    1   /*
    2    * Copyright 2003-2005 The Apache Software Foundation.
    3    *
    4    * Licensed under the Apache License, Version 2.0 (the "License");
    5    * you may not use this file except in compliance with the License.
    6    * You may obtain a copy of the License at
    7    *
    8    *      http://www.apache.org/licenses/LICENSE-2.0
    9    *
    10   * Unless required by applicable law or agreed to in writing, software
    11   * distributed under the License is distributed on an "AS IS" BASIS,
    12   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    13   * See the License for the specific language governing permissions and
    14   * limitations under the License.
    15   */
    16  package org.apache.commons.math.linear;
    17
    18  import junit.framework.Test;
    19  import junit.framework.TestCase;
    20  import junit.framework.TestSuite;
    21
    22  /***
    23   * Test cases for the {@link RealMatrixImpl} class.
    24   *
    25   * @version $Revision: 240244 $ $Date: 2005-08-26 06:40:32 -0700 (Fri, 26 Aug 2005) $
    26   */
    27
    28  public final class RealMatrixImplTest extends TestCase {
    29
    30      // 3 x 3 identity matrix
    31      protected double[][] id = { {1d,0d,0d}, {0d,1d,0d}, {0d,0d,1d} };
    32
    33      // Test data for group operations
    34      protected double[][] testData = { {1d,2d,3d}, {2d,5d,3d}, {1d,0d,8d} };
    35      protected double[][] testDataLU = {{2d, 5d, 3d}, {.5d, -2.5d, 6.5d}, {0.5d, 0.2d, .2d}};
    36      protected double[][] testDataPlus2 = { {3d,4d,5d}, {4d,7d,5d}, {3d,2d,10d} };
    37      protected double[][] testDataMinus = { {-1d,-2d,-3d}, {-2d,-5d,-3d},
    38         {-1d,0d,-8d} };
    39      protected double[] testDataRow1 = {1d,2d,3d};
    40      protected double[] testDataCol3 = {3d,3d,8d};
    41      protected double[][] testDataInv =
    42          { {-40d,16d,9d}, {13d,-5d,-3d}, {5d,-2d,-1d} };
    43      protected double[] preMultTest = {8,12,33};
    44      protected double[][] testData2 ={ {1d,2d,3d}, {2d,5d,3d}};
    45      protected double[][] testData2T = { {1d,2d}, {2d,5d}, {3d,3d}};
    46      protected double[][] testDataPlusInv =
    47          { {-39d,18d,12d}, {15d,0d,0d}, {6d,-2d,7d} };
    48
    49      // lu decomposition tests
    50      protected double[][] luData = { {2d,3d,3d}, {0d,5d,7d}, {6d,9d,8d} };
    51      protected double[][] luDataLUDecomposition = { {6d,9d,8d}, {0d,5d,7d},
    52              {0.33333333333333,0d,0.33333333333333} };
    53
    54      // singular matrices
    55      protected double[][] singular = { {2d,3d}, {2d,3d} };
    56      protected double[][] bigSingular = {{1d,2d,3d,4d}, {2d,5d,3d,4d},
    57          {7d,3d,256d,1930d}, {3d,7d,6d,8d}}; // 4th row = 1st + 2nd
    58      protected double[][] detData = { {1d,2d,3d}, {4d,5d,6d}, {7d,8d,10d} };
    59      protected double[][] detData2 = { {1d, 3d}, {2d, 4d}};
    60
    61      // vectors
    62      protected double[] testVector = {1,2,3};
    63      protected double[] testVector2 = {1,2,3,4};
    64
    65      // submatrix accessor tests
    66      protected double[][] subTestData = {{1, 2, 3, 4}, {1.5, 2.5, 3.5, 4.5},
    67              {2, 4, 6, 8}, {4, 5, 6, 7}};
    68      // array selections
    69      protected double[][] subRows02Cols13 = { {2, 4}, {4, 8}};
    70      protected double[][] subRows03Cols12 = { {2, 3}, {5, 6}};
    71      protected double[][] subRows03Cols123 = { {2, 3, 4} , {5, 6, 7}};
    72      // effective permutations
    73      protected double[][] subRows20Cols123 = { {4, 6, 8} , {2, 3, 4}};
    74      protected double[][] subRows31Cols31 = {{7, 5}, {4.5, 2.5}};
    75      // contiguous ranges
    76      protected double[][] subRows01Cols23 = {{3,4} , {3.5, 4.5}};
    77      protected double[][] subRows23Cols00 = {{2} , {4}};
    78      protected double[][] subRows00Cols33 = {{4}};
    79      // row matrices
    80      protected double[][] subRow0 = {{1,2,3,4}};
    81      protected double[][] subRow3 = {{4,5,6,7}};
    82      // column matrices
    83      protected double[][] subColumn1 = {{2}, {2.5}, {4}, {5}};
    84      protected double[][] subColumn3 = {{4}, {4.5}, {8}, {7}};
    85
    86      // tolerances
    87      protected double entryTolerance = 10E-16;
    88      protected double normTolerance = 10E-14;
    89
    90      public RealMatrixImplTest(String name) {
    91          super(name);
    92      }
    93
    94      public void setUp() {
