//u'' = f; u(a) = u0 u(b) = u1
public static void SolveSecondDerevetivWhithBounderyCondition(int SIZE, double a_border, double b_border,
ICardinalStratagy calculate,
double u0, double u1, FunctionLib.Function function)
{
int degree = 4;
int N = SIZE;
int M = N + degree - 2;
int m = degree - 2;
Matrix U = new Matrix(m, M);
double h = MyMath.Basic.GetStep(N, a_border, b_border);
CardinalSpline spline = new CardinalSpline(calculate);
Matrix D = (1d / Math.Pow(h, m)) * CardinalOperators.DerevetiveMatrix(degree, SIZE);
//условие 1: (c,ksi(a)) = u0
Vector ksi_a = spline.SplineVector(a_border, a_border, b_border, N, degree);
//условие 1: (c,ksi(b)) = u1
Vector ksi_b = spline.SplineVector(b_border, a_border, b_border, N, degree);
for (int i = 0; i < M; i++)
{
U[0, i] = ksi_a[i];
U[1, i] = ksi_b[i];
}
//-------------
//Составляем линейную систему
Matrix A = ConstructMatrix(D, U);
//Составляем правую часть
Vector b = MyMath.Basic.GetVectorFunction(N, a_border, b_border, function);
Vector y = Matrix.Transpose(D) * b;
Vector y_prime = new Vector(y.Length + m);
y_prime[y.Length] = u0;
y_prime[y.Length + 1] = u1;
for (int i = 0; i < y.Length; i++)
{
y_prime[i] = y[i];
}
Console.WriteLine("right part = " + y_prime);
// Console.WriteLine(A);
Vector x = Solver.BCG(A, y_prime, 0.0001d);
Console.WriteLine("x = " + x);
Vector c = x.SubVector(0, M);
Vector f = spline.GetVectorFunction(N, a_border, b_border, c, h, degree);
Console.WriteLine("f = " + f);
f = spline.GetVectorFunction(10 * N, a_border, b_border, c, h, degree);
b = MyMath.Basic.GetVectorFunction(10 * N, a_border, b_border, function);
Console.WriteLine("||err|| = " + (f - b).Norm);
}
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);
}