public void Start()
{
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] = 1;
matrix2[0, 1] = 0.99;
matrix2[1, 0] = 0.99;
matrix2[1, 1] = 0.98;
var vector2 = new Vector(new double[] { 2, 2 });
var exactSolution2 = new Vector(new double[] { 200, -200 });
equations.Add((matrix2, vector2, exactSolution2));
var matrix3 = new Matrix(7, 7);
for (var i = 0; i < 7; i++)
{
for (var j = 0; j < 7; j++)
{
matrix3[i, j] = 1;
matrix3[i, j] /= 1 + i + j;
}
}
var vector3 = new Vector(new double[] { 1, 1, 1, 1, 1, 1, 1 });
vector3[0] = vector3[0] * 5699 / 420;
vector3[1] = vector3[1] * 4103 / 420;
vector3[2] = vector3[2] * 19661 / 2520;
vector3[3] = vector3[3] * 157 / 24;
vector3[4] = vector3[4] * 156631 / 27720;
vector3[5] = vector3[5] * 34523 / 6930;
vector3[6] = vector3[6] * 146077 / 32760;
var exactSolution3 = new Vector(new double[] { 2, 9, 4, 7, 11, 9, 2 });
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 Vector(new double[] { -787, 1589 });
var exactSolution4 = new Vector(new double[] { 13, -2 });
equations.Add((matrix4, vector4, exactSolution4));
foreach (var equation in equations)
{
var conditionNumber = new ConditionNumber(equation.Item1, equation.Item2, equation.Item3);
Console.WriteLine("Left matrix is");
Console.WriteLine(equation.Item1.MatrixToString());
Console.WriteLine("Right matrix is");
for (var i = 0; i < equation.Item1.RowCount; i++)
{
Console.WriteLine(equation.Item2[i]);
}
Console.WriteLine();
Console.WriteLine("Exact solution is");
for (var i = 0; i < equation.Item1.RowCount; i++)
{
Console.WriteLine(equation.Item3[i]);
}
var spectralCriterion = conditionNumber.CalculateSpectralCriterion();
var volumetricCriterion = conditionNumber.CalculateVolumetricCriterion();
var angleCriterion = conditionNumber.CalculateAngleCriterion();
Console.WriteLine();
Console.WriteLine($"Spectral criterion is {spectralCriterion}.");
Console.WriteLine($"Volumetric criterion is {volumetricCriterion}.");
Console.WriteLine($"Angle criterion is {angleCriterion}.");
var variedSolution2 = conditionNumber.CalculateVariedSolution(0.01);
var variedSolution5 = conditionNumber.CalculateVariedSolution(0.00001);
var variedSolution8 = conditionNumber.CalculateVariedSolution(0.00000001);
var difference2 = equation.Item3 - variedSolution2;
var difference5 = equation.Item3 - variedSolution5;
var difference8 = equation.Item3 - variedSolution8;
double delta2 = 0;
double delta5 = 0;
double delta8 = 0;
for (var i = 0; i < conditionNumber.size; i++)
{
delta2 += difference2[i] * difference2[i];
delta5 += difference5[i] * difference5[i];
delta8 += difference8[i] * difference8[i];
}
delta2 = Math.Sqrt(delta2);
delta5 = Math.Sqrt(delta5);
delta8 = Math.Sqrt(delta8);
Console.WriteLine();
Console.WriteLine($"|x - x˜| is {delta2} when variation is 0.01.");
Console.WriteLine($"|x - x˜| is {delta5} when variation is 0.00001.");
Console.WriteLine($"|x - x˜| is {delta8} when variation is 0.00000001.");
Console.WriteLine();
Console.WriteLine();
}
}
public static void Main()
{
var conditionNumber = new ConditionNumber();
conditionNumber.Start();
}
