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Implemented a prototype for a polynomial class only based on real values (doubles)

ridge-regression
Tobias Glaubach 8 years ago
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  1. 471
      src/Numerics/Polynomial.cs

471
src/Numerics/Polynomial.cs
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using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Numerics;
using MathNet.Numerics;
using MathNet.Numerics.LinearAlgebra;
using MathNet.Numerics.LinearAlgebra.Double;
using MathNet.Numerics.Statistics;
using MathNet.Numerics.IntegralTransforms;
using MathNet.Numerics.LinearAlgebra.Factorization;
namespace MathNet.Numerics
{
/// <summary>
/// a class handlin REAL VALUED Polynomials, complex coefficients can not be handled (yet)
/// </summary>
public class Polynomial
{
public double[] Coeffs { get; set; }
/// <summary>
/// indicator if Polynomial was flipped
/// </summary>
public bool IsFlipped { get; }
/// <summary>
/// Only needed for the ToString method
/// </summary>
public string VarName = "x^";
/// <summary>
/// Length of Polynomial (max element + 1) e.G x^5 highest element, will give Length = 6
/// </summary>
public int Length
{
get
{
return (Coeffs.Length);
}
}
/// <summary>
/// constructor setting a Polynomial of size n containing only zeros
/// </summary>
/// <param name="n">size of Polynomial</param>
public Polynomial(int n)
{
Coeffs = new double[n];
}
/// <summary>
/// constructor setting Polynomial coefficiens and flipping them if necessary.
///
/// e.G:
/// var x = new double[] {5, 4, 3, 0, 2};
/// var xP1 = new Polynomial(x, isFlip:true);
/// var xP2 = new Polynomial(x, isFlip:false);
///
/// xP1: 5 x^3 + 4 x^2 + 3 x^2 + 0 x^1 + 2
/// xP2: 2 x^3 + 0 x^2 + 3 x^2 + 4 x^1 + 5
///
/// WARNING cut all trailing zeros before, since they would result in zeros at the end
/// </summary>
/// <param name="coeffs"> Polynomial coefficiens as array</param>
/// <param name="isFlip">use true for flipping</param>
public Polynomial(double[] coeffs, bool isFlip = false)
{
this.Coeffs = new double[Coeffs.Length];
Array.Copy(coeffs, Coeffs, coeffs.Length);
if (isFlip)
{
Coeffs = Coeffs.Reverse().ToArray();
IsFlipped = true;
}
}
/// <summary>
/// constructor setting Polynomial coefficiens
/// </summary>
/// <param name="coeff">just the x^0 part</param>
public Polynomial(double coeff)
{
IsFlipped = false;
this.Coeffs = new double[1];
Coeffs[0] = coeff;
}
/// <summary>
/// constructor setting Polynomial coefficiens
/// </summary>
/// <param name="Coeffs"> Polynomial coefficiens as array</param>
public Polynomial(double[] Coeffs)
{
this.Coeffs = new double[Coeffs.Length];
Array.Copy(Coeffs, this.Coeffs, Coeffs.Length);
}
/// <summary>
/// remove all trailing zeros, e.G before: "0.00 x^2 + 1.0 x^1 + 1.00" after: "1.0 x^1 + 1.00"
/// </summary>
public void CutTrailZeros()
{
int count = 0;
for (int ii = Length - 1; ii >= 0; ii--)
{
if (Coeffs[ii] == 0.0)
{
count++;
}
else
{
double[] CoeffsHold = new double[Length];
Coeffs.CopyTo(CoeffsHold, 0);
Array.Resize(ref CoeffsHold, Length - count);
Coeffs = new double[Length - count];
CoeffsHold.CopyTo(Coeffs, 0);
return;
}
}
}
#region Operators
/// <summary>
/// multiplies a Polynomial by a Polynomial using convolution [ASINCO.libs.subfun.conv(a.Coeffs, b.Coeffs)]
/// </summary>
/// <param name="a">left Polynomial</param>
/// <param name="b">right Polynomial</param>
/// <returns>resulting Polynomial</returns>
public static Polynomial operator *( Polynomial a, Polynomial b)
{
// do not cut trailing zeros, since it may corrupt the outcom, if the array is of form 1 + x^-1 + x^-2 + x^-3
