public void MultivariateLinearRegressionAgreement()
{
Random rng = new Random(1);
MultivariateSample SA = new MultivariateSample(2);
for (int i = 0; i < 10; i++)
{
SA.Add(rng.NextDouble(), rng.NextDouble());
}
RegressionResult RA = SA.LinearRegression(0);
ColumnVector PA = RA.Parameters.Best;
SymmetricMatrix CA = RA.Parameters.Covariance;
MultivariateSample SB = SA.Columns(1, 0);
RegressionResult RB = SB.LinearRegression(1);
ColumnVector PB = RB.Parameters.Best;
SymmetricMatrix CB = RB.Parameters.Covariance;
Assert.IsTrue(TestUtilities.IsNearlyEqual(PA[0], PB[1])); Assert.IsTrue(TestUtilities.IsNearlyEqual(PA[1], PB[0]));
Assert.IsTrue(TestUtilities.IsNearlyEqual(CA[0, 0], CB[1, 1])); Assert.IsTrue(TestUtilities.IsNearlyEqual(CA[0, 1], CB[1, 0])); Assert.IsTrue(TestUtilities.IsNearlyEqual(CA[1, 1], CB[0, 0]));
BivariateSample SC = SA.TwoColumns(1, 0);
RegressionResult RC = SC.LinearRegression();
ColumnVector PC = RC.Parameters.Best;
SymmetricMatrix CC = RC.Parameters.Covariance;
Assert.IsTrue(TestUtilities.IsNearlyEqual(PA, PC));
Assert.IsTrue(TestUtilities.IsNearlyEqual(CA, CC));
}
public void MultivariateLinearRegressionNullDistribution()
{
int d = 4;
Random rng = new Random(1);
NormalDistribution n = new NormalDistribution();
Sample fs = new Sample();
for (int i = 0; i < 64; i++)
{
MultivariateSample ms = new MultivariateSample(d);
for (int j = 0; j < 8; j++)
{
double[] x = new double[d];
for (int k = 0; k < d; k++)
{
x[k] = n.GetRandomValue(rng);
}
ms.Add(x);
}
RegressionResult r = ms.LinearRegression(0);
fs.Add(r.F.Statistic);
}
// conduct a KS test to check that F follows the expected distribution
TestResult ks = fs.KolmogorovSmirnovTest(new FisherDistribution(3, 4));
Assert.IsTrue(ks.LeftProbability < 0.95);
}
public RegressionResult RegressLine(List <Point> points)
{
if (points.Count == 0)
{
return(new RegressionResult());
}
var xtyAve = points.Select(p => p.X * p.Y).Average();
var xAve = points.Average(p => p.X);
var yAve = points.Average(p => p.Y);
var xsqAve = points.Select(p => p.X * p.X).Average();
var ysqAve = points.Select(p => p.Y * p.Y).Average();
var xAveSq = xAve * xAve;
var yAveSq = yAve * yAve;
var result = new RegressionResult();
result.Slope = (xtyAve - xAve * yAve) / (xsqAve - xAveSq);
if (double.IsNaN(result.Slope))
{
result.Slope = 100000;
}
result.Intercept = yAve - result.Slope * xAve;
result.RSquared = (xtyAve - xAve * yAve) / Math.Sqrt((xsqAve - xAveSq) * (ysqAve - yAveSq));
return(result);
}
//RegressionResult
double runCalculation(SimplexConstant[] consts)
{
ObjectiveFunctionDelegate objFunc = new ObjectiveFunctionDelegate(minimizeAngle);
RegressionResult result = NelderMeadSimplex.Regress(consts, tolerance, maxEvals, objFunc);
return(result.Constants[0]);
}
public List <Point> PointsOnLineDistanceAway(Point p, RegressionResult line, double dist)
{
//{{x1->(-a m+xo-Sqrt[d^2 (1+m^2)-(a+m xo-yo)^2]+m yo)/(1+m^2)}
//{ x1->(-a m+xo+Sqrt[d^2 (1+m^2)-(a+m xo-yo)^2]+m yo)/(1+m^2)}}
//{{x1->(-a*m+xo-Math.Sqrt[dsq*(1+msq)-(a+m*xo-yo)^2]+m*yo)/(1+msq)}
//{ x1->(-a*m+xo+Math.Sqrt[dsq*(1+msq)-(a+m*xo-yo)^2]+m*yo)/(1+msq)}}
var a = line.Intercept;
var m = line.Slope;
var d = dist;
var dsq = d * d;
var msq = m * m;
var xo = p.X;
var yo = p.Y;
var sqrtPart = Math.Sqrt(dsq * (1 + msq) - (a + m * xo - yo) * (a + m * xo - yo));
var xplus = (int)Math.Round((-a * m + xo - sqrtPart + m * yo) / (1 + msq));
var xminus = (int)Math.Round((-a * m + xo + sqrtPart + m * yo) / (1 + msq));
if (xminus == int.MinValue)
{
return(new List <Point>());
}
return(new List <Point>
{
new Point(xplus, (int)Math.Round(xplus * m + a)),
new Point(xminus, (int)Math.Round(xminus * m + a))
});
}
public Point Intersects(RegressionResult line1, RegressionResult line2)
{
//x=(a2-a1)/(m1-m2)
var x = (line2.Intercept - line1.Intercept) / (line1.Slope - line2.Slope);
var y = line1.Slope * x + line1.Intercept;
return(new Point(x, y));
}
private static void _printResult(RegressionResult result)
{
// a bit of reflection fun, why not...
