public void VolumetricAndAngleCriteriaEqualityTest()
{
var matrix = new Matrix(2, 2);
matrix[0, 0] = 4;
matrix[0, 1] = 3;
matrix[1, 0] = 9;
matrix[1, 1] = 2;
conditionNumber = new ConditionNumber(matrix, null, null);
Assert.AreEqual(conditionNumber.CalculateVolumetricCriterion(), conditionNumber.CalculateAngleCriterion());
}
public void CriteriaBadMatrixTest()
{
var matrix = new Matrix(2, 2);
matrix[0, 0] = 1;
matrix[0, 1] = 0.99;
matrix[1, 0] = 0.99;
matrix[1, 1] = 0.98;
conditionNumber = new ConditionNumber(matrix, null, null);
Assert.IsTrue(conditionNumber.CalculateSpectralCriterion() > 10000);
Assert.IsTrue(conditionNumber.CalculateVolumetricCriterion() > 10000);
Assert.IsTrue(conditionNumber.CalculateAngleCriterion() > 10000);
}
public void VolumetricAndAngleCriteriaDiagonalMatrixTest()
{
var matrix = new Matrix(3, 3);
matrix[0, 0] = -400.6;
matrix[0, 1] = 0;
matrix[0, 2] = 0;
matrix[1, 0] = 0;
matrix[1, 1] = -600.4;
matrix[1, 2] = 0;
matrix[2, 0] = 0;
matrix[2, 1] = 0;
matrix[2, 2] = 200.2;
conditionNumber = new ConditionNumber(matrix, null, null);
Assert.AreEqual(1, conditionNumber.CalculateVolumetricCriterion());
Assert.AreEqual(1, conditionNumber.CalculateAngleCriterion());
}
public void CriteriaGilbertMatrixTest()
{
var matrix = new Matrix(6, 6);
for (var i = 0; i < 6; i++)
{
for (var j = 0; j < 6; j++)
{
matrix[i, j] = 1;
matrix[i, j] /= 1 + i + j;
}
}
conditionNumber = new ConditionNumber(matrix, null, null);
Assert.IsTrue(conditionNumber.CalculateSpectralCriterion() > 10000);
Assert.IsTrue(conditionNumber.CalculateVolumetricCriterion() > 10000);
Assert.IsTrue(conditionNumber.CalculateAngleCriterion() > 10000);
}
public void VariedMatrixAndVectorCalculationTest()
{
var equations = new List <(Matrix, Vector, Vector)>();
var matrix1 = new Matrix(2, 2);
matrix1[0, 0] = -400.6;
matrix1[0, 1] = 199.8;
matrix1[1, 0] = 1198.8;
matrix1[1, 1] = -600.4;
var vector1 = new Vector(new double[] { 200, -600 });
var exactSolution1 = new Vector(new double[] { -0.2, 0.6 });
equations.Add((matrix1, vector1, exactSolution1));
var matrix2 = new Matrix(2, 2);
matrix2[0, 0] = -200.4;
matrix2[0, 1] = -398.6;
matrix2[1, 0] = 1060.8;
matrix2[1, 1] = 400.2;
var vector2 = new Vector(new double[] { -40.74, 728.58 });
var exactSolution2 = new Vector(new double[] { 0.8, -0.3 });
equations.Add((matrix2, vector2, exactSolution2));
var matrix3 = new Matrix(2, 2);
matrix3[0, 0] = 58.4;
matrix3[0, 1] = -60;
matrix3[1, 0] = 14.2;
matrix3[1, 1] = 34.6;
var vector3 = new Vector(new double[] { 47.68, -17.92 });
var exactSolution3 = new Vector(new double[] { 0.2, -0.6 });
equations.Add((matrix3, vector3, exactSolution3));
foreach (var equation in equations)
{
var conditionNumber = new ConditionNumber(equation.Item1, equation.Item2, equation.Item3);
var variedSolution1 = conditionNumber.CalculateVariedSolution(0.01);
var variedSolution2 = conditionNumber.CalculateVariedSolution(0.2);
var variedSolution3 = conditionNumber.CalculateVariedSolution(3);
var variedMatrix1 = equation.Item1.Clone();
var variedMatrix2 = equation.Item1.Clone();
var variedMatrix3 = equation.Item1.Clone();
var variedVector1 = equation.Item2.Clone();