    95
    96      }
    97
    98      public static Test suite() {
    99          TestSuite suite = new TestSuite(RealMatrixImplTest.class);
    100         suite.setName("RealMatrixImpl Tests");
    101         return suite;
    102     }
    103
    104     /*** test dimensions */
    105     public void testDimensions() {
    106         RealMatrixImpl m = new RealMatrixImpl(testData);
    107         RealMatrixImpl m2 = new RealMatrixImpl(testData2);
    108         assertEquals("testData row dimension",3,m.getRowDimension());
    109         assertEquals("testData column dimension",3,m.getColumnDimension());
    110         assertTrue("testData is square",m.isSquare());
    111         assertEquals("testData2 row dimension",m2.getRowDimension(),2);
    112         assertEquals("testData2 column dimension",m2.getColumnDimension(),3);
    113         assertTrue("testData2 is not square",!m2.isSquare());
    114     }
    115
    116     /*** test copy functions */
    117     public void testCopyFunctions() {
    118         RealMatrixImpl m = new RealMatrixImpl(testData);
    119         RealMatrixImpl m2 = new RealMatrixImpl(m.getData());
    120         assertEquals(m2,m);
    121     }
    122
    123     /*** test add */
    124     public void testAdd() {
    125         RealMatrixImpl m = new RealMatrixImpl(testData);
    126         RealMatrixImpl mInv = new RealMatrixImpl(testDataInv);
    127         RealMatrixImpl mPlusMInv = (RealMatrixImpl)m.add(mInv);
    128         double[][] sumEntries = mPlusMInv.getData();
    129         for (int row = 0; row < m.getRowDimension(); row++) {
    130             for (int col = 0; col < m.getColumnDimension(); col++) {
    131                 assertEquals("sum entry entry",
    132                     testDataPlusInv[row][col],sumEntries[row][col],
    133                         entryTolerance);
    134             }
    135         }
    136     }
    137
    138     /*** test add failure */
    139     public void testAddFail() {
    140         RealMatrixImpl m = new RealMatrixImpl(testData);
    141         RealMatrixImpl m2 = new RealMatrixImpl(testData2);
    142         try {
    143             RealMatrixImpl mPlusMInv = (RealMatrixImpl)m.add(m2);
    144             fail("IllegalArgumentException expected");
    145         } catch (IllegalArgumentException ex) {
    146             ;
    147         }
    148     }
    149
    150     /*** test norm */
    151     public void testNorm() {
    152         RealMatrixImpl m = new RealMatrixImpl(testData);
    153         RealMatrixImpl m2 = new RealMatrixImpl(testData2);
    154         assertEquals("testData norm",14d,m.getNorm(),entryTolerance);
    155         assertEquals("testData2 norm",7d,m2.getNorm(),entryTolerance);
    156     }
    157
    158      /*** test m-n = m + -n */
    159     public void testPlusMinus() {
    160         RealMatrixImpl m = new RealMatrixImpl(testData);
    161         RealMatrixImpl m2 = new RealMatrixImpl(testDataInv);
    162         assertClose("m-n = m + -n",m.subtract(m2),
    163             m2.scalarMultiply(-1d).add(m),entryTolerance);
    164         try {
    165             RealMatrix a = m.subtract(new RealMatrixImpl(testData2));
    166             fail("Expecting illegalArgumentException");
    167         } catch (IllegalArgumentException ex) {
    168             ;
    169         }
    170     }
    171
    172     /*** test multiply */
    173      public void testMultiply() {
    174         RealMatrixImpl m = new RealMatrixImpl(testData);
    175         RealMatrixImpl mInv = new RealMatrixImpl(testDataInv);
    176         RealMatrixImpl identity = new RealMatrixImpl(id);
    177         RealMatrixImpl m2 = new RealMatrixImpl(testData2);
    178         assertClose("inverse multiply",m.multiply(mInv),
    179             identity,entryTolerance);
    180         assertClose("inverse multiply",mInv.multiply(m),
    181             identity,entryTolerance);
    182         assertClose("identity multiply",m.multiply(identity),
    183             m,entryTolerance);
    184         assertClose("identity multiply",identity.multiply(mInv),
    185             mInv,entryTolerance);
    186         assertClose("identity multiply",m2.multiply(identity),
    187             m2,entryTolerance);
    188         try {
    189             RealMatrix a = m.multiply(new RealMatrixImpl(bigSingular));
    190             fail("Expecting illegalArgumentException");
