public static double Det(double[][] L, double[][] U, int n)
{
double detL = MatrixUtils.DeterminantSqM(L, n);
double detU = MatrixUtils.DeterminantSqM(U, n);
double detLU = detL * detU;
return(detLU);
}
static void Main(string[] args)
{
Random rnd = new Random();
const int n = 10;
// Conditions.
double[][] A = new double[n][];
A[0] = new double[] { 208, 90, -46, 5, -79, -116, -41, 45, -67, 94 };
A[1] = new double[] { 90, 185, -40, 120, -1, 27, 18, 48, -31, 38 };
A[2] = new double[] { -46, -40, 235, 15, 22, -47, -92, -46, -2, -149 };
A[3] = new double[] { 5, 120, 15, 190, 13, 111, 39, 21, -32, -37 };
A[4] = new double[] { -79, -1, 22, 13, 176, 62, 24, -36, 128, 43 };
A[5] = new double[] { -116, 27, -47, 111, 62, 186, 94, 4, 21, -16 };
A[6] = new double[] { -41, 18, -92, 39, 24, 94, 194, 154, 123, 110 };
A[7] = new double[] { 45, 48, -46, 21, -36, 4, 154, 249, 130, 127 };
A[8] = new double[] { -67, -31, -2, -32, 128, 21, 123, 130, 233, 117 };
A[9] = new double[] { 94, 38, -149, -37, 43, -16, 110, 127, 117, 246 };
double[] B = new double[] { -234, 55, 140, -163, -88, -40, -197, -99, 30, 250 };
// Buffers.
double[][] Inv = new double[n][];
double[][] R = new double[n][];
double[][] L = new double[n][];
double[][] Lt = new double[n][];
double[] X = new double[n];
for (int i = 0; i < n; i++)
{
Inv[i] = new double[n];
R[i] = new double[n];
L[i] = new double[n];
Lt[i] = new double[n];
X[i] = 0;
for (int j = 0; j < n; j++)
{
Inv[i][j] = 0;
R[i][j] = 0;
L[i][j] = 0;
Lt[i][j] = 0;
}
}
Console.WriteLine("A matrix: ");
MatrixUtils.ShowSqM(A, n);
Stopwatch stopWatch = new Stopwatch();
stopWatch.Start();
Console.WriteLine("Solving A using Choletsky.\n");
Choletsky.CholetskyL(A, L, n);
stopWatch.Stop();
Console.WriteLine("Resulting L matrix:");
MatrixUtils.ShowSqM(L, n);
Console.WriteLine("transposed l matrix");
MatrixUtils.CopySqM(Lt, L, n);
MatrixUtils.TransposeSqM(Lt, n);
MatrixUtils.ShowSqM(Lt, n);
Console.WriteLine("Check for Choletsky L matrix: A=L*L^t");
MatrixUtils.MultiplySqM(L, Lt, R, n);
MatrixUtils.ShowSqM(R, n);
Console.WriteLine("Get the roots using Choletsky method.");
Choletsky.Solve(L, Lt, B, X, n);
Console.WriteLine("Roots are:");
MatrixUtils.ShowVector(X, n);
double det = Choletsky.Det(L, n);
Console.WriteLine("Determinant is: {0}\n", det);
Stopwatch stopWatch2 = new Stopwatch();
stopWatch2.Start();
Console.WriteLine("Inverting using Choletsky method.");
Choletsky.Inv(L, Lt, Inv, n);
stopWatch2.Stop();
Console.WriteLine("Inverted matrix:");
MatrixUtils.ShowSqM(Inv, n);
Console.WriteLine("Check for the inverted matrix:");
MatrixUtils.MultiplySqM(A, Inv, R, n);
MatrixUtils.ShowSqM(R, n);
Console.WriteLine("Aglorithm time: {0}", stopWatch.Elapsed);
Console.WriteLine("Inverting matrix time: {0}", stopWatch2.Elapsed);
Console.ReadKey();
}
public static void GaussElimination(double[][] A, double[] X, int n)
{
int swappingFlag = 0;
// Pivoting.
for (int i = 0; i < n; i++)
{
for (int k = i + 1; k < n; k++)
{
if (Math.Abs(A[i][i]) < Math.Abs(A[k][i]))
{
swappingFlag++;
for (int j = 0; j <= n; j++)
{
double temp = A[i][j];
A[i][j] = A[k][j];
A[k][j] = temp;
}
}
}
}
Console.WriteLine("Matrix after pivoting:");
MatrixUtils.ShowM(A, n, n + 1);
// Elimination.
for (int i = 0; i < n - 1; i++)
{
for (int k = i + 1; k < n; k++)
{
double t = A[k][i] / A[i][i];
for (int j = 0; j <= n; j++)
{
//make the elements below the pivot elements equal to zero or elimnate the variables.
