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();
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.
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);
info_ = info;
// check requirements & endCriteria evaluation
if(info == 0) throw new ApplicationException("MINPACK: improper input parameters");
//if(info == 6) throw new ApplicationException("MINPACK: ftol is too small. no further " +
// "reduction in the sum of squares is possible.");
if (info != 6) ecType = EndCriteria.Type.StationaryFunctionValue;
//QL_REQUIRE(info != 5, "MINPACK: number of calls to fcn has reached or exceeded maxfev.");
endCriteria.checkMaxIterations(nfev, ref ecType);
if(info == 7) throw new ApplicationException("MINPACK: xtol is too small. no further " +
"improvement in the approximate " +
"solution x is possible.");
if(info == 8) throw new ApplicationException("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;
}
//! minimize the optimization problem P
public override EndCriteria.Type minimize(Problem P, EndCriteria endCriteria)
{
EndCriteria.Type ecType = EndCriteria.Type.None;
P.reset();
Vector x_ = P.currentValue();
int iterationNumber_ = 0;
int stationaryStateIterationNumber_ = 0;
lineSearch_.searchDirection = new Vector(x_.Count);
bool end;
// function and squared norm of gradient values;
double normdiff;
// classical initial value for line-search step
double t = 1.0;
// Set gold at the size of the optimization problem search direction
Vector gold = new Vector(lineSearch_.searchDirection.Count);
Vector gdiff = new Vector(lineSearch_.searchDirection.Count);
P.setFunctionValue(P.valueAndGradient(gold, x_));
lineSearch_.searchDirection = gold*-1.0;
P.setGradientNormValue(Vector.DotProduct(gold, gold));
normdiff = Math.Sqrt(P.gradientNormValue());
do
{
// Linesearch
t = lineSearch_.value(P, ref ecType, endCriteria, t);
if (!(lineSearch_.succeed()))
throw new ApplicationException("line-search failed!");
// End criteria
// FIXME: it's never been used! ???
// , normdiff
end = endCriteria.value(iterationNumber_, ref stationaryStateIterationNumber_, true, P.functionValue(), Math.Sqrt(P.gradientNormValue()), lineSearch_.lastFunctionValue(), Math.Sqrt(lineSearch_.lastGradientNorm2()), ref ecType);
// Updates
// New point
x_ = lineSearch_.lastX();
// New function value
P.setFunctionValue(lineSearch_.lastFunctionValue());
// New gradient and search direction vectors
gdiff = gold - lineSearch_.lastGradient();
normdiff = Math.Sqrt(Vector.DotProduct(gdiff, gdiff));
gold = lineSearch_.lastGradient();
lineSearch_.searchDirection = gold*-1.0;
// New gradient squared norm
P.setGradientNormValue(lineSearch_.lastGradientNorm2());
// Increase interation number
++iterationNumber_;
} while (end == false);
P.setCurrentValue(x_);
return ecType;
}
//! Perform line search
public override double value(Problem P, ref EndCriteria.Type ecType, EndCriteria endCriteria, double t_ini)
{
//OptimizationMethod& method = P.method();
Constraint constraint = P.constraint();
succeed_ = true;
bool maxIter = false;
double qtold;
double t = t_ini;
int loopNumber = 0;
double q0 = P.functionValue();
double qp0 = P.gradientNormValue();
qt_ = q0;
qpt_ = (gradient_.Count == 0) ? qp0 : -Vector.DotProduct(gradient_, searchDirection_);
// Initialize gradient
gradient_ = new Vector(P.currentValue().Count);
// Compute new point
xtd_ = (Vector)P.currentValue().Clone();
t = update(ref xtd_, searchDirection_, t, constraint);
// Compute function value at the new point
qt_ = P.value(xtd_);
// Enter in the loop if the criterion is not satisfied
if ((qt_ - q0) > -alpha_ * t * qpt_) {
do {
loopNumber++;
// Decrease step
t *= beta_;
// Store old value of the function
qtold = qt_;
// New point value
xtd_ = P.currentValue();
t = update(ref xtd_, searchDirection_, t, constraint);
// Compute function value at the new point
qt_ = P.value(xtd_);
P.gradient(gradient_, xtd_);
// and it squared norm
maxIter = endCriteria.checkMaxIterations(loopNumber, ref ecType);
} while ((((qt_ - q0) > (-alpha_ * t * qpt_)) || ((qtold - q0) <= (-alpha_ * t * qpt_ / beta_))) && (!maxIter));
}
if (maxIter)
succeed_ = false;
// Compute new gradient
P.gradient(gradient_, xtd_);
// and it squared norm
qpt_ = Vector.DotProduct(gradient_, gradient_);
// Return new step value
return t;
}
public void nestedOptimizationTest()
{
//("Testing nested optimizations...");
OptimizationBasedCostFunction optimizationBasedCostFunction = new OptimizationBasedCostFunction();
NoConstraint constraint = new NoConstraint();
Vector initialValues = new Vector(1, 0.0);
Problem problem = new Problem(optimizationBasedCostFunction, constraint, initialValues);
LevenbergMarquardt optimizationMethod = new LevenbergMarquardt();
//Simplex optimizationMethod(0.1);
//ConjugateGradient optimizationMethod;
//SteepestDescent optimizationMethod;
