Re: [ePiX-users] Histograms

[Marcus D. Hanwell]

On Wednesday 03 January 2007 02:46, Andrew D. Hwang wrote:
> My current line of thought has a "data_bin" class, which is created from
> a minimum and maximum value, an optional number of bins (1 by default),
> and perhaps a function that specifies bin widths in some convenient way.
> For example,
>
>    data_bin(0, 10);         // the interval [0,10]
>    data_bin(0, 10, 5);      // [0,2], [2,4], ..., [8,10]
>    data_bin(1, 8, 3, geom); // [1,2], [2,4], [4,8]; geom(x) = pow(2, x)
>
> Interval divisions can be added manually, e.g.
>
>    data_bin B(0, 10);
>    B.cut(3).cut(7); // B = [0,3], [3,7], [7,10]
>    B.cut(20);       // out of range, no effect

This sounds good. In my experience most histograms have equal sized bins as 
that most easily communicates the data. Also in my field people rarely scale 
the data and it is in fact preferred for most of my plots to have the raw 
numbers.
>
> Data can be read in from a vector of doubles or from a file. Once data has
> been read in, no further interval subdivision is permitted.
>
>    B.read("myfile.dat", 2); // read in column 2
>    B.cut(5.5);              // no effect
>
> Draw a histogram with specified vertical scale or area:
>
>    B.histogram();  // defaults to "area = number of data points"
>    B.histogram(3); // triple box heights or total area 3...?
>    B.histogram(1/B.pop()); // unit-area histogram; B.pop() = population
>    B.normalize();  // now histograms will have unit area by default
>
> Are there other features that would be useful? Does the syntax above seem
> natural and easy to use? Are there common or standard ways of dividing an
> interval into bins other than "equal length", and if so, what would be a
> convenient mathematical description? Would it be useful to apply a user-
> specified function to data as it's read in?

In my opinion this looks like a nice way to plot histograms that could be 
extended in future. One thing we sometimes want to do is plot the histogram 
feintly and then plot a trend line of the histogram points with cubic splines 
or something to smooth. I have seen this done in several places and it looks 
quite effective.

On an unrelated note is it currently possible to plot graphs on a log scale at 
all? Or would I be best just modifying the data for now and plotting log(y)? 
I would miss the tick marks as they get closer on the log plots but could 
live with it for now.
>
> Thanks in advance for your input.

I hope it is useful and I would be interested to hear what others think. I 
think with a few small additions ePiX would be very useful for data plotting. 
It is great being able to easily plot data along with arbitrary functions on 
the same graph too.

I would welcome a legend function to draw a box on my graph around an 
annotated legend but I think I have figured out how to do that quite 
effectively using a small function anyway.

I would love to be able to composite multiple graphs using this environment 
but it sounds like that is in the works for ePiX 2 - we often inlay a small 
graph in the top corner of the main graph in papers. There is also the use of 
two different x and y scales to compare data with different scales side by 
side but again I think that would be better implemented in ePiX 2.

Thanks,

Marcus