summaryrefslogtreecommitdiff
path: root/boost/math/interpolators/cubic_b_spline.hpp
diff options
context:
space:
mode:
Diffstat (limited to 'boost/math/interpolators/cubic_b_spline.hpp')
-rw-r--r--boost/math/interpolators/cubic_b_spline.hpp78
1 files changed, 78 insertions, 0 deletions
diff --git a/boost/math/interpolators/cubic_b_spline.hpp b/boost/math/interpolators/cubic_b_spline.hpp
new file mode 100644
index 0000000000..73ac1d0137
--- /dev/null
+++ b/boost/math/interpolators/cubic_b_spline.hpp
@@ -0,0 +1,78 @@
+// Copyright Nick Thompson, 2017
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt
+// or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+// This implements the compactly supported cubic b spline algorithm described in
+// Kress, Rainer. "Numerical analysis, volume 181 of Graduate Texts in Mathematics." (1998).
+// Splines of compact support are faster to evaluate and are better conditioned than classical cubic splines.
+
+// Let f be the function we are trying to interpolate, and s be the interpolating spline.
+// The routine constructs the interpolant in O(N) time, and evaluating s at a point takes constant time.
+// The order of accuracy depends on the regularity of the f, however, assuming f is
+// four-times continuously differentiable, the error is of O(h^4).
+// In addition, we can differentiate the spline and obtain a good interpolant for f'.
+// The main restriction of this method is that the samples of f must be evenly spaced.
+// Look for barycentric rational interpolation for non-evenly sampled data.
+// Properties:
+// - s(x_j) = f(x_j)
+// - All cubic polynomials interpolated exactly
+
+#ifndef BOOST_MATH_INTERPOLATORS_CUBIC_B_SPLINE_HPP
+#define BOOST_MATH_INTERPOLATORS_CUBIC_B_SPLINE_HPP
+
+#include <boost/math/interpolators/detail/cubic_b_spline_detail.hpp>
+
+namespace boost{ namespace math{
+
+template <class Real>
+class cubic_b_spline
+{
+public:
+ // If you don't know the value of the derivative at the endpoints, leave them as nans and the routine will estimate them.
+ // f[0] = f(a), f[length -1] = b, step_size = (b - a)/(length -1).
+ template <class BidiIterator>
+ cubic_b_spline(const BidiIterator f, BidiIterator end_p, Real left_endpoint, Real step_size,
+ Real left_endpoint_derivative = std::numeric_limits<Real>::quiet_NaN(),
+ Real right_endpoint_derivative = std::numeric_limits<Real>::quiet_NaN());
+ cubic_b_spline(const Real* const f, size_t length, Real left_endpoint, Real step_size,
+ Real left_endpoint_derivative = std::numeric_limits<Real>::quiet_NaN(),
+ Real right_endpoint_derivative = std::numeric_limits<Real>::quiet_NaN());
+
+ cubic_b_spline() = default;
+ Real operator()(Real x) const;
+
+ Real prime(Real x) const;
+
+private:
+ std::shared_ptr<detail::cubic_b_spline_imp<Real>> m_imp;
+};
+
+template<class Real>
+cubic_b_spline<Real>::cubic_b_spline(const Real* const f, size_t length, Real left_endpoint, Real step_size,
+ Real left_endpoint_derivative, Real right_endpoint_derivative) : m_imp(std::make_shared<detail::cubic_b_spline_imp<Real>>(f, f + length, left_endpoint, step_size, left_endpoint_derivative, right_endpoint_derivative))
+{
+}
+
+template <class Real>
+template <class BidiIterator>
+cubic_b_spline<Real>::cubic_b_spline(BidiIterator f, BidiIterator end_p, Real left_endpoint, Real step_size,
+ Real left_endpoint_derivative, Real right_endpoint_derivative) : m_imp(std::make_shared<detail::cubic_b_spline_imp<Real>>(f, end_p, left_endpoint, step_size, left_endpoint_derivative, right_endpoint_derivative))
+{
+}
+
+template<class Real>
+Real cubic_b_spline<Real>::operator()(Real x) const
+{
+ return m_imp->operator()(x);
+}
+
+template<class Real>
+Real cubic_b_spline<Real>::prime(Real x) const
+{
+ return m_imp->prime(x);
+}
+
+}}
+#endif