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Polynomial: reimplement arithmetics in immutable way

ridge-regression
Christoph Ruegg 8 years ago
parent
674a221956
commit
9a641040f9
2 changed files with 128 additions and 135 deletions
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  1. 57
      src/Numerics.Tests/PolynomialTests.cs
  2. 206
      src/Numerics/Polynomial.cs

57
src/Numerics.Tests/PolynomialTests.cs
View File

@ -66,8 +66,8 @@ namespace MathNet.Numerics.UnitTests
}
else
{
Assert.AreEqual(expected.Length, p_res.CoefficientCount, "length mismatch");
for (int k = 0; k < p_res.CoefficientCount; k++)
Assert.AreEqual(expected.Length, p_res.Coefficients.Length, "length mismatch");
for (int k = 0; k < p_res.Coefficients.Length; k++)
{
Assert.AreEqual(expected[k], p_res.Coefficients[k], "idx: " + k + " mismatch");
}
@ -89,8 +89,8 @@ namespace MathNet.Numerics.UnitTests
}
else
{
Assert.AreEqual(expected.Length, p_res.CoefficientCount, "length mismatch");
for (int k = 0; k < p_res.CoefficientCount; k++)
Assert.AreEqual(expected.Length, p_res.Coefficients.Length, "length mismatch");
for (int k = 0; k < p_res.Coefficients.Length; k++)
{
Assert.AreEqual(expected[k], p_res.Coefficients[k], "idx: " + k + " mismatch");
}
@ -125,8 +125,8 @@ namespace MathNet.Numerics.UnitTests
p_res.Trim();
p_tar.Trim();
Assert.AreEqual(p_tar.CoefficientCount, p_res.CoefficientCount, "length mismatch");
for (int k = 0; k < p_res.CoefficientCount; k++)
Assert.AreEqual(p_tar.Coefficients.Length, p_res.Coefficients.Length, "length mismatch");
for (int k = 0; k < p_res.Coefficients.Length; k++)
{
Assert.AreEqual(p_tar.Coefficients[k], p_res.Coefficients[k], msg);
}
@ -135,7 +135,7 @@ namespace MathNet.Numerics.UnitTests
}
[Test]
public void SubstractTest()
public void SubtractTest()
{
for (int i = 0; i < 5; i++)
{
@ -156,14 +156,14 @@ namespace MathNet.Numerics.UnitTests
var p1 = new Polynomial(c1);
var p2 = new Polynomial(c2);
var p_res = Polynomial.Substract(p1, p2);
var p_res = Polynomial.Subtract(p1, p2);
var p_tar = new Polynomial(tgt);
p_res.Trim();
p_tar.Trim();
Assert.AreEqual(p_tar.CoefficientCount, p_res.CoefficientCount, "length mismatch");
for (int k = 0; k < p_res.CoefficientCount; k++)
Assert.AreEqual(p_tar.Coefficients.Length, p_res.Coefficients.Length, "length mismatch");
for (int k = 0; k < p_res.Coefficients.Length; k++)
{
Assert.AreEqual(p_tar.Coefficients[k], p_res.Coefficients[k], msg);
}
@ -198,8 +198,8 @@ namespace MathNet.Numerics.UnitTests
p_res.Trim();
p_tar.Trim();
Assert.AreEqual(p_tar.CoefficientCount, p_res.CoefficientCount, "length mismatch");
for (int k = 0; k < p_res.CoefficientCount; k++)
Assert.AreEqual(p_tar.Coefficients.Length, p_res.Coefficients.Length, "length mismatch");
for (int k = 0; k < p_res.Coefficients.Length; k++)
{
Assert.AreEqual(p_tar.Coefficients[k], p_res.Coefficients[k], msg);
}
@ -256,14 +256,14 @@ namespace MathNet.Numerics.UnitTests
var p11 = new Polynomial(2.0d);
var p21 = new Polynomial(2.0d);
var tpl1 = Polynomial.DivideLong(p11, p21);
testEqual(new double[] { 1.0 }, tpl1.Item1);
testEqual(new double[] { 0.0 }, tpl1.Item2);
TestEqual(new double[] { 1.0 }, tpl1.Item1);
TestEqual(new double[] { 0.0 }, tpl1.Item2);
var p12 = new Polynomial(new double[] { 2.0d, 2.0d });
var p22 = new Polynomial(2.0d);
var tpl2 = Polynomial.DivideLong(p12, p22);
