public Func <double, double> AreaFromXToUpperLimitFn(SGNFnAParam A)
{
Func <double, double> dummy = null;
if (this.F == null)
{
dummy = delegate(double x)
{
return(Tools.NA);
};
}
else
{
Func <double, double> area = delegate(double xParm)
{
return(F(xParm, A));
};
dummy = delegate(double x)
{
Numerics.Integration.NumericIntegration.Results res;
res = Numerics.Integration.NumericIntegration.Integrate(area, x, A.UpperLimit);
return(res.Value);
};
}
return(dummy);
}
internal SGNFnAParam Clone()
{
SGNFnAParam a = (SGNFnAParam)this.MemberwiseClone();
if (this.Range == null)
{
a.Range = null;
}
else if (this.Range.Length == 0)
{
a.Range = new double[0];
}
else
{
a.Range = this.Range.Copy();
}
if (this.Truevalues == null)
{
a.Truevalues = null;
}
else if (this.Truevalues.Length == 0)
{
a.Truevalues = new double[0];
}
else
{
a.Truevalues = this.Truevalues.Copy();
}
return(a);
}
internal override double LogFSecond(double s, SGNFnAParam A)
{
double z = A.Mu / s;
LPhiObject l = WebExpoFunctions3.LPhi(z);
return(A.N / Math.Pow(s, 2) - 6.0 * A.B / Math.Pow(s, 4) + A.N * z * ((Math.Pow(z, 2) - 2.0) * l.R[0] + z * l.R2[0]) / Math.Pow(s, 2));
}
internal override double LogFSecond(double sigma, SGNFnAParam A)
{
double s2 = Math.Pow(sigma, 2);
double s4 = Math.Pow(s2, 2);
return(A.N / s2 - 6.0 * A.B / s4);
}
internal override double LogFPrime(double s, SGNFnAParam A)
{
double z = A.Mu / s;
LPhiObject l = WebExpoFunctions3.LPhi(z);
return(-A.N / s + 2.0 * A.B / Math.Pow(s, 3) + A.N * z * l.R[0] / s);
}
/*
* log.f.inv.remote <- function(target, A)
* {
* tmp <- 1 + c(-1,1)*sqrt(2*A$cv2*abs(target))
* tmp <- tmp[tmp>0]
* roots <- log(tmp/A$y)
*
* C <- -(A$y-1)^2/2/A$cv2 - A$mu^2/2/A$sigma2
* B <- -1 + (A$y-1)*A$y/A$cv2 + A$mu/A$sigma2
* qA <- -A$y2/2/A$cv2 - 1/2/A$sigma2
* tmp <- quadratic.solution(c(C, B, qA), target=target)
*
* roots <- c(roots, tmp)
* roots
* } # end of log.f.inv.remote
* }
*/
internal override List <double> LogFInvRemote(double target, SGNFnAParam A)
{
List <double> roots = new List <double>();
double z = Math.Sqrt(2.0 * A.CV2 * Math.Abs(target));
double pPetit = 1.0 - z;
double pGrand = 1.0 + z;
if (pPetit > 0.0)
{
roots.Add(Math.Log(pPetit / A.Y));
roots.Add(Math.Log(pGrand / A.Y));
}
else if (pGrand > 0.0)
{
roots.Add(Math.Log(pGrand / A.Y));
}
double C =
-Math.Pow(A.Y - 1.0, 2) / 2.0 / A.CV2
- Math.Pow(A.Mu, 2) / 2.0 / A.Sigma2;
double B =
-1.0
+ (A.Y - 1.0) * A.Y / A.CV2
+ A.Mu / A.Sigma2;
double qA =
-A.Y2 / 2.0 / A.CV2
- 1.0 / 2.0 / A.Sigma2;
roots.AddRange(QuadraticEquation.GetRealRoots(Tools.Combine(C, B, qA), target, ROrder: true));
return(roots);
}
internal override double LogF(double v, SGNFnAParam A)
{
return
(-A.N * Math.Log(v)
- A.B / Math.Pow(v, 2)
- A.N * NormalDistribution.PNorm(1.0 / v, log_p: true));
}
} //# end of leftSide.fastScan
private L1 DipCharacteristics(Bounds b, ISecuredNR o, SGNFnAParam A, double epsilon = 1e-8)
{
bool cntn = true;
double x = 0, h = 0, hp = 0;
while (cntn)
{
//# intersection between the tangents at both ends of bounds (b)
double bDiff = b.Hp.Diff()[0];
if (bDiff == 0)
{
x = (b.X.Mean());
}
else
{
x = (b.Hp.Multiply(b.X).Diff()[0] - b.H.Diff()[0]) / bDiff;
if (x <= b.X[0] | x >= b.X[1])
