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");
}
public void CanSolveForRandomMatrix(int order)
{
var matrixA = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var matrixB = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var monitor = new Iterator<Complex>(
new IterationCountStopCriterium<Complex>(1000),
new ResidualStopCriterium(1e-10));
var solver = new BiCgStab();
var matrixX = matrixA.SolveIterative(matrixB, solver, monitor);
// The solution X row dimension is equal to the column dimension of A
Assert.AreEqual(matrixA.ColumnCount, matrixX.RowCount);
// The solution X has the same number of columns as B
Assert.AreEqual(matrixB.ColumnCount, matrixX.ColumnCount);
var matrixBReconstruct = matrixA*matrixX;
// Check the reconstruction.
for (var i = 0; i < matrixB.RowCount; i++)
{
for (var j = 0; j < matrixB.ColumnCount; j++)
{
Assert.AreEqual(matrixB[i, j].Real, matrixBReconstruct[i, j].Real, 1.0e-5);
Assert.AreEqual(matrixB[i, j].Imaginary, matrixBReconstruct[i, j].Imaginary, 1.0e-5);
}
}
}
/// <summary>
/// Creates a default iterator with all the <see cref="IIterationStopCriterium"/> objects.
/// </summary>
/// <returns>A new <see cref="IIterator"/> object.</returns>
public static IIterator CreateDefault()
{
var iterator = new Iterator();
iterator.Add(new FailureStopCriterium());
iterator.Add(new DivergenceStopCriterium());
iterator.Add(new IterationCountStopCriterium());
iterator.Add(new ResidualStopCriterium());
return iterator;
}
public void SolveUnitMatrixAndBackMultiply()
{
// Create the identity matrix
var matrix = SparseMatrix.CreateIdentity(100);
// Create the y vector
var y = Vector<Complex>.Build.Dense(matrix.RowCount, 1);
// Create an iteration monitor which will keep track of iterative convergence
var monitor = new Iterator<Complex>(
new IterationCountStopCriterium<Complex>(MaximumIterations),
new ResidualStopCriterium<Complex>(ConvergenceBoundary),
new DivergenceStopCriterium<Complex>(),
new FailureStopCriterium<Complex>());
var solver = new TFQMR();
// Solve equation Ax = y
var x = matrix.SolveIterative(y, solver, monitor);
// Now compare the results
Assert.IsNotNull(x, "#02");
Assert.AreEqual(y.Count, x.Count, "#03");
// Back multiply the vector
var z = matrix.Multiply(x);
// Check that the solution converged
Assert.IsTrue(monitor.Status == IterationStatus.Converged, "#04");
// Now compare the vectors
Assert.LessOrEqual(Distance.Chebyshev(y, z), 2*ConvergenceBoundary);
}
public void SolvePoissonMatrixAndBackMultiply()
{
// Create the matrix
var matrix = new SparseMatrix(100);
// Assemble the matrix. We assume we're solving the Poisson equation
// on a rectangular 10 x 10 grid
const int GridSize = 10;
// The pattern is:
// 0 .... 0 -1 0 0 0 0 0 0 0 0 -1 4 -1 0 0 0 0 0 0 0 0 -1 0 0 ... 0
for (var i = 0; i < matrix.RowCount; i++)
{
// Insert the first set of -1's
if (i > (GridSize - 1))
{
matrix[i, i - GridSize] = -1;
}
// Insert the second set of -1's
if (i > 0)
{
matrix[i, i - 1] = -1;
}
// Insert the centerline values
matrix[i, i] = 4;
// Insert the first trailing set of -1's
if (i < matrix.RowCount - 1)
{
matrix[i, i + 1] = -1;
}
// Insert the second trailing set of -1's
if (i < matrix.RowCount - GridSize)
{
matrix[i, i + GridSize] = -1;
}
}
// Create the y vector
var y = Vector<Complex>.Build.Dense(matrix.RowCount, 1);
// Create an iteration monitor which will keep track of iterative convergence
var monitor = new Iterator<Complex>(
new IterationCountStopCriterium<Complex>(MaximumIterations),
new ResidualStopCriterium<Complex>(ConvergenceBoundary),
new DivergenceStopCriterium<Complex>(),
new FailureStopCriterium<Complex>());
var solver = new TFQMR();
// Solve equation Ax = y
var x = matrix.SolveIterative(y, solver, monitor);
// Now compare the results
Assert.IsNotNull(x, "#02");
Assert.AreEqual(y.Count, x.Count, "#03");
// Back multiply the vector
var z = matrix.Multiply(x);
// Check that the solution converged
Assert.IsTrue(monitor.Status == IterationStatus.Converged, "#04");
// Now compare the vectors
Assert.LessOrEqual(Distance.Chebyshev(y, z), 2*ConvergenceBoundary);
}
public void CanSolveForRandomVector(int order)
{
var matrixA = Matrix<Complex>.Build.Random(order, order, 1);
var vectorb = Vector<Complex>.Build.Random(order, 1);
var monitor = new Iterator<Complex>(
new IterationCountStopCriterium<Complex>(1000),
new ResidualStopCriterium<Complex>(1e-10));
var solver = new TFQMR();
var resultx = matrixA.SolveIterative(vectorb, solver, monitor);
Assert.AreEqual(matrixA.ColumnCount, resultx.Count);
var matrixBReconstruct = matrixA*resultx;
// Check the reconstruction.
