gt:         for (int i = 0; i < rows; ++i) {
context: /*
   * Licensed to the Apache Software Foundation (ASF) under one or more
   * contributor license agreements.  See the NOTICE file distributed with
   * this work for additional information regarding copyright ownership.
   * The ASF licenses this file to You under the Apache License, Version 2.0
   * (the "License"); you may not use this file except in compliance with
   * the License.  You may obtain a copy of the License at
   *
   *      http://www.apache.org/licenses/LICENSE-2.0
   *
   * Unless required by applicable law or agreed to in writing, software
   * distributed under the License is distributed on an "AS IS" BASIS,
   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   * See the License for the specific language governing permissions and
   * limitations under the License.
   */
  package org.apache.commons.math.linear;
  
  import java.util.Arrays;
  import java.util.Random;
  
  import junit.framework.Test;
  import junit.framework.TestCase;
  import junit.framework.TestSuite;
  
  import org.apache.commons.math.TestUtils;
  
  /**
   * Test cases for the {@link BlockRealMatrix} class.
   *
   * @version $Revision$ $Date$
   */
  
  public final class BlockRealMatrixTest extends TestCase {
  
      // 3 x 3 identity matrix
      protected double[][] id = { {1d,0d,0d}, {0d,1d,0d}, {0d,0d,1d} };
  
      // Test data for group operations
      protected double[][] testData = { {1d,2d,3d}, {2d,5d,3d}, {1d,0d,8d} };
      protected double[][] testDataLU = {{2d, 5d, 3d}, {.5d, -2.5d, 6.5d}, {0.5d, 0.2d, .2d}};
      protected double[][] testDataPlus2 = { {3d,4d,5d}, {4d,7d,5d}, {3d,2d,10d} };
      protected double[][] testDataMinus = { {-1d,-2d,-3d}, {-2d,-5d,-3d},
         {-1d,0d,-8d} };
      protected double[] testDataRow1 = {1d,2d,3d};
      protected double[] testDataCol3 = {3d,3d,8d};
      protected double[][] testDataInv =
          { {-40d,16d,9d}, {13d,-5d,-3d}, {5d,-2d,-1d} };
      protected double[] preMultTest = {8,12,33};
      protected double[][] testData2 ={ {1d,2d,3d}, {2d,5d,3d}};
      protected double[][] testData2T = { {1d,2d}, {2d,5d}, {3d,3d}};
      protected double[][] testDataPlusInv =
          { {-39d,18d,12d}, {15d,0d,0d}, {6d,-2d,7d} };
  
      // lu decomposition tests
      protected double[][] luData = { {2d,3d,3d}, {0d,5d,7d}, {6d,9d,8d} };
      protected double[][] luDataLUDecomposition = { {6d,9d,8d}, {0d,5d,7d},
              {0.33333333333333,0d,0.33333333333333} };
  
      // singular matrices
      protected double[][] singular = { {2d,3d}, {2d,3d} };
      protected double[][] bigSingular = {{1d,2d,3d,4d}, {2d,5d,3d,4d},
          {7d,3d,256d,1930d}, {3d,7d,6d,8d}}; // 4th row = 1st + 2nd
      protected double[][] detData = { {1d,2d,3d}, {4d,5d,6d}, {7d,8d,10d} };
      protected double[][] detData2 = { {1d, 3d}, {2d, 4d}};
  
      // vectors
      protected double[] testVector = {1,2,3};
      protected double[] testVector2 = {1,2,3,4};
  
      // submatrix accessor tests
      protected double[][] subTestData = {{1, 2, 3, 4}, {1.5, 2.5, 3.5, 4.5},
              {2, 4, 6, 8}, {4, 5, 6, 7}};
      // array selections
      protected double[][] subRows02Cols13 = { {2, 4}, {4, 8}};
      protected double[][] subRows03Cols12 = { {2, 3}, {5, 6}};
      protected double[][] subRows03Cols123 = { {2, 3, 4} , {5, 6, 7}};
      // effective permutations
      protected double[][] subRows20Cols123 = { {4, 6, 8} , {2, 3, 4}};
      protected double[][] subRows31Cols31 = {{7, 5}, {4.5, 2.5}};
      // contiguous ranges
      protected double[][] subRows01Cols23 = {{3,4} , {3.5, 4.5}};
      protected double[][] subRows23Cols00 = {{2} , {4}};
      protected double[][] subRows00Cols33 = {{4}};
      // row matrices
      protected double[][] subRow0 = {{1,2,3,4}};
      protected double[][] subRow3 = {{4,5,6,7}};
      // column matrices
      protected double[][] subColumn1 = {{2}, {2.5}, {4}, {5}};
      protected double[][] subColumn3 = {{4}, {4.5}, {8}, {7}};
  
      // tolerances
      protected double entryTolerance = 10E-16;
      protected double normTolerance = 10E-14;
  
      public BlockRealMatrixTest(String name) {
          super(name);
      }
  
      public static Test suite() {
          TestSuite suite = new TestSuite(BlockRealMatrixTest.class);
          suite.setName("BlockRealMatrix Tests");
          return suite;
      }
  
      /** test dimensions */
      public void testDimensions() {
          BlockRealMatrix m = new BlockRealMatrix(testData);
          BlockRealMatrix m2 = new BlockRealMatrix(testData2);
          assertEquals("testData row dimension",3,m.getRowDimension());
          assertEquals("testData column dimension",3,m.getColumnDimension());
          assertTrue("testData is square",m.isSquare());
          assertEquals("testData2 row dimension",m2.getRowDimension(),2);
          assertEquals("testData2 column dimension",m2.getColumnDimension(),3);
          assertTrue("testData2 is not square",!m2.isSquare());
      }
  
