dehint dehint_r deoint deoint_r qagi qagi_r qawf qawf_r qk15i qk15i_r

qawf_r() void qawf_r ( double  a, double  omega, int  integr, double  epsabs, int  limlst, int  limit, int  maxp1, double *  result, double *  abserr, int *  neval, int *  lst, double  work[], int  lwork, int  iwork[], int  liwork, int *  info, double *  xx, double  yy, int *  irev  ) Semi-infinite interval adaptive quadrature for Fourier integrals (25-point Clenshaw-Curtis and 15-point Gauss-Kronrod rule) (reverse communication version) Purpose The routine calculates an approximation result to a Fourier integral I = ∫ f(x)*w(x) dx over [a, +∞] satisfying the requested accuracy, where the weight function w(x) = cos(ω*x) or sin(ω*x). Result is obtained by the adaptive integration applying a 25-point modified Clenshaw-Curtis rule and a 15-point Gauss-Kronrod rule to satisfy the requested accuracy. Parameters [in] a Lower limit of integration. [in] omega Parameter ω in the weight function. [in] integr Indicates which weight function is to be used. = 1: w(x) = cos(ω*x) = 2: w(x) = sin(ω*x) [in] epsabs Absolute accuracy requested. (epsabs > 0) [in] limlst Upper bound on the number of cycles. (limlst >= 3) [in] limit Upper bound on the subintervals allowed in the partition of each cycle. (limit >= 1) [in] maxp1 Upper bound on the number of Chebyshev moments which can be stored. (maxp1 >= 1) For the intervals of lengths abs(b-a)*2^(-L), L = 0, 1, ..., maxp1-2. [out] result Approximation to I = integral of f(x)*w(x) over [a, +∞]. [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] lst Number of cycles actually needed for the integration. [out] work[] Array work[lwork] Work array. work[0], ..., work[lst-1]: The integral approximations over the cycles. work[limlst], ..., work[limlst+lst-1]: The error estimates over the cycles. Further elements of work[] have no specific meaning for the user. [in] lwork The length of work[]. (lwork >= 2*limlst + 4*limit + 25*maxp1) [out] iwork[] Array iwork[liwork] Work array. iwork[k] for k = 0, 1, ..., lst-1 contain the error flags on the cycles. [in] liwork The length of iwork[]. (liwork >= limlst + 2*limit) [out] info = 0: Successful exit = -3: The argument integr had an illegal value (integr != 1 and integr != 2) = -4: The argument epsabs had an illegal value (epsabs <= 0) = -5: The argument limlst had an illegal value (limlst < 3) = -6: The argument limit had an illegal value (limit < 1) = -7: The argument maxp1 had an illegal value (maxp1 < 1) = -13: The argument lwork had an illegal value (lwork < 2*limlst + 4*limit + 25*maxp1) = -15: The argument liwork had an illegal value (lwork < limlst + 2*limit) = 1: Maximum number of cycles allowed has been reached = 4: The extrapolation table does not converge to within the requested accuracy = 7: Bad integrand behaviour occurs within one or more of the cycles [out] xx irev = 1 to 48: xx contains the abscissa where the function value should be evaluated and given in the next call. [in] yy irev = 1 to 48: 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 48: User should set the function value at xx in yy. Do not alter any variables other than yy. Reference SLATEC (QUADPACK)