static void Main()
{
try
{
//методы на подпространствах Крылова: CSlR-формат матрицы
var T3 = new Thread(() =>
{
//разреженная матрица
var A = new CSlR_Matrix("Data\\Sparse_Format\\Systems1\\NonSPD\\");
//заполнение вектора истинного решения и правой части
var F = new Vector(A.N);
var X_True = new Vector(A.N);
int pre = 1;
//заполнение вектора истинного решения и правой части
for (int i = 0; i < A.N; i++)
{
X_True.Elem[i] = 1.0;
}
A.Mult_MV(X_True, F);
var Solver = new BCG(30000, 1e-12);
var X = Solver.Start_Solver(A, F, 2);
Console.WriteLine(Tools.Relative_Error(X, X_True));
});
//время решения
Console.WriteLine(Tools.Measurement_Time(T3));
}
catch (Exception E)
{
Console.WriteLine("\n*** Error! ***");
Console.WriteLine("Method: {0}", E.TargetSite);
Console.WriteLine("Message: {0}\n", E.Message);
}
}
public Diag_Predconditioner(CSlR_Matrix A)
{
Diag = new Vector(A.N);
for (int i = 0; i < A.N; i++)
{
Diag.Elem[i] = A.di[i];
}
}
public Diagonal_Preconditioner(CSlR_Matrix A)
{
Diag = new Vector(A.N);
for (int i = 0; i < A.N; i++)
{
if (Math.Abs(A.di[i]) < CONST.EPS)
{
throw new Exception("Diagonal_Preconditioner: " + (i + 1).ToString() + " position on di = " + A.di[i].ToString());
}
Diag.Elem[i] = A.di[i];
}
}
//-------------------------------------------------------------------------------------------------
//операция неполного ILU-разложения (Incomplete LU-decomposition) в формате CSlR
public CSlR_Matrix Create_ILU_Decomposition()
{
var Matrix = new CSlR_Matrix();
Matrix.N = N;
Matrix.iptr = iptr;
Matrix.jptr = jptr;
int N_autr = autr.Length;
Matrix.autr = new double[N_autr];
Matrix.altr = new double[N_autr];
Matrix.di = new double[N];
for (int i = 0; i < N_autr; i++)
{
Matrix.altr[i] = altr[i]; Matrix.autr[i] = autr[i];
}
for (int i = 0; i < N; i++)
{
Matrix.di[i] = di[i];
}
//начинаем с i = 1, т.к. в первой строке нижнего треугольника только диагональный элемент
for (int i = 1; i < N; i++)
{
for (int j = iptr[i] - 1; j < iptr[i + 1] - 1; j++)
{
for (int a = iptr[i] - 1; a < j; a++)
{
for (int b = iptr[jptr[j] - 1] - 1; b < iptr[jptr[j]] - 1; b++)
{
if (jptr[a] == jptr[b])
{
Matrix.altr[j] -= Matrix.altr[a] * Matrix.autr[b];
Matrix.autr[j] -= Matrix.autr[a] * Matrix.altr[b];
}
}
}
Matrix.autr[j] /= Matrix.di[jptr[j] - 1];
Matrix.di[i] -= Matrix.autr[j] * Matrix.altr[j];
}
}
return(Matrix);
}
//конструктор
public Incomplete_LU_Decomposition_CSlR(CSlR_Matrix A)
{
ILU = new CSlR_Matrix();
ILU.N = A.N;
ILU.iptr = A.iptr;
ILU.jptr = A.jptr;
int N_autr = A.autr.Length;
ILU.autr = new double[N_autr];
ILU.altr = new double[N_autr];
ILU.di = new double[A.N];
for (int i = 0; i < N_autr; i++)
{
ILU.altr[i] = A.altr[i]; ILU.autr[i] = A.autr[i];
}
for (int i = 0; i < A.N; i++)
{
ILU.di[i] = A.di[i];
}
//начинаем с i = 1, т.к. в первой строке нижнего треугольника только диагональный элемент
for (int i = 1; i < A.N; i++)
{
for (int j = A.iptr[i] - 1; j < A.iptr[i + 1] - 1; j++)
{
for (int a = A.iptr[i] - 1; a < j; a++)
{
for (int b = A.iptr[A.jptr[j] - 1] - 1; b < A.iptr[A.jptr[j]] - 1; b++)
{
if (A.jptr[a] == A.jptr[b])
{
ILU.altr[j] -= ILU.altr[a] * ILU.autr[b];
ILU.autr[j] -= ILU.autr[a] * ILU.altr[b];
}
}
}
ILU.autr[j] /= ILU.di[A.jptr[j] - 1];
ILU.di[i] -= ILU.autr[j] * ILU.altr[j];
}
}
}