      /** test copy functions */
      public void testCopyFunctions() {
          Random r = new Random(66636328996002l);
          BlockRealMatrix m1 = createRandomMatrix(r, 47, 83);
          BlockRealMatrix m2 = new BlockRealMatrix(m1.getData());
          assertEquals(m1, m2);
          BlockRealMatrix m3 = new BlockRealMatrix(testData);
          BlockRealMatrix m4 = new BlockRealMatrix(m3.getData());
          assertEquals(m3, m4);
      }
  
      /** test add */
      public void testAdd() {
          BlockRealMatrix m = new BlockRealMatrix(testData);
          BlockRealMatrix mInv = new BlockRealMatrix(testDataInv);
          RealMatrix mPlusMInv = m.add(mInv);
          double[][] sumEntries = mPlusMInv.getData();
          for (int row = 0; row < m.getRowDimension(); row++) {
              for (int col = 0; col < m.getColumnDimension(); col++) {
                  assertEquals("sum entry entry",
                      testDataPlusInv[row][col],sumEntries[row][col],
                          entryTolerance);
              }
          }
      }
  
      /** test add failure */
      public void testAddFail() {
          BlockRealMatrix m = new BlockRealMatrix(testData);
          BlockRealMatrix m2 = new BlockRealMatrix(testData2);
          try {
              m.add(m2);
              fail("IllegalArgumentException expected");
          } catch (IllegalArgumentException ex) {
              // ignored
          }
      }
  
      /** test norm */
      public void testNorm() {
          BlockRealMatrix m = new BlockRealMatrix(testData);
          BlockRealMatrix m2 = new BlockRealMatrix(testData2);
          assertEquals("testData norm",14d,m.getNorm(),entryTolerance);
          assertEquals("testData2 norm",7d,m2.getNorm(),entryTolerance);
      }
  
      /** test Frobenius norm */
      public void testFrobeniusNorm() {
          BlockRealMatrix m = new BlockRealMatrix(testData);
          BlockRealMatrix m2 = new BlockRealMatrix(testData2);
          assertEquals("testData Frobenius norm", Math.sqrt(117.0), m.getFrobeniusNorm(), entryTolerance);
          assertEquals("testData2 Frobenius norm", Math.sqrt(52.0), m2.getFrobeniusNorm(), entryTolerance);
      }
  
       /** test m-n = m + -n */
      public void testPlusMinus() {
          BlockRealMatrix m = new BlockRealMatrix(testData);
          BlockRealMatrix m2 = new BlockRealMatrix(testDataInv);
          assertClose(m.subtract(m2), m2.scalarMultiply(-1d).add(m), entryTolerance);
          try {
              m.subtract(new BlockRealMatrix(testData2));
              fail("Expecting illegalArgumentException");
          } catch (IllegalArgumentException ex) {
              // ignored
          }
      }
  
      /** test multiply */
       public void testMultiply() {
          BlockRealMatrix m = new BlockRealMatrix(testData);
          BlockRealMatrix mInv = new BlockRealMatrix(testDataInv);
          BlockRealMatrix identity = new BlockRealMatrix(id);
          BlockRealMatrix m2 = new BlockRealMatrix(testData2);
          assertClose(m.multiply(mInv), identity, entryTolerance);
          assertClose(mInv.multiply(m), identity, entryTolerance);
          assertClose(m.multiply(identity), m, entryTolerance);
          assertClose(identity.multiply(mInv), mInv, entryTolerance);
          assertClose(m2.multiply(identity), m2, entryTolerance);
          try {
              m.multiply(new BlockRealMatrix(bigSingular));
              fail("Expecting illegalArgumentException");
          } catch (IllegalArgumentException ex) {
              // expected
          }
      }
  
      public void testSeveralBlocks() {
  
          RealMatrix m = new BlockRealMatrix(35, 71);
          for (int i = 0; i < m.getRowDimension(); ++i) {
              for (int j = 0; j < m.getColumnDimension(); ++j) {
                  m.setEntry(i, j, i + j / 1024.0);
              }
          }
  
          RealMatrix mT = m.transpose();
          assertEquals(m.getRowDimension(), mT.getColumnDimension());
          assertEquals(m.getColumnDimension(), mT.getRowDimension());
          for (int i = 0; i < mT.getRowDimension(); ++i) {
              for (int j = 0; j < mT.getColumnDimension(); ++j) {
                  assertEquals(m.getEntry(j, i), mT.getEntry(i, j), 0);
              }
          }
  
          RealMatrix mPm = m.add(m);
          for (int i = 0; i < mPm.getRowDimension(); ++i) {
              for (int j = 0; j < mPm.getColumnDimension(); ++j) {
                  assertEquals(2 * m.getEntry(i, j), mPm.getEntry(i, j), 0);
              }
          }
  
          RealMatrix mPmMm = mPm.subtract(m);
          for (int i = 0; i < mPmMm.getRowDimension(); ++i) {
              for (int j = 0; j < mPmMm.getColumnDimension(); ++j) {
                  assertEquals(m.getEntry(i, j), mPmMm.getEntry(i, j), 0);
              }
          }
  
          RealMatrix mTm = mT.multiply(m);
          for (int i = 0; i < mTm.getRowDimension(); ++i) {
              for (int j = 0; j < mTm.getColumnDimension(); ++j) {
                  double sum = 0;
                  for (int k = 0; k < mT.getColumnDimension(); ++k) {
                      sum += (k + i / 1024.0) * (k + j / 1024.0);
                  }
                  assertEquals(sum, mTm.getEntry(i, j), 0);
              }
          }
  
          RealMatrix mmT = m.multiply(mT);
          for (int i = 0; i < mmT.getRowDimension(); ++i) {
              for (int j = 0; j < mmT.getColumnDimension(); ++j) {
                  double sum = 0;
                  for (int k = 0; k < m.getColumnDimension(); ++k) {
                      sum += (i + k / 1024.0) * (j + k / 1024.0);
                  }
                  assertEquals(sum, mmT.getEntry(i, j), 0);
              }
          }
  
