#markov

##Usage

1. Clone this library into your project

git clone https://github.com/NathanEpstein/markov.git

2. Make markov.o and libmarkov.a by calling make on this library's Makefile (assuming you aren't using a package manager which does this for you).

cd markov && make

3. Include the appropriate header in your project file

#include "../markov/markov.h"

int main(){
  // your code here...
}

4. Compile with g++ myFile.cpp -L ../markov -l markov

##Examples

####Poisson Process

#include "../markov/markov.h"

int main(){
  //SIMULATE A POISSON PROCESS
  double lambda = 6.2;
  double T = 10;
  std::vector<double> P = poissP(lambda,T) ;

  return 0;
}

Brownian Motion

#include "../markov/markov.h"

int main(){
  //SIMULATE BROWNIAN MOTION
  double mu = 0.8;
  double sigma = 0.2;
  double T = 10;
  int steps = 100;
  std::vector<double> brown = brownian(mu,sigma,T,steps);

  return 0;
}

Geometric Brownian Motion

#include "../markov/markov.h"

int main(){
  //SIMULATE GEOMETRIC BROWNIAN MOTION
  double S0 = 5;
  double mu = 0.8;
  double sigma = 0.2;
  double T = 10;
  int steps = 100;
  std::vector<double> geo = geoBrownian(S0,mu,sigma,T,steps);

  return 0;
}

Discrete Time Markov Chains

#include "../markov/markov.h"

int main(){
  //SIMULATE DISCRETE TIME MARKOV CHAIN
  std::vector< std::vector<double> > matrix(3,std::vector<double> (3)); //initializes a 3x3 matrix with zeros

  //set transition matrix
  matrix[0][1] = 1;
  matrix[1][2] = 1;
  matrix[2][0] = 1;

  int steps = 10;
  int start = 0;
  double T = 8.5;
  //simulate discrete time Markov Chain
  std::vector<int> discreteMC = DTMC(matrix,steps,start);

  return 0;
}

Continuous Time Markov Chains

#include "../markov/markov.h"

int main(){
  //SIMULATE CONTINUOUS TIME MARKOV CHAIN
  std::vector< std::vector<double> > matrix(3,std::vector<double> (3)); //initializes a 3x3 matrix with zeros

  //set transition matrix
  matrix[0][1] = 1;
  matrix[1][2] = 1;
  matrix[2][0] = 1;

  int start = 0;
  double T = 8.5;
  //simulate continuous time Markov Chain
  CTMC continuousMC(matrix);
  continuousMC.simulate(T,start);

  std::vector<double> times = continuousMC.transTimes();
  std::vector<int> states = continuousMC.getStates();

  return 0;
}

Previous Version

This library initially implemented CTMC as a function which returned a matrix instead of a class. To access the original (deprecated) version use git clone -b v1 https://github.com/NathanEpstein/markov.git

License

The MIT License (MIT)

Copyright (c) 2014 Nathan Epstein

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.