public ComboHelper(ISectionHelper quadraticHelper, ISectionHelper convMonoHelper, double quadraticity)
{
quadraticity_ = quadraticity;
quadraticHelper_ = quadraticHelper;
convMonoHelper_ = convMonoHelper;
Utils.QL_REQUIRE(quadraticity <1.0 && quadraticity> 0.0, () => "Quadratic value must lie between 0 and 1");
}
public ComboHelper(ISectionHelper quadraticHelper, ISectionHelper convMonoHelper, double quadraticity) {
quadraticity_ = quadraticity;
quadraticHelper_ = quadraticHelper;
convMonoHelper_ = convMonoHelper;
if (!(quadraticity < 1.0 && quadraticity > 0.0))
throw new ApplicationException("Quadratic value must lie between 0 and 1");
}
public ComboHelper(ISectionHelper quadraticHelper,
ISectionHelper convMonoHelper,
double quadraticity)
{
quadraticity_ = quadraticity;
_quadraticHelper = quadraticHelper;
_convMonoHelper = convMonoHelper;
}
public ComboHelper(ISectionHelper quadraticHelper, ISectionHelper convMonoHelper, double quadraticity)
{
quadraticity_ = quadraticity;
quadraticHelper_ = quadraticHelper;
convMonoHelper_ = convMonoHelper;
if (!(quadraticity < 1.0 && quadraticity > 0.0))
{
throw new Exception("Quadratic value must lie between 0 and 1");
}
}
public override void update()
{
sectionHelpers_.Clear();
if (size_ == 2) //single period
{
ISectionHelper singleHelper = new EverywhereConstantHelper(yBegin_[1], 0.0, xBegin_[0]);
sectionHelpers_.Add(xBegin_[1], singleHelper);
extrapolationHelper_ = singleHelper;
return;
}
List <double> f = new InitializedList <double>(size_);
sectionHelpers_ = new Dictionary <double, ISectionHelper>(preSectionHelpers_);
int startPoint = sectionHelpers_.Count + 1;
//first derive the boundary forwards.
for (int i = startPoint; i < size_ - 1; ++i)
{
double dxPrev = xBegin_[i] - xBegin_[i - 1];
double dx = xBegin_[i + 1] - xBegin_[i];
f[i] = dxPrev / (dx + dxPrev) * yBegin_[i]
+ dx / (dx + dxPrev) * yBegin_[i + 1];
}
if (startPoint > 1)
{
f[startPoint - 1] = preSectionHelpers_.Last().Value.fNext();
}
if (startPoint == 1)
{
f[0] = 1.5 * yBegin_[1] - 0.5 * f[1];
}
f[size_ - 1] = 1.5 * yBegin_[size_ - 1] - 0.5 * f[size_ - 2];
if (forcePositive_)
{
if (f[0] < 0)
{
f[0] = 0.0;
}
if (f[size_ - 1] < 0.0)
{
f[size_ - 1] = 0.0;
}
}
double primitive = 0.0;
for (int i = 0; i < startPoint - 1; ++i)
{
primitive += yBegin_[i + 1] * (xBegin_[i + 1] - xBegin_[i]);
}
int endPoint = size_;
//constantLastPeriod_ = false;
if (constantLastPeriod_)
{
endPoint = endPoint - 1;
}
for (int i = startPoint; i < endPoint; ++i)
{
double gPrev = f[i - 1] - yBegin_[i];
double gNext = f[i] - yBegin_[i];
//first deal with the zero gradient case
if (Math.Abs(gPrev) < 1.0E-14 && Math.Abs(gNext) < 1.0E-14)
{
ISectionHelper singleHelper = new ConstantGradHelper(f[i - 1], primitive,
xBegin_[i - 1],
xBegin_[i],
f[i]);
sectionHelpers_.Add(xBegin_[i], singleHelper);
}
else
{
double quadraticity = quadraticity_;