public Vector Start_Solver(CSlR_Matrix A, Vector F, Preconditioner.Type_Preconditioner PREC)
{
switch (PREC)
{
case Preconditioner.Type_Preconditioner.Diagonal_Preconditioner:
{
Preconditioner = new Diagonal_Preconditioner(A);
break;
}
case Preconditioner.Type_Preconditioner.LU_Decomposition:
{
Preconditioner = new LU_Preconditioner(A);
break;
}
}
int n = A.N;
Vector RES = new Vector(n);
for (int i = 0; i < n; i++)
{
RES.Elem[i] = 0.0;
}
Vector r = new Vector(n);
Vector rs = new Vector(n);
Vector p = new Vector(n);
Vector ps = new Vector(n);
Vector vec = new Vector(n);
Vector vec2 = new Vector(n);
double alpha, beta, sc1, sc2;
bool Flag = true;
A.Mult_MV(RES, vec);
for (int i = 0; i < n; i++)
{
r.Elem[i] = F.Elem[i] - vec.Elem[i];
}
Preconditioner.Start_Preconditioner(r, ps);
for (int i = 0; i < n; i++)
{
r.Elem[i] = ps.Elem[i];
rs.Elem[i] = ps.Elem[i];
p.Elem[i] = ps.Elem[i];
}
while (Flag && Iter < Max_Iter)
{
sc1 = r * rs;
A.Mult_MV(p, vec);
Preconditioner.Start_Preconditioner(vec, vec2);
sc2 = vec2 * ps;
alpha = sc1 / sc2;
for (int i = 0; i < n; i++)
{
RES.Elem[i] += alpha * p.Elem[i];
r.Elem[i] -= alpha * vec2.Elem[i];
}
Preconditioner.Start_Tr_Preconditioner(ps, vec);
A.Mult_MtV(vec, vec2);
for (int i = 0; i < n; i++)
{
rs.Elem[i] -= alpha * vec2.Elem[i];
}
sc2 = r * rs;
beta = sc2 / sc1;
double Norma_r = r.Norma();
if (Norma_r < Eps)
{
Flag = false;
}
if (Math.Abs(beta) < Double.Epsilon)
{
throw new Exception("BiConjurate_Gradient_Method: diverges given ~r(0)");
}
for (int i = 0; i < n; i++)
{
p.Elem[i] = r.Elem[i] + beta * p.Elem[i];
ps.Elem[i] = rs.Elem[i] + beta * ps.Elem[i];
}
Iter++;
Console.WriteLine("{0,-20} {1,-20}", Iter, Norma_r);
}
return(RES);
}
static void Main()
{
try
{
//прямые методы: Гаусс, LU-разложение, QR-разложение
var T1 = new Thread(() =>
{
int N = 5;
var A = new Matrix(N, N);
var X_true = new Vector(N);
//заполнение СЛАУ
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
A.Elem[i][j] = 1.0 / (i + j + 2.0);
}
X_true.Elem[i] = 1;
}
//правая часть
var F = A * X_true;
//метод Гаусса
var Solver = new Gauss_Method();
var X = Solver.Start_Solver(A, F);
});
//итерационные блочные методы: Якоби, Гаусса-Зейделя и SOR
var T2 = new Thread(() =>
{
//матрица
var A = new Matrix("Data\\Dense_Format\\");
//вектор правой части
var F = new Vector("Data\\Dense_Format\\");
//метод SOR при w = 1.8 (максимальное число итераций = 30000, точность = 1e-12)
var Solver = new SOR_Method(30000, 1e-12);
var X = Solver.Start_Solver(A, F, 1.85);
});
//методы на подпространствах Крылова: CSlR-формат матрицы
var T3 = new Thread(() =>
{
//разреженная СЛАУ
var A = new CSlR_Matrix("Data\\Sparse_Format\\Systems2\\NonSPD\\");
var F = new Vector(A.N);
var X_True = new Vector(A.N);
//заполнение вектора истинного решения и правой части
for (int i = 0; i < A.N; i++)
{
X_True.Elem[i] = 1.0;
}
A.Mult_MV(X_True, F);
});
//время решения задачи
Console.WriteLine(Tools.Measurement_Time(T3));
}
catch (Exception E)
{
Console.WriteLine("\n*** Error! ***");
Console.WriteLine("Method: {0}", E.TargetSite);
Console.WriteLine("Message: {0}\n", E.Message);
}
}
//конструктор LU-преобусловливателя
public LU_Preconditioner(CSlR_Matrix A)
{
ILU = new Incomplete_LU_Decomposition_CSlR(A);
}
public Vector Start_Solver(CSlR_Matrix A, Vector F, Preconditioner.Type_Preconditioner PREC)