var variedVector2 = equation.Item2.Clone();
var variedVector3 = equation.Item2.Clone();
for (var i = 0; i < conditionNumber.size; i++)
{
for (var j = 0; j < conditionNumber.size; j++)
{
variedMatrix1[i, j] += 0.01;
variedMatrix2[i, j] += 0.2;
variedMatrix3[i, j] += 3;
}
variedVector1[i] += 0.01;
variedVector2[i] += 0.2;
variedVector3[i] += 3;
}
var actualVector1 = variedMatrix1 * variedSolution1;
var actualVector2 = variedMatrix2 * variedSolution2;
var actualVector3 = variedMatrix3 * variedSolution3;
Assert.IsTrue(conditionNumber.CalculateSpectralCriterion() < 10000);
Assert.IsTrue(conditionNumber.CalculateVolumetricCriterion() < 10000);
Assert.IsTrue(conditionNumber.CalculateAngleCriterion() < 10000);
for (var i = 0; i < conditionNumber.size; i++)
{
Assert.That(variedVector1[i], Is.EqualTo(actualVector1[i, 0]).Within(Math.Pow(10, -10)));
Assert.That(variedVector2[i], Is.EqualTo(actualVector2[i, 0]).Within(Math.Pow(10, -10)));
Assert.That(variedVector3[i], Is.EqualTo(actualVector3[i, 0]).Within(Math.Pow(10, -10)));
}
}
}
public MainViewModel()
{
Model = new PlotModel {
Title = "Chart"
};
Model.Axes.Add(new LinearColorAxis {
Position = AxisPosition.None, Minimum = 0.1, Maximum = 0.9, HighColor = OxyColors.Red, LowColor = OxyColors.Black
});
Model.Axes.Add(new LinearAxis {
Position = AxisPosition.Bottom, Title = "Condition number", FontSize = 14
});
Model.Axes.Add(new LinearAxis {
Position = AxisPosition.Left, Title = "Solutions difference", FontSize = 14
});
var series = new ScatterSeries[8];
series[0] = new ScatterSeries {
MarkerType = MarkerType.Circle
};
series[1] = new ScatterSeries {
MarkerType = MarkerType.Circle
};
series[2] = new ScatterSeries {
MarkerType = MarkerType.Circle
};
series[3] = new ScatterSeries {
MarkerType = MarkerType.Circle
};
series[4] = new ScatterSeries {
MarkerType = MarkerType.Circle
};
series[5] = new ScatterSeries {
MarkerType = MarkerType.Circle
};
series[6] = new ScatterSeries {
MarkerType = MarkerType.Circle
};
series[7] = new ScatterSeries {
MarkerType = MarkerType.Circle
};
var equations = new List <(Matrix, DotNumerics.LinearAlgebra.Vector, DotNumerics.LinearAlgebra.Vector)>();
var matrix1 = new Matrix(2, 2);
matrix1[0, 0] = -400.6;
matrix1[0, 1] = 199.8;
matrix1[1, 0] = 1198.8;
matrix1[1, 1] = -600.4;
var vector1 = new DotNumerics.LinearAlgebra.Vector(new double[] { 200, -600 });
var exactSolution1 = new DotNumerics.LinearAlgebra.Vector(new double[] { -0.2, 0.6 });
equations.Add((matrix1, vector1, exactSolution1));
var matrix2 = new Matrix(2, 2);
matrix2[0, 0] = -401.98;
matrix2[0, 1] = 200.34;
matrix2[1, 0] = 1202.04;
matrix2[1, 1] = -602.32;
var vector2 = new DotNumerics.LinearAlgebra.Vector(new double[] { 722.264, -2166.272 });
var exactSolution2 = new DotNumerics.LinearAlgebra.Vector(new double[] { -0.8, 2 });
equations.Add((matrix2, vector2, exactSolution2));
var matrix3 = new Matrix(2, 2);
matrix3[0, 0] = -400.94;
matrix3[0, 1] = 200.2;
matrix3[1, 0] = 1200.12;
matrix3[1, 1] = -600.96;
var vector3 = new DotNumerics.LinearAlgebra.Vector(new double[] { -160.268, 480.408 });
var exactSolution3 = new DotNumerics.LinearAlgebra.Vector(new double[] { 0.2, -0.4 });
