defint defint_r qag qag_r qags qags_r qng qng_r

qag_r() void qag_r ( 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, double *  xx, double  yy, int *  irev  ) Finite interval adaptive quadrature (15/21/31/41/51/61 point Gauss-Kronrod rule) (reverse communication version) Purpose This routine computes I = integral of f over [a, b], satisfying the requested accuracy, where f is a given function. User should provide the necessary computed values of f according to the argument irev. 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] 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 = -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 reached = 2: Requested tolerance cannot be achieved due to roundoff error = 3: Bad integrand behavior found in the integration interval [out] xx irev = 1 to 15: xx contains the abscissa where the function value should be evaluated and given in the next call. [in] yy irev = 1 to 15: The function value f(xx) should be given in yy in the next call. [in,out] irev Control variable for reverse communication. [in] Before first call, irev should be initialized to zero. On succeeding calls, irev should not be altered. [out] If irev is not zero, complete the following tasks and call this routine again without changing irev. = 0: Computation finished. = 1 to 15: User should set the function value at xx in yy. Do not alter any variables other than yy. Reference SLATEC (QUADPACK)