PropertyInfo[] properties = result.GetType().GetProperties();
foreach (PropertyInfo p in properties)
{
Console.WriteLine(p.Name + ": " + p.GetValue(result, null).ToString());
}
}
/// <summary>
/// Test to see if we can fit a parabola
/// </summary>
public static void SimplexTest1()
{
Console.WriteLine("Starting SimplexTest1");
SimplexConstant[] constants = new SimplexConstant[] { new SimplexConstant(3, 1), new SimplexConstant(5, 1) };
double tolerance = 1e-6;
int maxEvals = 1000;
ObjectiveFunctionDelegate objFunction = new ObjectiveFunctionDelegate(_objFunction1);
RegressionResult result = NelderMeadSimplex.Regress(constants, tolerance, maxEvals, objFunction);
_printResult(result);
}
/// <summary>
/// Test on the Rosenbrock function
/// </summary>
public static void SimplexTest2()
{
Console.WriteLine("\n\nStarting SimplexTest2");
// we are regressing for frequency, amplitude, and phase offset
SimplexConstant[] constants = new SimplexConstant[] { new SimplexConstant(-1.2, .1), new SimplexConstant(1, .1)};
double tolerance = 1e-10;
int maxEvals = 1000;
ObjectiveFunctionDelegate objFunction = new ObjectiveFunctionDelegate(_objFunction2);
RegressionResult result = NelderMeadSimplex.Regress(constants, tolerance, maxEvals, objFunction);
_printResult(result);
}
/// <summary>
/// Test to see if we can fit a parabola
/// </summary>
private static void _simplexTest1()
{
Console.WriteLine("Starting SimplexTest1");
SimplexConstant[] nss = new SimplexConstant[] { new SimplexConstant(0, 1), new SimplexConstant(0, 1), new SimplexConstant(0, 1), new SimplexConstant(0, 1), new SimplexConstant(1, 1), new SimplexConstant(1, 1) };
double[] tt = { 5.0, 10.0, 15.0, 20.0, 25.0 };
double[] Y = { 0.001770949, 0.008396027, 0.013860686, 0.019379306, 0.023731833 };
double tolerance = 1e-6;
int maxEvals = 1000;
ObjectiveFunctionDelegate objFunction = new ObjectiveFunctionDelegate(_objFunction1);
RegressionResult result = NelderMeadSimplex.Regress(nss, tt, Y, tolerance, maxEvals, objFunction);
_printResult(result);
}
// Run cost minimization
Vector3 IDecisionManager.getNextDesiredPoint()
{
// What are the variables to minimize (position)
SimplexConstant[] constants = new SimplexConstant[] { new SimplexConstant(this.sensorModule.gps.position.x, 1),
new SimplexConstant(this.sensorModule.gps.position.y, 1),
new SimplexConstant(this.sensorModule.gps.position.z, 1) };
double tolerance = 1e-30;
int maxEvals = 10000;
// What's the objective function
ObjectiveFunctionDelegate objFunction = new ObjectiveFunctionDelegate(_objFunction1);
RegressionResult result = NelderMeadSimplex.Regress(constants, tolerance, maxEvals, objFunction);
Vector3 r = new Vector3((float)result.Constants[0], (float)result.Constants[1], (float)result.Constants[2]);
// Debug.Log (result.TerminationReason.ToString ());
return(r);
}
public void BivariateLinearPolynomialRegressionAgreement()
{
// A degree-1 polynomial fit should give the same answer as a linear fit
BivariateSample B = new BivariateSample();
B.Add(0.0, 5.0);
B.Add(3.0, 6.0);
B.Add(1.0, 7.0);
B.Add(4.0, 8.0);
B.Add(2.0, 9.0);
RegressionResult PR = B.PolynomialRegression(1);
RegressionResult LR = B.LinearRegression();
Assert.IsTrue(TestUtilities.IsNearlyEqual(PR.Parameters.Best, LR.Parameters.Best));
Assert.IsTrue(TestUtilities.IsNearlyEqual(PR.Parameters.Covariance, LR.Parameters.Covariance));
}
public void Minimize()
{
SetCoefficients();
Console.WriteLine("Starting minimization...");
SimplexConstant[] constants = new SimplexConstant[Coefficients.Length];
for (int i = 0; i < Coefficients.Length; i++)
{
constants[i] = new SimplexConstant(Coefficients[i], Math.Abs(Coefficients[i]) / 2);
}
double tolerance = 1e-6;
int maxEvals = 1000;
ObjectiveFunctionDelegate objFunction = new ObjectiveFunctionDelegate(SpiderObjectiveFunction);
RegressionResult result = NelderMeadSimplex.Regress(constants, tolerance, maxEvals, objFunction);
