public void SolveLongMatrixThrowsArgumentException()
{
var matrix = new SparseMatrix(3, 2);
var input = new DenseVector(3);
var solver = new MlkBiCgStab();
Assert.Throws<ArgumentException>(() => matrix.SolveIterative(input, solver));
}
public void SolveWideMatrixThrowsArgumentException()
{
var matrix = new SparseMatrix(2, 3);
var input = new DenseVector(2);
var solver = new TFQMR();
Assert.Throws<ArgumentException>(() => matrix.SolveIterative(input, solver));
}
public void SolveWideMatrixThrowsArgumentException()
{
var matrix = new SparseMatrix(2, 3);
var input = new DenseVector(2);
var solver = new MlkBiCgStab();
Assert.That(() => matrix.SolveIterative(input, solver), Throws.ArgumentException);
}
public void SolveLongMatrixThrowsArgumentException()
{
var matrix = new SparseMatrix(3, 2);
var input = new DenseVector(3);
var solver = new GpBiCg();
Assert.That(() => matrix.SolveIterative(input, solver), Throws.ArgumentException);
}
public void SolvePoissonMatrixAndBackMultiply()
{
// Create the matrix
var matrix = new SparseMatrix(25);
// Assemble the matrix. We assume we're solving the Poisson equation
// on a rectangular 5 x 5 grid
const int GridSize = 5;
// 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<float>(
new IterationCountStopCriterium<float>(MaximumIterations),
new ResidualStopCriterium(ConvergenceBoundary),
new DivergenceStopCriterium(),
new FailureStopCriterium());
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
for (var i = 0; i < y.Count; i++)
{
Assert.IsTrue(Math.Abs(y[i] - z[i]).IsSmaller(ConvergenceBoundary, 1), "#05-" + i);
}
}
public void SolvePoissonMatrixAndBackMultiply()
{
// Create the matrix
var matrix = new SparseMatrix(25);
// Assemble the matrix. We assume we're solving the Poisson equation
// on a rectangular 5 x 5 grid
const int GridSize = 5;
// 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);
// Due to datatype "float" it can happen that solution will not converge for specific random starting vectors
// That's why we will do 3 tries
for (var iteration = 0; iteration <= 3; iteration++)
{
// Create an iteration monitor which will keep track of iterative convergence
var monitor = new Iterator<float>(
new IterationCountStopCriterium<float>(MaximumIterations),
new ResidualStopCriterium<float>(ConvergenceBoundary),
new DivergenceStopCriterium<float>(),
new FailureStopCriterium<float>());
var solver = new MlkBiCgStab();
// Solve equation Ax = y
Vector<float> x;
try
{
x = matrix.SolveIterative(y, solver, monitor);
}
catch (Exception)
{
continue;
}
if (monitor.Status != IterationStatus.Converged)
{
continue;
}
// Now compare the results
Assert.IsNotNull(x, "#02");
Assert.AreEqual(y.Count, x.Count, "#03");
// Back multiply the vector
var z = matrix.Multiply(x);
// Now compare the vectors
for (var i = 0; i < y.Count; i++)
{
Assert.GreaterOrEqual(ConvergenceBoundary, Math.Abs(y[i] - z[i]), "#05-" + i);
}
return;
}
}
