dehint dehint_r deoint deoint_r qagi qagi_r qawf qawf_r qk15i qk15i_r

dehint() void dehint ( double(*)(double)  f, double  a, double  eps, double *  result, int *  neval, int *  l, int *  info  ) Semi-infinite interval automatic quadrature (double exponential (DE) formula) Purpose This routine computes the integral of f(x) over [a, +∞], satisfying the requested accuracy, where f(x) is a given function defined by a user supplied subroutine f. The result is obtained by the automatic integration applying the double exponential (DE) formula. The double exponential (DE) formulas (see defint) for semi-infinite interval [0, +∞] is obtained by using the following transformation functions. (1) φ(t) = exp(t/2 - exp(-t)) (2) φ(t) = exp(t - exp(-t)) (3) φ(t) = exp(2sinh(t)) (1) is suitable for the functions decaying very rapidly such as f(x) = f1(x)exp(-x^2). (2) is suitable for the functions with an exponential factor such as f(x) = f2(x)exp(-x). (3) is used for the slowly decaying rational or algebraic functions. This routine will automatically choose one of the above three functions by examining the behavior of the integrand. The argument l returns which transformation function was used. Parameters [in] f The user supplied subroutine which calculates the integrand function f(x) defined as follows. double f(double x) { return computed f(x) value } [in] a Lower limit of integration. [in] eps Absolute accuracy requested. max(|eps|, 1.0e-32) is used as the tolerance. [out] result Approximation to integral of f(x) over [a, +inf]. [out] neval Number of integrand evaluations. [out] l The mapping function used to integrate. = 0: x = exp(0.5*t-exp(-t)) = 1: x = exp(t-exp(-t)) = 2: x = exp(2*sinh(t)) [out] info = 0: Successful exit = 1: Slow decay on negative side = 2: Slow decay on positive side = 3: Both of above = 4: Insufficient mesh refinement Reference Masatake Mori "FORTRAN77 Numerical Calculation Programming (augmented edition)" Iwanami Shoten, 1987. (Japanese book)