public void SparseSample_ComplexFloat_Identity()
{
NumericsConfiguration.NativeProviderPath = @"C:\Program Files (x86)\Extreme Optimization\Numerical Libraries for .NET\bin\Net40";
NumericsConfiguration.Providers.RegisterSinglePrecisionProvider();
NumericsConfiguration.AutoLoadNativeProviders = true;
CoreImplementations<float>.UseNative();
Console.WriteLine(CoreImplementations<Complex<float>>.LinearAlgebra.Name);
SparseCompressedColumnMatrix<Complex<float>> matrixA = Matrix.CreateSparse<Complex<float>>(3, 3);
matrixA.SetValue(new Complex<float>(1, 0), 0, 0);
matrixA.SetValue(new Complex<float>(1, 0), 1, 1);
matrixA.SetValue(new Complex<float>(1, 0), 2, 2);
Vector<Complex<float>> vectorB = Vector.Create(new Complex<float>(1.0f, 0), new Complex<float>(2.0f, 0), new Complex<float>(3.0f, 0));
IterativeSparseSolver<Complex<float>> solver = new BiConjugateGradientSolver<Complex<float>>(matrixA);
DenseVector<Complex<float>> resultVector = solver.Solve(vectorB);
Console.WriteLine("Result: {0}", resultVector);
Console.WriteLine("Solved in {0} iterations.", solver.IterationsNeeded);
Console.WriteLine("Estimated error: {0}", solver.SolutionReport.Error);
// With incomplete LU preconditioner
solver.Preconditioner = new IncompleteLUPreconditioner<Complex<float>>(matrixA);
resultVector = solver.Solve(vectorB);
Console.WriteLine("Result: {0}", resultVector);
Console.WriteLine("Solved in {0} iterations.", solver.IterationsNeeded);
Console.WriteLine("Estimated error: {0}", solver.EstimatedError);
}
public void SparseSample_ComplexFloat_Identity()
{
NumericsConfiguration.NativeProviderPath = @"C:\Program Files (x86)\Extreme Optimization\Numerical Libraries for .NET\bin\Net40";
NumericsConfiguration.Providers.RegisterSinglePrecisionProvider();
NumericsConfiguration.AutoLoadNativeProviders = true;
CoreImplementations <float> .UseNative();
Console.WriteLine(CoreImplementations <Complex <float> > .LinearAlgebra.Name);
SparseCompressedColumnMatrix <Complex <float> > matrixA = Matrix.CreateSparse <Complex <float> >(3, 3);
matrixA.SetValue(new Complex <float>(1, 0), 0, 0);
matrixA.SetValue(new Complex <float>(1, 0), 1, 1);
matrixA.SetValue(new Complex <float>(1, 0), 2, 2);
Vector <Complex <float> > vectorB = Vector.Create(new Complex <float>(1.0f, 0), new Complex <float>(2.0f, 0), new Complex <float>(3.0f, 0));
IterativeSparseSolver <Complex <float> > solver = new BiConjugateGradientSolver <Complex <float> >(matrixA);
DenseVector <Complex <float> > resultVector = solver.Solve(vectorB);
Console.WriteLine("Result: {0}", resultVector);
Console.WriteLine("Solved in {0} iterations.", solver.IterationsNeeded);
Console.WriteLine("Estimated error: {0}", solver.SolutionReport.Error);
// With incomplete LU preconditioner
solver.Preconditioner = new IncompleteLUPreconditioner <Complex <float> >(matrixA);
resultVector = solver.Solve(vectorB);
Console.WriteLine("Result: {0}", resultVector);
Console.WriteLine("Solved in {0} iterations.", solver.IterationsNeeded);
Console.WriteLine("Estimated error: {0}", solver.EstimatedError);
}
public void ExecuteSample()
{
// The line below sets the path where the native assemblies
// are located. The "XO_LIBRARY_PATH" environment variable
// points here, too.
NumericsConfiguration.NativeProviderPath =
@"C:\Program Files (x86)\Extreme Optimization\Numerical Libraries for .NET\bin\Net40";
// Register the single precision providers.
NumericsConfiguration.Providers.RegisterSinglePrecisionProvider();
NumericsConfiguration.AutoLoadNativeProviders = true;
CoreImplementations <float> .UseNative();
// Which provider are we using?
Console.WriteLine(CoreImplementations <Complex <float> > .LinearAlgebra.Name);
int N = 228724; // size
int K = 96; // non-zeros per column
// Create some random matrices. Code is below.
// Use a seed so we can reproduce the same values.
