public static Vector GetCoef_2h(int degree)
{
double[] ksi = GetCardinalValue(degree, 1d);
Matrix A = new Matrix(degree + 1);
Vector y = new Vector(degree + 1);
for (int i = 0; i < y.Length; i++)
{
y[i] = CardinalSpline.Cardinal(degree, i + 1, 0d, 2d);
}
for (int i = 0; i < degree + 1; i++)
{
for (int j = 0; j < ksi.Length; j++)
{
if (i - j >= 0)
{
A[i, i - j] = ksi[ksi.Length - 1 - j];
}
}
}
Matrix A_t = Matrix.Transpose(A);
Console.WriteLine("y = " + y);
Console.WriteLine("A_T*A = " + A);
Vector c = new Vector();
c = Solver.BCGSTAB(A, y, 0.0000001d);
Console.WriteLine("SUM c = " + MyMath.Basic.SumArray(c.ToArray));
return(c);
}
private static double[] GetCardinalValue(int degree)
{
double[] mas = new double[degree - 1];
for (int i = 0; i < degree - 1; i++)
{
mas[i] = CardinalSpline.Cardinal(degree, (i + 1), 0d, 1d);
}
return(mas);
}
public static double[] GetCardinalValue(int degree, double h)
{
double[] mas = new double[degree - 1];
for (int i = 0; i < degree - 1; i++)
{
mas[i] = CardinalSpline.Cardinal(degree, (i + 1) * h, 0, h);
}
return(mas);
}
public static Matrix Create_Ah(int degree, int Size)
{
Matrix Ah = new Matrix(Size);
int p = degree;
for (int i = 0; i < Size; i++)
{
for (int j = 0; j < Size; j++)
{
Ah[i, j] = 2.0 * CardinalSpline.Cardinal(2 * (p - 1), (i - j) + p - 1, 0, 1);
//if(i - j + 1 < Size)
Ah[i, j] -= CardinalSpline.Cardinal(2 * (p - 1), (i - j) + p - 1 + 1, 0, 1);
//if (i - j - 1 >= 0)
Ah[i, j] -= CardinalSpline.Cardinal(2 * (p - 1), (i - j) + p - 1 - 1, 0, 1);
}
}
return(Ah);
}
public static Matrix Create_D2_Ah(int degree, int Size)
{
Matrix Ah = new Matrix(Size);
int p = degree;
int q = p - 2;
for (int k = 0; k < Size; k++)
{
for (int j = 0; j < Size; j++)
{
Ah[k, j] = 6d * CardinalSpline.Cardinal(2 * q, (k - j) + q, 0, 1);
//if (j + 1 < Size)
Ah[k, j] -= 4d * CardinalSpline.Cardinal(2 * q, (k - j) + q + 1, 0, 1);
//if (j - 1 >= 0)
Ah[k, j] -= 4d * CardinalSpline.Cardinal(2 * q, (k - j) + q - 1, 0, 1);
//if ( j + 2 < Size)
Ah[k, j] += CardinalSpline.Cardinal(2 * q, (k - j) + q + 2, 0, 1);
//if (j - 2 >= 0)
Ah[k, j] += CardinalSpline.Cardinal(2 * q, (k - j) + q - 2, 0, 1);
}
}
return(Ah);
}
public void Test()
{
int N = 10;
int degree = 2;
double h = 1;
double a_border = 0, b_border = 1;
double u0 = 1;
Matrix D = CardinalDifferentialEquation.FirstDirevetive(N);
Matrix KSI = CardinalDifferentialEquation.CreateKSIMatrix(degree, h, N + 1);
Matrix DD = D * Matrix.Transpose(D);
//KSI[0, 0] -= KSI[0, 1];
//KSI[N, N] -= KSI[0, 1];
//DD[0, 0] = DD[N, N] = 2d;
Console.WriteLine(DD);
Console.WriteLine(KSI);
Matrix A = KSI * DD;
//KSI[0, 0] += KSI[0, 1];
//KSI[N, N] += KSI[0, 1];
for (int i = 0; i < N + 1; i++)
{
A[i, i] *= 1d;
}
A = 2d * A;
//A[0, 0] = 1.5;
// A[N, N] = 1.5;
Console.WriteLine(A);
Vector y = Vector.GetConstVector(1d, N);
for (int i = 0; i < N; i++)
{
y[i] = i * h;
}
Console.WriteLine(D * y);
Vector Dy = (KSI * D) * y;
Vector b = new Vector(N + 2);
for (int i = 0; i < N + 1; i++)
{
b[i] = 2d * Dy[i];
}
b[N + 1] = u0;
Console.WriteLine("b = " + b);
Matrix B = new Matrix(N + 2);
for (int i = 0; i < N + 1; i++)
{
for (int j = 0; j < N + 1; j++)
{
B[i, j] = A[i, j];
}
}
for (int i = 0; i < N; i++)
{
B[N + 1, i] = CardinalSpline.Cardinal(degree + 1, a_border, a_border + (i - (degree + 1) + 1) * h, h);
B[i, N + 1] = -B[N + 1, i];
}
Console.WriteLine(B);
Vector x = Vector.GetConstVector(2d, N + 2);
x[N + 1] = 0;
