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 GpBiCg();
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 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 GpBiCg();
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);
}
}
}
public void CanSolveForRandomMatrix(int order)
{
var matrixA = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var matrixB = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var monitor = new Iterator(new IIterationStopCriterium<double>[]
{
new IterationCountStopCriterium(1000),
new ResidualStopCriterium(1e-10)
});
var solver = new GpBiCg(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.AreApproximatelyEqual(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 GpBiCg();
Assert.Throws<ArgumentException>(() => matrix.SolveIterative(input, solver));
}
public void SolveLongMatrixThrowsArgumentException()
{
var matrix = new SparseMatrix(3, 2);
Vector input = new DenseVector(3);
var solver = new GpBiCg();
Assert.Throws<ArgumentException>(() => solver.Solve(matrix, input));
}
public void SolveWideMatrixThrowsArgumentException()
{
var matrix = new SparseMatrix(2, 3);
var input = new DenseVector(2);
var solver = new GpBiCg();
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 GpBiCg();
Assert.Throws <ArgumentException>(() => solver.Solve(matrix, input));
}
public void SolveWideMatrixThrowsArgumentException()
{
var matrix = new SparseMatrix(2, 3);
var input = new DenseVector(2);
var solver = new GpBiCg();
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.Throws <ArgumentException>(() => matrix.SolveIterative(input, solver));
}
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 GpBiCg(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)
{
// 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 GpBiCg(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)
{
// 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 GpBiCg();
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)
{
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(1000),
new ResidualStopCriterium((float)Math.Pow(1.0 / 10.0, iteration))
});
var solver = new GpBiCg(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].Real, matrixBReconstruct[i, j].Real, (float)Math.Pow(1.0 / 10.0, iteration - 3));
Assert.AreApproximatelyEqual(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 = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var matrixB = MatrixLoader.GenerateRandomDenseMatrix(order, order);
var monitor = new Iterator(new IIterationStopCriterium<Complex32>[]
{
new IterationCountStopCriterium(1000),
new ResidualStopCriterium((float)Math.Pow(1.0 / 10.0, iteration))
});
var solver = new GpBiCg(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].Real, matrixBReconstruct[i, j].Real, (float)Math.Pow(1.0 / 10.0, iteration - 3));
Assert.AreApproximatelyEqual(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 SolveScaledUnitMatrixAndBackMultiply()
{
// Create the identity matrix
Matrix matrix = SparseMatrix.Identity(100);
// Scale it with a funny number
matrix.Multiply((float)Math.PI, matrix);
// Create the y vector
Vector y = new DenseVector(matrix.RowCount, 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 GpBiCg(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 = SparseMatrix.CreateIdentity(100);
// Scale it with a funny number
matrix.Multiply((float)Math.PI, matrix);
// Create the y vector
var y = Vector <float> .Build.Dense(matrix.RowCount, 1);
// Create an iteration monitor which will keep track of iterative convergence
var monitor = new Iterator <float>(
new IterationCountStopCriterion <float>(MaximumIterations),
new ResidualStopCriterion <float>(ConvergenceBoundary),
new DivergenceStopCriterion <float>(),
new FailureStopCriterion <float>());
var solver = new GpBiCg();
// 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 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 GpBiCg(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)
{
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 GpBiCg();
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)
{
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 GpBiCg(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 <float>[]
{
new IterationCountStopCriterium(MaximumIterations),
new ResidualStopCriterium((float)Math.Pow(1.0 / 10.0, iteration)),
});
var solver = new GpBiCg(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 SolveUnitMatrixAndBackMultiply()
{
// Create the identity matrix
var matrix = SparseMatrix.Identity(100);
// 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 <Complex32>(new IIterationStopCriterium <Complex32>[]
{
new IterationCountStopCriterium <Complex32>(MaximumIterations),
new ResidualStopCriterium(ConvergenceBoundary),
new DivergenceStopCriterium(),
new FailureStopCriterium()
});
var solver = new GpBiCg(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)
{
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 GpBiCg();
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([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 GpBiCg(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)
{
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 GpBiCg();
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([Values(4, 8, 10)] 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 GpBiCg(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], matrixBReconstruct[i], 1e-7);
}
}
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<double> y = new DenseVector(matrix.RowCount, 1);
// Create an iteration monitor which will keep track of iterative convergence
var monitor = new Iterator(new IIterationStopCriterium<double>[]
