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    * Licensed to the Apache Software Foundation (ASF) under one or more
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    * 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
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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,
   * 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.math4.legacy.linear;
  
  import org.apache.commons.math4.legacy.exception.MathIllegalArgumentException;
  import org.junit.Test;
  import org.junit.Assert;
  
  public class LUSolverTest {
      private double[][] testData = {
              { 1.0, 2.0, 3.0},
              { 2.0, 5.0, 3.0},
              { 1.0, 0.0, 8.0}
      };
      private double[][] luData = {
              { 2.0, 3.0, 3.0 },
              { 0.0, 5.0, 7.0 },
              { 6.0, 9.0, 8.0 }
      };
  
      // singular matrices
      private double[][] singular = {
              { 2.0, 3.0 },
              { 2.0, 3.0 }
      };
      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
  
      /** test threshold impact */
      @Test
      public void testThreshold() {
          final RealMatrix matrix = MatrixUtils.createRealMatrix(new double[][] {
                                                         { 1.0, 2.0, 3.0},
                                                         { 2.0, 5.0, 3.0},
                                                         { 4.000001, 9.0, 9.0}
                                                       });
          Assert.assertFalse(new LUDecomposition(matrix, 1.0e-5).getSolver().isNonSingular());
          Assert.assertTrue(new LUDecomposition(matrix, 1.0e-10).getSolver().isNonSingular());
      }
  
      /** test singular */
      @Test
      public void testSingular() {
          DecompositionSolver solver =
              new LUDecomposition(MatrixUtils.createRealMatrix(testData)).getSolver();
          Assert.assertTrue(solver.isNonSingular());
          solver = new LUDecomposition(MatrixUtils.createRealMatrix(singular)).getSolver();
          Assert.assertFalse(solver.isNonSingular());
          solver = new LUDecomposition(MatrixUtils.createRealMatrix(bigSingular)).getSolver();
          Assert.assertFalse(solver.isNonSingular());
      }
  
      /** test solve dimension errors */
      @Test
      public void testSolveDimensionErrors() {
          DecompositionSolver solver =
              new LUDecomposition(MatrixUtils.createRealMatrix(testData)).getSolver();
          RealMatrix b = MatrixUtils.createRealMatrix(new double[2][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 solve singularity errors */
      @Test
     public void testSolveSingularityErrors() {
         DecompositionSolver solver =
             new LUDecomposition(MatrixUtils.createRealMatrix(singular)).getSolver();
         RealMatrix b = MatrixUtils.createRealMatrix(new double[2][2]);
         try {
             solver.solve(b);
             Assert.fail("an exception should have been thrown");
         } catch (SingularMatrixException ime) {
             // expected behavior
         }
         try {
             solver.solve(b.getColumnVector(0));
             Assert.fail("an exception should have been thrown");
         } catch (SingularMatrixException ime) {
             // expected behavior
         }
         try {
             solver.solve(new ArrayRealVectorTest.RealVectorTestImpl(b.getColumn(0)));
             Assert.fail("an exception should have been thrown");
         } catch (SingularMatrixException ime) {
             // expected behavior
         }
     }
 
     /** test solve */
     @Test
     public void testSolve() {
         DecompositionSolver solver =
             new LUDecomposition(MatrixUtils.createRealMatrix(testData)).getSolver();
         RealMatrix b = MatrixUtils.createRealMatrix(new double[][] {
                 { 1, 0 }, { 2, -5 }, { 3, 1 }
         });
         RealMatrix xRef = MatrixUtils.createRealMatrix(new double[][] {
                 { 19, -71 }, { -6, 22 }, { -2, 9 }
         });
 
         // using RealMatrix
         Assert.assertEquals(0, solver.solve(b).subtract(xRef).getNorm(), 1.0e-13);
 
         // 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 determinant */
     @Test
     public void testDeterminant() {
         Assert.assertEquals( -1, getDeterminant(MatrixUtils.createRealMatrix(testData)), 1.0e-15);
         Assert.assertEquals(-10, getDeterminant(MatrixUtils.createRealMatrix(luData)), 1.0e-14);
         Assert.assertEquals(  0, getDeterminant(MatrixUtils.createRealMatrix(singular)), 1.0e-17);
         Assert.assertEquals(  0, getDeterminant(MatrixUtils.createRealMatrix(bigSingular)), 1.0e-10);
     }
 
     private double getDeterminant(RealMatrix m) {
         return new LUDecomposition(m).getDeterminant();
     }
 }