public void DetermineStatus()
{
var criteria = new List<IIterationStopCriterium<Complex>>
{
new FailureStopCriterium(),
new DivergenceStopCriterium(),
new IterationCountStopCriterium<Complex>(1)
};
var iterator = new Iterator<Complex>(criteria);
// First step, nothing should happen.
iterator.DetermineStatus(
0,
DenseVector.Create(3, i => 4),
DenseVector.Create(3, i => 4),
DenseVector.Create(3, i => 4));
Assert.AreEqual(IterationStatus.Continue, iterator.Status, "Incorrect status");
// Second step, should run out of iterations.
iterator.DetermineStatus(
1,
DenseVector.Create(3, i => 4),
DenseVector.Create(3, i => 4),
DenseVector.Create(3, i => 4));
Assert.AreEqual(IterationStatus.StoppedWithoutConvergence, iterator.Status, "Incorrect status");
}
/// <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);
}
public void DetermineStatusWithNegativeIterationNumberThrowsArgumentOutOfRangeException()
{
var criteria = new List<IIterationStopCriterium<Complex>>
{
new FailureStopCriterium(),
new DivergenceStopCriterium(),
new IterationCountStopCriterium<Complex>(),
new ResidualStopCriterium()
};
var iterator = new Iterator<Complex>(criteria);
Assert.Throws<ArgumentOutOfRangeException>(() => iterator.DetermineStatus(
-1,
DenseVector.Create(3, i => 4),
DenseVector.Create(3, i => 5),
DenseVector.Create(3, i => 6)));
}
public void ResetToPrecalculationState()
{
var criteria = new List<IIterationStopCriterium<Complex>>
{
new FailureStopCriterium(),
new DivergenceStopCriterium(),
new IterationCountStopCriterium<Complex>(1)
};
var iterator = new Iterator<Complex>(criteria);
// First step, nothing should happen.
iterator.DetermineStatus(
0,
DenseVector.Create(3, i => 4),
DenseVector.Create(3, i => 4),
DenseVector.Create(3, i => 4));
Assert.AreEqual(IterationStatus.Continue, iterator.Status, "Incorrect status");
iterator.Reset();
Assert.AreEqual(IterationStatus.Continue, iterator.Status, "Incorrect status");
Assert.AreEqual(IterationStatus.Continue, criteria[0].Status, "Incorrect status");
Assert.AreEqual(IterationStatus.Continue, criteria[1].Status, "Incorrect status");
Assert.AreEqual(IterationStatus.Continue, criteria[2].Status, "Incorrect status");
}
public void DetermineStatusWithoutStopCriteriaDoesNotThrow()
{
var iterator = new Iterator<Complex>();
Assert.DoesNotThrow(() => iterator.DetermineStatus(
0,
DenseVector.Create(3, i => 4),
DenseVector.Create(3, i => 5),
DenseVector.Create(3, i => 6)));
}
/// <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 <see cref="Matrix"/>, <c>A</c>.</param>
/// <param name="input">The solution <see cref="Vector"/>, <c>b</c>.</param>
/// <param name="result">The result <see cref="Vector"/>, <c>x</c>.</param>
/// <param name="iterator">The iterator to use to control when to stop iterating.</param>
/// <param name="preconditioner">The preconditioner to use for approximations.</param>
public void Solve(Matrix <Complex> matrix, Vector <Complex> input, Vector <Complex> result,
Iterator <Complex> iterator, IPreconditioner <Complex> preconditioner)
{
var A = (SparseMatrix)matrix;
var M = preconditioner;
var b = (DenseVector)input;
var x = (DenseVector)result;
double atolf = 0.0;
double rtol_1 = 0.0;
int recompute_residual_p = 0;
var p = new DenseVector(b.Count);
var s = new DenseVector(b.Count);
var r = new DenseVector(b.Count);
Complex alpha, beta;
Complex gamma, gamma_old;
Complex bi_prod;
Complex sdotp;
bool recompute_true_residual = false;
int i = 0;
M.Initialize(A);
// Start pcg solve
// bi_prod = <C*b,b>
//VectorHelper.Clear(p);
M.Approximate(input, p);
bi_prod = VectorHelper.DotProduct(p, b);
if (bi_prod.Real > 0.0)
{
if (atolf > 0) // mixed relative and absolute tolerance
{
bi_prod += atolf;
}
}
else // bi_prod==0.0: the rhs vector b is zero
{
// Set x equal to zero and return
VectorHelper.Copy(b, x);
return;
}
// r = b - Ax
VectorHelper.Copy(b, r);
A.Multiply(-1.0, result, 1.0, r);
// p = C*r
//VectorHelper.Clear(p);
M.Approximate(r, p);
// gamma = <r,p>
gamma = VectorHelper.DotProduct(r, p);
while (iterator.DetermineStatus(i, x, b, r) == IterationStatus.Continue)
{
// the core CG calculations...
i++;
// At user request, periodically recompute the residual from the formula
// r = b - A x (instead of using the recursive definition). Note that this
// is potentially expensive and can lead to degraded convergence (since it
// essentially a "restarted CG").
recompute_true_residual = (recompute_residual_p > 0) && !((i % recompute_residual_p) == 0);
// s = A*p
A.Multiply(1.0, p, 0.0, s);
// alpha = gamma / <s,p>
sdotp = VectorHelper.DotProduct(s, p);
if (sdotp == 0.0)
{
throw new NumericalBreakdownException();
}
alpha = gamma / sdotp;
gamma_old = gamma;
// x = x + alpha*p
VectorHelper.Add(alpha, p, x, x);
// r = r - alpha*s
if (recompute_true_residual)
{
//Recomputing the residual...
VectorHelper.Copy(b, r);
A.Multiply(-1.0, result, 1.0, r);
}
else
{
VectorHelper.Add(-alpha, s, r, r);
}
// s = C*r
VectorHelper.Clear(s);
M.Approximate(r, s);
// gamma = <r,s>
gamma = VectorHelper.DotProduct(r, s);
// residual-based stopping criteria: ||r_new-r_old||_C < rtol ||b||_C
if (rtol_1 > 0)
{
// use that ||r_new-r_old||_C^2 = (r_new ,C r_new) + (r_old, C r_old)
if (Complex.Abs((gamma + gamma_old) / bi_prod) < rtol_1 * rtol_1)
{
break;
}
}
// ... gamma should be >=0. IEEE subnormal numbers are < 2**(-1022)=2.2e-308
// (and >= 2**(-1074)=4.9e-324). So a gamma this small means we're getting
// dangerously close to subnormal or zero numbers (usually if gamma is small,
// so will be other variables). Thus further calculations risk a crash.
// Such small gamma generally means no hope of progress anyway.
if (Complex.Abs(gamma) < TINY)
{
throw new NumericalBreakdownException();
}
// beta = gamma / gamma_old
beta = gamma / gamma_old;
// p = s + beta p
if (recompute_true_residual)
{
VectorHelper.Copy(s, p);
}
else
{
p.Scale(beta);
VectorHelper.Add(1.0, s, p, p);
}
}
}
