private matrix FindU(matrix Ak)
{
double maxEl = 0;
int iMax = 0;
int jMax = 0;
for (int i = 0; i < dim; ++i)
{
for (int j = i + 1; j < dim; ++j)
{
if (Abs(Ak[i, j]) > maxEl)
{
iMax = i;
jMax = j;
maxEl = Abs(Ak[i, j]);
}
}
}
double phi = CountPhi(Ak, iMax, jMax);
var U = matrix.IdentityMatrix(dim);
U[iMax, jMax] = -Sin(phi);
U[jMax, iMax] = Sin(phi);
U[jMax, jMax] = Cos(phi);
U[iMax, iMax] = Cos(phi);
return(U);
}
public List <double> GetAnswer()
{
var vectorBeta = new List <double>(vectorB);
var matrixAlpha = new matrix(matrix);
var matrixDInverse = matrix.IdentityMatrix(matrixAlpha.ColumnCount);
for (int i = 0; i < dim; i++)
{
vectorBeta[i] /= matrix[i, i];
matrixDInverse[i, i] = 1 / matrix[i, i];
}
matrixAlpha = matrix.IdentityMatrix(matrixAlpha.ColumnCount) - matrixDInverse * matrix;
List <double> vectorX;
var vectorXk = new List <double>(vectorBeta);
var count = 0;
do
{
count++;
vectorX = new List <double>(vectorXk);
vectorXk = vectorBeta.Sum(matrixAlpha.Multiply(vectorX));
} while (!IsFinished(vectorX, vectorXk, matrixAlpha));
Console.WriteLine("Number of Simple iterations {0}", count);
return(vectorXk);
}
public List <double> GetAnswer2()
{
var vectorBeta = new List <double>(vectorB);
var matrixAlpha = new matrix(matrix);
var matrixDInverse = Matrix.Matrix.IdentityMatrix(dim);
for (int i = 0; i < dim; i++)
{
vectorBeta[i] /= matrix[i, i];
matrixDInverse[i, i] = 1 / matrix[i, i];
}
matrixAlpha = Matrix.Matrix.IdentityMatrix(dim) - matrixDInverse * matrix;
var matrixB = matrixAlpha.ToLower();
var matrixC = matrixAlpha - matrixB;
var matrixEbInverse = (Matrix.Matrix.IdentityMatrix(dim) - matrixB).Inverse();
List <double> vectorX;
var vectorXk = new List <double>(vectorBeta);
var count = 0;
do
{
count++;
vectorX = new List <double>(vectorXk);
vectorXk = ((matrixEbInverse * matrixC).Multiply(vectorX)).Sum(matrixEbInverse.Multiply(vectorBeta));
} while (!IsFinished(vectorX, vectorXk, matrixAlpha, matrixC));
Console.WriteLine("Number of Siedel2 iterations {0} ", count);
return(vectorXk);
}
private bool IsFinished(matrix Ak)
{
double sum = 0;
for (int i = 0; i < dim; ++i)
{
for (int j = i + 1; j < dim; ++j)
{
sum += Pow(Ak[i, j], 2);
}
}
return(Pow(sum, 0.5) < MatrixConstants.Eps);
}
public matrix GetAnswer()
{
var U = matrix.IdentityMatrix(dim);
var Ak = new matrix(A);
var count = 0;
while (!IsFinished(Ak))
{
count++;
var Uk = FindU(Ak);
Ak = Uk.Transpose() * Ak * Uk;
U = U * Uk;
}
Console.WriteLine("NumberOfIterations: {0}\n Lambda Matrix:", count);
Ak.Print();
return(U);
}
public bool IsFinished(List <double> vectorXCurrent, List <double> vectorXPrevious, matrix matrixAlpha)
{
var vectorDiffRate = vectorXCurrent.Difference(vectorXPrevious).RateC();
var matrixAlphaRate = matrixAlpha.RateC();
return(Math.Abs(matrixAlphaRate - 1) < Epsilon
? vectorDiffRate <= MatrixConstants.Eps
: vectorDiffRate *matrixAlphaRate / (1 - matrixAlphaRate) <= MatrixConstants.Eps);
}
public SimpleIterationSolution(matrix matrix, List <double> vectorB)
{
this.vectorB = vectorB;
this.matrix = matrix;
dim = matrix.ColumnCount;
}
public SeidelSolution(matrix matrix, List <double> vectorB)
{
this.vectorB = vectorB;
this.matrix = matrix;
dim = matrix.ColumnCount;
}
private double CountPhi(matrix Ak, int iMax, int jMax)
{
return(Abs(Ak[iMax, iMax] - Ak[jMax, jMax]) < Double.Epsilon
? PI / 4
: 0.5 * Atan(2.0 * Ak[iMax, jMax] / (Ak[iMax, iMax] - Ak[jMax, jMax])));
}
public RotationMethod(matrix A)
{
this.A = A;
dim = A.ColumnCount;
}
