public void CanSolveForRandomMatrix(int order)
{
var matrixA = Matrix<double>.Build.Random(order, order, 1);
var matrixB = Matrix<double>.Build.Random(order, order, 1);
var monitor = new Iterator<double>(
new IterationCountStopCriterium<double>(1000),
new ResidualStopCriterium<double>(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], matrixBReconstruct[i, j], 1.0e-7);
}
}
}
public void CanSolveForRandomVector(int order)
{
var matrixA = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var vectorb = MatrixLoader.GenerateRandomDenseVector(order);
var monitor = new Iterator(new IIterationStopCriterium[]
{
new IterationCountStopCriterium(1000),
new ResidualStopCriterium(1e-10),
});
var solver = new BiCgStab(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 CanSolveForRandomMatrix(int order)
{
var matrixA = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var matrixB = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var monitor = new Iterator(new IIterationStopCriterium[]
{
new IterationCountStopCriterium(1000),
new ResidualStopCriterium(1e-10)
});
var solver = new BiCgStab(monitor);
var matrixX = solver.Solve(matrixA, matrixB);
// 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], matrixBReconstruct[i, j], 1.0e-7);
}
}
}
public void CanSolveForRandomVector(int order)
{
// Due to datatype "float" it can happen that solution will not converge for specific random matrix
// That's why we will do 3 tries and downgrade stop criterion each time
for (var iteration = 6; iteration > 3; iteration--)
{
var matrixA = Matrix <float> .Build.Random(order, order, 1);
var vectorb = Vector <float> .Build.Random(order, 1);
var monitor = new Iterator <float>(
new IterationCountStopCriterion <float>(MaximumIterations),
new ResidualStopCriterion <float>(Math.Pow(1.0 / 10.0, iteration)));
var solver = new BiCgStab();
var resultx = matrixA.SolveIterative(vectorb, solver, monitor);
if (monitor.Status != IterationStatus.Converged)
{
// Solution was not found, try again downgrading convergence boundary
continue;
}
Assert.AreEqual(matrixA.ColumnCount, resultx.Count);
var matrixBReconstruct = matrixA * resultx;
// Check the reconstruction.
for (var i = 0; i < order; i++)
{
Assert.AreEqual(vectorb[i], matrixBReconstruct[i], (float)Math.Pow(1.0 / 10.0, iteration - 3));
}
return;
}
}
public void CanSolveForRandomMatrix(int order)
{
var matrixA = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var matrixB = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var monitor = new Iterator(new IIterationStopCriterium[]
{
new IterationCountStopCriterium(1000),
new ResidualStopCriterium(1e-10)
});
var solver = new BiCgStab(monitor);
var matrixX = solver.Solve(matrixA, matrixB);
// 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], matrixBReconstruct[i, j], 1.0e-7);
}
}
}
public void CanSolveForRandomMatrix(int order)
{
var matrixA = Matrix <double> .Build.Random(order, order, 100);
var matrixB = Matrix <double> .Build.Random(order, order, 200);
var monitor = new Iterator <double>(
new IterationCountStopCriterion <double>(1000),
new ResidualStopCriterion <double>(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], matrixBReconstruct[i, j], 1.0e-7);
}
}
}
public void SolveLongMatrixThrowsArgumentException()
{
var matrix = new SparseMatrix(3, 2);
var input = new DenseVector(3);
var solver = new BiCgStab();
Assert.Throws<ArgumentException>(() => matrix.SolveIterative(input, solver));
}
public void SolveWideMatrixThrowsArgumentException()
{
var matrix = new SparseMatrix(2, 3);
var input = new DenseVector(2);
var solver = new BiCgStab();
Assert.That(() => matrix.SolveIterative(input, solver), Throws.ArgumentException);
}
public void SolveLongMatrixThrowsArgumentException()
{
var matrix = new SparseMatrix(3, 2);
Vector input = new DenseVector(3);
var solver = new BiCgStab();
Assert.Throws<ArgumentException>(() => solver.Solve(matrix, input));
}
public void SolveLongMatrixThrowsArgumentException()
{
var matrix = new SparseMatrix(3, 2);
var input = new DenseVector(3);
var solver = new BiCgStab();
Assert.Throws <ArgumentException>(() => solver.Solve(matrix, input));
}
public void SolveLongMatrix()
{
var matrix = new SparseMatrix(3, 2);
Vector <double> input = new DenseVector(3);
var solver = new BiCgStab();
solver.Solve(matrix, input);
}
public void SolveWideMatrix()
{
var matrix = new SparseMatrix(2, 3);
Vector <Complex32> input = new DenseVector(2);
var solver = new BiCgStab();
solver.Solve(matrix, input);
}
public void SolveLongMatrixThrowsArgumentException()
{
var matrix = new SparseMatrix(3, 2);
var input = new DenseVector(3);
var solver = new BiCgStab();
Assert.That(() => matrix.SolveIterative(input, solver), Throws.ArgumentException);
}
public void SolveWideMatrixThrowsArgumentException()
{
var matrix = new SparseMatrix(2, 3);
var input = new DenseVector(2);
var solver = new BiCgStab();
Assert.Throws <ArgumentException>(() => matrix.SolveIterative(input, solver));
}
/// <summary>
/// The main method that runs the BiCGStab iterative solver.
/// </summary>
public void UseSolver()
{
// Create a sparse matrix. For now the size will be 10 x 10 elements
Matrix matrix = CreateMatrix(10);
// Create the right hand side vector. The size is the same as the matrix
// and all values will be 2.0.
Vector rightHandSideVector = new DenseVector(10, 2.0);
// Create a preconditioner. The possibilities are:
// 1) No preconditioner - Simply do not provide the solver with a preconditioner.
// 2) A simple diagonal preconditioner - Create an instance of the Diagonal class.
// 3) A ILU preconditioner - Create an instance of the IncompleteLu class.
// 4) A ILU preconditioner with pivoting and drop tolerances - Create an instance of the Ilutp class.
// Here we'll use the simple diagonal preconditioner.
// We need a link to the matrix so the pre-conditioner can do it's work.
IPreConditioner preconditioner = new Diagonal();
// Create a new iterator. This checks for convergence of the results of the
// iterative matrix solver.
// In this case we'll create the default iterator
IIterator iterator = Iterator.CreateDefault();
// Create the solver
BiCgStab solver = new BiCgStab(preconditioner, iterator);
// Now that all is set we can solve the matrix equation.
