ExplicitEquation::FitError ExplicitEquation::Fit(DataSource &series, double &r2) {
r2 = 0;
if (series.IsExplicit() || series.IsParam())
return InadequateDataSource;
if (series.GetCount() < coeff.GetCount())
return SmallDataSource;
ptrdiff_t numUnknowns = coeff.GetCount();
VectorXd x(numUnknowns);
for (int i = 0; i < numUnknowns; ++i)
x(i) = coeff[i];
Equation_functor functor;
functor.series = &series;
functor.fSource = this;
functor.unknowns = numUnknowns;
functor.datasetLen = series.GetCount();
NumericalDiff<Equation_functor> numDiff(functor);
LevenbergMarquardt<NumericalDiff<Equation_functor> > lm(numDiff);
// ftol is a nonnegative input variable that measures the relative error desired in the sum of squares
lm.parameters.ftol = 1.E4*NumTraits<double>::epsilon();
// xtol is a nonnegative input variable that measures the relative error desired in the approximate solution
lm.parameters.xtol = 1.E4*NumTraits<double>::epsilon();
lm.parameters.maxfev = maxFitFunctionEvaluations;
int ret = lm.minimize(x);
if (ret == LevenbergMarquardtSpace::ImproperInputParameters)
return ExplicitEquation::ImproperInputParameters;
if (ret == LevenbergMarquardtSpace::TooManyFunctionEvaluation)
return TooManyFunctionEvaluation;
double mean = series.AvgY();
double sse = 0, sst = 0;
for (int64 i = 0; i < series.GetCount(); ++i) {
double y = series.y(i);
if (!IsNull(y)) {
double res = y - f(series.x(i));
sse += res*res;
double d = y - mean;
sst += d*d;
}
}
r2 = 1 - sse/sst;
return NoError;
}
ExplicitEquation::FitError SplineEquation::Fit(DataSource &data, double &r2)
{
Vector<Pointf> seriesRaw;
for (int64 i = 0; i < data.GetCount(); ++i) { // Remove Nulls
if (!IsNull(data.x(i)) && !IsNull(data.y(i)))
seriesRaw << Pointf(data.x(i), data.y(i));
}
if(seriesRaw.IsEmpty())
return InadequateDataSource;
PointfLess less;
Sort(seriesRaw, less); // Sort
Vector<Pointf> series;
for (int i = 1; i < seriesRaw.GetCount(); ++i) { // Remove points with duplicate x
if (seriesRaw[i].x != seriesRaw[i - 1].x)
series << seriesRaw[i];
}
r2 = 0;
int n = int(series.GetCount()) - 1;
Buffer<double> h(n);
for(int i = 0; i < n; ++i)
h[i] = (series[i+1].x - series[i].x);
Buffer<double> alpha(n);
for(int i = 1; i < n; ++i)
alpha[i] = (3.*(series[i+1].y - series[i].y)/h[i] - 3*(series[i].y - series[i-1].y)/h[i-1]);
Buffer<double> c(n+1), l(n+1), mu(n+1), z(n+1);
l[0] = 1;
mu[0] = 0;
z[0] = 0;
for(int i = 1; i < n; ++i) {
l[i] = 2.*(series[i+1].x - series[i-1].x) - h[i-1]*mu[i-1];
mu[i] = h[i]/l[i];
z[i] = (alpha[i] - h[i-1]*z[i-1])/l[i];
}
l[n] = 1.;
z[n] = 0;
c[n] = 0;
Buffer<double> b(n), d(n);
for(int i = n-1; i >= 0; --i) {
c[i] = z[i] - mu[i] * c[i+1];
b[i] = (series[i+1].y - series[i].y)/h[i] - h[i]*(c[i+1] + 2*c[i])/3.;
d[i] = (c[i+1] - c[i])/3./h[i];
}
ncoeff = n;
coeff.Alloc(ncoeff);
for(int i = 0; i < n; ++i) {
coeff[i].x = series[i].x;
coeff[i].a = series[i].y;
coeff[i].b = b[i];
coeff[i].c = c[i];
coeff[i].d = d[i];
}
return NoError;
}