EndCriteria endCriteria = new EndCriteria(1000, 100, 1e-5, 1e-5, 1e-5);
optimizationMethod.minimize(problem, endCriteria);
}
// Optimization function for hypersphere and lower-diagonal algorithm
private static Matrix hypersphereOptimize(Matrix targetMatrix, Matrix currentRoot, bool lowerDiagonal)
{
int i,j,k,size = targetMatrix.rows();
Matrix result = new Matrix(currentRoot);
Vector variance = new Vector(size);
for (i=0; i<size; i++){
variance[i]=Math.Sqrt(targetMatrix[i,i]);
}
if (lowerDiagonal) {
Matrix approxMatrix = result*Matrix.transpose(result);
result = MatrixUtilities.CholeskyDecomposition(approxMatrix, true);
for (i=0; i<size; i++) {
for (j=0; j<size; j++) {
result[i,j]/=Math.Sqrt(approxMatrix[i,i]);
}
}
} else {
for (i=0; i<size; i++) {
for (j=0; j<size; j++) {
result[i,j]/=variance[i];
}
}
}
ConjugateGradient optimize = new ConjugateGradient();
EndCriteria endCriteria = new EndCriteria(100, 10, 1e-8, 1e-8, 1e-8);
HypersphereCostFunction costFunction = new HypersphereCostFunction(targetMatrix, variance, lowerDiagonal);
NoConstraint constraint = new NoConstraint();
// hypersphere vector optimization
if (lowerDiagonal) {
Vector theta = new Vector(size * (size-1)/2);
const double eps=1e-16;
for (i=1; i<size; i++) {
for (j=0; j<i; j++) {
theta[i*(i-1)/2+j]=result[i,j];
if (theta[i*(i-1)/2+j]>1-eps)
theta[i*(i-1)/2+j]=1-eps;
if (theta[i*(i-1)/2+j]<-1+eps)
theta[i*(i-1)/2+j]=-1+eps;
for (k=0; k<j; k++) {
theta[i*(i-1)/2+j] /= Math.Sin(theta[i*(i-1)/2+k]);
if (theta[i*(i-1)/2+j]>1-eps)
theta[i*(i-1)/2+j]=1-eps;
if (theta[i*(i-1)/2+j]<-1+eps)
theta[i*(i-1)/2+j]=-1+eps;
}
theta[i*(i-1)/2+j] = Math.Acos(theta[i*(i-1)/2+j]);
if (j==i-1) {
if (result[i,i]<0)
theta[i*(i-1)/2+j]=-theta[i*(i-1)/2+j];
}
}
}
Problem p = new Problem(costFunction, constraint, theta);
optimize.minimize(p, endCriteria);
theta = p.currentValue();
result.fill(1);
for (i=0; i<size; i++) {
for (k=0; k<size; k++) {
if (k>i) {
result[i,k]=0;
} else {
for (j=0; j<=k; j++) {
if (j == k && k!=i)
result[i,k] *= Math.Cos(theta[i*(i-1)/2+j]);
else if (j!=i)
result[i,k] *= Math.Sin(theta[i*(i-1)/2+j]);
}
}
}
}
} else {
Vector theta = new Vector(size * (size-1));
const double eps=1e-16;
for (i=0; i<size; i++) {
for (j=0; j<size-1; j++) {
theta[j*size+i]=result[i,j];
if (theta[j*size+i]>1-eps)
theta[j*size+i]=1-eps;
if (theta[j*size+i]<-1+eps)
theta[j*size+i]=-1+eps;
for (k=0;k<j;k++) {
theta[j*size+i] /= Math.Sin(theta[k*size+i]);
if (theta[j*size+i]>1-eps)
theta[j*size+i]=1-eps;
if (theta[j*size+i]<-1+eps)
theta[j*size+i]=-1+eps;
}
theta[j*size+i] = Math.Acos(theta[j*size+i]);
if (j==size-2) {
if (result[i,j+1]<0)
theta[j*size+i]=-theta[j*size+i];
}
}
}
Problem p = new Problem(costFunction, constraint, theta);
optimize.minimize(p, endCriteria);
theta=p.currentValue();
result.fill(1);
for (i = 0; i < size; i++) {
for (k=0; k<size; k++) {
for (j=0; j<=k; j++) {
if (j == k && k!=size-1)
result[i,k] *= Math.Cos(theta[j*size+i]);
else if (j!=size-1)
result[i,k] *= Math.Sin(theta[j*size+i]);
}
}
}
}
for (i=0; i<size; i++) {
for (j=0; j<size; j++) {
result[i,j]*=variance[i];
}
}
return result;
}
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_ = QLNet.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);
QLNet.AbcdMathFunction.validate(a_, b_, c_, d_);
a_ = result[0];
b_ = result[1];
c_ = result[2];
d_ = result[3];
}
}
public override EndCriteria.Type minimize(Problem P, EndCriteria endCriteria)
{
// set up of the problem
//double ftol = endCriteria.functionEpsilon(); // end criteria on f(x) (see Numerical Recipes in C++, p.410)
double xtol = endCriteria.rootEpsilon(); // end criteria on x (see GSL v. 1.9, http://www.gnu.org/software/gsl/)
int maxStationaryStateIterations_ = endCriteria.maxStationaryStateIterations();
EndCriteria.Type ecType = EndCriteria.Type.None;
P.reset();
Vector x_ = P.currentValue();
int iterationNumber_ = 0;
// Initialize vertices of the simplex
bool end = false;
int n = x_.Count;
vertices_ = new InitializedList<Vector>(n + 1, x_);
for (int i = 0; i < n; i++)
{
Vector direction = new Vector(n, 0.0);
direction[i] = 1.0;
P.constraint().update(vertices_[i + 1], direction, lambda_);
}
// Initialize function values at the vertices of the simplex
values_ = new Vector(n + 1, 0.0);
for (int i = 0; i <= n; i++)
values_[i] = P.value(vertices_[i]);
// Loop looking for minimum
do
{
sum_ = new Vector(n, 0.0);
for (int i = 0; i <= n; i++)
sum_ += vertices_[i];
// Determine the best (iLowest), worst (iHighest)
// and 2nd worst (iNextHighest) vertices
int iLowest = 0;
int iHighest;
int iNextHighest;
if (values_[0] < values_[1])
{
iHighest = 1;
iNextHighest = 0;
}
else
{
iHighest = 0;
iNextHighest = 1;
}
for (int i = 1; i <= n; i++)
{
if (values_[i] > values_[iHighest])
{
iNextHighest = iHighest;
iHighest = i;
}
else
{
if ((values_[i] > values_[iNextHighest]) && i != iHighest)