Vector solutionVector = solver.Solve(matrix, rightHandSideVector);
// Another way to get the values is by using the overloaded solve method
// In this case the solution vector needs to be of the correct size.
solver.Solve(matrix, rightHandSideVector, solutionVector);
// Finally you can check the reason the solver finished the iterative process
// by calling the SolutionStatus property on the iterator
ICalculationStatus status = iterator.Status;
if (status is CalculationCancelled)
Console.WriteLine("The user cancelled the calculation.");
if (status is CalculationIndetermined)
Console.WriteLine("Oh oh, something went wrong. The iterative process was never started.");
if (status is CalculationConverged)
Console.WriteLine("Yippee, the iterative process converged.");
if (status is CalculationDiverged)
Console.WriteLine("I'm sorry the iterative process diverged.");
if (status is CalculationFailure)
Console.WriteLine("Oh dear, the iterative process failed.");
if (status is CalculationStoppedWithoutConvergence)
Console.WriteLine("Oh dear, the iterative process did not converge.");
}
private Complex[] CalculateSystemOfLinearEquations(Complex[,] matrixSystem, Complex[] matrixRightSide)
{
var matrixA = DenseMatrix.OfArray(matrixSystem);
var vectorB = new DenseVector(matrixRightSide);
var iterationCountStopCriterion = new IterationCountStopCriterion <Complex>(1000);
var residualStopCriterion = new ResidualStopCriterion <Complex>(1e-10);
var monitor = new Iterator <Complex>(iterationCountStopCriterion, residualStopCriterion);
var solver = new BiCgStab();
return(matrixA.SolveIterative(vectorB, solver, monitor).ToArray());
}
// Method to set up parameters for iterative solver
// Code for this method taken from the lecture slides (Lectures 5 and 6, solving 1D Heat Equation)
private void SetUpSolver()
{
// Stop after 1000 iterations
IterationCountStopCriterion <double> iterationCountStopCriterion
= new IterationCountStopCriterion <double>(1000);
// Stop after the error is less than 1e-8
ResidualStopCriterion <double> residualStopCriterion
= new ResidualStopCriterion <double>(1e-8);
monitor = new Iterator <double>(iterationCountStopCriterion, residualStopCriterion);
solver = new BiCgStab();
}
//Method to set up parameters for iterative solver
private void SetUpSolver()
{
// Stop calculation if 1000 iterations reached during calculation
IterationCountStopCriterion <double> iterationCountStopCriterion
= new IterationCountStopCriterion <double>(1000);
// Stop calculation if residuals are below 1e-8
// i.e. the calculation is considered converged
ResidualStopCriterion <double> residualStopCriterion
= new ResidualStopCriterion <double>(1e-8);
// Create monitor with defined stop criteria
monitor = new Iterator <double>(iterationCountStopCriterion, residualStopCriterion);
solver = new BiCgStab();
}
private void SetUpSolver()
{
// Stop calculation if 1000 iterations reached during calculation
IterationCountStopCriterion <double> iterationCountStopCriterion = new IterationCountStopCriterion <double>(100);
// Stop calculation if residuals are below 1E-10 --> the calculation is considered converged
ResidualStopCriterion <double> residualStopCriterion = new ResidualStopCriterion <double>(1e-8);
// Create monitor with defined stop criteria
monitor = new Iterator <double>(iterationCountStopCriterion, residualStopCriterion);
// 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:
solver = new BiCgStab();
}
public void solve()
{
Matrix <float> A = null;
Vector <float> b = null;
Vector <float> x = null;
IIterationStopCriterion <float> count_stop_criterion = new IterationCountStopCriterion <float>(5000);
IIterationStopCriterion <float> residual_stop_criterion = new ResidualStopCriterion <float>(1e-10f);
Iterator <float> iterator = new Iterator <float>(count_stop_criterion, residual_stop_criterion);
IPreconditioner <float> preconditioner = null;
BiCgStab solver = new BiCgStab();
solver.Solve(A, b, x, iterator, preconditioner);
}
public void CanSolveForRandomMatrix(int order)
{
// Due to datatype "float" it can happen that solution will not converge for specific random matrix
// That's why we will do 3 tries and downgrade stop criterium each time
for (var iteration = 6; iteration > 3; iteration--)
{
var matrixA = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var matrixB = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var monitor = new Iterator(new IIterationStopCriterium <float>[]
{
new IterationCountStopCriterium(MaximumIterations),
new ResidualStopCriterium((float)Math.Pow(1.0 / 10.0, iteration))
});
var solver = new BiCgStab(monitor);
var matrixX = solver.Solve(matrixA, matrixB);
if (!(monitor.Status is CalculationConverged))
{
// Solution was not found, try again downgrading convergence boundary
continue;
}
// 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.AreApproximatelyEqual(matrixB[i, j], matrixBReconstruct[i, j], (float)Math.Pow(1.0 / 10.0, iteration - 3));
}
}
return;
}
Assert.Fail("Solution was not found in 3 tries");
}
public void CanSolveForRandomMatrix(int order)
{
for (var iteration = 5; iteration > 3; iteration--)
{
var matrixA = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var matrixB = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var monitor = new Iterator(new IIterationStopCriterium <Complex32>[]
{
new IterationCountStopCriterium <Complex32>(1000),
new ResidualStopCriterium((float)Math.Pow(1.0 / 10.0, iteration))
});
var solver = new BiCgStab(monitor);
var matrixX = solver.Solve(matrixA, matrixB);
if (!(monitor.Status is CalculationConverged))
{
// Solution was not found, try again downgrading convergence boundary
continue;
}
// 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, (float)Math.Pow(1.0 / 10.0, iteration - 3));
Assert.AreEqual(matrixB[i, j].Imaginary, matrixBReconstruct[i, j].Imaginary, (float)Math.Pow(1.0 / 10.0, iteration - 3));
}
}
return;
}
Assert.Fail("Solution was not found in 3 tries");
}
public void CanSolveForRandomMatrix(int order)
{
// Due to datatype "float" it can happen that solution will not converge for specific random matrix
// That's why we will do 3 tries and downgrade stop criterium each time
for (var iteration = 6; iteration > 3; iteration--)
{
var matrixA = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var matrixB = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var monitor = new Iterator(new IIterationStopCriterium<float>[]
{
new IterationCountStopCriterium(MaximumIterations),
new ResidualStopCriterium((float)Math.Pow(1.0/10.0, iteration))
});
var solver = new BiCgStab(monitor);
var matrixX = solver.Solve(matrixA, matrixB);
if (!(monitor.Status is CalculationConverged))
{
// Solution was not found, try again downgrading convergence boundary
continue;
}
// 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.AreApproximatelyEqual(matrixB[i, j], matrixBReconstruct[i, j], (float)Math.Pow(1.0 / 10.0, iteration - 3));
}
}
return;
}
Assert.Fail("Solution was not found in 3 tries");
}
public void CanSolveForRandomMatrix([Values(4)] int order)
{
for (var iteration = 5; iteration > 3; iteration--)
{
var matrixA = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var matrixB = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var monitor = new Iterator(new IIterationStopCriterium[]
