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 Interpolate_slow_deg2_tsin()
{
//setup
double EPS = 0.1d;
double a = 0d;
double b = 3d;
int GridSize = 20;
int deg = 2;
Vector grid = Vector.CreateUniformGrid(GridSize, a, b);
Vector y = MyMath.Basic.GetVectorFunction(GridSize, a, b, FunctionLib.tsin);
//run
BasisSpline bspline = new BasisSpline(deg, grid, y, GridType.ClassicSplineGrid);
//compare
int N = 150;
Vector expect = MyMath.Basic.GetVectorFunction(N, a, b, FunctionLib.tsin);
Vector actual = bspline.GetVectorFunction(N, a, b);
double result = (expect - actual).Norm;
Console.WriteLine("Степень сплайна = " + deg);
Console.WriteLine("Сетка по которой построен сплайн = " + bspline.grid.ToString());
Console.WriteLine("значения х = " + grid.ToString());
Console.WriteLine("значение f(x) = " + y.ToString());
Console.WriteLine("coef = " + bspline.COEFICIENT.ToString());
Console.WriteLine("||f - spline|| = " + result.ToString("0.0000"));
Assert.AreEqual(0, result, EPS, "Плохая интерполяция!");
}
public void Spline4_ExperimentUniformGrid()
{
//setup
int N = 17;
int n = 9;
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, grid_h, Vector.GetConstVector(2d, N), GridType.ExperimentSplineGrid);
BasisSpline spline_2h = new BasisSpline(4, grid_2h, Vector.GetConstVector(2d, n), GridType.UniformSplineGrid);
Matrix A = spline_h.GetMatrix();
Vector z;
Vector c;
//run
for (index = 0; index < 7; 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 Spline4_Experiment4()
{
//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, grid_h, Vector.GetConstVector(2d, N), GridType.ClassicSplineGrid);
BasisSpline spline_2h = new BasisSpline(4, grid_2h, Vector.GetConstVector(2d, n), GridType.ClassicSplineGrid);
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);
c = Solver.BCGSTAB(A, z, 0.0000000001d);
for (int i = 0; i < N; i++)
{
B[i, index] = c[i];
}
}
Console.WriteLine(Matrix.Transpose(B).ToString("0.00"));
Console.WriteLine("index = " + index);
}
public void create_proection_spline4_mat_test()
{
//setup
//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, grid_h, Vector.GetConstVector(2d, N), GridType.ClassicSplineGrid);
BasisSpline spline_2h = new BasisSpline(4, grid_2h, Vector.GetConstVector(2d, n), GridType.ClassicSplineGrid);
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);
c = Solver.BCGSTAB(A, z, 0.0000000001d);
for (int i = 0; i < N; i++)
{
B[index, i] = c[i];
}
}
//run
Matrix CREATE_B = MultyGrid.Proektor.create_proection_spline4_mat(n);
Matrix D = B - CREATE_B;
double actual = D.NORMF;
Console.WriteLine("полученная " + B.ToString());
Console.WriteLine("созданная " + CREATE_B.ToString());
//compare
Assert.AreEqual(0d, actual, 0.00000001d, "Эти матрицы не равны!");
}
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 RightUniformBSplineTest()
{
//setup
int GridSize = 5;
double a = 0;
double b = 5d;
int N = 1000;
double h = MyMath.Basic.GetStep(GridSize, a, b);
int deg = 4;
int index = 0;
//Vector x = new Vector(MyMath.Basic.CreateUniformGrid(N, a - 2 * h, b + deg * h));
BasisSpline spline = new BasisSpline(deg, GridSize, a, b, GridType.RightUniformSplineGrid);
//run
double Ba = spline.GetBasis(0.1d, index);
//compare
Assert.AreEqual(0d, Ba, 0.000001d);
}
public void Interpolate_slow_deg4_tsin_ZeroTrace_NewMethod()
{
//setup
double EPS = 0.1d;
double a = 0d;
double b = Math.PI;
int GridSize = 14;
int deg = 4;
int p = deg - 1;
Vector uni_grid = Vector.CreateUniformGrid(GridSize, a, b);
