//
// Math.NET Numerics, part of the Math.NET Project
// http://numerics.mathdotnet.com
// http://github.com/mathnet/mathnet-numerics
//
// Copyright (c) 2009-2013 Math.NET
//
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following
// conditions:
//
// The above copyright notice and this permission notice shall be
// included in all copies or substantial portions of the Software.
//
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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// OTHER DEALINGS IN THE SOFTWARE.
//
using System;
using System.Collections.Generic;
using IStation.Numerics.LinearAlgebra;
using IStation.Numerics.Providers.LinearAlgebra;
using IStation.Numerics.Statistics;
namespace IStation.Numerics
{
///
/// Metrics to measure the distance between two structures.
///
public static class Distance
{
///
/// Sum of Absolute Difference (SAD), i.e. the L1-norm (Manhattan) of the difference.
///
public static double SAD(Vector a, Vector b) where T : struct, IEquatable, IFormattable
{
return (a - b).L1Norm();
}
///
/// Sum of Absolute Difference (SAD), i.e. the L1-norm (Manhattan) of the difference.
///
public static double SAD(double[] a, double[] b)
{
if (a.Length != b.Length)
{
throw new ArgumentException("All vectors must have the same dimensionality.");
}
double sum = 0d;
for (var i = 0; i < a.Length; i++)
{
sum += Math.Abs(a[i] - b[i]);
}
return sum;
}
///
/// Sum of Absolute Difference (SAD), i.e. the L1-norm (Manhattan) of the difference.
///
public static float SAD(float[] a, float[] b)
{
if (a.Length != b.Length)
{
throw new ArgumentException("All vectors must have the same dimensionality.");
}
float sum = 0f;
for (var i = 0; i < a.Length; i++)
{
sum += Math.Abs(a[i] - b[i]);
}
return sum;
}
///
/// Mean-Absolute Error (MAE), i.e. the normalized L1-norm (Manhattan) of the difference.
///
public static double MAE(Vector a, Vector b) where T : struct, IEquatable, IFormattable
{
return (a - b).L1Norm()/a.Count;
}
///
/// Mean-Absolute Error (MAE), i.e. the normalized L1-norm (Manhattan) of the difference.
///
public static double MAE(double[] a, double[] b)
{
return SAD(a, b)/a.Length;
}
///
/// Mean-Absolute Error (MAE), i.e. the normalized L1-norm (Manhattan) of the difference.
///
public static float MAE(float[] a, float[] b)
{
return SAD(a, b)/a.Length;
}
///
/// Sum of Squared Difference (SSD), i.e. the squared L2-norm (Euclidean) of the difference.
///
public static double SSD(Vector a, Vector b) where T : struct, IEquatable, IFormattable
{
var norm = (a - b).L2Norm();
return norm*norm;
}
///
/// Sum of Squared Difference (SSD), i.e. the squared L2-norm (Euclidean) of the difference.
///
public static double SSD(double[] a, double[] b)
{
if (a.Length != b.Length)
{
throw new ArgumentException("All vectors must have the same dimensionality.");
}
var diff = new double[a.Length];
LinearAlgebraControl.Provider.SubtractArrays(a, b, diff);
return LinearAlgebraControl.Provider.DotProduct(diff, diff);
}
///
/// Sum of Squared Difference (SSD), i.e. the squared L2-norm (Euclidean) of the difference.
///
public static float SSD(float[] a, float[] b)
{
if (a.Length != b.Length)
{
throw new ArgumentException("All vectors must have the same dimensionality.");
}
var diff = new float[a.Length];
LinearAlgebraControl.Provider.SubtractArrays(a, b, diff);
return LinearAlgebraControl.Provider.DotProduct(diff, diff);
}
///
/// Mean-Squared Error (MSE), i.e. the normalized squared L2-norm (Euclidean) of the difference.
///
public static double MSE(Vector a, Vector b) where T : struct, IEquatable, IFormattable
{
var norm = (a - b).L2Norm();
return norm*norm/a.Count;
}
///
/// Mean-Squared Error (MSE), i.e. the normalized squared L2-norm (Euclidean) of the difference.
///
public static double MSE(double[] a, double[] b)
{
return SSD(a, b)/a.Length;
}
///
/// Mean-Squared Error (MSE), i.e. the normalized squared L2-norm (Euclidean) of the difference.
