// 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.qags;


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

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




///
void qags(Real, Func)(Func f, Real a, Real b, 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  dqags
//***date written   800101   (yymmdd)
//***revision date  830518   (yymmdd)
//***category no.  h2a1a1
//***keywords  automatic integrator, general-purpose,
//             (end-point) singularities, extrapolation,
//             globally adaptive
//***author  piessens,robert,appl. math. & progr. div. - k.u.leuven
//           de doncker,elise,appl. math. & prog. div. - k.u.leuven
//***purpose  the routine calculates an approximation result to a given
//            definite integral  i = integral of f over (a,b),
//            hopefully satisfying following claim for accuracy
//            abs(i-result).le.max(epsabs,epsrel*abs(i)).
//***description
//
//        computation of a definite integral
//        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
//
//            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 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 sub-
//                             divisions 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. if
//                             the position of a local difficulty can be
//                             determined (e.g. singularity,
//                             discontinuity within the interval) one
//                             will probably gain from splitting up the
//                             interval at this point and calling the
//                             integrator on the subranges. if possible,
//                             an appropriate special-purpose integrator
//                             should be used, which is designed for
//                             handling the type of difficulty involved.
//                         = 2 the occurrence of roundoff error is detec-
//                             ted, which prevents the requested
//                             tolerance from being achieved.
//                             the error may be under-estimated.
//                         = 3 extremely bad integrand behaviour
//                             occurs at some points of the integration
//                             interval.
//                         = 4 the algorithm does not converge.
//                             roundoff error is detected in the
//                             extrapolation table. it is presumed that
//                             the requested tolerance cannot be
//                             achieved, and that the returned result is
//                             the best which can be obtained.
//                         = 5 the integral is probably divergent, or
//                             slowly convergent. it must be noted that
//                             divergence can occur with any other value
//                             of ier.
//                         = 6 the input is invalid, because
//                             (epsabs.le.0 and
//                              epsrel.lt.max(50*rel.mach.acc.,0.5d-28)
//                             or limit.lt.1 or lenw.lt.limit*4.
//                             result, abserr, neval, last are set to
//                             zero.except when limit or lenw 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.1.
//                    if limit.lt.1, 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, detemines the
//                    number of significant elements actually in the work
//                    arrays.
//
//         work arrays
//            iwork - integer
//                    vector of dimension at least 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 at least 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  dqagse,xerror
//***end prologue  dqags
//
//
      int lvl=1,l1=1,l2=1,l3=1;
//
//         check validity of limit and lenw.
//
//***first executable statement  dqags
      ier = 6;
      neval = 0;
      last = 0;
      result = 0.0;
      abserr = 0.0;
      if(limit < 1 || lenw < limit*4) goto l10;
//
//         prepare call for dqagse.
//
      l1 = limit;
      l2 = limit+l1;
      l3 = limit+l2;
//
      qagse!(Real,Func)(f,a,b,epsabs,epsrel,limit,result,abserr,neval,
        ier,work,work+l1,work+l2,work+l3,iwork,last);
//
//         call error handler if necessary.
//
      lvl = 0;
l10:  if(ier == 6) lvl = 1;
      if(ier != 0)
        throw new Exception("abnormal return from  qags: "~to!string(ier));
      return;
}

unittest
{
    alias qags!(float, float delegate(float)) fqags;
    alias qags!(double, double delegate(double)) dqags;
    alias qags!(double, double function(double)) dfqags;
    alias qags!(real, real delegate(real)) rqags;
}

unittest
{
    double f(double x) { return x<=0.0 ? 0.0 : log(x)/sqrt(x); }

    enum : double
    {
        a = 0.0,
        b = 1.0,
        epsabs = 0.0,
        epsrel = 1e-10
    }
    double result, abserr;
    int neval, ier;
    enum
    {
        limit = 500,
        lenw = 4*limit
    }
    int last;

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

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

    assert (isAccurate(result, abserr, -4.0, epsrel, epsabs));
}