iNextHighest = i;
}
if (values_[i] < values_[iLowest])
iLowest = i;
}
// Now compute accuracy, update iteration number and check end criteria
//// Numerical Recipes exit strategy on fx (see NR in C++, p.410)
//double low = values_[iLowest];
//double high = values_[iHighest];
//double rtol = 2.0*std::fabs(high - low)/
// (std::fabs(high) + std::fabs(low) + QL_EPSILON);
//++iterationNumber_;
//if (rtol < ftol ||
// endCriteria.checkMaxIterations(iterationNumber_, ecType)) {
// GSL exit strategy on x (see GSL v. 1.9, http://www.gnu.org/software/gsl
double simplexSize = Utils.computeSimplexSize(vertices_);
++iterationNumber_;
if (simplexSize < xtol || endCriteria.checkMaxIterations(iterationNumber_, ref ecType))
{
endCriteria.checkStationaryPoint(0.0, 0.0, ref maxStationaryStateIterations_, ref ecType);
endCriteria.checkMaxIterations(iterationNumber_, ref ecType);
x_ = vertices_[iLowest];
double low = values_[iLowest];
P.setFunctionValue(low);
P.setCurrentValue(x_);
return ecType;
}
// If end criteria is not met, continue
double factor = -1.0;
double vTry = extrapolate(ref P, iHighest, ref factor);
if ((vTry <= values_[iLowest]) && (factor == -1.0))
{
factor = 2.0;
extrapolate(ref P, iHighest, ref factor);
}
else if (Math.Abs(factor) > Const.QL_Epsilon)
{
if (vTry >= values_[iNextHighest])
{
double vSave = values_[iHighest];
factor = 0.5;
vTry = extrapolate(ref P, iHighest, ref factor);
if (vTry >= vSave && Math.Abs(factor) > Const.QL_Epsilon)
{
for (int i = 0; i <= n; i++)
{
if (i != iLowest)
{
#if QL_ARRAY_EXPRESSIONS
vertices_[i] = 0.5 * (vertices_[i] + vertices_[iLowest]);
#else
vertices_[i] += vertices_[iLowest];
vertices_[i] *= 0.5;
#endif
values_[i] = P.value(vertices_[i]);
}
}
}
}
}
// If can't extrapolate given the constraints, exit
if (Math.Abs(factor) <= Const.QL_Epsilon)
{
x_ = vertices_[iLowest];
double low = values_[iLowest];
P.setFunctionValue(low);
P.setCurrentValue(x_);
return EndCriteria.Type.StationaryFunctionValue;
}
} while (end == false);
throw new ApplicationException("optimization failed: unexpected behaviour");
}
//! minimize the optimization problem P public abstract EndCriteria.Type minimize(Problem P, EndCriteria endCriteria);
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);
P.setCurrentValue(x_); // update problem current value
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);
}
++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();
}
//! Perform line search public abstract double value(Problem P, ref EndCriteria.Type ecType, EndCriteria NamelessParameter3, double t_ini); // initial value of line-search step
//! solve the optimization problem P
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; // stationaryStateIterationNumber_=0
lineSearch_.searchDirection = new Vector(x_.Count); // dimension line search
bool done = false;
// function and squared norm of gradient values;
double fnew;
double fold;
double gold2;
double c;
double fdiff;
double normdiff;
// 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.Count;
Vector g = new Vector(sz);
Vector d = new Vector(sz);
Vector sddiff = new Vector(sz);
// Initialize cost function, gradient g and search direction
P.setFunctionValue(P.valueAndGradient(g, x_));
P.setGradientNormValue(Vector.DotProduct(g, g));
lineSearch_.searchDirection = g * -1.0;
// Loop over iterations
do
{
// Linesearch
t = lineSearch_.value(P, ref ecType, endCriteria, t);
// don't throw: it can fail just because maxIterations exceeded
//QL_REQUIRE(lineSearch_->succeed(), "line-search failed!");
if (lineSearch_.succeed())
{
// Updates
d = lineSearch_.searchDirection;
// New point
x_ = lineSearch_.lastX();
// New function value
fold = P.functionValue();
P.setFunctionValue(lineSearch_.lastFunctionValue());
// New gradient and search direction vectors
g = lineSearch_.lastGradient();
// orthogonalization coef
gold2 = P.gradientNormValue();
P.setGradientNormValue(lineSearch_.lastGradientNorm2());
c = P.gradientNormValue() / gold2;
// conjugate gradient search direction
sddiff = ((g * -1.0) + c * d) - lineSearch_.searchDirection;
normdiff = Math.Sqrt(Vector.DotProduct(sddiff, sddiff));
lineSearch_.searchDirection = (g * -1.0) + c * d;
// 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) + Double.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);
}
//done = endCriteria(iterationNumber_,
// stationaryStateIterationNumber_,
// true, //FIXME: it should be in the problem
// fold,
// std::sqrt(gold2),
// P.functionValue(),
// std::sqrt(P.gradientNormValue()),
// ecType);
P.setCurrentValue(x_); // update problem current value
++iterationNumber_; // Increase iteration number
}
else
{
done = true;
}
} while (!done);
P.setCurrentValue(x_);
return(ecType);
}
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();
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.