///
public static float MSE(float[] a, float[] b)
{
return SSD(a, b)/a.Length;
}
///
/// Euclidean Distance, i.e. the L2-norm of the difference.
///
public static double Euclidean(Vector a, Vector b) where T : struct, IEquatable, IFormattable
{
return (a - b).L2Norm();
}
///
/// Euclidean Distance, i.e. the L2-norm of the difference.
///
public static double Euclidean(double[] a, double[] b)
{
return Math.Sqrt(SSD(a, b));
}
///
/// Euclidean Distance, i.e. the L2-norm of the difference.
///
public static float Euclidean(float[] a, float[] b)
{
return (float) Math.Sqrt(SSD(a, b));
}
///
/// Manhattan Distance, i.e. the L1-norm of the difference.
///
public static double Manhattan(Vector a, Vector b) where T : struct, IEquatable, IFormattable
{
return (a - b).L1Norm();
}
///
/// Manhattan Distance, i.e. the L1-norm of the difference.
///
public static double Manhattan(double[] a, double[] b)
{
return SAD(a, b);
}
///
/// Manhattan Distance, i.e. the L1-norm of the difference.
///
public static float Manhattan(float[] a, float[] b)
{
return SAD(a, b);
}
///
/// Chebyshev Distance, i.e. the Infinity-norm of the difference.
///
public static double Chebyshev(Vector a, Vector b) where T : struct, IEquatable, IFormattable
{
return (a - b).InfinityNorm();
}
///
/// Chebyshev Distance, i.e. the Infinity-norm of the difference.
///
public static double Chebyshev(double[] a, double[] b)
{
if (a.Length != b.Length)
{
throw new ArgumentException("All vectors must have the same dimensionality.");
}
double max = Math.Abs(a[0] - b[0]);
for (int i = 1; i < a.Length; i++)
{
var next = Math.Abs(a[i] - b[i]);
if (next > max)
{
max = next;
}
}
return max;
}
///
/// Chebyshev Distance, i.e. the Infinity-norm of the difference.
///
public static float Chebyshev(float[] a, float[] b)
{
if (a.Length != b.Length)
{
throw new ArgumentException("All vectors must have the same dimensionality.");
}
float max = Math.Abs(a[0] - b[0]);
for (int i = 1; i < a.Length; i++)
{
var next = Math.Abs(a[i] - b[i]);
if (next > max)
{
max = next;
}
}
return max;
}
///
/// Minkowski Distance, i.e. the generalized p-norm of the difference.
///
public static double Minkowski(double p, Vector a, Vector b) where T : struct, IEquatable, IFormattable
{
return (a - b).Norm(p);
}
///
/// Minkowski Distance, i.e. the generalized p-norm of the difference.
///
public static double Minkowski(double p, double[] a, double[] b)
{
if (a.Length != b.Length)
{
throw new ArgumentException("All vectors must have the same dimensionality.");
}
if (p < 0d)
{
throw new ArgumentOutOfRangeException(nameof(p));
}
if (p == 1d)
{
return Manhattan(a, b);
}
if (p == 2d)
{
return Euclidean(a, b);
}
if (double.IsPositiveInfinity(p))
{
return Chebyshev(a, b);
}
double sum = 0d;
for (var i = 0; i < a.Length; i++)
{
sum += Math.Pow(Math.Abs(a[i] - b[i]), p);
}
return Math.Pow(sum, 1.0 / p);
}
///
/// Minkowski Distance, i.e. the generalized p-norm of the difference.
///
public static float Minkowski(double p, float[] a, float[] b)
{
if (a.Length != b.Length)
{
throw new ArgumentException("All vectors must have the same dimensionality.");
}
if (p < 0d)
{
throw new ArgumentOutOfRangeException(nameof(p));
}
if (p == 1d)
{
return Manhattan(a, b);
}
if (p == 2d)
{
return Euclidean(a, b);
}
if (double.IsPositiveInfinity(p))
{
return Chebyshev(a, b);
}
double sum = 0d;
for (var i = 0; i < a.Length; i++)
{
sum += Math.Pow(Math.Abs(a[i] - b[i]), p);
}
return (float) Math.Pow(sum, 1.0/p);
}
///
/// Canberra Distance, a weighted version of the L1-norm of the difference.
///
public static double Canberra(double[] a, double[] b)
{
if (a.Length != b.Length)
{
throw new ArgumentException("All vectors must have the same dimensionality.");
}
double sum = 0d;
for (var i = 0; i < a.Length; i++)
{
sum += Math.Abs(a[i] - b[i]) / (Math.Abs(a[i]) + Math.Abs(b[i]));
}
return sum;
}
///
/// Canberra Distance, a weighted version of the L1-norm of the difference.
