public List <List <double> > solve(List <List <double> > f)
{
try
{
List <DiagMatrix> alpha = new List <DiagMatrix>(N);
List <List <double> > beta = new List <List <double> >(N + 1);
alpha.Add(null);
beta.Add(null);
alpha.Add(DiagMatrix.inverse(mainDiag[0]) * upDiag[0]);
beta.Add(DiagMatrix.inverse(mainDiag[0]) * f[0]);
for (int i = 1; i < N - 1; ++i)
{
DiagMatrix tmp = DiagMatrix.inverse(mainDiag[i] - downDiag[i] * alpha[i]);
alpha.Add(tmp * upDiag[i]);
beta.Add(tmp * diff(f[i], downDiag[i] * beta[i]));
}
beta.Add(DiagMatrix.inverse(mainDiag[N - 1] - downDiag[N - 1] * alpha[N - 1]) * diff(f[N - 1], downDiag[N - 1] * beta[N - 1]));
List <List <double> > x = new List <List <double> >(N);
for (int i = 0; i < N; ++i)
{
x.Add(null);
}
x[N - 1] = beta[N];
for (int i = N - 2; i >= 0; --i)
{
x[i] = diff(beta[i + 1], alpha[i + 1] * x[i + 1]);
}
return(x);
}
catch (Exception ex)
{
throw ex;
}
}
public static DiagMatrix inverse(DiagMatrix arg)
{
try
{
DiagMatrix res = new DiagMatrix(arg.order);
for (int i = 0; i < res.order; ++i)
{
if (arg.data[i] == 0)
{
throw new Exception("Inversion error: inverse matrix does not exist");
}
res.data[i] = 1.0 / arg.data[i];
}
return(res);
}
catch (Exception ex)
{
throw ex;
}
}
public static DiagMatrix operator -(DiagMatrix d1, DiagMatrix d2)
{
try
{
if (d1.order != d2.order)
{
throw new Exception("Subtraction error: different sizes of matrices");
}
int order = d1.order;
DiagMatrix res = new DiagMatrix(order);
for (int i = 0; i < order; ++i)
{
res.data[i] = d1.data[i] - d2.data[i];
}
return(res);
}
catch (Exception ex)
{
throw ex;
}
}
public DiagMatrix(DiagMatrix other)
{
order = other.order;
data = other.data;
}