public void Spline4_Experiment()
{
//setup
int N = 32;
int n = 16;
double a = 0d;
double b = 1d;
int index = 0;
Vector grid_h = Vector.CreateUniformGrid(N, a, b);
Vector grid_2h = Vector.CreateUniformGrid(n, a, b);
BasisSpline spline_h = new BasisSpline(4, N, a, b);
BasisSpline spline_2h = spline_h.GetBasisSpline_Down();
Matrix A = spline_h.GetMatrix();
Vector z;
Vector c;
//run
for (index = 0; index < n; index++)
{
z = spline_2h.GetVectorBasis(grid_h, index);
c = Solver.BCGSTAB(A, z, 0.0000000001d);
Console.WriteLine(index + ") " + c.ToString());
}
//Console.WriteLine(A.ToString());
Console.WriteLine("index = " + index);
}
public void FindMatrixTest()
{
//setup
int N = 17;
int n = 10;
double a = 0d;
double b = 1d;
Vector grid_h = Vector.CreateUniformGrid(N, a, b);
Vector grid_2h = Vector.CreateUniformGrid(n, a, b);
BasisSpline spline_h = new BasisSpline(4, N, a, b);
BasisSpline spline_2h = spline_h.GetBasisSpline_Down();
Matrix B = spline_2h.GetMatrix();
Matrix BR = new Matrix(n, n);
for (int i = 1; i < n - 1; i++)
{
Vector c = Solver.BCG(B, Vector.GetEn(i, n), 0.00000000001d);
for (int j = 0; j < n; j++)
{
BR[j, i] = c[j];
}
}
BR[0, 0] = 1;
BR[n - 1, n - 1] = 1;
Console.WriteLine(B);
Console.WriteLine(BR);
Console.WriteLine(BR * B);
Assert.AreEqual(0, 1);
}
public void FindProectorMatrixNew_Test()
{
//setup
int N = 17;
int n = 10;
double a = 0d;
double b = 1d;
Vector grid_h = Vector.CreateUniformGrid(N, a, b);
Vector grid_2h = Vector.CreateUniformGrid(n, a, b);
BasisSpline spline_h = new BasisSpline(4, N, a, b);
BasisSpline spline_2h = spline_h.GetBasisSpline_Down();
Matrix B = spline_h.GetMatrix();
Matrix BR = new Matrix(N, N);
for (int i = 1; i < N - 1; i++)
{
Vector c = Solver.BCG(B, Vector.GetEn(i, N), 0.00000000001d);
for (int j = 0; j < N; j++)
{
BR[j, i] = c[j];
}
}
BR[0, 0] = 1;
BR[N - 1, N - 1] = 1;
Matrix B_2h = new Matrix(N, n);
for (int i = 0; i < n; i++)
{
Vector z = spline_2h.GetVectorBasis(grid_h, i);
for (int j = 0; j < N; j++)
{
B_2h[j, i] = z[j];
}
}
Console.WriteLine(B_2h);
Console.WriteLine(BR * B_2h);
Assert.AreEqual(0, 1);
}
public void Interpolate_slow_deg4_tsin_CompareCoefs_test()
{
//setup
double EPS = 0.1d;
double a = 0d;
double b = 3 * Math.PI;
int GridSize = 17;
int deg = 4;
Vector grid = Vector.CreateUniformGrid(GridSize, a, b);
Vector y = MyMath.Basic.GetVectorFunction(GridSize, a, b, FunctionLib.tsin);
//run
BasisSpline bspline_h = new BasisSpline(deg, GridSize, a, b);
Vector c_h = BasisSpline.Interpolate(y, bspline_h.grid, deg);
bspline_h.SetNewCoefs(c_h);
Vector c_2h_actual = MultyGrid.Proektor.slow_spline_r(c_h);
BasisSpline bspline_2h = bspline_h.GetBasisSpline_Down();
Vector y_2h = MyMath.Basic.GetVectorFunction(c_2h_actual.Length, a, b, FunctionLib.tsin);
Vector c_2h_expect = BasisSpline.Interpolate(y_2h, bspline_2h.grid, deg);