///
public static float Canberra(float[] a, float[] b)
{
if (a.Length != b.Length)
{
throw new ArgumentException("All vectors must have the same dimensionality.");
}
float sum = 0f;
for (var i = 0; i < a.Length; i++)
{
sum += Math.Abs(a[i] - b[i]) / (Math.Abs(a[i]) + Math.Abs(b[i]));
}
return sum;
}
///
/// Cosine Distance, representing the angular distance while ignoring the scale.
///
public static double Cosine(double[] a, double[] b)
{
if (a.Length != b.Length)
{
throw new ArgumentException("All vectors must have the same dimensionality.");
}
var ab = LinearAlgebraControl.Provider.DotProduct(a, b);
var a2 = LinearAlgebraControl.Provider.DotProduct(a, a);
var b2 = LinearAlgebraControl.Provider.DotProduct(b, b);
return 1d - ab/Math.Sqrt(a2*b2);
}
///
/// Cosine Distance, representing the angular distance while ignoring the scale.
///
public static float Cosine(float[] a, float[] b)
{
if (a.Length != b.Length)
{
throw new ArgumentException("All vectors must have the same dimensionality.");
}
var ab = LinearAlgebraControl.Provider.DotProduct(a, b);
var a2 = LinearAlgebraControl.Provider.DotProduct(a, a);
var b2 = LinearAlgebraControl.Provider.DotProduct(b, b);
return (float)(1d - ab/Math.Sqrt(a2*b2));
}
///
/// Hamming Distance, i.e. the number of positions that have different values in the vectors.
///
public static double Hamming(double[] a, double[] b)
{
if (a.Length != b.Length)
{
throw new ArgumentException("All vectors must have the same dimensionality.");
}
int count = 0;
for (int i = 0; i < a.Length; i++)
{
if (a[i] != b[i])
{
count++;
}
}
return count;
}
///
/// Hamming Distance, i.e. the number of positions that have different values in the vectors.
///
public static float Hamming(float[] a, float[] b)
{
if (a.Length != b.Length)
{
throw new ArgumentException("All vectors must have the same dimensionality.");
}
int count = 0;
for (int i = 0; i < a.Length; i++)
{
if (a[i] != b[i])
{
count++;
}
}
return count;
}
///
/// Pearson's distance, i.e. 1 - the person correlation coefficient.
///
public static double Pearson(IEnumerable a, IEnumerable b)
{
return 1.0 - Correlation.Pearson(a, b);
}
///
/// Jaccard distance, i.e. 1 - the Jaccard index.
///
/// Thrown if a or b are null.
/// Throw if a and b are of different lengths.
/// Jaccard distance.
public static double Jaccard(double[] a, double[] b)
{
int intersection = 0, union = 0;
if (a == null)
{
throw new ArgumentNullException(nameof(a));
}
if (b == null)
{
throw new ArgumentNullException(nameof(b));
}
if (a.Length != b.Length)
{
throw new ArgumentException("All vectors must have the same dimensionality.");
}
if (a.Length == 0 && b.Length == 0)
{
return 0;
}
for (int x = 0, len = a.Length; x < len; x++)
{
if (a[x] != 0 && b[x] != 0)
{
if (a[x] == b[x])
{
intersection++;
}
union++;
}
}
return 1.0 - ((double)intersection / (double)union);
}
///
/// Jaccard distance, i.e. 1 - the Jaccard index.
///
/// Thrown if a or b are null.
/// Throw if a and b are of different lengths.
/// Jaccard distance.
public static double Jaccard(float[] a, float[] b)
{
int intersection = 0, union = 0;
if (a == null)
{
throw new ArgumentNullException(nameof(a));
}
if (b == null)
{
throw new ArgumentNullException(nameof(b));
}
if (a.Length != b.Length)
{
throw new ArgumentException("All vectors must have the same dimensionality.");
}
if (a.Length == 0 && b.Length == 0)
{
return 0;
}
for (int x = 0, len = a.Length; x < len; x++)
{
if (a[x] != 0 && b[x] != 0)
{
if (a[x] == b[x])
{
intersection++;
}
union++;
}
}
return 1.0 - ((float)intersection / (float)union);
}
}
}