{
new IterationCountStopCriterium(1000),
new ResidualStopCriterium((float)Math.Pow(1.0 / 10.0, iteration))
});
var solver = new BiCgStab(monitor);
var matrixX = solver.Solve(matrixA, matrixB);
if (!(monitor.Status is CalculationConverged))
{
// Solution was not found, try again downgrading convergence boundary
continue;
}
// 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, (float)Math.Pow(1.0 / 10.0, iteration - 3));
Assert.AreEqual(matrixB[i, j].Imaginary, matrixBReconstruct[i, j].Imaginary, (float)Math.Pow(1.0 / 10.0, iteration - 3));
}
}
return;
}
Assert.Fail("Solution was not found in 3 tries");
}
public void CanSolveForRandomMatrix(int order)
{
for (var iteration = 5; iteration > 3; iteration--)
{
var matrixA = Matrix<Complex32>.Build.Random(order, order, 1);
var matrixB = Matrix<Complex32>.Build.Random(order, order, 1);
var monitor = new Iterator<Complex32>(
new IterationCountStopCriterion<Complex32>(1000),
new ResidualStopCriterion<Complex32>(Math.Pow(1.0/10.0, iteration)));
var solver = new BiCgStab();
var matrixX = matrixA.SolveIterative(matrixB, solver, monitor);
if (monitor.Status != IterationStatus.Converged)
{
// Solution was not found, try again downgrading convergence boundary
continue;
}
// 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, (float)Math.Pow(1.0/10.0, iteration - 3));
Assert.AreEqual(matrixB[i, j].Imaginary, matrixBReconstruct[i, j].Imaginary, (float)Math.Pow(1.0/10.0, iteration - 3));
}
}
return;
}
Assert.Fail("Solution was not found in 3 tries");
}
public void CanSolveForRandomMatrix(int order)
{
// Due to datatype "float" it can happen that solution will not converge for specific random matrix
// That's why we will do 3 tries and downgrade stop criterion each time
for (var iteration = 6; iteration > 3; iteration--)
{
var matrixA = Matrix <float> .Build.Random(order, order, 1);
var matrixB = Matrix <float> .Build.Random(order, order, 1);
var monitor = new Iterator <float>(
new IterationCountStopCriterion <float>(MaximumIterations),
new ResidualStopCriterion <float>(Math.Pow(1.0 / 10.0, iteration)));
var solver = new BiCgStab();
var matrixX = matrixA.SolveIterative(matrixB, solver, monitor);
if (monitor.Status != IterationStatus.Converged)
{
// Solution was not found, try again downgrading convergence boundary
continue;
}
// 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], matrixBReconstruct[i, j], (float)Math.Pow(1.0 / 10.0, iteration - 3));
}
}
return;
}
}
public void CanSolveForRandomMatrix(int order)
{
// Due to datatype "float" it can happen that solution will not converge for specific random matrix
// That's why we will do 3 tries and downgrade stop criterion each time
for (var iteration = 6; iteration > 3; iteration--)
{
var matrixA = Matrix<float>.Build.Random(order, order, 1);
var matrixB = Matrix<float>.Build.Random(order, order, 1);
var monitor = new Iterator<float>(
new IterationCountStopCriterion<float>(MaximumIterations),
new ResidualStopCriterion<float>(Math.Pow(1.0/10.0, iteration)));
var solver = new BiCgStab();
var matrixX = matrixA.SolveIterative(matrixB, solver, monitor);
if (monitor.Status != IterationStatus.Converged)
{
// Solution was not found, try again downgrading convergence boundary
continue;
}
// 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], matrixBReconstruct[i, j], (float)Math.Pow(1.0/10.0, iteration - 3));
}
}
return;
}
}
public void SolveScaledUnitMatrixAndBackMultiply()
{
// Create the identity matrix
var matrix = SparseMatrix.Identity(100);
// Scale it with a funny number
matrix.Multiply((float)Math.PI, matrix);
// 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(new IIterationStopCriterium <float>[]
{
new IterationCountStopCriterium <float>(MaximumIterations),
new ResidualStopCriterium(ConvergenceBoundary),
new DivergenceStopCriterium(),
new FailureStopCriterium()
});
var solver = new BiCgStab(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.Status is CalculationConverged, "#04");
// Now compare the vectors
for (var i = 0; i < y.Count; i++)
{
Assert.IsTrue((y[i] - z[i]).IsSmaller(ConvergenceBoundary, 1), "#05-" + i);
}
}
public void SolveScaledUnitMatrixAndBackMultiply()
{
// Create the identity matrix
var matrix = Matrix <double> .Build.SparseIdentity(100);
// Scale it with a funny number
matrix.Multiply(Math.PI, matrix);
// Create the y vector
var y = Vector <double> .Build.Dense(matrix.RowCount, 1);
// Create an iteration monitor which will keep track of iterative convergence
var monitor = new Iterator <double>(
new IterationCountStopCriterion <double>(MaximumIterations),
new ResidualStopCriterion <double>(ConvergenceBoundary),
new DivergenceStopCriterion <double>(),
new FailureStopCriterion <double>());
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.GreaterOrEqual(ConvergenceBoundary, Math.Abs(y[i] - z[i]), "#05-" + i);
}
}
public static double CalculateSsu()
{
// Stopwatch start
Timer.Restart();
var evector = new DenseVector(Length);
for (var i = 0; i < Length; i++)
{
QMatrix[i, 0] = 1;
evector[i] = 0;
}
evector[0] = 1.0;
var qtilde = new SparseMatrix(QMatrix.Transpose().ToArray());
var v = new BiCgStab().Solve(qtilde, evector);
var result = v.Sum() - UpStates.Sum(i => v[i]);
// Stopwatch stop and store statistic
_timeToSSU = (ulong)Timer.ElapsedTicks;
Timer.Stop();
return(result);
}
public void CanSolveForRandomVector(int order)
{
var matrixA = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var vectorb = MatrixLoader.GenerateRandomDenseVector(order);
var monitor = new Iterator <double>(
new IterationCountStopCriterium <double>(1000),
new ResidualStopCriterium <double>(1e-10));
var solver = new BiCgStab();
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], matrixBReconstruct[i], 1e-7);
}
}
public void CanSolveForRandomVector(int order)
{
var matrixA = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var vectorb = MatrixLoader.GenerateRandomDenseVector(order);
var monitor = new Iterator(new IIterationStopCriterium<double>[]
{
new IterationCountStopCriterium(1000),
new ResidualStopCriterium(1e-10),
});
var solver = new BiCgStab(monitor);
var resultx = solver.Solve(matrixA, vectorb);
Assert.AreEqual(matrixA.ColumnCount, resultx.Count);
var bReconstruct = matrixA * resultx;
// Check the reconstruction.
for (var i = 0; i < order; i++)
{
Assert.AreApproximatelyEqual(vectorb[i], bReconstruct[i], 1e-7);
}
}
public void CanSolveForRandomVector(int order)
{
// Due to datatype "float" it can happen that solution will not converge for specific random matrix
// That's why we will do 3 tries and downgrade stop criterium each time
for (var iteration = 6; iteration > 3; iteration--)
{
var matrixA = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var vectorb = MatrixLoader.GenerateRandomDenseVector(order);
var monitor = new Iterator(new IIterationStopCriterium <float>[]
{
new IterationCountStopCriterium(MaximumIterations),
new ResidualStopCriterium((float)Math.Pow(1.0 / 10.0, iteration)),
});
var solver = new BiCgStab(monitor);
var resultx = solver.Solve(matrixA, vectorb);
if (!(monitor.Status is CalculationConverged))
{
// Solution was not found, try again downgrading convergence boundary
continue;
}
Assert.AreEqual(matrixA.ColumnCount, resultx.Count);
var bReconstruct = matrixA * resultx;
// Check the reconstruction.
