fraction(2), new Fraction(4) } });
588         assertEquals(expected, m);
589 
590         m.setSubMatrix(testDataPlus2, 0, 0);
591         expected = createSparseMatrix(new Fraction[][] {
592                 { new Fraction(3), new Fraction(4), new Fraction(5) }, { new Fraction(4), new Fraction(7), new Fraction(5) }, { new Fraction(3), new Fraction(2), new Fraction(10) } });
593         assertEquals(expected, m);
594 
595         // javadoc example
596         SparseFieldMatrix<Fraction> matrix = 
597             createSparseMatrix(new Fraction[][] { 
598         { new Fraction(1), new Fraction(2), new Fraction(3), new Fraction(4) }, { new Fraction(5), new Fraction(6), new Fraction(7), new Fraction(8) }, { new Fraction(9), new Fraction(0), new Fraction(1), new Fraction(2) } });
599         matrix.setSubMatrix(new Fraction[][] { { new Fraction(3), new Fraction(4) }, { new Fraction(5), new Fraction(6) } }, 1, 1);
600         expected = createSparseMatrix(new Fraction[][] {
601                 { new Fraction(1), new Fraction(2), new Fraction(3), new Fraction(4) }, { new Fraction(5), new Fraction(3), new Fraction(4), new Fraction(8) }, { new Fraction(9), new Fraction(5), new Fraction(6), new Fraction(2) } });
602         assertEquals(expected, matrix);
603 
604         // dimension overflow
605         try {
606             m.setSubMatrix(testData, 1, 1);
607             fail("expecting MatrixIndexException");
608         } catch (MatrixIndexException e) {
609             // expected
610         }
611         // dimension underflow
612         try {
613             m.setSubMatrix(testData, -1, 1);
614             fail("expecting MatrixIndexException");
615         } catch (MatrixIndexException e) {
616             // expected
617         }
618         try {
619             m.setSubMatrix(testData, 1, -1);
620             fail("expecting MatrixIndexException");
621         } catch (MatrixIndexException e) {
622             // expected
623         }
624 
625         // null
626         try {
627             m.setSubMatrix(null, 1, 1);
628             fail("expecting NullPointerException");
629         } catch (NullPointerException e) {
630             // expected
631         }
632         try {
633             new SparseFieldMatrix<Fraction>(field, 0, 0);
634             fail("expecting IllegalArgumentException");
635         } catch (IllegalArgumentException e) {
636             // expected
637         }
638 
639         // ragged
640         try {
641             m.setSubMatrix(new Fraction[][] { { new Fraction(1) }, { new Fraction(2), new Fraction(3) } }, 0, 0);
642             fail("expecting IllegalArgumentException");
643         } catch (IllegalArgumentException e) {
644             // expected
645         }
646 
647         // empty
648         try {
649             m.setSubMatrix(new Fraction[][] { {} }, 0, 0);
650             fail("expecting IllegalArgumentException");
651         } catch (IllegalArgumentException e) {
652             // expected
653         }
654 
655     }
656 
657     // --------------- -----------------Protected methods
658 
659     /** verifies that two matrices are close (1-norm) */
660     protected void assertClose(String msg, FieldMatrix<Fraction> m, FieldMatrix<Fraction> n,
661             double tolerance) {
662         for(int i=0; i < m.getRowDimension(); i++){
663             for(int j=0; j < m.getColumnDimension(); j++){
664                 assertEquals(msg, m.getEntry(i,j).doubleValue(), n.getEntry(i,j).doubleValue(), tolerance);
665             }
666             
667         }
668     }
669 
670     /** verifies that two vectors are close (sup norm) */
671     protected void assertClose(String msg, Fraction[] m, Fraction[] n,
672             double tolerance) {
673         if (m.length != n.length) {
674             fail("vectors not same length");
675         }
676         for (int i = 0; i < m.length; i++) {
677             assertEquals(msg + " " + i + " elements differ", m[i].doubleValue(), n[i].doubleValue(),
678                     tolerance);
679         }
680     }
681     
682     private SparseFieldMatrix<Fraction> createSparseMatrix(Fraction[][] data) {
683         SparseFieldMatrix<Fraction> matrix = new SparseFieldMatrix<Fraction>(field, data.length, data[0].length);
684         for (int row = 0; row < data.length; row++) {
685             for (int col = 0; col < data[row].length; col++) {
686                 matrix.setEntry(row, col, data[row][col]);
687             }
688         }
689         return matrix;
690     }
691 
692 }