    191         } catch (IllegalArgumentException ex) {
    192             ;
    193         }
    194     }
    195
    196     //Additional Test for RealMatrixImplTest.testMultiply
    197
    198     private double[][] d3 = new double[][] {{1,2,3,4},{5,6,7,8}};
    199     private double[][] d4 = new double[][] {{1},{2},{3},{4}};
    200     private double[][] d5 = new double[][] {{30},{70}};
    201
    202     public void testMultiply2() {
    203        RealMatrix m3 = new RealMatrixImpl(d3);
    204        RealMatrix m4 = new RealMatrixImpl(d4);
    205        RealMatrix m5 = new RealMatrixImpl(d5);
    206        assertClose("m3*m4=m5", m3.multiply(m4), m5, entryTolerance);
    207    }
    208
    209     /*** test isSingular */
    210     public void testIsSingular() {
    211         RealMatrixImpl m = new RealMatrixImpl(singular);
    212         assertTrue("singular",m.isSingular());
    213         m = new RealMatrixImpl(bigSingular);
    214         assertTrue("big singular",m.isSingular());
    215         m = new RealMatrixImpl(id);
    216         assertTrue("identity nonsingular",!m.isSingular());
    217         m = new RealMatrixImpl(testData);
    218         assertTrue("testData nonsingular",!m.isSingular());
    219     }
    220
    221     /*** test inverse */
    222     public void testInverse() {
    223         RealMatrixImpl m = new RealMatrixImpl(testData);
    224         RealMatrix mInv = new RealMatrixImpl(testDataInv);
    225         assertClose("inverse",mInv,m.inverse(),normTolerance);
    226         assertClose("inverse^2",m,m.inverse().inverse(),10E-12);
    227
    228         // Not square
    229         m = new RealMatrixImpl(testData2);
    230         try {
    231             m.inverse();
    232             fail("Expecting InvalidMatrixException");
    233         } catch (InvalidMatrixException ex) {
    234             // expected
    235         }
    236
    237         // Singular
    238         m = new RealMatrixImpl(singular);
    239         try {
    240             m.inverse();
    241             fail("Expecting InvalidMatrixException");
    242         } catch (InvalidMatrixException ex) {
    243             // expected
    244         }
    245     }
    246
    247     /*** test solve */
    248     public void testSolve() {
    249         RealMatrixImpl m = new RealMatrixImpl(testData);
    250         RealMatrix mInv = new RealMatrixImpl(testDataInv);
    251         // being a bit slothful here -- actually testing that X = A^-1 * B
    252         assertClose("inverse-operate",mInv.operate(testVector),
    253             m.solve(testVector),normTolerance);
    254         try {
    255             double[] x = m.solve(testVector2);
    256             fail("expecting IllegalArgumentException");
    257         } catch (IllegalArgumentException ex) {
    258             ;
    259         }
    260         RealMatrix bs = new RealMatrixImpl(bigSingular);
    261         try {
    262             RealMatrix a = bs.solve(bs);
    263             fail("Expecting InvalidMatrixException");
    264         } catch (InvalidMatrixException ex) {
    265             ;
    266         }
    267         try {
    268             RealMatrix a = m.solve(bs);
    269             fail("Expecting IllegalArgumentException");
    270         } catch (IllegalArgumentException ex) {
    271             ;
    272         }
    273         try {
    274             RealMatrix a = (new RealMatrixImpl(testData2)).solve(bs);
    275             fail("Expecting illegalArgumentException");
    276         } catch (IllegalArgumentException ex) {
    277             ;
    278         }
    279         try {
    280             (new RealMatrixImpl(testData2)).luDecompose();
    281             fail("Expecting InvalidMatrixException");
    282         } catch (InvalidMatrixException ex) {
    283             ;
    284         }
    285     }
    286
    287     /*** test determinant */
    288     public void testDeterminant() {
    289         RealMatrix m = new RealMatrixImpl(bigSingular);
    290         assertEquals("singular determinant",0,m.getDeterminant(),0);
    291         m = new RealMatrixImpl(detData);
    292         assertEquals("nonsingular test",-3d,m.getDeterminant(),normTolerance);
    293
    294         // Examples verified against R (version 1.8.1, Red Hat Linux 9)
    295         m = new RealMatrixImpl(detData2);
    296         assertEquals("nonsingular R test 1",-2d,m.getDeterminant(),normTolerance);