ISectionHelper quadraticHelper = null;
ISectionHelper convMonotoneHelper = null;
if (quadraticity_ > 0.0)
{
if (gPrev >= -2.0 * gNext && gPrev > -0.5 * gNext && forcePositive_)
{
quadraticHelper = new QuadraticMinHelper(xBegin_[i - 1],
xBegin_[i],
f[i - 1], f[i],
yBegin_[i],
primitive);
}
else
{
quadraticHelper = new QuadraticHelper(xBegin_[i - 1],
xBegin_[i],
f[i - 1], f[i],
yBegin_[i],
primitive);
}
}
if (quadraticity_ < 1.0)
{
if ((gPrev > 0.0 && -0.5 * gPrev >= gNext && gNext >= -2.0 * gPrev) ||
(gPrev < 0.0 && -0.5 * gPrev <= gNext && gNext <= -2.0 * gPrev))
{
quadraticity = 1.0;
if (quadraticity_ == 0)
{
if (forcePositive_)
{
quadraticHelper = new QuadraticMinHelper(
xBegin_[i - 1],
xBegin_[i],
f[i - 1], f[i],
yBegin_[i],
primitive);
}
else
{
quadraticHelper = new QuadraticHelper(
xBegin_[i - 1],
xBegin_[i],
f[i - 1], f[i],
yBegin_[i],
primitive);
}
}
}
else if ((gPrev < 0.0 && gNext > -2.0 * gPrev) ||
(gPrev > 0.0 && gNext < -2.0 * gPrev))
{
double eta = (gNext + 2.0 * gPrev) / (gNext - gPrev);
double b2 = (1.0 + monotonicity_) / 2.0;
if (eta < b2)
{
convMonotoneHelper = new ConvexMonotone2Helper(
xBegin_[i - 1],
xBegin_[i],
gPrev, gNext,
yBegin_[i],
eta, primitive);
}
else
{
if (forcePositive_)
{
convMonotoneHelper = new ConvexMonotone4MinHelper(
xBegin_[i - 1],
xBegin_[i],
gPrev, gNext,
yBegin_[i],
b2, primitive);
}
else
{
convMonotoneHelper = new ConvexMonotone4Helper(
xBegin_[i - 1],
xBegin_[i],
gPrev, gNext,
yBegin_[i],
b2, primitive);
}
}
}
else if ((gPrev > 0.0 && gNext < 0.0 && gNext > -0.5 * gPrev) ||
(gPrev < 0.0 && gNext > 0.0 && gNext < -0.5 * gPrev))
{
double eta = gNext / (gNext - gPrev) * 3.0;
double b3 = (1.0 - monotonicity_) / 2.0;
if (eta > b3)
{
convMonotoneHelper = new ConvexMonotone3Helper(
xBegin_[i - 1],
xBegin_[i],
gPrev, gNext,
yBegin_[i],
eta, primitive);
}
else
{
if (forcePositive_)
{
convMonotoneHelper = new ConvexMonotone4MinHelper(
xBegin_[i - 1],
xBegin_[i],
gPrev, gNext,
yBegin_[i],
b3, primitive);
}
else
{
convMonotoneHelper = new ConvexMonotone4Helper(
xBegin_[i - 1],
xBegin_[i],
gPrev, gNext,
yBegin_[i],
b3, primitive);
}
}
}
else
{
double eta = gNext / (gPrev + gNext);
double b2 = (1.0 + monotonicity_) / 2.0;
double b3 = (1.0 - monotonicity_) / 2.0;
if (eta > b2)
{
eta = b2;
}
if (eta < b3)
{
eta = b3;
}
if (forcePositive_)
{
convMonotoneHelper = new ConvexMonotone4MinHelper(
xBegin_[i - 1],
xBegin_[i],
gPrev, gNext,
yBegin_[i],
eta, primitive);
}
else
{
convMonotoneHelper = new ConvexMonotone4Helper(
xBegin_[i - 1],
xBegin_[i],
gPrev, gNext,
yBegin_[i],
eta, primitive);
}
}
}
if (quadraticity == 1.0)
{
sectionHelpers_.Add(xBegin_[i], quadraticHelper);
}
else if (quadraticity == 0.0)
{
sectionHelpers_.Add(xBegin_[i], convMonotoneHelper);
}
else
{
sectionHelpers_.Add(xBegin_[i], new ComboHelper(quadraticHelper, convMonotoneHelper, quadraticity));
}
}
primitive += yBegin_[i] * (xBegin_[i] - xBegin_[i - 1]);
