# [SciPy-User] Cubic splines - MATLAB vs Scipy.interpolate

Charles R Harris charlesr.harris@gmail....
Tue Sep 27 22:08:19 CDT 2011

```On Tue, Sep 27, 2011 at 5:50 PM, <josef.pktd@gmail.com> wrote:

> On Tue, Sep 27, 2011 at 7:27 PM, Charles R Harris
> <charlesr.harris@gmail.com> wrote:
> >
> >
> > On Tue, Sep 27, 2011 at 2:27 PM, Zachary Pincus <zachary.pincus@yale.edu
> >
> > wrote:
> >>
> >> scipy.signal has some cubic and quadratic spline functions:
> >> cspline1d
> >> cspline1d_eval
> >> cspline2d
> >>
> >> (and replace the c with q for the quadratic versions).
> >>
> >> I have no idea how fast they are, or if they're at all drop-in
> >> replacements for the matlab ones. The stuff in scipy.interpolate is
> >> powerful, but the fitpack spline-fitting operations can be a bit
> >> input-sensitive and prone to strange ringing.
> >>
> >> Zach
> >>
> >>
> >>
> >> On Sep 27, 2011, at 3:32 PM, Charles R Harris wrote:
> >>
> >> >
> >> >
> >> > On Tue, Sep 27, 2011 at 1:04 PM, Jaidev Deshpande
> >> > <deshpande.jaidev@gmail.com> wrote:
> >> > Hi
> >> >
> >> > The big question: Why does the MATLAB function spline operate faster
> >> > than the cubic spline alternatives in Scipy, especially splrep and
> splev ?
> >> >
> >> > ------
> >> >
> >> > The context: I'm working on an algorithm that bottlenecks on spline
> >> > interpolation.
> >> >
> >> > Some functions in Scipy return an interpolation object function
> >> > depending on the input data which needs to be evaluated independently
> over
> >> > the whole range.
> >> >
> >> > So I used 'lower order' functions like splrep and splev. Even that was
> >> > too slow.
> >> >
> >> > Then I tried to write my own code for cubic splines, generating and
> >> > solving a system of 4N simultaneous equations for interpolation
> between N+1
> >> > points.
> >> >
> >> > No matter what I do, the code is quite slow. How come the MATLAB
> >> > function spline operate so fast? What am I missing? What can I do to
> speed
> >> > it up?
> >> >
> >> >
> >> > I suspect it is because the scipy routines you reference are based on
> >> > b-splines, which are needed for least squares fits. Simple cubic
> spline
> >> > interpolation through a give set of points tends to be faster and I
> believe
> >> > that is what the Matlab spline function does. To get b-splines in
> Matlab you
> >> > need one of the toolboxes, it doesn't come with the core. I don't
> think
> >> > scipy has a simple cubic spline interpolation, but I may be wrong.
> >> >
> >
> > I believe the splines in signal are periodic and the boundary conditions
> > aren't flexible. The documentation is, um..., well, they are effectively
> > undocumented. We really need better spline support in scipy.
>
> I thought the main difference of the signal compared to interpolate
> splines is that they work only on a regular grid.
> They have a smoothing coefficient lambda, so they don't seem to be
> pure interpolating splines.
>
>
The equally spaced points are what I meant by periodic, i.e., the same basis
function can be repeated. The signal itself it periodic if extended to twice
its length with the mirror symmetry at the ends. I'm not sure how the
smoothing factor works. The ndimage map_coordinates would work for
interpolating equally spaced points and has more boundary conditions, but
they are still can't be arbitrary. I think scipy could use a simple
interpolating spline with not a knot default boundary conditions and no
repeated knot points. The not a knot boundary conditions means to use finite
differences at the ends to estimate the slopes which then become the
boundary conditions.

Chuck
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