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    * 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.math4.legacy.linear;
  
  import org.apache.commons.math4.legacy.exception.MathIllegalArgumentException;
  import org.apache.commons.math4.legacy.core.dfp.Dfp;
  import org.junit.Assert;
  import org.junit.Test;
  
  public class FieldLUSolverTest {
      private int[][] testData = {
              { 1, 2, 3},
              { 2, 5, 3},
              { 1, 0, 8}
      };
      private int[][] luData = {
              { 2, 3, 3 },
              { 0, 5, 7 },
              { 6, 9, 8 }
      };
  
      // singular matrices
      private int[][] singular = {
              { 2, 3 },
              { 2, 3 }
      };
      private int[][] bigSingular = {
              { 1, 2,   3,    4 },
              { 2, 5,   3,    4 },
              { 7, 3, 256, 1930 },
              { 3, 7,   6,    8 }
      }; // 4th row = 1st + 2nd
  
      public static FieldMatrix<Dfp> createDfpMatrix(final int[][] data) {
          final int numRows = data.length;
          final int numCols = data[0].length;
          final Array2DRowFieldMatrix<Dfp> m;
          m = new Array2DRowFieldMatrix<>(Dfp25.getField(),
                                                  numRows, numCols);
          for (int i = 0; i < numRows; i++) {
              for (int j = 0; j < numCols; j++) {
                  m.setEntry(i, j, Dfp25.of(data[i][j], 1));
              }
          }
          return m;
      }
  
      /** test singular */
      @Test
      public void testSingular() {
          FieldDecompositionSolver<Dfp> solver;
          solver = new FieldLUDecomposition<>(createDfpMatrix(testData))
              .getSolver();
          Assert.assertTrue(solver.isNonSingular());
          solver = new FieldLUDecomposition<>(createDfpMatrix(singular))
              .getSolver();
          Assert.assertFalse(solver.isNonSingular());
          solver = new FieldLUDecomposition<>(createDfpMatrix(bigSingular))
              .getSolver();
          Assert.assertFalse(solver.isNonSingular());
      }
  
      /** test solve dimension errors */
      @Test
      public void testSolveDimensionErrors() {
          FieldDecompositionSolver<Dfp> solver;
          solver = new FieldLUDecomposition<>(createDfpMatrix(testData))
              .getSolver();
          FieldMatrix<Dfp> b = createDfpMatrix(new int[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
          }
      }
  
      /** test solve singularity errors */
     @Test
     public void testSolveSingularityErrors() {
         FieldDecompositionSolver<Dfp> solver;
         solver = new FieldLUDecomposition<>(createDfpMatrix(singular))
             .getSolver();
         FieldMatrix<Dfp> b = createDfpMatrix(new int[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
         }
     }
 
     /** test solve */
     @Test
     public void testSolve() {
         FieldDecompositionSolver<Dfp> solver;
         solver = new FieldLUDecomposition<>(createDfpMatrix(testData))
             .getSolver();
         FieldMatrix<Dfp> b = createDfpMatrix(new int[][] {
                 { 1, 0 }, { 2, -5 }, { 3, 1 }
         });
         FieldMatrix<Dfp> xRef = createDfpMatrix(new int[][] {
                 { 19, -71 }, { -6, 22 }, { -2, 9 }
         });
 
         // using FieldMatrix
         FieldMatrix<Dfp> x = solver.solve(b);
         for (int i = 0; i < x.getRowDimension(); i++){
             for (int j = 0; j < x.getColumnDimension(); j++){
                 Assert.assertEquals("(" + i + ", " + j + ")",
                                     xRef.getEntry(i, j), x.getEntry(i, j));
             }
         }
 
         // using ArrayFieldVector
         for (int j = 0; j < b.getColumnDimension(); j++) {
             final FieldVector<Dfp> xj = solver.solve(b.getColumnVector(j));
             for (int i = 0; i < xj.getDimension(); i++){
                 Assert.assertEquals("(" + i + ", " + j + ")",
                                     xRef.getEntry(i, j), xj.getEntry(i));
             }
         }
 
         // using SparseFieldVector
         for (int j = 0; j < b.getColumnDimension(); j++) {
             final SparseFieldVector<Dfp> bj;
             bj = new SparseFieldVector<>(Dfp25.getField(),
                                                  b.getColumn(j));
             final FieldVector<Dfp> xj = solver.solve(bj);
             for (int i = 0; i < xj.getDimension(); i++) {
                 Assert.assertEquals("(" + i + ", " + j + ")",
                                     xRef.getEntry(i, j), xj.getEntry(i));
             }
         }
     }
 
     /** test determinant */
     @Test
     public void testDeterminant() {
         Assert.assertEquals( -1, getDeterminant(createDfpMatrix(testData)), 1E-15);
         Assert.assertEquals(-10, getDeterminant(createDfpMatrix(luData)), 1E-14);
         Assert.assertEquals(  0, getDeterminant(createDfpMatrix(singular)), 1E-15);
         Assert.assertEquals(  0, getDeterminant(createDfpMatrix(bigSingular)), 1E-15);
     }
 
     private double getDeterminant(final FieldMatrix<Dfp> m) {
         return new FieldLUDecomposition<>(m).getDeterminant().toDouble();
     }
 }