public static void RayleighQuotient(MatrixR A, double tolerance, int flag, out VectorR x, out double lambda)
{
int n = A.GetCols();
double delta = 0.0;
Random random = new Random();
x = new VectorR(n);
if (flag != 2)
{
for (int i = 0; i < n; i++)
{
x[i] = random.NextDouble();
}
x.Normalize();
lambda = VectorR.DotProduct(x, MatrixR.Transform(A, x));
}
else
{
lambda = 0.0;
Rayleigh(A, 1e-2, out x, out lambda);
}
double temp = lambda;
MatrixR identity = new MatrixR(n, n);
LinearSystem ls = new LinearSystem();
do
{
temp = lambda;
double d = ls.LUCrout(A - lambda * identity.Identity(), x);
x.Normalize();
lambda = VectorR.DotProduct(x, MatrixR.Transform(A, x));
delta = Math.Abs((temp - lambda) / lambda);
}while (delta > tolerance);
}
public static void Rayleigh(MatrixR A, double tolerance, out VectorR x, out double lambda)
{
int n = A.GetCols();
double delta = 0.0;
Random random = new Random();
x = new VectorR(n);
for (int i = 0; i < n; i++)
{
x[i] = random.NextDouble();
}
x.Normalize();
VectorR x0 = MatrixR.Transform(A, x);
x0.Normalize();
lambda = VectorR.DotProduct(x, x0);
double temp = lambda;
do
{
temp = lambda;
x0 = x;
x0.Normalize();
x = MatrixR.Transform(A, x0);
lambda = VectorR.DotProduct(x, x0);
delta = Math.Abs((temp - lambda) / lambda);
}while (delta > tolerance);
x.Normalize();
}
public static void Inverse(MatrixR A, double s, double tolerance, out VectorR x, out double lambda)
{
int n = A.GetCols();
x = new VectorR(n);
lambda = 0.0;
double delta = 0.0;
MatrixR identity = new MatrixR(n, n);
A = A - s * (identity.Identity());
LinearSystem ls = new LinearSystem();
A = ls.LUInverse(A);
Random random = new Random();
for (int i = 0; i < n; i++)
{
x[i] = random.NextDouble();
}
do
{
VectorR temp = x;
x = MatrixR.Transform(A, x);
x.Normalize();
if (VectorR.DotProduct(temp, x) < 0)
{
x = -x;
}
VectorR dx = temp - x;
delta = dx.GetNorm();
}while (delta > tolerance);
lambda = s + 1.0 / (VectorR.DotProduct(x, MatrixR.Transform(A, x)));
}
public static void Power(MatrixR A, double tolerance, out VectorR x, out double lambda)
{
int n = A.GetCols();
x = new VectorR(n);
lambda = 0.0;
double delta = 0.0;
Random random = new Random();
for (int i = 0; i < n; i++)
{
x[i] = random.NextDouble();
}
do
{
VectorR temp = x;
x = MatrixR.Transform(A, x);
x.Normalize();
if (VectorR.DotProduct(temp, x) < 0)
{
x = -x;
}
VectorR dx = temp - x;
delta = dx.GetNorm();
}while (delta > tolerance);
lambda = VectorR.DotProduct(x, MatrixR.Transform(A, x));
}
public VectorR GetUnitVector()
{
VectorR result = new VectorR(vector);
result.Normalize();
return(result);
}
public static VectorR TridiagonalEigenvector(double s, double tolerance, out double lambda)
{
int n = Alpha.GetLength(0);
double[] gamma = (double[])Beta.Clone();
double[] beta = (double[])Beta.Clone();
double[] alpha = new double[n];
for (int i = 0; i < n; i++)
{
alpha[i] = Alpha[i] - s;
}
double[] gamma1, alpha1, beta1;
LUDecomposition(gamma, alpha, beta, out gamma1, out alpha1, out beta1);
VectorR x = new VectorR(n);
Random random = new Random();
for (int i = 0; i < n; i++)
{
x[i] = random.NextDouble();
}
x.Normalize();
VectorR x1 = new VectorR(n);;
double sign;
do
{
x1 = x.Clone();
LUSolver(gamma1, alpha1, beta1, x);
x.Normalize();
if (VectorR.DotProduct(x1, x) < 0.0)
{
sign = -1.0;
x = -x;
}
else
{
sign = 1.0;
}
}while ((x - x1).GetNorm() > tolerance);
lambda = s + sign / x.GetNorm();
return(x);
}
