matlab - Solving two nonlinear equations with two unknowns in C++ -

i have 2 nonlinear equations 2 unknowns, i.e., tau , p. both equations are: p=1-(1-tau).^(n-1) , tau = 2*(1-2*p) ./ ( (1-2*p)*(w+1)+(p*w).*(1-(2*p).^m)).

i interested find value of tau. how can find value using c++ code, have done using matlab , here code used:

function result=tau_eq(tau)  n=6; w=32; m=5;  p=1-(1-tau).^(n-1); result=tau - 2*(1-2*p) ./ ( (1-2*p)*(w+1)+(p*w).*(1-(2*p).^m));  statement @ command window: result=fzero(@tau_eq,[0,1],[]) 

can 1 me in since new c++. in advance

1.the function fzero solves nonlinear equation rather system of equations.

2.the easiest method method of dichotomy. variant of implementation equation.

#include <iostream> #include <cmath> #include <functional>  std::pair<bool,double> simplesolve(std::function<double(double)> &func,                                    const double xbegin,                                    const double xend); int main()     {     std::function<double(const double)> func = [](const double &tau)         {         auto n=6;         auto w=32;         auto m=5;          auto p=1-pow((1-tau),(n-1));         return tau - 2*(1-2*p) / ( (1-2*p)*(w+1)+(p*w)*(1-pow((2*p),m)));         };     auto r = simplesolve(func,0,1);     if(r.first)         std::cout<<r.second<<std::endl;     else          std::cout<<"error"<<std::endl;     return 0;     }  std::pair<bool,double> simplesolve(std::function<double(double)> &func,                                    const double xbegin,                                    const double xend)     {     double a=xbegin;     double b=xend;     const double epsilon=0.0001;     const double delta=0.0001;     double f1=func(a);     int it=0;     while(true)         {         ++it;         double c=(b+a)/2;         if((b-a)<epsilon*2.0)             return std::make_pair(true,c);          if(fabs(func(c))<delta)             return std::make_pair(true,c);         ((func(a)*func(c))<0) ? b=c : a=c ;         if(it>1000)             {             return std::make_pair(false,c);             }         }     } 

3. in matlab functions written:

the algorithm, created t. dekker, uses combination of bisection, secant, , inverse quadratic interpolation methods. algol 60 version, improvements, given in brent, r., algorithms minimization without derivatives, prentice-hall, 1973. fortran version, upon fzero based, in forsythe, g. e., m. a. malcolm, , c. b. moler, computer methods mathematical computations, prentice-hall, 1976.

you can implement it.

4.see question: what libraries there solving system of non-linear equations in c++?