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);
info_ = info;
// check requirements & endCriteria evaluation
if (info == 0)
{
throw new ApplicationException("MINPACK: improper input parameters");
}
//if(info == 6) throw new ApplicationException("MINPACK: ftol is too small. no further " +
// "reduction in the sum of squares is possible.");
if (info != 6)
{
ecType = EndCriteria.Type.StationaryFunctionValue;
}
//QL_REQUIRE(info != 5, "MINPACK: number of calls to fcn has reached or exceeded maxfev.");
endCriteria.checkMaxIterations(nfev, ref ecType);
if (info == 7)
{
throw new ApplicationException("MINPACK: xtol is too small. no further " +
"improvement in the approximate " +
"solution x is possible.");
}
if (info == 8)
{
throw new ApplicationException("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);
}
// Optimization function for hypersphere and lower-diagonal algorithm
private static Matrix hypersphereOptimize(Matrix targetMatrix, Matrix currentRoot, bool lowerDiagonal)
{
int i, j, k, size = targetMatrix.rows();
Matrix result = new Matrix(currentRoot);
Vector variance = new Vector(size);
for (i = 0; i < size; i++)
{
variance[i] = Math.Sqrt(targetMatrix[i, i]);
}
if (lowerDiagonal)
{
Matrix approxMatrix = result * Matrix.transpose(result);
result = MatrixUtilities.CholeskyDecomposition(approxMatrix, true);
for (i = 0; i < size; i++)
{
for (j = 0; j < size; j++)
{
result[i, j] /= Math.Sqrt(approxMatrix[i, i]);
}
}
}
else
{
for (i = 0; i < size; i++)
{
for (j = 0; j < size; j++)
{
result[i, j] /= variance[i];
}
}
}
ConjugateGradient optimize = new ConjugateGradient();
EndCriteria endCriteria = new EndCriteria(100, 10, 1e-8, 1e-8, 1e-8);
HypersphereCostFunction costFunction = new HypersphereCostFunction(targetMatrix, variance, lowerDiagonal);
NoConstraint constraint = new NoConstraint();
// hypersphere vector optimization
if (lowerDiagonal)
{
Vector theta = new Vector(size * (size - 1) / 2);
const double eps = 1e-16;
for (i = 1; i < size; i++)
{
for (j = 0; j < i; j++)
{
theta[i * (i - 1) / 2 + j] = result[i, j];
if (theta[i * (i - 1) / 2 + j] > 1 - eps)
{
theta[i * (i - 1) / 2 + j] = 1 - eps;
}
if (theta[i * (i - 1) / 2 + j] < -1 + eps)
{
theta[i * (i - 1) / 2 + j] = -1 + eps;
}
for (k = 0; k < j; k++)
{
theta[i * (i - 1) / 2 + j] /= Math.Sin(theta[i * (i - 1) / 2 + k]);
if (theta[i * (i - 1) / 2 + j] > 1 - eps)
{
theta[i * (i - 1) / 2 + j] = 1 - eps;
}
if (theta[i * (i - 1) / 2 + j] < -1 + eps)
{
theta[i * (i - 1) / 2 + j] = -1 + eps;
}
}
theta[i * (i - 1) / 2 + j] = Math.Acos(theta[i * (i - 1) / 2 + j]);
if (j == i - 1)
{
if (result[i, i] < 0)
{
theta[i * (i - 1) / 2 + j] = -theta[i * (i - 1) / 2 + j];
}
}
}
}
Problem p = new Problem(costFunction, constraint, theta);
optimize.minimize(p, endCriteria);
theta = p.currentValue();
result.fill(1);
for (i = 0; i < size; i++)
{
for (k = 0; k < size; k++)
{
if (k > i)
{
result[i, k] = 0;
}
else
{
for (j = 0; j <= k; j++)
{
if (j == k && k != i)
{
result[i, k] *= Math.Cos(theta[i * (i - 1) / 2 + j]);
}
else if (j != i)
{
result[i, k] *= Math.Sin(theta[i * (i - 1) / 2 + j]);
}
}
}
}
}
}
else
{
Vector theta = new Vector(size * (size - 1));
const double eps = 1e-16;
for (i = 0; i < size; i++)
{
for (j = 0; j < size - 1; j++)
{
theta[j * size + i] = result[i, j];
if (theta[j * size + i] > 1 - eps)
{
theta[j * size + i] = 1 - eps;
}
if (theta[j * size + i] < -1 + eps)
{
theta[j * size + i] = -1 + eps;
}
for (k = 0; k < j; k++)
{
theta[j * size + i] /= Math.Sin(theta[k * size + i]);
if (theta[j * size + i] > 1 - eps)
{
theta[j * size + i] = 1 - eps;
}
if (theta[j * size + i] < -1 + eps)
{
theta[j * size + i] = -1 + eps;
}
}
theta[j * size + i] = Math.Acos(theta[j * size + i]);
if (j == size - 2)
{
if (result[i, j + 1] < 0)
{
theta[j * size + i] = -theta[j * size + i];
}
}
}
}
Problem p = new Problem(costFunction, constraint, theta);
optimize.minimize(p, endCriteria);
theta = p.currentValue();
result.fill(1);
for (i = 0; i < size; i++)
{
for (k = 0; k < size; k++)
{
for (j = 0; j <= k; j++)
{
if (j == k && k != size - 1)
{
result[i, k] *= Math.Cos(theta[j * size + i]);
}
else if (j != size - 1)
{
result[i, k] *= Math.Sin(theta[j * size + i]);
}
}
}
}
}
for (i = 0; i < size; i++)
{
for (j = 0; j < size; j++)
{
result[i, j] *= variance[i];
}
}
return(result);
}
//! solve the optimization problem P
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; // stationaryStateIterationNumber_=0
lineSearch_.searchDirection = new Vector(x_.Count); // dimension line search
bool done = false;
