public PolynomialND Evaluate(double Val, int Dim) // turn a ND Polynomial into a (N-1)D one
{
var OrderNew = (int [])Order.Clone();
OrderNew [Dim] = 1;
int Length = Order [Dim];
var Id = new Index(OrderNew);
var IdOld = new Index(Order);
var ans = new PolynomialND(OrderNew);
for (int i = 0; i < ans.Coefficients.Length; i++)
{
double LocalCoeff = 0;
var sub = Id.Ind2Sub(i);
int[] subAns = (int[])sub.Clone();
for (int j = 0; j < Length; j++)
{
int idx = IdOld.Sub2Ind(subAns);
LocalCoeff = LocalCoeff + Math.Pow(Val, j) * Coefficients [idx];
subAns[Dim]++;
}
ans.Coefficients [i] = LocalCoeff;
}
return(ans);
}
public static PolynomialND operator *(PolynomialND p2, PolynomialND p1)
{
var p3Extent = new int[p1.Rank];
for (int i = 0; i < p3Extent.Length; i++)
{
p3Extent [i] = p1.Order [i] + p2.Order [i];
}
var p3 = new PolynomialND(p3Extent);
var idA = new Index(p1.Order);
var idB = new Index(p2.Order);
var idC = new Index(p3.Order);
int[] subC = new int[p3.Rank];
for (int i = 0; i < p1.Coefficients.Length; i++)
{
var subA = idA.Ind2Sub(i);
for (int j = 0; j < p2.Coefficients.Length; j++)
{
var subB = idB.Ind2Sub(j);
for (int k = 0; k < subC.Length; k++)
{
subC [k] = subA [k] + subB [k];
}
int idx = idC.Sub2Ind(subC);
p3.Coefficients [idx] = p1.Coefficients [i] * p2.Coefficients [j];
}
}
return(p3);
}
public static PolynomialND operator *(PolynomialND p1, double Scalar)
{
var p2 = new PolynomialND(p1.Order);
for (int i = 0; i < p2.Coefficients.Length; i++)
{
p2.Coefficients [i] = p1.Coefficients [i] * Scalar;
}
return(p2);
}
public static PolynomialND operator +(PolynomialND p2, PolynomialND p1)
{
int[] extent;
if (p1.Rank != p2.Rank)
{
throw new Exception("Both polynomials need to be the same number of dimensions");
}
var coefficients = addArrays(p2.Coefficients, p1.Coefficients, p1.Order, p2.Order, out extent);
var p3 = new PolynomialND(extent, coefficients);
return(p3);
}
public PolynomialND Convert_ND(int Dim, int Rank = 3)
{
var Order = new int[Rank];
for (int i = 0; i < Rank; i++)
{
Order [i] = 1;
}
Order [Dim] = coefficients.Length;
var Ans = new PolynomialND(Order, coefficients);
return(Ans);
}
public PolynomialND Differentiate(int Dim)
{
int[] OrderNew = (int[])Order.Clone();
OrderNew [Dim]--;
var ans = new PolynomialND(OrderNew);
var Id_Old = new Index(Order);
var Id = new Index(ans.Order);
for (int i = 0; i < ans.Coefficients.Length; i++)
{
var subAns = Id.Ind2Sub(i);
subAns [Dim]++;
int idx = Id_Old.Sub2Ind(subAns);
ans.Coefficients [i] = Coefficients [idx] * subAns [Dim];
}
return(ans);
}
public PolynomialND Integrate(int Dim)
{
int[] OrderNew = (int[])Order.Clone();
OrderNew [Dim]++;
var ans = new PolynomialND(OrderNew);
var Id_Old = new Index(Order);
var Id = new Index(ans.Order);
for (int i = 0; i < Coefficients.Length; i++)
{
var subAns = Id_Old.Ind2Sub(i);
subAns [Dim]++;
int idx = Id.Sub2Ind(subAns);
ans.Coefficients [idx] = Coefficients [i] * (1.0d / (double)subAns [Dim]);
}
return(ans);
}