    297         m = new RealMatrixImpl(testData);
    298         assertEquals("nonsingular  R test 2",-1d,m.getDeterminant(),normTolerance);
    299
    300         try {
    301             double a = new RealMatrixImpl(testData2).getDeterminant();
    302             fail("Expecting InvalidMatrixException");
    303         } catch (InvalidMatrixException ex) {
    304             ;
    305         }
    306     }
    307
    308     /*** test trace */
    309     public void testTrace() {
    310         RealMatrix m = new RealMatrixImpl(id);
    311         assertEquals("identity trace",3d,m.getTrace(),entryTolerance);
    312         m = new RealMatrixImpl(testData2);
    313         try {
    314             double x = m.getTrace();
    315             fail("Expecting illegalArgumentException");
    316         } catch (IllegalArgumentException ex) {
    317             ;
    318         }
    319     }
    320
    321     /*** test sclarAdd */
    322     public void testScalarAdd() {
    323         RealMatrix m = new RealMatrixImpl(testData);
    324         assertClose("scalar add",new RealMatrixImpl(testDataPlus2),
    325             m.scalarAdd(2d),entryTolerance);
    326     }
    327
    328     /*** test operate */
    329     public void testOperate() {
    330         RealMatrix m = new RealMatrixImpl(id);
    331         double[] x = m.operate(testVector);
    332         assertClose("identity operate",testVector,x,entryTolerance);
    333         m = new RealMatrixImpl(bigSingular);
    334         try {
    335             x = m.operate(testVector);
    336             fail("Expecting illegalArgumentException");
    337         } catch (IllegalArgumentException ex) {
    338             ;
    339         }
    340     }
    341
    342     /*** test transpose */
    343     public void testTranspose() {
    344         RealMatrix m = new RealMatrixImpl(testData);
    345         assertClose("inverse-transpose",m.inverse().transpose(),
    346             m.transpose().inverse(),normTolerance);
    347         m = new RealMatrixImpl(testData2);
    348         RealMatrix mt = new RealMatrixImpl(testData2T);
    349         assertClose("transpose",mt,m.transpose(),normTolerance);
    350     }
    351
    352     /*** test preMultiply by vector */
    353     public void testPremultiplyVector() {
    354         RealMatrix m = new RealMatrixImpl(testData);
    355         assertClose("premultiply",m.preMultiply(testVector),preMultTest,normTolerance);
    356         m = new RealMatrixImpl(bigSingular);
    357         try {
    358             m.preMultiply(testVector);
    359             fail("expecting IllegalArgumentException");
    360         } catch (IllegalArgumentException ex) {
    361             ;
    362         }
    363     }
    364
    365     public void testPremultiply() {
    366         RealMatrix m3 = new RealMatrixImpl(d3);
    367         RealMatrix m4 = new RealMatrixImpl(d4);
    368         RealMatrix m5 = new RealMatrixImpl(d5);
    369         assertClose("m3*m4=m5", m4.preMultiply(m3), m5, entryTolerance);
    370
    371         RealMatrixImpl m = new RealMatrixImpl(testData);
    372         RealMatrixImpl mInv = new RealMatrixImpl(testDataInv);
    373         RealMatrixImpl identity = new RealMatrixImpl(id);
    374         RealMatrixImpl m2 = new RealMatrixImpl(testData2);
    375         assertClose("inverse multiply",m.preMultiply(mInv),
    376                 identity,entryTolerance);
    377         assertClose("inverse multiply",mInv.preMultiply(m),
    378                 identity,entryTolerance);
    379         assertClose("identity multiply",m.preMultiply(identity),
    380                 m,entryTolerance);
    381         assertClose("identity multiply",identity.preMultiply(mInv),
    382                 mInv,entryTolerance);
    383         try {
    384             RealMatrix a = m.preMultiply(new RealMatrixImpl(bigSingular));
    385             fail("Expecting illegalArgumentException");
    386         } catch (IllegalArgumentException ex) {
    387             ;
    388         }
    389     }
    390
    391     public void testGetVectors() {
    392         RealMatrix m = new RealMatrixImpl(testData);
    393         assertClose("get row",m.getRow(0),testDataRow1,entryTolerance);
    394         assertClose("get col",m.getColumn(2),testDataCol3,entryTolerance);
    395         try {
    396             double[] x = m.getRow(10);