NumericsConfiguration.DefaultRandomNumberGenerator = new Extreme.Mathematics.Random.MersenneTwister(117);
var matrixA = CreateSparseRandom(N, K);
var vectorB = CreateRandom(N);// CreateRandom(N);
// Now run the solver with and without preconditioner:
var sw = Stopwatch.StartNew();
var solver = new BiConjugateGradientSolver <Complex <float> >(matrixA);
Console.WriteLine("Starting solve...");
Vector <Complex <float> > resultVector;
resultVector = solver.Solve(vectorB);
sw.Stop();
Console.WriteLine("Result: {0}", resultVector.GetSlice(0, 10));
Console.WriteLine("Solved in {0} iterations.", solver.IterationsNeeded);
Console.WriteLine("Estimated error: {0}", solver.SolutionReport.Error);
Console.WriteLine("Total time: {0} s", sw.Elapsed.TotalSeconds);
// With incomplete LU preconditioner
sw.Restart();
solver.Preconditioner = new IncompleteLUPreconditioner <Complex <float> >(matrixA);
resultVector = solver.Solve(vectorB);
sw.Stop();
Console.WriteLine("Result: {0}", resultVector.GetSlice(0, 10));
Console.WriteLine("Solved in {0} iterations.", solver.IterationsNeeded);
Console.WriteLine("Estimated error: {0}", solver.EstimatedError);
Console.WriteLine("Total time: {0} s", sw.Elapsed.TotalSeconds);
Console.WriteLine("Press any key to exit.");
Console.ReadLine();
}
public void SimpleSample_Double_Identity()
{
Console.WriteLine(CoreImplementations<Complex<float>>.LinearAlgebra.Name);
// We load a sparse matrix and right-hand side from a data file:
SparseCompressedColumnMatrix<double> matrixA = SparseCompressedColumnMatrix<double>.CreateIdentity(3);
Vector<double> vectorB = Vector.Create(1.0, 2.0, 3.0);
IterativeSparseSolver<double> solver = new BiConjugateGradientSolver<double>(matrixA);
var resultVector = solver.Solve(vectorB);
Console.WriteLine("Result: {0}", resultVector);
Console.WriteLine("Solved in {0} iterations.", solver.IterationsNeeded);
Console.WriteLine("Estimated error: {0}", solver.SolutionReport.Error);
// With incomplete LU preconditioner
solver.Preconditioner = new IncompleteLUPreconditioner<double>(matrixA);
resultVector = solver.Solve(vectorB);
Console.WriteLine("Result: {0}", resultVector);
Console.WriteLine("Solved in {0} iterations.", solver.IterationsNeeded);
Console.WriteLine("Estimated error: {0}", solver.EstimatedError);
}
public void SimpleSample_Double_Identity()
{
Console.WriteLine(CoreImplementations <Complex <float> > .LinearAlgebra.Name);
// We load a sparse matrix and right-hand side from a data file:
SparseCompressedColumnMatrix <double> matrixA = SparseCompressedColumnMatrix <double> .CreateIdentity(3);
Vector <double> vectorB = Vector.Create(1.0, 2.0, 3.0);
IterativeSparseSolver <double> solver = new BiConjugateGradientSolver <double>(matrixA);
var resultVector = solver.Solve(vectorB);
Console.WriteLine("Result: {0}", resultVector);
Console.WriteLine("Solved in {0} iterations.", solver.IterationsNeeded);
Console.WriteLine("Estimated error: {0}", solver.SolutionReport.Error);
// With incomplete LU preconditioner
solver.Preconditioner = new IncompleteLUPreconditioner <double>(matrixA);
resultVector = solver.Solve(vectorB);
Console.WriteLine("Result: {0}", resultVector);
Console.WriteLine("Solved in {0} iterations.", solver.IterationsNeeded);
Console.WriteLine("Estimated error: {0}", solver.EstimatedError);
}
/// <summary>
/// Конструктор.
/// </summary>
/// <param name="elements">Список элементов.</param>
public FEMethod(IEnumerable <Triangle> elements)
{
// Узлы с неизвестными потенциалами.
nullPoints = elements.SelectMany(p => p.Points).Distinct().Where(p => p.Potential == null).ToArray();
// Идентификаторы узлов с неизвестными потенциалами.
foreach (var p in nullPoints)
{
p.ID = n++;
}
// Расчет базисных функций и матрицы коеффициентов.
foreach (var elem in elements)
{
elem.BasicFunctionElement();
}
// Построение разреженной СЛАУ.
timeFill = Stopwatch.StartNew();
FillSparseMatrix();
timeFill.Stop();
// Решение разреженной СЛАУ.
timeSol = Stopwatch.StartNew();
var conjugate = new BiConjugateGradientSolver <double>(matrixA);
conjugate.Preconditioner = new IncompleteLUPreconditioner <double>(matrixA);
var sol = conjugate.Solve(vectorB);
timeSol.Stop();
SetPotential(sol);
matrixA.Dispose();
vectorB.Dispose();
sol.Dispose();
}
