static public Vector Modified_withReverse(ScalarFunk1_N[][] matrixFunks, ScalarFunk1_N[] vectorFunks, double Eps = 10e-5)
{
Console.Write("Begin vector: ");
var vectorX_next = new Vector(vectorFunks.Length);
vectorX_next.SetValues(new double[] { 0.5, 0.5, 1.5, -1.0, -0.5, 1.5, 0.5, -0.5, 1.5, -1.5 });
vectorX_next.Show();
Console.WriteLine("Fill matrix: ");
var matrixJ = new Matrix(matrixFunks.Length);
matrixJ.SetValueByFunks(matrixFunks, vectorX_next.data);
matrixJ.Show();
Console.WriteLine("Reverse matrix with LU: ");
var matrixJ_L = new Matrix(matrixJ.N);
var matrixJ_U = new Matrix(matrixJ.N);
var matrixJ_P = new Matrix(matrixJ.N);
LUP_decomposition.LUP(matrixJ, matrixJ_L, matrixJ_U, matrixJ_P);
var matrixJ_reverse = LUP_decomposition.Reverse(matrixJ_L, matrixJ_U, matrixJ_P);
matrixJ_reverse.Show();
var vectorF = new Vector(vectorFunks.Length);
var vectorX_current = new Vector(vectorFunks.Length);
var countIter = 0;
do
{
countIter++;
vectorX_current.Copy(vectorX_next);
vectorF.SetValueByFunks(vectorFunks, vectorX_current.data);
vectorX_next = vectorX_current - matrixJ_reverse * vectorF;
Console.Write("Next vector: ");
vectorX_next.Show();
} while ((vectorX_next - vectorX_current).Norm() >= Eps);
Console.Write("Count iter: " + countIter.ToString() + '\n');
return(vectorX_next);
}
static void Task_1()
{
using (StreamReader reader = new StreamReader("InputMatrixs.txt"))
{
var strLine = "";
while (!reader.EndOfStream)
{
Console.Write("______________________________________\n");
#region Считывание матрицы
strLine = reader.ReadLine();
if (strLine == "")
{
break;
}
var sizeMatrix = Int32.Parse(strLine);
var matrixA = new Matrix(sizeMatrix);
for (int i = 0; i < sizeMatrix; i++)
{
strLine = reader.ReadLine();
var values = strLine.Split(' ');
for (int j = 0; j < sizeMatrix; j++)
{
matrixA.data[i][j] = Int32.Parse(values[j]);
}
}
#endregion
#region LU разложение
var matrixL = new Matrix(sizeMatrix);
var matrixU = new Matrix(sizeMatrix);
var matrixP = new Matrix(sizeMatrix);
LUP_decomposition.LUP(matrixA, matrixL, matrixU, matrixP);
Console.Write('\n');
Console.Write("Matrix L\n");
matrixL.Show();
Console.Write('\n');
Console.Write("Matrix U\n");
matrixU.Show();
Console.Write('\n');
Console.Write("Matrix P\n");
matrixP.Show();
Console.Write('\n');
var checkMatrixLeft = matrixL * matrixU;
Console.Write("Matrix L * U\n");
checkMatrixLeft.Show();
Console.Write('\n');
var checkMatrixRigth = matrixP * matrixA;
Console.Write("Matrix P * A\n");
checkMatrixRigth.Show();
#endregion
#region Определитель
Console.Write('\n');
var detA = LUP_decomposition.Det(matrixL, matrixU, matrixP);
Console.Write("Det A with LU: " + detA.ToString() + '\n');
#endregion
#region Обратная матрица
Console.Write('\n');
var A_reverse = LUP_decomposition.Reverse(matrixL, matrixU, matrixP);
Console.Write("A_reverse with LU:\n");
A_reverse.Show();
Console.Write('\n');
var CheckReverse_1 = matrixA * A_reverse;
Console.Write("Check Reverse (A * A_reverse):\n");
CheckReverse_1.Show();
Console.Write('\n');
var CheckReverse_2 = A_reverse * matrixA;
Console.Write("Check Reverse (A_reverse * A):\n");
CheckReverse_2.Show();
#endregion
#region СЛАУ
Console.Write('\n');
Console.Write("SLAU with LU:\n");
Random rnd = new Random();
Vector b = new Vector(matrixA.N);
Console.Write("Generate vector b: ");
for (int i = 0; i < b.data.Length; i++)
{
b.data[i] = rnd.Next() % 100;
Console.Write(b.data[i].ToString("0.00") + ' ');
}
Console.Write("\nResult x: ");
var x = LUP_decomposition.SLAU(matrixL, matrixU, matrixP, b);
for (int i = 0; i < x.data.Length; i++)
{
Console.Write(x.data[i].ToString("0.00") + ' ');
}
Console.Write('\n');
#endregion
#region Число обусловленности
Console.Write('\n');
Console.Write("Condition number: ");
var condNumber = matrixA.Norm() * LUP_decomposition.Reverse(matrixL, matrixU, matrixP).Norm();
Console.Write(condNumber.ToString("0.00") + '\n');
#endregion
}
}
}