for (var i = 0; i < order; i++)
{
Assert.AreEqual(vectorb[i].Real, matrixBReconstruct[i].Real, 1e-5);
Assert.AreEqual(vectorb[i].Imaginary, matrixBReconstruct[i].Imaginary, 1e-5);
}
}
public void SolveUnitMatrixAndBackMultiply()
{
// Create the identity matrix
var matrix = SparseMatrix.Identity(100);
// Create the y vector
var y = DenseVector.Create(matrix.RowCount, i => Complex.One);
// Create an iteration monitor which will keep track of iterative convergence
var monitor = new Iterator<Complex>(
new IterationCountStopCriterium<Complex>(MaximumIterations),
new ResidualStopCriterium(ConvergenceBoundary),
new DivergenceStopCriterium(),
new FailureStopCriterium());
var solver = new BiCgStab();
// Solve equation Ax = y
var x = matrix.SolveIterative(y, solver, monitor);
// Now compare the results
Assert.IsNotNull(x, "#02");
Assert.AreEqual(y.Count, x.Count, "#03");
// Back multiply the vector
var z = matrix.Multiply(x);
// Check that the solution converged
Assert.IsTrue(monitor.Status == IterationStatus.Converged, "#04");
// Now compare the vectors
for (var i = 0; i < y.Count; i++)
{
Assert.IsTrue((y[i] - z[i]).Magnitude.IsSmaller(ConvergenceBoundary, 1), "#05-" + i);
}
}
public void SolveScaledUnitMatrixAndBackMultiply()
{
// Create the identity matrix
var matrix = SparseMatrix.CreateIdentity(100);
// Scale it with a funny number
matrix.Multiply(Math.PI, matrix);
// Create the y vector
var y = Vector<Complex>.Build.Dense(matrix.RowCount, 1);
// Create an iteration monitor which will keep track of iterative convergence
var monitor = new Iterator<Complex>(
new IterationCountStopCriterion<Complex>(MaximumIterations),
new ResidualStopCriterion<Complex>(ConvergenceBoundary),
new DivergenceStopCriterion<Complex>(),
new FailureStopCriterion<Complex>());
var solver = new MlkBiCgStab();
// Solve equation Ax = y
var x = matrix.SolveIterative(y, solver, monitor);
// Now compare the results
Assert.IsNotNull(x, "#02");
Assert.AreEqual(y.Count, x.Count, "#03");
// Back multiply the vector
var z = matrix.Multiply(x);
// Check that the solution converged
Assert.IsTrue(monitor.Status == IterationStatus.Converged, "#04");
// Now compare the vectors
for (var i = 0; i < y.Count; i++)
{
Assert.GreaterOrEqual(ConvergenceBoundary, (y[i] - z[i]).Magnitude, "#05-" + i);
}
}
public void SolvePoissonMatrixAndBackMultiply()
{
// Create the matrix
var matrix = new SparseMatrix(100);
// Assemble the matrix. We assume we're solving the Poisson equation
// on a rectangular 10 x 10 grid
const int GridSize = 10;
// The pattern is:
// 0 .... 0 -1 0 0 0 0 0 0 0 0 -1 4 -1 0 0 0 0 0 0 0 0 -1 0 0 ... 0
for (var i = 0; i < matrix.RowCount; i++)
{
// Insert the first set of -1's
if (i > (GridSize - 1))
{
matrix[i, i - GridSize] = -1;
}
// Insert the second set of -1's
if (i > 0)
{
matrix[i, i - 1] = -1;
}
// Insert the centerline values
matrix[i, i] = 4;
// Insert the first trailing set of -1's
if (i < matrix.RowCount - 1)
{
matrix[i, i + 1] = -1;
}
// Insert the second trailing set of -1's
if (i < matrix.RowCount - GridSize)
{
matrix[i, i + GridSize] = -1;
}
}
// Create the y vector
var y = DenseVector.Create(matrix.RowCount, i => 1);
// Create an iteration monitor which will keep track of iterative convergence
var monitor = new Iterator<Complex>(new IIterationStopCriterium<Complex>[]
