public override Vector UtMult(Vector x, bool UseDiagonal)
{
if (n == x.Size)
{
Vector result = new Vector(n);
result.Nullify();
if (UseDiagonal)
{
result[0] = di[0] * x[0];
// Обработка части al, где есть 0
for (int i = 1; i < bandWidth; i++)// обрабатываем i строку
{
for (int j = bandWidth - i; j < bandWidth; j++)
result[i] += au[i][j] * x[j + i - bandWidth];
result[i] += di[i] * x[i];
}
//Обработка без 0
for (int i = bandWidth; i < n; i++)
{
for (int j = i - bandWidth; j < i; j++)
result[i] += au[i][j - i + bandWidth] * x[j];
result[i] += di[i] * x[i];
}
}
else
{
// Обработка части al, где есть 0
for (int i = 1; i < bandWidth; i++)// обрабатываем i строку
for (int j = bandWidth - i; j < bandWidth; j++)
result[i] += au[i][j] * x[j + i - bandWidth];
//Обработка без 0
for (int i = bandWidth; i < n; i++)
for (int j = i - bandWidth; j < i; j++)
result[i] += au[i][j - i + bandWidth] * x[j];
}
return result;
}
else
throw new Exception("Ленточный формат: Несовпадение размерностей матрицы и вектора при умножении верхнего(T) треугольника");
}
public override Vector TMultiply(Vector x)
{
Vector result = new Vector(n);
result.Nullify();
if (n == x.Size)
{
// Верхний треугольник
// Обработка части au, где есть 0
for (int i = 1; i < bandWidth; i++)// обрабатываем i строку
for (int j = bandWidth - i; j < bandWidth; j++)
result[i] += au[i][j] * x[j + i - bandWidth];
//Обработка без 0
for (int i = bandWidth; i < n; i++)
for (int j = i - bandWidth; j < i; j++)
result[i] += au[i][j - i + bandWidth] * x[j];
//Диагональ
for (int i = 0; i < n; i++)
result[i] += di[i] * x[i];
//Нижний треугольник
for (int j = 0; j < bandWidth; j++)
{
for (int i = bandWidth - j; i < n; i++)
result[i - bandWidth + j] += al[i][j] * x[i];
}
return result;
}
throw new Exception("Ленточный формат: Несовпадение размерностей матрицы и вектора при умножении(T)");
}
public override Vector UMult(Vector x, bool UseDiagonal)
{
if (n == x.Size)
{
Vector result = new Vector(n);
result.Nullify();
for (int j = 0; j < bandWidth; j++)
{
for (int i = bandWidth - j; i < n; i++)
result[i - bandWidth + j] += au[i][j] * x[i];
}
if (UseDiagonal)
{
for (int i = 0; i < n; i++)
result[i] += di[i] * x[i];
}
return result;
}
else
throw new Exception("Ленточный формат: Несовпадение размерностей матрицы и вектора при умножении верхнего треугольника");
}
public override Vector Solve(IPreconditioner matrix, Vector rightPart, Vector initialSolution,
ILogger logger, ISolverLogger solverLogger, ISolverParametrs solverParametrs)
{
GMRESParameters GMRESParameters = solverParametrs as GMRESParameters;
if (GMRESParameters != null)
{
Vector[] V, H;
Vector residual, x, d, z, w, tmp;
bool continueCalculations;
double epsilon = GMRESParameters.Epsilon;
int m = GMRESParameters.M;
int maxIterations = GMRESParameters.MaxIterations;
int n = rightPart.Size;
x = initialSolution;
residual = rightPart - matrix.SourceMatrix.Multiply(x);
residual = matrix.SSolve(residual);
double rightPartNorm = matrix.SSolve(rightPart).Norm();
double residualNorm = residual.Norm();
if (System.Double.IsInfinity(residualNorm / rightPartNorm))
{
logger.Error("Residual is infinity. It is impossible to solve this SLAE by GMRES.");
return x;
}
if (System.Double.IsNaN(residualNorm / rightPartNorm))
{
logger.Error("Residual is NaN. It is impossible to solve this SLAE by GMRES.");
return x;
}
x = matrix.QMultiply(initialSolution);
V = new Vector[m];
for (int i = 0; i < m; i++)
V[i] = new Vector(n);
H = new Vector[m];
for (int i = 0; i < m; i++)
H[i] = new Vector(m + 1);
d = new Vector(m + 1);
for (int k = 1; k <= maxIterations && residualNorm / rightPartNorm > epsilon; k++)
{
d.Nullify();
V[0] = residual * (1.0 / residualNorm);
continueCalculations = true;
for (int j = 1; j <= m && continueCalculations; j++)
{
tmp = matrix.QSolve(V[j - 1]);
w = matrix.SSolve(matrix.SourceMatrix.Multiply(tmp));
for (int l = 1; l <= j; l++)
{
H[j - 1][l - 1] = V[l - 1] * w;
w = w - V[l - 1] * H[j - 1][l - 1];
}
H[j - 1][j] = w.Norm();
if (Math.Abs(H[j - 1][j]) < 1e-10)
{
m = j;
continueCalculations = false;
}
else
{
if(j != m)
V[j] = w * (1.0 / H[j - 1][j]);
}
}
d[0] = residualNorm;
z = solveMinSqrProblem(d, H, m);
x = x + multiplyMatrixVector(z, V);
tmp = rightPart - matrix.SourceMatrix.Multiply(matrix.QSolve(x));
residual = matrix.SSolve(tmp);
residualNorm = residual.Norm();
