//smoothed.area.estimate
internal static double SmoothedAreaEstimate(Func <double, SGNFnAParam, double> area, double x, SGNFnAParam A, double mathLowerLimit, double[] refRange, bool inestimableLowerLimit, bool remoteRight = false, int hpMult = 1, int maxCount = 10000)
{
double expectedSlope = Tools.NA; // non défini
double fX = A.F(x, A);
double[] a = Tools.Rep(Tools.NA, 3);
// # values around x
double d = 1e-4;
double tmp = (refRange[1] - refRange[0]) / 1000.0;
if (tmp < d)
{
d = tmp;
}
double[] xStar = Tools.Combine(x - d, x, x + d);
if (xStar[0] < mathLowerLimit)
{
//xStar[0] = inestimableLowerLimit ? ((x + mathLowerLimit) / 2.0) : mathLowerLimit;
if (inestimableLowerLimit)
{
xStar[0] = (x + mathLowerLimit) / 2.0;
}
else
{
xStar[0] = mathLowerLimit;
}
}
for (int i = 0; i < 3; i++)
{
a[i] = area(xStar[i], A);
}
double aX = a[1];
double[] observedSlopes = a.Diff().Divide(xStar.Diff()).Multiply(hpMult);
expectedSlope = fX;
double[] observedSlopeAngles = Tools.Combine(Math.Atan(observedSlopes[0]), Math.Atan(observedSlopes[1]));
double expectedSlopeAngle = Math.Atan(expectedSlope);
double angleDiff = Math.Abs(expectedSlopeAngle - observedSlopeAngles[0]);
tmp = Math.Abs(expectedSlopeAngle - observedSlopeAngles[1]);
if (tmp > angleDiff)
{
angleDiff = tmp;
}
bool estimateOk = (angleDiff < 0.035) && observedSlopes.All(z => z > 0);
//# 0.035 radians is approximately 2 degrees
bool cntn = !estimateOk;
SAEList found = new SAEList();
if (cntn)
{
/*
* # We look for a point on the left side of x and one on its right side
* # where the integral [area] seems to be correctly estimated
* # (with positive slopes of value close to expected value [density])
* # If we are estimating the area on the remote right end of the distrn (remote.right=T)
* # then we will be happy if an estimate to the left of x is obtained
*
*/
int side = -1;
//# Store starting points
double[] tmpX = xStar.Copy(); //?
double[] tmpA = a.Copy(); //?
while (cntn)
{
side = side + 1; // # side = 0 -> Left of x
// # side = 1 -> Right of x
int direction = side == 0 ? -1 : 1;
if (side == 1)
{
xStar = tmpX.Copy(); //?
a = tmpA.Copy();
}
int j = side == 0 ? 0 : 2;
double z = xStar[j];
int count = 0;
bool onBorder = false;
double aZ = Tools.NA;
while (cntn)
{
z = z + direction * d;
//# make sure that we don't step to the left of mathematical lower limit
if (z <= mathLowerLimit)
{
if (inestimableLowerLimit)
{
z = (mathLowerLimit + z + d) / 2.0;
}
else
{
z = mathLowerLimit;
onBorder = true;
}
}
if ((side == 0) && z == mathLowerLimit)
{
//# This is still possible even with the above 'protection' against
//# this scenario, due to numerical imprecision
aZ = 0;
cntn = false;
estimateOk = true;
}
else
{
aZ = area(z, A);
if (side == 0)
{
xStar = Tools.Combine(z, xStar[0], xStar[1]); //[-3]
a = Tools.Combine(aZ, a[0], a[1]);
}
else
{
xStar = Tools.Combine(xStar[1], xStar[1], z); //[-1]
a = Tools.Combine(a[1], a[2], aZ);
}
//a.Diff().Divide(xStar.Diff()).Multiply(hpMult);
observedSlopes = a.Diff().Divide(xStar.Diff()).Multiply(hpMult);
expectedSlope = A.F(z, A);
observedSlopeAngles = Tools.Combine(Math.Atan(observedSlopes[0]), Math.Atan(observedSlopes[1]));
expectedSlopeAngle = Math.Atan(expectedSlope);
angleDiff = Math.Abs(expectedSlopeAngle - observedSlopeAngles[0]);
tmp = Math.Abs(expectedSlopeAngle - observedSlopeAngles[1]);
if (tmp > angleDiff)
{
angleDiff = tmp;
}
estimateOk = ((angleDiff < 0.035) && observedSlopes.All(w => w > 0)) || (angleDiff < 1E-6);
