public void When_SingletonPivoting_Expect_NoException()
{
// Build the solver with only the singleton pivoting
var solver = new SparseRealSolver();
solver.Parameters.Strategies.Clear();
solver.Parameters.Strategies.Add(new MarkowitzSingleton <double>());
// Build the matrix that should be solvable using only the singleton pivoting strategy
double[][] matrix =
{
new double[] { 0, 0, 1, 0 },
new double[] { 1, 1, 1, 1 },
new double[] { 0, 0, 0, 1 },
new double[] { 1, 0, 0, 0 }
};
double[] rhs = { 0, 1, 0, 0 };
for (var r = 0; r < matrix.Length; r++)
{
for (var c = 0; c < matrix[r].Length; c++)
{
if (!matrix[r][c].Equals(0.0))
{
solver.GetElement(new MatrixLocation(r + 1, c + 1)).Value = matrix[r][c];
}
}
if (!rhs[r].Equals(0.0))
{
solver.GetElement(r + 1).Value = rhs[r];
}
}
// This should run without throwing an exception
Assert.AreEqual(solver.Size, solver.OrderAndFactor());
}
public void When_PartialDecomposition_Expect_Reference()
{
var solver = new SparseRealSolver
{
PivotSearchReduction = 2, // Limit to only the 2 first elements
Degeneracy = 2 // Only perform elimination on the first two rows
};
solver[1, 2] = 2;
solver[2, 1] = 1;
solver[1, 3] = 4;
solver[4, 2] = 4;
solver[3, 3] = 2;
solver[3, 4] = 4;
solver[4, 4] = 1;
Assert.AreEqual(2, solver.OrderAndFactor());
// We are testing two things here:
// - First, the solver should not have chosen a pivot in the lower-right submatrix
// - Second, the submatrix should be equal to A_cc - A_c1 * A^-1 * A_1c with A the top-left
// matrix, A_cc the bottom-right submatrix, A_1c and A_c1 the off-diagonal matrices
Assert.AreEqual(2.0, solver[3, 3], 1e-12);
Assert.AreEqual(4.0, solver[3, 4], 1e-12);
Assert.AreEqual(-8.0, solver[4, 3], 1e-12);
Assert.AreEqual(1.0, solver[4, 4], 1e-12);
}
public void When_OrderAndFactoring2_Expect_Reference()
{
var solver = new SparseRealSolver();
solver.GetElement(new MatrixLocation(1, 1)).Value = 1.0;
solver.GetElement(new MatrixLocation(2, 1)).Value = 0.0;
solver.GetElement(new MatrixLocation(2, 2)).Value = 1.0;
solver.GetElement(new MatrixLocation(2, 5)).Value = 0.0;
solver.GetElement(new MatrixLocation(3, 3)).Value = 1.0;
solver.GetElement(new MatrixLocation(3, 4)).Value = 1e-4;
solver.GetElement(new MatrixLocation(3, 5)).Value = -1e-4;
solver.GetElement(new MatrixLocation(4, 4)).Value = 1.0;
solver.GetElement(new MatrixLocation(5, 1)).Value = 5.38e-23;
solver.GetElement(new MatrixLocation(5, 4)).Value = -1e-4;
solver.GetElement(new MatrixLocation(5, 5)).Value = 1e-4;
Assert.AreEqual(5, solver.OrderAndFactor());
AssertInternal(solver, 1, 1, 1.0);
AssertInternal(solver, 2, 1, 0.0);
AssertInternal(solver, 2, 2, 1.0);
AssertInternal(solver, 2, 5, 0.0);
AssertInternal(solver, 3, 3, 1.0);
AssertInternal(solver, 3, 4, 1e-4);
AssertInternal(solver, 3, 5, -1e-4);
AssertInternal(solver, 4, 4, 1.0);
AssertInternal(solver, 5, 1, 5.38e-23);
AssertInternal(solver, 5, 4, -1e-4);