//a.CutTrailZeros();
//b.CutTrailZeros();
double[] ret = conv(a.Coeffs, b.Coeffs);
Polynomial ret_p = new Polynomial(ret);
//ret_p.CutTrailZeros();
return (ret_p);
}
/// <summary>
/// multiplies a Polynomial by a scalar
/// </summary>
/// <param name="a">left Polynomial</param>
/// <param name="k">scalar value</param>
/// <returns>resulting Polynomial</returns>
public static Polynomial operator *( Polynomial a, double k)
{
for (int ii = 0; ii < a.Length; ii++)
a.Coeffs[ii] *= k;
return a;
}
/// <summary>
/// adds a scalar to a Polynomial (to the x^0 element)
/// </summary>
/// <param name="a">left Polynomial</param>
/// <param name="k">scalar value</param>
/// <returns>resulting Polynomial</returns>
public static Polynomial operator +( Polynomial a, double k)
{
a.Coeffs[0] += k;
return a;
}
/// <summary>
/// substracs a scalar from a Polynomial (from the x^0 element)
/// </summary>
/// <param name="a">left Polynomial</param>
/// <param name="k">scalar value</param>
/// <returns>resulting Polynomial</returns>
public static Polynomial operator -( Polynomial a, double k)
{
a.Coeffs[0] -= k;
return a;
}
/// <summary>
/// divide Polynomial by scalar value
/// </summary>
/// <param name="a">left Polynomial</param>
/// <param name="k">scalar value</param>
/// <returns>resulting Polynomial</returns>
public static Polynomial operator /( Polynomial a, double k)
{
for (int ii = 0; ii < a.Length; ii++)
a.Coeffs[ii] /= k;
return a;
}
/// <summary>
/// Addition of two Polynomials (piecewise)
/// </summary>
/// <param name="a">left Polynomial</param>
/// <param name="b">right Polynomial</param>
/// <returns>resulting Polynomial</returns>
public static Polynomial operator +( Polynomial a, Polynomial b)
{
return add(a, b);
}
/// <summary>
/// substraction of two Polynomials (piecewise)
/// </summary>
/// <param name="a">left Polynomial</param>
/// <param name="b">right Polynomial</param>
/// <returns>resulting Polynomial</returns>
public static Polynomial operator -( Polynomial a, Polynomial b)
{
return substract(a, b);
}
/// <summary>
/// Calculates the complex roots of the Polynomial in the same way as matlab does
/// </summary>
/// <returns>a vector of complex numbers with the roots</returns>
public Complex[] GetRoots()
{
DenseMatrix A = this.GetEigValMatrix();
Complex[] c_vec;
if (A == null)
{
if (Coeffs.Length < 2)
{
var val = Coeffs.Length == 1 ? Coeffs[0] : Double.NaN;
c_vec = new Complex[1] { val };
}
else
c_vec = new Complex[1] { new Complex(-Coeffs[0] / Coeffs[1], 0) };
}
else
{
Evd<double> eigen = A.Evd(Symmetricity.Asymmetric);
c_vec = eigen.EigenValues.ToArray();
}
return c_vec;
}
/// <summary>
/// get the eigenvalue matrix A of this Polynomial such that eig(A) = roots of this Polynomial
/// </summary>
/// <returns>Eigenvalue matrix A</returns>
public DenseMatrix GetEigValMatrix()
{
Polynomial pLoc = new Polynomial(this.Coeffs);
pLoc.CutTrailZeros();
int n = pLoc.Length - 1;
if (n < 2)
return null;
double[] p = new double[n];
double a0 = pLoc.Coeffs[p.Length];
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;
}
/// <summary>
/// pointwise division of two Polynomials
/// </summary>
/// <param name="a">left Polynomial</param>
/// <param name="b">right Polynomial</param>
/// <returns>resulting Polynomial</returns>
public static Polynomial DividePointwise( Polynomial a, Polynomial b)
{
if (a.Length != b.Length)
mkSameLength(ref a, ref b);
int n = a.Length;
double[] res = new double[a.Length];
for (int ii = 0; ii < n; ii++)
{
res[ii] = a.Coeffs[ii] / b.Coeffs[ii];
}