equations.Add((matrix3, vector3, exactSolution3));
var matrix4 = new Matrix(2, 2);
matrix4[0, 0] = -41;
matrix4[0, 1] = 127;
matrix4[1, 0] = 113;
matrix4[1, 1] = -60;
var vector4 = new DotNumerics.LinearAlgebra.Vector(new double[] { -787, 1589 });
var exactSolution4 = new DotNumerics.LinearAlgebra.Vector(new double[] { 13, -2 });
equations.Add((matrix4, vector4, exactSolution4));
var matrix5 = new Matrix(2, 2);
matrix5[0, 0] = -402.9;
matrix5[0, 1] = 200.7;
matrix5[1, 0] = 1204.2;
matrix5[1, 1] = -603.6;
var vector5 = new DotNumerics.LinearAlgebra.Vector(new double[] { 201, -603 });
var exactSolution5 = new DotNumerics.LinearAlgebra.Vector(new double[] { -0.2, 0.6 });
equations.Add((matrix5, vector5, exactSolution5));
// bad condition matrix
var matrix6 = new Matrix(2, 2);
matrix6[0, 0] = 1;
matrix6[0, 1] = 0.99;
matrix6[1, 0] = 0.99;
matrix6[1, 1] = 0.98;
var vector6 = new DotNumerics.LinearAlgebra.Vector(new double[] { 2, 2 });
var exactSolution6 = new DotNumerics.LinearAlgebra.Vector(new double[] { 200, -200 });
equations.Add((matrix6, vector6, exactSolution6));
// Hilbert matrix
var matrix7 = new Matrix(7, 7);
for (var i = 0; i < 7; i++)
{
for (var j = 0; j < 7; j++)
{
matrix7[i, j] = 1;
matrix7[i, j] /= 1 + i + j;
}
}
var vector7 = new DotNumerics.LinearAlgebra.Vector(new double[] { 1, 1, 1, 1, 1, 1, 1 });
vector7[0] = vector7[0] * 5699 / 420;
vector7[1] = vector7[1] * 4103 / 420;
vector7[2] = vector7[2] * 19661 / 2520;
vector7[3] = vector7[3] * 157 / 24;
vector7[4] = vector7[4] * 156631 / 27720;
vector7[5] = vector7[5] * 34523 / 6930;
vector7[6] = vector7[6] * 146077 / 32760;
var exactSolution7 = new DotNumerics.LinearAlgebra.Vector(new double[] { 2, 9, 4, 7, 11, 9, 2 });
equations.Add((matrix7, vector7, exactSolution7));
for (var i = 0; i < 7; i++)
{
var conditionNumber = new ConditionNumber(equations[i].Item1, equations[i].Item2, equations[i].Item3);
var spectralCriterion = conditionNumber.CalculateSpectralCriterion();
var volumetricCriterion = conditionNumber.CalculateVolumetricCriterion();
var angleCriterion = conditionNumber.CalculateAngleCriterion();
var variedSolution1 = conditionNumber.CalculateVariedSolution(0.1);
var variedSolution2 = conditionNumber.CalculateVariedSolution(0.01);
var variedSolution3 = conditionNumber.CalculateVariedSolution(0.001);
var difference1 = equations[i].Item3 - variedSolution1;
var difference2 = equations[i].Item3 - variedSolution2;
var difference3 = equations[i].Item3 - variedSolution3;
double delta1 = 0;
double delta2 = 0;
double delta3 = 0;
for (var j = 0; j < equations[i].Item1.RowCount; j++)
{
delta1 += difference1[j] * difference1[j];
delta2 += difference2[j] * difference2[j];
delta3 += difference3[j] * difference3[j];
}
delta1 = Math.Sqrt(delta1);
delta2 = Math.Sqrt(delta2);
delta3 = Math.Sqrt(delta3);
// red dots
series[i].Points.Add(new ScatterPoint(spectralCriterion, delta1, 3, 1));
// green dots
series[i].Points.Add(new ScatterPoint(spectralCriterion, delta2, 3, 0.4));
// black dots
series[i].Points.Add(new ScatterPoint(spectralCriterion, delta3, 3, 0));
Model.Series.Add(series[i]);
}
}