Source code

001/*
002 * $Id$
003 */
004
005package edu.jas.jlinalg;
006
007
008import org.jlinalg.LinSysSolver;
009import org.jlinalg.Matrix;
010import org.jlinalg.Vector;
011import org.jlinalg.polynomial.Polynomial;
012
013import edu.jas.arith.BigRational;
014import edu.jas.poly.GenPolynomial;
015import edu.jas.vector.GenMatrix;
016import edu.jas.vector.GenMatrixRing;
017import edu.jas.vector.GenVector;
018import edu.jas.vector.GenVectorModul;
019
020
021/**
022 * Example that computes a solution of a linear equation system.
023 * @author Heinz Kredel
024 */
025
026public class MatrixExamples {
027
028
029    public static void main(String[] argv) {
030        example1();
031        example2();
032        example3();
033    }
034
035
036    @SuppressWarnings({ "unchecked" })
037    public static void example1() {
038        BigRational r1, r2, r3, r4, r5, r6, z;
039        r1 = new BigRational(1, 10);
040        r2 = new BigRational(6, 5);
041        r3 = new BigRational(1, 9);
042        r4 = new BigRational(1, 1);
043        r5 = r2.sum(r3);
044        r6 = r1.multiply(r4);
045        z = new BigRational();
046
047        JLAdapter<BigRational> r1a, r2a, r3a, r4a, r5a, r6a, d, t, za;
048        r1a = new JLAdapter<BigRational>(r1);
049        r2a = new JLAdapter<BigRational>(r2);
050        r3a = new JLAdapter<BigRational>(r3);
051        r4a = new JLAdapter<BigRational>(r4);
052        r5a = new JLAdapter<BigRational>(r5);
053        r6a = new JLAdapter<BigRational>(r6);
054        za = new JLAdapter<BigRational>(z);
055
056        Matrix<JLAdapter<BigRational>> a = new Matrix<JLAdapter<BigRational>>(
057                        new JLAdapter[][] { { r1a, r2a, r3a }, { r4a, r5a, r6a } });
058
059        System.out.println("system = " + a);
060
061        Vector<JLAdapter<BigRational>> b = new Vector<JLAdapter<BigRational>>(new JLAdapter[] { r1a, r2a });
062        System.out.println("rhs = " + b);
063
064        Vector<JLAdapter<BigRational>> solution = LinSysSolver.solve(a, b);
065        System.out.println("x = " + solution);
066
067        System.out.println("solutionSpace = " + LinSysSolver.solutionSpace(a, b));
068        Vector<JLAdapter<BigRational>> bz = new Vector<JLAdapter<BigRational>>(new JLAdapter[] { za, za });
069        System.out.println("rhs = " + bz);
070        System.out.println("nullSolutionSpace = " + LinSysSolver.solutionSpace(a, bz));
071
072        Matrix<JLAdapter<BigRational>> m = new Matrix<JLAdapter<BigRational>>(
073                        new JLAdapter[][] { { r1a, r2a, r3a }, { r4a, r5a, r6a }, { r2a, r1a, r3a } });
074        System.out.println("matrix = " + m);
075
076        m = m.multiply(m);
077        System.out.println("matrix^2 = " + m);
078
079        d = m.det();
080        System.out.println("det(matrix^2) = " + d);
081
082        t = m.trace();
083        System.out.println("trace(matrix^2) = " + t);
084
085        Polynomial<JLAdapter<BigRational>> cp = m.characteristicPolynomial();
086        System.out.println("charPol(matrix^2) = " + cp);
087
088        Polynomial<JLAdapter<BigRational>> mp = m.minimalPolynomial();
089        System.out.println("minPol(matrix^2) = " + mp);
090
091        Matrix<JLAdapter<BigRational>> mg = m.gausselim();
092        System.out.println("matrix, gauss = " + mg);
093
094        Matrix<JLAdapter<BigRational>> m2 = new Matrix<JLAdapter<BigRational>>(new JLAdapter[][] {
095                { r1a, r2a, r3a, r4a }, { r4a, r5a, r6a, r1a }, { r2a, r1a, r3a, r5a } });
096        System.out.println("matrix_2 = " + m2);
097        Matrix<JLAdapter<BigRational>> mj = m2.gaussjord();
098        System.out.println("matrix,gauss-jordan = " + mj);
099
100        try {
101            System.out.println("matrix,eigenvalue = "); // + m.eig()); fails for Double
102        } catch (org.jlinalg.InvalidOperationException e) {
103            System.out.println("" + e);
104        }
105    }
106
107
108    @SuppressWarnings({ "unchecked" })
109    public static void example2() {
110        BigRational r1, r2, r3, r4, r5, r6, z;
111        r1 = new BigRational(1, 10);
