public static bool TryFindRootWithJacobianStep(Func <Real[], Real[]> f,
Real[] initialGuess,
Real accuracy,
int maxIterations,
Real jacobianStepSize,
out Real[] root)
{
DenseVector denseVector1 = new DenseVector(initialGuess);
Real[] numArray = f(initialGuess);
DenseVector denseVector2 = new DenseVector(numArray);
Real num1 = ToReal(denseVector2.L2Norm());
Matrix <Real> approximateJacobian =
Broyden.CalculateApproximateJacobian(f, initialGuess, numArray, jacobianStepSize);
for (int index = 0; index <= maxIterations; ++index)
{
DenseVector denseVector3 = (DenseVector)(-approximateJacobian.LU().Solve(denseVector2));
DenseVector denseVector4 = denseVector1 + denseVector3;
DenseVector denseVector5 = new DenseVector(f(denseVector4.Values));
Real num2 = ToReal(denseVector5.L2Norm());
if (num2 > num1)
{
Real num3 = num1 * num1;
Real num4 = num3 / (num3 + num2 * num2);
if (num4 == 0.0)
{
num4 = ToReal(0.0001);
}
denseVector3 = num4 * denseVector3;
denseVector4 = denseVector1 + denseVector3;
denseVector5 = new DenseVector(f(denseVector4.Values));
num2 = ToReal(denseVector5.L2Norm());
}
if (num2 < accuracy)
{
root = denseVector4.Values;
return(true);
}
Matrix <Real> matrix =
(denseVector5 - denseVector2 - approximateJacobian.Multiply(denseVector3)).ToColumnMatrix()
* denseVector3.Multiply(ToReal(1.0) / Math.Pow(ToReal(denseVector3.L2Norm()), ToReal(2.0)))
.ToRowMatrix();
approximateJacobian += matrix;
denseVector1 = denseVector4;
denseVector2 = denseVector5;
num1 = num2;
}
root = null;
return(false);
}
/// <summary>Find a solution of the equation f(x)=0.</summary>
/// <param name="f">The function to find roots from.</param>
/// <param name="initialGuess">Initial guess of the root.</param>
/// <param name="accuracy">Desired accuracy. The root will be refined until the accuracy or the maximum number of iterations is reached.</param>
/// <param name="maxIterations">Maximum number of iterations. Usually 100.</param>
/// <param name="root">The root that was found, if any. Undefined if the function returns false.</param>
/// <returns>True if a root with the specified accuracy was found, else false.</returns>
public static bool TryFindRoot(Func <Real[], Real[]> f,
Real[] initialGuess,
Real accuracy,
int maxIterations,
out Real[] root)
{
return(Broyden.TryFindRootWithJacobianStep(f,
initialGuess,
accuracy,
maxIterations,
ToReal(0.0001),
out root));
}