Time series analysis plugin

[Jean Bréfort <jean brefort normalesup org>]

Hi,

Seems I never communicated about the API included in this plugin. I
thought I did, but I am unable to find any trace in the mail
archives :-(
As I'll have more available time starting from now and that most of the
things I'm writing for goffice/gnumeric are waiting for goffice
branching, I might come back to this plugin these days.

Currently the plugin contains two sheet functions: interpolation and
periodogram. Follows a short description of what they provide and how
things work.

interpolation(abscissas,ordinates,targets[,interpolation])
- abscissas: the known x values
- ordinates: the known y values
- targets: the x values for which we want the interpolated values
- interpolation: the wanted interpolation type
        0: linear
        1: linear with averaging
        2: staircase
        3: staircase with averaging
        4: natural cubic spline
        5: natural cubic spline with averaging
Default interpolation type is linear.
The interpolated values are returned as a one column matrix.
Instead of using numerical values for the interpolation type, I would
have preferred to use more descriptive strings, but it appeared that it
would end with serious localization issues, so I kept these numerical
constants, even if they are not so easy to use.

periodogram(ordinates,[filter,[abscissas,[interpolation,[number]]]])
This functions does an fft, after applying a filter function. It uses
only real values both as data and returned data (also a one column
matrix).
- ordinates: the y values to transform
- filter: the optional filter type; currently implemented:
        0: no filter (rectangular window)
        1: Bartlett (triangular window)
        2: Hahn (cosine window)
        3: Welch (parabolic window)
with the same concern as for the interpolation method;
- abscissas: optional x values, mostly useful when the data are not
regularly spaced
- interpolation: the interpolation method to use to get y values
corresponding to regularly spaced x values; the value has the same
meaning than in the interpolation function;
- number: the number to use for the interpolation, by default the power
of 2 just over the data number.

The original code has been written by Franck Laurency, and had more
functions (the two above were split in various functions were the names
of the filter or the interpolation method was explicit with the drawback
of a lot of duplicated code). The extra function I need to add are
convolution and various filters (based on convolution methods).
Everything was also originally implemented as tools.

Now, I'd like to have comments on the already implemented things (should
I add linear_interpolation (or lininterp or whatever) and other easier
to use functions) and on the new functions : which arguments are needed?
do we need an optional interpolation of the entered data? And last,
should everything be also implemented as tools?

Cheers,
Jean