public void SecondEquationTest()
{
Matrix variableCoefficients = new Matrix(new float[, ]
{
{ 2, -1, -1 },
{ 1, 3, -2 },
{ 1, 2, 3 }
});
Matrix freeCoefficients = new Matrix(new float[, ]
{
{ 5 },
{ 7 },
{ 10 }
});
Matrix expectedResult = new Matrix(new float[, ]
{
{ 61f / 16f },
{ 27f / 16f },
{ 15f / 16f }
});
float epsilon = 0.0001f;
float relaxationWeight = 0.8f;
Matrix result = RelaxationMethod.Solve(variableCoefficients, freeCoefficients, epsilon, relaxationWeight);
Assert.True(expectedResult.NearEquals(result), "Matrices are not equal:\nExpected:{0}\nResult:{1}",
expectedResult.ToString(), result.ToString());
}
public void ThirdEquationTest()
{
Matrix variableCoefficients = new Matrix(new float[, ]
{
{ 8, 5, 3 },
{ -2, 8, 1 },
{ 1, 3, -10 }
});
Matrix freeCoefficients = new Matrix(new float[, ]
{
{ 30 },
{ 15 },
{ 42 }
});
Matrix expectedResult = new Matrix(new float[, ]
{
{ 3f },
{ 3f },
{ -3f }
});
float epsilon = 0.0001f;
float relaxationWeight = 0.8f;
Matrix result = RelaxationMethod.Solve(variableCoefficients, freeCoefficients, epsilon, relaxationWeight);
Assert.True(expectedResult.NearEquals(result), "Matrices are not equal:\nExpected:{0}\nResult:{1}",
expectedResult.ToString(), result.ToString());
}
public void FirstEquationTest()
{
Matrix variableCoefficients = new Matrix(new float[, ]
{
{ 1, -2, 1 },
{ 2, -5, -1 },
{ -7, 0, 1 }
});
Matrix freeCoefficients = new Matrix(new float[, ]
{
{ 2 },
{ -1 },
{ -2 }
});
float epsilon = 0.0001f;
float relaxationWeight = 0.8f;
Matrix expectedResult = new Matrix(new float[, ] {
{ 13f / 25f },
{ 2f / 25f },
{ 41f / 25f }
});
Matrix result = RelaxationMethod.Solve(variableCoefficients, freeCoefficients, epsilon, relaxationWeight);
Assert.True(expectedResult.NearEquals(result), "Matrices are not equal:\nExpected:{0}\nResult:{1}",
expectedResult.ToString(), result.ToString());
}
static void Test(int iterations, Matrix variableCoefficients, Matrix freeCoefficients)
{
float epsilon = 0.0001f;
float relaxationWeight = 0.8f;
var stopwatch = new Stopwatch();
Console.Write("######################################################\nSelect the algorithm:\n1.Gauss\n2.Jacobi\n3.Gauss-Seidel\n4.Relaxation\nEnter the choice:");
int algorithm = Convert.ToInt32(Console.ReadLine());
switch (algorithm)
{
case 1:
{
stopwatch.Start();
for (int i = 0; i < iterations; i++)
{
var result = GaussMethod.Solve(Matrix.Clone(variableCoefficients), Matrix.Clone(freeCoefficients));
}
stopwatch.Stop();
Console.WriteLine("Total elapsed time: " + stopwatch.Elapsed + "\n######################################################");
break;
}
case 2:
{
stopwatch.Start();
for (int i = 0; i < iterations; i++)
{
var result = JacobiMethod.Solve(Matrix.Clone(variableCoefficients), Matrix.Clone(freeCoefficients), epsilon);
}
stopwatch.Stop();
Console.WriteLine("Total elapsed time: " + stopwatch.Elapsed);
break;
}
case 3:
{
stopwatch.Start();
for (int i = 0; i < iterations; i++)
{
var result = GaussZeidelMethod.Solve(Matrix.Clone(variableCoefficients), Matrix.Clone(freeCoefficients), epsilon);
}
stopwatch.Stop();
Console.WriteLine("Total elapsed time: " + stopwatch.Elapsed);
break;
}
case 4:
{
stopwatch.Start();
for (int i = 0; i < iterations; i++)
{
var result = RelaxationMethod.Solve(Matrix.Clone(variableCoefficients), Matrix.Clone(freeCoefficients), epsilon, relaxationWeight);
}
stopwatch.Stop();
Console.WriteLine("Total elapsed time: " + stopwatch.Elapsed);
break;
}
}
}
/// <summary>
/// Perform the approximation using the x and y values from matrices
/// </summary>
/// <param name="xValues">X values of the points provided - horizontal vector</param>
/// <param name="yValues">Y values of the points provided - vertical vector</param>
/// <returns>Matrix with A values for each X variable</returns>
public static Matrix Approximate(Matrix xValues, Matrix yValues, int k)
{
if (xValues.Height != 1 || yValues.Width != 1)
{
throw new Exception("Incorrect input");
}
if (k < 1)
{
return(new Matrix(0, 0));
}
if (k < yValues.Height - 1)
{
xValues = new Matrix(xValues[0].Take(k + 1).ToArray());
yValues = yValues.RowSlice(0, k);
}
Matrix xMatrix = new Matrix(yValues.Height, xValues.Width);
Matrix yMatrix = new Matrix(yValues.Height, 1);
// Raise bets
for (int y = 0; y < yValues.Height; y++)
{
for (int x = 0; x < xValues.Width; x++)
{
float xSum = 0;
for (int i = 0; i < xValues.Width; i++)
{
xSum += (float)Math.Pow(xValues[0, i], y + x);
}
xMatrix[y, x] = xSum;
}
float ySum = 0;
for (int i = 0; i < yValues.Height; i++)
{
ySum += (float)Math.Pow(xValues[0, i], y) * yValues[i, 0];
}
yMatrix[y, 0] = ySum;
}
// Solving
Matrix aMatrix = RelaxationMethod.Solve(xMatrix, yMatrix, 0.00001f, 0.8f);
// GaussZeidelMethod.Solve(xMatrix, yMatrix, 0.00001f);
/*
* Matrix aMatrix = new Matrix(new float[,] {
* { 21.655175185f },
* { -69.1485164816f },
* { 30.3403573138f },
* { 22.8318150818f },
* { -11.6418820939f },
* { -1.52035040089f },
* { 0.85228321723f }
* });
*/
return(aMatrix);
}