          RealMatrix sub1 = m.getSubMatrix(2, 9, 5, 20);
          for (int i = 0; i < sub1.getRowDimension(); ++i) {
              for (int j = 0; j < sub1.getColumnDimension(); ++j) {
                  assertEquals((i + 2) + (j + 5) / 1024.0, sub1.getEntry(i, j), 0);
              }
          }
  
          RealMatrix sub2 = m.getSubMatrix(10, 12, 3, 70);
          for (int i = 0; i < sub2.getRowDimension(); ++i) {
              for (int j = 0; j < sub2.getColumnDimension(); ++j) {
                  assertEquals((i + 10) + (j + 3) / 1024.0, sub2.getEntry(i, j), 0);
              }
          }
  
          RealMatrix sub3 = m.getSubMatrix(30, 34, 0, 5);
          for (int i = 0; i < sub3.getRowDimension(); ++i) {
              for (int j = 0; j < sub3.getColumnDimension(); ++j) {
                  assertEquals((i + 30) + (j + 0) / 1024.0, sub3.getEntry(i, j), 0);
              }
          }
  
          RealMatrix sub4 = m.getSubMatrix(30, 32, 62, 65);
          for (int i = 0; i < sub4.getRowDimension(); ++i) {
              for (int j = 0; j < sub4.getColumnDimension(); ++j) {
                  assertEquals((i + 30) + (j + 62) / 1024.0, sub4.getEntry(i, j), 0);
              }
          }
  
      }
  
      //Additional Test for BlockRealMatrixTest.testMultiply
  
      private double[][] d3 = new double[][] {{1,2,3,4},{5,6,7,8}};
      private double[][] d4 = new double[][] {{1},{2},{3},{4}};
      private double[][] d5 = new double[][] {{30},{70}};
  
      public void testMultiply2() {
         RealMatrix m3 = new BlockRealMatrix(d3);
         RealMatrix m4 = new BlockRealMatrix(d4);
         RealMatrix m5 = new BlockRealMatrix(d5);
         assertClose(m3.multiply(m4), m5, entryTolerance);
     }
  
      /** test trace */
      public void testTrace() {
          RealMatrix m = new BlockRealMatrix(id);
          assertEquals("identity trace",3d,m.getTrace(),entryTolerance);
          m = new BlockRealMatrix(testData2);
          try {
              m.getTrace();
              fail("Expecting NonSquareMatrixException");
          } catch (NonSquareMatrixException ex) {
              // ignored
          }
      }
  
      /** test scalarAdd */
      public void testScalarAdd() {
          RealMatrix m = new BlockRealMatrix(testData);
          assertClose(new BlockRealMatrix(testDataPlus2), m.scalarAdd(2d), entryTolerance);
      }
  
      /** test operate */
      public void testOperate() {
          RealMatrix m = new BlockRealMatrix(id);
          assertClose(testVector, m.operate(testVector), entryTolerance);
          assertClose(testVector, m.operate(new ArrayRealVector(testVector)).getData(), entryTolerance);
          m = new BlockRealMatrix(bigSingular);
          try {
              m.operate(testVector);
              fail("Expecting illegalArgumentException");
          } catch (IllegalArgumentException ex) {
              // ignored
          }
      }
  
      public void testOperateLarge() {
          int p = (7 * BlockRealMatrix.BLOCK_SIZE) / 2;
          int q = (5 * BlockRealMatrix.BLOCK_SIZE) / 2;
          int r =  3 * BlockRealMatrix.BLOCK_SIZE;
          Random random = new Random(111007463902334l);
          RealMatrix m1 = createRandomMatrix(random, p, q);
          RealMatrix m2 = createRandomMatrix(random, q, r);
          RealMatrix m1m2 = m1.multiply(m2);
          for (int i = 0; i < r; ++i) {
              checkArrays(m1m2.getColumn(i), m1.operate(m2.getColumn(i)));
          }
      }
  
      public void testOperatePremultiplyLarge() {
          int p = (7 * BlockRealMatrix.BLOCK_SIZE) / 2;
          int q = (5 * BlockRealMatrix.BLOCK_SIZE) / 2;
          int r =  3 * BlockRealMatrix.BLOCK_SIZE;
          Random random = new Random(111007463902334l);
          RealMatrix m1 = createRandomMatrix(random, p, q);
          RealMatrix m2 = createRandomMatrix(random, q, r);
          RealMatrix m1m2 = m1.multiply(m2);
          for (int i = 0; i < p; ++i) {
              checkArrays(m1m2.getRow(i), m2.preMultiply(m1.getRow(i)));
          }
      }
  
      /** test issue MATH-209 */
      public void testMath209() {
          RealMatrix a = new BlockRealMatrix(new double[][] {
                  { 1, 2 }, { 3, 4 }, { 5, 6 }
          });
          double[] b = a.operate(new double[] { 1, 1 });
          assertEquals(a.getRowDimension(), b.length);
          assertEquals( 3.0, b[0], 1.0e-12);
          assertEquals( 7.0, b[1], 1.0e-12);
          assertEquals(11.0, b[2], 1.0e-12);
      }
  
      /** test transpose */
      public void testTranspose() {
          RealMatrix m = new BlockRealMatrix(testData);
          RealMatrix mIT = new LUDecompositionImpl(m).getSolver().getInverse().transpose();
          RealMatrix mTI = new LUDecompositionImpl(m.transpose()).getSolver().getInverse();
          assertClose(mIT, mTI, normTolerance);
          m = new BlockRealMatrix(testData2);
          RealMatrix mt = new BlockRealMatrix(testData2T);
          assertClose(mt, m.transpose(), normTolerance);
      }
  
