sources added

CC = g++

CFLAGS = -Wall -O3

all: random_shannon random_collision random_product random_geometric random_text 

random_product: 

	g++ $(CFLAGS) src/random_product.cpp -o random_product -lm

random_text: 

	g++ $(CFLAGS) src/random_text.cpp -o random_text -lm

random_geometric: 

	g++ $(CFLAGS) src/random_geometric.cpp -o random_geometric -lm

random_collision: 

	g++ $(CFLAGS) src/random_collision.cpp -o random_collision -lm

random_shannon: 

	g++ $(CFLAGS) src/random_shannon.cpp -o random_shannon -lm

clean:

	rm -f src/*.o

	rm -f random_collision

	rm -f random_shannon

	rm -f random_product

	rm -f random_geometric

	rm -f random_text

# Vectors

This project contains:

Random generators of stochastic vectors with fixed:

 - Shannon Entropy

 - Collision Entropy

 - Product

 - Geometric Mean

And also random text generators whose ditributions on the alphabet have one of

the cited properties.

## What do I need to use it

## Getting started

A g++ compiler

To make it easy for you to get started with GitLab, here's a list of recommended next steps.

## How to use it

Already a pro? Just edit this README.md and make it your own. Want to make it easy? [Use the template at the bottom](#editing-this-readme)!

### Compile the project

`make`

## Add your files

- [ ] [Create](https://docs.gitlab.com/ee/user/project/repository/web_editor.html#create-a-file) or [upload](https://docs.gitlab.com/ee/user/project/repository/web_editor.html#upload-a-file) files

- [ ] [Add files using the command line](https://docs.gitlab.com/ee/gitlab-basics/add-file.html#add-a-file-using-the-command-line) or push an existing Git repository with the following command:

### Random stochestic vectors with fixed property

./name_of_the_program [dimension] [target_value]

```

cd existing_repo

git remote add origin https://git.unicaen.fr/julien.david/vectors.git

git branch -M master

git push -uf origin master

```

Let k be the dimension of the vector, please note that

 - Shannon Entropy: t < log(k)/log(2)

 - Collision Entropy: t < log(k)/log(2)

 - Product: t < 1/k**k

 - Geometric Mean: t < 1/k

## Integrate with your tools

- [ ] [Set up project integrations](https://git.unicaen.fr/julien.david/vectors/-/settings/integrations)

## Collaborate with your team

- [ ] [Invite team members and collaborators](https://docs.gitlab.com/ee/user/project/members/)

- [ ] [Create a new merge request](https://docs.gitlab.com/ee/user/project/merge_requests/creating_merge_requests.html)

- [ ] [Automatically close issues from merge requests](https://docs.gitlab.com/ee/user/project/issues/managing_issues.html#closing-issues-automatically)

- [ ] [Enable merge request approvals](https://docs.gitlab.com/ee/user/project/merge_requests/approvals/)

- [ ] [Set auto-merge](https://docs.gitlab.com/ee/user/project/merge_requests/merge_when_pipeline_succeeds.html)

## Test and Deploy

Use the built-in continuous integration in GitLab.

- [ ] [Get started with GitLab CI/CD](https://docs.gitlab.com/ee/ci/quick_start/index.html)

- [ ] [Analyze your code for known vulnerabilities with Static Application Security Testing (SAST)](https://docs.gitlab.com/ee/user/application_security/sast/)

- [ ] [Deploy to Kubernetes, Amazon EC2, or Amazon ECS using Auto Deploy](https://docs.gitlab.com/ee/topics/autodevops/requirements.html)

- [ ] [Use pull-based deployments for improved Kubernetes management](https://docs.gitlab.com/ee/user/clusters/agent/)

- [ ] [Set up protected environments](https://docs.gitlab.com/ee/ci/environments/protected_environments.html)

***

# Editing this README

When you're ready to make this README your own, just edit this file and use the handy template below (or feel free to structure it however you want - this is just a starting point!). Thanks to [makeareadme.com](https://www.makeareadme.com/) for this template.

## Suggestions for a good README

Every project is different, so consider which of these sections apply to yours. The sections used in the template are suggestions for most open source projects. Also keep in mind that while a README can be too long and detailed, too long is better than too short. If you think your README is too long, consider utilizing another form of documentation rather than cutting out information.

