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    *
    *      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,
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  package org.apache.commons.math4.legacy.linear;
  
  import org.apache.commons.math4.legacy.exception.MathIllegalArgumentException;
  import org.junit.Assert;
  import org.junit.Test;
  
  public class SingularValueSolverTest {
  
      private double[][] testSquare = {
              { 24.0 / 25.0, 43.0 / 25.0 },
              { 57.0 / 25.0, 24.0 / 25.0 }
      };
      private double[][] bigSingular = {
          { 1.0, 2.0,   3.0,    4.0 },
          { 2.0, 5.0,   3.0,    4.0 },
          { 7.0, 3.0, 256.0, 1930.0 },
          { 3.0, 7.0,   6.0,    8.0 }
      }; // 4th row = 1st + 2nd
  
      private static final double normTolerance = 10e-14;
  
      /** test solve dimension errors */
      @Test
      public void testSolveDimensionErrors() {
          DecompositionSolver solver =
              new SingularValueDecomposition(MatrixUtils.createRealMatrix(testSquare)).getSolver();
          RealMatrix b = MatrixUtils.createRealMatrix(new double[3][2]);
          try {
              solver.solve(b);
              Assert.fail("an exception should have been thrown");
          } catch (MathIllegalArgumentException iae) {
              // expected behavior
          }
          try {
              solver.solve(b.getColumnVector(0));
              Assert.fail("an exception should have been thrown");
          } catch (MathIllegalArgumentException iae) {
              // expected behavior
          }
          try {
              solver.solve(new ArrayRealVectorTest.RealVectorTestImpl(b.getColumn(0)));
              Assert.fail("an exception should have been thrown");
          } catch (MathIllegalArgumentException iae) {
              // expected behavior
          }
      }
  
      /** test least square solve */
      @Test
      public void testLeastSquareSolve() {
          RealMatrix m =
              MatrixUtils.createRealMatrix(new double[][] {
                                     { 1.0, 0.0 },
                                     { 0.0, 0.0 }
                                 });
          DecompositionSolver solver = new SingularValueDecomposition(m).getSolver();
          RealMatrix b = MatrixUtils.createRealMatrix(new double[][] {
              { 11, 12 }, { 21, 22 }
          });
          RealMatrix xMatrix = solver.solve(b);
          Assert.assertEquals(11, xMatrix.getEntry(0, 0), 1.0e-15);
          Assert.assertEquals(12, xMatrix.getEntry(0, 1), 1.0e-15);
          Assert.assertEquals(0, xMatrix.getEntry(1, 0), 1.0e-15);
          Assert.assertEquals(0, xMatrix.getEntry(1, 1), 1.0e-15);
          RealVector xColVec = solver.solve(b.getColumnVector(0));
          Assert.assertEquals(11, xColVec.getEntry(0), 1.0e-15);
          Assert.assertEquals(0, xColVec.getEntry(1), 1.0e-15);
          RealVector xColOtherVec = solver.solve(new ArrayRealVectorTest.RealVectorTestImpl(b.getColumn(0)));
          Assert.assertEquals(11, xColOtherVec.getEntry(0), 1.0e-15);
          Assert.assertEquals(0, xColOtherVec.getEntry(1), 1.0e-15);
      }
  
      /** test solve */
      @Test
      public void testSolve() {
          DecompositionSolver solver =
              new SingularValueDecomposition(MatrixUtils.createRealMatrix(testSquare)).getSolver();
          RealMatrix b = MatrixUtils.createRealMatrix(new double[][] {
                  { 1, 2, 3 }, { 0, -5, 1 }
          });
          RealMatrix xRef = MatrixUtils.createRealMatrix(new double[][] {
                  { -8.0 / 25.0, -263.0 / 75.0, -29.0 / 75.0 },
                 { 19.0 / 25.0,   78.0 / 25.0,  49.0 / 25.0 }
         });
 
         // using RealMatrix
         Assert.assertEquals(0, solver.solve(b).subtract(xRef).getNorm(), normTolerance);
 
         // using ArrayRealVector
         for (int i = 0; i < b.getColumnDimension(); ++i) {
             Assert.assertEquals(0,
                          solver.solve(b.getColumnVector(i)).subtract(xRef.getColumnVector(i)).getNorm(),
                          1.0e-13);
         }
 
         // using RealVector with an alternate implementation
         for (int i = 0; i < b.getColumnDimension(); ++i) {
             ArrayRealVectorTest.RealVectorTestImpl v =
                 new ArrayRealVectorTest.RealVectorTestImpl(b.getColumn(i));
             Assert.assertEquals(0,
                          solver.solve(v).subtract(xRef.getColumnVector(i)).getNorm(),
                          1.0e-13);
         }
     }
 
     /** test condition number */
     @Test
     public void testConditionNumber() {
         SingularValueDecomposition svd =
             new SingularValueDecomposition(MatrixUtils.createRealMatrix(testSquare));
         // replace 1.0e-15 with 1.5e-15
         Assert.assertEquals(3.0, svd.getConditionNumber(), 1.5e-15);
     }
 
     @Test
     public void testMath320B() {
         RealMatrix rm = new Array2DRowRealMatrix(new double[][] {
             { 1.0, 2.0 }, { 1.0, 2.0 }
         });
         SingularValueDecomposition svd =
             new SingularValueDecomposition(rm);
         RealMatrix recomposed = svd.getU().multiply(svd.getS()).multiply(svd.getVT());
         Assert.assertEquals(0.0, recomposed.subtract(rm).getNorm(), 2.0e-15);
     }
 
     @Test
     public void testSingular() {
       SingularValueDecomposition svd =
           new SingularValueDecomposition(MatrixUtils.createRealMatrix(bigSingular));
       RealMatrix pseudoInverse = svd.getSolver().getInverse();
       RealMatrix expected = new Array2DRowRealMatrix(new double[][] {
           {-0.0355022687,0.0512742236,-0.0001045523,0.0157719549},
           {-0.3214992438,0.3162419255,0.0000348508,-0.0052573183},
           {0.5437098346,-0.4107754586,-0.0008256918,0.132934376},
           {-0.0714905202,0.053808742,0.0006279816,-0.0176817782}
       });
       Assert.assertEquals(0, expected.subtract(pseudoInverse).getNorm(), 1.0e-9);
     }
 }