{
switch (PREC)
{
case Preconditioner.Type_Preconditioner.Diagonal_Preconditioner:
{
Preconditioner = new Diagonal_Preconditioner(A);
break;
}
case Preconditioner.Type_Preconditioner.LU_Decomposition:
{
Preconditioner = new LU_Preconditioner(A);
break;
}
}
int n = A.N;
Vector RES = new Vector(n);
for (int i = 0; i < n; i++)
{
RES.Elem[i] = 0.0;
}
Vector r = new Vector(n);
Vector p = new Vector(n);
Vector vec = new Vector(n);
double alpha, beta, sc1, sc2;
bool Flag = true;
double Norma_r = 0;
A.Mult_MV(RES, vec);
for (int i = 0; i < n; i++)
{
r.Elem[i] = F.Elem[i] - vec.Elem[i];
}
Preconditioner.Start_Preconditioner(r, p);
while (Flag && Iter < Max_Iter)
{
sc1 = p * r;
A.Mult_MV(p, vec);
sc2 = vec * p;
alpha = sc1 / sc2;
for (int i = 0; i < n; i++)
{
RES.Elem[i] += alpha * p.Elem[i];
r.Elem[i] -= alpha * vec.Elem[i];
}
Preconditioner.Start_Preconditioner(r, vec);
sc2 = vec * r;
beta = sc2 / sc1;
Norma_r = r.Norma();
if (Norma_r < Eps)
{
Flag = false;
}
if (Flag)
{
for (int i = 0; i < n; i++)
{
p.Elem[i] = vec.Elem[i] + beta * p.Elem[i];
}
}
Iter++;
Console.WriteLine("{0,-20} {1,-20}", Iter, Norma_r.ToString("E"));
}
return(RES);
}
public Vector Start_Solver(CSlR_Matrix A, Vector F, int PREC)
{
int n = A.N;
// решение
Vector RES = new Vector(n);
for (int i = 0; i < n; i++)
{
RES.Elem[i] = 0.0;
}
//реализация предобусловливателя
switch (PREC)
{
case 1: { Pr = new Diag_Predconditioner(A); break; }
case 2: { Pr = new ILU_Decomposition(A); break; }
//default: { Pr = new E_Predconditioner(); break; }
}
var r = new Vector(n);
var p = new Vector(n);
var vec = new Vector(n);
// параметры
double alpha, betta, sc1, sc2;
// флаг для остановки
int Flag = 0;
// ||r||
double nev_r = 0;
// начало CG
A.Mult_MV(RES, vec);
for (int i = 0; i < n; i++)
{
r.Elem[i] = F.Elem[i] - vec.Elem[i];
}
Pr.Start_Predconditioner(r, p); // в r предобусловленная система-невязка
while (Flag != 1 && Iter < Max_Iter)
{
sc1 = p * r;
A.Mult_MV(p, vec);
sc2 = vec * p;
alpha = sc1 / sc2;
for (int i = 0; i < n; i++)
{
RES.Elem[i] += alpha * p.Elem[i];
r.Elem[i] -= alpha * vec.Elem[i];
}
Pr.Start_Tr_Predconditioner(r, vec);
sc2 = vec * p;
betta = sc2 / sc1;
nev_r = r.Norm();
if (nev_r < Eps)
{
Flag = 1;
}
if (Flag == 0)
{
for (int i = 0; i < n; i++)
{
p.Elem[i] = vec.Elem[i] + betta * p.Elem[i];
}
}
Console.WriteLine("{0,-20} {1,-20}", Iter, nev_r.ToString("E"));
Iter++;
}
return(RES);
}
static void Main()
{
try
{
//прямые методы: Гаусс, LU-разложение, QR-разложение
var T1 = new Thread(() =>
{
//int N = 10;
//var A = new Matrix(N, N);
//var X_true = new Vector(N);
//заполнение СЛАУ
//for (int i = 0; i < N; i++)
//{
// for (int j = 0; j < N; j++)
// {
// A.Elem[i][j] = 1.0 / (i + j + 1.0);
// }
// X_true.Elem[i] = 1;
//}
// for (int i = 0; i < N; i++)
// {
// for (int j = 0; j < N; j++)
// {
// //A.Elem[i][j] = 1.0 / (i + j + 1.0);
// }
// X_true.Elem[i] = 1;
// }
// var ElemMatrix = new double[][]
// {
// //new double[]{-2,-2,-1},
// //new double[]{1,0,-2},
// //new double[]{0,1,2}
// new double[]{5,1,9},
// new double[]{1,4,1},
// new double[]{5,1,3}
// };
// A.Elem = ElemMatrix;
// //правая часть
// var F = A * X_true;
// //решатель
// //var Solver = new Gauss_Method();
