/* test program... */
int main() {
int i;
double z,w,err;
for (i=0; i<100; i++) {
z=i/100.0-0.3678794411714423215955; w=LambertW(z);
err=exp(w)-z/w;
printf("W(%8.4f)=%22.16f, check: exp(W(z))-z/W(z)=%e\n",z,w,err);
}
for (i=0; i<100; i++) {
z=i/1.0e-1-0.3; w=LambertW(z);
err=exp(w)-z/w;
printf("W(%8.4f)=%22.16f, check: exp(W(z))-z/W(z)=%e\n",z,w,err);
}
return 0;
}
Real
RichardsSeff1BWsmall::seff(std::vector<VariableValue *> p, unsigned int qp) const
{
Real pp = (*p[0])[qp];
if (pp >= 0)
return 1.0;
Real x = (_c - 1)*std::exp(_c - 1 - _c*pp/_las);
Real th = _c/(1 + LambertW(x)); // use branch 0 for positive x
return _sn + (_ss - _sn)*th;
}
int main() {
int i,n=1000;
double w,z,s=0,err;
for (i=1; i<=n; i++) {
z=i/(double)n;
w=LambertW(1/z)/(1+z);
s+=w;
printf("%8.4f %8.4f\n",z,w);
}
fprintf(stderr,"%8.4f\n",exp(s/n/log(2)));
return 0;
}
void
RichardsSeff1BWsmall::d2seff(std::vector<VariableValue *> p, unsigned int qp, std::vector<std::vector<Real> > &result) const
{
result[0][0] = 0.0;
Real pp = (*p[0])[qp];
if (pp >= 0)
return;
Real x = (_c - 1)*std::exp(_c - 1 - _c*pp/_las);
Real lamw = LambertW(x);
result[0][0] = -std::pow(_c, 3)/std::pow(_las, 2)*lamw*(1 - 2*lamw)/std::pow(1 + lamw, 5);
}
void
RichardsSeff1BWsmall::dseff(std::vector<const VariableValue *> p, unsigned int qp, std::vector<Real> &result) const
{
result[0] = 0.0;
Real pp = (*p[0])[qp];
if (pp >= 0)
return;
Real x = (_c - 1)*std::exp(_c - 1 - _c*pp/_las);
Real lamw = LambertW(x);
result[0] = std::pow(_c, 2)/_las*lamw/std::pow(1 + lamw, 3);
}
void
RichardsSeff1BWsmall::d2seff(std::vector<const VariableValue *> p,
unsigned int qp,
std::vector<std::vector<Real>> & result) const
{
result[0][0] = 0.0;
Real pp = (*p[0])[qp];
if (pp >= 0)
return;
Real x = (_c - 1) * std::exp(_c - 1 - _c * pp / _las);
Real lamw = LambertW(x);
result[0][0] = -Utility::pow<3>(_c) / Utility::pow<2>(_las) * lamw * (1.0 - 2.0 * lamw) /
Utility::pow<5>(1 + lamw);
}