/usr/include/ql/math/bspline.hpp is in libquantlib0-dev 1.7.1-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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/*
Copyright (C) 2007 Allen Kuo
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license. You should have received a
copy of the license along with this program; if not, please email
<quantlib-dev@lists.sf.net>. The license is also available online at
<http://quantlib.org/license.shtml>.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the license for more details.
*/
/*! \file bspline.hpp
\brief B-spline basis functions
*/
#ifndef quantlib_bspline_hpp
#define quantlib_bspline_hpp
#include <ql/types.hpp>
#include <vector>
namespace QuantLib {
//! B-spline basis functions
/*! Follows treatment and notation from:
Weisstein, Eric W. "B-Spline." From MathWorld--A Wolfram Web
Resource. <http://mathworld.wolfram.com/B-Spline.html>
\f$ (p+1) \f$-th order B-spline (or p degree polynomial) basis
functions \f$ N_{i,p}(x), i = 0,1,2 \ldots n \f$, with \f$ n+1 \f$
control points, or equivalently, an associated knot vector
of size \f$ p+n+2 \f$ defined at the increasingly sorted points
\f$ (x_0, x_1 \ldots x_{n+p+1}) \f$. A linear B-spline has
\f$ p=1 \f$, quadratic B-spline has \f$ p=2 \f$, a cubic
B-spline has \f$ p=3 \f$, etc.
The B-spline basis functions are defined recursively
as follows:
\f[
\begin{array}{rcl}
N_{i,0}(x) &=& 1 \textrm{\ if\ } x_{i} \leq x < x_{i+1} \\
&=& 0 \textrm{\ otherwise} \\
N_{i,p}(x) &=& N_{i,p-1}(x) \frac{(x - x_{i})}{ (x_{i+p-1} - x_{i})} +
N_{i+1,p-1}(x) \frac{(x_{i+p} - x)}{(x_{i+p} - x_{i+1})}
\end{array}
\f]
*/
class BSpline {
public:
BSpline(Natural p,
Natural n,
const std::vector<Real>& knots);
Real operator()(Natural i, Real x) const;
private:
// recursive definition of N, the B-spline basis function
Real N(Natural i, Natural p, Real x) const;
// e.g. p_=2 is a quadratic B-spline, p_=3 is a cubic B-Spline, etc.
Natural p_;
// n_ + 1 = "control points" = max number of basis functions
Natural n_;
std::vector<Real> knots_;
};
}
#endif
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