{
x = b.X.Mean();
}
}
h = o.H(x, A);
hp = o.HPrime(x, A);
int side = hp < 0 ? 0 : 1;
b.X[side] = x;
b.H[side] = h;
b.Hp[side] = hp;
cntn = b.X.Diff()[0] > epsilon;
}
return(new L1(x, h, hp));
//TODO Voir si l'on peut partager a l'intérieur de SecuredNRSearch, en utilisant des champs, x, h et hp et possiblement d'autres
//list(x = x, h = h, hp = hp)
} //# end of dip.characteristics
//sqrt.invertedGamma.gen <- function(n, beta, xrange, o=list(), beta.min=1e-8)
internal static double SqrtInvertedGammaGen(int n, double beta, double[] xRange, GenObject o, double betaMin = 1E-8)
{
//# Sample a value from the distrn
//#
//# f(x) = 1
//# ------- . exp(-beta/x^2)
//# x^n
double x = Tools.ND;
if (n <= 1)
{
SGNFnAParam A = o.A.Clone();
A.B = beta;
Icdf icdf = new Icdf(o, A, xRange);
x = icdf.Bidon(start: Math.Sqrt(2.0 * beta), inestLowerLim: xRange[0] == 0);
}
else if (beta < betaMin)
{
if (xRange[0] == 0)
{
xRange[0] = 0.0001;
}
x = RandomPow(n, xRange);
}
else
{
double alpha = (n - 1) / 2.0;
double[] invX2Range = xRange.Sqr().Reverse().ToArray().Reciprocal();
double invX2 = RGammaTruncated(alpha, beta, invX2Range);
x = 1 / Math.Sqrt(invX2);
}
return(x);
} //# end of sqrt.invertedGamma.gen
internal override double LogF(double s, SGNFnAParam A)
{
return
(-s
- Math.Pow(A.Y * Math.Exp(-s) - 1.0, 2) / 2.0 / A.CV2
- Math.Pow(s - A.Mu, 2) / 2.0 / A.Sigma2);
}
internal override double LogFSecond(double s, SGNFnAParam A)
{
return
(-2.0 * A.Y2 * Math.Exp(-2 * s) / A.CV2
+ A.Y * Math.Exp(-s) / A.CV2
- 1 / A.Sigma2);
}
internal override double LogFPrime(double t, SGNFnAParam A)
{
return
(-1.0 / t
- (A.Y / Math.Pow(t, 2) - A.Y2 / Math.Pow(t, 3)) / A.CV2
+ (A.Mu - t) / A.Sigma2);
}
internal override double LogFPrime(double mu, SGNFnAParam A)
{
double z = mu / A.S;
LPhiObject lphio = WebExpoFunctions3.LPhi(z);
return(-A.N * (mu - A.MuMean) / A.S2 - A.N * lphio.R[0] / A.S);
}
internal override double LogFSecond(double mu, SGNFnAParam A)
{
double z = mu / A.S;
LPhiObject lphio = WebExpoFunctions3.LPhi(z);
return(A.N / A.S2 * (z * lphio.R[0] + lphio.R2[0] - 1));
}
internal override double LogF(double s, SGNFnAParam A)
{
return
(-NormalDistribution.PNorm(Math.Exp(s) / A.Ksi, log_p: true)
- Math.Pow((A.Y - Math.Exp(s)), 2) / 2.0 / A.Ksi2
- Math.Pow((s - A.Mu), 2) / 2.0 / A.Sigma2);
}
internal override double LogF(double t, SGNFnAParam A)
{
return
(-Math.Log(t)
- Math.Pow(A.Y - t, 2) / 2.0 / A.CV2 / Math.Pow(t, 2)
- Math.Pow(t - A.Mu, 2) / 2.0 / A.Sigma2);
}
private double TrueValueGen(GenObject genO, MeasurementError me, double y, double mu, double logY)
{
SGNFnAParam localA = genO.A.Clone();
localA.Mu = mu;
if (genO.LogNormalDistrn)
{
localA.LogY = logY;
}
localA.Y = y;
localA.Y2 = y * y;
if (genO.ThroughSD)
{
localA.Ksi = me.Parm;
localA.Ksi2 = me.Parm * me.Parm;
}
else
{
localA.CV2 = me.Parm * me.Parm;
}
double[] start = genO.Start(localA);
//start.Any(zz => !zz.IsFinite());
Icdf icdf = new Icdf(genO, localA, range: genO.Range);
double x = icdf.Bidon(start, inestLowerLim: !genO.LogNormalDistrn);
if (genO.LogNormalDistrn)
{
x = Math.Exp(x);// # new_0.11
}
return(x);
} //# end of truevalue.gen
internal override double LogFSecond(double t, SGNFnAParam A)
