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);
}
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;
}
// 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 override void update()
{
this.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]) * this.coeff_.t_);
coeff_.weights_.Add(coeff_.model_.weight(xBegin_[i], forward_, stdDev, this.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;
}
else
{
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].Value;
}
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].Value;
}
}
}
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));
NoConstraint raint = new NoConstraint();
Problem problem = new Problem(rainedXABRError, raint, 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 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 => j.setTermStructure(ts_));
// 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(ts_);
}
// calculate dates and times
ts_.dates_ = new InitializedList <Date>(nInsts + 1);
ts_.times_ = new InitializedList <double>(nInsts + 1);
ts_.dates_[0] = ts_.initialDate(ts_);
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(ts_, ts_.dates_[iInst]);
}
else
{
startArray[localisation_ - dataAdjust] = ts_.data_[0];
}
var currentCost = new PenaltyFunction <PiecewiseYieldCurve>(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;
}
// 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];
}
}