testEqual(new double[] { 1.0, 1.0 }, tpl2.Item1);
testEqual(new double[] { 0.0 }, tpl2.Item2);
TestEqual(new double[] { 1.0, 1.0 }, tpl2.Item1);
TestEqual(new double[] { 0.0 }, tpl2.Item2);
for (int i = 0; i < 5; i++)
{
@ -286,7 +286,7 @@ namespace MathNet.Numerics.UnitTests
var pres = (pquo * pi) + prem;
pres.Trim();
testEqual(pres, tgt, msg);
TestEqual(pres, tgt, msg);
}
}
}
@ -314,23 +314,23 @@ namespace MathNet.Numerics.UnitTests
var x_2 = new double[] { -1.0, 1.0 };
var expected_2 = new List<Complex>();
expected_2.Add(new Complex(1.0, 0.0));
testEqual(x_2, expected_2);
TestEqual(x_2, expected_2);
var x_3 = new double[] { -1.0, 0.0, 1.0 };
var expected_3 = new List<Complex>();
expected_3.Add(new Complex(1.0, 0.0));
expected_3.Add(new Complex(-1.0, 0.0));
testEqual(x_3, expected_3);
TestEqual(x_3, expected_3);
var x_4 = new double[] { -1.0, -0.33333333333333337, 0.33333333333333326, 1.0 };
var expected_4 = new List<Complex>();
expected_4.Add(new Complex(0.9999999999999996, 0.0));
expected_4.Add(new Complex(-0.6666666666666666, 0.7453559924999296));
expected_4.Add(new Complex(-0.6666666666666666, -0.7453559924999296));
testEqual(x_4, expected_4);
TestEqual(x_4, expected_4);
}
private void testEqual(double[] x, List<Complex> eIn)
static void TestEqual(double[] x, List<Complex> eIn)
{
var tol = 1e-10;
var r0 = new Polynomial(x).GetRoots().ToList();
@ -348,7 +348,7 @@ namespace MathNet.Numerics.UnitTests
}
}
private void testEqual(double[] p_tar, double[] p_res, string msg = null)
static void TestEqual(double[] p_tar, double[] p_res, string msg = null)
{
Assert.AreEqual(p_tar.Length, p_res.Length, "length mismatch");
for (int k = 0; k < p_res.Length; k++)
@ -357,19 +357,20 @@ namespace MathNet.Numerics.UnitTests
}
}
private void testEqual(double[] p_tar, Polynomial p_res, string msg = null)
static void TestEqual(double[] p_tar, Polynomial p_res, string msg = null)
{
Assert.AreEqual(p_tar.Length, p_res.CoefficientCount, "length mismatch");
for (int k = 0; k < p_res.CoefficientCount; k++)
Assert.AreEqual(p_tar.Length, p_res.Coefficients.Length, "length mismatch");
for (int k = 0; k < p_res.Coefficients.Length; k++)
{
Assert.AreEqual(p_tar[k], p_res.Coefficients[k], msg);
}
}
private void testEqual(Polynomial p_tar, Polynomial p_res, string msg = null)
static void TestEqual(Polynomial p_tar, Polynomial p_res, string msg = null)
{
Assert.AreEqual(p_tar.CoefficientCount, p_res.CoefficientCount, "length mismatch");
for (int k = 0; k < p_res.CoefficientCount; k++)
Assert.AreEqual(p_tar.Coefficients.Length, p_res.Coefficients.Length, "length mismatch");
for (int k = 0; k < p_res.Coefficients.Length; k++)
{
Assert.AreEqual(p_tar.Coefficients[k], p_res.Coefficients[k], msg);
}

206
src/Numerics/Polynomial.cs
View File

@ -17,24 +17,13 @@ namespace MathNet.Numerics
/// <summary>
/// The coefficients of the polynomial in a
/// </summary>
public double[] Coefficients { get; set; }
public double[] Coefficients { get; private set; }
/// <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 CoefficientCount
{
get
{
return (Coefficients == null ? 0 : Coefficients.Length);
}
}
/// <summary>
/// Degree of the polynomial, i.e. the largest monomial exponent. For example, the degree of x^2+x^5 is 5.
/// The null-polynomial returns degree -1 because the correct degree, negative infinity, cannot be represented by integers.
