// This code has been mechanically translated from the original FORTRAN
// code at http://netlib.org/quadpack.

/** Authors:    Lars Tandle Kyllingstad
    Copyright:  Copyright (c) 2009, Lars T. Kyllingstad. All rights reserved.
    License:    Boost License 1.0
*/
module scid.ports.quadpack.qaws;


import std.conv;
import scid.ports.quadpack.qawse;

version(unittest)
{
    import std.math;
    import scid.core.testing;
}




///
void qaws(Real, Func)(Func f, Real a, Real b, Real alfa, Real beta,
    int integr, Real epsabs, Real epsrel, out Real result, out Real abserr,
    out int neval, out int ier, int limit, int lenw, out int last,
    int* iwork, Real* work)
{
//***begin prologue  dqaws
//***date written   800101   (yymmdd)
//***revision date  830518   (yymmdd)
//***category no.  h2a2a1
//***keywords  automatic integrator, special-purpose,
//             algebraico-logarithmic end-point singularities,
//             clenshaw-curtis, globally adaptive
//***author  piessens,robert,appl. math. & progr. div. -k.u.leuven
//           de doncker,elise,appl. math. & progr. div. - k.u.leuven
//***purpose  the routine calculates an approximation result to a given
//            definite integral i = integral of f*w over (a,b),
//            (where w shows a singular behaviour at the end points
//            see parameter integr).
//            hopefully satisfying following claim for accuracy
//            abs(i-result).le.max(epsabs,epsrel*abs(i)).
//***description
//
//        integration of functions having algebraico-logarithmic
//        end point singularities
//        standard fortran subroutine
//        double precision version
//
//        parameters
//         on entry
//            f      - double precision
//                     function subprogram defining the integrand
//                     function f(x). the actual name for f needs to be
//                     declared e x t e r n a l in the driver program.
//
//            a      - double precision
//                     lower limit of integration
//
//            b      - double precision
//                     upper limit of integration, b.gt.a
//                     if b.le.a, the routine will end with ier = 6.
//
//            alfa   - double precision
//                     parameter in the integrand function, alfa.gt.(-1)
//                     if alfa.le.(-1), the routine will end with
//                     ier = 6.
//
//            beta   - double precision
//                     parameter in the integrand function, beta.gt.(-1)
//                     if beta.le.(-1), the routine will end with
//                     ier = 6.
//
//            integr - integer
//                     indicates which weight function is to be used
//                     = 1  (x-a)**alfa*(b-x)**beta
//                     = 2  (x-a)**alfa*(b-x)**beta*log(x-a)
//                     = 3  (x-a)**alfa*(b-x)**beta*log(b-x)
//                     = 4  (x-a)**alfa*(b-x)**beta*log(x-a)*log(b-x)
//                     if integr.lt.1 or integr.gt.4, the routine
//                     will end with ier = 6.
//
//            epsabs - double precision
//                     absolute accuracy requested
//            epsrel - double precision
//                     relative accuracy requested
//                     if  epsabs.le.0
//                     and epsrel.lt.max(50*rel.mach.acc.,0.5d-28),
//                     the routine will end with ier = 6.
//
//         on return
//            result - double precision
//                     approximation to the integral
//
//            abserr - double precision
//                     estimate of the modulus of the absolute error,
//                     which should equal or exceed abs(i-result)
//
//            neval  - integer
//                     number of integrand evaluations
//
//            ier    - integer
//                     ier = 0 normal and reliable termination of the
//                             routine. it is assumed that the requested
//                             accuracy has been achieved.
//                     ier.gt.0 abnormal termination of the routine
//                             the estimates for the integral and error
//                             are less reliable. it is assumed that the
//                             requested accuracy has not been achieved.
//            error messages
//                     ier = 1 maximum number of subdivisions allowed
//                             has been achieved. one can allow more
//                             subdivisions by increasing the value of
//                             limit (and taking the according dimension
//                             adjustments into account). however, if
//                             this yields no improvement it is advised
//                             to analyze the integrand, in order to
//                             determine the integration difficulties
//                             which prevent the requested tolerance from
//                             being achieved. in case of a jump
//                             discontinuity or a local singularity
