public static void LU_Decompose(Matrix A, Matrix L, Matrix U)
{
A.Copy(U);
Vector F = new Vector(A.N);
Gaussian_Methods.Direct_Way(U, F);
for (int i = 1; i < A.M; i++)
{
for (int j = 0; j < i; j++)
{
double sum = 0;
for (int k = 1; k <= j - 1; k++)
{
sum += L.Elem[i][k] * U.Elem[k][j];
}
L.Elem[i][j] = (A.Elem[i][j] - sum) / U.Elem[j][j];
}
}
for (int i = 0; i < A.M; i++)
{
L.Elem[i][i] = 1;
}
}
public static double MeasureTime(Matrix A, Vector F, int mode)
{
Stopwatch sw = new Stopwatch();
Vector X;
sw.Start();
if (mode == -2)
{
X = Gaussian_Methods.Start_Solver(A, F);
}
else if (mode == -1)
{
X = LU_Methods.Start_Solver(A, F);
}
else
{
X = QR_Methods.Start_Solver(A, F, mode);
}
sw.Stop();
return(sw.Elapsed.TotalSeconds);
}
static void Main(string[] args)
{
int N = 3;
var A = new Matrix(N, N);
var F = new Vector(N);
string[] names = new string[] { "Gauss", "LU", "QR Gramm", "QR GrammMod", "QR Givens", "QR Householder" };
Vector X_GAUSS;
Vector X_LU;
Vector X_QR_Gramm;
Vector X_QR_GrammMod;
Vector X_QR_Givens;
Vector X_QR_Householder;
var Elem = new double[][]
{
new double[] { -2, -2, -1 },
new double[] { 1, 0, -2 },
new double[] { 0, 1, 2 }
};
A.Elem = Elem;
var ElemV = new double[] { -5, -1, 3 };
F.Elem = ElemV;
X_GAUSS = Gaussian_Methods.Start_Solver(A, F);
X_LU = LU_Methods.Start_Solver(A, F);
X_QR_Gramm = QR_Methods.Start_Solver(A, F, MODE.QR_GRAMM);
X_QR_GrammMod = QR_Methods.Start_Solver(A, F, MODE.QR_GRAMM_MOD);
X_QR_Givens = QR_Methods.Start_Solver(A, F, MODE.QR_GIVENS);
X_QR_Householder = QR_Methods.Start_Solver(A, F, MODE.QR_HOUSEHOLDER);
Console.WriteLine("==================SOLVE=================");
Console.WriteLine(names[0] + "\t\t" + X_GAUSS.ToString());
Console.WriteLine(names[1] + "\t\t" + X_LU.ToString());
Console.WriteLine(names[2] + "\t" + X_QR_Gramm.ToString());
Console.WriteLine(names[3] + "\t" + X_QR_GrammMod.ToString());
Console.WriteLine(names[4] + "\t" + X_QR_Givens.ToString());
Console.WriteLine(names[5] + "\t" + X_QR_Householder.ToString());
Console.WriteLine("==================TIME==================");
var rand = new Random();
for (int c = 100; c <= 500; c += 100)
{
Matrix At = new Matrix(c, c);
Vector Vt = new Vector(c);
At.SetI();
Vt.SetI();
for (int i = 0; i < c; i++)
{
for (int I = 0; I < c; I++)
{
double rt = rand.NextDouble() * 100;
Vt.Elem[I] += Vt.Elem[i] * rt;
At.Elem[I][i] += At.Elem[i][i] * rt;
}
}
Console.WriteLine(c + "x" + c);
for (int mode = MODE.QR_GRAMM - 2; mode <= MODE.QR_HOUSEHOLDER; mode++)
{
double t = 0;
for (int time = 0; time < 10; time++)
{
t += MeasureTime(At, Vt, mode);
}
Console.WriteLine(names[mode + 2] + "\t" + (t / 10));
}
}
Console.ReadKey();
}