      /** test preMultiply by vector */
      public void testPremultiplyVector() {
          RealMatrix m = new BlockRealMatrix(testData);
          assertClose(m.preMultiply(testVector), preMultTest, normTolerance);
          assertClose(m.preMultiply(new ArrayRealVector(testVector).getData()),
                      preMultTest, normTolerance);
          m = new BlockRealMatrix(bigSingular);
          try {
              m.preMultiply(testVector);
              fail("expecting IllegalArgumentException");
          } catch (IllegalArgumentException ex) {
              // ignored
          }
      }
  
      public void testPremultiply() {
          RealMatrix m3 = new BlockRealMatrix(d3);
          RealMatrix m4 = new BlockRealMatrix(d4);
          RealMatrix m5 = new BlockRealMatrix(d5);
          assertClose(m4.preMultiply(m3), m5, entryTolerance);
  
          BlockRealMatrix m = new BlockRealMatrix(testData);
          BlockRealMatrix mInv = new BlockRealMatrix(testDataInv);
          BlockRealMatrix identity = new BlockRealMatrix(id);
          assertClose(m.preMultiply(mInv), identity, entryTolerance);
          assertClose(mInv.preMultiply(m), identity, entryTolerance);
          assertClose(m.preMultiply(identity), m, entryTolerance);
          assertClose(identity.preMultiply(mInv), mInv, entryTolerance);
          try {
              m.preMultiply(new BlockRealMatrix(bigSingular));
              fail("Expecting illegalArgumentException");
          } catch (IllegalArgumentException ex) {
              // ignored
          }
      }
  
      public void testGetVectors() {
          RealMatrix m = new BlockRealMatrix(testData);
          assertClose(m.getRow(0), testDataRow1, entryTolerance);
          assertClose(m.getColumn(2), testDataCol3, entryTolerance);
          try {
              m.getRow(10);
              fail("expecting MatrixIndexException");
          } catch (MatrixIndexException ex) {
              // ignored
          }
          try {
              m.getColumn(-1);
              fail("expecting MatrixIndexException");
          } catch (MatrixIndexException ex) {
              // ignored
          }
      }
  
      public void testGetEntry() {
          RealMatrix m = new BlockRealMatrix(testData);
          assertEquals("get entry",m.getEntry(0,1),2d,entryTolerance);
          try {
              m.getEntry(10, 4);
              fail ("Expecting MatrixIndexException");
          } catch (MatrixIndexException ex) {
              // expected
          }
      }
  
      /** test examples in user guide */
      public void testExamples() {
          // Create a real matrix with two rows and three columns
          double[][] matrixData = { {1d,2d,3d}, {2d,5d,3d}};
          RealMatrix m = new BlockRealMatrix(matrixData);
          // One more with three rows, two columns
          double[][] matrixData2 = { {1d,2d}, {2d,5d}, {1d, 7d}};
          RealMatrix n = new BlockRealMatrix(matrixData2);
          // Now multiply m by n
          RealMatrix p = m.multiply(n);
          assertEquals(2, p.getRowDimension());
          assertEquals(2, p.getColumnDimension());
          // Invert p
          RealMatrix pInverse = new LUDecompositionImpl(p).getSolver().getInverse();
          assertEquals(2, pInverse.getRowDimension());
          assertEquals(2, pInverse.getColumnDimension());
  
          // Solve example
          double[][] coefficientsData = {{2, 3, -2}, {-1, 7, 6}, {4, -3, -5}};
          RealMatrix coefficients = new BlockRealMatrix(coefficientsData);
          double[] constants = {1, -2, 1};
          double[] solution = new LUDecompositionImpl(coefficients).getSolver().solve(constants);
          assertEquals(2 * solution[0] + 3 * solution[1] -2 * solution[2], constants[0], 1E-12);
          assertEquals(-1 * solution[0] + 7 * solution[1] + 6 * solution[2], constants[1], 1E-12);
          assertEquals(4 * solution[0] - 3 * solution[1] -5 * solution[2], constants[2], 1E-12);
  
      }
  
      // test submatrix accessors
      public void testGetSubMatrix() {
          RealMatrix m = new BlockRealMatrix(subTestData);
          checkGetSubMatrix(m, subRows23Cols00,  2 , 3 , 0, 0);
          checkGetSubMatrix(m, subRows00Cols33,  0 , 0 , 3, 3);
          checkGetSubMatrix(m, subRows01Cols23,  0 , 1 , 2, 3);
          checkGetSubMatrix(m, subRows02Cols13,  new int[] { 0, 2 }, new int[] { 1, 3 });
          checkGetSubMatrix(m, subRows03Cols12,  new int[] { 0, 3 }, new int[] { 1, 2 });
          checkGetSubMatrix(m, subRows03Cols123, new int[] { 0, 3 }, new int[] { 1, 2, 3 });
          checkGetSubMatrix(m, subRows20Cols123, new int[] { 2, 0 }, new int[] { 1, 2, 3 });
          checkGetSubMatrix(m, subRows31Cols31,  new int[] { 3, 1 }, new int[] { 3, 1 });
          checkGetSubMatrix(m, subRows31Cols31,  new int[] { 3, 1 }, new int[] { 3, 1 });
          checkGetSubMatrix(m, null,  1, 0, 2, 4);
          checkGetSubMatrix(m, null, -1, 1, 2, 2);
          checkGetSubMatrix(m, null,  1, 0, 2, 2);
          checkGetSubMatrix(m, null,  1, 0, 2, 4);
          checkGetSubMatrix(m, null, new int[] {},    new int[] { 0 });
          checkGetSubMatrix(m, null, new int[] { 0 }, new int[] { 4 });
      }
  
