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Non-numerical Gaussian elimination #56

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Non-numerical Gaussian elimination #56

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3882bd6
Non-numeric Gaussian elimination determinant
WhiteBlackGoose Jul 18, 2020
0b45464
Spaces -> tabs
WhiteBlackGoose Jul 18, 2020
3a2826d
Removed useless code & spaces -> tabs
WhiteBlackGoose Jul 18, 2020
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7 changes: 6 additions & 1 deletion Sources/Towel/Constant.cs
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Original file line number Diff line number Diff line change
@@ -1,5 +1,6 @@
using System;
using System.Linq.Expressions;
using System.Reflection;
using static Towel.Syntax;

namespace Towel
Expand Down Expand Up @@ -87,7 +88,11 @@ public static T ComputePi(Predicate<T> predicate = null)
}
pi = Multiplication(Constant<T>.Two, pi);
}
pi = Maximum(pi, Constant<T>.Three);

// this is necessary because user's classes may not contain <, >, etc. operators, but they shouldn't be required
// to define them to work with, say, matrices
if (!(typeof(T).GetMethod("op_GreaterThanOrEqual", BindingFlags.Static | BindingFlags.Public) is null) || typeof(T) == typeof(int))
pi = Maximum(pi, Constant<T>.Three);
return pi;
}

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54 changes: 52 additions & 2 deletions Sources/Towel/Mathematics/Matrix.cs
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Original file line number Diff line number Diff line change
Expand Up @@ -384,8 +384,7 @@ internal static void GetCofactor(Matrix<T> a, Matrix<T> temp, int p, int q, int

#endregion

#region GetDeterminant Gaussian elimination

// Used for determinants
#region MatrixElementFraction
/// <summary>
/// Used to avoid issues when 1/2 + 1/2 = 0 + 0 = 0 instead of 1 for types, where division results in precision loss
Expand Down Expand Up @@ -465,6 +464,34 @@ public MatrixElementFraction<T> Abs()
}
#endregion

#region GetDeterminant Gaussian elimination analytically
internal static T GetDeterminantNonNumericGaussian(Matrix<T> matrix, int n)
{
if (n == 1)
return matrix.Get(0, 0);

var elemMatrix = new Matrix<MatrixElementFraction<T>>(n, n,
(x, y) => new MatrixElementFraction<T>(matrix.Get(x, y)));
for (int k = 1; k < n; k++)
for (int j = k; j < n; j++)
{
var m = elemMatrix.Get(j, k - 1) / elemMatrix.Get(k - 1, k - 1);
for (int i = 0; i < n + 0; i++)
elemMatrix.Set(j, i, elemMatrix.Get(j, i) - m * elemMatrix.Get(k - 1, i));
}

var det = new MatrixElementFraction<T>(Constant<T>.One);
for (int i = 0; i < n; i++)
det *= elemMatrix.Get(i, i);

return det.Value;
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There should be a check where det's Denominator is 0

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Hmm but then it won't fully non-numeric. So if you take this method, you might want to add

if (det.IsDividedByZero)
    return Constant<T>.Zero;

}
#endregion

#region GetDeterminant Gaussian elimination



/// <summary>
/// Reference: https://codereview.stackexchange.com/questions/204135/determinant-using-gauss-elimination
/// </summary>
Expand Down Expand Up @@ -1297,6 +1324,22 @@ public static T DeterminantGaussian(Matrix<T> a)
return GetDeterminantGaussian(a, a.Rows);
}

/// <summary>Computes the determinant of a square matrix via Gaussian elimination
/// for elements which don't have less, greater operators implemented
/// </summary>
/// <param name="a">The matrix to compute the determinant of.</param>
/// <returns>The computed determinant.</returns>
/// <runtime>O((n^3 + 2n^−3) / 3)</runtime>
public static T DeterminantNonNumericGaussian(Matrix<T> a)
{
_ = a ?? throw new ArgumentNullException(nameof(a));
if (!a.IsSquare)
{
throw new MathematicsException("Argument invalid !(" + nameof(a) + "." + nameof(a.IsSquare) + ")");
}
return GetDeterminantNonNumericGaussian(a, a.Rows);
}

/// <summary>Computes the determinant of a square matrix via Laplace's method.</summary>
/// <param name="a">The matrix to compute the determinant of.</param>
/// <returns>The computed determinant.</returns>
Expand Down Expand Up @@ -1332,6 +1375,13 @@ public T DeterminantGaussian()
return DeterminantGaussian(this);
}

/// <summary>Computes the determinant of a square matrix via Gaussian elimination.</summary>
/// <returns>The computed determinant.</returns>
public T DeterminantNonNumericGaussian()
{
return DeterminantNonNumericGaussian(this);
}

#endregion

#region Trace
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12 changes: 12 additions & 0 deletions Sources/Towel/Towel.xml
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Expand Up @@ -16885,6 +16885,14 @@
<returns>The computed determinant.</returns>
<runtime>O((n^3 + 2n^−3) / 3)</runtime>
</member>
<member name="M:Towel.Mathematics.Matrix`1.DeterminantNonNumericGaussian(Towel.Mathematics.Matrix{`0})">
<summary>Computes the determinant of a square matrix via Gaussian elimination
for elements which don't have less, greater operators implemented
</summary>
<param name="a">The matrix to compute the determinant of.</param>
<returns>The computed determinant.</returns>
<runtime>O((n^3 + 2n^−3) / 3)</runtime>
</member>
<member name="M:Towel.Mathematics.Matrix`1.DeterminantLaplace(Towel.Mathematics.Matrix{`0})">
<summary>Computes the determinant of a square matrix via Laplace's method.</summary>
<param name="a">The matrix to compute the determinant of.</param>
Expand All @@ -16903,6 +16911,10 @@
<summary>Computes the determinant of a square matrix via Gaussian elimination.</summary>
<returns>The computed determinant.</returns>
</member>
<member name="M:Towel.Mathematics.Matrix`1.DeterminantNonNumericGaussian">
<summary>Computes the determinant of a square matrix via Gaussian elimination.</summary>
<returns>The computed determinant.</returns>
</member>
<member name="M:Towel.Mathematics.Matrix`1.Trace(Towel.Mathematics.Matrix{`0})">
<summary>Computes the trace of a square matrix.</summary>
<param name="a">The matrix to compute the trace of.</param>
Expand Down