public override IVector Solve(IMatrix A, IVector b, IVector x0)
{
IVector x_prev= new Vector(b.Size);
IVector result = new Vector(b.Size);
IVector difference = new Vector(b.Size);//f-Ax
double residual1, residual2;
double residual_prev;//для проверки изменения невязки
residual =1;
residual1 = b.Norm;
x_prev.Equalize(x0);
for (int i = 0; i < b.Size; i++)
if (Math.Abs(A.Diagonal[i]) < EPS_NULL)
throw new Exception("Divide by NULL in GaussZeidel_solver: diagonal");
residual_prev = 2 * residual;
for (iteration = 0; iteration < maxIteration && residual > minResidual && residual_prev > residual; iteration++)
{
difference.Equalize(b);
//result.Nullify();
for (int i = 0; i < b.Size; i++)
{
for (int j = 0; j < i; j++)
difference[i] -= A[i,j]*result[j];
for (int j = i; j < b.Size; j++)
{
difference[i] -= A[i,j]*x_prev[j];
}
difference[i] *= (relaxation/A.Diagonal[i]);
result[i] = x_prev[i] + difference[i];
}
difference.Equalize(b);
difference.Add(MatrixAssistant.multMatrixVector(A, result), -1);
residual2 = difference.Norm;
residual_prev = residual;
residual = residual2 / residual1;
//Debugger.DebugSolver(iteration, residual, result);
x_prev.Equalize(result);
}
return result;
}
public override IVector Solve(IMatrix A, IVector b, IVector x0)
{
IVector x_prev= new Vector(b.Size);
IVector result = new Vector(b.Size);
IVector difference = new Vector(b.Size);//f-Ax
double residual1, residual2;
double residual_prev;//для проверки изменения невязки
residual =1;
residual1 = b.Norm;
x_prev.Equalize(x0);
for (int i = 0; i < b.Size; i++)
if (Math.Abs(A.Diagonal[i]) < EPS_NULL)
throw new Exception("Divide by NULL in GaussZeidel_solver: diagonal");
residual_prev = 2 * residual;
for (iteration = 0; iteration < maxIteration && residual > minResidual && residual_prev > residual; iteration++)
{
difference.Equalize(b);
difference.Add(MatrixAssistant.multMatrixUpperVector(A,x_prev),-1);
for (int i = 0; i < b.Size; i++)
{
double sum = 0;
IVector Lx = MatrixAssistant.multMatrixLowerVector(A, result, i);
for (int ii = 0; ii < Lx.Size; ii++)
sum += Lx[ii];
difference[i] -= sum;
result[i] = relaxation*difference[i]/A.Diagonal[i];
}
difference.Equalize(b);
difference.Add(MatrixAssistant.multMatrixVector(A, result), -1);
residual2 = difference.Norm;
residual_prev = residual;
residual = residual2 / residual1;
Debugger.DebugSolver(iteration, residual, result);
x_prev.Equalize(result);
}
return result;
}
public override IVector Solve(IMatrix A, IVector b, IVector x0)
{
IVector result = new Vector(b.Size);
IVector difference = new Vector(b.Size);//f-Ax
double residual1, residual2;
double residual_prev;//для проверки изменения невязки
residual = 1;
residual1 = b.Norm;
result.Equalize(x0);
difference.Equalize(b);
difference.Add(MatrixAssistant.multMatrixVector(A, result), -1);
for (int i = 0; i < b.Size; i++)
if (Math.Abs(A.Diagonal[i]) < EPS_NULL)
throw new Exception("Divide by NULL in Jacobi_solver: diagonal");
residual_prev = 2 * residual;
for (iteration = 0; iteration < maxIteration && residual > minResidual && residual_prev > residual; iteration++)
{
for (int i = 0; i < b.Size; i++)
{
difference[i] = difference[i] / A.Diagonal[i];
}
result.Add(difference, relaxation);
difference.Equalize(b);
difference.Add(MatrixAssistant.multMatrixVector(A, result), -1);
residual2 = difference.Norm;
if (Math.Abs(residual1) < EPS_NULL)
throw new Exception("Divide by NULL in Jacobi_solver: residual1");
residual_prev = residual;
residual = residual2 / residual1;
//Debugger.DebugSolver(iteration, residual, result);
}
return result;
}
public override IVector Solve(IMatrix A, IVector b, IVector x0)
{
IVector result = new Vector(b.Size);
IVector r = new Vector(b.Size);
IVector p = new Vector(b.Size);
IVector z = new Vector(b.Size);
double alpha, betta;
double p_scal;
r.Equalize(b);
result.Equalize(x0);
r.Add(MatrixAssistant.multMatrixVector(A, result), -1);
z.Equalize(r);
p.Equalize(MatrixAssistant.multMatrixVector(A, z));
p_scal = VectorAssistant.multVector(p, p);
residual = VectorAssistant.multVector(r, r);
residual = Math.Sqrt(VectorAssistant.multVector(r, r)) / b.Norm;
for (iteration = 1; iteration <= maxIteration && residual > minResidual; iteration++)
{
alpha = VectorAssistant.multVector(p, r) / p_scal;
result.Add(z, alpha);
r.Add(p, -alpha);
betta = -VectorAssistant.multVector(p, MatrixAssistant.multMatrixVector(A, r)) / p_scal;
z = VectorAssistant.multScalar(betta, z);
z.Add(r, 1);
p = VectorAssistant.multScalar(betta, p);
p.Add(MatrixAssistant.multMatrixVector(A, r), 1);
/* residual -= alpha * alpha * p_scal;
if (residual < 0) //она всё равно отрицательная
{
residual += alpha * alpha * p_scal;
return result;
}
if (alpha * alpha * p_scal < residual * 10E-5)
return result;
*/
p_scal = VectorAssistant.multVector(p, p);
residual = Math.Sqrt(VectorAssistant.multVector(r, r)) / b.Norm;
Debugger.DebugSolver(iteration, residual, result);
}
return result;
}
public override IVector Solve(IMatrix A, IVector b, IVector x0)
{
IVector x = new Vector(b.Size);
IVector r = new Vector(b.Size);
IVector z = new Vector(b.Size);
// Check errors
double Azz, rr;
double norm;
norm = b.Norm;
if (norm < EPS_NULL)
{
x.Nullify();
return x;
}
x.Equalize(x0);
r.Equalize(b);
r.Add(MatrixAssistant.multMatrixVector(A,x),-1);
z.Equalize(r);
alpha = 1000;
for (iteration = 0; iteration < maxIteration && residual > minResidual; iteration++ )
{
rr = VectorAssistant.multVector(r, r);
var Az = MatrixAssistant.multMatrixVector(A, z);
Azz = VectorAssistant.multVector(Az, z);
if (Math.Abs(Azz) < EPS_NULL) return x;
alpha = rr / Azz;
x.Add(z,alpha);
r.Add(Az, -alpha);
betta = VectorAssistant.multVector(r, r) / rr;
z=VectorAssistant.multScalar(z,betta);
z.Add(r, 1);
residual = r.Norm / norm;
}
return x;
}