for (int i = 0; i < N + 1; i++)
{
x[i] = i + 1;
}
Console.WriteLine("x = " + x);
Console.WriteLine("B*x = " + B * x);
Console.WriteLine("b = " + b);
Vector c = Solver.BCG(B, b, 0.00000001d);
Console.WriteLine("anser = " + c);
Console.WriteLine(B * c);
}
public void SecondDerevitiveSinTest()
{
int N = 50;
int degree = 2;
double a_border = 0, b_border = 6.29;
double h = MyMath.Basic.GetStep(N, a_border, b_border);
double u0 = FunctionLib.cos(a_border), u1 = FunctionLib.cos(b_border);
Vector f = MyMath.Basic.GetVectorFunction(N, a_border, b_border, FunctionLib.cos);
Matrix D = CardinalDifferentialEquation.SecondDirevetive(N);
Matrix DD = D * Matrix.Transpose(D);
// Console.WriteLine(DD);
Matrix A = (1d / (h * h)) * DD;
Console.WriteLine(D * f);
Vector Dy = D * f;
Vector b = new Vector(N + 4);
for (int i = 0; i < N + 2; i++)
{
b[i] = Dy[i];
}
b[N + 2] = u0;
b[N + 3] = u1;
Console.WriteLine("b = " + b);
Matrix B = new Matrix(N + 4);
for (int i = 0; i < N + 2; i++)
{
for (int j = 0; j < N + 2; j++)
{
B[i, j] = A[i, j];
}
}
for (int i = 0; i < N + 2; i++)
{
B[N + 2, i] = CardinalSpline.Cardinal(degree + 2, a_border, a_border + (i - (degree + 2) + 1) * h, h);
B[N + 3, i] = CardinalSpline.Cardinal(degree + 2, b_border, a_border + (i - (degree + 2) + 1) * h, h);
B[i, N + 2] = -B[N + 2, i];
B[i, N + 3] = -B[N + 3, i];
}
// Console.WriteLine(B);
//Console.WriteLine("b = " + b);
Vector c = Solver.BCG(B, b, 0.00000001d);
Console.WriteLine("anser = " + c);
Console.WriteLine("Ax = " + B * c);
Vector d = c.SubVector(0, N + 2);
CardinalSpline spline = new CardinalSpline();
Vector anser = spline.GetVectorFunction(10, a_border, b_border, d, h, degree + 2);
Vector expect = MyMath.Basic.GetVectorFunction(10, a_border, b_border, FunctionLib.cos);
Console.WriteLine(anser); Console.WriteLine(expect);
Console.WriteLine("||u - u_spl|| = " + (expect - anser).Norm);
}
public void SinTest()
{
int N = 50;
int degree = 2;
double a_border = 0, b_border = 6.29;
double h = MyMath.Basic.GetStep(N, a_border, b_border);
double u0 = 0;
Vector f = MyMath.Basic.GetVectorFunction(N, a_border, b_border, FunctionLib.cos);
Matrix D = CardinalDifferentialEquation.FirstDirevetive(N);
//Matrix KSI = CardinalDifferentialEquation.CreateKSIMatrix(degree, h, N + 1);
Matrix DD = D * Matrix.Transpose(D);
//KSI[0, 0] -= KSI[0, 1];
//KSI[N, N] -= KSI[0, 1];
//DD[0, 0] = DD[N, N] = 2d;
Console.WriteLine(DD);
//Console.WriteLine(KSI);
Matrix A = (1d / h) * DD;
// Console.WriteLine(A);
Console.WriteLine(D * f);
Vector Dy = D * f;
Vector b = new Vector(N + 2);
for (int i = 0; i < N + 1; i++)
{
b[i] = Dy[i];
}
b[N + 1] = u0;
Console.WriteLine("b = " + b);
Matrix B = new Matrix(N + 2);
for (int i = 0; i < N + 1; i++)
{
for (int j = 0; j < N + 1; j++)
{
B[i, j] = A[i, j];
}
}
for (int i = 0; i < N; i++)
{
B[N + 1, i] = CardinalSpline.Cardinal(degree + 1, a_border, a_border + (i - (degree + 1) + 1) * h, h);
B[i, N + 1] = -B[N + 1, i];
}
//Console.WriteLine(B);
Console.WriteLine("b = " + b);
Vector c = Solver.BCG(B, b, 0.00000001d);
Console.WriteLine("anser = " + c);
Console.WriteLine("Ax = " + B * c);
Vector d = c.SubVector(0, N + 1);
CardinalSpline spline = new CardinalSpline();
Vector anser = spline.GetVectorFunction(100, a_border, b_border, d, h, degree + 1);
Vector expect = MyMath.Basic.GetVectorFunction(100, a_border, b_border, FunctionLib.sin);
Console.WriteLine("||u - u_spl|| = " + (expect - anser).Norm);
}