}
if (constantLastPeriod_)
{
sectionHelpers_.Add(xBegin_[size_ - 1], new EverywhereConstantHelper(yBegin_[size_ - 1], primitive, xBegin_[size_ - 2]));
extrapolationHelper_ = sectionHelpers_[xBegin_[size_ - 1]];
}
else
{
extrapolationHelper_ = new EverywhereConstantHelper((sectionHelpers_.Last()).Value.value(xBegin_.Last()),
primitive, xBegin_.Last());
}
}
public ConvexMonoticInterpolator(
IEnumerable <Tuple <double, double> > points,
double quadraticity = 0.3,
double monotonicity = 0.7,
bool forcePositive = true,
bool constFinalPeriod = false,
bool allowExtrapolation = true)
{
_keyPoints = points.ToArray();
_xArr = _keyPoints.Select(x => x.Item1).ToArray();
_yArr = _keyPoints.Select(x => x.Item2).ToArray();
_quadraticity = quadraticity;
_monotonicity = monotonicity;
_forcePositive = forcePositive;
_constFinalPeriod = constFinalPeriod;
_allowExtrapolation = allowExtrapolation;
var length = _keyPoints.Length;
_helpers = new ISectionHelper[length];
if (length < 2)
{
throw new PricingLibraryException("Convex monotonic interpolator must have at least 2 points");
}
if (_keyPoints.Length == 2)
{
var helper = new EverywhereConstantHelper(_keyPoints.Last().Item2, 0.0, _keyPoints.First().Item1);
_helpers[1] = helper;
_extrapolationHelper = helper;
}
var f = new double[length];
for (var i = 1; i < length - 1; ++i)
{
var dxPrev = _xArr[i] - _xArr[i - 1];
var dx = _xArr[i + 1] - _xArr[i];
f[i] = dxPrev / (dx + dxPrev) * _yArr[i] + dx / (dx + dxPrev) * _yArr[i + 1];
}
f[0] = 1.5 * _yArr[1] - 0.5 * f[1];
f[length - 1] = 1.5 * _yArr.Last() - 0.5 * f[length - 2];
if (_forcePositive)
{
if (f[0] < 0.0)
{
f[0] = 0;
}
if (f[length - 1] < 0.0)
{
f[length - 1] = 0.0;
}
}
var integral = 0.0;
var end = constFinalPeriod ? length - 1 : length;
for (var i = 1; i < end; ++i)
{
var gPrev = f[i - 1] - _yArr[i];
var gNext = f[i] - _yArr[i];
if (gPrev.IsAlmostZero() && gNext.IsAlmostZero())
{
_helpers[i] = new ConstantGradHelper(f[i - 1], integral, _xArr[i - 1], _xArr[i], f[i]);
}
else
{
quadraticity = _quadraticity;
ISectionHelper quadraticHelper = null;
ISectionHelper convMonotoneHelper = null;
if (_quadraticity > 0.0)
{
if (gPrev >= -2.0 * gNext && gPrev > -0.5 * gNext && _forcePositive)
{
quadraticHelper = new QuadraticMinHelper(_xArr[i - 1], _xArr[i], f[i - 1], f[i], _yArr[i], integral);
}
else
{
quadraticHelper = new QuadraticHelper(_xArr[i - 1], _xArr[i], f[i - 1], f[i], _yArr[i], integral);
}
}
if (_quadraticity < 1.0)
{
if ((gPrev > 0.0 && -0.5 * gPrev >= gNext && gNext >= -2.0 * gPrev) ||
(gPrev < 0.0 && -0.5 * gPrev <= gNext && gNext <= -2.0 * gPrev))
{
quadraticity = 1.0;
if (_quadraticity.IsAlmostZero())
{
quadraticHelper = _forcePositive
? (ISectionHelper) new QuadraticMinHelper(_xArr[i - 1], _xArr[i], f[i - 1], f[i], _yArr[i], integral)
: new QuadraticHelper(_xArr[i - 1], _xArr[i], f[i - 1], f[i], _yArr[i], integral);
}
}
