/*
    * 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.junit.Test;
  import org.junit.Assert;
  
  public class CholeskyDecompositionTest {
  
      private double[][] testData = new double[][] {
              {  1,  2,   4,   7,  11 },
              {  2, 13,  23,  38,  58 },
              {  4, 23,  77, 122, 182 },
              {  7, 38, 122, 294, 430 },
              { 11, 58, 182, 430, 855 }
      };
  
      /** test dimensions */
      @Test
      public void testDimensions() {
          CholeskyDecomposition llt =
              new CholeskyDecomposition(MatrixUtils.createRealMatrix(testData));
          Assert.assertEquals(testData.length, llt.getL().getRowDimension());
          Assert.assertEquals(testData.length, llt.getL().getColumnDimension());
          Assert.assertEquals(testData.length, llt.getLT().getRowDimension());
          Assert.assertEquals(testData.length, llt.getLT().getColumnDimension());
      }
  
      /** test non-square matrix */
      @Test(expected = NonSquareMatrixException.class)
      public void testNonSquare() {
          new CholeskyDecomposition(MatrixUtils.createRealMatrix(new double[3][2]));
      }
  
      /** test non-symmetric matrix */
      @Test(expected = NonSymmetricMatrixException.class)
      public void testNotSymmetricMatrixException() {
          double[][] changed = testData.clone();
          changed[0][changed[0].length - 1] += 1.0e-5;
          new CholeskyDecomposition(MatrixUtils.createRealMatrix(changed));
      }
  
      /** test non positive definite matrix */
      @Test(expected = NonPositiveDefiniteMatrixException.class)
      public void testNotPositiveDefinite() {
          new CholeskyDecomposition(MatrixUtils.createRealMatrix(new double[][] {
                  { 14, 11, 13, 15, 24 },
                  { 11, 34, 13, 8,  25 },
                  { 13, 13, 14, 15, 21 },
                  { 15, 8,  15, 18, 23 },
                  { 24, 25, 21, 23, 45 }
          }));
      }
  
      @Test(expected = NonPositiveDefiniteMatrixException.class)
      public void testMath274() {
          new CholeskyDecomposition(MatrixUtils.createRealMatrix(new double[][] {
                  { 0.40434286, -0.09376327, 0.30328980, 0.04909388 },
                  {-0.09376327,  0.10400408, 0.07137959, 0.04762857 },
                  { 0.30328980,  0.07137959, 0.30458776, 0.04882449 },
                  { 0.04909388,  0.04762857, 0.04882449, 0.07543265 }
          }));
      }
  
      /** test A = LLT */
      @Test
      public void testAEqualLLT() {
          RealMatrix matrix = MatrixUtils.createRealMatrix(testData);
          CholeskyDecomposition llt = new CholeskyDecomposition(matrix);
          RealMatrix l  = llt.getL();
          RealMatrix lt = llt.getLT();
          double norm = l.multiply(lt).subtract(matrix).getNorm();
          Assert.assertEquals(0, norm, 1.0e-15);
      }
  
      /** test that L is lower triangular */
      @Test
      public void testLLowerTriangular() {
          RealMatrix matrix = MatrixUtils.createRealMatrix(testData);
          RealMatrix l = new CholeskyDecomposition(matrix).getL();
          for (int i = 0; i < l.getRowDimension(); i++) {
              for (int j = i + 1; j < l.getColumnDimension(); j++) {
                  Assert.assertEquals(0.0, l.getEntry(i, j), 0.0);
              }
         }
     }
 
     /** test that LT is transpose of L */
     @Test
     public void testLTTransposed() {
         RealMatrix matrix = MatrixUtils.createRealMatrix(testData);
         CholeskyDecomposition llt = new CholeskyDecomposition(matrix);
         RealMatrix l  = llt.getL();
         RealMatrix lt = llt.getLT();
         double norm = l.subtract(lt.transpose()).getNorm();
         Assert.assertEquals(0, norm, 1.0e-15);
     }
 
     /** test matrices values */
     @Test
     public void testMatricesValues() {
         RealMatrix lRef = MatrixUtils.createRealMatrix(new double[][] {
                 {  1,  0,  0,  0,  0 },
                 {  2,  3,  0,  0,  0 },
                 {  4,  5,  6,  0,  0 },
                 {  7,  8,  9, 10,  0 },
                 { 11, 12, 13, 14, 15 }
         });
        CholeskyDecomposition llt =
             new CholeskyDecomposition(MatrixUtils.createRealMatrix(testData));
 
         // check values against known references
         RealMatrix l = llt.getL();
         Assert.assertEquals(0, l.subtract(lRef).getNorm(), 1.0e-13);
         RealMatrix lt = llt.getLT();
         Assert.assertEquals(0, lt.subtract(lRef.transpose()).getNorm(), 1.0e-13);
 
         // check the same cached instance is returned the second time
         Assert.assertSame(l, llt.getL());
         Assert.assertSame(lt, llt.getLT());
     }
 }