public void Create()
{
var criterium = new ResidualStopCriterium(1e-8, 50);
Assert.IsNotNull(criterium, "There should be a criterium");
Assert.AreEqual(1e-8, criterium.Maximum, "Incorrect maximum");
Assert.AreEqual(50, criterium.MinimumIterationsBelowMaximum, "Incorrect iteration count");
}
public void Clone()
{
var criterium = new ResidualStopCriterium(1e-3, 10);
Assert.IsNotNull(criterium, "There should be a criterium");
var clone = criterium.Clone();
Assert.IsInstanceOf(typeof (ResidualStopCriterium), clone, "Wrong criterium type");
var clonedCriterium = clone as ResidualStopCriterium;
Assert.IsNotNull(clonedCriterium);
// ReSharper disable PossibleNullReferenceException
Assert.AreEqual(criterium.Maximum, clonedCriterium.Maximum, "Clone failed");
Assert.AreEqual(criterium.MinimumIterationsBelowMaximum, clonedCriterium.MinimumIterationsBelowMaximum, "Clone failed");
// ReSharper restore PossibleNullReferenceException
}
/// <summary>
/// Run example
/// </summary>
public void Run()
{
// Format matrix output to console
var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
formatProvider.TextInfo.ListSeparator = " ";
// Solve next system of linear equations (Ax=b):
// 5*x + 2*y - 4*z = -7
// 3*x - 7*y + 6*z = 38
// 4*x + 1*y + 5*z = 43
// Create matrix "A" with coefficients
var matrixA = DenseMatrix.OfArray(new[,] { { 5.00, 2.00, -4.00 }, { 3.00, -7.00, 6.00 }, { 4.00, 1.00, 5.00 } });
Console.WriteLine(@"Matrix 'A' with coefficients");
Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// Create vector "b" with the constant terms.
var vectorB = new DenseVector(new[] { -7.0, 38.0, 43.0 });
Console.WriteLine(@"Vector 'b' with the constant terms");
Console.WriteLine(vectorB.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// Create stop criteriums to monitor an iterative calculation. There are next available stop criteriums:
// - DivergenceStopCriterium: monitors an iterative calculation for signs of divergence;
// - FailureStopCriterium: monitors residuals for NaN's;
// - IterationCountStopCriterium: monitors the numbers of iteration steps;
// - ResidualStopCriterium: monitors residuals if calculation is considered converged;
// Stop calculation if 1000 iterations reached during calculation
var iterationCountStopCriterium = new IterationCountStopCriterium<double>(1000);
// Stop calculation if residuals are below 1E-10 --> the calculation is considered converged
var residualStopCriterium = new ResidualStopCriterium(1e-10);
// Create monitor with defined stop criteriums
var monitor = new Iterator<double>(new IIterationStopCriterium<double>[] { iterationCountStopCriterium, residualStopCriterium });
// Create Transpose Free Quasi-Minimal Residual solver
var solver = new TFQMR(monitor);
// 1. Solve the matrix equation
var resultX = solver.Solve(matrixA, vectorB);
Console.WriteLine(@"1. Solve the matrix equation");
Console.WriteLine();
// 2. Check solver status of the iterations.
// Solver has property IterationResult which contains the status of the iteration once the calculation is finished.