      private void checkGetSubMatrix(RealMatrix m, double[][] reference,
                                     int startRow, int endRow, int startColumn, int endColumn) {
          try {
              RealMatrix sub = m.getSubMatrix(startRow, endRow, startColumn, endColumn);
              if (reference != null) {
                  assertEquals(new BlockRealMatrix(reference), sub);
              } else {
                  fail("Expecting MatrixIndexException");
              }
          } catch (MatrixIndexException e) {
              if (reference != null) {
                  throw e;
              }
          }
      }
  
      private void checkGetSubMatrix(RealMatrix m, double[][] reference,
                                     int[] selectedRows, int[] selectedColumns) {
          try {
              RealMatrix sub = m.getSubMatrix(selectedRows, selectedColumns);
              if (reference != null) {
                  assertEquals(new BlockRealMatrix(reference), sub);
              } else {
                  fail("Expecting MatrixIndexException");
              }
          } catch (MatrixIndexException e) {
              if (reference != null) {
                  throw e;
              }
          }
      }
  
      public void testGetSetMatrixLarge() {
          int n = 3 * BlockRealMatrix.BLOCK_SIZE;
          RealMatrix m = new BlockRealMatrix(n, n);
          RealMatrix sub = new BlockRealMatrix(n - 4, n - 4).scalarAdd(1);
  
          m.setSubMatrix(sub.getData(), 2, 2);
          for (int i = 0; i < n; ++i) {
              for (int j = 0; j < n; ++j) {
                  if ((i < 2) || (i > n - 3) || (j < 2) || (j > n - 3)) {
                      assertEquals(0.0, m.getEntry(i, j), 0.0);
                  } else {
                      assertEquals(1.0, m.getEntry(i, j), 0.0);
                  }
              }
          }
          assertEquals(sub, m.getSubMatrix(2, n - 3, 2, n - 3));
  
      }
  
      public void testCopySubMatrix() {
          RealMatrix m = new BlockRealMatrix(subTestData);
          checkCopy(m, subRows23Cols00,  2 , 3 , 0, 0);
          checkCopy(m, subRows00Cols33,  0 , 0 , 3, 3);
          checkCopy(m, subRows01Cols23,  0 , 1 , 2, 3);
          checkCopy(m, subRows02Cols13,  new int[] { 0, 2 }, new int[] { 1, 3 });
          checkCopy(m, subRows03Cols12,  new int[] { 0, 3 }, new int[] { 1, 2 });
          checkCopy(m, subRows03Cols123, new int[] { 0, 3 }, new int[] { 1, 2, 3 });
          checkCopy(m, subRows20Cols123, new int[] { 2, 0 }, new int[] { 1, 2, 3 });
          checkCopy(m, subRows31Cols31,  new int[] { 3, 1 }, new int[] { 3, 1 });
          checkCopy(m, subRows31Cols31,  new int[] { 3, 1 }, new int[] { 3, 1 });
  
          checkCopy(m, null,  1, 0, 2, 4);
          checkCopy(m, null, -1, 1, 2, 2);
          checkCopy(m, null,  1, 0, 2, 2);
          checkCopy(m, null,  1, 0, 2, 4);
          checkCopy(m, null, new int[] {},    new int[] { 0 });
          checkCopy(m, null, new int[] { 0 }, new int[] { 4 });
      }
  
      private void checkCopy(RealMatrix m, double[][] reference,
                             int startRow, int endRow, int startColumn, int endColumn) {
          try {
              double[][] sub = (reference == null) ?
                               new double[1][1] :
                               new double[reference.length][reference[0].length];
              m.copySubMatrix(startRow, endRow, startColumn, endColumn, sub);
              if (reference != null) {
                  assertEquals(new BlockRealMatrix(reference), new BlockRealMatrix(sub));
              } else {
                  fail("Expecting MatrixIndexException");
              }
          } catch (MatrixIndexException e) {
              if (reference != null) {
                  throw e;
              }
          }
      }
  
      private void checkCopy(RealMatrix m, double[][] reference,
                             int[] selectedRows, int[] selectedColumns) {
          try {
              double[][] sub = (reference == null) ?
                      new double[1][1] :
                      new double[reference.length][reference[0].length];
              m.copySubMatrix(selectedRows, selectedColumns, sub);
              if (reference != null) {
                  assertEquals(new BlockRealMatrix(reference), new BlockRealMatrix(sub));
              } else {
                  fail("Expecting MatrixIndexException");
              }
          } catch (MatrixIndexException e) {
              if (reference != null) {
                  throw e;
              }
          }
      }
  
      public void testGetRowMatrix() {
          RealMatrix m     = new BlockRealMatrix(subTestData);
          RealMatrix mRow0 = new BlockRealMatrix(subRow0);
          RealMatrix mRow3 = new BlockRealMatrix(subRow3);
          assertEquals("Row0", mRow0, m.getRowMatrix(0));
          assertEquals("Row3", mRow3, m.getRowMatrix(3));
          try {
              m.getRowMatrix(-1);
              fail("Expecting MatrixIndexException");
          } catch (MatrixIndexException ex) {
              // expected
          }
          try {
              m.getRowMatrix(4);
              fail("Expecting MatrixIndexException");
          } catch (MatrixIndexException ex) {
              // expected
          }
      }
  
      public void testSetRowMatrix() {
          RealMatrix m = new BlockRealMatrix(subTestData);
          RealMatrix mRow3 = new BlockRealMatrix(subRow3);
          assertNotSame(mRow3, m.getRowMatrix(0));
          m.setRowMatrix(0, mRow3);
          assertEquals(mRow3, m.getRowMatrix(0));
          try {
              m.setRowMatrix(-1, mRow3);
              fail("Expecting MatrixIndexException");
          } catch (MatrixIndexException ex) {
              // expected
          }
          try {
              m.setRowMatrix(0, m);
              fail("Expecting InvalidMatrixException");
          } catch (InvalidMatrixException ex) {
              // expected
          }
      }
  
      public void testGetSetRowMatrixLarge() {
          int n = 3 * BlockRealMatrix.BLOCK_SIZE;
          RealMatrix m = new BlockRealMatrix(n, n);
          RealMatrix sub = new BlockRealMatrix(1, n).scalarAdd(1);
  
          m.setRowMatrix(2, sub);
          for (int i = 0; i < n; ++i) {
              for (int j = 0; j < n; ++j) {
                  if (i != 2) {
                      assertEquals(0.0, m.getEntry(i, j), 0.0);
                  } else {
                      assertEquals(1.0, m.getEntry(i, j), 0.0);
                  }
              }
          }
          assertEquals(sub, m.getRowMatrix(2));
  