else if ((gPrev < 0.0 && gNext > -2.0 * gPrev) || (gPrev > 0.0 && gNext < -2.0 * gPrev))
{
var eta = (gNext + 2.0 * gPrev) / (gNext - gPrev);
var b2 = (1.0 + _monotonicity) / 2.0;
if (eta < b2)
{
convMonotoneHelper = new ConvexMonotone2Helper(_xArr[i - 1], _xArr[i], gPrev, gNext, _yArr[i], eta, integral);
}
else
{
convMonotoneHelper = _forcePositive
? new ConvexMonotone4MinHelper(_xArr[i - 1], _xArr[i], gPrev, gNext, _yArr[i], b2, integral)
: new ConvexMonotone4Helper(_xArr[i - 1], _xArr[i], gPrev, gNext, _yArr[i], b2, integral);
}
}
else if ((gPrev > 0.0 && gNext < 0.0 && gNext > -0.5 * gPrev) || (gPrev < 0.0 && gNext > 0.0 && gNext < -0.5 * gPrev))
{
var eta = gNext / (gNext - gPrev) * 3.0;
var b3 = (1.0 - _monotonicity) / 2.0;
if (eta > b3)
{
convMonotoneHelper = new ConvexMonotone3Helper(_xArr[i - 1], _xArr[i], gPrev, gNext, _yArr[i], eta, integral);
}
else
{
convMonotoneHelper = _forcePositive ? new ConvexMonotone4MinHelper(_xArr[i - 1], _xArr[i], gPrev, gNext, _yArr[i], b3, integral) : new ConvexMonotone4Helper(_xArr[i - 1], _xArr[i], gPrev, gNext, _yArr[i], b3, integral);
}
}
else
{
var eta = gNext / (gPrev + gNext);
var b2 = (1.0 + _monotonicity) / 2.0;
var b3 = (1.0 - _monotonicity) / 2.0;
if (eta > b2)
{
eta = b2;
}
if (eta < b3)
{
eta = b3;
}
convMonotoneHelper = _forcePositive
? new ConvexMonotone4MinHelper(_xArr[i - 1], _xArr[i], gPrev, gNext, _yArr[i], eta, integral)
: new ConvexMonotone4Helper(_xArr[i - 1], _xArr[i], gPrev, gNext, _yArr[i], eta, integral);
}
}
if (quadraticity.AlmostEqual(1.0))
{
_helpers[i] = quadraticHelper;
}
else if (quadraticity.IsAlmostZero())
{
_helpers[i] = convMonotoneHelper;
}
else
{
_helpers[i] = new ComboHelper(quadraticHelper, convMonotoneHelper, quadraticity);
}
}
integral += _yArr[i] * (_xArr[i] - _xArr[i - 1]);
}
if (_constFinalPeriod)
{
_helpers[length - 1] = new EverywhereConstantHelper(_yArr[length - 1], integral, _xArr[length - 2]);
_extrapolationHelper = _helpers[length - 1];
}
else
{
_extrapolationHelper = new EverywhereConstantHelper(_helpers[length - 1].GetValue(_xArr.Last()), integral, _xArr.Last());
}
}
public Regression(ISectionHelper sectionHelper, IOLDBConnection oldbConnection)
{
_sectionHelper = sectionHelper;
_oldbConnection = oldbConnection;
}
public MergedToEpic(ISectionHelper sectionHelper, IOLDBConnection oldbConnection)
{
_sectionHelper = sectionHelper;
_oldbConnection = oldbConnection;
}
public override void update()
{
sectionHelpers_.Clear();
if (size_ == 2) { //single period
ISectionHelper singleHelper = new EverywhereConstantHelper(yBegin_[1], 0.0, xBegin_[0]);
sectionHelpers_.Add(xBegin_[1], singleHelper);
extrapolationHelper_ = singleHelper;
return;
}
List<double> f = new InitializedList<double>(size_);
sectionHelpers_ = new Dictionary<double,ISectionHelper>(preSectionHelpers_);
int startPoint = sectionHelpers_.Count+1;
//first derive the boundary forwards.