AssertInternal(solver, 5, 5, 10000);
}
public void When_OrderAndFactoring_Expect_Reference()
{
var solver = new SparseRealSolver();
solver.GetElement(new MatrixLocation(1, 1)).Value = 0.0001;
solver.GetElement(new MatrixLocation(1, 4)).Value = -0.0001;
solver.GetElement(new MatrixLocation(1, 5)).Value = 0.0;
solver.GetElement(new MatrixLocation(2, 1)).Value = 0.0;
solver.GetElement(new MatrixLocation(2, 2)).Value = 1.0;
solver.GetElement(new MatrixLocation(2, 5)).Value = 0.0;
solver.GetElement(new MatrixLocation(3, 1)).Value = -0.0001;
solver.GetElement(new MatrixLocation(3, 3)).Value = 1.0;
solver.GetElement(new MatrixLocation(3, 4)).Value = 0.0001;
solver.GetElement(new MatrixLocation(4, 4)).Value = 1.0;
solver.GetElement(new MatrixLocation(5, 5)).Value = 1.0;
// Order and factor
Assert.AreEqual(5, solver.OrderAndFactor());
// Compare
Assert.AreEqual(solver.GetElement(new MatrixLocation(1, 1)).Value, 1.0e4);
Assert.AreEqual(solver.GetElement(new MatrixLocation(1, 4)).Value, -0.0001);
Assert.AreEqual(solver.GetElement(new MatrixLocation(1, 5)).Value, 0.0);
Assert.AreEqual(solver.GetElement(new MatrixLocation(2, 1)).Value, 0.0);
Assert.AreEqual(solver.GetElement(new MatrixLocation(2, 2)).Value, 1.0);
Assert.AreEqual(solver.GetElement(new MatrixLocation(2, 5)).Value, 0.0);
Assert.AreEqual(solver.GetElement(new MatrixLocation(3, 1)).Value, -0.0001);
Assert.AreEqual(solver.GetElement(new MatrixLocation(3, 3)).Value, 1.0);
Assert.AreEqual(solver.GetElement(new MatrixLocation(3, 4)).Value, 0.0001);
Assert.AreEqual(solver.GetElement(new MatrixLocation(4, 4)).Value, 1.0);
Assert.AreEqual(solver.GetElement(new MatrixLocation(5, 5)).Value, 1.0);
}
public void When_BigMatrix_Expect_NoException()
{
// Test factoring a big matrix
var solver = new SparseRealSolver();
ReadMatrix(solver, Path.Combine(TestContext.CurrentContext.TestDirectory, Path.Combine("Algebra", "Matrices", "fidapm05")));
// Order and factor this larger matrix
Assert.AreEqual(solver.Size, solver.OrderAndFactor());
}
public void When_EntireMatrixPivoting_Expect_NoException()
{
// Build the solver with only the quick diagonal pivoting
var solver = new SparseRealSolver();
var strategy = solver.Parameters;
strategy.Strategies.Clear();
strategy.Strategies.Add(new MarkowitzEntireMatrix <double>());
// Build the matrix that should be solvable using only the singleton pivoting strategy
double[][] matrix =
{
new[] { 1, 0.5, 0, 2 },
new double[] { 2, 5, 4, 3 },
new double[] { 0, 3, 2, 0 },
new[] { 4, 1.8, -0.01, 8 }
};
double[] rhs = { 1, 2, 3, 4 };
for (var r = 0; r < matrix.Length; r++)
{
for (var c = 0; c < matrix[r].Length; c++)
{
if (!matrix[r][c].Equals(0.0))
{
solver.GetElement(new MatrixLocation(r + 1, c + 1)).Value = matrix[r][c];
}
}
if (!rhs[r].Equals(0.0))
{
solver.GetElement(r + 1).Value = rhs[r];
}
}
// This should run without throwing an exception
Assert.AreEqual(solver.Size, solver.OrderAndFactor());
}
