public async Task <double> Integrate(Function f, int nodesCount, TransformableVariable x, TransformableVariable y,
Boundary xBounds, Boundary yBounds)
{
this.RefreshCoefficients(nodesCount);
Tuple <double[], double[]> coefficients;
// TODO add concurrency checks
this.coefficientsCache.TryGetValue(nodesCount, out coefficients);
var weights = coefficients.Item2;
var nodes = coefficients.Item1;
// cache this values for linear transform of gauss coefficients and nodes
var xDiff = xBounds.High - xBounds.Low;
var xSum = xBounds.High + xBounds.Low;
var yDiff = yBounds.High - yBounds.Low;
var ySum = yBounds.High + yBounds.Low;
double total = 0;
for (int i = 0; i < nodesCount; ++i)
{
for (int j = 0; j < nodesCount; ++j)
{
double transformedX = 0.5 * xSum + 0.5 * xDiff * nodes[i];
double transformedY = 0.5 * ySum + 0.5 * yDiff * nodes[j];
double currentSum = weights[i] * weights[j]
* f.Value(x | x.Rule(transformedX, transformedY),
y | y.Rule(transformedX, transformedY));
Add(ref total, currentSum);
}
}
return(total * 0.5 * xDiff * 0.5 * yDiff);
}
public async Task <Tuple <Function, Variable, Variable> > Solve(double M, int n, double cylinderRadius,
double sphereRadius, double speedAtInfinity)
{
var coordFunctions = this.coordinateFunctions.Get(n);
var coordFunctionsCount = coordFunctions.Count;
#region Variables
var rr = new TransformableVariable(0);
var zz = new TransformableVariable(1);
var ro = new TransformableVariable(0, (a, b) =>
Math.Sqrt(Math.Pow(a, 2) + Math.Pow(b, 2)));
var phi = new TransformableVariable(1, (a, b) =>
{
if (a < 0)
{
return(Math.Atan2(b, a) + Math.PI);
}
return(Math.Atan2(b, a));
});
#endregion
#region Variable boundaries
var xBounds = new Boundary()
{
Low = -M, High = M
};
var yBounds = new Boundary()
{
Low = 0, High = cylinderRadius
};
var roBounds = new Boundary()
{
Low = 0, High = sphereRadius
};
var phiBounds = new Boundary()
{
Low = 0, High = Math.PI
};
#endregion
#region Functions definition
Func <Function, Variable, Variable, Function> A =
(Function f, Variable r, Variable z) => (-1 / r) *
f.Derivative(z, 2) - (((1 / r) * f.Derivative(r)).Derivative(r));
Func <Variable, Variable, Function> omega1 =
(Variable r, Variable z) => Function.Pow(r, 2)
* (Function.Pow(z, 2) + Function.Pow(r, 2)
- Math.Pow(sphereRadius, 2));
Func <Variable, Variable, Function> omega2 =
(Variable r, Variable z) => 1 - Function.Pow(r, 2);
Func <Variable, Variable, Function> omega =
(Variable r, Variable z) => omega1(r, z) * omega2(r, z)
/ Function.Pow((1 + Function.Pow(z, 2)), 2);
Func <Variable, Variable, Function> X =
(Variable r, Variable z) => 1 + Function.Pow(z, 2);
// c - значение функции на Г2 - радиус трубы
Func <Variable, Variable, double, Function> F0 =
(Variable r, Variable z, double c) => c *omega1(r, z)
/ (omega1(r, z) + X(r, z) * omega2(r, z));
Func <double[], Variable, Variable, Function> result =
(double[] coeff, Variable r, Variable z) =>
{
return(omega(r, z) * coeff.Select((c, i) => c * coordFunctions[i](r, z))
.ToList()
.Aggregate <Function>((sum, current) => sum + current));
};
#endregion
var matrix = new double[coordFunctionsCount, coordFunctionsCount];
var rightPart = new double[coordFunctionsCount];
for (int i = 0; i < coordFunctionsCount; ++i)
{
var right = A(F0(rr, zz, cylinderRadius), rr, zz) * coordFunctions[(int)i](rr, zz);
for (int j = 0; j < coordFunctionsCount; ++j)
{
var cylinderPart = A(coordFunctions[(int)i](rr, zz), rr, zz) * coordFunctions[(int)j](rr, zz);
var spherePart = A(coordFunctions[(int)i](ro, phi), ro, phi) * coordFunctions[(int)j](ro, phi);
matrix[(int)i, (int)j] = await integrationService.Integrate(
cylinderPart, 10, rr, zz, xBounds, yBounds)
- await integrationService.Integrate(
spherePart, 10, ro, phi, roBounds, phiBounds);
}
rightPart[i] = await integrationService.Integrate(right, 10, rr, zz, xBounds, yBounds);
}
int info;
double[] coefficients;
alglib.densesolverreport report;
alglib.rmatrixsolve(matrix, coordFunctionsCount, rightPart, out info, out report, out coefficients);
return(Tuple.Create(result(coefficients, rr, zz), rr as Variable, zz as Variable));
}
