dehint dehint_r deoint deoint_r qagi qagi_r qawf qawf_r qk15i qk15i_r

qagi() void qagi ( double(*)(double)  f, double  bound, int  inf, double  epsabs, double  epsrel, int  limit, double *  result, double *  abserr, int *  neval, int *  last, double  work[], int  lwork, int  iwork[], int *  info  ) Semi-infinite/infinite interval adaptive quadrature (15-point Gauss-Kronrod rule) Purpose This routine computes I = integral of f(x) over [bound, +inf], [-inf, bound] or [-inf, +inf], satisfying the requested accuracy, where f(x) is a given function defined by a user supplied subroutine. 15-point Gauss-Kronrod rule is used, and the integration interval will be adaptively subdivided to satisfy the requested accuracy. The semi-infinite integration range is mapped onto the interval [0, 1], and then the integration rule is applied to compute the required integral. ∫ f(x)dx [bound, +∞] = ∫ f(bound + (1 - t)/t) / t^2 dt [0, 1] The infinite integral will be computed as the sum of two semi-infinite integrals. ∫ f(x)dx [-∞, +∞] = ∫ (f(x) + f(-x)) dx [0, +∞] 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] bound The finite bound of original integration range. (Not referenced if interval is doubly infinite (inf = 2)) [in] inf The kind of integration range. = 1: Semi-infinite integral [bound, +∞] = -1: Semi-infinite integral [-∞, bound] = 2: Infinite integral [-∞, +∞] (If other value is specified, inf = 2 is assumed) [in] epsabs Absolute accuracy requested. The requested accuracy is assumed to be satisfied if abserr <= max(epsabs, epsrel*|result|)). [in] epsrel Relative accuracy requested. The requested accuracy is assumed to be satisfied if abserr <= max(epsabs, epsrel*|result|)). If epsabs <= 0 and epsrel < 50*eps, epsrel is assumed to be 50*eps, where eps is the machine precision. [in] limit Maximum number of subintervals in the partition of the given integration interval. (limit >= 1) [out] result Approximation to the integral. [out] abserr Estimate of the modulus of the absolute error, which should equal or exceed the true error. [out] neval Number of integrand evaluations. [out] last Number of subintervals produced in the subdivision process. [out] work[] Array work[lwork] Work array. work[0], ..., work[last-1]: Left end points of the subintervals work[limit], ..., work[limit+last-1]: Right end poits of the subintervals. work[2*limit], ..., work[2*limit+last-1]: The integral approximations over the subintervals. work[3*limit], ..., work[3*limit+last-1]: The error estimates over the subintervals. [in] lwork The length of work[]. (lwork >= 4*limit) [out] iwork[] Array iwork[liwork] (liwork >= limit) Work array. The first k elements contain pointers to the error estimates over the subintervals, such that work[3*limit+iwork[0]-1], ..., work[3*limit+iwork[k-1]-1] form a decreasing sequence with k = last if last <= limit/2+2, and k = limit+1-last otherwise. [out] info = 0: Successful exit = -6: The argument limit had an illegal value (limit < 1) = -12: The argument lwork had an illegal value (lwork < 4*limit) = 1: Maximum number of subdivisions allowed has been achieved = 2: The occurrence of roundoff error is detected, which prevents the requested tolerance from being achieved = 3: Extremely bad integrand behavior occurs at some points of the integration interval = 4: The algorithm does not converge. It is presumed that the requested tolerance cannot be achieved, and that the returned result is the best which can be obtained = 5: The integral is probably divergent, or slowly convergent Reference SLATEC (QUADPACK)