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Class implementing cubic splines. More...
#include <opm/material/common/TridiagonalMatrix.hpp>
#include <opm/material/common/PolynomialUtils.hpp>
#include <opm/material/common/Exceptions.hpp>
#include <ostream>
#include <vector>
#include <tuple>
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Classes | |
class | Opm::Spline< Scalar > |
Class implementing cubic splines. More... | |
struct | Opm::Spline< Scalar >::ComparatorX_ |
Helper class needed to sort the input sampling points. More... | |
Class implementing cubic splines.
This class supports full, natural, periodic and monotonic cubic splines.
Full a splines are splines which, given
sampling points
, fulfill the following conditions
for any given boundary slopes and
.
Natural splines which are defined by
For periodic splines of splines the slopes at the boundaries are identical:
Finally, there are monotonic splines which guarantee that the curve is confined by its sampling points, i.e.,
For more information on monotonic splines, see http://en.wikipedia.org/wiki/Monotone_cubic_interpolation
Full, natural and periodic splines are continuous in their first and second derivatives, i.e.,
holds for such splines. Monotonic splines are only continuous up to their first derivative, i.e., for these only
is true.