A[k][j] = A[k][j] - t * A[i][j];
}
}
}
Console.WriteLine("Matrix after elimination:");
MatrixUtils.ShowM(A, n, n + 1);
// Check if some of the arguments on the main diagonal equals to 0.
for (int i = 0; i < n; i++)
{
if (A[i][i] == 0)
{
Console.WriteLine("Noticed FREE argument with index {0}, starting from 0", i);
}
}
// Check if at least one B[i] after elimination does not equal to 0.
bool matrixHasSolution = false;
for (int i = 0; i < n; i++)
{
if (A[i][n] != 0)
{
matrixHasSolution = true;
}
}
if (!matrixHasSolution)
{
Console.WriteLine("Matrix A does not have solutions.");
Console.WriteLine("Reason: after elimination there are no B[i], which does not equal to 0");
throw new ArgumentException();
}
// Check if there are MORE AMOUNT OF VARIABLES THAN EQUATIONS.
for (int i = 0; i < n; i++)
{ /* TODO */
}
// Back-substitution.
for (int i = n - 1; i >= 0; i--)
{
X[i] = A[i][n];
for (int j = n - 1; j > i; j--)
{
X[i] -= A[i][j] * X[j];
}
X[i] = X[i] / A[i][i];
}
// Determinant of a matrix.
double det = 1;
for (int i = 0; i < n; i++)
{
det *= A[i][i];
}
det = (swappingFlag % 2 == 0) ? det : -det;
Console.WriteLine("Determinant is: {0}\n", det);
}
public static void Inv(double[][] A, int n)
{
// Init n*2 matrix to invert.
double[][] Inv = new double[n][];
for (int i = 0; i < n; i++)
{
Inv[i] = new double[n * 2];
for (int j = 0; j < n * 2; j++)
{
Inv[i][j] = 0;
}
}
// LEFT SIDE: Fill up Inv matrix with values from A.
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
Inv[i][j] = A[i][j];
}
}
// RIGHT SIDE: Full up with ones on the main diagonal.
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n * 2; j++)
{
if (j == (i + n))
{
Inv[i][j] = 1;
}
}
}
Console.WriteLine("Inverting, using such matrix:");
MatrixUtils.ShowM(Inv, n, n * 2);
// Pivoting.
for (int i = n - 1; i >= 1; i--)
{
// if (Inv[i - 1][0] < Inv[i][0])
if (Math.Abs(Inv[i - 1][0]) < Math.Abs(Inv[i][0]))
{
for (int j = 0; j < n * 2; j++)
{
double d = Inv[i][j];
Inv[i][j] = Inv[i - 1][j];
Inv[i - 1][j] = d;
}
}
}
Console.WriteLine("Matrix after pivoting:");
MatrixUtils.ShowM(Inv, n, n * 2);
// Reducing.
for (int j = 0; j < n; j++)
{
for (int i = 0; i < n; i++)
{
if (i != j)
{
double d = Inv[i][j];
for (int k = 0; k < 2 * n; k++)
{
Inv[i][k] -= (Inv[j][k] / Inv[j][j]) * d;
}
}
else
{
double d = Inv[i][j];
for (int k = 0; k < 2 * n; k++)
{
Inv[i][k] /= d;
}
}
}
}
Console.WriteLine("Matrix after reducing:");
MatrixUtils.ShowM(Inv, n, n * 2);
Console.WriteLine("The inversed matrix is on the right side.");
}
public static void Solve(double[][] A, double[] B, double[] X, int n)
{
double[] Tau = new double[n];
double[] Delta = new double[n];
double[] Lmbd = new double[n];
for (int i = 0; i < n; i++)
{
Tau[i] = 0;
Delta[i] = 0;
Lmbd[i] = 0;
}
Console.WriteLine("Solving A matrix using triagonal algorithm.");
MatrixUtils.ShowSqM(A, n);
// The algorithm.
// Note, that in ditriagonal method there are specific first and last iterations.
// First iteration.
Tau[0] = A[0][0];
Delta[0] = (-1) * A[0][1] / Tau[0];
Lmbd[0] = B[0] / Tau[0];
// Other iterations.
for (int i = 1; i < n - 1; i++)
{
Tau[i] = A[i][i] + A[i][i - 1] * Delta[i - 1];
Delta[i] = (-1) * A[i][i + 1] / Tau[i];
Lmbd[i] = (B[i] - A[i][i - 1] * Lmbd[i - 1]) / Tau[i];
}
// Last iteration.
Tau[n - 1] = A[n - 1][n - 1] + A[n - 1][n - 2] * Delta[n - 2];
Delta[n - 1] = 0;
Lmbd[n - 1] = (B[n - 1] - A[n - 1][n - 2] * Lmbd[n - 2]) / Tau[n - 1];
// Check for the coef znamennik.
for (int i = 0; i < n; i++)
{
if (Tau[i] == 0)
{
Console.WriteLine("TDMA is incorrect, because one of the znamennik equals to 0");
}
}
Console.WriteLine("Coefficients:");
MatrixUtils.ShowVector(Tau, n);
Console.WriteLine("Alpha:");
MatrixUtils.ShowVector(Delta, n);
Console.WriteLine("Betha:");
MatrixUtils.ShowVector(Lmbd, n);
// Solving for X.
X[n - 1] = Lmbd[n - 1]; // last element.
for (int i = n - 2; i >= 0; i--) // others.
{
X[i] = Delta[i] * X[i + 1] + Lmbd[i];
}
double det = Det(Tau, n);
Console.WriteLine("Determinant for the A matrix is: {0}\n", det);
//// The algorithm.
//for (int i = 1; i < n; i++)
//{
// double m = Ad[i - 1] / Bd[i - 1];
// Bd[i] -= m * Cd[i - 1];
// B[i] -= m * B[i - 1];
//}
//// solve for the last x:
//X[n - 1] = B[n - 1] / Bd[n - 1];
//// remaining x, using back substitution:
//for (int i = n - 2; i >= 0; i--)
// X[i] = (B[i] - Cd[i] * X[i + 1]) / Bd[i];
}