/// <summary>
/// The linear flux of the underlying PDE, expressed as F(U) =
/// M * U + n. The flux may depend on the space
/// variable <see cref="CommonParamsVol.Xglobal"/> and on the field
/// values of <see cref="CommonParamsVol.Parameters" /> that can
/// be defined in <see cref="IEquationComponent.ParameterOrdering" />.
/// In this implementation, the resulting flux solely depends on the
/// implementation of <see cref="INonlinearFlux.Flux"/> that
/// has been supplied to the constructor.
/// </summary>
/// <param name="inp"></param>
/// <param name="U"></param>
/// <param name="output"></param>
protected override void Flux(ref CommonParamsVol inp, double[] U, double[] output)
{
MultidimensionalArray refFlux = MultidimensionalArray.Create(1, 1, inp.D);
baseFlux.Flux(
0.0,
MultidimensionalArray.CreateWrapper(inp.Xglobal, 1, 1, inp.D),
inp.Parameters.Select(p =>
MultidimensionalArray.CreateWrapper(new double[] { p }, 1, 1)).ToArray(),
0,
1,
refFlux);
double[,] FunctionMatrix = new double[inp.D, inp.Parameters.Length];
for (int i = 0; i < inp.Parameters.Length; i++)
{
double[] perturbedParameters = inp.Parameters.CloneAs();
double stepSize = GetStepSize(perturbedParameters[i]);
perturbedParameters[i] += stepSize;
MultidimensionalArray perturbedFlux = MultidimensionalArray.Create(1, 1, inp.D);
baseFlux.Flux(
0.0,
MultidimensionalArray.CreateWrapper(inp.Xglobal, 1, 1, inp.D),
perturbedParameters.Select(p =>
MultidimensionalArray.CreateWrapper(new double[] { p }, 1, 1)).ToArray(),
0,
1,
perturbedFlux);
for (int d = 0; d < inp.D; d++)
{
FunctionMatrix[d, i] = (perturbedFlux[0, 0, d] - refFlux[0, 0, d]) / stepSize;
}
}
for (int d = 0; d < inp.D; d++)
{
output[d] = refFlux[0, 0, d];
for (int i = 0; i < inp.Parameters.Length; i++)
{
output[d] += FunctionMatrix[d, i] * (U[i] - inp.Parameters[i]);
}
}
}
/// <summary>
/// <see cref="INonlinearFlux.Flux"/>
/// </summary>
public void Flux(double time, Vector2D x, Vector2D[] FunctionMatrix, out Vector2D AffineOffset)
{
Array.Clear(m_Arguments, 0, m_Arguments.Length);
AffineOffset = m_Flux.Flux(time, x, m_Arguments);
for (int i = m_Arguments.Length - 1; i >= 0; i--)
{
m_Arguments[i] = 1;
FunctionMatrix[i] = m_Flux.Flux(time, x, m_Arguments);
FunctionMatrix[i].Sub(AffineOffset);
m_Arguments[i] = 0;
}
if (!Local)
{
Array.Clear(FunctionMatrix, 0, FunctionMatrix.Length);
AffineOffset = new Vector2D(0.0, 0.0);
}
}