{
return
(1.0 / Math.Pow(t, 2)
+ (2.0 * A.Y / Math.Pow(t, 3)
- 3.0 * A.Y2 / Math.Pow(t, 4)) / A.CV2
- 1.0 / A.Sigma2);
}
internal override double LogF(double s, SGNFnAParam A)
{
return
(-(A.N + 1) * Math.Log(s)
- A.B / Math.Pow(s, 2)
- A.N * NormalDistribution.PNorm(A.Mu / s, log_p: true)
- (Math.Pow(Math.Log(s) - A.LM, 2)) / (2.0 * A.LS2));
}
}//LogFPrime
internal override double LogFSecond(double sigma, SGNFnAParam A)
{
//(A$N + 1)/ sigma ^ 2 - 6 * A$b / sigma ^ 4 + (log(sigma) - A$lm - 1)/ (A$ls2* sigma^ 2)
double s2 = Math.Pow(sigma, 2);
double s4 = Math.Pow(s2, 2);
double x = (A.N + 1.0) / s2 - (6.0 * A.B / s4) + ((Math.Log(sigma) - A.LM - 1.0) / (A.LS2 * s2));
return(x);
} //LogFSecond
internal override double LogFPrime(double s, SGNFnAParam A)
{
return(-1.0
+ (
A.Y2 * Math.Exp(-2 * s)
- A.Y * Math.Exp(-s)
) / A.CV2
- (s - A.Mu) / A.Sigma2);
}
internal Icdf(GenObject o, SGNFnAParam a, double[] range, double precision = 1E-6, int NRMaxIteration = 200)
{
this.Ob01 = o;
this.A = a == null ? o.A : a;
this.Range = (range == null) ? new double[0] : range;
this.Start = Tools.Combine(Range.Mean()); // donne NaN si range est de longueur 0.
this.Precision = precision;
this.NRMaxIter = NRMaxIteration;
}
internal override double LogFPrime(double v, SGNFnAParam A)
{
LPhiObject l = WebExpoFunctions3.LPhi(1 / v);
return
(-A.N / v
+ 2.0 * A.B / Math.Pow(v, 3)
+ A.N * l.R[0] / Math.Pow(v, 2));
}
internal static MEParmGen GetInstance(GenObject o, MeasurementError me, DataSummary data, YGen genY, TrueValuesGen genTV)
{
MEParmGen instance = new MEParmGen();
double b;
double[] tmpY, tmpT;
if (me.ThroughCV)
{
if (o.LogNormalDistrn)
{
tmpY = Tools.Combine(data.LogY, genY.LogGT, genY.LogLT, genY.LogI);
tmpT = Tools.Combine(genTV.LogY, genTV.LogGT, genTV.LogLT, genTV.LogI);
b = tmpY.Substract(tmpT).Exp().Substract(1.0).Sqr().Sum();
b /= 2.0;
}
else
{
tmpY = Tools.Combine(data.Y, genY.GT, genY.LT, genY.I);
tmpT = Tools.Combine(genTV.Y, genTV.GT, genTV.LT, genTV.I);
b = tmpY.Divide(tmpT).Substract(1.0).Sqr().Reverse().Sum();
b /= 2.0;
}
SGNFnAParam localA = o.A.Clone();
localA.B = b;
localA.Range = me.GetRange();
double[] range = me.GetRange();
Icdf icdf = new Icdf(o, localA, range);
instance.Parm = icdf.Bidon(o.Start(localA), inestLowerLim: range[0] == 0);
}
else
{
tmpY = Tools.Combine(data.Y, genY.GT, genY.LT, genY.I);
tmpT = Tools.Combine(genTV.Y, genTV.GT, genTV.LT, genTV.I);
b = tmpY.Substract(tmpT).Sqr().Sum();
b /= 2.0;
if (o.LogNormalDistrn)
{
SGNFnAParam localA = o.A.Clone();
localA.B = b;
localA.Range = me.GetRange();
localA.Truevalues = Tools.Copy(tmpT);
//me.parm <- dens.gen.icdf(o, A, range=me$range, inestimable.lower.limit=me$range[1]==0)
double[] range = me.GetRange();
Icdf icdf = new Icdf(o, localA, range);
instance.Parm = icdf.Bidon(inestLowerLim: range[0] == 0.0);
}
else
{
instance.Parm = WebExpoFunctions3.SqrtInvertedGammaGen(data.N, b, me.GetRange(), o);
}
}
return(instance);
}
internal override List <double> LogFInvRemote(double target, SGNFnAParam A)
{
/*
# solutions for large s
# tmp <- A$y + c(-1,1)*sqrt(2*abs(target)*A$ksi2) # vector of length 2
# tmp <- tmp[tmp>0]
# roots <- log(tmp)
#
*/
// solutions for large s