// Possible values are:
// - CalculationCancelled: calculation was cancelled by the user;
// - CalculationConverged: calculation has converged to the desired convergence levels;
// - CalculationDiverged: calculation diverged;
// - CalculationFailure: calculation has failed for some reason;
// - CalculationIndetermined: calculation is indetermined, not started or stopped;
// - CalculationRunning: calculation is running and no results are yet known;
// - CalculationStoppedWithoutConvergence: calculation has been stopped due to reaching the stopping limits, but that convergence was not achieved;
Console.WriteLine(@"2. Solver status of the iterations");
Console.WriteLine(solver.IterationResult);
Console.WriteLine();
// 3. Solution result vector of the matrix equation
Console.WriteLine(@"3. Solution result vector of the matrix equation");
Console.WriteLine(resultX.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 4. Verify result. Multiply coefficient matrix "A" by result vector "x"
var reconstructVecorB = matrixA * resultX;
Console.WriteLine(@"4. Multiply coefficient matrix 'A' by result vector 'x'");
Console.WriteLine(reconstructVecorB.ToString("#0.00\t", formatProvider));
Console.WriteLine();
}
public void ResetMaximum()
{
var criterium = new ResidualStopCriterium(1e-8, 50);
Assert.IsNotNull(criterium, "There should be a criterium");
criterium.ResetMaximumResidualToDefault();
Assert.AreEqual(ResidualStopCriterium.DefaultMaximumResidual, criterium.Maximum, "Incorrect maximum");
}
public void ResetMinimumIterationsBelowMaximum()
{
var criterium = new ResidualStopCriterium(1e-8, 50);
Assert.IsNotNull(criterium, "There should be a criterium");
criterium.ResetMinimumIterationsBelowMaximumToDefault();
Assert.AreEqual(ResidualStopCriterium.DefaultMinimumIterationsBelowMaximum, criterium.MinimumIterationsBelowMaximum, "Incorrect iteration count");
}
public void DetermineStatusWithSourceNaN()
{
var criterium = new ResidualStopCriterium(1e-3, 10);
Assert.IsNotNull(criterium, "There should be a criterium");
var solution = new DenseVector(new[] {1.0, 1.0, 2.0});
var source = new DenseVector(new[] {1.0, 1.0, double.NaN});
var residual = new DenseVector(new[] {1000.0, 1000.0, 2001.0});
var status = criterium.DetermineStatus(5, solution, source, residual);
Assert.AreEqual(IterationStatus.Diverged, status, "Should be diverged");
}
public void ResetCalculationState()
{
var criterium = new ResidualStopCriterium(1e-3, 10);
Assert.IsNotNull(criterium, "There should be a criterium");
var solution = new DenseVector(new[] {0.001, 0.001, 0.002});
var source = new DenseVector(new[] {0.001, 0.001, 0.002});
var residual = new DenseVector(new[] {1.000, 1.000, 2.001});
var status = criterium.DetermineStatus(5, solution, source, residual);
Assert.AreEqual(IterationStatus.Continue, status, "Should be running");
criterium.Reset();
Assert.AreEqual(IterationStatus.Continue, criterium.Status, "Should not have started");
}
public void DetermineStatusWithNonMatchingSourceVectorThrowsArgumentException()
{
var criterium = new ResidualStopCriterium(1e-8, 50);
Assert.IsNotNull(criterium, "There should be a criterium");
Assert.Throws<ArgumentException>(() => criterium.DetermineStatus(
1,
DenseVector.Create(3, i => 4),
DenseVector.Create(4, i => 4),
DenseVector.Create(3, i => 4)));
}
public void DetermineStatusWithIllegalIterationNumberThrowsArgumentOutOfRangeException()
{
var criterium = new ResidualStopCriterium(1e-8, 50);
Assert.IsNotNull(criterium, "There should be a criterium");
Assert.Throws<ArgumentOutOfRangeException>(() => criterium.DetermineStatus(
-1,
DenseVector.Create(3, i => 4),
DenseVector.Create(3, i => 5),
DenseVector.Create(3, i => 6)));
}
public void DetermineStatusWithConvergenceAtFirstIteration()
{
var criterium = new ResidualStopCriterium();
Assert.IsNotNull(criterium, "There should be a criterium");
var solution = new DenseVector(new[] {1.0, 1.0, 1.0});
var source = new DenseVector(new[] {1.0, 1.0, 1.0});
var residual = new DenseVector(new[] {0.0, 0.0, 0.0});
var status = criterium.DetermineStatus(0, solution, source, residual);
Assert.AreEqual(IterationStatus.Converged, status, "Should be done");
}
public void DetermineStatus()
{
var criterium = new ResidualStopCriterium(1e-3, 10);
Assert.IsNotNull(criterium, "There should be a criterium");
// the solution vector isn't actually being used so ...