//                             of algebraico-logarithmic type at one or
//                             more interior points of the integration
//                             range, one should proceed by splitting up
//                             the interval at these points and calling
//                             the integrator on the subranges.
//                         = 2 the occurrence of roundoff error is
//                             detected, which prevents the requested
//                             tolerance from being achieved.
//                         = 3 extremely bad integrand behaviour occurs
//                             at some points of the integration
//                             interval.
//                         = 6 the input is invalid, because
//                             b.le.a or alfa.le.(-1) or beta.le.(-1) or
//                             or integr.lt.1 or integr.gt.4 or
//                             (epsabs.le.0 and
//                              epsrel.lt.max(50*rel.mach.acc.,0.5d-28))
//                             or limit.lt.2 or lenw.lt.limit*4.
//                             result, abserr, neval, last are set to
//                             zero. except when lenw or limit is invalid
//                             iwork(1), work(limit*2+1) and
//                             work(limit*3+1) are set to zero, work(1)
//                             is set to a and work(limit+1) to b.
//
//         dimensioning parameters
//            limit  - integer
//                     dimensioning parameter for iwork
//                     limit determines the maximum number of
//                     subintervals in the partition of the given
//                     integration interval (a,b), limit.ge.2.
//                     if limit.lt.2, the routine will end with ier = 6.
//
//            lenw   - integer
//                     dimensioning parameter for work
//                     lenw must be at least limit*4.
//                     if lenw.lt.limit*4, the routine will end
//                     with ier = 6.
//
//            last   - integer
//                     on return, last equals the number of
//                     subintervals produced in the subdivision process,
//                     which determines the significant number of
//                     elements actually in the work arrays.
//
//         work arrays
//            iwork  - integer
//                     vector of dimension limit, the first k
//                     elements of which contain pointers
//                     to the error estimates over the subintervals,
//                     such that work(limit*3+iwork(1)), ...,
//                     work(limit*3+iwork(k)) form a decreasing
//                     sequence with k = last if last.le.(limit/2+2),
//                     and k = limit+1-last otherwise
//
//            work   - double precision
//                     vector of dimension lenw
//                     on return
//                     work(1), ..., work(last) contain the left
//                      end points of the subintervals in the
//                      partition of (a,b),
//                     work(limit+1), ..., work(limit+last) contain
//                      the right end points,
//                     work(limit*2+1), ..., work(limit*2+last)
//                      contain the integral approximations over
//                      the subintervals,
//                     work(limit*3+1), ..., work(limit*3+last)
//                      contain the error estimates.
//
//***references  (none)
//***routines called  dqawse,xerror
//***end prologue  dqaws
//
      int l1,l2,l3;
//
//         check validity of limit and lenw.
//
//***first executable statement  dqaws
      ier = 6;
      neval = 0;
      last = 0;
      result = 0.0;
      abserr = 0.0;
      if(limit < 2 || lenw < limit*4) goto l10;
//
//         prepare call for dqawse.
//
      l1 = limit;
      l2 = limit+l1;
      l3 = limit+l2;
//
      qawse!(Real,Func)(f,a,b,alfa,beta,integr,epsabs,epsrel,limit,result,
        abserr,neval,ier,work,work+l1,work+l2,work+l3,iwork,last);
//
//         call error handler if necessary.
//
l10:  if(ier != 0)
        throw new Exception("abnormal return from qaws: "~to!string(ier));
      return;
}

unittest
{
    alias qaws!(float, float delegate(float)) fqaws;
    alias qaws!(double, double delegate(double)) dqaws;
    alias qaws!(double, double function(double)) dfqaws;
    alias qaws!(real, real delegate(real)) rqaws;
}

unittest
{
    // From QUADPACK book
    double f(double x)
    {
        if (x <= 0.0) return 0.0;
        double logx2 = log(x)^^2;
        return (1+logx2)^^(-2.0);
    }

    double a = 0.0, b = 1.0, alfa = 0.0, beta = 0.0;
    int integr = 2, neval, ier, last;
    double epsabs = 0.0, epsrel = 1e-8;
    double result, abserr;
    enum
    {
        limit = 500,
        lenw = 4*limit
    }

    int[limit] iwork;
    double[lenw] work;

    qaws(&f, a, b, alfa, beta, integr, epsabs, epsrel, result, abserr,
        neval, ier, limit, lenw, last, iwork.ptr, work.ptr);

    double ans = -0.18927518788;
    assert (isAccurate(result, abserr, ans, epsrel, epsabs));
}