/// <summary>
/// Cubic spline is obtained by solving a linear problem Ax=b where A is a square matrix and x,b are vector
/// This can be done by LU decomposition </summary>
/// <param name="doubMat"> Matrix A </param>
/// <param name="doubVec"> Vector B </param>
/// <returns> Solution to the linear equation, x </returns>
protected internal virtual double[] matrixEqnSolver(double[][] doubMat, double[] doubVec)
{
LUDecompositionResult result = _luObj.apply(DoubleMatrix.copyOf(doubMat));
double[][] lMat = result.L.toArray();
double[][] uMat = result.U.toArray();
DoubleArray doubVecMod = ((DoubleArray)OG_ALGEBRA.multiply(result.P, DoubleArray.copyOf(doubVec)));
return(backSubstitution(uMat, forwardSubstitution(lMat, doubVecMod)));
}
private GeneralizedLeastSquareResults <T> solveImp <T>(IList <T> x, IList <double> y, IList <double> sigma, IList <System.Func <T, double> > basisFunctions, double lambda, int differenceOrder)
{
int n = x.Count;
int m = basisFunctions.Count;
double[] b = new double[m];
double[] invSigmaSqr = new double[n];
//JAVA TO C# CONVERTER NOTE: The following call to the 'RectangularArrays' helper class reproduces the rectangular array initialization that is automatic in Java:
//ORIGINAL LINE: double[][] f = new double[m][n];
double[][] f = RectangularArrays.ReturnRectangularDoubleArray(m, n);
int i, j, k;
for (i = 0; i < n; i++)
{
double temp = sigma[i];
ArgChecker.isTrue(temp > 0, "sigma must be greater than zero");
invSigmaSqr[i] = 1.0 / temp / temp;
}
for (i = 0; i < m; i++)
{
for (j = 0; j < n; j++)
{
f[i][j] = basisFunctions[i](x[j]);
}
}
double sum;
for (i = 0; i < m; i++)
{
sum = 0;
for (k = 0; k < n; k++)
{
sum += y[k] * f[i][k] * invSigmaSqr[k];
}
b[i] = sum;
}
DoubleArray mb = DoubleArray.copyOf(b);
DoubleMatrix ma = getAMatrix(f, invSigmaSqr);
if (lambda > 0.0)
{
DoubleMatrix d = getDiffMatrix(m, differenceOrder);
ma = (DoubleMatrix)_algebra.add(ma, _algebra.scale(d, lambda));
}
DecompositionResult decmp = _decomposition.apply(ma);
DoubleArray w = decmp.solve(mb);
DoubleMatrix covar = decmp.solve(DoubleMatrix.identity(m));
double chiSq = 0;
for (i = 0; i < n; i++)
{
double temp = 0;
for (k = 0; k < m; k++)
{
temp += w.get(k) * f[k][i];
}
chiSq += FunctionUtils.square(y[i] - temp) * invSigmaSqr[i];
}
return(new GeneralizedLeastSquareResults <T>(basisFunctions, chiSq, w, covar));
}