qk15 qk15_r qk21 qk21_r qk31 qk31_r qk41 qk41_r qk51 qk51_r qk61 qk61_r

qk15_r() void qk15_r ( double  a, double  b, double *  result, double *  abserr, double *  resabs, double *  resasc, double *  xx, double  yy, int *  irev  ) Finite interval quadrature (15 point Gauss-Kronrod rule) (reverse communication version) Purpose This routine computes   I = integral of f over [a, b] with error estimate, and   J = integral of abs(f) over [a, b], where f is a given function. User should provide the necessary computed values of f according to the argument irev. The integral will be evaluated with the 15 point Gauss-Kronrod rule. Parameters [in] a Lower limit of integration. [in] b Upper limit of integration. [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] resabs Approximation to J = integral of abs(f) over [a, b]. [out] resasc Approximation to the integral of abs(f - I/(b - a)) over [a, b]. [out] xx irev = 1 to 5: xx contains the abscissa where the function value should be evaluated and given in the next call. [in] yy irev = 1 to 5: 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 5: User should set the function value at xx in yy. Do not alter any variables other than yy. Reference SLATEC (QUADPACK)