private Tuple <Vectors, double, double> HalfSolve(int len)
{
SqMatrix iD1 = D1.SubMatrix(len), iD2 = D2.SubMatrix(len), iS = S.SubMatrix(len);
Vectors iR1 = R1.SubVector(len), iR2 = R2.SubVector(len);
SqMatrix iD1m = D1m.SubMatrix(len), iD2m = D2m.SubMatrix(len), idl;
Vectors idr;
idl = (D2 - S * (D1m * S)).SubMatrix(len);
idr = (R2 + S * D1m * R1).SubVector(len);
Vectors id = idl.Solve(idr), icnew = (D1m * (R1 + S * id)).SubVector(len);
Vectors res = Vectors.Union2(icnew, id);
double p1 = IntegralClass.IntegralCurve((Point y) => (TestFuncAndCurve.Grads[GF - 1](y) * TestFuncAndCurve.Norm[CIRCLE - 1](y)).Sqr(), CIRCLE - 1);
double p2 = IntegralClass.IntegralCurve((Point y) => (U(y)).Sqr(), CIRCLE - 1);
Functional fif = (Point x) =>
{
double s = 0;
for (int i = 0; i < id.Deg; i++)
{
s += icnew[i] * alpha(x, i) + id[i] * beta(x, i);
}
return(Math.Abs(s - KursMethods.U(x)));
};
double L = IntegralClass.Integral(fif, CIRCLE - 1);
$"len = {len}, L = {this.F(res)}".Show();
return(new Tuple <Vectors, double, double>(res, F(res), L));
}
public void TestInteg()
{
Vectors ce = Vectors.Random(dim, -5, 9);
Vectors de = Vectors.Random(dim, -5, 5);
Func <double> FF = () =>
{
Functional f1 = (Point y) => {
double sum = U(y);
for (int i = 0; i < dim; i++)
{
sum -= ce[i] * alpha(y, i) + de[i] * beta(y, i);
}
return(sum * sum);
};
Functional f2 = (Point y) => {
double sum = Unu(y);
for (int i = 0; i < dim; i++)
{
sum -= ce[i] * alphanu(y, i) + de[i] * betanu(y, i);
}
return(sum * sum);
};
return(IntegralClass.IntegralCurve((Point p) => f1(p) + f2(p), CIRCLE - 1));
};
$"Погрешность представления 1){FF()} 2){F(Vectors.Union2(ce,de))}".Show();
}
/// <summary>
/// Созадть систему матриц и векторов по базисным функция
/// </summary>
/// <param name="n">Число базисных функций. Если -1, то берутся все функции</param>
public BiharmonicEquation(int n = -1)
{
if (n == -1)
{
n = masPoints.Length;
}
D1 = new SqMatrix(n);
D2 = new SqMatrix(n);
S = new SqMatrix(n);
R1 = new Vectors(n);
R2 = new Vectors(n);
Parallel.For(0, n, (int i) =>
{
for (int j = i; j < n; j++)
{
D1[i, j] = IntegralClass.IntegralCurve((Point x) => alpha(x, i) * alpha(x, j) + alphanu(x, i) * alphanu(x, j), CIRCLE - 1);
D2[i, j] = IntegralClass.IntegralCurve((Point x) => beta(x, i) * beta(x, j) + betanu(x, i) * betanu(x, j), CIRCLE - 1);
S[i, j] = IntegralClass.IntegralCurve((Point x) => alpha(x, i) * beta(x, j) + alphanu(x, i) * betanu(x, j), CIRCLE - 1);
}
R1[i] = IntegralClass.IntegralCurve((Point y) => alphanu(y, i) * Unu(y) + alpha(y, i) * U(y), CIRCLE - 1);
R2[i] = IntegralClass.IntegralCurve((Point y) => betanu(y, i) * Unu(y) + beta(y, i) * U(y), CIRCLE - 1);
for (int j = i + 1; j < n; j++)
{
D1[j, i] = D1[i, j];
D2[j, i] = D2[i, j];
S[j, i] = S[i, j];
}
});
d = new Vectors(n);
cnew = new Vectors(n);
ErrorsMasL = new double[n];
ErrorsMasQ = new double[n];
p1 = IntegralClass.IntegralCurve((Point y) => Unu(y).Sqr(), CIRCLE - 1);
p2 = IntegralClass.IntegralCurve((Point y) => U(y).Sqr(), CIRCLE - 1);
$"p1 = {p1}, p2 = {p2}".Show();
var mems = new Memoize <Point, Vectors[]>((Point p) => {
Vectors[] r = new Vectors[4];
for (int i = 0; i < 4; i++)
{
r[i] = new Vectors(dim);
}
for (int i = 0; i < dim; i++)
{
r[0][i] = alpha(p, i);
r[1][i] = alphanu(p, i);
r[2][i] = beta(p, i);
r[3][i] = betanu(p, i);
}
return(r);
}).Value;
Func <Point, Vectors[]> AB = (Point p) => mems(p);
Func <Vectors, double> FF = (Vectors v) =>
{
Vectors ce = new Vectors(this.dim);
Vectors de = new Vectors(this.dim);
for (int i = 0; i < v.Deg / 2; i++)
{
ce[i] = v[i];
de[i] = v[i + v.Deg / 2];
}
Functional func = (Point p) => {
var vec = AB(p);
return((U(p) - ce * vec[0] - de * vec[2]).Sqr() + (Unu(p) - ce * vec[2] - de * vec[3]).Sqr());
};
return(IntegralClass.IntegralCurve(func, CIRCLE - 1));
Functional f1 = (Point y) => {
double sum = U(y);
for (int i = 0; i < dim; i++)
{
sum -= ce[i] * alpha(y, i) + de[i] * beta(y, i);
}
return(sum * sum);
};
Functional f2 = (Point y) => {
double sum = Unu(y);
for (int i = 0; i < dim; i++)
{
sum -= ce[i] * alphanu(y, i) + de[i] * betanu(y, i);
}
return(sum * sum);
};
return(IntegralClass.IntegralCurve((Point p) => f1(p) + f2(p), CIRCLE - 1));
};
F = (Vectors v) =>
{
return(FF(v));
Vectors cc = new Vectors(this.dim);
Vectors dd = new Vectors(this.dim);
for (int i = 0; i < v.Deg / 2; i++)
{
cc[i] = v[i];
dd[i] = v[i + v.Deg / 2];
}
int k = this.dim;
double sum = p1 + p2 - 2 * (cc * R1 + dd * R2);
for (int i = 0; i < k; i++)
{
for (int j = 0; j < k; j++)
{
sum += 2 * cc[i] * dd[j] * S[i, j] + cc[i] * cc[j] * D1[i, j] + dd[i] * dd[j] * D2[i, j];
}
}
return(sum);
};
Vectors tmp = Vectors.Union2(new Vectors(dim), Vectors.Random(dim, -4, 4));
$"Error! {FF(tmp)} != {F(tmp)}".Show();
// Parallel.Invoke(
//() => D1m = D1.Invertion,
//() => D2m = D2.Invertion
//);
// dl = D2 - S * (D1m * S);
// dr = R2 + S * D1m * R1;
// slau = new SLAU(dl, dr);
}