static void Main()
{
for (int n = 200; n < 1001; n += 100)
{
matrix A = rand_matrix(n);
vector v = rand_vector(n);
vector b = v.copy();
Stopwatch cd_time = new Stopwatch();
cd_time.Start();
var cd = new cholesky(A);
vector x_cd = cd.solve(v);
cd_time.Stop();
Stopwatch qr_time = new Stopwatch();
qr_time.Start();
var qr = new gs(A);
var x_qr = qr.solve(b);
qr_time.Stop();
///// matrix dimension n*n cd_runtime qr_runtime
WriteLine($"{n} \t {cd_time.ElapsedMilliseconds} \t {qr_time.ElapsedMilliseconds}");
}
} //Method: Main
static void Main()
{
//// Del A ////
int n = 3;
matrix A = rand_matrix(n);
var cd = new cholesky(A);
var L = cd.L;
var LT = cd.LT;
WriteLine("_____________________________________"); WriteLine();
WriteLine("Part A - decomposit A into L*LT");
(A).print("Matrix A="); WriteLine();
(L).print("Matrix L="); WriteLine();
(LT).print("Matrix LT="); WriteLine();
WriteLine("Check if L*LT=A");
matrix LLT = L * LT;
LLT.print("L*LT="); WriteLine();
if (A.approx(LLT))
{
WriteLine("L*LT=A\tTEST PASSED");
}
else
{
WriteLine("L*LT!=A\tTEST FAILED");
}
//// Del B ////
vector v = rand_vector(n);
vector b = v.copy();
vector x = cd.solve(v);
WriteLine("_____________________________________"); WriteLine();
WriteLine("Part B - Solving linear equation: A*x=b");
A.print("Matrix A="); WriteLine();
b.print("Vector b="); WriteLine();
x.print("Solution x="); WriteLine();
vector Ax = (A * x);
Ax.print("Check A*x="); WriteLine();
if (b.approx(Ax))
{
WriteLine("A*x=b TEST PASSED");
}
else
{
WriteLine("A*x!=b TEST FAILED");
}
//// Del C ////
WriteLine("_____________________________________"); WriteLine();
WriteLine("Part C - Determinant of A");
double D = cd.determinant();
WriteLine($"det(A)={D}"); WriteLine();
//Determinant test is only avalible for n=3
if (n == 3)
{
double D_alt = A[0, 0] * A[1, 1] * A[2, 2] + A[0, 1] * A[1, 2] * A[2, 0]
+ A[0, 2] * A[1, 0] * A[2, 1] - A[0, 2] * A[1, 1] * A[2, 0]
- A[0, 1] * A[1, 0] * A[2, 2] - A[1, 2] * A[2, 1] * A[0, 0];
if (matrix.approx(D_alt, D))
{
WriteLine("TEST PASSED");
}
else
{
WriteLine("TEST FAILED");
}
}
//// Del D ////
WriteLine("_____________________________________"); WriteLine();
WriteLine("Part D - find the inverse matrix of A");
var A_inv = cd.inverse();
A_inv.print("A_inv="); WriteLine();
WriteLine("Check if A_inv is the inverse:"); WriteLine();
matrix AA_inv1 = A * A_inv;
AA_inv1.print("A*A_inv="); WriteLine();
matrix AA_inv2 = A * A_inv;
AA_inv2.print("A_inv*A="); WriteLine();
matrix I = matrix.id(n);
if (I.approx(AA_inv1) && I.approx(AA_inv2))
{
WriteLine("A*A_inv=I\tTEST PASSED");
}
else
{
WriteLine("A*A_inv=I\tTEST FAILED");
}
} //Method: Main
