qag qagi qk15

qk15() def qk15 ( f  , a  , b    ) Finite interval quadrature (15 point Gauss-Kronrod rule) Purpose This routine computes   I = integral of f over [a, b] with error estimate, and   J = integral of abs(f) over [a, b], where f is a given function defined by a user supplied subroutine. The integral will be evaluated with the 15 point Gauss-Kronrod rule. Returns (result, abserr) result (float): Approximation to I = integral of f over [a, b]. abserr (float): Estimate of the modulus of the absolute error, which should equal or exceed the true error. Parameters [in] f The user supplied subroutine which calculates the integrand function f(x) defined as follows. _CODE def f(x): return computed function value f(x) _ENDCODE [in] a Lower limit of integration. [in] b Upper limit of integration. Reference SLATEC (QUADPACK) Example Program Compute the following integral. ∫ 1/(1 + x^2) dx [0, 4] (= atan(4)) def f(x): return 1/(1 + x**2) def TestQk15(): a = 0 b = 4 s, abserr = qk15(f, a, b) print(s, abserr) Example Results >>> TestQk15() 1.3258176613637855 0.0014827239412162237