    397             fail("expecting MatrixIndexException");
    398         } catch (MatrixIndexException ex) {
    399             ;
    400         }
    401         try {
    402             double[] x = m.getColumn(-1);
    403             fail("expecting MatrixIndexException");
    404         } catch (MatrixIndexException ex) {
    405             ;
    406         }
    407     }
    408
    409     public void testGetEntry() {
    410         RealMatrix m = new RealMatrixImpl(testData);
    411         assertEquals("get entry",m.getEntry(0,1),2d,entryTolerance);
    412         try {
    413             m.getEntry(10, 4);
    414             fail ("Expecting MatrixIndexException");
    415         } catch (MatrixIndexException ex) {
    416             // expected
    417         }
    418     }
    419
    420     public void testLUDecomposition() throws Exception {
    421         RealMatrixImpl m = new RealMatrixImpl(testData);
    422         RealMatrix lu = m.getLUMatrix();
    423         assertClose("LU decomposition", lu, (RealMatrix) new RealMatrixImpl(testDataLU), normTolerance);
    424         verifyDecomposition(m, lu);
    425         // access LU decomposition on same object to verify caching.
    426         lu = m.getLUMatrix();
    427         assertClose("LU decomposition", lu, (RealMatrix) new RealMatrixImpl(testDataLU), normTolerance);
    428         verifyDecomposition(m, lu);
    429
    430         m = new RealMatrixImpl(luData);
    431         lu = m.getLUMatrix();
    432         assertClose("LU decomposition", lu, (RealMatrix) new RealMatrixImpl(luDataLUDecomposition), normTolerance);
    433         verifyDecomposition(m, lu);
    434         m = new RealMatrixImpl(testDataMinus);
    435         lu = m.getLUMatrix();
    436         verifyDecomposition(m, lu);
    437         m = new RealMatrixImpl(id);
    438         lu = m.getLUMatrix();
    439         verifyDecomposition(m, lu);
    440         try {
    441             m = new RealMatrixImpl(bigSingular); // singular
    442             lu = m.getLUMatrix();
    443             fail("Expecting InvalidMatrixException");
    444         } catch (InvalidMatrixException ex) {
    445             // expected
    446         }
    447         try {
    448             m = new RealMatrixImpl(testData2);  // not square
    449             lu = m.getLUMatrix();
    450             fail("Expecting InvalidMatrixException");
    451         } catch (InvalidMatrixException ex) {
    452             // expected
    453         }
    454     }
    455
    456     /*** test examples in user guide */
    457     public void testExamples() {
    458         // Create a real matrix with two rows and three columns
    459         double[][] matrixData = { {1d,2d,3d}, {2d,5d,3d}};
    460         RealMatrix m = new RealMatrixImpl(matrixData);
    461         // One more with three rows, two columns
    462         double[][] matrixData2 = { {1d,2d}, {2d,5d}, {1d, 7d}};
    463         RealMatrix n = new RealMatrixImpl(matrixData2);
    464         // Now multiply m by n
    465         RealMatrix p = m.multiply(n);
    466         assertEquals(2, p.getRowDimension());
    467         assertEquals(2, p.getColumnDimension());
    468         // Invert p
    469         RealMatrix pInverse = p.inverse();
    470         assertEquals(2, pInverse.getRowDimension());
    471         assertEquals(2, pInverse.getColumnDimension());
    472
    473         // Solve example
    474         double[][] coefficientsData = {{2, 3, -2}, {-1, 7, 6}, {4, -3, -5}};
    475         RealMatrix coefficients = new RealMatrixImpl(coefficientsData);
    476         double[] constants = {1, -2, 1};
    477         double[] solution = coefficients.solve(constants);
    478         assertEquals(2 * solution[0] + 3 * solution[1] -2 * solution[2], constants[0], 1E-12);
    479         assertEquals(-1 * solution[0] + 7 * solution[1] + 6 * solution[2], constants[1], 1E-12);
    480         assertEquals(4 * solution[0] - 3 * solution[1] -5 * solution[2], constants[2], 1E-12);
    481
    482     }
    483
    484     // test submatrix accessors
    485     public void testSubMatrix() {
    486         RealMatrix m = new RealMatrixImpl(subTestData);
    487         RealMatrix mRows23Cols00 = new RealMatrixImpl(subRows23Cols00);
    488         RealMatrix mRows00Cols33 = new RealMatrixImpl(subRows00Cols33);
    489         RealMatrix mRows01Cols23 = new RealMatrixImpl(subRows01Cols23);
