      recursive subroutine dqk15w(f,w,p1,p2,p3,p4,kp,a,b,result,abserr,
     *   resabs,resasc)
c***begin prologue  dqk15w
c***date written   810101   (yymmdd)
c***revision date  830518   (mmddyy)
c***category no.  h2a2a2
c***keywords  15-point gauss-kronrod rules
c***author  piessens,robert,appl. math. & progr. div. - k.u.leuven
c           de doncker,elise,appl. math. & progr. div. - k.u.leuven
c***purpose  to compute i = integral of f*w over (a,b), with error
c                           estimate
c                       j = integral of abs(f*w) over (a,b)
c***description
c
c           integration rules
c           standard fortran subroutine
c           double precision version
c
c           parameters
c             on entry
c              f      - double precision
c                       function subprogram defining the integrand
c                       function f(x). the actual name for f needs to be
c                       declared e x t e r n a l in the driver program.
c
c              w      - double precision
c                       function subprogram defining the integrand
c                       weight function w(x). the actual name for w
c                       needs to be declared e x t e r n a l in the
c                       calling program.
c
c              p1, p2, p3, p4 - double precision
c                       parameters in the weight function
c
c              kp     - integer
c                       key for indicating the type of weight function
c
c              a      - double precision
c                       lower limit of integration
c
c              b      - double precision
c                       upper limit of integration
c
c            on return
c              result - double precision
c                       approximation to the integral i
c                       result is computed by applying the 15-point
c                       kronrod rule (resk) obtained by optimal addition
c                       of abscissae to the 7-point gauss rule (resg).
c
c              abserr - double precision
c                       estimate of the modulus of the absolute error,
c                       which should equal or exceed abs(i-result)
c
c              resabs - double precision
c                       approximation to the integral of abs(f)
c
c              resasc - double precision
c                       approximation to the integral of abs(f-i/(b-a))
c
c
c***references  (none)
c***routines called  d1mach
c***end prologue  dqk15w
c
      double precision a,absc,absc1,absc2,abserr,b,centr,dabs,dhlgth,
     *  dmax1,dmin1,d1mach,epmach,f,fc,fsum,fval1,fval2,fv1,fv2,hlgth,
     *  p1,p2,p3,p4,resabs,resasc,resg,resk,reskh,result,uflow,w,wg,wgk,
     *  xgk
      integer j,jtw,jtwm1,kp
      external f,w
c
      dimension fv1(7),fv2(7),xgk(8),wgk(8),wg(4)
c
c           the abscissae and weights are given for the interval (-1,1).
c           because of symmetry only the positive abscissae and their
c           corresponding weights are given.
c
c           xgk    - abscissae of the 15-point gauss-kronrod rule
c                    xgk(2), xgk(4), ... abscissae of the 7-point
c                    gauss rule
c                    xgk(1), xgk(3), ... abscissae which are optimally
c                    added to the 7-point gauss rule
c
c           wgk    - weights of the 15-point gauss-kronrod rule
c
c           wg     - weights of the 7-point gauss rule
c
      data xgk(1),xgk(2),xgk(3),xgk(4),xgk(5),xgk(6),xgk(7),xgk(8)/
     *     0.9914553711208126d+00,     0.9491079123427585d+00,
     *     0.8648644233597691d+00,     0.7415311855993944d+00,
     *     0.5860872354676911d+00,     0.4058451513773972d+00,
     *     0.2077849550078985d+00,     0.0000000000000000d+00/
c
      data wgk(1),wgk(2),wgk(3),wgk(4),wgk(5),wgk(6),wgk(7),wgk(8)/
     *     0.2293532201052922d-01,     0.6309209262997855d-01,
     *     0.1047900103222502d+00,     0.1406532597155259d+00,
     *     0.1690047266392679d+00,     0.1903505780647854d+00,
     *     0.2044329400752989d+00,     0.2094821410847278d+00/
c
      data wg(1),wg(2),wg(3),wg(4)/
     *     0.1294849661688697d+00,    0.2797053914892767d+00,
     *     0.3818300505051189d+00,    0.4179591836734694d+00/
c
c
c           list of major variables
c           -----------------------
c
c           centr  - mid point of the interval
c           hlgth  - half-length of the interval
c           absc*  - abscissa
c           fval*  - function value
c           resg   - result of the 7-point gauss formula
c           resk   - result of the 15-point kronrod formula
c           reskh  - approximation to the mean value of f*w over (a,b),
c                    i.e. to i/(b-a)
c
c           machine dependent constants
c           ---------------------------
c
c           epmach is the largest relative spacing.
c           uflow is the smallest positive magnitude.
c
c***first executable statement  dqk15w
      epmach = d1mach(4)
      uflow = d1mach(1)
c
      centr = 0.5d+00*(a+b)
      hlgth = 0.5d+00*(b-a)
      dhlgth = dabs(hlgth)
c
c           compute the 15-point kronrod approximation to the
c           integral, and estimate the error.
c
      fc = f(centr)*w(centr,p1,p2,p3,p4,kp)
      resg = wg(4)*fc
      resk = wgk(8)*fc
      resabs = dabs(resk)
      do 10 j=1,3
        jtw = j*2
        absc = hlgth*xgk(jtw)
        absc1 = centr-absc
        absc2 = centr+absc
        fval1 = f(absc1)*w(absc1,p1,p2,p3,p4,kp)
        fval2 = f(absc2)*w(absc2,p1,p2,p3,p4,kp)
        fv1(jtw) = fval1
        fv2(jtw) = fval2
        fsum = fval1+fval2
        resg = resg+wg(j)*fsum
        resk = resk+wgk(jtw)*fsum
        resabs = resabs+wgk(jtw)*(dabs(fval1)+dabs(fval2))
   10 continue
      do 15 j=1,4
        jtwm1 = j*2-1
        absc = hlgth*xgk(jtwm1)
        absc1 = centr-absc
        absc2 = centr+absc
        fval1 = f(absc1)*w(absc1,p1,p2,p3,p4,kp)
        fval2 = f(absc2)*w(absc2,p1,p2,p3,p4,kp)
        fv1(jtwm1) = fval1
        fv2(jtwm1) = fval2
        fsum = fval1+fval2
        resk = resk+wgk(jtwm1)*fsum
        resabs = resabs+wgk(jtwm1)*(dabs(fval1)+dabs(fval2))
   15 continue
      reskh = resk*0.5d+00
      resasc = wgk(8)*dabs(fc-reskh)
      do 20 j=1,7
        resasc = resasc+wgk(j)*(dabs(fv1(j)-reskh)+dabs(fv2(j)-reskh))
   20 continue
      result = resk*hlgth
      resabs = resabs*dhlgth
      resasc = resasc*dhlgth
      abserr = dabs((resk-resg)*hlgth)
      if(resasc.ne.0.0d+00.and.abserr.ne.0.0d+00)
     *  abserr = resasc*dmin1(0.1d+01,(0.2d+03*abserr/resasc)**1.5d+00)
      if(resabs.gt.uflow/(0.5d+02*epmach)) abserr = dmax1((epmach*
     *  0.5d+02)*resabs,abserr)
      return
      end
