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Copy file name to clipboardExpand all lines: doc/Interpolations.jl.ipynb
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"You'll notice that when creating the quadratic interpolation, we had to give another input parameter to the interpolation type: the `Line(OnCell())` argument which specifies the boundary condition. The first term (`Line`) specifies the behavior of the boundary condition, the second (`OnCell`) specifies where it applies. In this case `yitp_quadratic` will become linear for `x < 0.5` or `x > 10.5`. The alternative, `OnGrid`, would apply the boundary condition for `x < 1` or `x > 10`.\n",
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"All interpolations of quadratic degree or higher require a prefiltering step, which entails solving a tridiagonal system of equations (details can be found for example in [this paper](http://dx.doi.org/10.1109/42.875199)), in order to make the interpolating function pass through the data points. `Interpolations.jl` takes care of solving this system for you, but in order to close the system a boundary condition is requred."
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"All interpolations of quadratic degree or higher require a prefiltering step, which entails solving a tridiagonal system of equations (details can be found for example in [this paper](http://dx.doi.org/10.1109/42.875199)), in order to make the interpolating function pass through the data points. `Interpolations.jl` takes care of solving this system for you, but in order to close the system a boundary condition is required."
1. For this reason, linear B-splines are often referred to as *2nd order*, which may be a source of confusion since the interpolating function itself is linear, i.e. of first order. In `Interpolations.jl`, we will try to avoid this confusion by referring to interpolation degree by "linear", "quadratic" etc.
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2. Although the separation of concepts 1-3 from extrapolation behavior is computationally sound, it does allow for some interesting, yet probably nonsensical, combinations of interpolation degrees, boundary conditions and extrapolation behavior. One could imagine for example a constant interpolation (which needs no boundary condition) with linear extrapolation, in which case the interpolating function is a sequence of "steps" with 0-derivative inside the domain, while suddenly having a nonzero derivative outside. Similarly, in most cases where the extrapolation behavior is defined as constant or reflecting, it will make sense to specify matching boundary conditions, but other combinations are entirely supported by `Interpolations.jl`; your milage may vary, very much...
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2. Although the separation of concepts 1-3 from extrapolation behavior is computationally sound, it does allow for some interesting, yet probably nonsensical, combinations of interpolation degrees, boundary conditions and extrapolation behavior. One could imagine for example a constant interpolation (which needs no boundary condition) with linear extrapolation, in which case the interpolating function is a sequence of "steps" with 0-derivative inside the domain, while suddenly having a nonzero derivative outside. Similarly, in most cases where the extrapolation behavior is defined as constant or reflecting, it will make sense to specify matching boundary conditions, but other combinations are entirely supported by `Interpolations.jl`; your mileage may vary, very much...
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