112        r2 = new BigRational(6, 5);
113        r3 = new BigRational(1, 9);
114        r4 = new BigRational(1, 1);
115        r5 = r2.sum(r3);
116        r6 = r1.multiply(r4);
117        z = new BigRational();
118
119        JLAdapter<BigRational> d, t;
120
121        Matrix<JLAdapter<BigRational>> a = new Matrix<JLAdapter<BigRational>>(JLAdapterUtil
122                        .<BigRational> toJLAdapter(new BigRational[][] { { r1, r2, r3 }, { r4, r5, r6 } }));
123        System.out.println("system = " + a);
124
125        Vector<JLAdapter<BigRational>> b = new Vector<JLAdapter<BigRational>>(
126                        JLAdapterUtil.<BigRational> toJLAdapter(new BigRational[] { r1, r2 }));
127        System.out.println("rhs = " + b);
128
129        Vector<JLAdapter<BigRational>> solution = LinSysSolver.solve(a, b);
130        System.out.println("x = " + solution);
131
132        System.out.println("solutionSpace = " + LinSysSolver.solutionSpace(a, b));
133
134        Vector<JLAdapter<BigRational>> bz = new Vector<JLAdapter<BigRational>>(
135                        JLAdapterUtil.<BigRational> toJLAdapter(new BigRational[] { z, z }));
136        System.out.println("rhs = " + bz);
137        System.out.println("nullSolutionSpace = " + LinSysSolver.solutionSpace(a, bz));
138
139        Matrix<JLAdapter<BigRational>> m = new Matrix<JLAdapter<BigRational>>(
140                        JLAdapterUtil.<BigRational> toJLAdapter(new BigRational[][] { { r1, r2, r3 },
141                                { r4, r5, r6 }, { r2, r1, r3 } }));
142        System.out.println("matrix = " + m);
143
144        m = m.multiply(m);
145        System.out.println("matrix^2 = " + m);
146
147        d = m.det();
148        System.out.println("det(matrix^2) = " + d);
149
150        t = m.trace();
151        System.out.println("trace(matrix^2) = " + t);
152
153        Polynomial<JLAdapter<BigRational>> cp = m.characteristicPolynomial();
154        System.out.println("charPol(matrix^2) = " + cp);
155
156        Polynomial<JLAdapter<BigRational>> mp = m.minimalPolynomial();
157        System.out.println("minPol(matrix^2) = " + mp);
158
159        Matrix<JLAdapter<BigRational>> mg = m.gausselim();
160        System.out.println("matrix, gauss = " + mg);
161
162        Matrix<JLAdapter<BigRational>> m2 = new Matrix<JLAdapter<BigRational>>(
163                        JLAdapterUtil.<BigRational> toJLAdapter(new BigRational[][] { { r1, r2, r3, r4 },
164                                { r4, r5, r6, r1 }, { r2, r1, r3, r5 } }));
165        System.out.println("matrix_2 = " + m2);
166        Matrix<JLAdapter<BigRational>> mj = m2.gaussjord();
167        System.out.println("matrix,gauss-jordan = " + mj);
168
169        try {
170            System.out.println("matrix,eigenvalue = "); // + m.eig()); fails for Double
171        } catch (org.jlinalg.InvalidOperationException e) {
172            System.out.println("" + e);
173        }
174    }
175
176
177    @SuppressWarnings({ "unchecked" })
178    public static void example3() {
179        BigRational r1, r2, r3, r4, r5, r6, fac;
180        r1 = new BigRational(1, 10);
181        r2 = new BigRational(6, 5);
182        r3 = new BigRational(1, 9);
183        r4 = new BigRational(1, 1);
184        r5 = r2.sum(r3);
185        r6 = r1.multiply(r4);
186
187        fac = new BigRational();
188
189        //JLAdapter<BigRational> d, t;
190
191        BigRational[][] aa = new BigRational[][] { { r1, r2, r3 }, { r4, r5, r6 } };
192        GenMatrixRing<BigRational> mfac = new GenMatrixRing<BigRational>(fac, aa.length, aa[0].length);
193        GenMatrix<BigRational> a = new GenMatrix<BigRational>(mfac, JLAdapterUtil.<BigRational> toList(aa));
194        System.out.println("system = " + a);
195
196        BigRational[] ba = new BigRational[] { r1, r2 };
197        GenVectorModul<BigRational> vfac = new GenVectorModul<BigRational>(fac, ba.length);
198        GenVector<BigRational> b = new GenVector<BigRational>(vfac, JLAdapterUtil.<BigRational> toList(ba));
199        System.out.println("right hand side = " + b);
200
