public static void Jacobi(SquareMatrix q, double e, bool write)
{
if (write)
{
Start("Найдём все собственные числа и вектора",
"методом Якоби", " с заданной погрешностью", e);
}
A = q.DeepClone;
int n = A.Rows;
SquareMatrix X = Id(n);
while (true)
{
double max = 0;
int mi = 0, mj = 0;
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
if ((i != j) & (Abs(A[i, j]) > max))
{
max = Abs(A[i, j]);
mi = i;
mj = j;
}
}
}
if (max < e)
{
JacobiEnd(q, X.T);
return;
}
double d = Sqrt((A[mi, mi] - A[mj, mj]) *
(A[mi, mi] - A[mj, mj]) + 4 * A[mi, mj] * A[mi, mj]);
double ds = Sqrt(0.5 * (1 + Abs(A[mi, mi] - A[mj, mj]) / d));
double dc = Sign(A[mi, mj] * (A[mi, mi] - A[mj, mj])) *
Sqrt(0.5 * (1 - Abs(A[mi, mi] - A[mj, mj]) / d));
var L = new SquareMatrix(n);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
if ((i == j) & (j != mi) & (j != mj))
{
L[i, j] = 1;
}
else
if ((i != mj) & (i != mi) & (j != mj) & (j != mi))
{
L[i, j] = 0;
}
else
if ((i == mi) & (j == mi))
{
L[i, j] = dc;
}
else
if ((i == mj) & (j == mj))
{
L[i, j] = dc;
}
else
if ((i == mi) & (j == mj))
{
L[i, j] = ds;
}
else
if ((i == mj) & (j == mi))
{
L[i, j] = -ds;
}
}
}
X = X * L;
SquareMatrix B = A.DeepClone;
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
if ((i == mi) & (j == mj))
{
B[i, j] = 0;
}
else
if ((i == mj) & (j == mi))
{
B[i, j] = 0;
}
else
if ((i == mi) & (j != mj) & (j != mi))
{
B[i, j] = dc * A[j, mi] - ds * A[j, mj];
}
else
if ((i != mj) & (i != mi) & (j == mi))
{
B[i, j] = dc * A[i, mi] - ds * A[i, mj];
}
else
if ((i == mj) & (j != mi) & (j != mj))
{
B[i, j] = ds * A[j, mi] + dc * A[j, mj];
}
else
if ((i != mi) & (i != mj) & (j == mj))
{
B[i, j] = ds * A[i, mi] + dc * A[i, mj];
}
else
if ((i == mi) & (j == mi))
{
B[i, j] = dc * dc * A[mi, mi] -
2 * ds * dc * A[mi, mj] + ds * ds * A[mj, mj];
}
else
if ((i == mj) & (j == mj))
{
B[i, j] = ds * ds * A[mi, mi] +
2 * ds * dc * A[mi, mj] + dc * dc * A[mj, mj];
}
else
{
B[i, j] = A[i, j];
}
}
}
A = B;
}
}
public static T Do <T>(SquareMatrix q, T t, bool write)
where T : class, IMatrix
{
return(new GaussMod().Start(q, t, write));
}
protected override void Init(SquareMatrix q, IMatrix t, bool write)
{
base.Init(q, t, write);
index = new int[n];
}
static void Main(string[] args)
{
Init();
Title = "Task2 Итерационные методы решения линейных систем";
OutputEncoding = Encoding.GetEncoding(1251);
var A = new SquareMatrix(100, 6, 2, 2, 100, 5, 3, 4, 100);
var B = new Vector(60, 70, 80);
Left("Рассмотрим исходную систему AX = B");
Right(A, B);
if (!CheckConvergenceCondition(A))
{
return;
}
xGauss = GaussMod.Do(A, B, false);
Left("Решение модифицированным методом Гаусса");
Right(xGauss);
OutputResidual(A * xGauss - B);
Line();
var D = A.DiagonalInvert();
var H = Id(A.Rows) - D * A;
var g = D * B;
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
if (i != j)
{
H[i, j] = 1 / System.Math.Pow(2, System.Math.Abs(i - j) + 1);
}
else
{
H[i, j] = 0;
}
}
}
g = new Vector(3);
for (int i = 0; i < 3; i++)
{
g[i] = 1;
}
Left("Приведём систему к виду X = HX + G");
Right(H, g);
Iteration.A = A;
Iteration.B = B;
FixedPoint(H, g, steps);
FixedPoint(H, g, e);
Seidel(H, g, steps);
Seidel(H, g, e);
SuccessiveOverRelaxation(H, g, steps);
ReadKey();
}
public static bool DiagonallyDominant(this SquareMatrix q)
{
return(q.X.Select((x, i) => 2 * x[i] - x.N8).All(x => x > 0));
}
public static bool Seidel(SquareMatrix q, Vector u, double e)
{
return(new Iteration(q, u, e).SeidelByE());
}
public static void SuccessiveOverRelaxation(SquareMatrix q, Vector u,
int steps)
{
new Iteration(q, u, steps).SuccessiveOverRelaxationBySteps();
}
public static bool Seidel(SquareMatrix q, Vector u, int steps)
{
return(new Iteration(q, u, steps).SeidelBySteps());
}
public static bool FixedPoint(SquareMatrix q, Vector u, int steps)
{
return(new Iteration(q, u, steps).FixedPointBySteps());
}
public static bool FixedPoint(SquareMatrix q, Vector u, double e)
{
return(new Iteration(q, u, e).FixedPointByE());
}
Iteration(SquareMatrix q, Vector u, int steps)
: this(q, u)
{
this.steps = steps;
}
Iteration(SquareMatrix q, Vector u, double e)
: this(q, u)
{
this.e = e;
}