@ -115,17 +104,25 @@ namespace MathNet.Numerics
/// </summary>
public void Trim()
{
if (CoefficientCount == 1)
if (Coefficients.Length == 1)
{
return;
}
int i = CoefficientCount - 1;
int i = Coefficients.Length - 1;
while (i >= 0 && Coefficients[i] == 0.0)
{
i--;
}
if (i < 0)
{
Coefficients = new[] { 0.0 };
}
else if (i == 0)
{
Coefficients = new[] { Coefficients[0] };
}
else
{
var hold = new double[i+1];
@ -304,7 +301,7 @@ namespace MathNet.Numerics
/// <returns>resulting Polynomial</returns>
public static Polynomial operator -(Polynomial a, Polynomial b)
{
return Substract(a, b);
return Subtract(a, b);
}
/// <summary>
@ -368,128 +365,147 @@ namespace MathNet.Numerics
}
/// <summary>
/// pointwise division of two Polynomials
/// Point-wise 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)
/// <param name="a">Left Polynomial</param>
/// <param name="b">Right Polynomial</param>
/// <returns>Resulting Polynomial</returns>
public static Polynomial PointwiseDivide(Polynomial a, Polynomial b)
{
var aa = a.Clone() as Polynomial;
var bb = b.Clone() as Polynomial;
var ac = a.Coefficients;
var bc = b.Coefficients;
if (aa.Coefficients.Length != bb.Coefficients.Length)
var degree = a.Degree;
var result = new double[degree + 1];
var commonLength = Math.Min(Math.Min(ac.Length, bc.Length), result.Length);
for (int i = 0; i < commonLength; i++)
{
MakeSameLength(ref aa, ref bb);
result[i] = ac[i] / bc[i];
}
int n = aa.Coefficients.Length;
double[] res = new double[aa.Coefficients.Length];
for (int ii = 0; ii < n; ii++)
for (int i = commonLength; i < result.Length; i++)
{
res[ii] = aa.Coefficients[ii] / bb.Coefficients[ii];
result[i] = ac[i] / 0.0;
}
return new Polynomial(res);
return new Polynomial(result);
}
/// <summary>
/// pointwise multiplication of two Polynomials
/// Point-wise 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)
/// <param name="a">Left Polynomial</param>
/// <param name="b">Right Polynomial</param>
/// <returns>Resulting Polynomial</returns>
public static Polynomial PointwiseMultiply(Polynomial a, Polynomial b)
{
var aa = a.Clone() as Polynomial;
var bb = b.Clone() as Polynomial;
if (aa.Coefficients.Length != bb.Coefficients.Length)
{
MakeSameLength(ref aa, ref bb);
}
var ac = a.Coefficients;
var bc = b.Coefficients;
int n = aa.Coefficients.Length;
double[] res = new double[aa.Coefficients.Length];
for (int ii = 0; ii < n; ii++)
var degree = Math.Min(a.Degree, b.Degree);
var result = new double[degree + 1];
for (int i = 0; i < result.Length; i++)
{
res[ii] = aa.Coefficients[ii] * bb.Coefficients[ii];
result[i] = ac[i] * bc[i];
}
return new Polynomial(res);
return new Polynomial(result);
}
/// <summary>
/// Addition of two Polynomials (piecewise)
/// Addition of two Polynomials (point-wise).
/// </summary>
/// <param name="a">left Polynomial</param>
/// <param name="b">right Polynomial</param>
/// <returns>resulting Polynomial</returns>
/// <param name="a">Left Polynomial</param>
/// <param name="b">Right Polynomial</param>
/// <returns>Resulting Polynomial</returns>
public static Polynomial Add(Polynomial a, Polynomial b)
{
var aa = a.Clone() as Polynomial;
var bb = b.Clone() as Polynomial;
var ac = a.Coefficients;
var bc = b.Coefficients;
if (aa.CoefficientCount != bb.CoefficientCount)
var degree = Math.Max(a.Degree, b.Degree);
var result = new double[degree + 1];
var commonLength = Math.Min(Math.Min(ac.Length, bc.Length), result.Length);
for (int i = 0; i < commonLength; i++)
{
MakeSameLength(ref aa, ref bb);
result[i] = ac[i] + bc[i];
}
int n = aa.CoefficientCount;
double[] res = new double[n];
for (int ii = 0; ii < n; ii++)
int acLength = Math.Min(ac.Length, result.Length);
for (int i = commonLength; i < acLength; i++)
{
res[ii] = aa.Coefficients[ii] + bb.Coefficients[ii];
// no need to add since only one of both applies
result[i] = ac[i];
}
return new Polynomial(res);
int bcLength = Math.Min(bc.Length, result.Length);
for (int i = commonLength; i < bcLength; i++)
{
// no need to add since only one of both applies
result[i] = bc[i];
}
return new Polynomial(result);
}
/// <summary>
/// substraction of two Polynomials (piecewise)
/// Subtraction of two Polynomials (point-wise).