var solution = new DenseVector(new[] {double.NaN, double.NaN, double.NaN});
// Set the source values
var source = new DenseVector(new[] {1.000, 1.000, 2.001});
// Set the residual values
var residual = new DenseVector(new[] {0.001, 0.001, 0.002});
var status = criterium.DetermineStatus(5, solution, source, residual);
Assert.AreEqual(IterationStatus.Continue, status, "Should still be running");
var status2 = criterium.DetermineStatus(16, solution, source, residual);
Assert.AreEqual(IterationStatus.Converged, status2, "Should be done");
}
/// <summary>
/// Run example
/// </summary>
public void Run()
{
// Format matrix output to console
var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
formatProvider.TextInfo.ListSeparator = " ";
// Solve next system of linear equations (Ax=b):
// 5*x + 2*y - 4*z = -7
// 3*x - 7*y + 6*z = 38
// 4*x + 1*y + 5*z = 43
// Create matrix "A" with coefficients
var matrixA = new DenseMatrix(new[,] { { 5.00, 2.00, -4.00 }, { 3.00, -7.00, 6.00 }, { 4.00, 1.00, 5.00 } });
Console.WriteLine(@"Matrix 'A' with coefficients");
Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// Create vector "b" with the constant terms.
var vectorB = new DenseVector(new[] { -7.0, 38.0, 43.0 });
Console.WriteLine(@"Vector 'b' with the constant terms");
Console.WriteLine(vectorB.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// Create stop criteriums to monitor an iterative calculation. There are next available stop criteriums:
// - DivergenceStopCriterium: monitors an iterative calculation for signs of divergence;
// - FailureStopCriterium: monitors residuals for NaN's;
// - IterationCountStopCriterium: monitors the numbers of iteration steps;
// - ResidualStopCriterium: monitors residuals if calculation is considered converged;
// Stop calculation if 1000 iterations reached during calculation
var iterationCountStopCriterium = new IterationCountStopCriterium(1000);
// Stop calculation if residuals are below 1E-10 --> the calculation is considered converged
var residualStopCriterium = new ResidualStopCriterium(1e-10);
// Create monitor with defined stop criteriums
var monitor = new Iterator(new IIterationStopCriterium[] { iterationCountStopCriterium, residualStopCriterium });
// Load all suitable solvers from current assembly. Below in this example, there is user-defined solver
// "class UserBiCgStab : IIterativeSolverSetup<double>" which uses regular BiCgStab solver. But user may create any other solver
// and solver setup classes which implement IIterativeSolverSetup<T> and pass assembly to next function:
CompositeSolver.LoadSolverInformationFromAssembly(Assembly.GetExecutingAssembly());
// Create composite solver
var solver = new CompositeSolver(monitor);
// 1. Solve the matrix equation
var resultX = solver.Solve(matrixA, vectorB);
Console.WriteLine(@"1. Solve the matrix equation");
Console.WriteLine();
// 2. Check solver status of the iterations.
// Solver has property IterationResult which contains the status of the iteration once the calculation is finished.
// Possible values are:
// - CalculationCancelled: calculation was cancelled by the user;
// - CalculationConverged: calculation has converged to the desired convergence levels;
// - CalculationDiverged: calculation diverged;
// - CalculationFailure: calculation has failed for some reason;
// - CalculationIndetermined: calculation is indetermined, not started or stopped;
// - CalculationRunning: calculation is running and no results are yet known;
// - CalculationStoppedWithoutConvergence: calculation has been stopped due to reaching the stopping limits, but that convergence was not achieved;
Console.WriteLine(@"2. Solver status of the iterations");
Console.WriteLine(solver.IterationResult);
Console.WriteLine();
// 3. Solution result vector of the matrix equation
Console.WriteLine(@"3. Solution result vector of the matrix equation");
Console.WriteLine(resultX.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 4. Verify result. Multiply coefficient matrix "A" by result vector "x"
var reconstructVecorB = matrixA * resultX;
Console.WriteLine(@"4. Multiply coefficient matrix 'A' by result vector 'x'");
Console.WriteLine(reconstructVecorB.ToString("#0.00\t", formatProvider));
Console.WriteLine();
}