/// <summary>
/// Calculates the normalized contrast angle dot-product or 1 - angle/90 between two vectors,
/// using the square roots of the values in the vectors.
/// </summary>
/// <param name="s">The other vector</param>
/// <returns>Normalized contrast angle dot-product of square roots of values in vectors</returns>
public double NormalizedContrastAngleSqrt(Statistics s)
{
var stat1 = new Statistics(_list.Select(Math.Sqrt));
var stat2 = new Statistics(s._list.Select(Math.Sqrt));
return stat1.NormalizedContrastAngle(stat2);
}
public void DotpTest()
{
{
var stat1 = new Statistics(new[] { 1.0, 2.0, 3.0 });
Assert.AreEqual(1.0, stat1.Angle(stat1));
Assert.AreEqual(1.0, stat1.AngleSqrt(stat1));
Assert.AreEqual(1.0, stat1.AngleUnitVector(stat1));
Assert.AreEqual(1.0, stat1.NormalizedContrastAngleSqrt(stat1));
// Dot-product of zero should yield zero cos(angle)
var stat2 = new Statistics(new[] { -3.0, 3.0, -1.0 });
Assert.AreEqual(0.0, stat1.Angle(stat2));
Assert.AreEqual(double.NaN, stat1.AngleSqrt(stat2));
Assert.AreEqual(0.0, stat1.AngleUnitVector(stat2));
// Without negatives this is only possible with vectors containing zeros
var statZeros1 = new Statistics(new[] { 1.0, 0.0, 2.0, 0.0, 3.0, 0.0 });
var statZeros2 = new Statistics(new[] { 0.0, 1.0, 0.0, 1.0, 0.0, 3.0 });
Assert.AreEqual(0.0, statZeros1.Angle(statZeros2));
// And this should work for square rooted angle
Assert.AreEqual(0.0, statZeros1.AngleSqrt(statZeros2));
Assert.AreEqual(0.0, statZeros1.AngleUnitVector(statZeros2));
Assert.AreEqual(0.0, statZeros1.NormalizedContrastAngleSqrt(statZeros2));
}
{
var stat0 = new Statistics(new[] { 0.0, 10.0 });
var stat1 = new Statistics(new[] { 0.1, 10.0 });
var stat2 = new Statistics(new[] { 1.0, 10.0 });
var stat3 = new Statistics(new[] { 2.0, 10.0 });
var stat4 = new Statistics(new[] { 5.0, 10.0 });
var stat5 = new Statistics(new[] { 10.0, 10.0 });
double a1 = stat0.Angle(stat1);
double aN1 = stat0.NormalizedContrastAngle(stat1);
Assert.AreEqual(1.0, a1, 0.01);
Assert.AreEqual(0.99, aN1, 0.01);
Assert.AreEqual(a1, Statistics.NormalizedContrastAngleToAngle(aN1), 0.0001);
Assert.AreEqual(aN1, Statistics.AngleToNormalizedContrastAngle(a1), 0.0001);
double a2 = stat0.Angle(stat2);
double aN2 = stat0.NormalizedContrastAngle(stat2);
Assert.AreEqual(0.99, a2, 0.01);
Assert.AreEqual(0.94, aN2, 0.01);
Assert.AreEqual(a2, Statistics.NormalizedContrastAngleToAngle(aN2), 0.0001);
Assert.AreEqual(aN2, Statistics.AngleToNormalizedContrastAngle(a2), 0.0001);
double a3 = stat0.Angle(stat3);
double aN3 = stat0.NormalizedContrastAngle(stat3);
Assert.AreEqual(0.98, a3, 0.01);
Assert.AreEqual(0.87, aN3, 0.01);
Assert.AreEqual(a3, Statistics.NormalizedContrastAngleToAngle(aN3), 0.0001);
Assert.AreEqual(aN3, Statistics.AngleToNormalizedContrastAngle(a3), 0.0001);
double a4 = stat0.Angle(stat4);
double aN4 = stat0.NormalizedContrastAngle(stat4);
Assert.AreEqual(0.89, a4, 0.01);
Assert.AreEqual(0.7, aN4, 0.01);
Assert.AreEqual(a4, Statistics.NormalizedContrastAngleToAngle(aN4), 0.0001);
Assert.AreEqual(aN4, Statistics.AngleToNormalizedContrastAngle(a4), 0.0001);
double a5 = stat0.Angle(stat5);
double aN5 = stat0.NormalizedContrastAngle(stat5);
Assert.AreEqual(0.7, a5, 0.01);
Assert.AreEqual(0.5, aN5, 0.01);
Assert.AreEqual(a5, Statistics.NormalizedContrastAngleToAngle(aN5), 0.0001);
Assert.AreEqual(aN5, Statistics.AngleToNormalizedContrastAngle(a5), 0.0001);
}
}