Coefficients = result.Constants;
PrintCoefficients(Coefficients);
}
/// <summary>
/// Calculates the regression function between the original and predicted or
/// </summary>
/// <param name="peptideScans"></param>
/// <param name="peptidePredictedNET"></param>
/// <returns></returns>
public RegressionResult CalculateRegression(List <float> observed, List <float> basis)
{
float[] observedArray = new float[observed.Count];
float[] basisArray = new float[basis.Count];
observed.CopyTo(observedArray);
basis.CopyTo(basisArray);
m_regressor.SetPoints(ref observedArray, ref basisArray);
m_regressor.PerformRegression((Regressor.RegressionType)RegressionType);
RegressionResult result = new RegressionResult();
result.NETSlope = m_regressor.Slope;
result.NETIntercept = m_regressor.Intercept;
result.NETRSquared = m_regressor.RSquared;
return(result);
}
public Point PointAlongLine(RegressionResult line, Point point, double distance)
{
//d2 = dx2 + dy2
//m = dy / dx => m2 = dy2 / dx2
//m2* dx2 = dy2
//d2 = dx2 + m2 * dx2 => (1 + m2) * dx2
//sqrt(d2 / (1 + m2)) = dx
//sqrt(d2 - dx2) = dy
var dx = Math.Sqrt(distance * distance / (1 + (line.Slope * line.Slope)));
var dy = Math.Sqrt(distance * distance - dx * dx);
return(new Point
(
point.X + (int)dx * Math.Sign(distance),
point.Y + (int)dy * Math.Sign(distance)
));
}
static void PrintResult(string title, Bacterium bacterium, RegressionResult result)
{
double matchSum = 0;
Console.WriteLine("\n");
Console.WriteLine($"{title} on {bacterium.ASV}. Used {result.FormulaUsed}");
for (var i = 0; i < result.TestY.Length; i++)
{
var match = GetMatch(result.TestX[i], result.PredictionOnTestSet[i]);
Console.WriteLine(String.Format("Timestamp {0} is {1:0.00} and predicted {2:0.00}. Prediction is {3:0.0000}% of actual value",
result.TestY[i],
result.TestX[i],
result.PredictionOnTestSet[i],
match
));
matchSum += match;
}
var matchAverage = matchSum / result.TestY.Length;
Console.WriteLine($"Error on training set: {result.Error}");
Console.WriteLine($"Average match on test set (closer to 100 is better): {Math.Round(matchAverage, 4)}");
}
private const double JITTER = 1e-10d; // a small value used to protect against floating point noise
public static RegressionResult Regress(SimplexConstant[] simplexConstants, double convergenceTolerance, int maxEvaluations,
ObjectiveFunctionDelegate objectiveFunction)
{
// confirm that we are in a position to commence
if (objectiveFunction == null)
{
throw new InvalidOperationException("ObjectiveFunction must be set to a valid ObjectiveFunctionDelegate"); // Not L10N
}
if (simplexConstants == null)
{
throw new InvalidOperationException("SimplexConstants must be initialized"); // Not L10N
}
// create the initial simplex
int numDimensions = simplexConstants.Length;
int numVertices = numDimensions + 1;
Vector <double>[] vertices = InitializeVertices(simplexConstants);
int evaluationCount = 0;
TerminationReason terminationReason;
ErrorProfile errorProfile;
double[] errorValues = InitializeErrorValues(vertices, objectiveFunction);
// iterate until we converge, or complete our permitted number of iterations
while (true)
{
errorProfile = EvaluateSimplex(errorValues);
// see if the range in point heights is small enough to exit
if (HasConverged(convergenceTolerance, errorProfile, errorValues))
{
terminationReason = TerminationReason.Converged;
break;
}
// attempt a reflection of the simplex
double reflectionPointValue = TryToScaleSimplex(-1.0, ref errorProfile, vertices, errorValues, objectiveFunction);
++evaluationCount;
if (reflectionPointValue <= errorValues[errorProfile.LowestIndex])
{
// it's better than the best point, so attempt an expansion of the simplex
TryToScaleSimplex(2.0, ref errorProfile, vertices, errorValues, objectiveFunction);
++evaluationCount;
}
else if (reflectionPointValue >= errorValues[errorProfile.NextHighestIndex])