//# 0.035 radians is approximately 2 degrees
cntn = !estimateOk && (!onBorder);
}
if (cntn)
{
if (remoteRight && (side == 0))
{
cntn = (expectedSlope / fX) < 10000;
}
else
{
count = count + 1;
cntn = count <= maxCount;
}
}
}
if ((side == 0) && remoteRight)
{
cntn = !estimateOk;
if (estimateOk)
{
aX = aZ;
}
}
else
{
cntn = side == 0;
}
//# Store results
found.Ok[side] = estimateOk;
found.X[side] = z;
found.A[side] = aZ;
found.F[side] = expectedSlope;
} //# end of while-continue
if (!remoteRight || !found.Ok[0])
{
if (found.Ok[0] && found.Ok[1])
{
double fDiff = found.F.Diff()[0];
bool extrapolate = fDiff == 0;
if (!extrapolate)
{
//- (diff(found$a) - diff(found$f*found$x)) / f.diff
double t1 = (found.A[1] - found.A[0]); //diff(found$a)
double t2 = (found.F[1] * found.X[1]) - (found.F[0] * found.X[0]); //diff(found$f*found$x)
double xIntersect = -(t1 - t2) / fDiff;
extrapolate = (xIntersect < found.X[0]) || (xIntersect > found.X[1]);
if (!extrapolate)
{
int j = x <= xIntersect ? 0 : 1;
aX = found.A[j] + found.F[j] * (x - found.X[j]);
}
}
if (extrapolate)
{
aX = found.A[0] + Diff(found.A)[0] / Diff(found.X)[0] * (x - found.X[0]);
}
}
else if (found.Ok[0] || found.Ok[1])
{
int j = found.Ok[0] ? 0 : 1;
aX = found.A[j] + found.F[j] * (x - found.X[j]);
}
else
{
//TODO Exception
throw new WEException("Could not get a smoothed cumulative density estimate.");
}
}
}
return(aX);
} // end of smoothed.area.estimate
internal static double PingpongTieBreaker(
Func <double, SGNFnAParam, double> area,
SGNFnAParam A,
double start,
double areaX,
double target,
double mathLowerLimit,
double[] refRange,
bool inestimableLowerLimit,
double epsilon,
bool distrnLeftSide = false,
int maxCount = 100)
{
int hpMult = distrnLeftSide ? -1 : 1;
bool cntn = true;
int count = 0;
double x = start;
Visits visitedX = new Visits(maxCount);
visitedX.Add(x);
bool converged = false;
bool caughtInLoop = false;
while (cntn)
{
double hp = A.F(x, A) * hpMult;
double change = (target - areaX) / hp;
x = x + change;
// new_0.11
if (x < refRange[0])
{
x = (refRange[0] == mathLowerLimit) && inestimableLowerLimit ? (x - change + mathLowerLimit) / 2.0 : refRange[0];
}
areaX = WebExpoFunctions3.SmoothedAreaEstimate(area, x, A, mathLowerLimit, refRange, inestimableLowerLimit, hpMult: hpMult);
count++;
converged = Math.Abs(areaX - target) < epsilon;
visitedX.Add(x);
caughtInLoop = visitedX.CaughtInLoop; // La propiété CaughtInLoop est mise à jour à chaque ajout d'un x.
// x doit être fini, et avoir déjà été visité.
cntn = !converged && (visitedX.Count <= maxCount) && !caughtInLoop;
}
if (!converged && caughtInLoop)
{
// We have found the series of points that are repeatedly visited:
// recalibrate and try Newton-Raphson again
double[] tail = visitedX.GetFromTail(x);
x = (distrnLeftSide) ? x = tail.Max() : tail.Min();
areaX = WebExpoFunctions3.SmoothedAreaEstimate(area, x, A, mathLowerLimit, refRange, inestimableLowerLimit, hpMult: hpMult);
if (distrnLeftSide)
{
A.UpperLimit = x;
}
else
{
A.LowerLimit = x;
}
target = target - areaX;
areaX = 0.0;
count = 0;
cntn = true;
while (cntn)
{
double hp = A.F(x, A) * hpMult;
double change = (target - areaX) / hp;
x = x + change;
areaX = area(x, A);
count = count + 1;
converged = Math.Abs(areaX - target) < epsilon;
cntn = !converged && (count <= maxCount);
}
}
if (!converged)
{
//TODO Exception
throw new WEException("Newton-Raphson algorithm did not converge. Sorry.\n");
}
return(x);
} // end of ping.pong.tie.breaker
