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R7917/Test.cpp
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Test.cpp
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#include <iostream>
#include <math.h>
#include <iostream>
#include <vector>
#include <gtest/gtest.h>
#include "IntegrationSolver1D.hpp"
#include "IntegrationSolver2DCartesian.hpp"
using namespace std;
/**
* User defined functions
* @param x: vector of double
* @return: double
* Function is defined as f: Rn -> R where n is at least 1
*/
double myFunction1D(vector<double> x) {
return x[0] * x[0];
}
double myFunction2D(vector<double> x) {
return x[1] + x[0];
}
/**
* Testing the accuracy of integration of the 1D methods
*/
TEST(IntegrationAcurracy, Method1D){
// Exact value of the integral of x² on [0,5]:
double exactValue = 41.6666666;
// Function
double (*functionPointer1D)(vector<double>); // Function method
functionPointer1D = &myFunction1D; // Function pointer
FunctionRntoR function1D(functionPointer1D); // Function object
// Domain
DomainCartesian domain1D(0, 5, 100); // x from 0 to 5, 100 subdivisions
// Method
Method Midpoint1D("Midpoint");
Method Simpson1D("Simpson");
Method Trapz1D("Trapz");
// Solving
IntegrationSolver1D Midpoint(function1D, domain1D, Midpoint1D);
IntegrationSolver1D Simpson(function1D, domain1D, Simpson1D);
IntegrationSolver1D Trapz(function1D, domain1D, Trapz1D);
double MidpointResult = Midpoint.GetResult();
double SimpsonResult = Simpson.GetResult();
double TrapzResult = Trapz.GetResult();
std::cout << "The exact result of 1D integration is: " << exactValue << "\n";
std::cout << "The result of 1D integration is: " << MidpointResult << " using " << Midpoint1D.name << "'s method." << "\n";
std::cout << "The result of 1D integration is: " << SimpsonResult << " using " << Simpson1D.name << "'s method." << "\n";
std::cout << "The result of 1D integration is: " << TrapzResult << " using " << Trapz1D.name << "'s method." << "\n";
// Testing
ASSERT_NEAR(exactValue, MidpointResult, 0.01);
ASSERT_NEAR(exactValue, SimpsonResult, 0.01);
ASSERT_NEAR(exactValue, TrapzResult, 0.01);
}
/**
* Testing the accuracy of integration of the 2D methods
*/
TEST(IntegrationAcurracy, Method2D){
// Exact value of the integral of x+y on {[0,5][0,5]}:
double exactValue = 125;
// Function
double (*functionPointer2D)(vector<double>); // Function method
functionPointer2D = &myFunction2D; // Function pointer
FunctionRntoR function1D(functionPointer2D); // Function object
// Boundaries matrix : x and y from 0 to 5
vector<vector<double>> boundaries2D;
vector<double> dim1;
vector<double> dim2;
dim1.push_back(0);
dim1.push_back(5);
dim2.push_back(0);
dim2.push_back(5);
boundaries2D.push_back(dim1);
boundaries2D.push_back(dim2);
// Subdivision vector : 100 x 100 subdivisions
vector<int> subdivision;
subdivision.push_back(100);
subdivision.push_back(100);
// Creation of the domain of integration - Cartesian domain (rectangle of n dimensions)
DomainCartesian domain2D(boundaries2D, subdivision);
// Method
Method Midpoint2D("Midpoint");
Method Simpson2D("Simpson");
Method Trapz2D("Trapz");
// Solving
IntegrationSolver2DCartesian Midpoint(function1D, domain2D, Midpoint2D);
IntegrationSolver2DCartesian Simpson(function1D, domain2D, Simpson2D);
IntegrationSolver2DCartesian Trapz(function1D, domain2D, Trapz2D);
double MidpointResult = Midpoint.GetResult();
double SimpsonResult = Simpson.GetResult();
double TrapzResult = Trapz.GetResult();
std::cout << "The exact result of 2D integration is: " << exactValue << "\n";
std::cout << "The result of 2D integration is: " << MidpointResult << " using " << Midpoint2D.name << "'s method." << "\n";
std::cout << "The result of 2D integration is: " << SimpsonResult << " using " << Simpson2D.name << "'s method." << "\n";
std::cout << "The result of 2D integration is: " << TrapzResult << " using " << Trapz2D.name << "'s method." << "\n";
// Testing
ASSERT_NEAR(exactValue, MidpointResult, 0.01);
ASSERT_NEAR(exactValue, SimpsonResult, 0.3); // this method is less accurate so the tolerance is higher.
ASSERT_NEAR(exactValue, TrapzResult, 0.01);
}
int main(int argc, char **argv) {
// running tests
testing::InitGoogleTest(&argc, argv);
return RUN_ALL_TESTS();
}
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