// //var Solver = new LU_Decomposition(A);
// var Solver = new QR_Decomposition(A, QR_Decomposition.QR_Algorithm.Householder);
// var X = Solver.Start_Solver(F);
// //X.Console_Write_Vector();
// Console.WriteLine("\nError: {0}\n", Tools.Relative_Error(X, X_true));
});
//Итерационные методы
var T2 = new Thread(() =>
{
});
//итерационные методы: Якоби и SOR
var T3 = new Thread(() =>
{
int SIZE_BLOCK = 450;
double m = 1e+4;
double z = 1.2;
for (int k = 0; k < 1; k++)
{
//var Solver = new Jacobi_Method(30000, 1e-12);
var Solver = new SOR_Method(30000, 1e-4);
//Вычисление точного решения
//var A_g = new Matrix("Data\\System3\\", m);
//var F_g = new Vector("Data\\System3\\");
//var GSolver = new Gauss_Method();
//var sw = new Stopwatch();
//sw.Start();
//var X_true = GSolver.Start_Solver(A_g, F_g);
//sw.Stop();
//Console.WriteLine($"\nTime: {sw.Elapsed}");
//Блочная или обычная матрица/вектор
//var A = new Block_Matrix("Data\\System3\\", SIZE_BLOCK, m);
//var F = new Block_Vector("Data\\System3\\", SIZE_BLOCK);
//var A = new Matrix("Data\\System3\\", m);
//var F = new Vector("Data\\System3\\");
var A = new Matrix(3, 3);
var F = new Vector(3);
F.Elem[0] = 8;
F.Elem[1] = 8;
F.Elem[2] = 11;
var ElemMatrix = new double[][]
{
//new double[]{-2,-2,-1},
//new double[]{1,0,-2},
//new double[]{0,1,2}
new double[] { 10, 1, 0 },
new double[] { 1, 10, 0 },
new double[] { 0, 0, 10 }
};
A.Elem = ElemMatrix;
var sw = new Stopwatch();
sw.Start();
//var X = Solver.Start_Solver(A, F);
var X = Solver.Start_Solver(A, F, 1);
//var X = Solver.Start_Solver(A, F, z);
sw.Stop();
Console.WriteLine($"\nTime: {sw.Elapsed}");
//var X_true_Norm = X_true.Norma();
//ДЛЯ ОБЫЧНОЙ МАТРИЦЫ
//for (int j = 0; j < 900; j++)
//{
// X_true.Elem[j] = X.Elem[j] - X_true.Elem[j];
//}
//ДЛЯ БЛОЧНОЙ МАТРИЦЫ
//int q = 0;
//for (int i = 0; i < X.N; i++)
//{
// for (int j = 0; j < SIZE_BLOCK; j++)
// {
// X_true.Elem[q] = X.Block[i].Elem[j] - X_true.Elem[q];
// q++;
// }
//}
//Console.WriteLine("delta = " + (X_true.Norma() / X_true_Norm));
//Console.WriteLine("Cond(A) = " + A.Cond_InfinityNorm() + "\n");
//Console.WriteLine("m = " + m);
//Console.WriteLine("z = " + z);
Console.WriteLine("--------------------------");
//m /= 100;
//z += 0.1;
}
});
var T4 = new Thread(() =>
{
var A = new CSlR_Matrix("Data\\Sparse_Format\\Systems2\\nonSPD\\");
var X_true = new Vector(A.N);
var F = new Vector(A.N);
for (int i = 0; i < A.N; i++)
{
X_true.Elem[i] = 1.0;
}
A.Mult_MV(X_true, F);
var Solver = new Conjurate_Gradient_Method(30000, 1e-12);
//var Solver = new BiConjurate_Gradient_Method(30000, 1e-12);
var sw = new Stopwatch();
sw.Start();
var X = Solver.Start_Solver(A, F, Preconditioner.Type_Preconditioner.LU_Decomposition);
sw.Stop();
Console.WriteLine($"\nTime: {sw.Elapsed}");
Console.WriteLine("Relative_Error: {0}", Tools.Relative_Error(X, X_true));
Console.ReadLine();
for (int i = 0; i < X.N; i++)
{
Console.WriteLine("X[{0}] = {1}", i + 1, X.Elem[i]);
}
});
//время решения
Console.WriteLine(Tools.Measurement_Time(T4));
}
catch (Exception E)
{
Console.WriteLine("\n*** Error! ***");
Console.WriteLine("Method: {0}", E.TargetSite);
Console.WriteLine("Message: {0}\n", E.Message);
}
Console.ReadLine();
}
public ILU_Decomposition(CSlR_Matrix A)
{
LU = A.Create_ILU_Decomposition();
}
