// Perform a left Reimann sum
public static double ReimannSum(Fxy f, double x, double x0 = 0, double y0 = 0, double dx = 1e-6)
{
if (dx <= 0)
{
throw new ArgumentOutOfRangeException("dx", "dx must be greater than zero.");
}
if (x0 > x)
{
throw new ArgumentOutOfRangeException("x0, x", "x0 must be less than x.");
}
double intervalSize = Abs(x - x0);
uint n = checked ((uint)(intervalSize / dx));
double sum = y0;
for (uint i = 0; i < n; i++)
{
sum += f(x0 + i * dx, sum) * dx;
}
// Sum the last term that will be left over if the interval isn't divisible by the increment
double summedIntervalSize = n * dx;
if (summedIntervalSize < intervalSize)
{
double lastDx = intervalSize - summedIntervalSize;
sum += f(x - lastDx, sum) * lastDx;
}
return(sum);
}
public static async Task <object> binaryOpAsync(AsyncExprCtx ae,
Fxy op, object a, object b, bool resultCanBeLazy)
{
var valueA = await ConstValueOf(ae, a);
var valueB = await ConstValueOf(ae, b);
return(binaryOpConst(op, valueA, valueB, resultCanBeLazy));
}
public static object GenFxyCall(Fxy op, object a, object b, ValueKind kind, bool resultCanBeLazy)
{
switch (kind)
{
case ValueKind.Const:
return(binaryOpConst(op, a, b, resultCanBeLazy));
case ValueKind.Sync:
return((LazySync) delegate() { return binaryOpSync(op, a, b, resultCanBeLazy); });
case ValueKind.Async:
return((LazyAsync) delegate(AsyncExprCtx ae)
{ return binaryOpAsync(ae, op, a, b, resultCanBeLazy); });
}
throw new InvalidOperationException();
}
// Perform the left ReimannSum until the target value is reached
public static double ReimannSumTo(
Fxy f, double y, double x = 1000, double x0 = 0, double y0 = 0, double dx = 1e-6)
{
if (dx <= 0)
{
throw new ArgumentOutOfRangeException("dx", "dx must be greater than zero.");
}
if (x0 > x)
{
throw new ArgumentOutOfRangeException("x0, x", "x0 must be less than x.");
}
if (y == y0)
{
return(x0);
}
double intervalSize = Abs(x - x0);
uint n = checked ((uint)(intervalSize / dx));
double sum = y0;
// We can be approaching the target value from above or below depending on the initial value
IsSumReached isSumReached = y > y0 ? (IsSumReached)(() => sum >= y) : () => sum <= y;
for (uint i = 0; i < n; i++)
{
sum += f(x0 + i * dx, sum) * dx;
if (isSumReached())
{
return(x0 + (i + 1) * dx);
}
}
// Sum the last term that will be left over if the interval isn't divisible by the increment
double summedIntervalSize = n * dx;
if (summedIntervalSize < intervalSize)
{
double lastDx = intervalSize - summedIntervalSize;
sum += f(x - lastDx, sum) * lastDx;
if (isSumReached())
{
return(x);
}
}
return(double.NaN);
}
public CallExpr(Fxy func, params Expr[] args) : this((Delegate)func, args)
{
}
public CallExpr(Fxy func, IList <Expr> args) : this((Delegate)func, args)
{
}
public static object binaryOpSync(Fxy op, object a, object b, bool resultCanBeLazy)
{
return(binaryOpConst(op, ConstValueOf(a), ConstValueOf(b), resultCanBeLazy));
}
public static object binaryOpConst(Fxy op, object constA, object constB, bool resultCanBeLazy)
{
IList arrA = constA as IList;
IList arrB = constB as IList;
if (arrA == null && arrB == null)
{
return(op(constA, constB));
}
try
{
ArrayList result;
if (arrA == null) // || arrA.Count == 1)
{
object a = constA; // arrA == null ? argA : arrA[0];
if (resultCanBeLazy)
{
result = new ListOfVals(arrB.Count);
}
else
{
result = new ListOfConst(arrB.Count);
}
for (int i = 0; i < arrB.Count; i++)
{
result.Add(op(a, arrB[i]));
}
}
else if (arrB == null) // || arrB.Count == 1)
{
object b = constB; // arrB == null ? argB : arrB[0];
if (resultCanBeLazy)
{
result = new ListOfVals(arrA.Count);
}
else
{
result = new ListOfConst(arrA.Count);
}
for (int i = 0; i < arrA.Count; i++)
{
result.Add(op(arrA[i], b));
}
}
else if (arrA.Count == arrB.Count)
{
int n = arrA.Count;
if (resultCanBeLazy)
{
result = new ListOfVals(n);
}
else
{
result = new ListOfConst(n);
}
for (int i = 0; i < n; i++)
{
result.Add(op(arrA[i], arrB[i]));
}
}
else
{
return(new ArgumentOutOfRangeException("binaryOp: arguments dimensions mismatch").Wrap());
}
return(result);
}
catch (Exception ex) { return(ex.Wrap()); }// new Exception(string.Format("binaryOp: " + ex.Message)); }
}