Examples

Table of Contents

• Multivariate Normal
  • Using Eigen containers
  • Using STL containers

Example usage code

This page contains examples of how to use the library in your code.

Multivariate Normal

Using Eigen containers

#include <iostream>
#include "NormalDist.h"

int main(int argc, char* argv[])
{
    std::cout.precision(4); //Set the output to have 4 decimal digits
    //Construct the mean vector with values [1 ; -1]
    Eigen::Vector2d MeanVector;
    MeanVector(0)=1.0;
    MeanVector(1)=-1.0;
    //Construct the Var-Cov matrix so that the variance of both margins is 3 and the covariance is 1
    Eigen::Matrix2d VarMatrix;
    VarMatrix(0,0)=3;
    VarMatrix(0,1)=1;
    VarMatrix(1,0)=1;
    VarMatrix(1,1)=3;
    //Construct a Bivariate Normal with the above parameters
    Multivariate::NormalDistribution BivarNorm(2,MeanVector,VarMatrix);
    //Set the random number generator seed so that results are 100% reproducible
    BivarNorm.SetRandomSeed(99);
    //Compute and print the density and the cumulative density of the distribution in the point [1 ; 0.5]
    Eigen::Vector2d TempCoords;
    TempCoords(0)=1.0;
    TempCoords(1)=0.5;
    double Density=BivarNorm.GetDensity(TempCoords);
    double CumDensity=BivarNorm.GetCumulativeDesity(TempCoords);
    
    std::cout << "Density in [1 ; 0.5] = " << std::fixed << Density
        << std::endl << "Cumulative Density in [1 ; 0.5] = " << std::fixed << CumDensity;
    // Compute the 83rd percentile
    Eigen::Vector2d Quant83=BivarNorm.GetQuantile(0.83);
    std::cout << std::endl << "83rd Percentile = [" << Quant83.transpose()<< "] " << "that has cdf: " << BivarNorm.GetCumulativeDesity(Quant83);

    //Simulate 10 realizations and print the results
    Eigen::Matrix<double,10,2> Samples=BivarNorm.ExtractSamples(10);
    std::cout << std::endl << "Simulation Results:" << std::endl << "   Var 1\t Var2"<< std::endl << Samples << std::endl;
    return 0;
}

The output produced will be:

Density in [1 ; 0.5] = 0.0369
Cumulative Density in [1 ; 0.5] = 0.4390
Simulation Results:
Var 1 Var2
2.7742 -0.7284
0.6430 -3.0028
4.3652 1.1009
1.2452 -1.2843
1.2112 -0.4647
1.2562 1.1469
6.0257 2.0565
4.2924 -0.5663
1.2785 -0.5571
2.9207 -2.2104


Using STL containers

#include <iostream>
#include <vector>
#include "NormalDist.h"

int main(int argc, char* argv[])
{
    std::cout.precision(4); //Set the output to have 4 decimal digits

    //Construct a Bivariate Normal Distribution
    Multivariate::NormalDistribution BivarNorm(2);

    //Set the random number generator seed so that results are 100% reproducible
    BivarNorm.SetRandomSeed(88);

    // Set the mean vector to [1 ; -1]
    std::vector<double> MeanVector(2);
    MeanVector[0]=1.0;
    MeanVector[1]=-1.0;
    BivarNorm.SetMeanVector(MeanVector);

    //Set the variance of both margins to 3 and the covariance to 1
    std::vector<double> VarMatrix(4);
    VarMatrix[0]=3.0;
    VarMatrix[1]=1.0;
    VarMatrix[2]=1.0;
    VarMatrix[3]=3.0;
    BivarNorm.SetVarCovMatrix(VarMatrix);

    //Compute and print the density and the cumulative density of the distribution in the point [1 ; 0.5]
    std::vector<double> TempCoords;
    TempCoords.push_back(1.0);
    TempCoords.push_back(0.5);
    double Density=BivarNorm.GetDensity(TempCoords);
    double CumDensity=BivarNorm.GetCumulativeDesity(TempCoords);
    std::cout << "Density in [1 ; 0.5] = " << std::fixed << Density 
        << std::endl << "Cumulative Density in [1 ; 0.5] = " << std::fixed << CumDensity ;

    //Simulate 10 realizations and print the results
    std::map<unsigned int,std::vector<double> > Samples=BivarNorm.ExtractSamplesMap(10);
    std::cout << std::endl << "Simulation Results:"<< std::endl << "Var 1\t| Var2"<< std::endl << "_________________";
    for(int j=0;j<10;j++){
        std::cout << std::endl;
        for(unsigned int i=0;i<BivarNorm.GetDimension();i++){
            std::cout << std::fixed << Samples.at(i).at(j);
             if(i<BivarNorm.GetDimension()-1) std::cout << "\t| ";
        }
    }
    std::cout << std::endl;

    return 0;
}

The output produced will be:

Density in [1 ; 0.5] = 0.0369
Cumulative Density in [1 ; 0.5] = 0.4431
Simulation Results:
Var 1 | Var2
_________________
4.3795 | -0.0478
3.7745 | -3.0145
-0.7895 | -2.9816
-0.1412 | -0.4594
1.9040 | -2.3109
3.2947 | 1.9221
0.4840 | -3.7591
0.5675 | -1.0132
0.4181 | -1.6335
1.8001 | -4.1868