Polynomial res_poly = new Polynomial(res);
return (res_poly);
}
/// <summary>
/// pointwise multiplication of two Polynomials
/// </summary>
/// <param name="a">left Polynomial</param>
/// <param name="b">right Polynomial</param>
/// <returns>resulting Polynomial</returns>
public static Polynomial MultiplyPointwise( Polynomial a, Polynomial b)
{
if (a.Length != b.Length)
mkSameLength(ref a, ref b);
int n = a.Length;
double[] res = new double[a.Length];
for (int ii = 0; ii < n; ii++)
{
res[ii] = a.Coeffs[ii] * b.Coeffs[ii];
}
Polynomial res_poly = new Polynomial(res);
return (res_poly);
}
/// <summary>
/// Addition of two Polynomials (piecewise)
/// </summary>
/// <param name="a">left Polynomial</param>
/// <param name="b">right Polynomial</param>
/// <returns>resulting Polynomial</returns>
public static Polynomial add( Polynomial a, Polynomial b)
{
if (a.Length != b.Length)
mkSameLength(ref a, ref b);
int n = a.Length;
double[] res = new double[a.Length];
for (int ii = 0; ii < n; ii++)
{
res[ii] = a.Coeffs[ii] + b.Coeffs[ii];
}
Polynomial res_poly = new Polynomial(res);
return (res_poly);
}
/// <summary>
/// substraction of two Polynomials (piecewise)
/// </summary>
/// <param name="a">left Polynomial</param>
/// <param name="b">right Polynomial</param>
/// <returns>resulting Polynomial</returns>
public static Polynomial substract( Polynomial a, Polynomial b)
{
if (a.Length != b.Length)
mkSameLength(ref a, ref b);
int n = a.Length;
double[] res = new double[a.Length];
for (int ii = 0; ii < n; ii++)
{
res[ii] = a.Coeffs[ii] - b.Coeffs[ii];
}
Polynomial res_poly = new Polynomial(res);
return (res_poly);
}
#endregion
#region Displaying
/// <summary>
/// "0.00 x^3 + 0.00 x^2 + 0.00 x^1 + 0.00" like display of this Polynomial
/// </summary>
/// <returns>string in displayed format</returns>
public override string ToString()
{
string strLoc = "";
for (int ii = Length - 1; ii >= 0; ii--)
{
if (ii == 0)
strLoc = String.Concat(strLoc, this.Coeffs[ii].ToString());
else
strLoc = String.Concat(strLoc, this.Coeffs[ii].ToString(), VarName, ii.ToString(), " + ");
}
return strLoc;
}
#endregion
#region Interfacing
/// <summary>
/// This method returns the coefficcients of the Polynomial as an array the "IsFlipped" property,
/// which is set during construction is taken into account automatically.
/// </summary>
/// <returns>the coefficcients of the Polynomial as an array</returns>
public double[] ToArray()
{
if (IsFlipped == true)
return (Coeffs.Reverse().ToArray());
else
return (Coeffs);
}
#endregion
#region Helpers
private static void mkSameLength(ref Polynomial a, ref Polynomial b)
{
double[] aHold = new double[a.Length];
double[] bHold = new double[b.Length];
Array.Copy(a.Coeffs, aHold, a.Length);
Array.Copy(b.Coeffs, bHold, b.Length);
if (a.Length < b.Length)
{
a.Coeffs = new double[b.Length];
b.Coeffs = new double[b.Length];
Array.Copy(aHold, a.Coeffs, aHold.Length);
Array.Copy(bHold, b.Coeffs, bHold.Length);
}
else
{
a.Coeffs = new double[a.Length];
b.Coeffs = new double[a.Length];
Array.Copy(aHold, a.Coeffs, aHold.Length);
Array.Copy(bHold, b.Coeffs, bHold.Length);
}
}
/// <summary>
/// (full) convolution of two arrays
/// </summary>
/// <param name="a">left vector</param>
/// <param name="b">right vector</param>
/// <returns>convolution of a and b as vector</returns>
private static double[] conv(double[] a, double[] b)
{
double[] ret = new double[a.Length + b.Length];
for (int i = 0; i < a.Length; i++)
{
for (int j = 0; j < b.Length; j++)
{
ret[i + j] += a[i] * b[j];
}
}
return ret;
}
#endregion
}
}
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