private IterativeStatistics SolveInternal(int maxIterations)
{
// δnew = δ0 = r * r
resDotRes = residual.DotProduct(residual);
// The convergence criterion must be initialized immediately after the first r and r*r are computed.
residualConvergence.Initialize(this);
// This is also used as output
double residualNormRatio = double.NaN;
// d = r
direction = residual.Copy();
// Allocate memory for other vectors, which will be reused during each iteration
matrixTimesDirection = Rhs.CreateZeroVectorWithSameFormat();
for (Iteration = 0; Iteration < maxIterations; ++Iteration)
{
// q = A * d
Matrix.Multiply(direction, matrixTimesDirection);
// α = δnew / (d * q)
StepSize = ResDotRes / (direction.DotProduct(matrixTimesDirection));
// x = x + α * d
solution.AxpyIntoThis(direction, StepSize);
// δold = δnew
double resDotResOld = ResDotRes;
// Normally the residual vector is updated as: r = r - α * q and δnew = r * r.
// However corrections might need to be applied.
residualUpdater.UpdateResidual(this, residual, out resDotRes);
// At this point we can check if CG has converged and exit, thus avoiding the uneccesary operations that follow.
residualNormRatio = residualConvergence.EstimateResidualNormRatio(this);
if (residualNormRatio <= residualTolerance)
{
return(new IterativeStatistics
{
AlgorithmName = name,
HasConverged = true,
NumIterationsRequired = Iteration + 1,
ResidualNormRatioEstimation = residualNormRatio
});
}
// β = δnew / δold
ParamBeta = ResDotRes / resDotResOld;
// d = r + β * d
//TODO: benchmark the two options to find out which is faster
//direction = residual.Axpy(direction, beta); //This allocates a new vector d, copies r and GCs the existing d.
direction.LinearCombinationIntoThis(ParamBeta, residual, 1.0); //This performs additions instead of copying and needless multiplications.
}
// We reached the max iterations before CG converged
return(new IterativeStatistics
{
AlgorithmName = name,
HasConverged = false,
NumIterationsRequired = maxIterations,
ResidualNormRatioEstimation = residualNormRatio
});
}