201        GaussElimination<BigRational> ge = new GaussElimination<BigRational>();
202        GenVector<BigRational> x = ge.solve(a, b);
203        System.out.println("solution = " + x);
204
205        BigRational[][] am = new BigRational[][] { { r1, r2, r3 }, { r4, r5, r6 }, { r2, r1, r3 } };
206        GenMatrixRing<BigRational> mfacm = new GenMatrixRing<BigRational>(fac, am.length, am[0].length);
207        GenMatrix<BigRational> m = new GenMatrix<BigRational>(mfacm, JLAdapterUtil.<BigRational> toList(am));
208        System.out.println("matrix = " + m);
209        GenPolynomial<BigRational> p = ge.characteristicPolynomial(m);
210        System.out.println("characteristicPolynomial = " + p);
211
212        //         m = m.multiply(m);
213        //         System.out.println("matrix = " + m);
214        //         p = ge.characteristicPolynomial(m);
215        //         System.out.println("characteristicPolynomial = " + p);
216
217        m = mfacm.getONE();
218        System.out.println("matrix = " + m);
219        p = ge.characteristicPolynomial(m);
220        System.out.println("characteristicPolynomial = " + p);
221
222        m = mfacm.getZERO();
223        System.out.println("matrix = " + m);
224        p = ge.characteristicPolynomial(m);
225        System.out.println("characteristicPolynomial = " + p);
226
227        m = mfacm.getONE();
228        System.out.println("matrix = " + m);
229        GenMatrix<BigRational> ns = ge.nullSpace(m);
230        System.out.println("nullSpace = " + ns);
231        System.out.println("isNullSpace = " + ge.isNullSpace(m, ns));
232
233        am = new BigRational[][] { { r1, r2, r3 }, { r4, r5, r6 }, { r4, r5, r6 } };
234        mfacm = new GenMatrixRing<BigRational>(fac, am.length, am[0].length);
235        m = new GenMatrix<BigRational>(mfacm, JLAdapterUtil.<BigRational> toList(am));
236        System.out.println("matrix = " + m);
237
238        ns = ge.nullSpace(m);
239        System.out.println("nullSpace = " + ns);
240        System.out.println("isNullSpace = " + ge.isNullSpace(m, ns));
241        //System.out.println("isNullSpace = " + ge.isNullSpace(ns,m));
242        //System.out.println("isNullSpace = " + ge.isNullSpace(m,ns.transpose(mfacm)));
243
244        m = mfacm.getZERO();
245        System.out.println("matrix = " + m);
246        ns = ge.nullSpace(m);
247        System.out.println("nullSpace = " + ns);
248        System.out.println("isNullSpace = " + ge.isNullSpace(m, ns));
249
250        int kl = 3;
251        int ll = 10;
252        mfac = new GenMatrixRing<BigRational>(fac, ll, ll + 1);
253        m = mfac.random(kl);
254        System.out.println("matrix = " + m);
255        m = ge.gaussElimination(m);
256        System.out.println("Gauss elimination = " + m);
257
258        m = ge.gaussJordanElimination(m);
259        System.out.println("Gauss-Jordan elimination = " + m);
260
261        mfac = new GenMatrixRing<BigRational>(fac, ll, ll);
262        m = mfac.random(kl);
263        System.out.println("matrix = " + m);
264        GenMatrix<BigRational> mi = null;
265        try {
266            mi = ge.inverse(m);
267            System.out.println("inverse = " + mi);
268            if (mi != null) {
269                GenMatrix<BigRational> tt = m.multiply(mi);
270                boolean inv = tt.isONE();
271                if (!inv) {
272                    System.out.println("m * inverse = " + tt);
273                }
274                System.out.println("isInverse = " + inv);
275            }
276        } catch (Exception ignored) {
277        }
278        kl = 3;
279        ll = 10; // for ll > 40 must adjust JVM parameters, e.g. -Xms500M -Xmx600M
280        mfac = new GenMatrixRing<BigRational>(fac, ll, ll);
281        m = mfac.random(kl);
282        //System.out.println("matrix = " + m);
283        m = ge.gaussElimination(m);
284        //System.out.println("Gauss elimination = " + m);
285
286        m = ge.gaussJordanElimination(m);
287        //System.out.println("Gauss-Jordan elimination = " + m);
288        System.out.println("is Gauss-Jordan elimination = " + m.isONE());
289    }
290
291}