public DiagonalPreconditioner(CSlRMatrix A)
{
diag = new Vector(A.Row);
for (int i = 0; i < A.Row; i++)
{
diag.Elem[i] = A.di[i];
}
}
public static double RelativeDiscrepancy(CSlRMatrix A, Vector x, Vector f)
{
var q = new Vector(A.Row);
A.MultMtV(x, q);
for (int i = 0; i < x.Size; i++)
{
q.Elem[i] -= f.Elem[i];
}
return(Math.Sqrt((q * q) / (f * f)));
}
//-------------------------------------------------------------------------------------------------
//операция неполного LU-разложения в формате CSlR
public CSlRMatrix ILU_CSlR()
{
var matrix = new CSlRMatrix();
matrix.Column = Column;
matrix.Row = Row;
matrix.iptr = iptr;
matrix.jptr = jptr;
int nAutr = autr.Length;
matrix.autr = new double[nAutr];
matrix.altr = new double[nAutr];
matrix.di = new double[Column];
for (int i = 0; i < nAutr; i++)
{
matrix.altr[i] = altr[i];
matrix.autr[i] = autr[i];
}
for (int i = 0; i < Column; i++)
{
matrix.di[i] = di[i];
}
for (int i = 1; i < Column; 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]] - 2; 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);
}
public IncompleteLUPreconditioner(CSlRMatrix A)
{
ILU = A.ILU_CSlR();
}
public Vector StartSolver(CSlRMatrix A, Vector F, Preconditioner.PreconditionerType prec)
{
switch (prec)
{
case ComMethods.Preconditioner.PreconditionerType.Diagonal:
{
Preconditioner = new DiagonalPreconditioner(A);
break;
}
case ComMethods.Preconditioner.PreconditionerType.ILU:
{
Preconditioner = new IncompleteLUPreconditioner(A);
break;
}
}
int n = A.Row;
var res = new Vector(n);
// auxiliary vectors
var r = new Vector(n);
var p = new Vector(n);
var vec = new Vector(n);
// methods parameters
double alpha, beta, sc1, sc2;
bool flag = true;
// residual norm
double rNorm = 0;
// residual: r = F - Ax
A.MultMtV(res, vec);
for (int i = 0; i < n; i++)
{
r.Elem[i] = F.Elem[i] - vec.Elem[i];
}
// search vector: Mp = r
Preconditioner.StartPreconditioner(r, p);
// iterative process
while (flag && Iter < MaxIter)
{
sc1 = p * r; // (M^(-1) * r; r)
A.MultMtV(p, vec); // vec = A * p
sc2 = vec * p; // sc2 = (A * p; p)
alpha = sc1 / sc2; // linear search coefficient
// result vector & residual
for (int i = 0; i < n; i++)
{
res.Elem[i] += alpha * p.Elem[i];
r.Elem[i] -= alpha * vec.Elem[i];
}
Preconditioner.StartPreconditioner(r, vec); // vec := M^(-1) * r
sc2 = vec * r; // (M^(-1) * r; r)
beta = sc2 / sc1; // coefficient in choosing a search direction
rNorm = r.Normal(); // residual norm
if (rNorm < 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("\n{0, -20} {1, 20:E}", Iter, rNorm);
}
Console.WriteLine("Iter: {0, -20} \nNorm: {1, 20:E}", Iter, rNorm);
return(res);
}
public Vector StartSolver(CSlRMatrix A, Vector F, Preconditioner.PreconditionerType prec)
{
switch (prec)
{
case ComMethods.Preconditioner.PreconditionerType.Diagonal:
{
Preconditioner = new DiagonalPreconditioner(A);
break;
}
case ComMethods.Preconditioner.PreconditionerType.ILU:
{
Preconditioner = new IncompleteLUPreconditioner(A);
break;
}
}
int n = A.Row;
var res = new Vector(n);
// auxiliary vectors
var r = new Vector(n); // ordinary residual
var r_ = new Vector(n); // new residual
var p = new Vector(n);
var p_ = new Vector(n);
var vec = new Vector(n);
var vec_ = new Vector(n);
var vec_help = new Vector(n);
// methods parameters
double alpha, beta, sc1, sc2;
bool flag = true;
// residual norm
double rNorm = 0;
// residual: r = M^-1 * (F - Ax)
A.MultMtV(res, vec_help);
for (int i = 0; i < n; i++)
{
vec_help.Elem[i] = F.Elem[i] - vec_help.Elem[i];
}
Preconditioner.StartPreconditioner(vec_help, r);
for (int i = 0; i < n; i++)
{
res.Elem[i] = 0.0;
p.Elem[i] = r_.Elem[i] = p_.Elem[i] = r.Elem[i];
}
while (flag && Iter < MaxIter)
{
sc1 = r * r_; // scalar product sc1 = (r; r_)
A.MultMV(p, vec_help); // vec_help = A * p
// vec = M^(-1) * A * p
Preconditioner.StartPreconditioner(vec_help, vec);
sc2 = vec * p_; // (M^(-1) * A * p; p_)
alpha = sc1 / sc2; // linear search coefficient
// result vector & residual
for (int i = 0; i < n; i++)
{
res.Elem[i] += alpha * p.Elem[i];
r.Elem[i] -= alpha * vec.Elem[i];
}
// p_ into the preconditioned system
Preconditioner.StartTrPreconditioner(p_, vec_help);
A.MultMtV(vec_help, vec_); // vec_ = A_t * M^(-t) * p_
// new residual r_
for (int i = 0; i < n; i++)
{
r_.Elem[i] -= alpha * vec_.Elem[i];
}
sc2 = r * r_; // (r_new; (r_)_new)
beta = sc2 / sc1; // coefficient in choosing a search direction
rNorm = r.Normal(); // ordinary residual norm
if (rNorm < Eps)
{
flag = false;
}
// new search directions
if (flag)
{
for (int i = 0; i < n; i++)
{
p.Elem[i] = r.Elem[i] + beta * p.Elem[i];
p_.Elem[i] = r_.Elem[i] + beta * p_.Elem[i];
}
}
Iter++;
// Console.WriteLine("\n{0, -20} {1, 20:E}", Iter, rNorm);
}
Console.WriteLine("Iter: {0, -20} \nNorm: {0, 20:E}", Iter, rNorm);
return(res);
}