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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
    * 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 java.util.Random;
  
  import org.apache.commons.math4.legacy.exception.MathIllegalArgumentException;
  import org.apache.commons.numbers.core.Precision;
  import org.junit.Test;
  import org.junit.Assert;
  
  public class EigenSolverTest {
  
      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 non invertible matrix */
      @Test
      public void testNonInvertible() {
          Random r = new Random(9994100315209L);
          RealMatrix m =
              EigenDecompositionTest.createTestMatrix(r, new double[] { 1.0, 0.0, -1.0, -2.0, -3.0 });
          DecompositionSolver es = new EigenDecomposition(m).getSolver();
          Assert.assertFalse(es.isNonSingular());
          try {
              es.getInverse();
              Assert.fail("an exception should have been thrown");
          } catch (SingularMatrixException ime) {
              // expected behavior
          }
      }
  
      /** test invertible matrix */
      @Test
      public void testInvertible() {
          Random r = new Random(9994100315209L);
          RealMatrix m =
              EigenDecompositionTest.createTestMatrix(r, new double[] { 1.0, 0.5, -1.0, -2.0, -3.0 });
          DecompositionSolver es = new EigenDecomposition(m).getSolver();
          Assert.assertTrue(es.isNonSingular());
          RealMatrix inverse = es.getInverse();
          RealMatrix error =
              m.multiply(inverse).subtract(MatrixUtils.createRealIdentityMatrix(m.getRowDimension()));
          Assert.assertEquals(0, error.getNorm(), 4.0e-15);
      }
  
      /**
       * Verifies operation on very small values.
       * Matrix with eigenvalues {8e-100, -1e-100, -1e-100}
       */
      @Test
      public void testInvertibleTinyValues() {
          final double tiny = 1e-100;
          RealMatrix m = MatrixUtils.createRealMatrix(new double[][] {
                  {3,  2,  4},
                  {2,  0,  2},
                  {4,  2,  3}
          });
          m = m.scalarMultiply(tiny);
  
          final EigenDecomposition ed = new EigenDecomposition(m);
          RealMatrix inv = ed.getSolver().getInverse();
  
          final RealMatrix id = m.multiply(inv);
          for (int i = 0; i < m.getRowDimension(); i++) {
              for (int j = 0; j < m.getColumnDimension(); j++) {
                  if (i == j) {
                      Assert.assertTrue(Precision.equals(1, id.getEntry(i, j), 1e-15));
                  } else {
                      Assert.assertTrue(Precision.equals(0, id.getEntry(i, j), 1e-15));
                  }
              }
          }
      }
  
      @Test(expected=SingularMatrixException.class)
      public void testNonInvertibleMath1045() {
          EigenDecomposition eigen =
              new EigenDecomposition(MatrixUtils.createRealMatrix(bigSingular));
          eigen.getSolver().getInverse();
     }
 
     @Test(expected=SingularMatrixException.class)
     public void testZeroMatrix() {
         EigenDecomposition eigen =
             new EigenDecomposition(MatrixUtils.createRealMatrix(new double[][] {{0}}));
         eigen.getSolver().getInverse();
     }
 
     @Test
     public void testIsNonSingularTinyOutOfOrderEigenvalue() {
         final EigenDecomposition eigen
             = new EigenDecomposition(MatrixUtils.createRealMatrix(new double[][] {
                         { 1e-13, 0 },
                         { 1,     1 },
                     }));
         Assert.assertFalse("Singular matrix not detected",
                            eigen.getSolver().isNonSingular());
     }
 
     /** test solve dimension errors */
     @Test
     public void testSolveDimensionErrors() {
         final double[] refValues = new double[] {
             2.003, 2.002, 2.001, 1.001, 1.000, 0.001
         };
         final RealMatrix matrix = EigenDecompositionTest.createTestMatrix(new Random(35992629946426L), refValues);
 
         DecompositionSolver es = new EigenDecomposition(matrix).getSolver();
         RealMatrix b = MatrixUtils.createRealMatrix(new double[2][2]);
         try {
             es.solve(b);
             Assert.fail("an exception should have been thrown");
         } catch (MathIllegalArgumentException iae) {
             // expected behavior
         }
         try {
             es.solve(b.getColumnVector(0));
             Assert.fail("an exception should have been thrown");
         } catch (MathIllegalArgumentException iae) {
             // expected behavior
         }
         try {
             es.solve(new ArrayRealVectorTest.RealVectorTestImpl(b.getColumn(0)));
             Assert.fail("an exception should have been thrown");
         } catch (MathIllegalArgumentException iae) {
             // expected behavior
         }
     }
 
     /** test solve */
     @Test
     public void testSolve() {
         RealMatrix m = MatrixUtils.createRealMatrix(new double[][] {
                 { 91,  5, 29, 32, 40, 14 },
                 {  5, 34, -1,  0,  2, -1 },
                 { 29, -1, 12,  9, 21,  8 },
                 { 32,  0,  9, 14,  9,  0 },
                 { 40,  2, 21,  9, 51, 19 },
                 { 14, -1,  8,  0, 19, 14 }
         });
         DecompositionSolver es = new EigenDecomposition(m).getSolver();
         RealMatrix b = MatrixUtils.createRealMatrix(new double[][] {
                 { 1561, 269, 188 },
                 {   69, -21,  70 },
                 {  739, 108,  63 },
                 {  324,  86,  59 },
                 { 1624, 194, 107 },
                 {  796,  69,  36 }
         });
         RealMatrix xRef = MatrixUtils.createRealMatrix(new double[][] {
                 { 1,   2, 1 },
                 { 2,  -1, 2 },
                 { 4,   2, 3 },
                 { 8,  -1, 0 },
                 { 16,  2, 0 },
                 { 32, -1, 0 }
         });
 
         // using RealMatrix
         RealMatrix solution=es.solve(b);
         Assert.assertEquals(0, solution.subtract(xRef).getNorm(), 2.5e-12);
 
         // using RealVector
         for (int i = 0; i < b.getColumnDimension(); ++i) {
             Assert.assertEquals(0,
                          es.solve(b.getColumnVector(i)).subtract(xRef.getColumnVector(i)).getNorm(),
                          2.0e-11);
         }
 
         // 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,
                          es.solve(v).subtract(xRef.getColumnVector(i)).getNorm(),
                          2.0e-11);
         }
     }
 }