Integration

Numerical integration for Ruby, with a simple interface. Several different integration methods are implemented.

$ gem install integration

You can install GSL (please use your package manager) for better performance and support for infinite bounds. After successfully installing the library:

$ gem install rb-gsl

You can see the latest documentation for Integration at Rubydoc: rubydoc.info/github/sciruby/integration.

• Use only one method: Integration.integrate
• Rectangular, Trapezoidal, Simpson, Adaptive quadrature, Monte Carlo and Romberg integration methods available on pure Ruby.
• If available, uses Ruby/GSL QNG non-adaptive Gauss-Kronrod integration and QAG adaptive integration, with support for Infinity+ and Infinity-

# Integrate x^2 in [1, 2] using Simpson's rule.
Integration.integrate(1, 2, tolerance: 1e-10, method: :simpson) do |x|
  x**2
end
# => 2.333333

# Support for infinity bounds with GSL QAG adaptative integration.

normal_pdf = lambda do |x|
  (1 / Math.sqrt(2 * Math::PI)) * Math.exp(-0.5 * (x**2))
end

Integration.integrate(Integration::MInfinity, 0, tolerance: 1e-10, &normal_pdf) # => 0.5
Integration.integrate(0, Integration::Infinity , tolerance: 1e-10, &normal_pdf) # => 0.5

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