// function and squared norm of gradient values;
double fnew;
double fold;
double gold2;
double c;
double fdiff;
double normdiff;
// 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.Count;
Vector g = new Vector(sz);
Vector d = new Vector(sz);
Vector sddiff = new Vector(sz);
// Initialize cost function, gradient g and search direction
P.setFunctionValue(P.valueAndGradient(g, x_));
P.setGradientNormValue(Vector.DotProduct(g, g));
lineSearch_.searchDirection = g * -1.0;
// Loop over iterations
do
{
// Linesearch
t = lineSearch_.value(P, ref ecType, endCriteria, t);
// don't throw: it can fail just because maxIterations exceeded
//QL_REQUIRE(lineSearch_->succeed(), "line-search failed!");
if (lineSearch_.succeed())
{
// Updates
d = lineSearch_.searchDirection;
// New point
x_ = lineSearch_.lastX();
// New function value
fold = P.functionValue();
P.setFunctionValue(lineSearch_.lastFunctionValue());
// New gradient and search direction vectors
g = lineSearch_.lastGradient();
// orthogonalization coef
gold2 = P.gradientNormValue();
P.setGradientNormValue(lineSearch_.lastGradientNorm2());
c = P.gradientNormValue() / gold2;
// conjugate gradient search direction
sddiff = ((g*-1.0) + c * d) - lineSearch_.searchDirection;
normdiff = Math.Sqrt(Vector.DotProduct(sddiff, sddiff));
lineSearch_.searchDirection = (g*-1.0) + c * d;
// 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) + Double.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;
}
//done = endCriteria(iterationNumber_,
// stationaryStateIterationNumber_,
// true, //FIXME: it should be in the problem
// fold,
// std::sqrt(gold2),
// P.functionValue(),
// std::sqrt(P.gradientNormValue()),
// ecType);
P.setCurrentValue(x_); // update problem current value
++iterationNumber_; // Increase iteration number
}
else
{
done =true;
}
} while (!done);
P.setCurrentValue(x_);
return ecType;
}
//! Perform line search public abstract double value(Problem P, ref EndCriteria.Type ecType, EndCriteria NamelessParameter3, double t_ini); // initial value of line-search step
public void calculate()
{
validCurve_ = false;
int nInsts = ts_.instruments_.Count, i;
// ensure rate helpers are sorted
ts_.instruments_.Sort((x, y) => x.latestDate().CompareTo(y.latestDate()));
// check that there is no instruments with the same maturity
for (i = 1; i < nInsts; ++i)
{
Date m1 = ts_.instruments_[i - 1].latestDate(),
m2 = ts_.instruments_[i].latestDate();
if (m1 == m2)
{
throw new ArgumentException("two instruments have the same maturity (" + m1 + ")");
}
}
// check that there is no instruments with invalid quote
if ((i = ts_.instruments_.FindIndex(x => !x.quoteIsValid())) != -1)
{
throw new ArgumentException("instrument " + i + " (maturity: " + ts_.instruments_[i].latestDate() +
") has an invalid quote");
}
// setup instruments and register with them
ts_.instruments_.ForEach(j => ts_.setTermStructure(j));
// set initial guess only if the current curve cannot be used as guess
if (validCurve_)
{
if (ts_.data_.Count != nInsts + 1)
{
throw new ArgumentException("dimension mismatch: expected " + nInsts + 1 + ", actual " + ts_.data_.Count);
}
}
else
{
ts_.data_ = new InitializedList <double>(nInsts + 1);
ts_.data_[0] = ts_.initialValue();
}
// calculate dates and times
ts_.dates_ = new InitializedList <Date>(nInsts + 1);
ts_.times_ = new InitializedList <double>(nInsts + 1);
ts_.dates_[0] = ts_.initialDate();
ts_.times_[0] = ts_.timeFromReference(ts_.dates_[0]);
for (i = 0; i < nInsts; ++i)
{
ts_.dates_[i + 1] = ts_.instruments_[i].latestDate();
ts_.times_[i + 1] = ts_.timeFromReference(ts_.dates_[i + 1]);
if (!validCurve_)
{
ts_.data_[i + 1] = ts_.data_[i];
}
}
LevenbergMarquardt solver = new LevenbergMarquardt(ts_.accuracy_, ts_.accuracy_, ts_.accuracy_);
EndCriteria endCriteria = new EndCriteria(100, 10, 0.00, ts_.accuracy_, 0.00);
PositiveConstraint posConstraint = new PositiveConstraint();
NoConstraint noConstraint = new NoConstraint();
Constraint solverConstraint = forcePositive_ ? (Constraint)posConstraint : (Constraint)noConstraint;
// now start the bootstrapping.
int iInst = localisation_ - 1;
int dataAdjust = (ts_.interpolator_ as ConvexMonotone).dataSizeAdjustment;
do
{
int initialDataPt = iInst + 1 - localisation_ + dataAdjust;
Vector startArray = new Vector(localisation_ + 1 - dataAdjust);
for (int j = 0; j < startArray.size() - 1; ++j)
{
startArray[j] = ts_.data_[initialDataPt + j];
}
// here we are extending the interpolation a point at a
// time... but the local interpolator can make an
// approximation for the final localisation period.