for (var i = 0; i < order; i++)
{
Assert.AreApproximatelyEqual(vectorb[i], bReconstruct[i], (float)Math.Pow(1.0 / 10.0, iteration - 3));
}
return;
}
Assert.Fail("Solution was not found in 3 tries");
}
public void CanSolveForRandomVector(int order)
{
for (var iteration = 5; iteration > 3; iteration--)
{
var matrixA = Matrix <Complex32> .Build.Random(order, order, 1);
var vectorb = Vector <Complex32> .Build.Random(order, 1);
var monitor = new Iterator <Complex32>(
new IterationCountStopCriterion <Complex32>(1000),
new ResidualStopCriterion <Complex32>(Math.Pow(1.0 / 10.0, iteration)));
var solver = new BiCgStab();
var resultx = matrixA.SolveIterative(vectorb, solver, monitor);
if (monitor.Status != IterationStatus.Converged)
{
// Solution was not found, try again downgrading convergence boundary
continue;
}
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, (float)Math.Pow(1.0 / 10.0, iteration - 3));
Assert.AreEqual(vectorb[i].Imaginary, matrixBReconstruct[i].Imaginary, (float)Math.Pow(1.0 / 10.0, iteration - 3));
}
return;
}
Assert.Fail("Solution was not found in 3 tries");
}
public void CanSolveForRandomVector(int order)
{
for (var iteration = 5; iteration > 3; iteration--)
{
var matrixA = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var vectorb = MatrixLoader.GenerateRandomDenseVector(order);
var monitor = new Iterator(new IIterationStopCriterium <Complex32>[]
{
new IterationCountStopCriterium <Complex32>(1000),
new ResidualStopCriterium((float)Math.Pow(1.0 / 10.0, iteration)),
});
var solver = new BiCgStab(monitor);
var resultx = solver.Solve(matrixA, vectorb);
if (!(monitor.Status is CalculationConverged))
{
// Solution was not found, try again downgrading convergence boundary
continue;
}
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, (float)Math.Pow(1.0 / 10.0, iteration - 3));
Assert.AreEqual(vectorb[i].Imaginary, matrixBReconstruct[i].Imaginary, (float)Math.Pow(1.0 / 10.0, iteration - 3));
}
return;
}
Assert.Fail("Solution was not found in 3 tries");
}
public void SolveUnitMatrixAndBackMultiply()
{
// Create the identity matrix
var matrix = SparseMatrix.CreateIdentity(100);
// Create the y vector
var y = DenseVector.Create(matrix.RowCount, Complex.One);
// 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 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.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, Complex.One);
// 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 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.GreaterOrEqual(ConvergenceBoundary, (y[i] - z[i]).Magnitude, "#05-" + i);
}
}
/// <summary>
/// Run example
/// </summary>
/// <seealso cref="http://en.wikipedia.org/wiki/Biconjugate_gradient_stabilized_method">Biconjugate gradient stabilized method</seealso>
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<double>(1e-10);
// Create monitor with defined stop criteriums
var monitor = new Iterator<double>(iterationCountStopCriterium, residualStopCriterium);
// Create Bi-Conjugate Gradient Stabilized solver
var solver = new BiCgStab();
// 1. Solve the matrix equation
var resultX = matrixA.SolveIterative(vectorB, solver, monitor);
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(monitor.Status);
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 CanSolveForRandomVector([Values(4)] int order)
{
for (var iteration = 5; iteration > 3; iteration--)
{
var matrixA = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var vectorb = MatrixLoader.GenerateRandomDenseVector(order);
var monitor = new Iterator(new IIterationStopCriterium[]
{
new IterationCountStopCriterium(1000),
new ResidualStopCriterium((float)Math.Pow(1.0 / 10.0, iteration)),
});
var solver = new BiCgStab(monitor);
var resultx = solver.Solve(matrixA, vectorb);
if (!(monitor.Status is CalculationConverged))
{
// Solution was not found, try again downgrading convergence boundary
continue;
}
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, (float)Math.Pow(1.0 / 10.0, iteration - 3));
Assert.AreEqual(vectorb[i].Imaginary, matrixBReconstruct[i].Imaginary, (float)Math.Pow(1.0 / 10.0, iteration - 3));
}
return;
}
Assert.Fail("Solution was not found in 3 tries");
}
public void CanSolveForRandomVector(int order)
{
// Due to datatype "float" it can happen that solution will not converge for specific random matrix
// That's why we will do 3 tries and downgrade stop criterium each time
for (var iteration = 6; iteration > 3; iteration--)
{
var matrixA = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var vectorb = MatrixLoader.GenerateRandomDenseVector(order);
var monitor = new Iterator(new IIterationStopCriterium[]
{
new IterationCountStopCriterium(MaximumIterations),
new ResidualStopCriterium((float) Math.Pow(1.0/10.0, iteration)),
});
var solver = new BiCgStab(monitor);
var resultx = solver.Solve(matrixA, vectorb);
if (!(monitor.Status is CalculationConverged))
{
// Solution was not found, try again downgrading convergence boundary
continue;
}
Assert.AreEqual(matrixA.ColumnCount, resultx.Count);
var matrixBReconstruct = matrixA*resultx;
// Check the reconstruction.
for (var i = 0; i < order; i++)
{
Assert.AreEqual(vectorb[i], matrixBReconstruct[i], (float) Math.Pow(1.0/10.0, iteration - 3));
}
return;
}
}
public override void ExecuteExample()
{
// <seealso cref="http://en.wikipedia.org/wiki/Biconjugate_gradient_stabilized_method">Biconjugate gradient stabilized method</seealso>
MathDisplay.WriteLine("<b>Biconjugate gradient stabilised iterative solver</b>");
// 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 }
});
MathDisplay.WriteLine(@"Matrix 'A' with coefficients");
MathDisplay.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// Create vector "b" with the constant terms.
