N-dimensional integration object.

This object is used to perform n-dimensional integration of a function using different methods.

The integration can be performed using the cubature library. The cubature library is a library for adaptive multidimensional integration. The original code can be found at https://github.com/stevengj/cubature.

To use this object, the user must initialize a child object that implements two functions: get_dimensions and integrand. To do so, the user must first define these two functions as the prototypes described in ncm_integral_nd.h. The get dimensions function should return the dimension of the arguments to be integrated and the function dimension. For instance, if the integrand is given by $F(x,y) = x + y$, the get dimensions function must return $(2,1)$, such that it will compute \begin{align} \int \int F(x, y) dxdy ,\end{align} returning a scalar for the integral evaluated in the given intervals.

This object can also be used with multi-dimensional functions that return an array instead of a scalar. Considering the integrand $F(x,y,z) = [x^2, y+z ]$, the get dimensions method should return $(3,2)$ and the object will compute the integral \begin{align} \int \int \int F(x,y,z) dxdy = [\frac{yzx^3}{3}, frac{x(y^2+z^2)}{2}] \end{align} for the given intervals.

Having the functions, the user must instantiate an object of the type NcmIntegralNDClass defined with these functions. To do so, one must call the macro

NCM_INTEGRAL_ND_DEFINE_TYPE to define the new object type, which

will later be instantiable. Examples of how to define the objects containing the integrand can be found in the test folder under test\textunderscore ncm\textunderscore integral\textunderscore nd.c. For an example of the Python implementation of the integrand in a class, check test\textunderscore py\textunderscore integralnd.py in the same folder. This object cannot be used without the child object containing the cited functions.

After defining the child class with the necessary functions, the user may use the integration object with the preferred method from the cubature library.

The user may provide the input values for: rel_tol - ncm_integral_nd_set_reltol(), abs_tol - ncm_integral_nd_set_abstol(), integ_method - ncm_integral_nd_set_method(), max_eval - ncm_integral_nd_set_maxeval(), error - ncm_integral_nd_set_error(). If these functions are not called, default parameters are chosen.