{
new IterationCountStopCriterium<Complex>(MaximumIterations),
new ResidualStopCriterium(ConvergenceBoundary),
new DivergenceStopCriterium(),
new FailureStopCriterium()
});
var solver = new MlkBiCgStab(monitor);
// Solve equation Ax = y
var x = solver.Solve(matrix, y);
// Now compare the results
Assert.IsNotNull(x, "#02");
Assert.AreEqual(y.Count, x.Count, "#03");
// Back multiply the vector
var z = matrix.Multiply(x);
// Check that the solution converged
Assert.IsTrue(monitor.HasConverged, "#04");
// Now compare the vectors
for (var i = 0; i < y.Count; i++)
{
Assert.IsTrue((y[i] - z[i]).Magnitude.IsSmaller(ConvergenceBoundary, 1), "#05-" + i);
}
}
public void CanSolveForRandomVector(int order)
{
var matrixA = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var vectorb = MatrixLoader.GenerateRandomDenseVector(order);
var monitor = new Iterator<Complex>(new IIterationStopCriterium<Complex>[]
{
new IterationCountStopCriterium<Complex>(1000),
new ResidualStopCriterium(1e-10),
});
var solver = new MlkBiCgStab(monitor);
var resultx = solver.Solve(matrixA, vectorb);
Assert.AreEqual(matrixA.ColumnCount, resultx.Count);
var matrixBReconstruct = matrixA*resultx;
// Check the reconstruction.
for (var i = 0; i < order; i++)
{
Assert.AreEqual(vectorb[i].Real, matrixBReconstruct[i].Real, 1e-5);
Assert.AreEqual(vectorb[i].Imaginary, matrixBReconstruct[i].Imaginary, 1e-5);
}
}
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 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>
/// <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)
{
if (matrix.RowCount != matrix.ColumnCount)
{
throw new ArgumentException(Resources.ArgumentMatrixSquare, nameof(matrix));
}
if (result.Count != input.Count)
{
throw new ArgumentException(Resources.ArgumentVectorsSameLength);
}
if (iterator == null)
{
iterator = new Iterator <Complex>();
}
if (preconditioner == null)
{
preconditioner = new UnitPreconditioner <Complex>();
}
// Create a copy of the solution and result vectors so we can use them
// later on
var internalInput = input.Clone();
var internalResult = result.Clone();
foreach (var solver in _solvers)
{
// Store a reference to the solver so we can stop it.
IterationStatus status;
try
{
// Reset the iterator and pass it to the solver
iterator.Reset();
// Start the solver
solver.Item1.Solve(matrix, internalInput, internalResult, iterator, solver.Item2 ?? preconditioner);
status = iterator.Status;
}
catch (Exception)
{
// The solver broke down.
// Log a message about this
// Switch to the next preconditioner.
// Reset the solution vector to the previous solution
input.CopyTo(internalInput);
continue;
}
// There was no fatal breakdown so check the status
if (status == IterationStatus.Converged)
{
// We're done
internalResult.CopyTo(result);
break;
}
// We're not done
// Either:
// - calculation finished without convergence
if (status == IterationStatus.StoppedWithoutConvergence)
{
// Copy the internal result to the result vector and
// continue with the calculation.
internalResult.CopyTo(result);
}
else
{
// - calculation failed --> restart with the original vector
// - calculation diverged --> restart with the original vector
// - Some unknown status occurred --> To be safe restart.
input.CopyTo(internalInput);
}
}
}