    490         RealMatrix mRows02Cols13 = new RealMatrixImpl(subRows02Cols13);
    491         RealMatrix mRows03Cols12 = new RealMatrixImpl(subRows03Cols12);
    492         RealMatrix mRows03Cols123 = new RealMatrixImpl(subRows03Cols123);
    493         RealMatrix mRows20Cols123 = new RealMatrixImpl(subRows20Cols123);
    494         RealMatrix mRows31Cols31 = new RealMatrixImpl(subRows31Cols31);
    495         assertEquals("Rows23Cols00", mRows23Cols00,
    496                 m.getSubMatrix(2 , 3 , 0, 0));
    497         assertEquals("Rows00Cols33", mRows00Cols33,
    498                 m.getSubMatrix(0 , 0 , 3, 3));
    499         assertEquals("Rows01Cols23", mRows01Cols23,
    500                 m.getSubMatrix(0 , 1 , 2, 3));
    501         assertEquals("Rows02Cols13", mRows02Cols13,
    502                 m.getSubMatrix(new int[] {0,2}, new int[] {1,3}));
    503         assertEquals("Rows03Cols12", mRows03Cols12,
    504                 m.getSubMatrix(new int[] {0,3}, new int[] {1,2}));
    505         assertEquals("Rows03Cols123", mRows03Cols123,
    506                 m.getSubMatrix(new int[] {0,3}, new int[] {1,2,3}));
    507         assertEquals("Rows20Cols123", mRows20Cols123,
    508                 m.getSubMatrix(new int[] {2,0}, new int[] {1,2,3}));
    509         assertEquals("Rows31Cols31", mRows31Cols31,
    510                 m.getSubMatrix(new int[] {3,1}, new int[] {3,1}));
    511         assertEquals("Rows31Cols31", mRows31Cols31,
    512                 m.getSubMatrix(new int[] {3,1}, new int[] {3,1}));
    513
    514         try {
    515             m.getSubMatrix(1,0,2,4);
    516             fail("Expecting MatrixIndexException");
    517         } catch (MatrixIndexException ex) {
    518             // expected
    519         }
    520         try {
    521             m.getSubMatrix(-1,1,2,2);
    522             fail("Expecting MatrixIndexException");
    523         } catch (MatrixIndexException ex) {
    524             // expected
    525         }
    526         try {
    527             m.getSubMatrix(1,0,2,2);
    528             fail("Expecting MatrixIndexException");
    529         } catch (MatrixIndexException ex) {
    530             // expected
    531         }
    532         try {
    533             m.getSubMatrix(1,0,2,4);
    534             fail("Expecting MatrixIndexException");
    535         } catch (MatrixIndexException ex) {
    536             // expected
    537         }
    538         try {
    539             m.getSubMatrix(new int[] {}, new int[] {0});
    540             fail("Expecting MatrixIndexException");
    541         } catch (MatrixIndexException ex) {
    542             // expected
    543         }
    544         try {
    545             m.getSubMatrix(new int[] {0}, new int[] {4});
    546             fail("Expecting MatrixIndexException");
    547         } catch (MatrixIndexException ex) {
    548             // expected
    549         }
    550     }
    551
    552     public void testGetRowMatrix() {
    553         RealMatrix m = new RealMatrixImpl(subTestData);
    554         RealMatrix mRow0 = new RealMatrixImpl(subRow0);
    555         RealMatrix mRow3 = new RealMatrixImpl(subRow3);
    556         assertEquals("Row0", mRow0,
    557                 m.getRowMatrix(0));
    558         assertEquals("Row3", mRow3,
    559                 m.getRowMatrix(3));
    560         try {
    561             m.getRowMatrix(-1);
    562             fail("Expecting MatrixIndexException");
    563         } catch (MatrixIndexException ex) {
    564             // expected
    565         }
    566         try {
    567             m.getRowMatrix(4);
    568             fail("Expecting MatrixIndexException");
    569         } catch (MatrixIndexException ex) {
    570             // expected
    571         }
    572     }
    573
    574     public void testGetColumnMatrix() {
    575         RealMatrix m = new RealMatrixImpl(subTestData);
    576         RealMatrix mColumn1 = new RealMatrixImpl(subColumn1);
    577         RealMatrix mColumn3 = new RealMatrixImpl(subColumn3);
    578         assertEquals("Column1", mColumn1,
    579                 m.getColumnMatrix(1));
    580         assertEquals("Column3", mColumn3,
    581                 m.getColumnMatrix(3));
    582         try {
    583             m.getColumnMatrix(-1);
    584             fail("Expecting MatrixIndexException");
    585         } catch (MatrixIndexException ex) {
