/// <summary>
/// get the eigenvalue matrix A of this Polynomial such that eig(A) = roots of this Polynomial.
/// </summary>
/// <returns>Eigenvalue matrix A</returns>
/// <note>this matrix is similar to the companion matrix of this polynomial, in such a way, that it's transpose is the columnflip of the companion matrix</note>
public DenseMatrix GetEigValMatrix()
{
Polynomial pLoc = new Polynomial(this.Coeffs);
pLoc.Trim();
int n = pLoc.Coeffs.Length - 1;
if (n < 2)
{
return(null);
}
double[] p = new double[n];
double a0 = pLoc.Coeffs[n];
for (int ii = n - 1; ii >= 0; ii--)
{
p[ii] = -pLoc.Coeffs[ii] / a0;
}
DenseMatrix A0 = DenseMatrix.CreateDiagonal(n - 1, n - 1, 1.0);
DenseMatrix A = new DenseMatrix(n);
A.SetSubMatrix(1, 0, A0);
A.SetRow(0, p.Reverse().ToArray());
return(A);
}
public Polynomial Integrate()
{
var t = this.Clone() as Polynomial;
t.Trim();
var cNew = new double[t.Coeffs.Length + 1];
for (int i = 1; i < cNew.Length; i++)
{
cNew[i] = t.Coeffs[i - 1] / i;
}
var p = new Polynomial(cNew);
p.Trim();
return(p);
}
public Polynomial Differentiate()
{
if (Coeffs.Length == 0)
{
return(null);
}
var t = this.Clone() as Polynomial;
t.Trim();
var cNew = new double[t.Coeffs.Length - 1];
for (int i = 1; i < t.Coeffs.Length; i++)
{
cNew[i - 1] = t.Coeffs[i] * i;
}
var p = new Polynomial(cNew);
p.Trim();
return(p);
}
/// <summary>
/// Division of two polynomials returning the quotient-with-remainder of the two polynomials given
/// </summary>
/// <param name="a">left polynomial</param>
/// <param name="b">right polynomial</param>
/// <returns>a tuple holding quotient in first and remainder in second</returns>
public static Tuple <Polynomial, Polynomial> DivideLong(Polynomial a, Polynomial b)
{
if (a == null)
{
throw new ArgumentNullException("a");
}
if (b == null)
{
throw new ArgumentNullException("b");
}
if (a.Degree <= 0)
{
throw new ArgumentOutOfRangeException("a Degree must be greater than zero");
}
if (b.Degree <= 0)
{
throw new ArgumentOutOfRangeException("b Degree must be greater than zero");
}
if (b.Coeffs[b.Degree - 1] == 0)
{
throw new DivideByZeroException("b polynomial ends with zero");
}
var c1 = a.Coeffs.ToArray();
var c2 = b.Coeffs.ToArray();
var n1 = c1.Length;
var n2 = c2.Length;
double[] quo = null;
double[] rem = null;
if (n2 == 1) // division by scalar
{
var fact = c2[0];
quo = new double[n1];
for (int i = 0; i < n1; i++)
{
quo[i] = c1[i] / fact;
}
rem = new double[] { 0 };
}
else if (n1 < n2) // denominator degree higher than nominator degree
{
// quotient always be 0 and return c1 as remainder
quo = new double[] { 0 };
rem = c1.ToArray();
}
else
{
var dn = n1 - n2;
var scl = c2[n2 - 1];
var c22 = new double[n2 - 1];
for (int ii = 0; ii < c22.Length; ii++)
{
c22[ii] = c2[ii] / scl;
}
int i = dn;
int j = n1 - 1;
while (i >= 0)
{
var v = c1[j];
var vals = new double[j - i];
for (int k = i; k < j; k++)
{
c1[k] -= c22[k - i] * v;
}
i--;
j--;
}
var j1 = j + 1;
var l1 = n1 - j1;
rem = new double[j1];
quo = new double[l1];
for (int k = 0; k < l1; k++)
{
quo[k] = c1[k + j1] / scl;
}
for (int k = 0; k < j1; k++)
{
rem[k] = c1[k];
}
}
if (rem == null)
{
throw new NullReferenceException("resulting remainder was null");
}
if (quo == null)
{
throw new NullReferenceException("resulting quotient was null");
}
// output mapping
var pQuo = new Polynomial(quo);
var pRem = new Polynomial(rem);
pRem.Trim();
pQuo.Trim();
return(new Tuple <Polynomial, Polynomial>(pQuo, pRem));
}