public override EndCriteria.Type minimize(Problem P, EndCriteria endCriteria)
{
// Initializations
double ftol = endCriteria.functionEpsilon();
int maxStationaryStateIterations_ = endCriteria.maxStationaryStateIterations();
EndCriteria.Type ecType = EndCriteria.Type.None; // reset end criteria
P.reset(); // reset problem
Vector x_ = P.currentValue(); // store the starting point
int iterationNumber_ = 0;
// dimension line search
lineSearch_.searchDirection = new Vector(x_.size());
bool done = false;
// function and squared norm of gradient values
double fnew, fold, gold2;
double fdiff;
// classical initial value for line-search step
double t = 1.0;
// Set gradient g at the size of the optimization problem
// search direction
int sz = lineSearch_.searchDirection.size();
Vector prevGradient = new Vector(sz), d = new Vector(sz), sddiff = new Vector(sz), direction = new Vector(sz);
// Initialize cost function, gradient prevGradient and search direction
P.setFunctionValue(P.valueAndGradient(ref prevGradient, x_));
P.setGradientNormValue(Vector.DotProduct(prevGradient, prevGradient));
lineSearch_.searchDirection = prevGradient * -1;
bool first_time = true;
// Loop over iterations
do
{
// Linesearch
if (!first_time)
{
prevGradient = lineSearch_.lastGradient();
}
t = (lineSearch_.value(P, ref ecType, endCriteria, t));
// don't throw: it can fail just because maxIterations exceeded
if (lineSearch_.succeed())
{
// Updates
// New point
x_ = lineSearch_.lastX();
// New function value
fold = P.functionValue();
P.setFunctionValue(lineSearch_.lastFunctionValue());
// New gradient and search direction vectors
// orthogonalization coef
gold2 = P.gradientNormValue();
P.setGradientNormValue(lineSearch_.lastGradientNorm2());
// conjugate gradient search direction
direction = getUpdatedDirection(P, gold2, prevGradient);
sddiff = direction - lineSearch_.searchDirection;
lineSearch_.searchDirection = direction;
// Now compute accuracy and check end criteria
// Numerical Recipes exit strategy on fx (see NR in C++, p.423)
fnew = P.functionValue();
fdiff = 2.0 * Math.Abs(fnew - fold) /
(Math.Abs(fnew) + Math.Abs(fold) + Const.QL_EPSILON);
if (fdiff < ftol ||
endCriteria.checkMaxIterations(iterationNumber_, ref ecType))
{
endCriteria.checkStationaryFunctionValue(0.0, 0.0, ref maxStationaryStateIterations_, ref ecType);
endCriteria.checkMaxIterations(iterationNumber_, ref ecType);
return(ecType);
}
P.setCurrentValue(x_); // update problem current value
++iterationNumber_; // Increase iteration number
first_time = false;
}
else
{
done = true;
}
}while (!done);
P.setCurrentValue(x_);
return(ecType);
}
//! computes the new search direction
protected virtual Vector getUpdatedDirection(Problem P, double gold2, Vector gradient)
{
throw new NotImplementedException();
}
// LineSearchBasedMethod interface
protected override Vector getUpdatedDirection(Problem P, double gold2, Vector oldGradient)
{
if (inverseHessian_.rows() == 0)
{
// first time in this update, we create needed structures
inverseHessian_ = new Matrix(P.currentValue().size(), P.currentValue().size(), 0.0);
for (int i = 0; i < P.currentValue().size(); ++i)
{
inverseHessian_[i, i] = 1.0;
}
}
Vector diffGradient = new Vector();
Vector diffGradientWithHessianApplied = new Vector(P.currentValue().size(), 0.0);
diffGradient = lineSearch_.lastGradient() - oldGradient;
for (int i = 0; i < P.currentValue().size(); ++i)
{
for (int j = 0; j < P.currentValue().size(); ++j)
{
diffGradientWithHessianApplied[i] += inverseHessian_[i, j] * diffGradient[j];
}
}
double fac, fae, fad;
double sumdg, sumxi;
fac = fae = sumdg = sumxi = 0.0;
for (int i = 0; i < P.currentValue().size(); ++i)
{
fac += diffGradient[i] * lineSearch_.searchDirection[i];
fae += diffGradient[i] * diffGradientWithHessianApplied[i];
sumdg += Math.Pow(diffGradient[i], 2.0);
sumxi += Math.Pow(lineSearch_.searchDirection[i], 2.0);
}
if (fac > Math.Sqrt(1e-8 * sumdg * sumxi)) // skip update if fac not sufficiently positive
{
fac = 1.0 / fac;
fad = 1.0 / fae;
for (int i = 0; i < P.currentValue().size(); ++i)
{
diffGradient[i] = fac * lineSearch_.searchDirection[i] - fad * diffGradientWithHessianApplied[i];
}
for (int i = 0; i < P.currentValue().size(); ++i)
{
for (int j = 0; j < P.currentValue().size(); ++j)
{
inverseHessian_[i, j] += fac * lineSearch_.searchDirection[i] * lineSearch_.searchDirection[j];
inverseHessian_[i, j] -= fad * diffGradientWithHessianApplied[i] * diffGradientWithHessianApplied[j];
inverseHessian_[i, j] += fae * diffGradient[i] * diffGradient[j];
}
}
}
Vector direction = new Vector(P.currentValue().size());
for (int i = 0; i < P.currentValue().size(); ++i)
{
direction[i] = 0.0;
for (int j = 0; j < P.currentValue().size(); ++j)
{
direction[i] -= inverseHessian_[i, j] * lineSearch_.lastGradient()[j];
}
}
return(direction);
}
public override EndCriteria.Type minimize(Problem P, EndCriteria endCriteria)
{
EndCriteria.Type ecType = EndCriteria.Type.None;
P.reset();
Vector x_ = P.currentValue();
currentProblem_ = P;
initCostValues_ = P.costFunction().values(x_);
int m = initCostValues_.size();
int n = x_.size();
if (useCostFunctionsJacobian_)
{
initJacobian_ = new Matrix(m, n);
P.costFunction().jacobian(initJacobian_, x_);
}
Vector xx = new Vector(x_);
Vector fvec = new Vector(m), diag = new Vector(n);
int mode = 1;
double factor = 1;
int nprint = 0;
int info = 0;
int nfev = 0;
Matrix fjac = new Matrix(m, n);
int ldfjac = m;
List <int> ipvt = new InitializedList <int>(n);
Vector qtf = new Vector(n), wa1 = new Vector(n), wa2 = new Vector(n), wa3 = new Vector(n), wa4 = new Vector(m);
// call lmdif to minimize the sum of the squares of m functions
// in n variables by the Levenberg-Marquardt algorithm.