    586             // expected
    587         }
    588         try {
    589             m.getColumnMatrix(4);
    590             fail("Expecting MatrixIndexException");
    591         } catch (MatrixIndexException ex) {
    592             // expected
    593         }
    594     }
    595
    596     public void testEqualsAndHashCode() {
    597         RealMatrixImpl m = new RealMatrixImpl(testData);
    598         RealMatrixImpl m1 = (RealMatrixImpl) m.copy();
    599         RealMatrixImpl mt = (RealMatrixImpl) m.transpose();
    600         assertTrue(m.hashCode() != mt.hashCode());
    601         assertEquals(m.hashCode(), m1.hashCode());
    602         assertEquals(m, m);
    603         assertEquals(m, m1);
    604         assertFalse(m.equals(null));
    605         assertFalse(m.equals(mt));
    606         assertFalse(m.equals(new RealMatrixImpl(bigSingular)));
    607     }
    608
    609     public void testToString() {
    610         RealMatrixImpl m = new RealMatrixImpl(testData);
    611         assertEquals("RealMatrixImpl{{1.0,2.0,3.0},{2.0,5.0,3.0},{1.0,0.0,8.0}}",
    612                 m.toString());
    613         m = new RealMatrixImpl();
    614         assertEquals("RealMatrixImpl{}",
    615                 m.toString());
    616     }
    617
    618     public void testSetSubMatrix() throws Exception {
    619         RealMatrixImpl m = new RealMatrixImpl(testData);
    620         m.setSubMatrix(detData2,1,1);
    621         RealMatrix expected = MatrixUtils.createRealMatrix
    622             (new double[][] {{1.0,2.0,3.0},{2.0,1.0,3.0},{1.0,2.0,4.0}});
    623         assertEquals(expected, m);
    624
    625         m.setSubMatrix(detData2,0,0);
    626         expected = MatrixUtils.createRealMatrix
    627             (new double[][] {{1.0,3.0,3.0},{2.0,4.0,3.0},{1.0,2.0,4.0}});
    628         assertEquals(expected, m);
    629
    630         m.setSubMatrix(testDataPlus2,0,0);
    631         expected = MatrixUtils.createRealMatrix
    632             (new double[][] {{3.0,4.0,5.0},{4.0,7.0,5.0},{3.0,2.0,10.0}});
    633         assertEquals(expected, m);
    634
    635         // javadoc example
    636         RealMatrixImpl matrix = (RealMatrixImpl) MatrixUtils.createRealMatrix
    637             (new double[][] {{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 0, 1 , 2}});
    638         matrix.setSubMatrix(new double[][] {{3, 4}, {5, 6}}, 1, 1);
    639         expected = MatrixUtils.createRealMatrix
    640             (new double[][] {{1, 2, 3, 4}, {5, 3, 4, 8}, {9, 5 ,6, 2}});
    641         assertEquals(expected, matrix);
    642
    643         // dimension overflow
    644         try {
    645             m.setSubMatrix(testData,1,1);
    646             fail("expecting MatrixIndexException");
    647         } catch (MatrixIndexException e) {
    648             // expected
    649         }
    650         // dimension underflow
    651         try {
    652             m.setSubMatrix(testData,-1,1);
    653             fail("expecting MatrixIndexException");
    654         } catch (MatrixIndexException e) {
    655             // expected
    656         }
    657         try {
    658             m.setSubMatrix(testData,1,-1);
    659             fail("expecting MatrixIndexException");
    660         } catch (MatrixIndexException e) {
    661             // expected
    662         }
    663
    664         // null
    665         try {
    666             m.setSubMatrix(null,1,1);
    667             fail("expecting NullPointerException");
    668         } catch (NullPointerException e) {
    669             // expected
    670         }
    671         RealMatrixImpl m2 = new RealMatrixImpl();
    672         try {
    673             m2.setSubMatrix(testData,0,1);
    674             fail("expecting MatrixIndexException");
    675         } catch (MatrixIndexException e) {
    676             // expected
    677         }
    678         try {
    679             m2.setSubMatrix(testData,1,0);
    680             fail("expecting MatrixIndexException");
    681         } catch (MatrixIndexException e) {
    682             // expected
    683         }
    684
    685         // ragged
    686         try {
    687             m.setSubMatrix(new double[][] {{1}, {2, 3}}, 0, 0);
    688             fail("expecting IllegalArgumentException");
    689         } catch (IllegalArgumentException e) {
    690             // expected
    691         }
