static int Main()
{
matrix A = new matrix(3, 3); //matrix taken from wiki
A[0, 0] = 6; A[0, 1] = 5; A[0, 2] = 0;
A[1, 0] = 5; A[1, 1] = 1; A[1, 2] = 4;
A[2, 0] = 0; A[2, 1] = 4; A[2, 2] = 3;
gi_rot a = new gi_rot(A);
matrix a1 = a.A;
WriteLine("Matrix generated by function:");
for (int n = 0; n < A.size1; n++)
{
for (int n1 = 0; n1 < A.size2; n1++)
{
Write($"{a1[n,n1]} ");
} //end for
Write("\n");
} //end for
vector b = new vector(A.size1);
b[0] = 1; b[1] = 3; b[2] = -1;
vector x = a.solve(b);
vector ax = A * x;
WriteLine($"Test Ax=b:");
for (int n1 = 0; n1 < b.size; n1++)
{
WriteLine($"Ax= {ax[n1]}, b= {b[n1]}");
}
return(0);
} //end main}
static int Main()
{
//generating a random matrix
matrix A = randmatrix(4, 4);
//givens:
gi_rot a = new gi_rot(A);
//grams-schmitt
gram_s gs = new gram_s(A);
//random vector b:
vector b = randvector(4);
//solve Ax=b using givens:
vector x = a.solve(b);
vector ax = A * x;
WriteLine("Part C");
WriteLine($"Givens rotation");
WriteLine($"Random generated matrix A:");
for (int i = 0; i < A.size1; i++)
{
Write("\n");
for (int j = 0; j < A.size2; j++)
{
Write($"{A[i,j]} ");
}
}
Write("\n \n");
WriteLine("The calculated matrix G, with stored rotation angles:");
for (int i = 0; i < a.A.size1; i++)
{
Write("\n");
for (int j = 0; j < a.A.size2; j++)
{
Write($"{a.A[i,j]} ");
}
}
Write("\n \n");
WriteLine("R-matrix from Gram-Schmitt to comparison:");
for (int i = 0; i < gs.R.size1; i++)
{
Write("\n");
for (int j = 0; j < gs.R.size2; j++)
{
Write($"{gs.R[i,j]} ");
}
}
Write("\n \n");
WriteLine("Note: the similarities between the upper triangle.");
WriteLine("");
WriteLine("Random vector b:");
for (int i = 0; i < b.size; i++)
{
WriteLine($"{b[i]}");
} //end for
WriteLine("");
WriteLine("Givens rotations was used to solve Ax=b, yielding x:");
for (int i = 0; i < x.size; i++)
{
WriteLine($"{x[i]}");
} //end for
WriteLine("Ax gives:");
for (int i = 0; i < ax.size; i++)
{
WriteLine($"{ax[i]}");
} //end for
WriteLine("Note: the same as b.");
WriteLine("");
return(0);
}
