dehint dehint_r deoint deoint_r qagi qagi_r qawf qawf_r qk15i qk15i_r

qk15i_r() void qk15i_r ( double  bound, int  inf, double  a, double  b, double *  result, double *  abserr, double *  resabs, double *  resasc, double *  xx, double  yy, int *  irev  ) Semi-infinite/infinite interval quadrature (15-point Gauss-Kronrod rule) (reverse communication version) Purpose The routine computes an approximation to the integral of function f(x) over a semi-infinite or infinite interval with the 15 point Gauss-Kronrod rule. The integrand f(x) is computed and provided by the user in accordance with irev. The function f(x) is transformed to the function f01(t) so that the semi-infinite integration is obtained by computing the finite integration over [0, 1]. ∫ f(x)dx [bound, +∞] = ∫ f01(t)dt [0, 1] where f01(t) = f(bound + (1 - t)/t)/t^2 The infinite integral is computed as the sum of two semi-infinite integrals. ∫ f(x)dx [-∞, +∞] = ∫ (f(x) + f(-x)) dx [0, +∞] This routine computes   I = integral of f01 over [a, b] with error estimate, and   J = integral of abs(f01) over [a, b], where [a, b] is a part of [0, 1]. Parameters [in] bound The finite bound of original integration range. (Not referenced if interval is doubly infinite (inf = 2)) [in] inf The kind of original integration range. = 1: Semi-infinite integral [bound, +∞] = -1: Semi-infinite integral [-∞, bound] = 2: Infinite integral [-∞, +∞] (If other value is specified, inf = 2 is assumed) [in] a Lower limit of transformed interval. (0 <= a <= 1) [in] b Upper limit of transformed interval. (0 <= b <= 1) [out] result Approximation to I = integral of f01 over [a, b]. [out] abserr Estimate of the modulus of the absolute error, which should equal or exceed the true error. [out] resabs Approximation to J = integral of abs(f01) over [a, b]. [out] resasc Approximation to the integral of abs(f01 - I/(b - a)) over [a, b]. [out] xx irev = 1 to 6: xx contains the abscissa where the function value should be evaluated and given in the next call. [in] yy irev = 1 to 6: 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 6: User should set the function value at xx in yy. Do not alter any variables other than yy. Reference SLATEC (QUADPACK)