var vectorB = new DenseVector(new[] { -7.0, 38.0, 43.0 });
MathDisplay.WriteLine(@"Vector 'b' with the constant terms");
MathDisplay.WriteLine(vectorB.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// Create stop criteria to monitor an iterative calculation. There are next available stop criteria:
// - DivergenceStopCriterion: monitors an iterative calculation for signs of divergence;
// - FailureStopCriterion: monitors residuals for NaN's;
// - IterationCountStopCriterion: monitors the numbers of iteration steps;
// - ResidualStopCriterion: monitors residuals if calculation is considered converged;
// Stop calculation if 1000 iterations reached during calculation
var iterationCountStopCriterion = new IterationCountStopCriterion <double>(1000);
// Stop calculation if residuals are below 1E-10 --> the calculation is considered converged
var residualStopCriterion = new ResidualStopCriterion <double>(1e-10);
// Create monitor with defined stop criteria
var monitor = new Iterator <double>(iterationCountStopCriterion, residualStopCriterion);
// Create Bi-Conjugate Gradient Stabilized solver
var solverBiCgStab = new BiCgStab();
// 1. Solve the matrix equation
var resultX = matrixA.SolveIterative(vectorB, solverBiCgStab, monitor);
MathDisplay.WriteLine(@"1. Solve the matrix equation");
MathDisplay.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;
MathDisplay.WriteLine(@"2. Solver status of the iterations");
MathDisplay.WriteLine(monitor.Status.ToString());
MathDisplay.WriteLine();
// 3. Solution result vector of the matrix equation
MathDisplay.WriteLine(@"3. Solution result vector of the matrix equation");
MathDisplay.WriteLine(resultX.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 4. Verify result. Multiply coefficient matrix "A" by result vector "x"
var reconstructVecorB = matrixA * resultX;
MathDisplay.WriteLine(@"4. Multiply coefficient matrix 'A' by result vector 'x'");
MathDisplay.WriteLine(reconstructVecorB.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
MathDisplay.WriteLine("<b>Generalized product biconjugate gradient solver</b>");
// 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
matrixA = DenseMatrix.OfArray(new[, ] {
{ 5.00, 2.00, -4.00 }, { 3.00, -7.00, 6.00 }, { 4.00, 1.00, 5.00 }
});
MathDisplay.WriteLine(@"Matrix 'A' with coefficients");
MathDisplay.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// Create vector "b" with the constant terms.
vectorB = new DenseVector(new[] { -7.0, 38.0, 43.0 });
MathDisplay.WriteLine(@"Vector 'b' with the constant terms");
MathDisplay.WriteLine(vectorB.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// Create stop criteria to monitor an iterative calculation. There are next available stop criteria:
// - DivergenceStopCriterion: monitors an iterative calculation for signs of divergence;
// - FailureStopCriterion: monitors residuals for NaN's;
// - IterationCountStopCriterion: monitors the numbers of iteration steps;
// - ResidualStopCriterion: monitors residuals if calculation is considered converged;
// Stop calculation if 1000 iterations reached during calculation
iterationCountStopCriterion = new IterationCountStopCriterion <double>(1000);
// Stop calculation if residuals are below 1E-10 --> the calculation is considered converged
residualStopCriterion = new ResidualStopCriterion <double>(1e-10);
// Create monitor with defined stop criteria
monitor = new Iterator <double>(iterationCountStopCriterion, residualStopCriterion);
// Create Generalized Product Bi-Conjugate Gradient solver
var solverGpBiCg = new GpBiCg();
// 1. Solve the matrix equation
resultX = matrixA.SolveIterative(vectorB, solverGpBiCg, monitor);
MathDisplay.WriteLine(@"1. Solve the matrix equation");
MathDisplay.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;
MathDisplay.WriteLine(@"2. Solver status of the iterations");
MathDisplay.WriteLine(monitor.Status.ToString());
MathDisplay.WriteLine();
// 3. Solution result vector of the matrix equation
MathDisplay.WriteLine(@"3. Solution result vector of the matrix equation");
MathDisplay.WriteLine(resultX.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 4. Verify result. Multiply coefficient matrix "A" by result vector "x"
reconstructVecorB = matrixA * resultX;
MathDisplay.WriteLine(@"4. Multiply coefficient matrix 'A' by result vector 'x'");
MathDisplay.WriteLine(reconstructVecorB.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
MathDisplay.WriteLine("<b>Composite linear equation solver</b>");
// 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
matrixA = DenseMatrix.OfArray(new[, ] {
{ 5.00, 2.00, -4.00 }, { 3.00, -7.00, 6.00 }, { 4.00, 1.00, 5.00 }
});
MathDisplay.WriteLine(@"Matrix 'A' with coefficients");
MathDisplay.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// Create vector "b" with the constant terms.
vectorB = new DenseVector(new[] { -7.0, 38.0, 43.0 });
MathDisplay.WriteLine(@"Vector 'b' with the constant terms");
MathDisplay.WriteLine(vectorB.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// Create stop criteria to monitor an iterative calculation. There are next available stop criteria:
// - DivergenceStopCriterion: monitors an iterative calculation for signs of divergence;
// - FailureStopCriterion: monitors residuals for NaN's;
// - IterationCountStopCriterion: monitors the numbers of iteration steps;
// - ResidualStopCriterion: monitors residuals if calculation is considered converged;
// Stop calculation if 1000 iterations reached during calculation
iterationCountStopCriterion = new IterationCountStopCriterion <double>(1000);
// Stop calculation if residuals are below 1E-10 --> the calculation is considered converged
residualStopCriterion = new ResidualStopCriterion <double>(1e-10);
// Create monitor with defined stop criteria
monitor = new Iterator <double>(iterationCountStopCriterion, residualStopCriterion);
// Load all suitable solvers from current assembly. Below (see UserBiCgStab) there is a custom user-defined solver
// "class UserBiCgStab : IIterativeSolverSetup<double>" which derives from the regular BiCgStab solver. However users can
// create any other solver and solver setup classes that implement IIterativeSolverSetup<T> and load the assembly that
// contains them using the following function:
var solverComp = new CompositeSolver(SolverSetup <double> .LoadFromAssembly(Assembly.GetExecutingAssembly()));
// 1. Solve the linear system
resultX = matrixA.SolveIterative(vectorB, solverComp, monitor);
MathDisplay.WriteLine(@"1. Solve the matrix equation");
MathDisplay.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;
MathDisplay.WriteLine(@"2. Solver status of the iterations");
MathDisplay.WriteLine(monitor.Status.ToString());
MathDisplay.WriteLine();
// 3. Solution result vector of the matrix equation
MathDisplay.WriteLine(@"3. Solution result vector of the matrix equation");
MathDisplay.WriteLine(resultX.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 4. Verify result. Multiply coefficient matrix "A" by result vector "x"
reconstructVecorB = matrixA * resultX;
MathDisplay.WriteLine(@"4. Multiply coefficient matrix 'A' by result vector 'x'");
MathDisplay.WriteLine(reconstructVecorB.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
MathDisplay.WriteLine("<b>Multiple-Lanczos biconjugate gradient stabilised iterative solver</b>");
// 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
matrixA = DenseMatrix.OfArray(new[, ] {
{ 5.00, 2.00, -4.00 }, { 3.00, -7.00, 6.00 }, { 4.00, 1.00, 5.00 }
});
MathDisplay.WriteLine(@"Matrix 'A' with coefficients");
MathDisplay.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// Create vector "b" with the constant terms.
