static void Main()
{
int n = 5, m = 4;
matrix A1 = new matrix(n, m);
var rnd = new Random(1);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < m; j++)
{
A1[i, j] = 2 * (rnd.NextDouble() - 0.5);
}
}
WriteLine("____Assignment A1____");
A1.print($"QR-decomposition:\nrandom {n}x{m} matrix A:");
(matrix Q, matrix R1) = qrDecomp.qr_gs_decomp(A1);
R1.print("matrix R:");
matrix QTQ = Q.T * Q;
matrix QR = Q * R1;
QTQ.print("Q^T*Q:");
QR.print("Q*R:");
if (A1.approx(QR))
{
WriteLine("Q*R=A, test passed");
}
else
{
WriteLine("Q*R!=A, test failed");
}
Write("\n\n");
matrix A2 = new matrix(n, n);
rnd = new Random(2);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
A2[i, j] = 2 * (rnd.NextDouble() - 0.5);
}
}
vector b = new vector(n);
rnd = new Random(3);
for (int i = 0; i < n; i++)
{
b[i] = 2 * (rnd.NextDouble() - 0.5);
}
WriteLine("____Assignment A2____");
A2.print($"Solving system of equations A*x=Q*R*x=b:\nrandom {n}x{n} matrix A:");
(matrix Q2, matrix R2) = qrDecomp.qr_gs_decomp(A2);
Q2.print("matrix Q:");
R2.print("matrix R:");
b.print("vector b:");
vector x2 = qrDecomp.qr_gs_solve(Q2, R2, b);
vector Ax2 = A2 * x2;
x2.print("solution vector x:");
Ax2.print("A*x:");
if (b.approx(A2 * x2))
{
WriteLine("A*x=b, test passed");
}
else
{
WriteLine("A*x!=b, test failed");
}
Write("\n\n");
matrix A3 = new matrix(n, n);
rnd = new Random(4);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
A3[i, j] = 2 * (rnd.NextDouble() - 0.5);
}
}
WriteLine("____Assignment B____");
A3.print($"Decomposing A into Q*R:\nrandom {n}x{n} matrix A:");
(matrix Q3, matrix R3) = qrDecomp.qr_gs_decomp(A3);
Q3.print("matrix Q:");
R3.print("matrix R:");
matrix B = qrDecomp.qr_gs_inverse(Q3, R3);
matrix I = new matrix(n, n);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
I[i, j] = 0;
if (i == j)
{
I[i, j] = 1;
}
}
}
I.print($"Idenity matrix I({n}):");
B.print("Inverse matrix B:");
matrix AB = A3 * B;
matrix AB_round = new matrix(n, n); // rounded matrix to 10th decimal to get a nicer output
for (int i = 0; i <= n - 1; i++)
{
for (int j = 0; j <= n - 1; j++)
{
AB_round[i, j] = Math.Round((Double)AB[i, j], 10);
}
}
AB_round.print("A*B:");
if (AB.approx(I))
{
WriteLine("A*B=I, test passed"); // test is still with unrounded matrix
}
else
{
WriteLine("A*B!=I, test failed");
}
Write("\n\n");
WriteLine("____Assignment C____");
A2.print($"Givens rotation of the same coefficient matrix as in part A(2):\nrandom {n}x{m} matrix A:");
matrix T = A2.copy();
qrDecomp.qr_givens_decomp(T);
T.print("Matrix with R in the upper trinagle and angles of the Givens rotation below, T:");
b.print("Same vector b as in A(2):");
vector Gb = b.copy();
vector x4 = qrDecomp.qr_givens_solve(T, Gb);
vector Ax4 = A2 * x4;
x4.print("solution vector x:");
Ax4.print("A*x:");
if (b.approx(A2 * x4))
{
WriteLine("A*x=b, test passed");
}
else
{
WriteLine("A*x!=b, test failed");
}
Write("\n\n");
}