// vres =v1+cv2;
public static Interface.IVector Add(Interface.IVector v1, Interface.IVector v2, double c)
{
Vector result = new Vector(v1.Size);
for (int i = 0; i < v2.Size; i++)
{
v1[i] += v2[i] * c;
}
return result;
}
public void ReadFromFile(out IMatrix A, out Vector b, out Vector x_init)
{
// Не хватает проверки path
using (System.IO.StreamReader file = new System.IO.StreamReader(path))
{
var st = file.ReadToEnd().Replace('.',',').Split(new char[] { '\n', ' ', '\t', '\r' },
StringSplitOptions.RemoveEmptyEntries);
int n, m;
if (!int.TryParse(st[0], out n))
throw new Exception("Bad file format");
n = int.Parse(st[0]);
int[] ia = new int[n + 1];
double[] d = new double[n];
double[] rightPart = new double[n];
double[] x0 = new double[n];
long offset = 1;
for (int i = 0; i < n + 1; i++, offset++)
ia[i] = int.Parse(st[offset]);
m = ia[n] - 1;
int[] ja = new int[m];
double[] al = new double[m];
double[] au = new double[m];
for (int i = 0; i < m; i++, offset++)
ja[i] = int.Parse(st[offset]);
if (ia[0] != 0)
{
for (int i = 0; i < n + 1; i++)
ia[i]--;
for (int i = 0; i < m; i++)
ja[i]--;
}
for (int i = 0; i < m; i++,offset++)
al[i] = double.Parse(st[offset]);
for (int i = 0; i < m; i++, offset++)
au[i] = double.Parse(st[offset]);
for (int i = 0; i < n; i++,offset++)
d[i] = double.Parse(st[offset]);
for (int i = 0; i < n; i++,offset++)
rightPart[i] = double.Parse(st[offset]);
for (int i = 0; i < n; i++, offset++)
x0[i] = double.Parse(st[offset]);
A = new RowColumnSparseMatrix(n, ia, ja, al, au, d);
b = new Vector(rightPart);
x_init = new Vector(x0);
}
}
public CoordinateMatrix(int _size, int[] _iaddr, int[] _jaddr, double[] _elem)
{
size = _size;
iaddr = _iaddr;
jaddr = _jaddr;
elem = _elem;
di = new Vector(size);
for (int j = 0; j < size; j++ )
for (int i = 0; i < elem.Length; i++)
{
if (iaddr[i] == jaddr[i]) di[j] = elem[i];
}
}
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_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 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;
}
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 void ReadFromFileCoordinate(out IMatrix A, out Vector b, out Vector x_init)
{
using (System.IO.StreamReader file = new System.IO.StreamReader(path))
{
var st = file.ReadToEnd().Replace('.',',').Split(new char[] { '\n', ' ', '\t', '\r' },
StringSplitOptions.RemoveEmptyEntries);
int n, m;
if (!int.TryParse(st[0], out n))
throw new Exception("Bad file format");
m = int.Parse(st[0]);
double[] elem = new double[m];
int[] iaddr = new int[m];
int[] jaddr = new int[m];
long offset = 1;
for (int i = 0; i < m; i++, offset++)
{
iaddr[i] = int.Parse(st[offset]);
offset++;
jaddr[i] = int.Parse(st[offset]);
offset++;
elem[i] = double.Parse(st[offset]);
}
if (iaddr[0] != 0)
{
for (int i = 0; i < m; i++)
iaddr[i]--;
for (int i = 0; i < m; i++)
jaddr[i]--;
}
n = int.Parse(st[offset]);
double[] rightPart = new double[n];
double[] x0 = new double[n];
offset++;
for (int i = 0; i < n; i++, offset++)
rightPart[i] = double.Parse(st[offset]);
for (int i = 0; i < n; i++ /*offset++*/)
x0[i] = 0;/*double.Parse(st[offset]);*/
A = new CoordinateMatrix(n, iaddr, jaddr, elem);
b = new Vector(rightPart);
x_init = new Vector(x0);
}
}
public void ReadFromFileDense(out IMatrix A, out Vector b, out Vector x_init)
{
using (System.IO.StreamReader file = new System.IO.StreamReader(path))
{
var st = file.ReadToEnd().Replace('.', ',').Split(new char[] { '\n', ' ', '\t', '\r' },
StringSplitOptions.RemoveEmptyEntries);
int n;
if (!int.TryParse(st[0], out n))
throw new Exception("Bad file format");
n = int.Parse(st[0]);
double[,] a = new double[n,n];
double[] rightPart = new double[n];
double[] x0 = new double[n];
long offset = 1;
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++, offset++)
a[i,j] = double.Parse(st[offset]);
for (int i = 0; i < n; i++, offset++)
rightPart[i] = double.Parse(st[offset]);
for (int i = 0; i < n; i++, offset++)
x0[i] = double.Parse(st[offset]);
A = new DenseMatrix(n, a);
b = new Vector(rightPart);
x_init = new Vector(x0);
}
}
public RowColumnSparseMatrix(int sz, int[] _ia, int[] _ja,
double[] _al, double[] _au, double[] _di)
{
size = sz;
ia = _ia; ja = _ja; al = new Vector(_al); di = new Vector(_di);
au = new Vector(_au);
}
public ProfileMatrix(int sz, int[] _ial, int[] _iau,
double[] _al, double[] _au, double[] _di)
{
size = sz;
ial = _ial; iau = _iau; al = new Vector(_al);
au = new Vector(_au); di = new Vector(_di);
}
public DenseMatrix(int sz, double[,] _a)
{
size = sz;
a = new double[size, size];
a = _a;
di = new Vector(size);
for (int i=0; i< size; i++)
{
di[i] = a[i, i];
}
}