// e.g. if the localisation is 2, then the first section
// of the curve will be solved using the first 2
// instruments... with the local interpolator making
// suitable boundary conditions.
ts_.interpolation_ = (ts_.interpolator_ as ConvexMonotone).localInterpolate(ts_.times_, iInst + 2, ts_.data_,
localisation_, ts_.interpolation_ as ConvexMonotoneInterpolation, nInsts + 1);
if (iInst >= localisation_)
{
startArray[localisation_ - dataAdjust] = ts_.guess(iInst, ts_, false, 0);
}
else
{
startArray[localisation_ - dataAdjust] = ts_.data_[0];
}
var currentCost = new PenaltyFunction <T, U>(ts_, initialDataPt, ts_.instruments_,
iInst - localisation_ + 1, iInst + 1);
Problem toSolve = new Problem(currentCost, solverConstraint, startArray);
EndCriteria.Type endType = solver.minimize(toSolve, endCriteria);
// check the end criteria
if (!(endType == EndCriteria.Type.StationaryFunctionAccuracy ||
endType == EndCriteria.Type.StationaryFunctionValue))
{
throw new ApplicationException("Unable to strip yieldcurve to required accuracy ");
}
++iInst;
} while (iInst < nInsts);
validCurve_ = true;
}
private double extrapolate(ref Problem P, int iHighest, ref double factor)
{
Vector pTry;
do
{
int dimensions = values_.Count - 1;
double factor1 = (1.0 - factor) / dimensions;
double factor2 = factor1 - factor;
// #if QL_ARRAY_EXPRESSIONS
pTry = sum_ * factor1 - vertices_[iHighest] * factor2;
//#else
// // composite expressions fail to compile with gcc 3.4 on windows
// pTry = sum_ * factor1;
// pTry -= vertices_[iHighest] * factor2;
//#endif
factor *= 0.5;
} while (!P.constraint().test(pTry) && Math.Abs(factor) > Const.QL_Epsilon);
if (Math.Abs(factor) <= Const.QL_Epsilon)
{
return values_[iHighest];
}
factor *= 2.0;
double vTry = P.value(pTry);
if (vTry < values_[iHighest])
{
values_[iHighest] = vTry;
//#if QL_ARRAY_EXPRESSIONS
sum_ += pTry - vertices_[iHighest];
//#else
// sum_ += pTry;
// sum_ -= vertices_[iHighest];
//#endif
vertices_[iHighest] = pTry;
}
return vTry;
}
public override void update()
{
coeff_.updateModelInstance();
// we should also check that y contains positive values only
// we must update weights if it is vegaWeighted
if (vegaWeighted_)
{
coeff_.weights_.Clear();
double weightsSum = 0.0;
for (int i = 0; i < xBegin_.Count; i++)
{
double stdDev = Math.Sqrt((yBegin_[i]) * (yBegin_[i]) * coeff_.t_);
coeff_.weights_.Add(coeff_.model_.weight(xBegin_[i], forward_, stdDev, coeff_.addParams_));
weightsSum += coeff_.weights_.Last();
}
// weight normalization
for (int i = 0; i < coeff_.weights_.Count; i++)
{
coeff_.weights_[i] /= weightsSum;
}
}
// there is nothing to optimize
if (coeff_.paramIsFixed_.Aggregate((a, b) => b && a))
{
coeff_.error_ = interpolationError();
coeff_.maxError_ = interpolationMaxError();
coeff_.XABREndCriteria_ = EndCriteria.Type.None;
return;
}
XABRError costFunction = new XABRError(this);
Vector guess = new Vector(coeff_.model_.dimension());
for (int i = 0; i < guess.size(); ++i)
{
guess[i] = coeff_.params_[i].GetValueOrDefault();
}
int iterations = 0;
int freeParameters = 0;
double bestError = double.MaxValue;
Vector bestParameters = new Vector();
for (int i = 0; i < coeff_.model_.dimension(); ++i)
{
if (!coeff_.paramIsFixed_[i])
{
++freeParameters;
}
}
HaltonRsg halton = new HaltonRsg(freeParameters, 42);
EndCriteria.Type tmpEndCriteria;
double tmpInterpolationError;
do
{
if (iterations > 0)
{
Sample <List <double> > s = halton.nextSequence();
coeff_.model_.guess(guess, coeff_.paramIsFixed_, forward_, coeff_.t_, s.value, coeff_.addParams_);
for (int i = 0; i < coeff_.paramIsFixed_.Count; ++i)
{
if (coeff_.paramIsFixed_[i])
{
guess[i] = coeff_.params_[i].GetValueOrDefault();
}
}
}
Vector inversedTransformatedGuess =
new Vector(coeff_.model_.inverse(guess, coeff_.paramIsFixed_, coeff_.params_, forward_));
ProjectedCostFunction rainedXABRError = new ProjectedCostFunction(costFunction,
inversedTransformatedGuess,
coeff_.paramIsFixed_);
Vector projectedGuess = new Vector(rainedXABRError.project(inversedTransformatedGuess));
constraint_.config(rainedXABRError, coeff_, forward_);
Problem problem = new Problem(rainedXABRError, constraint_, projectedGuess);
tmpEndCriteria = optMethod_.minimize(problem, endCriteria_);
Vector projectedResult = new Vector(problem.currentValue());
