double Ln_Gamma_Function(double x)
{
// For a positive argument, 0 < x <= Gamma_Function_Max_Arg() //
// then return log Gamma(x). //
if (x <= Gamma_Function_Max_Arg()) return log(Gamma_Function(x));
// otherwise return result from asymptotic expansion of ln Gamma(x). //
return (double) xLnGamma_Asymptotic_Expansion( (long double) x );
}
void Gamma_Distribution_Tables(double a, double start, double delta,
int nsteps, double *density, double* distribution_function)
{
double x = start;
int i;
for (i = 0; i <= nsteps; i++) {
if (x <= 0.0) {
density[i] = 0.0;
distribution_function[i] = 0.0;
}
else {
if (a <= Gamma_Function_Max_Arg() )
density[i] = pow(x,a-1.0) * exp(-x) / Gamma_Function(a);
else density[i] = exp( (a - 1.0) * log(x) - x - Ln_Gamma_Function(a) );
distribution_function[i] = Entire_Incomplete_Gamma_Function(x,a);
}
x += delta;
}
}
bool computeRootDensity(Crit3DCrop* myCrop, soil::Crit3DLayer* layers, int nrLayers, double soilDepth)
{
int i, j, layer;
// Initialize
for (i=0; i<nrLayers; i++)
myCrop->roots.rootDensity[i]=0.0;
if ((! myCrop->isLiving) || (myCrop->roots.rootLength <= 0 )) return true;
if ((myCrop->roots.rootShape == CARDIOID_DISTRIBUTION) || (myCrop->roots.rootShape == CYLINDRICAL_DISTRIBUTION))
{
double minimumThickness;
int *atoms = (int *) calloc(nrLayers, sizeof(int));
int numberOfRootedLayers, numberOfTopUnrootedLayers, totalLayers;
totalLayers = root::nrAtoms(layers, nrLayers, myCrop->roots.rootDepthMin, &minimumThickness, atoms);
numberOfTopUnrootedLayers = int(round(myCrop->roots.rootDepthMin / minimumThickness));
numberOfRootedLayers = int(ceil(minValue(myCrop->roots.rootLength, soilDepth) / minimumThickness));
double *densityThinLayers = (double *) calloc(totalLayers+1, sizeof(double));
densityThinLayers[totalLayers] = 0.;
for (i=0; i < totalLayers; i++)
densityThinLayers[i] = 0.;
if (myCrop->roots.rootShape == CARDIOID_DISTRIBUTION)
{
cardioidDistribution(myCrop->roots.shapeDeformation, numberOfRootedLayers,
numberOfTopUnrootedLayers, totalLayers, densityThinLayers);
}
else if (myCrop->roots.rootShape == CYLINDRICAL_DISTRIBUTION)
{
cylindricalDistribution(myCrop->roots.shapeDeformation, numberOfRootedLayers,
numberOfTopUnrootedLayers, totalLayers, densityThinLayers);
}
int counter =0;
for (layer=0; layer<nrLayers; layer++)
{
for (j=counter; j<counter + atoms[layer]; j++)
{
if (j < totalLayers)
myCrop->roots.rootDensity[layer] += densityThinLayers[j];
}
counter = j;
}
free(atoms);
free(densityThinLayers);
}
else if (myCrop->roots.rootShape == GAMMA_DISTRIBUTION)
{
double normalizationFactor ;
double kappa, theta,a,b;
double mean, mode;
mean = myCrop->roots.rootLength * 0.5;
mode = myCrop->roots.rootLength * 0.2;
theta = mean - mode;
kappa = mean / theta;
// complete gamma function
normalizationFactor = Gamma_Function(kappa);
for (i=1 ; i<nrLayers ; i++)
{
b = maxValue(layers[i].depth + layers[i].thickness*0.5 - myCrop->roots.rootDepthMin,0); // right extreme
if (b>0)
{
a = maxValue(layers[i].depth - layers[i].thickness*0.5 - myCrop->roots.rootDepthMin,0); //left extreme
myCrop->roots.rootDensity[i] = Incomplete_Gamma_Function(b/theta,kappa) - Incomplete_Gamma_Function(a/theta,kappa);
myCrop->roots.rootDensity[i] /= normalizationFactor;
}
}
}
double rootDensitySum = 0. ;
for (i=0 ; i<nrLayers ; i++)
{
myCrop->roots.rootDensity[i] *= layers[i].soilFraction;
rootDensitySum += myCrop->roots.rootDensity[i];
}
for (i=0 ; i<nrLayers ; i++)
{
myCrop->roots.rootDensity[i] /= rootDensitySum;
}
myCrop->roots.firstRootLayer = 0;
layer = 0;
while ((myCrop->roots.rootDensity[layer] == 0)
&& (layer < nrLayers))
{
layer++;
(myCrop->roots.firstRootLayer)++;
}
myCrop->roots.lastRootLayer = myCrop->roots.firstRootLayer;
while ((myCrop->roots.rootDensity[layer] != 0)
&& (layer < nrLayers))
{
(myCrop->roots.lastRootLayer) = layer;
layer++;
}
return true;
}
