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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.optim.linear;
  
  import java.util.ArrayList;
  import java.util.Collection;
  
  import org.apache.commons.math4.legacy.optim.nonlinear.scalar.GoalType;
  import org.junit.Assert;
  import org.junit.Test;
  
  public class SimplexTableauTest {
  
      @Test
      public void testInitialization() {
          LinearObjectiveFunction f = createFunction();
          Collection<LinearConstraint> constraints = createConstraints();
          SimplexTableau tableau =
              new SimplexTableau(f, constraints, GoalType.MAXIMIZE, false, 1.0e-6);
          double[][] expectedInitialTableau = {
                                               {-1, 0,  -1,  -1,  2, 0, 0, 0, -4},
                                               { 0, 1, -1.875, -1.25, 3.125, 0, 0, 0,  0},
                                               { 0, 0,   1,   0, -1, 1, 0, 0,  2},
                                               { 0, 0,   0,   1, -1, 0, 1, 0,  3},
                                               { 0, 0,   1,   1, -2, 0, 0, 1,  4}
          };
          assertMatrixEquals(expectedInitialTableau, tableau.getData());
      }
  
      @Test
      public void testDropPhase1Objective() {
          LinearObjectiveFunction f = createFunction();
          Collection<LinearConstraint> constraints = createConstraints();
          SimplexTableau tableau =
              new SimplexTableau(f, constraints, GoalType.MAXIMIZE, false, 1.0e-6);
          double[][] expectedTableau = {
                                        { 1, -1.875, -1.25, 0, 0, 0, 0},
                                        { 0,   1,   0, 1, 0, 0, 2},
                                        { 0,   0,   1, 0, 1, 0, 3},
                                        { 0,   1,   1, 0, 0, 1, 4}
          };
          tableau.dropPhase1Objective();
          assertMatrixEquals(expectedTableau, tableau.getData());
      }
  
      @Test
      public void testTableauWithNoArtificialVars() {
          LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] {15, 10}, 0);
          Collection<LinearConstraint> constraints = new ArrayList<>();
          constraints.add(new LinearConstraint(new double[] {1, 0}, Relationship.LEQ, 2));
          constraints.add(new LinearConstraint(new double[] {0, 1}, Relationship.LEQ, 3));
          constraints.add(new LinearConstraint(new double[] {1, 1}, Relationship.LEQ, 4));
          SimplexTableau tableau =
              new SimplexTableau(f, constraints, GoalType.MAXIMIZE, false, 1.0e-6);
          double[][] initialTableau = {
                                       {1, -1.875, -1.25, 3.125, 0, 0, 0, 0},
                                       {0,   1,   0, -1, 1, 0, 0, 2},
                                       {0,   0,   1, -1, 0, 1, 0, 3},
                                       {0,   1,   1, -2, 0, 0, 1, 4}
          };
          assertMatrixEquals(initialTableau, tableau.getData());
      }
  
      private LinearObjectiveFunction createFunction() {
          return new LinearObjectiveFunction(new double[] {15, 10}, 0);
      }
  
      private Collection<LinearConstraint> createConstraints() {
          Collection<LinearConstraint> constraints = new ArrayList<>();
          constraints.add(new LinearConstraint(new double[] {1, 0}, Relationship.LEQ, 2));
          constraints.add(new LinearConstraint(new double[] {0, 1}, Relationship.LEQ, 3));
          constraints.add(new LinearConstraint(new double[] {1, 1}, Relationship.EQ, 4));
          return constraints;
      }
  
      private void assertMatrixEquals(double[][] expected, double[][] result) {
          Assert.assertEquals("Wrong number of rows.", expected.length, result.length);
          for (int i = 0; i < expected.length; i++) {
              Assert.assertEquals("Wrong number of columns.", expected[i].length, result[i].length);
              for (int j = 0; j < expected[i].length; j++) {
                  Assert.assertEquals("Wrong value at position [" + i + "," + j + "]", expected[i][j], result[i][j], 1.0e-15);
              }
          }
      }
  }