Vector transfResult = new Vector(rainedXABRError.include(projectedResult));
Vector result = coeff_.model_.direct(transfResult, coeff_.paramIsFixed_, coeff_.params_, forward_);
tmpInterpolationError = useMaxError_
? interpolationMaxError()
: interpolationError();
if (tmpInterpolationError < bestError)
{
bestError = tmpInterpolationError;
bestParameters = result;
coeff_.XABREndCriteria_ = tmpEndCriteria;
}
}while (++iterations < maxGuesses_ &&
tmpInterpolationError > errorAccept_);
for (int i = 0; i < bestParameters.size(); ++i)
{
coeff_.params_[i] = bestParameters[i];
}
coeff_.error_ = interpolationError();
coeff_.maxError_ = interpolationMaxError();
}
public override Vector values(Vector x)
{
// dummy nested optimization
Vector coefficients = new Vector(3, 1.0);
OneDimensionalPolynomialDegreeN oneDimensionalPolynomialDegreeN = new OneDimensionalPolynomialDegreeN(coefficients);
NoConstraint constraint = new NoConstraint();
Vector initialValues = new Vector(1, 100.0);
Problem problem = new Problem(oneDimensionalPolynomialDegreeN, constraint, initialValues);
LevenbergMarquardt optimizationMethod = new LevenbergMarquardt();
//Simplex optimizationMethod(0.1);
//ConjugateGradient optimizationMethod;
//SteepestDescent optimizationMethod;
EndCriteria endCriteria = new EndCriteria(1000, 100, 1e-5, 1e-5, 1e-5);
optimizationMethod.minimize(problem, endCriteria);
// return dummy result
Vector dummy = new Vector(1,0);
return dummy;
}
//! Perform line search public abstract double value(Problem P, ref EndCriteria.Type ecType, EndCriteria NamelessParameter3, double t_ini);
public void OptimizersTest()
{
//("Testing optimizers...");
setup();
// Loop over problems (currently there is only 1 problem)
for (int i=0; i<costFunctions_.Count; ++i) {
Problem problem = new Problem(costFunctions_[i], constraints_[i], initialValues_[i]);
Vector initialValues = problem.currentValue();
// Loop over optimizers
for (int j = 0; j < (optimizationMethods_[i]).Count; ++j) {
double rootEpsilon = endCriterias_[i].rootEpsilon();
int endCriteriaTests = 1;
// Loop over rootEpsilon
for(int k=0; k<endCriteriaTests; ++k) {
problem.setCurrentValue(initialValues);
EndCriteria endCriteria = new EndCriteria(endCriterias_[i].maxIterations(),
endCriterias_[i].maxStationaryStateIterations(),
rootEpsilon,
endCriterias_[i].functionEpsilon(),
endCriterias_[i].gradientNormEpsilon());
rootEpsilon *= .1;
EndCriteria.Type endCriteriaResult =
optimizationMethods_[i][j].optimizationMethod.minimize(problem, endCriteria);
Vector xMinCalculated = problem.currentValue();
Vector yMinCalculated = problem.values(xMinCalculated);
// Check optimization results vs known solution
if (endCriteriaResult==EndCriteria.Type.None ||
endCriteriaResult==EndCriteria.Type.MaxIterations ||
endCriteriaResult==EndCriteria.Type.Unknown)
Assert.Fail("function evaluations: " + problem.functionEvaluation() +
" gradient evaluations: " + problem.gradientEvaluation() +
" x expected: " + xMinExpected_[i] +
" x calculated: " + xMinCalculated +
" x difference: " + (xMinExpected_[i]- xMinCalculated) +
" rootEpsilon: " + endCriteria.rootEpsilon() +
" y expected: " + yMinExpected_[i] +
" y calculated: " + yMinCalculated +
" y difference: " + (yMinExpected_[i]- yMinCalculated) +
" functionEpsilon: " + endCriteria.functionEpsilon() +
" endCriteriaResult: " + endCriteriaResult);
}
}
}
}
//! Solve least square problem using numerix solver
public Vector perform(ref LeastSquareProblem lsProblem)
{
double eps = accuracy_;
// wrap the least square problem in an optimization function
LeastSquareFunction lsf = new LeastSquareFunction(lsProblem);
// define optimization problem
Problem P = new Problem(lsf, c_, initialValue_);
// minimize
EndCriteria ec = new EndCriteria(maxIterations_, Math.Min((int)(maxIterations_ / 2), (int)(100)), eps, eps, eps);
exitFlag_ = (int)om_.minimize(P, ec);
// summarize results of minimization
// nbIterations_ = om_->iterationNumber();
results_ = P.currentValue();
resnorm_ = P.functionValue();
bestAccuracy_ = P.functionValue();
return results_;
}
//! Calibrate to a set of market instruments (caps/swaptions)
/*! An additional constraint can be passed which must be
satisfied in addition to the constraints of the model.