for (int i=startPoint; i<size_-1; ++i) {
double dxPrev = xBegin_[i] - xBegin_[i-1];
double dx = xBegin_[i+1] - xBegin_[i];
f[i] = dxPrev/(dx+dxPrev) * yBegin_[i]
+ dx/(dx+dxPrev) * yBegin_[i+1];
}
if (startPoint > 1)
f[startPoint-1] = preSectionHelpers_.Last().Value.fNext();
if (startPoint == 1)
f[0] = 1.5 * yBegin_[1] - 0.5 * f[1];
f[size_-1] = 1.5 * yBegin_[size_-1] - 0.5 * f[size_-2];
if (forcePositive_) {
if (f[0] < 0)
f[0] = 0.0;
if (f[size_-1] < 0.0)
f[size_-1] = 0.0;
}
double primitive = 0.0;
for (int i = 0; i < startPoint-1; ++i)
primitive += yBegin_[i+1] * (xBegin_[i+1]-xBegin_[i]);
int endPoint = size_;
//constantLastPeriod_ = false;
if (constantLastPeriod_)
endPoint = endPoint-1;
for (int i=startPoint; i< endPoint; ++i) {
double gPrev = f[i-1] - yBegin_[i];
double gNext = f[i] - yBegin_[i];
//first deal with the zero gradient case
if ( Math.Abs(gPrev) < 1.0E-14 && Math.Abs(gNext) < 1.0E-14 ) {
ISectionHelper singleHelper = new ConstantGradHelper(f[i - 1], primitive,
xBegin_[i-1],
xBegin_[i],
f[i]);
sectionHelpers_.Add(xBegin_[i], singleHelper);
} else {
double quadraticity = quadraticity_;
ISectionHelper quadraticHelper = null;
ISectionHelper convMonotoneHelper = null;
if (quadraticity_ > 0.0) {
if (gPrev >= -2.0*gNext && gPrev > -0.5*gNext && forcePositive_) {
quadraticHelper = new QuadraticMinHelper(xBegin_[i-1],
xBegin_[i],
f[i-1], f[i],
yBegin_[i],
primitive);
} else {
quadraticHelper = new QuadraticHelper(xBegin_[i-1],
xBegin_[i],
f[i-1], f[i],
yBegin_[i],
primitive);
}
}
if (quadraticity_ < 1.0) {
if ((gPrev > 0.0 && -0.5*gPrev >= gNext && gNext >= -2.0*gPrev) ||
(gPrev < 0.0 && -0.5*gPrev <= gNext && gNext <= -2.0*gPrev)) {
quadraticity = 1.0;
if (quadraticity_ == 0) {
if (forcePositive_) {
quadraticHelper = new QuadraticMinHelper(
xBegin_[i-1],
xBegin_[i],
f[i-1], f[i],
yBegin_[i],
primitive);
} else {
quadraticHelper = new QuadraticHelper(
xBegin_[i-1],
xBegin_[i],
f[i-1], f[i],
yBegin_[i],
primitive);
}
}
}
else if ( (gPrev < 0.0 && gNext > -2.0*gPrev) ||
(gPrev > 0.0 && gNext < -2.0*gPrev)) {
double eta = (gNext + 2.0*gPrev)/(gNext - gPrev);
double b2 = (1.0 + monotonicity_)/2.0;
if (eta < b2) {
convMonotoneHelper = new ConvexMonotone2Helper(
xBegin_[i-1],