{
new IterationCountStopCriterium(MaximumIterations),
new ResidualStopCriterium(ConvergenceBoundary),
new DivergenceStopCriterium(),
new FailureStopCriterium()
});
var solver = new GpBiCg(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(System.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 = Vector<Complex32>.Build.Dense(matrix.RowCount, 1);
// Create an iteration monitor which will keep track of iterative convergence
var monitor = new Iterator<Complex32>(
new IterationCountStopCriterion<Complex32>(MaximumIterations),
new ResidualStopCriterion<Complex32>(ConvergenceBoundary),
new DivergenceStopCriterion<Complex32>(),
new FailureStopCriterion<Complex32>());
var solver = new GpBiCg();
// 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>
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 Generalized Product Bi-Conjugate Gradient solver
var solver = new GpBiCg();
// 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 SolvePoissonMatrixAndBackMultiply()
{
// Create the matrix
var matrix = Matrix <double> .Build.Sparse(100, 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 <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 GpBiCg();
// 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);
}
}
/// <summary>
/// Run example
/// </summary>
public void Run()
{
// Format matrix output to console
var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
formatProvider.TextInfo.ListSeparator = " ";
// Solve next system of linear equations (Ax=b):
// 5*x + 2*y - 4*z = -7
// 3*x - 7*y + 6*z = 38
// 4*x + 1*y + 5*z = 43
// Create matrix "A" with coefficients
var matrixA = DenseMatrix.OfArray(new[, ] {
{ 5.00, 2.00, -4.00 }, { 3.00, -7.00, 6.00 }, { 4.00, 1.00, 5.00 }
});
Console.WriteLine(@"Matrix 'A' with coefficients");
Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// Create vector "b" with the constant terms.
var vectorB = new DenseVector(new[] { -7.0, 38.0, 43.0 });
Console.WriteLine(@"Vector 'b' with the constant terms");
Console.WriteLine(vectorB.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// Create stop criteriums to monitor an iterative calculation. There are next available stop criteriums:
// - DivergenceStopCriterium: monitors an iterative calculation for signs of divergence;
// - FailureStopCriterium: monitors residuals for NaN's;
// - IterationCountStopCriterium: monitors the numbers of iteration steps;
// - ResidualStopCriterium: monitors residuals if calculation is considered converged;
// Stop calculation if 1000 iterations reached during calculation
var iterationCountStopCriterium = new IterationCountStopCriterium <double>(1000);
// Stop calculation if residuals are below 1E-10 --> the calculation is considered converged
var residualStopCriterium = new ResidualStopCriterium <double>(1e-10);
// Create monitor with defined stop criteriums
var monitor = new Iterator <double>(iterationCountStopCriterium, residualStopCriterium);
// Create Generalized Product Bi-Conjugate Gradient solver
var solver = new GpBiCg();
// 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 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 void SolveUnitMatrixAndBackMultiply()
{
// Create the identity matrix
var matrix = Matrix<double>.Build.SparseIdentity(100);
// 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 GpBiCg();
// 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 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 GpBiCg();
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 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 GpBiCg();
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 SolveWideMatrix()
{
var matrix = new SparseMatrix(2, 3);
Vector<float> input = new DenseVector(2);
var solver = new GpBiCg();
solver.Solve(matrix, input);
}
public void SolveUnitMatrixAndBackMultiply()
{
// Create the identity matrix
Matrix<double> matrix = SparseMatrix.Identity(100);
// Create the y vector
Vector<double> y = new DenseVector(matrix.RowCount, 1);
// Create an iteration monitor which will keep track of iterative convergence
var monitor = new Iterator(new IIterationStopCriterium<double>[]
{
new IterationCountStopCriterium(MaximumIterations),
new ResidualStopCriterium(ConvergenceBoundary),
new DivergenceStopCriterium(),
new FailureStopCriterium()
});
var solver = new GpBiCg(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 CanSolveForRandomVector([Values(4, 8, 10)] 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 GpBiCg(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 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<Complex32>(
new IterationCountStopCriterium<Complex32>(MaximumIterations),
new ResidualStopCriterium(ConvergenceBoundary),
new DivergenceStopCriterium(),
new FailureStopCriterium());
var solver = new GpBiCg();
// 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 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<Complex>(1e-10));
var solver = new GpBiCg();
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 SolveLongMatrix()
{
var matrix = new SparseMatrix(3, 2);
Vector<double> input = new DenseVector(3);
var solver = new GpBiCg();
solver.Solve(matrix, input);
}
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 GpBiCg();
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 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
Vector y = new DenseVector(matrix.RowCount, 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 GpBiCg(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 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 GpBiCg(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");
}