*/
//public void calibrate(List<CalibrationHelper> instruments, OptimizationMethod method, EndCriteria endCriteria,
// Constraint constraint = new Constraint(), List<double> weights = new List<double>()) {
public void calibrate(List<CalibrationHelper> instruments, OptimizationMethod method, EndCriteria endCriteria,
Constraint additionalConstraint, List<double> weights)
{
if (!(weights.Count == 0 || weights.Count == instruments.Count))
throw new ApplicationException("mismatch between number of instruments and weights");
Constraint c;
if (additionalConstraint.empty())
c = constraint_;
else
c = new CompositeConstraint(constraint_,additionalConstraint);
List<double> w = weights.Count == 0 ? new InitializedList<double>(instruments.Count, 1.0): weights;
CalibrationFunction f = new CalibrationFunction(this, instruments, w);
Problem prob = new Problem(f, c, parameters());
shortRateEndCriteria_ = method.minimize(prob, endCriteria);
Vector result = new Vector(prob.currentValue());
setParams(result);
// recheck
Vector shortRateProblemValues_ = prob.values(result);
notifyObservers();
}
public override EndCriteria.Type minimize(Problem P, EndCriteria endCriteria)
{
// set up of the problem
//double ftol = endCriteria.functionEpsilon(); // end criteria on f(x) (see Numerical Recipes in C++, p.410)
double xtol = endCriteria.rootEpsilon(); // end criteria on x (see GSL v. 1.9, http://www.gnu.org/software/gsl/)
int maxStationaryStateIterations_ = endCriteria.maxStationaryStateIterations();
EndCriteria.Type ecType = EndCriteria.Type.None;
P.reset();
Vector x_ = P.currentValue();
int iterationNumber_ = 0;
// Initialize vertices of the simplex
bool end = false;
int n = x_.Count;
vertices_ = new InitializedList <Vector>(n + 1, x_);
for (int i = 0; i < n; i++)
{
Vector direction = new Vector(n, 0.0);
Vector vertice = vertices_[i + 1];
direction[i] = 1.0;
P.constraint().update(ref vertice, direction, lambda_);
vertices_[i + 1] = vertice;
}
// Initialize function values at the vertices of the simplex
values_ = new Vector(n + 1, 0.0);
for (int i = 0; i <= n; i++)
{
values_[i] = P.value(vertices_[i]);
}
// Loop looking for minimum
do
{
sum_ = new Vector(n, 0.0);
for (int i = 0; i <= n; i++)
{
sum_ += vertices_[i];
}
// Determine the best (iLowest), worst (iHighest)
// and 2nd worst (iNextHighest) vertices
int iLowest = 0;
int iHighest;
int iNextHighest;
if (values_[0] < values_[1])
{
iHighest = 1;
iNextHighest = 0;
}
else
{
iHighest = 0;
iNextHighest = 1;
}
for (int i = 1; i <= n; i++)
{
if (values_[i] > values_[iHighest])
{
iNextHighest = iHighest;
iHighest = i;
}
else
{
if ((values_[i] > values_[iNextHighest]) && i != iHighest)
{
iNextHighest = i;
}
}
if (values_[i] < values_[iLowest])
{
iLowest = i;
}
}
// Now compute accuracy, update iteration number and check end criteria
//// Numerical Recipes exit strategy on fx (see NR in C++, p.410)
//double low = values_[iLowest];
//double high = values_[iHighest];
//double rtol = 2.0*std::fabs(high - low)/
// (std::fabs(high) + std::fabs(low) + QL_EPSILON);
//++iterationNumber_;
//if (rtol < ftol ||
// endCriteria.checkMaxIterations(iterationNumber_, ecType)) {
// GSL exit strategy on x (see GSL v. 1.9, http://www.gnu.org/software/gsl
double simplexSize = Utils.computeSimplexSize(vertices_);
++iterationNumber_;
if (simplexSize < xtol || endCriteria.checkMaxIterations(iterationNumber_, ref ecType))
{
endCriteria.checkStationaryPoint(0.0, 0.0, ref maxStationaryStateIterations_, ref ecType);
endCriteria.checkMaxIterations(iterationNumber_, ref ecType);
x_ = vertices_[iLowest];
double low = values_[iLowest];
P.setFunctionValue(low);
P.setCurrentValue(x_);
return(ecType);
}
// If end criteria is not met, continue
double factor = -1.0;
double vTry = extrapolate(ref P, iHighest, ref factor);
if ((vTry <= values_[iLowest]) && (factor == -1.0))
{
factor = 2.0;
extrapolate(ref P, iHighest, ref factor);
}
else if (Math.Abs(factor) > Const.QL_EPSILON)
{
if (vTry >= values_[iNextHighest])
{
double vSave = values_[iHighest];
factor = 0.5;
vTry = extrapolate(ref P, iHighest, ref factor);
if (vTry >= vSave && Math.Abs(factor) > Const.QL_EPSILON)
{
for (int i = 0; i <= n; i++)
{
if (i != iLowest)
{
#if QL_ARRAY_EXPRESSIONS
vertices_[i] = 0.5 * (vertices_[i] + vertices_[iLowest]);
#else
vertices_[i] += vertices_[iLowest];
vertices_[i] *= 0.5;
#endif
values_[i] = P.value(vertices_[i]);
}
}
}
}
}
// If can't extrapolate given the constraints, exit
if (Math.Abs(factor) <= Const.QL_EPSILON)
{
x_ = vertices_[iLowest];
double low = values_[iLowest];
P.setFunctionValue(low);
P.setCurrentValue(x_);
return(EndCriteria.Type.StationaryFunctionValue);
}
} while (end == false);
throw new ApplicationException("optimization failed: unexpected behaviour");
}
