public virtual double Laguerre(double lo, double hi, double fLo, double fHi)
{
Complex[] c = ComplexUtils.convertToComplex(Coefficients);
Complex initial = new Complex(0.5 * (lo + hi), 0);
Complex z = ComplexSolver.Solve(c, initial);
if (ComplexSolver.IsRoot(lo, hi, z))
{
return z.Real;
}
else
{
double r = double.NaN;
// Solve all roots and select the one we are seeking.
Complex[] root = ComplexSolver.SolveAll(c, initial);
for (int i = 0; i < root.Length; i++)
{
if (ComplexSolver.IsRoot(lo, hi, root[i]))
{
r = root[i].Real;
break;
}
}
return r;
}
}
public void When_ExampleComplexMatrix1_Expect_MatlabReference()
{
// Build the example matrix
Complex[][] matrix =
{
new Complex[] { 0, 0, 0, 0, 1, 0, 1, 0 },
new Complex[] { 0, 0, 0, 0, -1, 1, 0, 0 },
new[] { 0, 0, new Complex(0.0, 0.000628318530717959), 0, 0, 0, -1, 1 },
new Complex[] { 0, 0, 0, 0.001, 0, 0, 0, -1 },
new Complex[] { 1, -1, 0, 0, 0, 0, 0, 0 },
new Complex[] { 0, 1, 0, 0, 0, 0, 0, 0 },
new Complex[] { 1, 0, -1, 0, 0, 0, 0, 0 },
new[] { 0, 0, 1, -1, 0, 0, 0, new Complex(0.0, -1.5707963267949)}
};
Complex[] rhs = { 0, 0, 0, 0, 0, 24.0 };
Complex[] reference =
{
new Complex(24, 0),
new Complex(24, 0),
new Complex(24, 0),
new Complex(23.999940782519708, -0.037699018824477),
new Complex(-0.023999940782520, -0.015041945718407),
new Complex(-0.023999940782520, -0.015041945718407),
new Complex(0.023999940782520, 0.015041945718407),
new Complex(0.023999940782520, -0.000037699018824)
};
// build the matrix
var solver = new ComplexSolver();
for (var r = 0; r < matrix.Length; r++)
{
for (var c = 0; c < matrix[r].Length; c++)
{
if (!matrix[r][c].Equals(Complex.Zero))
{
solver.GetMatrixElement(r + 1, c + 1).Value = matrix[r][c];
}
}
}
// Add some zero elements
solver.GetMatrixElement(7, 7);
solver.GetRhsElement(5);
// Build the Rhs vector
for (var r = 0; r < rhs.Length; r++)
{
if (!rhs[r].Equals(Complex.Zero))
{
solver.GetRhsElement(r + 1).Value = rhs[r];
}
}
// Solver
solver.OrderAndFactor();
var solution = new DenseVector <Complex>(solver.Order);
solver.Solve(solution);
// Check!
for (var r = 0; r < reference.Length; r++)
{
Assert.AreEqual(reference[r].Real, solution[r + 1].Real, 1e-12);
Assert.AreEqual(reference[r].Imaginary, solution[r + 1].Imaginary, 1e-12);
}
}
static void Main()
{
//library uses one solver type (more will come if there will be demand): dense output stepper based on runge_kutta_dopri5 with standard error bounds 10^(-6) for the steps.
var solver = new Solver();
const double @from = 0.0;
const double to = 25.0;
const double step = 0.1;
//Say we have a class describing our system:
var myLorenz = new LorenzOde
{
InitialConditions = new StateType(new[] { 10, 1.0, 1.0 })
};
// All we need to solve it:
solver.ConvenienceSolve(myLorenz, from, to, step);
//library class provides a simple to use Lambda API for ODE system defenition (example of lorenz, 50 steps)
var lorenz = new LambdaOde
{
InitialConditions = new StateType(new[] { 10, 1.0, 1.0 }),
OdeObserver = (x, t) => Console.WriteLine("{0} : {1} : {2}", x[0], x[1], x[2]),
OdeSystem =
(x, dxdt, t) => {
const double sigma = 10.0;
const double r = 28.0;
const double b = 8.0 / 3.0;
dxdt[0] = sigma * (x[1] - x[0]);
dxdt[1] = r * x[0] - x[1] - x[0] * x[2];
dxdt[2] = -b * x[2] + x[0] * x[1];
}
};
// And all we need to solve it:
solver.ConvenienceSolve(lorenz, from, to, step);
// We can select stepper that our stepper would use
solver.StepperCode = StepperTypeCode.RungeKutta4;
// We can select how our IntegrateFunction will work:
solver.Solve(lorenz, from, step, to, IntegrateFunctionTypeCode.Adaptive);
// We can integrate for first N steps
solver.Solve(lorenz, from, step, 5);
// Or at given time periods
solver.Solve(lorenz, new StateType(new[] { 0, 10.0, 100.0, 1000.0 }), step);
Console.ReadLine();
Console.WriteLine("Complex Test");
var complexSolver = new ComplexSolver();
const double eta = 2;
const double alpha = 1;
var complexEta = new Complex(1, eta);
var complexAlpha = new Complex(1, alpha);
var stuartLandauOscillator = new ComplexLambdaOde
{
InitialConditions = new ComplexStateType {
new Complex(1, 0)
},
OdeObserver = (x, t) => Console.WriteLine("{0}", x[0]),
OdeSystem =
(x, dxdt, t) =>
{
dxdt[0] = complexEta * x[0] - (complexAlpha * x[0].Norm()) * x[0];
}
};
// And all we need to solve it:
complexSolver.ConvenienceSolve(stuartLandauOscillator, from, to, step);
// We can select stepper that our stepper would use
complexSolver.StepperCode = StepperTypeCode.RungeKutta4;
// We can select how our IntegrateFunction will work:
complexSolver.Solve(stuartLandauOscillator, from, step, to, IntegrateFunctionTypeCode.Adaptive);
// We can integrate for first N steps
complexSolver.Solve(stuartLandauOscillator, from, step, 5);
// Or at given time periods
complexSolver.Solve(stuartLandauOscillator, new StateType(new[] { 0, 10.0, 100.0, 1000.0 }), step);
Console.ReadLine();
}
/// <summary>
/// Find a complex root for the polynomial with the given coefficients,
/// starting from the given initial value.
/// <br/>
/// Note: This method is not part of the API of <seealso cref="BaseUnivariateSolver"/>.
/// </summary>
/// <param name="coefficients"> Polynomial coefficients. </param>
/// <param name="initial"> Start value. </param>
/// <returns> the point at which the function value is zero. </returns>
/// <exception cref="org.apache.commons.math3.exception.TooManyEvaluationsException">
/// if the maximum number of evaluations is exceeded. </exception>
/// <exception cref="NullArgumentException"> if the {@code coefficients} is
/// {@code null}. </exception>
/// <exception cref="NoDataException"> if the {@code coefficients} array is empty.
/// @since 3.1 </exception>
public virtual Complex SolveComplex(double[] coefficients, double initial)
{
Setup(int.MaxValue, new PolynomialFunction(coefficients), double.NegativeInfinity, double.PositiveInfinity, initial);
return ComplexSolver.Solve(ComplexUtils.convertToComplex(coefficients), new Complex(initial, 0d));
}