defint defint_r qag qag_r qags qags_r qng qng_r

qag() void qag ( double(*)(double)  f, double  a, double  b, double  epsabs, double  epsrel, int  key, int  limit, double *  result, double *  abserr, int *  neval, int *  last, double  work[], int  lwork, int  iwork[], int *  info  ) Finite interval adaptive quadrature (15/21/31/41/51/61 point Gauss-Kronrod rule) Purpose This routine computes I = integral of f over [a, b], satisfying the requested accuracy, where f is a given function defined by a user supplied subroutine. 15, 21, 31, 41, 51 or 61 point Gauss-Kronrod rule is used, and the integration interval will be adaptively subdivided to satisfy the requested accuracy. 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] b Upper limit of integration. [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] key Key for choice of local integration rule. = 1: qk15 = 2: qk21 = 3: qk31 = 4: qk41 = 5: qk51 = 6: qk61 If key < 1, key = 1 is assumed. If key > 6, key = 6 is assumed. [in] limit Maximum number of subintervals in the partition of the given integration interval [a, b]. (limit >= 1) [out] result Approximation to I = integral of f over [a, b]. [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 in the partition of [a, b]. 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 = -7: The argument limit had an illegal value (limit < 1) = -13: The argument lwork had an illegal value (lwork < 4*limit) = 1: Maximum number of subdivisions allowed has been reached = 2: Requested tolerance cannot be achieved due to roundoff error = 3: Bad integrand behavior found in the integration interval Reference SLATEC (QUADPACK)