if (System.Double.IsInfinity(residualNorm / rightPartNorm))
{
logger.Error("Residual is infinity. It is impossible to solve this SLAE by GMRES.");
return x;
}
if (System.Double.IsNaN(residualNorm / rightPartNorm))
{
logger.Error("Residual is NaN. It is impossible to solve this SLAE by GMRES.");
return x;
}
solverLogger.AddIterationInfo(k, residualNorm / rightPartNorm);
}
return matrix.QSolve(x);
}
else {
logger.Error("Incorrect " + solverParametrs.GetType().Name.ToString() + " as a SolverParametrs in GMRES");
throw new Exception("Incorrect " + solverParametrs.GetType().Name.ToString() + " as a SolverParametrs in GMRES");
}
}
Vector multiplyMatrixVector(Vector vector, Vector[] matrix)
{
int n_lines = matrix[0].Size;
int n_columns = matrix.Length;
Vector result = new Vector(n_lines);
result.Nullify();
if(vector.Size == n_columns)
{
for (int j = 0; j < n_columns; j++)
for (int i = 0; i < n_lines; i++)
result[i] += matrix[j][i] * vector[j];
}
else
throw new Exception("GMRES: Несовпадение длины вектора и числа столбцов матрицы");
return result;
}
public override Vector UtMult(Vector x, bool UseDiagonal)
{
if (di.Length == x.Size)
{
Vector result = new Vector(di.Length);
result.Nullify();
for (int j = 0; j < shift_u.Length; j++)
for (int i = shift_u[j]; i < di.Length; i++)
result[i] += au[i][j] * x[i - shift_u[j]];
if (UseDiagonal)
for (int i = 0; i < di.Length; i++)
result[i] += di[i] * x[i];
return result;
}
else
throw new Exception("Диагональный формат: Несовпадение размерностей матрицы и вектора в умножении верхнего(T) треугольника");
}
public override Vector TMultiply(Vector x)
{
if (di.Length == x.Size)
{
Vector result = new Vector(di.Length);
result.Nullify();
// Верхний треугольник
for (int j = 0; j < shift_u.Length; j++)
for (int i = shift_u[j]; i < di.Length; i++)
result[i] += au[i][j] * x[i - shift_u[j]];
// Диагональ
for (int i = 0; i < di.Length; i++)
result[i] += di[i] * x[i];
// Нижний треугольник
for (int j = 0; j < shift_l.Length; j++)
for (int i = shift_l[j]; i < di.Length; i++)
result[i - shift_l[j]] += al[j][i] * x[i];
return result;
}
else
throw new Exception("Диагональный формат: Несовпадение размерностей матрицы и вектора в умножении (T)");
}
public override Vector Solve(IPreconditioner matrix, Vector rightPart, Vector initialSolution, ILogger logger, ISolverLogger solverLogger, ISolverParametrs solverParametrs)
{
BCGStabParametrs ConGradParametrs = solverParametrs as BCGStabParametrs;
if (ConGradParametrs == null)
{
logger.Error("Incorrect " + solverParametrs.GetType().Name.ToString() + " as a SolverParametrs in BSGStab");
throw new Exception("Incorrect " + solverParametrs.GetType().Name.ToString() + " as a SolverParametrs in BSGSTab");
}
else
{
int oIter = 0;
double nPi, oPi, alpha, w, oNev, bNev, betta;
oPi = alpha = w = 1;
int size = rightPart.Size;
Vector x, r, rTab, s, t, z, sqt, y;
Vector v = new Vector(size);
Vector p = new Vector(size);
v.Nullify();
p.Nullify();
x = initialSolution;
r = rightPart - matrix.SourceMatrix.Multiply(x);
rTab = r;
bNev = rightPart.Norm();
oNev = r.Norm() / bNev;
solverLogger.AddIterationInfo(oIter, oNev);//logger
if (System.Double.IsInfinity(oNev))
{
logger.Error("Residual is infinity. It is impossible to solve this SLAE by BSG Stab.");
return x;
}
if (System.Double.IsNaN(oNev))
{
logger.Error("Residual is NaN. It is impossible to solve this SLAE by BSG Stab.");
return x;
}
while (oIter < ConGradParametrs.MaxIterations && oNev > ConGradParametrs.Epsilon)
{
nPi = rTab * r;
betta = (nPi / oPi) * (alpha / w);
p = r + (p - v * w) * betta;
y= matrix.QSolve(matrix.SSolve(p));
v = matrix.SourceMatrix.Multiply(y);
alpha = nPi / (rTab * v);
x = x + y * alpha;//УТОЧНИТЬ!!!!!!!!!!!!!!!
s = r - v * alpha;
if (s.Norm() / bNev < ConGradParametrs.Epsilon) return x;
z = matrix.QSolve(matrix.SSolve(s));
t = matrix.SourceMatrix.Multiply(z);
sqt = matrix.QSolve(matrix.SSolve(t));
w = (z * sqt) / (sqt * sqt);
x = x + z * w;//УТОЧНИТЬ!!!!!!!!!!!!!!!!!!!
r = s - t * w;
oPi = nPi;
oIter++;
oNev = r.Norm() / bNev;
if (System.Double.IsInfinity(oNev))
{
logger.Error("Residual is infinity. It is impossible to solve this SLAE by BSG Stab.");
return x;
}
if (System.Double.IsNaN(oNev))
{
logger.Error("Residual is NaN. It is impossible to solve this SLAE by BSG Stab.");
return x;
}
solverLogger.AddIterationInfo(oIter, oNev);//logger
}
return x;
}
}