Func <int, int, Vector, int, Matrix> j = null;
if (useCostFunctionsJacobian_)
{
j = jacFcn;
}
// requirements; check here to get more detailed error messages.
Utils.QL_REQUIRE(n > 0, () => "no variables given");
Utils.QL_REQUIRE(m >= n, () => $"less functions ({m}) than available variables ({n})");
Utils.QL_REQUIRE(endCriteria.functionEpsilon() >= 0.0, () => "negative f tolerance");
Utils.QL_REQUIRE(xtol_ >= 0.0, () => "negative x tolerance");
Utils.QL_REQUIRE(gtol_ >= 0.0, () => "negative g tolerance");
Utils.QL_REQUIRE(endCriteria.maxIterations() > 0, () => "null number of evaluations");
MINPACK.lmdif(m, n, xx, ref fvec,
endCriteria.functionEpsilon(),
xtol_,
gtol_,
endCriteria.maxIterations(),
epsfcn_,
diag, mode, factor,
nprint, ref info, ref nfev, ref fjac,
ldfjac, ref ipvt, ref qtf,
wa1, wa2, wa3, wa4,
fcn, j);
info_ = info;
// check requirements & endCriteria evaluation
Utils.QL_REQUIRE(info != 0, () => "MINPACK: improper input parameters");
if (info != 6)
{
ecType = EndCriteria.Type.StationaryFunctionValue;
}
endCriteria.checkMaxIterations(nfev, ref ecType);
Utils.QL_REQUIRE(info != 7, () => "MINPACK: xtol is too small. no further " +
"improvement in the approximate " +
"solution x is possible.");
Utils.QL_REQUIRE(info != 8, () => "MINPACK: gtol is too small. fvec is " +
"orthogonal to the columns of the " +
"jacobian to machine precision.");
// set problem
x_ = new Vector(xx.GetRange(0, n));
P.setCurrentValue(x_);
P.setFunctionValue(P.costFunction().value(x_));
return(ecType);
}
public void compute()
{
if (vegaWeighted_)
{
double weightsSum = 0.0;
for (int i = 0; i < times_.Count; i++)
{
double stdDev = Math.Sqrt(blackVols_[i] * blackVols_[i] * times_[i]);
// when strike==forward, the blackFormulaStdDevDerivative becomes
weights_[i] = new CumulativeNormalDistribution().derivative(.5 * stdDev);
weightsSum += weights_[i];
}
// weight normalization
for (int i = 0; i < times_.Count; i++)
{
weights_[i] /= weightsSum;
}
}
// there is nothing to optimize
if (aIsFixed_ && bIsFixed_ && cIsFixed_ && dIsFixed_)
{
abcdEndCriteria_ = QLCore.EndCriteria.Type.None;
return;
}
else
{
AbcdError costFunction = new AbcdError(this);
transformation_ = new AbcdParametersTransformation();
Vector guess = new Vector(4);
guess[0] = a_;
guess[1] = b_;
guess[2] = c_;
guess[3] = d_;
List <bool> parameterAreFixed = new InitializedList <bool>(4);
parameterAreFixed[0] = aIsFixed_;
parameterAreFixed[1] = bIsFixed_;
parameterAreFixed[2] = cIsFixed_;
parameterAreFixed[3] = dIsFixed_;
Vector inversedTransformatedGuess = new Vector(transformation_.inverse(guess));
ProjectedCostFunction projectedAbcdCostFunction = new ProjectedCostFunction(costFunction,
inversedTransformatedGuess, parameterAreFixed);
Vector projectedGuess = new Vector(projectedAbcdCostFunction.project(inversedTransformatedGuess));
NoConstraint constraint = new NoConstraint();
Problem problem = new Problem(projectedAbcdCostFunction, constraint, projectedGuess);
abcdEndCriteria_ = optMethod_.minimize(problem, endCriteria_);
Vector projectedResult = new Vector(problem.currentValue());
Vector transfResult = new Vector(projectedAbcdCostFunction.include(projectedResult));
Vector result = transformation_.direct(transfResult);
QLCore.AbcdMathFunction.validate(a_, b_, c_, d_);
a_ = result[0];
b_ = result[1];
c_ = result[2];
d_ = result[3];
}
}