      }
  
      public void testGetColumnMatrix() {
          RealMatrix m = new BlockRealMatrix(subTestData);
          RealMatrix mColumn1 = new BlockRealMatrix(subColumn1);
          RealMatrix mColumn3 = new BlockRealMatrix(subColumn3);
          assertEquals(mColumn1, m.getColumnMatrix(1));
          assertEquals(mColumn3, m.getColumnMatrix(3));
          try {
              m.getColumnMatrix(-1);
              fail("Expecting MatrixIndexException");
          } catch (MatrixIndexException ex) {
              // expected
          }
          try {
              m.getColumnMatrix(4);
              fail("Expecting MatrixIndexException");
          } catch (MatrixIndexException ex) {
              // expected
          }
      }
  
      public void testSetColumnMatrix() {
          RealMatrix m = new BlockRealMatrix(subTestData);
          RealMatrix mColumn3 = new BlockRealMatrix(subColumn3);
          assertNotSame(mColumn3, m.getColumnMatrix(1));
          m.setColumnMatrix(1, mColumn3);
          assertEquals(mColumn3, m.getColumnMatrix(1));
          try {
              m.setColumnMatrix(-1, mColumn3);
              fail("Expecting MatrixIndexException");
          } catch (MatrixIndexException ex) {
              // expected
          }
          try {
              m.setColumnMatrix(0, m);
              fail("Expecting InvalidMatrixException");
          } catch (InvalidMatrixException ex) {
              // expected
          }
      }
  
      public void testGetSetColumnMatrixLarge() {
          int n = 3 * BlockRealMatrix.BLOCK_SIZE;
          RealMatrix m = new BlockRealMatrix(n, n);
          RealMatrix sub = new BlockRealMatrix(n, 1).scalarAdd(1);
  
          m.setColumnMatrix(2, sub);
          for (int i = 0; i < n; ++i) {
              for (int j = 0; j < n; ++j) {
                  if (j != 2) {
                      assertEquals(0.0, m.getEntry(i, j), 0.0);
                  } else {
                      assertEquals(1.0, m.getEntry(i, j), 0.0);
                  }
              }
          }
          assertEquals(sub, m.getColumnMatrix(2));
  
      }
  
      public void testGetRowVector() {
          RealMatrix m = new BlockRealMatrix(subTestData);
          RealVector mRow0 = new ArrayRealVector(subRow0[0]);
          RealVector mRow3 = new ArrayRealVector(subRow3[0]);
          assertEquals(mRow0, m.getRowVector(0));
          assertEquals(mRow3, m.getRowVector(3));
          try {
              m.getRowVector(-1);
              fail("Expecting MatrixIndexException");
          } catch (MatrixIndexException ex) {
              // expected
          }
          try {
              m.getRowVector(4);
              fail("Expecting MatrixIndexException");
          } catch (MatrixIndexException ex) {
              // expected
          }
      }
  
      public void testSetRowVector() {
          RealMatrix m = new BlockRealMatrix(subTestData);
          RealVector mRow3 = new ArrayRealVector(subRow3[0]);
          assertNotSame(mRow3, m.getRowMatrix(0));
          m.setRowVector(0, mRow3);
          assertEquals(mRow3, m.getRowVector(0));
          try {
              m.setRowVector(-1, mRow3);
              fail("Expecting MatrixIndexException");
          } catch (MatrixIndexException ex) {
              // expected
          }
          try {
              m.setRowVector(0, new ArrayRealVector(5));
              fail("Expecting InvalidMatrixException");
          } catch (InvalidMatrixException ex) {
              // expected
          }
      }
  
      public void testGetSetRowVectorLarge() {
          int n = 3 * BlockRealMatrix.BLOCK_SIZE;
          RealMatrix m = new BlockRealMatrix(n, n);
          RealVector sub = new ArrayRealVector(n, 1.0);
  
          m.setRowVector(2, sub);
          for (int i = 0; i < n; ++i) {
              for (int j = 0; j < n; ++j) {
                  if (i != 2) {
                      assertEquals(0.0, m.getEntry(i, j), 0.0);
                  } else {
                      assertEquals(1.0, m.getEntry(i, j), 0.0);
                  }
              }
          }
          assertEquals(sub, m.getRowVector(2));
  
      }
  
      public void testGetColumnVector() {
          RealMatrix m = new BlockRealMatrix(subTestData);
          RealVector mColumn1 = columnToVector(subColumn1);
          RealVector mColumn3 = columnToVector(subColumn3);
          assertEquals(mColumn1, m.getColumnVector(1));
          assertEquals(mColumn3, m.getColumnVector(3));
          try {
              m.getColumnVector(-1);
              fail("Expecting MatrixIndexException");
          } catch (MatrixIndexException ex) {
              // expected
          }
          try {
              m.getColumnVector(4);
              fail("Expecting MatrixIndexException");
          } catch (MatrixIndexException ex) {
              // expected
          }
      }
  
