private static void SelectMainElement(SquareMatrix matrix, VectorColumn freeElems, int pos)
{
var maxrow = pos;
var size = matrix.Size;
for (int i = pos; i < size; i++)
{
if (Abs(matrix[i, pos]) > Abs(matrix[maxrow, pos]))
{
maxrow = i;
}
}
if (maxrow == pos)
{
return;
}
var temprow = new double[size + 1];
for (int i = 0; i < size; i++)
{
temprow[i] = matrix[pos, i];
matrix[pos, i] = matrix[maxrow, i];
matrix[maxrow, i] = temprow[i];
}
temprow[size] = freeElems[pos];
freeElems[pos] = freeElems[maxrow];
freeElems[maxrow] = temprow[size];
return;
}
public static VectorColumn Calculate(SquareMatrix matrix, VectorColumn freeElems)
{
if (matrix.Size != freeElems.Length)
{
throw new Exception(
"In GaussSolve.Calculate: " +
"Size of matrix isn't equal size of free element's vector.");
}
var det = matrix.GetDeterminant();
if (det == 0)
{
throw new Exception("Determinant of matrix is 0. The system can't be solved.");
}
if (Abs(det) < 1)
{
Console.WriteLine("The system is poorly conditioned, solutions can not be calculated accurately.");
}
var _matrix = new SquareMatrix(matrix.ToDoubleArray());
var _freeElems = new VectorColumn(freeElems.ToDoubleArray());
ToTriangle(_matrix, _freeElems);
return(Reverce(_matrix, _freeElems));
}
public static VectorColumn CalculateClassic(SquareMatrix matrix, VectorColumn freeElems, double allowResidual)
{
if (matrix.Size != freeElems.Length)
{
throw new Exception(
"In SimpleIteration.CalculateClassic: " +
"Size of matrix isn't equal size of free element's vector.");
}
var det = matrix.GetDeterminant();
if (det == 0)
{
throw new Exception("Determinant of matrix is 0. The system can't be solved.");
}
var invMatrix = matrix.GetInvertibleMatrix();
var deltaMatrix = GetDeltaMatrix(matrix.Size);
var D = invMatrix - deltaMatrix;
var X = new VectorColumn(freeElems.Length);
var alpha = deltaMatrix * matrix;
var beta = D * freeElems;
while (MaxResidual(matrix, freeElems, X) > allowResidual)
{
X = alpha * X + beta;
}
return(X);
}
private static LSystem BuildSystem(Matrix mainEquations, BoundaryConditions boundaryConditions)
{
if (boundaryConditions.first.Length != X.Length + 1 ||
boundaryConditions.second.Length != X.Length + 1 ||
mainEquations.Rows != X.Length - 2 ||
mainEquations.Columns != X.Length + 1)
{
throw new ArgumentException();
}
SquareMatrix matrix = new SquareMatrix(X.Length);
VectorColumn freeElems = new VectorColumn(X.Length);
for (int row = 1; row < X.Length - 1; row++)
{
for (int column = 0; column < X.Length; column++)
{
matrix[row, column] = mainEquations[row - 1, column];
}
freeElems[row] = mainEquations[row - 1, X.Length];
}
for (int column = 0; column < X.Length; column++)
{
matrix[0, column] = boundaryConditions.first[column];
matrix[X.Length - 1, column] = boundaryConditions.second[column];
}
freeElems[0] = boundaryConditions.first[X.Length];
freeElems[X.Length - 1] = boundaryConditions.second[X.Length];
return(new LSystem(matrix, freeElems));
}
private static double Max(VectorColumn vector)
{
var max = Math.Abs(vector[0]);
for (int i = 0; i < vector.Length; i++)
{
if (Math.Abs(vector[i]) > max)
{
max = Math.Abs(vector[i]);
}
}
return(max);
}
private static PowerSeries[] BuildSpline_M_i(VectorColumn M)
{
PowerSeries[] spline = new PowerSeries[X.Length - 1];
for (int i = 0; i < X.Length - 1; i++)
{
spline[i] =
Y[i] * (1 - T(i))
+ Y[i + 1] * T(i)
- H(i) * H(i) * T(i) / 6 * (1 - T(i))
* ((2 - T(i)) * M[i] + (1 + T(i)) * M[i + 1]);
}
return(spline);
}
private static PowerSeries[] BuildSpline_m_i(VectorColumn m)
{
PowerSeries[] spline = new PowerSeries[X.Length - 1];
for (int i = 0; i < X.Length - 1; i++)
{
spline[i] =
Y[i] * (1 - T(i)) * (1 - T(i)) * (1 + 2 * T(i))
