Numerary

Numerary is open source Scientific Library that contains many numerical methods. Numerary have been written from scratch in C++.

Features

The library covers a list of topics in numerical computing. Features are available for the following areas,

Root-Finding	Minimizing	Linear Systems Of Equations
Integration	Maximizing	Nonlinear Systems Of Equations
Differentiation	Regression	Ordinary Differential Equations
Gamma Functions	Interpolation

Root-Finding

You can find the root of the function f at any segment [a, b]:

#include <iostream>
#include "src/numerary.hpp" // Numerary library

using namespace std;
using namespace numerary;

double f(double x) {
    return sin(x); // Function to found the root
}

/* The main function */
int main() {
    double a = -1, b = 1; // "a" and "b" value of segment [a, b]
    double root; // Founded result of the root will be stored in this variable
    short int is_found;

    is_found = Numerary::root(f, a, b, &root);

    if (is_found == 1)
        cout << "Root is in x = " << root << endl;
    else
        cout << "Method not allowed!" << endl;

    return 0;
}

And you can do it with several numerical methods such as Secant and Bisection provided by the library. To do this, you simply need to specify the method that you want to apply as an additional parameter:

Numerary::root(f, a, b, &root, "bisection"); // To use Bisection method
Numerary::root(f, a, b, &root, "secant"); // To use Secant method

In addition, you can adjust the results of the methods using additional parameters, such as eps:

Numerary::root(f, a, b, &root, "secant", 1.e-9); // To set eps = 1.e-9

Minimizing

You can minimize function f at any segment [a, b]:

Numerary::minimum(f, a, b, &minimum);

For the minimum method, as with all other library methods, you can apply additional parameters:

Numerary::minimum(f, a, b, &minimum, "golden_ratio", 1.e-7);

Integration

You want to calculate the integrals, like this ?

Numerary library can do it too. To do this, you just need to write:

double *I = Numerary::integrate(f, from, to);

cout << "ans = " << I[0] << endl; // Value of calculated integral
cout << "err = " << I[1] << endl; // Error of calculated integral value

Regression

With the helping of Numerary library you can also use regression models. Here is an example of linear regression:

// Get predicted linear regression line
predicted_kc = Numerary::linear_regression(X, Y, N);

// Equation of regression line
cout << "y = " << predicted_kc[0] << "*x + " << predicted_kc[1] << endl; // y=k*x+c

Solving Nonlinear System Of Equations

Numerary library allows you to solve systems of nonlinear equations like:

To do this, you just need to write:

#include <iostream>
#include "../src/numerary.hpp" // Numerary library

using namespace std;
using namespace numerary;

/* System to solve */
void system(double *x, double *fv, int n) {
    fv[0] = x[0]*x[0] + x[1]*x[1] - 5;
    fv[1] = x[1] - 3*x[0] + 5;
}

int main() {
    double *x = new double[2], *fv = new double[2];
    short int is_solved;

    x[0] = 1; x[1] = 2; // Initial point

    is_solved = Numerary::nonlinear_systems_of_equations(system, x, fv, 2);

    if (is_solved == 1) {
        cout << "Solved!" << endl;
        cout << "x = " << x[0] << endl;
        cout << "y = " << x[1] << endl;
    } else {
        cout << "Method not allowed!";
    }

    delete[] x;
    delete[] fv;

    return 0;
}

And Many Other Useful Features

In addition to the above, Numerary library has a lot more.

The detail use of these features is described in the documentation. The documentation for each method details the algorithm, definitions and examples of their use.

Documentation

The Numerary documentation is hosted at Read the docs.

License

Numerary is released under the MIT License. See the LICENSE file for details.