Vector f = MyMath.Basic.GetVectorFunction(GridSize, a, b, FunctionLib.tttsin);
//run
BasisSpline bspline = new BasisSpline(deg, uni_grid, f, GridType.SimpleSplineGrid);
Vector c = BasisSpline.SimpleInterpolate(f, bspline.grid, deg);
Vector basis_c = new Vector(c.Length + 2 * (deg - 1));
for (int i = 0; i < c.Length; i++)
{
basis_c[i + p] = c[i];
}
bspline.SetNewCoefs(basis_c);
Vector bf = bspline.GetVectorFunction(uni_grid);
////compare
int N = 150;
Vector expect = MyMath.Basic.GetVectorFunction(N, a, b, FunctionLib.tttsin);
Vector actual = bspline.GetVectorFunction(N, a, b);
double result = (expect - actual).Norm;
Console.WriteLine("Степень сплайна = " + deg);
Console.WriteLine("Сетка по которой построен сплайн = " + uni_grid.ToString());
Console.WriteLine("trace( f ) = <" + f[0].ToString("0.000") + ", " + f.Last.ToString("0.000") + ">");
Console.WriteLine("coef = " + basis_c); //bspline.COEFICIENT.ToString());
Console.WriteLine("значение f(x) = " + f.ToString());
Console.WriteLine("значение bf(x) = " + bf.ToString());
Console.WriteLine("||f - spline|| = " + result.ToString("0.0000"));
Assert.AreEqual(0, result, EPS, "Плохая интерполяция!");
}
public void SimpleUniformBSplineTest_dim()
{
//setup
int GridSize = 2;
double a = 0;
double b = 7d;
int deg = 4;
int index = 0;
BasisSpline spline = new BasisSpline(deg, GridSize, a, b, GridType.SimpleSplineGrid);
Console.WriteLine(new Vector(MyMath.Basic.CreateUniformGrid(GridSize, a, b)));
int expect = GridSize + 2 * (deg - 1) + 2 * (deg - 2);
//run
int actual = spline.grid.Count;
//compare
Console.WriteLine("expect = " + expect + "; actual = " + actual);
Assert.AreEqual(expect, actual, "размерности совпадают");
}
public void CompareConvolutionWhithBasisSplineTest()
{
//setup
int GridSize = 1000;
double a = -3d;
double b = 5d;
Vector grid = Vector.CreateUniformGrid(GridSize, a, b);
BasisSpline spline = new BasisSpline(3, 10, a, b);
// Console.WriteLine("grid = " + spline.grid);
Vector expect = spline.GetVectorBasis(grid, 3);
Console.WriteLine("expect = " + expect);
//run
Vector actual = MyMath.Operations.GetConvolutionVector(FunctionLib.conv_tri_test, FunctionLib.conv_tri_test, GridSize, a, b);
Console.WriteLine("actual = " + actual);
//compare
double NORM = (expect - actual).Norm;
Console.WriteLine("Норма разности = " + NORM);
Assert.AreEqual(0d, NORM, 0.1d);
}
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 DeBoorB_Integrate()
{
//setup
int GridSize = 20;
double a = 0;
double b = 1d;
double c = 10d;
double EPS = 0.01d;
int N = 1000;
int index = 2;
Vector grid1 = Vector.CreateUniformGrid(N, a, b);
Vector grid2 = Vector.CreateUniformGrid(N, a, c);
int deg = 4;
BasisSpline spline1 = new BasisSpline(deg, GridSize, a, b);
BasisSpline spline2 = new BasisSpline(deg, GridSize, a, c);
//run
for (index = 0; index < GridSize; index++)
{
Console.WriteLine("index = " + index);
Vector f1 = spline1.GetVectorBasis(grid1, index);
Vector f2 = spline2.GetVectorBasis(grid2, index);
double I1 = MyMathLib.Integrate.RiemannSum(f1.ToArray, MyMathLib.MyMath.Basic.GetStep(N, a, b));
double I2 = MyMathLib.Integrate.RiemannSum(f2.ToArray, MyMathLib.MyMath.Basic.GetStep(N, a, c));
Console.WriteLine("Integral B" + index + " on [0, 1] = " + I1);
Console.WriteLine("Integral B" + index + " on [0, 10] = " + I2);
//comp
Assert.IsTrue(I2 > I1, "Интеграл с функции большем носителем должен быть больше!");
}
}
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);
}