Typically, the user should know something about the function to be integrated and carefully selectĪny method that can handle the second case can be used to handle There many different methods for handling a wide variety of conditions, including integrating over infinite or semi-infinite bounds. Most numerical integration libraries handle the first case, and In the secondĬase, the value of the function to be integrated is only know at some discrete set Of the function to be integrated can be calculated for any argument value. There are two basic types of numerical integration. $ conan search -r cd3 # list all packages To install the library, clone this and checkout the latest release, LibIntegrate is a header-only library that uses CMake for building unit tests and installing. Gauss-Kronrod Quadrature (arbitrary order).Note that the library depends on Boost, and does provide some (incomplete) wrappers to the Boost.Math quadrature functions. Gauss-Legendre Quadrature of order 8, 16, 32, and 64.Riemann sum (the one that every undergrad physics major writes).It is released under a permissive license, so you are free to do whatever you If you need to integrate discretized data and occasionally some simple functions that canīe evaluated, this library may be for you. You should use one of these libraries instead. If you need to integrate a known function with some requirement on accuracy, (actually, not very complete at all), as the Gnu Scientific Library While this library does provide methods for integrating functions that can be evaluated too, they are not nearly asĪs sophisticated (actually, not very sophisticated at all), or complete So this library was created to make using "better" methods on discretized data easy. I noticed that, when needing to integrate some discretized function, I would often just use a Riemann sum and say to myself "I'll come back and use a better method after I get this working", but For non-uniform data, it is a bit more involved. Simpson's rule is simple enough for uniform data, but again requires care at the end of the loop. To index out of range at the end of the loop. Writing the Trapezoid rule isn't difficult either, but you need to be careful not Quickly writing a Riemann sum loop to compute the integral of some discretized function is pretty easy. Higher-order interpolating functions are of course possible, but may not be appropriate, just as fitting high order polynomials Uses a quadratic (second degree polynomial). Riemann sum uses a constant (zero'th order polynomial), the Trapezoid rule uses a linear function (first order polynomial), and the 1/3 Simpson's rule Each of these methods basically interpolate the function over some interval and use the integral of the interpolating function to estimate There is the Riemann sum, the Trapezoid rule, and If the function you need to integrate is already discretized, there are not many options to choose from. Most libraries for numerical integration provide routines for integrating functions that can be evaluated, notįor functions that have already been discretized, and are therefore not suitable for this. In either case, we will have a discrete set of points to use for the integration. Or, we might have a measured spectrum for a broadband source that we need to integrate to compute the total power emitted. If we then want to compute probabilities, we will need to integrate the wavefunction (actually, we will need to integrate the modulus squared of the wavefunction). It is often necessary to integrate functions that have been discretized when doing physics simulations or working withįor example, we might use a finite-difference method to solve Schrodinger's equation and compute the time-evolution of a wavefunction describing some system. Apply lazy transformations to discrete data before integrating.Support for non-uniform discretization.That provide element access with operator(int) or operator()(int) and a method for getting the size (. Handles several common random access, continuous memory container interfacess (std::vector, Eigen::Vector, etc). Integration methods are implemented as classes with operator()(.) methods. Integrate one and two dimensional discretized functions, with Riemann, Trapezoid, and Simpson rules.LibIntegrate is a collection of methods for numerical integration, including discretized data.
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