    692
    693         // empty
    694         try {
    695             m.setSubMatrix(new double[][] {{}}, 0, 0);
    696             fail("expecting IllegalArgumentException");
    697         } catch (IllegalArgumentException e) {
    698             // expected
    699         }
    700
    701     }
    702
    703     //--------------- -----------------Protected methods
    704
    705     /*** verifies that two matrices are close (1-norm) */
    706     protected void assertClose(String msg, RealMatrix m, RealMatrix n,
    707         double tolerance) {
    708         assertTrue(msg,m.subtract(n).getNorm() < tolerance);
    709     }
    710
    711     /*** verifies that two vectors are close (sup norm) */
    712     protected void assertClose(String msg, double[] m, double[] n,
    713         double tolerance) {
    714         if (m.length != n.length) {
    715             fail("vectors not same length");
    716         }
    717         for (int i = 0; i < m.length; i++) {
    718             assertEquals(msg + " " +  i + " elements differ",
    719                 m[i],n[i],tolerance);
    720         }
    721     }
    722
    723     /*** extracts the l  and u matrices from compact lu representation */
    724     protected void splitLU(RealMatrix lu, double[][] lowerData, double[][] upperData) throws InvalidMatrixException {
    725         if (!lu.isSquare() || lowerData.length != lowerData[0].length || upperData.length != upperData[0].length ||
    726                 lowerData.length != upperData.length
    727                 || lowerData.length != lu.getRowDimension()) {
    728             throw new InvalidMatrixException("incorrect dimensions");
    729         }
    730         int n = lu.getRowDimension();
    731         for (int i = 0; i < n; i++) {
    732             for (int j = 0; j < n; j++) {
    733                 if (j < i) {
    734                     lowerData[i][j] = lu.getEntry(i, j);
    735                     upperData[i][j] = 0d;
    736                 } else if (i == j) {
    737                     lowerData[i][j] = 1d;
    738                     upperData[i][j] = lu.getEntry(i, j);
    739                 } else {
    740                     lowerData[i][j] = 0d;
    741                     upperData[i][j] = lu.getEntry(i, j);
    742                 }
    743             }
    744         }
    745     }
    746
    747     /*** Returns the result of applying the given row permutation to the matrix */
    748     protected RealMatrix permuteRows(RealMatrix matrix, int[] permutation) {
    749         if (!matrix.isSquare() || matrix.getRowDimension() != permutation.length) {
    750             throw new IllegalArgumentException("dimension mismatch");
    751         }
    752         int n = matrix.getRowDimension();
    753         int m = matrix.getColumnDimension();
    754         double out[][] = new double[m][n];
    755         for (int i = 0; i < n; i++) {
    756             for (int j = 0; j < m; j++) {
    757                 out[i][j] = matrix.getEntry(permutation[i], j);
    758             }
    759         }
    760         return new RealMatrixImpl(out);
    761     }
    762
    763     /*** Extracts l and u matrices from lu and verifies that matrix = l times u modulo permutation */
    764     protected void verifyDecomposition(RealMatrix matrix, RealMatrix lu) throws Exception{
    765         int n = matrix.getRowDimension();
    766         double[][] lowerData = new double[n][n];
    767         double[][] upperData = new double[n][n];
    768         splitLU(lu, lowerData, upperData);
    769         RealMatrix lower =new RealMatrixImpl(lowerData);
    770         RealMatrix upper = new RealMatrixImpl(upperData);
    771         int[] permutation = ((RealMatrixImpl) matrix).getPermutation();
    772         RealMatrix permuted = permuteRows(matrix, permutation);
    773         assertClose("lu decomposition does not work", permuted, lower.multiply(upper), normTolerance);
    774     }
    775
    776
    777     /*** Useful for debugging */
    778     private void dumpMatrix(RealMatrix m) {
    779           for (int i = 0; i < m.getRowDimension(); i++) {
    780               String os = "";
    781               for (int j = 0; j < m.getColumnDimension(); j++) {
    782                   os += m.getEntry(i, j) + " ";
    783               }
    784               System.out.println(os);
    785           }
    786     }
    787
    788 }
    789