+ Y[i + 1] * T(i) * T(i) * (3 - 2 * T(i))
+ m[i] * H(i) * T(i) * (1 - T(i)) * (1 - T(i))
- m[i + 1] * H(i) * T(i) * T(i) * (1 - T(i));
}
return(spline);
}
private static VectorColumn Reverce(SquareMatrix triangleMatrix, VectorColumn freeElems)
{
var size = triangleMatrix.Size;
var solutions = new VectorColumn(size);
for (int i = size - 1; i >= 0; i--)
{
double accum = 0.0;
for (int j = size - 1; j > i; j--)
{
accum += triangleMatrix[i, j] * solutions[j];
}
solutions[i] = (freeElems[i] - accum) / triangleMatrix[i, i];
}
return(solutions);
}
public static Spline Calculate_M_i(double[] x, double[] y)
{
if (x.Length != y.Length)
{
throw new ArgumentException("y", "Array of function's values must has same length as array of arguments.");
}
X = x;
Y = y;
Matrix mainEquations = PrepareEquations_M_i();
BoundaryConditions boundaryConditions = GetBoundaryConditions_M_i();
LSystem system = BuildSystem(mainEquations, boundaryConditions);
VectorColumn solutions = Tridiagonal.Calculate(system);
return(new Spline(BuildSpline_M_i(solutions), X));
}
public static VectorColumn CalculateZeidel(SquareMatrix smatrix, VectorColumn freeElems, double allowResidual)
{
if (smatrix.Size != freeElems.Length)
{
throw new Exception(
"In SimpleIteration.CalculateZeidel: " +
"Size of matrix isn't equal size of free element's vector.");
}
var det = smatrix.GetDeterminant();
if (det == 0)
{
throw new Exception("Determinant of matrix is 0. The system can't be solved.");
}
var invMatrix = smatrix.GetInvertibleMatrix();
var deltaMatrix = GetDeltaMatrix(smatrix.Size);
var D = invMatrix - deltaMatrix;
var X = new VectorColumn(freeElems.Length);
var alpha = deltaMatrix * smatrix;
var beta = D * freeElems;
while (MaxResidual(smatrix, freeElems, X) > allowResidual)
{
for (int i = 0; i < X.Length; i++)
{
var buf = 0.0;
for (int j = 0; j < X.Length; j++)
{
buf += alpha[i, j] * X[j];
}
X[i] = buf + beta[i];
}
}
return(X);
}
private static void ToTriangle(SquareMatrix matrix, VectorColumn freeElems)
{
var size = matrix.Size;
for (int i = 0; i < size - 1; i++)
{
SelectMainElement(matrix, freeElems, i);
Parallel.For(i + 1, size, Matrix.options, j => {
if (matrix[j, i] == 0)
{
return;
}
var cf = matrix[j, i] / matrix[i, i];
for (int k = 0; k < size; k++)
{
matrix[j, k] -= matrix[i, k] * cf;
}
freeElems[j] -= freeElems[i] * cf;
});
}
}
private static double MaxResidual(Matrix matrix, VectorColumn freeElems, VectorColumn solutions) => Max(new VectorColumn((matrix * solutions - freeElems).ToDoubleArray()));
public static VectorColumn Calculate(SquareMatrix matrix, VectorColumn freeElems)
{
if (matrix.Size != freeElems.Length)
{
throw new Exception(
"In Tridiagonal.Calculate: " +
"Size of matrix isn't equal size of free element's vector.");
}
var n = freeElems.Length;
var a = new VectorColumn(n);
var b = new VectorColumn(n);
var c = new VectorColumn(n);
var d = new VectorColumn(n);
for (int i = 0; i < n; i++)
{
if (i > 0)
{
a[i] = matrix[i, i - 1];
}
b[i] = -matrix[i, i];
if (i < n - 1)
{
c[i] = matrix[i, i + 1];
}
d[i] = freeElems[i];
}
for (int i = 0; i < n; i++)
{
if (Abs(b[i]) < Abs(a[i]) + Abs(c[i]))
{
throw new Exception(
"In Tridiagonal.Calculate: " +
"There is no diagonal domination, the system can't be solved.");
}
}
var xi = new VectorColumn(n + 1);
var eta = new VectorColumn(n + 1);
for (int i = 0; i < n; i++)
{
xi[i + 1] = c[i] / (b[i] - a[i] * xi[i]);
eta[i + 1] = (a[i] * eta[i] - d[i]) / (b[i] - a[i] * xi[i]);
}
var solutions = new VectorColumn(n + 1);
for (int i = n - 1; i >= 0; i--)
{
solutions[i] = xi[i + 1] * solutions[i + 1] + eta[i + 1];
}
var _solutions = new VectorColumn(n);
for (int i = 0; i < n; i++)
{
_solutions[i] = solutions[i];
}
return(_solutions);
}