vectorB = new DenseVector(new[] { -7.0, 38.0, 43.0 });
MathDisplay.WriteLine(@"Vector 'b' with the constant terms");
MathDisplay.WriteLine(vectorB.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// Create stop criteria to monitor an iterative calculation. There are next available stop criteria:
// - DivergenceStopCriterion: monitors an iterative calculation for signs of divergence;
// - FailureStopCriterion: monitors residuals for NaN's;
// - IterationCountStopCriterion: monitors the numbers of iteration steps;
// - ResidualStopCriterion: monitors residuals if calculation is considered converged;
// Stop calculation if 1000 iterations reached during calculation
iterationCountStopCriterion = new IterationCountStopCriterion <double>(1000);
// Stop calculation if residuals are below 1E-10 --> the calculation is considered converged
residualStopCriterion = new ResidualStopCriterion <double>(1e-10);
// Create monitor with defined stop criteria
monitor = new Iterator <double>(iterationCountStopCriterion, residualStopCriterion);
// Create Multiple-Lanczos Bi-Conjugate Gradient Stabilized solver
var solverLanczos = new MlkBiCgStab();
// 1. Solve the matrix equation
resultX = matrixA.SolveIterative(vectorB, solverLanczos, monitor);
MathDisplay.WriteLine(@"1. Solve the matrix equation");
MathDisplay.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;
MathDisplay.WriteLine(@"2. Solver status of the iterations");
MathDisplay.WriteLine(monitor.Status.ToString());
MathDisplay.WriteLine();
// 3. Solution result vector of the matrix equation
MathDisplay.WriteLine(@"3. Solution result vector of the matrix equation");
MathDisplay.WriteLine(resultX.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 4. Verify result. Multiply coefficient matrix "A" by result vector "x"
reconstructVecorB = matrixA * resultX;
MathDisplay.WriteLine(@"4. Multiply coefficient matrix 'A' by result vector 'x'");
MathDisplay.WriteLine(reconstructVecorB.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
MathDisplay.WriteLine("<b>Transpose freee quasi-minimal residual iterative solver</b>");
// 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
matrixA = DenseMatrix.OfArray(new[, ] {
{ 5.00, 2.00, -4.00 }, { 3.00, -7.00, 6.00 }, { 4.00, 1.00, 5.00 }
});
MathDisplay.WriteLine(@"Matrix 'A' with coefficients");
MathDisplay.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// Create vector "b" with the constant terms.
vectorB = new DenseVector(new[] { -7.0, 38.0, 43.0 });
MathDisplay.WriteLine(@"Vector 'b' with the constant terms");
MathDisplay.WriteLine(vectorB.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// Create stop criteria to monitor an iterative calculation. There are next available stop criteria:
// - DivergenceStopCriterion: monitors an iterative calculation for signs of divergence;
// - FailureStopCriterion: monitors residuals for NaN's;
// - IterationCountStopCriterion: monitors the numbers of iteration steps;
// - ResidualStopCriterion: monitors residuals if calculation is considered converged;
// Stop calculation if 1000 iterations reached during calculation
iterationCountStopCriterion = new IterationCountStopCriterion <double>(1000);
// Stop calculation if residuals are below 1E-10 --> the calculation is considered converged
residualStopCriterion = new ResidualStopCriterion <double>(1e-10);
// Create monitor with defined stop criteria
monitor = new Iterator <double>(iterationCountStopCriterion, residualStopCriterion);
// Create Transpose Free Quasi-Minimal Residual solver
var solverTFQMR = new TFQMR();
// 1. Solve the matrix equation
resultX = matrixA.SolveIterative(vectorB, solverTFQMR, monitor);
MathDisplay.WriteLine(@"1. Solve the matrix equation");
MathDisplay.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;
MathDisplay.WriteLine(@"2. Solver status of the iterations");
MathDisplay.WriteLine(monitor.Status.ToString());
MathDisplay.WriteLine();
// 3. Solution result vector of the matrix equation
MathDisplay.WriteLine(@"3. Solution result vector of the matrix equation");
MathDisplay.WriteLine(resultX.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
// 4. Verify result. Multiply coefficient matrix "A" by result vector "x"
reconstructVecorB = matrixA * resultX;
MathDisplay.WriteLine(@"4. Multiply coefficient matrix 'A' by result vector 'x'");
MathDisplay.WriteLine(reconstructVecorB.ToString("#0.00\t", formatProvider));
MathDisplay.WriteLine();
}
public static void MinimizeDivergence()
{
CalculateGradients();
CreateWindArrays();
CreateTCWindArrays();
CreateLambda();
FillMatrixA();
//#region ---Load MS Excel and write A---
//Excel.Application oExcel = new Excel.Application { Visible = true };
//oExcel.Workbooks.Add();
//Excel._Worksheet workSheet = oExcel.ActiveSheet;
//var arrA = A;
//for (int i = 0; i < (Meteorology.NumberOfMetCellsX * Meteorology.NumberOfMetCellsY * Meteorology.NumberOfMetCellsZ); i++)
//{
// for (excelColumnNumber = 0; excelColumnNumber < (Meteorology.NumberOfMetCellsX * Meteorology.NumberOfMetCellsY * Meteorology.NumberOfMetCellsZ); excelColumnNumber++)
// {
// workSheet.Cells[i + 1, excelColumnNumber + 1] = arrA[i, excelColumnNumber];
// }
//}
//#endregion
BiCgStab b = new BiCgStab();
b.SetIterator(dnAnalytics.LinearAlgebra.Solvers.Iterator.CreateDefault());
b.SetPreconditioner(new Diagonal());
bool divergenceMinimized = false;
for (int p = 0; p < 50000; p++)
{
CalculateDivergence();
double count = 0;
foreach (double d in B.ToArray())
{
count += 1;
if (-d > minimumDivergence)
{
break;
}
else if (count == B.Count)
{
divergenceMinimized = true;
break;
}
}
if (divergenceMinimized)
{
break;
}
else
{
var M = b.Solve(A, B);
for (int i = 0; i < M.Count; i++)
{
Lambda[i] = M[i];
}
UpdateWindArrays();
}
}
CalculateCartesianWindComponents();
UpdateMeteorology();
}
public void CanSolveForRandomVector(int order)
{
// Due to datatype "float" it can happen that solution will not converge for specific random matrix
// That's why we will do 3 tries and downgrade stop criterion each time
for (var iteration = 6; iteration > 3; iteration--)
{
var matrixA = Matrix<float>.Build.Random(order, order, 1);
var vectorb = Vector<float>.Build.Random(order, 1);
var monitor = new Iterator<float>(
new IterationCountStopCriterion<float>(MaximumIterations),
new ResidualStopCriterion<float>(Math.Pow(1.0/10.0, iteration)));
var solver = new BiCgStab();
var resultx = matrixA.SolveIterative(vectorb, solver, monitor);
if (monitor.Status != IterationStatus.Converged)
{
// Solution was not found, try again downgrading convergence boundary
continue;
}
Assert.AreEqual(matrixA.ColumnCount, resultx.Count);
var matrixBReconstruct = matrixA*resultx;
// Check the reconstruction.