xBegin_[i],
gPrev, gNext,
yBegin_[i],
eta, primitive);
} else {
if (forcePositive_) {
convMonotoneHelper = new ConvexMonotone4MinHelper(
xBegin_[i-1],
xBegin_[i],
gPrev, gNext,
yBegin_[i],
b2, primitive);
} else {
convMonotoneHelper = new ConvexMonotone4Helper(
xBegin_[i-1],
xBegin_[i],
gPrev, gNext,
yBegin_[i],
b2, primitive);
}
}
}
else if ( (gPrev > 0.0 && gNext < 0.0 && gNext > -0.5*gPrev) ||
(gPrev < 0.0 && gNext > 0.0 && gNext < -0.5*gPrev) ) {
double eta = gNext/(gNext-gPrev) * 3.0;
double b3 = (1.0 - monotonicity_) / 2.0;
if (eta > b3) {
convMonotoneHelper = new ConvexMonotone3Helper(
xBegin_[i-1],
xBegin_[i],
gPrev, gNext,
yBegin_[i],
eta, primitive);
} else {
if (forcePositive_) {
convMonotoneHelper = new ConvexMonotone4MinHelper(
xBegin_[i-1],
xBegin_[i],
gPrev, gNext,
yBegin_[i],
b3, primitive);
} else {
convMonotoneHelper = new ConvexMonotone4Helper(
xBegin_[i-1],
xBegin_[i],
gPrev, gNext,
yBegin_[i],
b3, primitive);
}
}
} else {
double eta = gNext/(gPrev + gNext);
double b2 = (1.0 + monotonicity_) / 2.0;
double b3 = (1.0 - monotonicity_) / 2.0;
if (eta > b2)
eta = b2;
if (eta < b3)
eta = b3;
if (forcePositive_) {
convMonotoneHelper = new ConvexMonotone4MinHelper(
xBegin_[i-1],
xBegin_[i],
gPrev, gNext,
yBegin_[i],
eta, primitive);
} else {
convMonotoneHelper = new ConvexMonotone4Helper(
xBegin_[i-1],
xBegin_[i],
gPrev, gNext,
yBegin_[i],
eta, primitive);
}
}
}
if (quadraticity == 1.0) {
sectionHelpers_.Add(xBegin_[i], quadraticHelper);
} else if (quadraticity == 0.0) {
sectionHelpers_.Add(xBegin_[i], convMonotoneHelper);
} else {
sectionHelpers_.Add(xBegin_[i], new ComboHelper(quadraticHelper, convMonotoneHelper, quadraticity));
}
}
primitive += yBegin_[i] * (xBegin_[i]-xBegin_[i-1]);
}
if (constantLastPeriod_) {
sectionHelpers_.Add(xBegin_[size_-1], new EverywhereConstantHelper(yBegin_[size_-1], primitive, xBegin_[size_-2]));
extrapolationHelper_ = sectionHelpers_[xBegin_[size_-1]];
} else {
extrapolationHelper_ = new EverywhereConstantHelper((sectionHelpers_.Last()).Value.value(xBegin_.Last()),
primitive, xBegin_.Last());
}
}
public InProgess(ISectionHelper sectionHelper, IOLDBConnection oldbConnection)
{
_sectionHelper = sectionHelper;
_oldbConnection = oldbConnection;
}