bspline_2h.SetNewCoefs(c_2h_actual);
//compare
Console.WriteLine((c_2h_expect - c_2h_actual).ToString());
double result = (c_2h_expect - c_2h_actual).Norm;
Console.WriteLine("Степень сплайна = " + deg);
Console.WriteLine("Сетка по которой построен сплайн = " + bspline_2h.grid.ToString());
Console.WriteLine("f(x) = " + y);
Console.WriteLine("f(x) 2h = " + y_2h);
Console.WriteLine("actual c 2h = " + c_2h_actual.ToString());
Console.WriteLine("expect c 2h = " + c_2h_expect.ToString());
Console.WriteLine("||f - spline|| = " + result.ToString("0.0000"));
Assert.AreEqual(0, result, EPS, "Плохая интерполяция!");
}
public void Interpolate_slow_deg4_tsin_PROJECTION_test()
{
//setup
double EPS = 0.1d;
double a = 0d;
double b = 2 * Math.PI;
int GridSize = 17;
int deg = 4;
Vector grid = Vector.CreateUniformGrid(GridSize, a, b);
Vector y = MyMath.Basic.GetVectorFunction(GridSize, a, b, FunctionLib.tsin);
//run
BasisSpline bspline_h = new BasisSpline(deg, GridSize, a, b);
Vector c_h = BasisSpline.Interpolate(y, bspline_h.grid, deg);
bspline_h.SetNewCoefs(c_h);
Vector c_2h = MultyGrid.Proektor.slow_spline_r(c_h);
BasisSpline bspline_2h = bspline_h.GetBasisSpline_Down();
bspline_2h.SetNewCoefs(c_2h);
//compare
int N = 50;
Vector expect = MyMath.Basic.GetVectorFunction(N, a, b, FunctionLib.tsin);
Vector actual = bspline_2h.GetVectorFunction(N, a, b);
Console.WriteLine((expect - actual).ToString());
double result = (expect - actual).Norm;
Console.WriteLine("Степень сплайна = " + deg);
Console.WriteLine("Сетка по которой построен сплайн = " + bspline_2h.grid.ToString());
Console.WriteLine("значения х = " + grid.ToString());
Console.WriteLine("значение f(x) = " + y.ToString());
Console.WriteLine("coef h = " + c_h.ToString());
Console.WriteLine("coef 2h = " + bspline_2h.COEFICIENT.ToString());
Console.WriteLine("||f - spline|| = " + result.ToString("0.0000"));
Assert.AreEqual(0, result, EPS, "Плохая интерполяция!");
}
public void Spline4_Experiment5_CompareMatr()
{
//setup
int N = 17;
int n = 10;
double a = 0d;
double b = 1d;
int index = 0;
Vector grid_h = Vector.CreateUniformGrid(N, a, b);
Vector grid_2h = Vector.CreateUniformGrid(n, a, b);
BasisSpline spline_h = new BasisSpline(4, N, a, b);
BasisSpline spline_2h = spline_h.GetBasisSpline_Down();
Matrix A = spline_h.GetMatrix();
Matrix B = new Matrix(N, n);
Vector z;
Vector c;
//run
for (index = 0; index < n; index++)
{
z = spline_2h.GetVectorBasis(grid_h, index);
Vector zz = spline_2h.GetVectorBasis(grid_2h, index);
c = Solver.BCGSTAB(A, z, 0.0000000001d);
for (int i = 0; i < N; i++)
{
B[i, index] = c[i];
}
Console.WriteLine((zz).ToString());
}
Console.WriteLine(spline_2h.GetMatrix());
//Console.WriteLine((A*c).ToString());
Console.WriteLine("index = " + index);
}