for (var i = 0; i < order; i++)
{
Assert.AreEqual(vectorb[i], matrixBReconstruct[i], (float)Math.Pow(1.0/10.0, iteration - 3));
}
return;
}
}
/// <summary>
/// Run example
/// </summary>
/// <seealso cref="http://en.wikipedia.org/wiki/Biconjugate_gradient_stabilized_method">Biconjugate gradient stabilized method</seealso>
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 criteria to monitor an iterative calculation. There are next available stop criteria:
// - DivergenceStopCriterion: monitors an iterative calculation for signs of divergence;
// - FailureStopCriterion: monitors residuals for NaN's;
// - IterationCountStopCriterion: monitors the numbers of iteration steps;
// - ResidualStopCriterion: monitors residuals if calculation is considered converged;
// Stop calculation if 1000 iterations reached during calculation
var iterationCountStopCriterion = new IterationCountStopCriterion <double>(1000);
// Stop calculation if residuals are below 1E-10 --> the calculation is considered converged
var residualStopCriterion = new ResidualStopCriterion <double>(1e-10);
// Create monitor with defined stop criteria
var monitor = new Iterator <double>(iterationCountStopCriterion, residualStopCriterion);
// Create Bi-Conjugate Gradient Stabilized solver
var solver = new BiCgStab();
// 1. Solve the matrix equation
var resultX = matrixA.SolveIterative(vectorB, solver, monitor);
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(monitor.Status);
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 SolveScaledUnitMatrixAndBackMultiply()
{
// Create the identity matrix
var matrix = SparseMatrix.Identity(100);
// Scale it with a funny number
matrix.Multiply(new Complex32((float) Math.PI, (float) Math.PI), matrix);
// Create the y vector
var y = DenseVector.Create(matrix.RowCount, i => Complex32.One);
// Create an iteration monitor which will keep track of iterative convergence
var monitor = new Iterator<Complex32>(new IIterationStopCriterium<Complex32>[]
{
new IterationCountStopCriterium<Complex32>(MaximumIterations),
new ResidualStopCriterium(ConvergenceBoundary),
new DivergenceStopCriterium(),
new FailureStopCriterium()
});
var solver = new BiCgStab(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 = Matrix<double>.Build.Random(order, order, 1);
var vectorb = Vector<double>.Build.Random(order, 1);
var monitor = new Iterator<double>(
new IterationCountStopCriterium<double>(1000),
new ResidualStopCriterium<double>(1e-10));
var solver = new BiCgStab();
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], matrixBReconstruct[i], 1e-7);
}
}
/// <summary>
/// Start Image Fusion
/// Based on Poisson Image Editing. P Perez et. al. SIGGRAPH 2003
/// </summary>
/// <param name="sender"></param>
/// <param name="e"></param>
private void buttonImageFusion_Click(object sender, EventArgs e)
{
if (zoomSrcImg != null && tarImg != null)
{
DateTime startTime = DateTime.Now;
// Set the boundary value of zoomSrcImg
pointId = new int [zoomSrcImg.Height, zoomSrcImg.Width];
// +----------+
// + +
// +----------+
for (var r = 0; r < zoomSrcImg.Height; ++r)
{
pointId[r, 0] = -1;
pointId[r, zoomSrcImg.Width - 1] = -1;
}
// -++++++++++-
// - -
// -++++++++++-
for (var c = 1; c < zoomSrcImg.Width - 1; ++c)
{
pointId[0, c] = -1;
pointId[zoomSrcImg.Height - 1, c] = -1;
}
// Set mapping between point Id and the position
List<Point> contentList = new List<Point>();
for (var r = 1; r < zoomSrcImg.Height - 1; ++r)
for (var c = 1; c < zoomSrcImg.Width - 1; ++c)
{
pointId[r, c] = contentList.Count;
contentList.Add(new Point(r, c));
}
Console.WriteLine("Mark every points with -1, 0, ...Time:" + DateTime.Now.Subtract(startTime).TotalSeconds);
// Solve AX=B problem using solutions from the paper: Poisson Image Editing.
int contentNum = contentList.Count;
// To solve AX=B, get matrix A and B first
//var matA = LA.Matrix<double>.Build.Sparse(contentNum, contentNum);
//var matB = LA.Double.Vector.Build.Dense(contentNum);
// top, right, bottom, left. In order to use for-loop.
int[] dx = new int[] {-1, 0, 1, 0};
int[] dy = new int[] { 0, 1, 0, -1 };
Image<Bgr, byte> resultImg = imgList[currImgIdFusion].Copy();
//int[,] contentColor = new int[3, contentNum];
// Parallelize color channel B, G, R
System.Threading.Tasks.Parallel.For(0, 3, (k) =>
//for (var k = 0; k <= 2; ++k)
{
Console.WriteLine("Generate Matrix No. " + k);
// Set matrix A & B to zero
var matA = LA.Matrix<double>.Build.Sparse(contentNum, contentNum);
var matB = LA.Double.Vector.Build.Dense(contentNum);
//matA.Clear();
//matB.Clear();
// Point P's neighbours.
List<Point> Np = new List<Point>();
// Generate matrix A & B
for (var id = 0; id < contentNum; ++id)
{
// For each point, use equation No.7 & No.8 in the paper
// Which means one row in the matrix
// Matrix A
Np.Clear();
// Old Point P: position in the zoomSrcImg. New Point P: position in the tarImg
Point oldP = contentList[id];
Point newP = new Point(oldP.X + tarTopLeftX, oldP.Y + tarTopLeftY);
for (var i = 0; i < 4; ++i)
{
// New Point Q: P's neighbour in the WHOLE target image
Point newQ = new Point(newP.X + dx[i], newP.Y + dy[i]);
if (newQ.X >= 0 && newQ.X < resultImg.Height && newQ.Y >= 0 && newQ.Y < resultImg.Width)
{
// Point Q is inside the area Omiga
Np.Add(newQ);
}
}
matA.At(id, id, Np.Count);
foreach (Point newQ in Np)
{
// Check Point Id of Old Q
int qID = pointId[newQ.X - tarTopLeftX, newQ.Y - tarTopLeftY];
// Old Q is inside Omiga
if (qID >= 0)
{
matA.At(id, qID, -1);
}
}
// Matrix B
double Bi = 0;
foreach (Point newQ in Np)
{
// Check Point Id of Old Q
int qID = pointId[newQ.X - tarTopLeftX, newQ.Y - tarTopLeftY];
// Q is on the boundry
if (qID == -1)
{
Bi += resultImg.Data[newQ.X, newQ.Y, k];
}
Point oldQ = new Point(newQ.X - tarTopLeftX, newQ.Y - tarTopLeftY);
Bi += zoomSrcImg.Data[oldP.X, oldP.Y, k] - zoomSrcImg.Data[oldQ.X, oldQ.Y, k];
}
matB.At(id, Bi);
}//);
Console.WriteLine("Generate Matrix Done. Time:" + DateTime.Now.Subtract(startTime).TotalSeconds);
// Solve the sparse linear equation using BiCgStab (Bi-Conjugate Gradient Stabilized)
var fp = LA.Double.Vector.Build.Dense(contentNum);
BiCgStab solver = new BiCgStab();
// Choose stop criterias
// Learn about stop criteria from: wo80, http://mathnetnumerics.codeplex.com/discussions/404689
var stopCriterias = new List<IIterationStopCriterion<double>>()
{
new ResidualStopCriterion<double>(1e-5),
new IterationCountStopCriterion<double>(1000),
