public void LogLikelihoodDerivative_MultipleResponses_MatchesFiniteDifferenceDerivative()
{
double alpha1 = .3;
double delta1 = .1;
double chi1 = .2;
ThreeParamModelParameters modelParameters1 = new ThreeParamModelParameters(alpha1, delta1, chi1);
double alpha2 = .5;
double delta2 = .6;
double chi2 = .7;
ThreeParamModelParameters modelParameters2 = new ThreeParamModelParameters(alpha2, delta2, chi2);
ThreeParamModelParameters modelParameters3 = new ThreeParamModelParameters(alpha2, delta2, chi2);
List <IModelParameters> modelParameterList = new List <IModelParameters>();
modelParameterList.Add(modelParameters1);
modelParameterList.Add(modelParameters2);
modelParameterList.Add(modelParameters3);
LogLikelihoodFunction logLikelihoodFunction = new LogLikelihoodFunction(modelParameterList);
double theta = .4;
List <int> responseVector = new List <int>()
{
1, 0, 1
};
OneDimensionalFunction function = x => logLikelihoodFunction.LogLikelihood(responseVector, x);
FiniteDifferencer finiteDifferencer = new FiniteDifferencer(function);
double logLikelihoodDerivative = logLikelihoodFunction.LogLikelihoodFirstDerivative(responseVector, theta);
double finiteDifferenceDerivative = finiteDifferencer.ApproximateDerivative(theta);
Assert.AreEqual(finiteDifferenceDerivative, logLikelihoodDerivative, Tolerance);
}
public BisectionSolver(OneDimensionalFunction function, double lowerBound, double upperBound)
{
_function = function;
_initialLowerBound = lowerBound;
_initialUpperBound = upperBound;
ValidateBounds();
}
public GlobalMaximizer(OneDimensionalFunction function, OneDimensionalFunction derivativeFunction, double lowerBound, double upperBound, double tolerance = .001)
{
_lowerBound = lowerBound;
_upperBound = upperBound;
_function = function;
_extremaFinder = new GradientDescentExtremaFinder(derivativeFunction, tolerance);
}
public BisectionSolver(OneDimensionalFunction function, double lowerBound, double upperBound)
{
_function = function;
_initialLowerBound = lowerBound;
_initialUpperBound = upperBound;
ValidateBounds();
}
public void ApproximateDerivative_SimpleQuadraticAtNonZeroDerivative_ReturnsApproxDerivativeWithinTolerance()
{
OneDimensionalFunction f = x => x * x;
FiniteDifferencer finiteDifferencer = new FiniteDifferencer(f);
var approxDerivative = finiteDifferencer.ApproximateDerivative(.5);
double expectedDerivative = 2 * .5;
CheckWithinTolerance(expectedDerivative, approxDerivative);
}
public void ApproximateDerivative_CosAtZeroDerivative_ReturnsApproxDerivativeWithinTolerance()
{
OneDimensionalFunction f = Math.Cos;
FiniteDifferencer finiteDifferencer = new FiniteDifferencer(f);
var approxDerivative = finiteDifferencer.ApproximateDerivative(0);
double expectedDerivative = 0;
CheckWithinTolerance(expectedDerivative, approxDerivative);
}
public void FindMaximum_XSquared_ThrowsExceptions()
{
OneDimensionalFunction derivative = x => 2 * x;
GradientDescentExtremaFinder extremaFinder = new GradientDescentExtremaFinder(derivative);
double initialGuess = 3;
var calculatedMinimum = extremaFinder.FindMaximum(initialGuess);
double expectedMinimum = 0;
Assert.AreEqual(expectedMinimum, calculatedMinimum, Tolerance);
}
public void FindMaximum_SinX_ReturnsPiOverTwo()
{
OneDimensionalFunction derivative = x => Math.Cos(x);
GradientDescentExtremaFinder extremaFinder = new GradientDescentExtremaFinder(derivative);
double initialGuess = 0;
var calculatedMinimumLoc = extremaFinder.FindMaximum(initialGuess);
double expectedMinimumLoc = Math.PI / 2;
Assert.AreEqual(expectedMinimumLoc, calculatedMinimumLoc, Tolerance);
}
public void FindRoot_CosFunction_ReturnsRootWithinTolerance()
{
OneDimensionalFunction f = Math.Cos;
OneDimensionalFunction fPrime = x => - Math.Sin(x);
const double initialGuess = .5;
NewtonRhapsonSolver solver = new NewtonRhapsonSolver(f, fPrime, initialGuess);
var root = solver.FindRoot();
Assert.IsTrue(Math.Abs(f(root)) < solver.Tolerance);
}
public void FindRoot_CosFunction_ReturnsRootWithinTolerance()
{
OneDimensionalFunction f = Math.Cos;
double lowerBound = -Math.PI / 2;
double upperBound = Math.PI;
BisectionSolver solver = new BisectionSolver(f, lowerBound, upperBound);
var root = solver.FindRoot();
Assert.IsTrue(Math.Abs(f(root)) < solver.Tolerance);
}
public void FindRoot_PolynomialLowerBoundIsZero_ReturnsExactRoot()
{
OneDimensionalFunction f = x => x * x - 4;
double lowerBound = -2;
double upperBound = 3;
BisectionSolver solver = new BisectionSolver(f, lowerBound, upperBound);
var root = solver.FindRoot();
Assert.AreEqual(lowerBound, root);
}
