| 1 | /* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */ |
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| 2 | |
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| 3 | /* |
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| 4 | Copyright (C) 2015 Ferdinando Ametrano |
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| 5 | Copyright (C) 2015 Paolo Mazzocchi |
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| 6 | |
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| 7 | This file is part of QuantLib, a free-software/open-source library |
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| 8 | for financial quantitative analysts and developers - http://quantlib.org/ |
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| 9 | |
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| 10 | QuantLib is free software: you can redistribute it and/or modify it |
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| 11 | under the terms of the QuantLib license. You should have received a |
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| 12 | copy of the license along with this program; if not, please email |
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| 13 | <quantlib-dev@lists.sf.net>. The license is also available online at |
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| 14 | <http://quantlib.org/license.shtml>. |
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| 15 | |
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| 16 | This program is distributed in the hope that it will be useful, but WITHOUT |
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| 17 | ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS |
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| 18 | FOR A PARTICULAR PURPOSE. See the license for more details. |
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| 19 | */ |
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| 20 | |
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| 21 | #include <ql/math/polynomialmathfunction.hpp> |
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| 22 | #include <ql/math/pascaltriangle.hpp> |
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| 23 | |
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| 24 | namespace QuantLib { |
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| 25 | |
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| 26 | PolynomialFunction::PolynomialFunction(const std::vector<Real>& coeff) { |
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| 27 | |
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| 28 | QL_REQUIRE(!coeff.empty(), "empty coefficient vector" ); |
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| 29 | order_ = coeff.size(); |
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| 30 | c_ = coeff; |
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| 31 | derC_ = std::vector<Real>(order_-1); |
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| 32 | prC_ = std::vector<Real>(order_); |
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| 33 | K_ = 0.0; |
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| 34 | eqs_ = Matrix(order_, order_, 0.0); |
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| 35 | |
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| 36 | Size i; |
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| 37 | for (i=0; i<order_-1; ++i) { |
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| 38 | prC_[i] = c_[i]/(i+1); |
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| 39 | derC_[i] = c_[i+1]*(i+1); |
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| 40 | } |
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| 41 | prC_[i] = c_[i]/(i + 1); |
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| 42 | } |
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| 43 | |
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| 44 | Real PolynomialFunction::operator()(Time t) const { |
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| 45 | Real result=0.0, tPower=1.0; |
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| 46 | for (Size i=0; i<order_; ++i) { |
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| 47 | result += c_[i] * tPower; |
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| 48 | tPower *= t; |
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| 49 | } |
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| 50 | return result; |
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| 51 | } |
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| 52 | |
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| 53 | Real PolynomialFunction::derivative(Time t) const { |
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| 54 | Real result=0.0, tPower=1.0; |
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| 55 | for (Size i=0; i<order_-1; ++i) { |
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| 56 | result += derC_[i] * tPower; |
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| 57 | tPower *= t; |
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| 58 | } |
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| 59 | return result; |
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| 60 | } |
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| 61 | |
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| 62 | Real PolynomialFunction::primitive(Time t) const { |
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| 63 | Real result=K_, tPower=t; |
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| 64 | for (Size i=0; i<order_; ++i) { |
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| 65 | result += prC_[i] * tPower; |
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| 66 | tPower *= t; |
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| 67 | } |
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| 68 | return result; |
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| 69 | } |
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| 70 | |
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| 71 | Real PolynomialFunction::definiteIntegral(Time t1, |
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| 72 | Time t2) const { |
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| 73 | return primitive(t: t2)-primitive(t: t1); |
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| 74 | } |
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| 75 | |
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| 76 | void PolynomialFunction::initializeEqs_(Time t, |
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| 77 | Time t2) const { |
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| 78 | Time dt = t2 - t; |
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| 79 | Real tau; |
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| 80 | for (Size i=0; i<order_; ++i) { |
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| 81 | tau = 1.0; |
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| 82 | for (Size j=i; j<order_; ++j) { |
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| 83 | tau *= dt; |
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| 84 | eqs_[i][j] = (tau * PascalTriangle::get(order: j + 1)[i]) / (j + 1); |
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| 85 | } |
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| 86 | } |
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| 87 | } |
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| 88 | |
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| 89 | std::vector<Real> |
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| 90 | PolynomialFunction::definiteIntegralCoefficients(Time t, |
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| 91 | Time t2) const { |
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| 92 | Array k(c_.begin(), c_.end()); |
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| 93 | initializeEqs_(t, t2); |
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| 94 | Array coeff = eqs_ * k; |
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| 95 | std::vector<Real> result(coeff.begin(), coeff.end()); |
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| 96 | return result; |
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| 97 | } |
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| 98 | |
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| 99 | std::vector<Real> |
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| 100 | PolynomialFunction::definiteDerivativeCoefficients(Time t, |
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| 101 | Time t2) const { |
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| 102 | Array k(c_.begin(), c_.end()); |
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| 103 | initializeEqs_(t, t2); |
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| 104 | Array coeff = inverse(m: eqs_) * k; |
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| 105 | std::vector<Real> result(coeff.begin(), coeff.end()); |
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| 106 | return result; |
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| 107 | } |
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| 108 | |
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| 109 | } |
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| 110 | |
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