deiint deiint_r

deiint() void deiint ( double(*)(double)  f, double  eps, double *  result, int *  neval, int *  info  ) Infinite interval automatic quadrature (double exponential (DE) formula) Purpose This routine computes the integral of f(x) over [-∞, +∞], 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 infinite interval [-∞, +∞] is obtained by using the following transformation function. φ(t) = sinh((π/2)sinh(t)) This formula is suitable for the slowly decaying functions. 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] eps Absolute accuracy requested. max(|eps|, 1.0e-32) is used as the tolerance. [out] result Approximation to integral of f(x) over [-inf, +inf]. [out] neval Number of integrand evaluations. [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)