public void FindRoot_QuadraticIncorrectIntialGuess_ReturnsRootWithinTolerance()
{
OneDimensionalFunction f = x => x * x - 4;
double lowerBound = -1;
double upperBound = 3;
BisectionSolver solver = new BisectionSolver(f, lowerBound, upperBound);
var root = solver.FindRoot();
Assert.IsTrue(Math.Abs(f(root)) < solver.Tolerance);
}
public void FindRoot_QuadraticIncorrectIntialGuess_ReturnsRootWithinTolerance()
{
OneDimensionalFunction f = x => x * x;
OneDimensionalFunction fPrime = x => 2 * x;
const double initialGuess = 4;
NewtonRhapsonSolver solver = new NewtonRhapsonSolver(f, fPrime, initialGuess);
var root = solver.FindRoot();
Assert.IsTrue(Math.Abs(f(root)) < solver.Tolerance);
}
public void FindRoot_PolynomialExactIntialGuess_ReturnsExactRoot()
{
OneDimensionalFunction f = x => x * x - 4;
OneDimensionalFunction fPrime = x => 2 * x;
const double initialGuess = 2;
NewtonRhapsonSolver solver = new NewtonRhapsonSolver(f, fPrime, initialGuess);
var root = solver.FindRoot();
Assert.AreEqual(initialGuess, root);
}
public void FindMaximize_MaxiumOccursAtBoundary_ReturnsCorrectValue()
{
OneDimensionalFunction function = x => - x * x * x * x - x * x * x + 11 * x * x + 9 * x - 18;
OneDimensionalFunction derivativeFunction = x => - 4 * x * x * x - 3 * x * x + 22 * x + 9;
double lowerBound = -5;
double upperBound = 5;
GlobalMaximizer maximizer = new GlobalMaximizer(function, derivativeFunction, lowerBound, upperBound);
var maxLocation = maximizer.FindPosOfMaximum();
double expectedMaxPostion = 2.20582;
Assert.AreEqual(expectedMaxPostion, maxLocation, Tolerance);
}
public void FindMaximize_FunctionWithSeveralEqualGlobalMinima_ReturnsAValueWhichGivesMax()
{
OneDimensionalFunction function = Math.Sin;
OneDimensionalFunction derivativeFunction = Math.Cos;
double lowerBound = -5;
double upperBound = 5;
GlobalMaximizer maximizer = new GlobalMaximizer(function, derivativeFunction, lowerBound, upperBound);
var x = maximizer.FindPosOfMaximum();
double max = function(x);
double expectedMax = 1;
Assert.AreEqual(expectedMax, max, Tolerance);
}
private double InternalFindMin(double initialGuess, OneDimensionalFunction derivativeFunction)
{
double x = initialGuess;
for (int i = 0; i < MaxIterations; i++)
{
var derivative = derivativeFunction(x);
double newX = x - Alpha * derivative;
if (DifferenceWithinTolerance(x, newX))
{
return(newX);
}
x = newX;
}
throw new Exception(String.Format("Unable to find minimum using gradient descent within {0} iterations",
MaxIterations));
}
public double GetMle(List <int> responseVector)
{
LogLikelihoodFunction logLikelihoodFunction = new LogLikelihoodFunction(_modelParametersList);
//const double initialGuess = 0;
OneDimensionalFunction function = x => logLikelihoodFunction.LogLikelihood(responseVector, x);
OneDimensionalFunction firstDerivativeFunction = x => logLikelihoodFunction.LogLikelihoodFirstDerivative(responseVector, x);
//OneDimensionalFunction secondDerivativeFunction = x => logLikelihoodFunction.LogLikelihoodSecondDerivative(responseVector, x);
//NewtonRhapsonSolver rootSolver = new NewtonRhapsonSolver(firstDerivativeFunction, secondDerivativeFunction, initialGuess);
//BisectionSolver rootSolver = new BisectionSolver(firstDerivativeFunction, -6, 6);
//double mle = rootSolver.FindRoot();
//double mle = rootSolver.FindRoot();
GlobalMaximizer globalMaximizer = new GlobalMaximizer(function, firstDerivativeFunction, -6, 6, _gradientDescentTolerance);
var mle = globalMaximizer.FindPosOfMaximum();
return(mle);
}
public FiniteDifferencer(OneDimensionalFunction function)
{
_function = function;
}
public GradientDescentExtremaFinder(OneDimensionalFunction derivativeFunction, double tolerance = .001)
{
_derivativeFunction = derivativeFunction;
_tolerance = tolerance;
}
public double FindMaximum(double initialGuess)
{
OneDimensionalFunction negativeOfDerivative = x => - _derivativeFunction(x);
return(InternalFindMin(initialGuess, negativeOfDerivative));
}
public FiniteDifferencer(OneDimensionalFunction function)
{
_function = function;
}
// Newton Rhapson root finder for one dimensional functions.
public NewtonRhapsonSolver(OneDimensionalFunction function, OneDimensionalFunction fDerivative, double initialGuess)
{
_function = function;
_fDerivative = fDerivative;
_initialGuess = initialGuess;
}
// Newton Rhapson root finder for one dimensional functions.
public NewtonRhapsonSolver(OneDimensionalFunction function, OneDimensionalFunction fDerivative, double initialGuess)
{
_function = function;
_fDerivative = fDerivative;
_initialGuess = initialGuess;
}