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_PartialSolve_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, 1] = 1;
solver[1, 3] = 2;
solver[1, 4] = 3;
solver[1] = 1;
solver[2, 2] = 2;
solver[2, 3] = 4;
solver[2] = 2;
solver.Factor();
// We should now be able to solve for multiple solutions, where the last two elements
// will determine the result.
var solution = new DenseVector <double>(4);
solution[3] = 0;
solution[4] = 0;
solver.Solve(solution);
Assert.AreEqual(1.0, solution[1], 1e-12);
Assert.AreEqual(1.0, solution[2], 1e-12);
solution[3] = 1.0;
solution[4] = 2.0;
solver.Solve(solution);
Assert.AreEqual(-7.0, solution[1], 1e-12);
Assert.AreEqual(-1.0, solution[2], 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);
}
/// <summary>
/// Reads a file for vectors.
/// </summary>
/// <param name="solver">The solver.</param>
/// <param name="filename">The filename.</param>
protected static void ReadRhs(SparseRealSolver solver, string filename)
{
using var sr = new StreamReader(filename);
// The first line is a comment
sr.ReadLine();
// The second line tells us the dimensions
var line = sr.ReadLine() ?? throw new Exception("Invalid Mtx file");
var match = Regex.Match(line, @"^(?<rows>\d+)\s+(\d+)");
var size = int.Parse(match.Groups["rows"].Value);
// All subsequent lines are of the format [row] [column] [value]
while (!sr.EndOfStream)
{
// Read the next line
line = sr.ReadLine();
if (line == null)
{
break;
}
match = Regex.Match(line, @"^(?<row>\d+)\s+(?<value>.*)\s*$");
if (!match.Success)
{
throw new Exception("Could not recognize file");
}
var row = int.Parse(match.Groups["row"].Value);
var value = double.Parse(match.Groups["value"].Value, CultureInfo.InvariantCulture);
// Set the value in the matrix
solver.GetElement(row).Value = value;
}
}
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_Preorder_Expect_Reference()
{
var solver = new SparseRealSolver();
solver.GetElement(new MatrixLocation(1, 1)).Value = 1e-4;
solver.GetElement(new MatrixLocation(1, 2)).Value = 0.0;
solver.GetElement(new MatrixLocation(1, 3)).Value = -1e-4;
solver.GetElement(new MatrixLocation(2, 1)).Value = 0.0;
solver.GetElement(new MatrixLocation(2, 2)).Value = 0.0;
solver.GetElement(new MatrixLocation(2, 5)).Value = 1.0;
solver.GetElement(new MatrixLocation(3, 1)).Value = -1e-4;
solver.GetElement(new MatrixLocation(3, 3)).Value = 1e-4;
solver.GetElement(new MatrixLocation(3, 4)).Value = 1.0;
solver.GetElement(new MatrixLocation(4, 3)).Value = 1.0;
solver.GetElement(new MatrixLocation(5, 2)).Value = 1.0;
SpiceSharp.Simulations.ModifiedNodalAnalysisHelper <double> .Magnitude = Math.Abs;
solver.Precondition((matrix, vector) => SpiceSharp.Simulations.ModifiedNodalAnalysisHelper <double> .PreorderModifiedNodalAnalysis(matrix, matrix.Size));
AssertInternal(solver, 1, 1, 1e-4);
AssertInternal(solver, 1, 4, -1e-4);
AssertInternal(solver, 1, 5, 0.0);
AssertInternal(solver, 2, 1, 0.0);
AssertInternal(solver, 2, 2, 1.0);
AssertInternal(solver, 2, 5, 0.0);
AssertInternal(solver, 3, 1, -1e-4);
AssertInternal(solver, 3, 3, 1.0);
AssertInternal(solver, 3, 4, 1e-4);
AssertInternal(solver, 4, 4, 1.0);
AssertInternal(solver, 5, 5, 1.0);
}
/// <summary>
/// Creates solver used to solve equations.
/// </summary>
/// <returns>A solver that can be used to solve equations.</returns>
public ISparsePivotingSolver <double> CreateSolver()
{
var solver = new SparseRealSolver();
solver.Parameters.AbsolutePivotThreshold = AbsolutePivotThreshold;
solver.Parameters.RelativePivotThreshold = RelativePivotThreshold;
return(solver);
}
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());
}
/// <summary>
/// Reads a matrix file generated by Spice 3f5.
/// </summary>
/// <param name="matFilename">The matrix filename.</param>
/// <param name="vecFilename">The vector filename.</param>
/// <returns></returns>
protected static SparseRealSolver ReadSpice3f5File(string matFilename, string vecFilename)
{
var solver = new SparseRealSolver();
// Read the spice file
string line;
using (var reader = new StreamReader(matFilename))
{
// The file is organized using (row) (column) (value) (imag value)
while (!reader.EndOfStream && (line = reader.ReadLine()) != null)
{
if (line == "first")
{
continue;
}
// Try to read an element
var match = Regex.Match(line, @"^(?<row>\d+)\s+(?<col>\d+)\s+(?<value>[^\s]+)(\s+[^\s]+)?$");
if (match.Success)
{
int row = int.Parse(match.Groups["row"].Value);
int col = int.Parse(match.Groups["col"].Value);
var value = double.Parse(match.Groups["value"].Value, CultureInfo.InvariantCulture);
solver.GetElement(new MatrixLocation(row, col)).Value = value;
}
}
}
// Read the vector file
using (var reader = new StreamReader(vecFilename))
{
var index = 1;
while (!reader.EndOfStream && (line = reader.ReadLine()) != null)
{
var value = double.Parse(line, CultureInfo.InvariantCulture);
solver.GetElement(index).Value = value;
index++;
}
}
return(solver);
}
public void When_PartialDecompositionSingular_Expect_Reference()
{
var solver = new SparseRealSolver();
solver[1, 1] = 1;
solver[2, 2] = 1;
solver[2, 3] = 1;
solver[3, 1] = 1;
solver[3, 2] = 1;
solver[3, 3] = 1;
solver.Degeneracy = 1;
Assert.AreEqual(true, solver.Factor());
AssertInternal(solver, 1, 1, 1);
AssertInternal(solver, 2, 2, 1);
AssertInternal(solver, 2, 3, 1);
AssertInternal(solver, 3, 1, 1);
AssertInternal(solver, 3, 2, 1);
AssertInternal(solver, 3, 3, 0);
}
public void When_Factoring_Expect_Reference()
{
double[][] matrixElements =
{
new[] { 1.0, 1.0, 1.0 },
new[] { 2.0, 3.0, 5.0 },
new[] { 4.0, 6.0, 8.0 }
};
double[][] expected =
{
new[] { 1.0, 1.0, 1.0 },
new[] { 2.0, 1.0, 3.0 },
new[] { 4.0, 2.0, -0.5 }
};
// Create matrix
var solver = new SparseRealSolver();
for (var r = 0; r < matrixElements.Length; r++)
{
for (var c = 0; c < matrixElements[r].Length; c++)
{
solver.GetElement(new MatrixLocation(r + 1, c + 1)).Value = matrixElements[r][c];
}
}
// Factor
solver.Factor();
// Compare
for (var r = 0; r < matrixElements.Length; r++)
{
for (var c = 0; c < matrixElements[r].Length; c++)
{
Assert.AreEqual(expected[r][c], solver.GetElement(new MatrixLocation(r + 1, c + 1)).Value, 1e-12);
}
}
}
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());
}