## Name

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## Description

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## Badges

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#ifndef __COLLISION_ENTROPY_HPP__

#define __COLLISION_ENTROPY_HPP__

#include"SumConcaveFunction.hpp"

class CollisionEntropy: public SumConcaveFunction{

public:

  int sign(){

    return -1;

  }

  long double g(long double x, int k){

    return x*x;

  }

  long double h(long double y, int k){

    return -log2(y);

  }

  long double h_inv(long double y, int k){

    return powl(2,-y);

  }

  long double aim_with_target(long double x, long double s, long double t){

    return -log(x*x+(s-x)*(s-x)) - t;

  }

  long double diff_aim(long double x, long double s){

    return -(4*x-2*s)/((x*x+(s-x)*-(s-x))*log(2));

  }

  long double diff_maxInv(long double x, long double s){

    return -(3*x-s)/((x*x+(s-x)*(s-x)/2)*log(2));

  }

  long double diff_minInv(long double x, long double s){

    return -(4*x-2*s+2*EPSILON)/((x*x+(s-x-EPSILON)*(s-x-EPSILON)+EPSILON*EPSILON)*log(2));

  }

  CollisionEntropy(){}

};

#endif

#ifndef __CONCAVE_FUNCTION_HPP__

#define __CONCAVE_FUNCTION_HPP__

#include<math.h>

#include<iostream>

#define EPSILON powl(2,-64)

class ConcaveFunction{

public:

  virtual int sign() = 0;

  virtual long double g(long double x, int k) = 0;

  virtual long double h(long double x, int k) = 0;

  virtual long double h_inv(long double x, int k) = 0;

  virtual long double contribution(long double * t, int n) = 0;

  long double aim(long double * t, int n){

    return h(contribution(t,n),n);

  }

  virtual long double update(long double t, long double * x, int k, int l) = 0;

  virtual long double update_target(long double t, long double t2, int k, int l) = 0;

  long double newton(long double (*function)(long double x, long double s, long double t),

		     long double (*derivate)(long double x, long double s),

		     long double s, long double t, long double x, long double max_step){

    int step = 0;

    for(; step < max_step && function(x,s,t) != 0; step++){

      x = x - function(x,s,t)/derivate(x,s);

      x = (x<0)? -x:x;

    }

    return x;

  }

  long double newton_max(long double s, long double t, long double x, long double max_step){

    int step = 0;

    for(; step < max_step && maxInv(x,s,t) != 0 && x>= EPSILON && x<= s; step++){

      x = x - maxInv(x,s,t)/diff_maxInv(x,s);

      x = (x<0)? -x:x;

    }

    return x;

  }

  long double newton_min(long double s, long double t, long double x, long double max_step){

    int step = 0;

    for(; step < max_step && minInv(x,s,t) != 0 && x>= EPSILON && x<= s; step++){

      //std::cout<<"x:"<<x<<" s:"<<s<<" diff"<<diff_minInv(x,s)<<" t:"<<t<<std::endl;

      x = x - minInv(x,s,t)/diff_minInv(x,s);

      x = (x<0)? -x:x;

    }

    return x;

  }

  long double aim_double(long double x1, long double x2){

    long double t[2] = {x1, x2};

    return aim(t, 2);

  }

  long double aim_triple(long double x1, long double x2, long double x3){

    long double t[3] = {x1, x2, x3};

    return aim(t, 3);

  }

  virtual long double aim_with_target(long double x, long double s, long double t) = 0;

  virtual long double diff_aim(long double x, long double s) = 0;

  virtual long double maximal_of_two_values(long double partial_sum)  = 0;  

  virtual long double maxInv(long double x, long double s, long double t) = 0;

  virtual long double diff_maxInv(long double x, long double s) = 0;

  virtual long double minimal_of_two_values(long double partial_sum) = 0;

  virtual long double minInv(long double x, long double s, long double t) = 0;

  virtual long double diff_minInv(long double x, long double s) = 0;

  ConcaveFunction(){}

};

#endif

#ifndef __PRODUCT_FUNCTION_HPP__

#define __PRODUCT_FUNCTION_HPP__

#include"ProductConcaveFunction.hpp"

class GeometricMean: public ProductConcaveFunction{

public:

  int sign(){

    return 1;

  }

  long double g(long double x, int k){

    return x;

  }

  long double h(long double y, int k){

    return powl(y,1./k);

  }

  long double h_inv(long double y, int k){

    return powl(y,k);

  }

  long double aim_with_target(long double x, long double s, long double t){

    return sqrt(x*(s-x)) - t;

  }

  long double diff_aim(long double x, long double s){

    return (s-2*x)/(2*sqrt(x*(s-x)));

  }

  long double diff_maxInv(long double x, long double s){

    return ((s-x)*(s-x)-2*(s-x)*x)/(4*sqrt(s*(s-x)*(s-x)));

  }

  long double diff_minInv(long double x, long double s){

    return ((s-x-EPSILON)*EPSILON-x*EPSILON)/(3*powl((x*(s-x-EPSILON)*EPSILON),2/3));

  }

  GeometricMean(){}

};

#endif