defint defint_r qag qag_r qags qags_r qng qng_r

qng_r() void qng_r ( double  a, double  b, double  epsabs, double  epsrel, double *  result, double *  abserr, int *  neval, int *  info, double *  xx, double  yy, int *  irev  ) Finite interval automatic quadrature (21/43/87 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. The appropriate one is automatically selected from 21, 43 or 87 point Gauss-Kronrod rules 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. [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] info = 0: Successful exit = 1: The maximum number of steps has been executed. The integral is probably too difficult to be computed by qng_r. [out] xx irev = 1 to 9: xx contains the abscissa where the function value should be evaluated and given in the next call. [in] yy irev = 1 to 9: 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 9: User should set the function value at xx in yy. Do not alter any variables other than yy. Reference SLATEC (QUADPACK)