/// </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)
/// <param name="a">Left Polynomial</param>
/// <param name="b">Right Polynomial</param>
/// <returns>Resulting Polynomial</returns>
public static Polynomial Subtract(Polynomial a, Polynomial b)
{
var aa = a.Clone() as Polynomial;
var bb = b.Clone() as Polynomial;
var ac = a.Coefficients;
var bc = b.Coefficients;
var degree = Math.Max(a.Degree, b.Degree);
var result = new double[degree + 1];
var commonLength = Math.Min(Math.Min(ac.Length, bc.Length), result.Length);
for (int i = 0; i < commonLength; i++)
{
result[i] = ac[i] - bc[i];
}
if (aa.CoefficientCount != bb.CoefficientCount)
int acLength = Math.Min(ac.Length, result.Length);
for (int i = commonLength; i < acLength; i++)
{
MakeSameLength(ref aa, ref bb);
// no need to add since only one of both applies
result[i] = ac[i];
}
int n = aa.CoefficientCount;
double[] res = new double[n];
for (int ii = 0; ii < n; ii++)
int bcLength = Math.Min(bc.Length, result.Length);
for (int i = commonLength; i < bcLength; i++)
{
res[ii] = aa.Coefficients[ii] - bb.Coefficients[ii];
// no need to add since only one of both applies
result[i] = -bc[i];
}
return new Polynomial(res);
return new Polynomial(result);
}
/// <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>
/// <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");
throw new ArgumentNullException(nameof(a));
if (b == null)
throw new ArgumentNullException("b");
throw new ArgumentNullException(nameof(b));
if (a.CoefficientCount <= 0)
if (a.Coefficients.Length <= 0)
throw new ArgumentOutOfRangeException("a Degree must be greater than zero");
if (b.CoefficientCount <= 0)
if (b.Coefficients.Length <= 0)
throw new ArgumentOutOfRangeException("b Degree must be greater than zero");
if (b.Coefficients[b.CoefficientCount-1] == 0)
if (b.Coefficients[b.Coefficients.Length - 1] == 0)
throw new DivideByZeroException("b polynomial ends with zero");
var c1 = a.Coefficients.ToArray();
@ -572,8 +588,8 @@ namespace MathNet.Numerics
/// <summary>
/// Division of two polynomials returning the quotient-with-remainder of the two polynomials given
/// </summary>
/// <param name="b">right polynomial</param>
/// <returns>a tuple holding quotient in first and remainder in second</returns>
/// <param name="b">Right polynomial</param>
/// <returns>A tuple holding quotient in first and remainder in second</returns>
public Tuple<Polynomial, Polynomial> DivideLong(Polynomial b)
{
return DivideLong(this, b);
@ -643,30 +659,6 @@ namespace MathNet.Numerics
return Coefficients.ToArray();
}
static void MakeSameLength(ref Polynomial a, ref Polynomial b)
{
double[] aHold = new double[a.Coefficients.Length];
double[] bHold = new double[b.Coefficients.Length];
Array.Copy(a.Coefficients, aHold, a.Coefficients.Length);
Array.Copy(b.Coefficients, bHold, b.Coefficients.Length);
if (a.Coefficients.Length < b.Coefficients.Length)
{
a.Coefficients = new double[b.Coefficients.Length];
b.Coefficients = new double[b.Coefficients.Length];
Array.Copy(aHold, a.Coefficients, aHold.Length);
Array.Copy(bHold, b.Coefficients, bHold.Length);
}
else
{
a.Coefficients = new double[a.Coefficients.Length];
b.Coefficients = new double[a.Coefficients.Length];
Array.Copy(aHold, a.Coefficients, aHold.Length);
Array.Copy(bHold, b.Coefficients, bHold.Length);
}
}
/// <summary>
/// Full convolution of two arrays
/// </summary>

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