public void SparseSquareMatrixSolutionAgreement()
{
Random rng = new Random(2);
int n = 16;
//for (int n = 8; n < 100; n+= 11) {
// create dense and sparse matrices with the same entries
SquareMatrix M = new SquareMatrix(n);
SparseSquareMatrix S = new SparseSquareMatrix(n);
for (int r = 0; r < n; r++)
{
for (int c = 0; c < n; c++)
{
if (rng.NextDouble() < 0.5)
{
M[r, c] = rng.NextDouble();
S[r, c] = M[r, c];
}
}
}
// pick a RHS
ColumnVector b = new ColumnVector(n);
for (int i = 0; i < n; i++)
{
b[i] = rng.NextDouble();
}
// solve each
ColumnVector Mx = M.LUDecomposition().Solve(b);
ColumnVector Sx = S.Solve(b);
// the solutions should be the same
Assert.IsTrue(TestUtilities.IsNearlyEqual(Mx, Sx, TestUtilities.TargetPrecision * 100.0));
//}
}
public void SparseSquareMatrixPotential()
{
// An 2D electrostatic boundary value problem in cartesian coordinates
// A square of length n, with specified constant potentials on each wall
// Discritized Laplace equation is
// u_{x,y-1} + u_{x+1,y} + u_{x,y+1} + u_{x-1,y} - 4 u_{x,y} = 0
// Number interior points sequentially row-wise i.e. i = x + n * y
// Points nearest the walls will pick up a boundary value, which because it is not a variable we move to the RHS
// Points closer to the interior pick up no boundary value, so their RHS is zero
int n = 100;
double pn = 0.0; double pe = 1.0; double ps = 0.0; double pw = 1.0;
SparseSquareMatrix A = new SparseSquareMatrix(n * n);
ColumnVector b = new ColumnVector(n * n);
// set up A and b
for (int y = 0; y < n; y++)
{
for (int x = 0; x < n; x++)
{
int i = x + n * y;
// center value
A[i, i] = 4.0;
// north
if (y == 0)
{
b[i] += pn;
}
else
{
int j = x + n * (y - 1);
A[i, j] = -1.0;
}
// east
if (x == (n - 1))
{
b[i] += pe;
}
else
{
int j = (x + 1) + n * y;
A[i, j] = -1.0;
}
// south
if (y == (n - 1))
{
b[i] += ps;
}
else
{
int j = x + n * (y + 1);
A[i, j] = -1.0;
}
// west
if (x == 0)
{
b[i] += pw;
}
else
{
int j = (x - 1) + n * y;
A[i, j] = -1.0;
}
}
}
ColumnVector u = A.Solve(b);
for (int y = 0; y < 10; y++)
{
for (int x = 0; x < 10; x++)
{
int i = x + n * y;
Console.Write("{0} ", u[i]);
}
Console.WriteLine();
}
Console.WriteLine(PotentialSolution(1, 2, n));
}