new DivergenceStopCriterion<double>(),
new FailureStopCriterion<double>()
};
solver.Solve(matA, matB, fp, new Iterator<double>(stopCriterias), new DiagonalPreconditioner());
Console.WriteLine("Equation Solved. Time:" + DateTime.Now.Subtract(startTime).TotalSeconds);
// Console.WriteLine(fp);
// Set the color
for (var id = 0; id < contentNum; ++id)
{
int color = (int)fp.At(id);
if (color < 0)
color = 0;
if (color > 255)
color = 255;
//contentColor[k, id] = color;
resultImg.Data[contentList[id].X + tarTopLeftX, contentList[id].Y + tarTopLeftY, k] = (Byte)color;
}
});
//Paint
//for (var id = 0; id < contentNum; ++id)
//{
// resultImg[contentList[id].X + tarTopLeftX, contentList[id].Y + tarTopLeftY] = new Bgr(
// contentColor[0, id], contentColor[1, id], contentColor[2, id]);
//}
imgModifiedList[currImgIdFusion] = resultImg.Copy();
pictureBoxImgFusion.Image = resultImg.ToBitmap();
Console.WriteLine("Painting Finished. Time:" + DateTime.Now.Subtract(startTime).TotalSeconds);
}
}
public void CanSolveForRandomVector(int order)
{
var matrixA = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var vectorb = MatrixLoader.GenerateRandomDenseVector(order);
var monitor = new Iterator<Complex>(
new IterationCountStopCriterium<Complex>(1000),
new ResidualStopCriterium(1e-10));
var solver = new BiCgStab();
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 SolveWideMatrix()
{
var matrix = new SparseMatrix(2, 3);
Vector<Complex32> input = new DenseVector(2);
var solver = new BiCgStab();
solver.Solve(matrix, input);
}
public void SolveLongMatrix()
{
var matrix = new SparseMatrix(3, 2);
Vector<Complex> input = new DenseVector(3);
var solver = new BiCgStab();
solver.Solve(matrix, input);
}
public void CanSolveForRandomVector(int order)
{
for (var iteration = 5; iteration > 3; iteration--)
{
var matrixA = Matrix<Complex32>.Build.Random(order, order, 1);
var vectorb = Vector<Complex32>.Build.Random(order, 1);
var monitor = new Iterator<Complex32>(
new IterationCountStopCriterium<Complex32>(1000),
new ResidualStopCriterium<Complex32>(Math.Pow(1.0 / 10.0, iteration)));
var solver = new BiCgStab();
var resultx = matrixA.SolveIterative(vectorb, solver, monitor);
if (monitor.Status != IterationStatus.Converged)
{
// Solution was not found, try again downgrading convergence boundary
continue;
}
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, (float) Math.Pow(1.0/10.0, iteration - 3));
Assert.AreEqual(vectorb[i].Imaginary, matrixBReconstruct[i].Imaginary, (float) Math.Pow(1.0/10.0, iteration - 3));
}
return;
}
Assert.Fail("Solution was not found in 3 tries");
}
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(new IIterationStopCriterium <float>[]
{
new IterationCountStopCriterium <float>(MaximumIterations),
new ResidualStopCriterium(ConvergenceBoundary),
new DivergenceStopCriterium(),
new FailureStopCriterium()
});
var solver = new BiCgStab(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.Status is CalculationConverged, "#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 => Complex32.One);
// Create an iteration monitor which will keep track of iterative convergence
var monitor = new Iterator<Complex32>(
new IterationCountStopCriterium<Complex32>(MaximumIterations),
new ResidualStopCriterium<Complex32>(ConvergenceBoundary),
new DivergenceStopCriterium<Complex32>(),
new FailureStopCriterium<Complex32>());
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.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
Vector y = DenseVector.Create(matrix.RowCount, i => 1);
// Create an iteration monitor which will keep track of iterative convergence
var monitor = new Iterator(new IIterationStopCriterium[]
{
new IterationCountStopCriterium(MaximumIterations),
new ResidualStopCriterium(ConvergenceBoundary),
new DivergenceStopCriterium(),
new FailureStopCriterium()
});
var solver = new BiCgStab(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.Status is CalculationConverged, "#04");
// Now compare the vectors
for (var i = 0; i < y.Count; i++)
{
#if !PORTABLE
Assert.IsTrue(Math.Abs(y[i] - z[i]).IsSmaller(ConvergenceBoundary, 1), "#05-" + i);
#else
Assert.IsTrue(Math.Abs(y[i] - z[i]).IsSmaller(ConvergenceBoundary * 100.0, 1), "#05-" + i);
#endif
}
}
public void SolveUnitMatrixAndBackMultiply()
{
// Create the identity matrix
var matrix = SparseMatrix.CreateIdentity(100);
// Create the y vector
var y = DenseVector.Create(matrix.RowCount, i => Complex32.One);
// Create an iteration monitor which will keep track of iterative convergence
var monitor = new Iterator<Complex32>(
new IterationCountStopCriterium<Complex32>(MaximumIterations),
new ResidualStopCriterium<Complex32>(ConvergenceBoundary),
new DivergenceStopCriterium<Complex32>(),
new FailureStopCriterium<Complex32>());
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.GreaterOrEqual(ConvergenceBoundary, (y[i] - z[i]).Magnitude, "#05-" + i);
}
}
public void SolveUnitMatrixAndBackMultiply()
{
// Create the identity matrix
Matrix matrix = SparseMatrix.Identity(100);
// Create the y vector
Vector y = DenseVector.Create(matrix.RowCount, i => 1);
// Create an iteration monitor which will keep track of iterative convergence
var monitor = new Iterator(new IIterationStopCriterium[]
{
new IterationCountStopCriterium(MaximumIterations),
new ResidualStopCriterium(ConvergenceBoundary),
new DivergenceStopCriterium(),
new FailureStopCriterium()
});
var solver = new BiCgStab(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.Status is CalculationConverged, "#04");
// Now compare the vectors
for (var i = 0; i < y.Count; i++)
{
Assert.IsTrue((y[i] - z[i]).IsSmaller(ConvergenceBoundary, 1), "#05-" + i);
}
}
public void SolveScaledUnitMatrixAndBackMultiply()
{
// Create the identity matrix
var matrix = Matrix<double>.Build.SparseIdentity(100);
// Scale it with a funny number
matrix.Multiply(Math.PI, matrix);
// Create the y vector
var y = Vector<double>.Build.Dense(matrix.RowCount, 1);
// Create an iteration monitor which will keep track of iterative convergence
var monitor = new Iterator<double>(
new IterationCountStopCriterium<double>(MaximumIterations),
new ResidualStopCriterium<double>(ConvergenceBoundary),
new DivergenceStopCriterium<double>(),
new FailureStopCriterium<double>());
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.GreaterOrEqual(ConvergenceBoundary, Math.Abs(y[i] - z[i]), "#05-" + i);
}
}