qagp qagp_r qawc qawc_r qawo qawo_r qaws qaws_r

qawo_r() void qawo_r ( double  a, double  b, double  omega, int  integr, double  epsabs, double  epsrel, int  limit, int  maxp1, double *  result, double *  abserr, int *  neval, int *  last, double  work[], int  lwork, int  iwork[], int  liwork, int *  info, double *  xx, double  yy, int *  irev  ) Finite interval adaptive quadrature for oscillatory functions (25-point Clenshaw-Curtis and 15-point Gauss-Kronrod rule) (reverse communication version) Purpose The routine calculates an approximation result to a definite integral I = integral of f(x)*w(x) over [a, b] 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] b Upper 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. 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 [a, b]. (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, 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. work[4*limit], ..., work[4*limit+25*maxp1-1]: Space for storing the Chebyshev moments. [in] lwork The length of work[]. (lwork >= 4*limit + 25*maxp1) [out] iwork[] Array iwork[liwork] 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. iwork[limit], ..., iwork[limit+last-1] indicate the subdivision levels of the subintervals, such that iwork[limit+i-1] = L means that the subinterval numbered i is of length abs(b-a)*2^(1-L). [in] liwork The length of iwork[]. (liwork >= 2*limit) [out] info = 0: Successful exit = -4: The argument integr had an illegal value (integr != 1 and integr != 2) = -7: The argument limit had an illegal value (limit < 1) = -8: The argument maxp1 had an illegal value (maxp1 < 1) = -14: The argument lwork had an illegal value (lwork < 4*limit + 25*maxp1) = -16: The argument liwork had an illegal value (lwork < 2*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 = 4: Algorithm does not converge due to the roundoff error in the extrapolation table = 5: The integral is probably divergent, or slowly convergent [out] xx irev = 1 to 30: xx contains the abscissa where the function value should be evaluated and given in the next call. [in] yy irev = 1 to 30: 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 30: User should set the function value at xx in yy. Do not alter any variables other than yy. Reference SLATEC (QUADPACK)