      public void testSetColumnVector() {
          RealMatrix m = new BlockRealMatrix(subTestData);
          RealVector mColumn3 = columnToVector(subColumn3);
          assertNotSame(mColumn3, m.getColumnVector(1));
          m.setColumnVector(1, mColumn3);
          assertEquals(mColumn3, m.getColumnVector(1));
          try {
              m.setColumnVector(-1, mColumn3);
              fail("Expecting MatrixIndexException");
          } catch (MatrixIndexException ex) {
              // expected
          }
          try {
              m.setColumnVector(0, new ArrayRealVector(5));
              fail("Expecting InvalidMatrixException");
          } catch (InvalidMatrixException ex) {
              // expected
          }
      }
  
      public void testGetSetColumnVectorLarge() {
          int n = 3 * BlockRealMatrix.BLOCK_SIZE;
          RealMatrix m = new BlockRealMatrix(n, n);
          RealVector sub = new ArrayRealVector(n, 1.0);
  
          m.setColumnVector(2, sub);
          for (int i = 0; i < n; ++i) {
              for (int j = 0; j < n; ++j) {
                  if (j != 2) {
                      assertEquals(0.0, m.getEntry(i, j), 0.0);
                  } else {
                      assertEquals(1.0, m.getEntry(i, j), 0.0);
                  }
              }
          }
          assertEquals(sub, m.getColumnVector(2));
  
      }
  
      private RealVector columnToVector(double[][] column) {
          double[] data = new double[column.length];
          for (int i = 0; i < data.length; ++i) {
              data[i] = column[i][0];
          }
          return new ArrayRealVector(data, false);
      }
  
      public void testGetRow() {
          RealMatrix m = new BlockRealMatrix(subTestData);
          checkArrays(subRow0[0], m.getRow(0));
          checkArrays(subRow3[0], m.getRow(3));
          try {
              m.getRow(-1);
              fail("Expecting MatrixIndexException");
          } catch (MatrixIndexException ex) {
              // expected
          }
          try {
              m.getRow(4);
              fail("Expecting MatrixIndexException");
          } catch (MatrixIndexException ex) {
              // expected
          }
      }
  
      public void testSetRow() {
          RealMatrix m = new BlockRealMatrix(subTestData);
          assertTrue(subRow3[0][0] != m.getRow(0)[0]);
          m.setRow(0, subRow3[0]);
          checkArrays(subRow3[0], m.getRow(0));
          try {
              m.setRow(-1, subRow3[0]);
              fail("Expecting MatrixIndexException");
          } catch (MatrixIndexException ex) {
              // expected
          }
          try {
              m.setRow(0, new double[5]);
              fail("Expecting InvalidMatrixException");
          } catch (InvalidMatrixException ex) {
              // expected
          }
      }
  
      public void testGetSetRowLarge() {
          int n = 3 * BlockRealMatrix.BLOCK_SIZE;
          RealMatrix m = new BlockRealMatrix(n, n);
          double[] sub = new double[n];
          Arrays.fill(sub, 1.0);
  
          m.setRow(2, sub);
          for (int i = 0; i < n; ++i) {
              for (int j = 0; j < n; ++j) {
                  if (i != 2) {
                      assertEquals(0.0, m.getEntry(i, j), 0.0);
                  } else {
                      assertEquals(1.0, m.getEntry(i, j), 0.0);
                  }
              }
          }
          checkArrays(sub, m.getRow(2));
  
      }
  
      public void testGetColumn() {
          RealMatrix m = new BlockRealMatrix(subTestData);
          double[] mColumn1 = columnToArray(subColumn1);
          double[] mColumn3 = columnToArray(subColumn3);
          checkArrays(mColumn1, m.getColumn(1));
          checkArrays(mColumn3, m.getColumn(3));
          try {
              m.getColumn(-1);
              fail("Expecting MatrixIndexException");
          } catch (MatrixIndexException ex) {
              // expected
          }
          try {
              m.getColumn(4);
              fail("Expecting MatrixIndexException");
          } catch (MatrixIndexException ex) {
              // expected
          }
      }
  
      public void testSetColumn() {
          RealMatrix m = new BlockRealMatrix(subTestData);
          double[] mColumn3 = columnToArray(subColumn3);
          assertTrue(mColumn3[0] != m.getColumn(1)[0]);
          m.setColumn(1, mColumn3);
          checkArrays(mColumn3, m.getColumn(1));
          try {
              m.setColumn(-1, mColumn3);
              fail("Expecting MatrixIndexException");
          } catch (MatrixIndexException ex) {
              // expected
          }
          try {
              m.setColumn(0, new double[5]);
              fail("Expecting InvalidMatrixException");
          } catch (InvalidMatrixException ex) {
              // expected
          }
      }
  
      public void testGetSetColumnLarge() {
          int n = 3 * BlockRealMatrix.BLOCK_SIZE;
          RealMatrix m = new BlockRealMatrix(n, n);
          double[] sub = new double[n];
          Arrays.fill(sub, 1.0);
  
          m.setColumn(2, sub);
          for (int i = 0; i < n; ++i) {
              for (int j = 0; j < n; ++j) {
                  if (j != 2) {
                      assertEquals(0.0, m.getEntry(i, j), 0.0);
                  } else {
                      assertEquals(1.0, m.getEntry(i, j), 0.0);
                  }
              }
          }
          checkArrays(sub, m.getColumn(2));
  
