/// <summary>
/// Determine if calculation should continue
/// </summary>
/// <param name="iterationNumber">Number of iterations passed</param>
/// <param name="result">Result <see cref="Vector"/>.</param>
/// <param name="source">Source <see cref="Vector"/>.</param>
/// <param name="residuals">Residual <see cref="Vector"/>.</param>
/// <returns><c>true</c> if continue, otherwise <c>false</c></returns>
bool ShouldContinue(int iterationNumber, Vector <Complex> result, Vector <Complex> source, Vector <Complex> residuals)
{
// We stop if either:
// - the user has stopped the calculation
// - the calculation needs to be stopped from a numerical point of view (divergence, convergence etc.)
if (_hasBeenStopped)
{
_iterator.Cancel();
return(true);
}
var status = _iterator.DetermineStatus(iterationNumber, result, source, residuals);
return(status == IterationStatus.Running || status == IterationStatus.Indetermined);
}
/// <summary>
/// Solves the matrix equation Ax = b, where A is the coefficient matrix, b is the
/// solution vector and x is the unknown vector.
/// </summary>
/// <param name="matrix">The coefficient matrix, <c>A</c>.</param>
/// <param name="input">The solution vector, <c>b</c></param>
/// <param name="result">The result vector, <c>x</c></param>
public void Solve(Matrix <Complex> matrix, Vector <Complex> input, Vector <Complex> result)
{
// If we were stopped before, we are no longer
// We're doing this at the start of the method to ensure
// that we can use these fields immediately.
_hasBeenStopped = false;
// Error checks
if (matrix == null)
{
throw new ArgumentNullException("matrix");
}
if (matrix.RowCount != matrix.ColumnCount)
{
throw new ArgumentException(Resources.ArgumentMatrixSquare, "matrix");
}
if (input == null)
{
throw new ArgumentNullException("input");
}
if (result == null)
{
throw new ArgumentNullException("result");
}
if (input.Count != matrix.RowCount || result.Count != input.Count)
{
throw Matrix.DimensionsDontMatch <ArgumentException>(matrix, input, result);
}
// Initialize the solver fields
// Set the convergence monitor
if (_iterator == null)
{
_iterator = Iterator.CreateDefault();
}
if (_preconditioner == null)
{
_preconditioner = new UnitPreconditioner <Complex>();
}
_preconditioner.Initialize(matrix);
var d = new DenseVector(input.Count);
var r = DenseVector.OfVector(input);
var uodd = new DenseVector(input.Count);
var ueven = new DenseVector(input.Count);
var v = new DenseVector(input.Count);
var pseudoResiduals = DenseVector.OfVector(input);
var x = new DenseVector(input.Count);
var yodd = new DenseVector(input.Count);
var yeven = DenseVector.OfVector(input);
// Temp vectors
var temp = new DenseVector(input.Count);
var temp1 = new DenseVector(input.Count);
var temp2 = new DenseVector(input.Count);
// Define the scalars
Complex alpha = 0;
Complex eta = 0;
double theta = 0;
// Initialize
var tau = input.L2Norm().Real;
Complex rho = tau * tau;
// Calculate the initial values for v
// M temp = yEven
_preconditioner.Approximate(yeven, temp);
// v = A temp
matrix.Multiply(temp, v);
// Set uOdd
v.CopyTo(ueven);
// Start the iteration
var iterationNumber = 0;
while (ShouldContinue(iterationNumber, result, input, pseudoResiduals))
{
// First part of the step, the even bit
if (IsEven(iterationNumber))
{
// sigma = (v, r)
var sigma = r.ConjugateDotProduct(v);
if (sigma.Real.AlmostEqual(0, 1) && sigma.Imaginary.AlmostEqual(0, 1))
{
// FAIL HERE
_iterator.Cancel();
break;
}
// alpha = rho / sigma
alpha = rho / sigma;
// yOdd = yEven - alpha * v
v.Multiply(-alpha, temp1);
yeven.Add(temp1, yodd);
// Solve M temp = yOdd
_preconditioner.Approximate(yodd, temp);
// uOdd = A temp
matrix.Multiply(temp, uodd);
}
// The intermediate step which is equal for both even and
// odd iteration steps.
// Select the correct vector
var uinternal = IsEven(iterationNumber) ? ueven : uodd;
var yinternal = IsEven(iterationNumber) ? yeven : yodd;
// pseudoResiduals = pseudoResiduals - alpha * uOdd
uinternal.Multiply(-alpha, temp1);
pseudoResiduals.Add(temp1, temp2);
temp2.CopyTo(pseudoResiduals);
// d = yOdd + theta * theta * eta / alpha * d
d.Multiply(theta * theta * eta / alpha, temp);
yinternal.Add(temp, d);
// theta = ||pseudoResiduals||_2 / tau
theta = pseudoResiduals.L2Norm().Real / tau;
var c = 1 / Math.Sqrt(1 + (theta * theta));
// tau = tau * theta * c
tau *= theta * c;
// eta = c^2 * alpha
eta = c * c * alpha;
// x = x + eta * d
d.Multiply(eta, temp1);
x.Add(temp1, temp2);
temp2.CopyTo(x);
// Check convergence and see if we can bail
if (!ShouldContinue(iterationNumber, result, input, pseudoResiduals))
{
// Calculate the real values
_preconditioner.Approximate(x, result);
// Calculate the true residual. Use the temp vector for that
// so that we don't pollute the pseudoResidual vector for no
// good reason.
CalculateTrueResidual(matrix, temp, result, input);
// Now recheck the convergence
if (!ShouldContinue(iterationNumber, result, input, temp))
{
// We're all good now.
return;
}
}
// The odd step
if (!IsEven(iterationNumber))
{
if (rho.Real.AlmostEqual(0, 1) && rho.Imaginary.AlmostEqual(0, 1))
{
// FAIL HERE
_iterator.Cancel();
break;
}
var rhoNew = r.ConjugateDotProduct(pseudoResiduals);
var beta = rhoNew / rho;
// Update rho for the next loop
rho = rhoNew;
// yOdd = pseudoResiduals + beta * yOdd
yodd.Multiply(beta, temp1);
pseudoResiduals.Add(temp1, yeven);
// Solve M temp = yOdd
_preconditioner.Approximate(yeven, temp);
// uOdd = A temp
matrix.Multiply(temp, ueven);
// v = uEven + beta * (uOdd + beta * v)
v.Multiply(beta, temp1);
uodd.Add(temp1, temp);
temp.Multiply(beta, temp1);
ueven.Add(temp1, v);
}
// Calculate the real values
_preconditioner.Approximate(x, result);
iterationNumber++;
}
}