{
// it would be worse than the second best point, so attempt a contraction to look
// for an intermediate point
double currentWorst = errorValues[errorProfile.HighestIndex];
double contractionPointValue = TryToScaleSimplex(0.5, ref errorProfile, vertices, errorValues, objectiveFunction);
++evaluationCount;
if (contractionPointValue >= currentWorst)
{
// that would be even worse, so let's try to contract uniformly towards the low point;
// don't bother to update the error profile, we'll do it at the start of the
// next iteration
ShrinkSimplex(errorProfile, vertices, errorValues, objectiveFunction);
evaluationCount += numVertices; // that required one function evaluation for each vertex; keep track
}
}
// check to see if we have exceeded our alloted number of evaluations
if (evaluationCount >= maxEvaluations)
{
terminationReason = TerminationReason.MaxFunctionEvaluations;
break;
}
}
RegressionResult regressionResult = new RegressionResult(terminationReason,
vertices[errorProfile.LowestIndex].ToArray(), errorValues[errorProfile.LowestIndex], evaluationCount);
return(regressionResult);
}
public static RegressionResult Regress(SimplexConstant[] simplexConstants, double convergenceTolerance, int maxEvaluations,
ObjectiveFunctionDelegate objectiveFunction)
{
// confirm that we are in a position to commence
if (objectiveFunction == null)
throw new InvalidOperationException("ObjectiveFunction must be set to a valid ObjectiveFunctionDelegate"); // Not L10N
if (simplexConstants == null)
throw new InvalidOperationException("SimplexConstants must be initialized"); // Not L10N
// create the initial simplex
int numDimensions = simplexConstants.Length;
int numVertices = numDimensions + 1;
Vector<double>[] vertices = InitializeVertices(simplexConstants);
int evaluationCount = 0;
TerminationReason terminationReason;
ErrorProfile errorProfile;
double[] errorValues = InitializeErrorValues(vertices, objectiveFunction);
// iterate until we converge, or complete our permitted number of iterations
while (true)
{
errorProfile = EvaluateSimplex(errorValues);
// see if the range in point heights is small enough to exit
if (HasConverged(convergenceTolerance, errorProfile, errorValues))
{
terminationReason = TerminationReason.Converged;
break;
}
// attempt a reflection of the simplex
double reflectionPointValue = TryToScaleSimplex(-1.0, ref errorProfile, vertices, errorValues, objectiveFunction);
++evaluationCount;
if (reflectionPointValue <= errorValues[errorProfile.LowestIndex])
{
// it's better than the best point, so attempt an expansion of the simplex
TryToScaleSimplex(2.0, ref errorProfile, vertices, errorValues, objectiveFunction);
++evaluationCount;
}
else if (reflectionPointValue >= errorValues[errorProfile.NextHighestIndex])
{
// it would be worse than the second best point, so attempt a contraction to look
// for an intermediate point
double currentWorst = errorValues[errorProfile.HighestIndex];
double contractionPointValue = TryToScaleSimplex(0.5, ref errorProfile, vertices, errorValues, objectiveFunction);
++evaluationCount;
if (contractionPointValue >= currentWorst)
{
// that would be even worse, so let's try to contract uniformly towards the low point;
// don't bother to update the error profile, we'll do it at the start of the
// next iteration
ShrinkSimplex(errorProfile, vertices, errorValues, objectiveFunction);
evaluationCount += numVertices; // that required one function evaluation for each vertex; keep track
}
}
// check to see if we have exceeded our alloted number of evaluations
if (evaluationCount >= maxEvaluations)
{
terminationReason = TerminationReason.MaxFunctionEvaluations;
break;
}
}
RegressionResult regressionResult = new RegressionResult(terminationReason,
vertices[errorProfile.LowestIndex].ToArray(), errorValues[errorProfile.LowestIndex], evaluationCount);
return regressionResult;
}