List <double> roots = new List <double>();
double z = Math.Sqrt(2 * Math.Abs(target) * A.Ksi2);
double pp = A.Y - z;
double pg = A.Y + z;
if (pp > 0.0)
{
roots.Add(Math.Log(pp));
roots.Add(Math.Log(pg));
}
else if (pg > 0.0)
{
roots.Add(Math.Log(pg));
}
/*
* C <- log(2) -A$y2/2/A$ksi2 - A$mu^2/2/A$sigma2
* B <- A$mu/A$sigma2
* qA <- -1/2/A$sigma2
* tmp <- quadratic.solution(c(C, B, qA), target=target)
* roots <- c(roots, tmp)
*
*/
//# solutions for small s (large negative values)
double C = Math.Log(2) - A.Y2 / 2.0 / A.Ksi2 - Math.Pow(A.Mu, 2) / 2.0 / A.Sigma2;
double B = A.Mu / A.Sigma2;
double qA = -1.0 / 2.0 / A.Sigma2;
roots.AddRange(QuadraticEquation.GetRealRoots(Tools.Combine(C, B, qA), target, ROrder: true));
/*
* C <- log(2) -A$y2/2/A$ksi2 - A$mu^2/2/A$sigma2
* B <- A$mu/A$sigma2
* qA <- -1/2/A$sigma2
* tmp <- quadratic.solution(c(C, B, qA), target=target)
* roots <- c(roots, tmp)
*/
//# solutions around 0
C = Math.Log(1.0 / A.Ksi) - Math.Pow(A.Y - 1.0, 2) / 2.0 / A.Ksi2 - Math.Pow(A.Mu, 2) / 2.0 / A.Sigma2;
B = A.Mu / A.Sigma2;
qA = -1.0 / 2.0 / A.Sigma2;
roots.AddRange(QuadraticEquation.GetRealRoots(Tools.Combine(C, B, qA), target, ROrder: true));
return(roots);
} // # end of log.f.inv.remote
internal override double[] Start(SGNFnAParam A)
{
double s0 = Math.Sqrt(2.0 * A.B / A.N);
if ((s0 < A.Range[0]) || (s0 > A.Range[1]))
{
s0 = A.Range.Mean();
}
return(Tools.Combine(s0));
}
internal override double LogFSecond(double s, SGNFnAParam A)
{
// log.f.prime <- function(s, A){z <- exp(s)/A$ksi; l <- lphi(z); -l$r*z + A$y*z/A$ksi - z^2 - (s-A$mu)/A$sigma2}
double[] z = new double[] { Math.Exp(s) / A.Ksi };
LPhiObject lphio = WebExpoFunctions3.LPhi(z);
double r0 = lphio.R[0];
double z0 = z[0];
return(r0 * (Math.Pow(z0, 3) - z[0]) + Math.Pow(r0 * z0, 2) + (A.Y * Math.Exp(s) - 2.0 * Math.Exp(2 * s)) / A.Ksi2 - 1.0 / A.Sigma2);
}
/*
* start <- function(A)
* {
* C <- -1 + A$y2/A$cv2 - A$y/A$cv2 + A$mu/A$sigma2
* B <- -2*A$y2/A$cv2 + A$y/A$cv2 - 1/A$sigma2
* qA <- 2*A$y2/A$cv2 - A$y/2/A$cv2
* tmp <- quadratic.solution(c(C, B, qA))
*
* start <- c(tmp, A$mu - A$sigma2)
* start
* } # end of start
*/
internal override double[] Start(SGNFnAParam A)
{
double C = -1.0 + A.Y2 / A.CV2 - A.Y / A.CV2 + A.Mu / A.Sigma2;
double B = -2.0 * A.Y2 / A.CV2 + A.Y / A.CV2 - 1.0 / A.Sigma2;
double qA = 2.0 * A.Y2 / A.CV2 - A.Y / 2.0 / A.CV2;
List <double> roots = QuadraticEquation.GetRealRoots(Tools.Combine(C, B, qA), ROrder: true);
roots.Add(A.Mu - A.Sigma2);
return(roots.ToArray());
}
internal override List <double> LogFInvRemote(double target, SGNFnAParam A)
{
List <double> roots = new List <double>();
double D = -A.B;
double B = -A.N * (Math.Log(A.Mode) - 1.0) - target;
double qA = -A.N / A.Mode;
roots.AddRange(CubicEquation.GetRealRoots(Util.Tools.Combine(D, 0, B, qA), l: 0, u: A.Mode, ROrder: true));// # modif_0.11
roots.Add(Math.Exp(Math.Log(2.0) - target / A.N));
return(roots);
}
internal override double LogFSecond(double v, SGNFnAParam A)
{
LPhiObject l = WebExpoFunctions3.LPhi(1 / v);
double v2 = Math.Pow(v, 2);
double v4 = Math.Pow(v2, 2);
return
(A.N / v2
- 6.0 * A.B / v4
+ A.N / v4 * (l.R[0] * (1 / v - 2.0 * v) + l.R2[0]));
}
