public static void Verrier(double[][] A, double start, double end, double eps, out double[] self_values, out double[][] self_vectors)
{
self_values = null;
self_vectors = null;
if (A == null || A.Count() == 0)
{
return;
}
if (A.Count() != A[0].Count())
{
return;
}
double[][][] A_pows = new double[A.Count()][][];
A_pows[0] = A;
for (int i = 1; i < A_pows.Count(); i++)
{
A_pows[i] = Matrix_multiplication(A_pows[i - 1], A);
}
double[] S = new double[A_pows.Count()];
for (int i = 0; i < S.Count(); i++)
{
S[i] = 0;
for (int j = 0; j < A_pows[i].Count(); j++)
{
S[i] += A_pows[i][j][j];
}
}
double[] p = new double[A_pows.Count()];
p[0] = S[0];
for (int i = 1; i < p.Count(); i++)
{
p[i] = 1.0 / (i + 1.0);
double pi = S[i];
for (int j = 0; j <= i - 1; j++)
{
pi -= (p[j] * S[i - 1 - j]);
}
p[i] *= pi;
}
Func <double, double> lambda_function = delegate(double lambda)
{
double lambda_root = Math.Pow(lambda, p.Count());
for (int i = 0; i < p.Count() - 1; i++)
{
lambda_root -= p[i] * Math.Pow(lambda, p.Count() - 1 - i);
}
lambda_root -= p[p.Count() - 1];
return(lambda_root);
};
self_values = Lab2.Chords_multi(lambda_function, p.Count(), start, end, eps);
}
public static void Krylov(double[][] A, double start, double end, double eps, out double[] self_values, out double[][] self_vectors)
{
self_values = null;
self_vectors = null;
if (A == null || A.Count() == 0)
{
return;
}
if (A.Count() != A[0].Count())
{
return;
}
double[][] y = new double[A.Count() + 1][];
for (int i = 0; i < y.Count(); i++)
{
y[i] = new double[A.Count()];
for (int j = 0; j < y[i].Count(); j++)
{
if (i == 0)
{
if (j == 0)
{
y[i][j] = 1;
}
else
{
y[i][j] = 0;
}
}
else
{
y[i] = Matrix_multiplication(A, y[i - 1]);
}
}
}
double[][] p_matrix = new double[y.Count() - 1][];
for (int i = 0; i < p_matrix.Count(); i++)
{
p_matrix[i] = new double[p_matrix.Count() + 1];
for (int j = 0; j < p_matrix.Count(); j++)
{
p_matrix[i][j] = y[y.Count() - 2 - j][i];
}
p_matrix[i][p_matrix.Count()] = y[y.Count() - 1][i];
}
double[] p = Lab1.Gauss_main(p_matrix);
Func <double, double> lambda_function = delegate(double lambda)
{
double lambda_root = Math.Pow(lambda, p.Count());
for (int i = 0; i < p.Count() - 1; i++)
{
lambda_root -= p[i] * Math.Pow(lambda, p.Count() - 1 - i);
}
lambda_root -= p[p.Count() - 1];
return(lambda_root);
};
self_values = Lab2.Chords_multi(lambda_function, p.Count(), start, end, eps);
double[][] q = new double[self_values.Count()][];
for (int i = 0; i < q.Count(); i++)
{
q[i] = new double[q.Count()];
for (int j = 0; j < q[i].Count(); j++)
{
if (j == 0)
{
q[i][j] = 1;
}
else
{
q[i][j] = self_values[i] * q[i][j - 1] - p[j - 1];
}
}
}
double[][] x = new double[self_values.Count()][];
for (int i = 0; i < x.Count(); i++)
{
x[i] = y[y.Count() - 2];
for (int j = 0; j < x[i].Count() - 1; j++)
{
x[i] = Matrix_addition(x[i], Matrix_multiplication(y[y.Count() - 3 - j], q[i][j + 1]));
}
}
self_vectors = x;
}