      }
  
      private double[] columnToArray(double[][] column) {
          double[] data = new double[column.length];
          for (int i = 0; i < data.length; ++i) {
              data[i] = column[i][0];
          }
          return data;
      }
  
      private void checkArrays(double[] expected, double[] actual) {
          assertEquals(expected.length, actual.length);
          for (int i = 0; i < expected.length; ++i) {
              assertEquals(expected[i], actual[i]);
          }
      }
  
      public void testEqualsAndHashCode() {
          BlockRealMatrix m = new BlockRealMatrix(testData);
          BlockRealMatrix m1 = m.copy();
          BlockRealMatrix mt = m.transpose();
          assertTrue(m.hashCode() != mt.hashCode());
          assertEquals(m.hashCode(), m1.hashCode());
          assertEquals(m, m);
          assertEquals(m, m1);
          assertFalse(m.equals(null));
          assertFalse(m.equals(mt));
          assertFalse(m.equals(new BlockRealMatrix(bigSingular)));
      }
  
      public void testToString() {
          BlockRealMatrix m = new BlockRealMatrix(testData);
          assertEquals("BlockRealMatrix{{1.0,2.0,3.0},{2.0,5.0,3.0},{1.0,0.0,8.0}}",
                  m.toString());
      }
  
      public void testSetSubMatrix() throws Exception {
          BlockRealMatrix m = new BlockRealMatrix(testData);
          m.setSubMatrix(detData2,1,1);
          RealMatrix expected = new BlockRealMatrix
              (new double[][] {{1.0,2.0,3.0},{2.0,1.0,3.0},{1.0,2.0,4.0}});
          assertEquals(expected, m);
  
          m.setSubMatrix(detData2,0,0);
          expected = new BlockRealMatrix
              (new double[][] {{1.0,3.0,3.0},{2.0,4.0,3.0},{1.0,2.0,4.0}});
          assertEquals(expected, m);
  
          m.setSubMatrix(testDataPlus2,0,0);
          expected = new BlockRealMatrix
              (new double[][] {{3.0,4.0,5.0},{4.0,7.0,5.0},{3.0,2.0,10.0}});
          assertEquals(expected, m);
  
          // javadoc example
          BlockRealMatrix matrix = new BlockRealMatrix
              (new double[][] {{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 0, 1 , 2}});
          matrix.setSubMatrix(new double[][] {{3, 4}, {5, 6}}, 1, 1);
          expected = new BlockRealMatrix
              (new double[][] {{1, 2, 3, 4}, {5, 3, 4, 8}, {9, 5 ,6, 2}});
          assertEquals(expected, matrix);
  
          // dimension overflow
          try {
              m.setSubMatrix(testData,1,1);
              fail("expecting MatrixIndexException");
          } catch (MatrixIndexException e) {
              // expected
          }
          // dimension underflow
          try {
              m.setSubMatrix(testData,-1,1);
              fail("expecting MatrixIndexException");
          } catch (MatrixIndexException e) {
              // expected
          }
          try {
              m.setSubMatrix(testData,1,-1);
              fail("expecting MatrixIndexException");
          } catch (MatrixIndexException e) {
              // expected
          }
  
          // null
          try {
              m.setSubMatrix(null,1,1);
              fail("expecting NullPointerException");
          } catch (NullPointerException e) {
              // expected
          }
  
          // ragged
          try {
              m.setSubMatrix(new double[][] {{1}, {2, 3}}, 0, 0);
              fail("expecting IllegalArgumentException");
          } catch (IllegalArgumentException e) {
              // expected
          }
  
          // empty
          try {
              m.setSubMatrix(new double[][] {{}}, 0, 0);
              fail("expecting IllegalArgumentException");
          } catch (IllegalArgumentException e) {
              // expected
          }
  
      }
  
      public void testWalk() {
          int rows    = 150;
          int columns = 75;
  
          RealMatrix m = new BlockRealMatrix(rows, columns);
          m.walkInRowOrder(new SetVisitor());
          GetVisitor getVisitor = new GetVisitor();
          m.walkInOptimizedOrder(getVisitor);
          assertEquals(rows * columns, getVisitor.getCount());
  
          m = new BlockRealMatrix(rows, columns);
          m.walkInRowOrder(new SetVisitor(), 1, rows - 2, 1, columns - 2);
          getVisitor = new GetVisitor();
          m.walkInOptimizedOrder(getVisitor, 1, rows - 2, 1, columns - 2);
          assertEquals((rows - 2) * (columns - 2), getVisitor.getCount());
          for (int i = 0; i < rows; ++i) {
              assertEquals(0.0, m.getEntry(i, 0), 0);
              assertEquals(0.0, m.getEntry(i, columns - 1), 0);
          }
          for (int j = 0; j < columns; ++j) {
              assertEquals(0.0, m.getEntry(0, j), 0);
              assertEquals(0.0, m.getEntry(rows - 1, j), 0);
          }
  
          m = new BlockRealMatrix(rows, columns);
          m.walkInColumnOrder(new SetVisitor());
          getVisitor = new GetVisitor();
          m.walkInOptimizedOrder(getVisitor);
          assertEquals(rows * columns, getVisitor.getCount());
  
          m = new BlockRealMatrix(rows, columns);
          m.walkInColumnOrder(new SetVisitor(), 1, rows - 2, 1, columns - 2);
          getVisitor = new GetVisitor();
          m.walkInOptimizedOrder(getVisitor, 1, rows - 2, 1, columns - 2);
          assertEquals((rows - 2) * (columns - 2), getVisitor.getCount());
          for (int i = 0; i < rows; ++i) {
              assertEquals(0.0, m.getEntry(i, 0), 0);
              assertEquals(0.0, m.getEntry(i, columns - 1), 0);
          }
          for (int j = 0; j < columns; ++j) {
              assertEquals(0.0, m.getEntry(0, j), 0);
              assertEquals(0.0, m.getEntry(rows - 1, j), 0);
          }
  
          m = new BlockRealMatrix(rows, columns);
          m.walkInOptimizedOrder(new SetVisitor());
          getVisitor = new GetVisitor();
          m.walkInRowOrder(getVisitor);
          assertEquals(rows * columns, getVisitor.getCount());
  
          m = new BlockRealMatrix(rows, columns);
          m.walkInOptimizedOrder(new SetVisitor(), 1, rows - 2, 1, columns - 2);
          getVisitor = new GetVisitor();
          m.walkInRowOrder(getVisitor, 1, rows - 2, 1, columns - 2);
          assertEquals((rows - 2) * (columns - 2), getVisitor.getCount());
  