NAME
Math::Histogram - N-dimensional histogramming library
SYNOPSIS
use Math::Histogram;
my @dimensions = (
Math::Histogram::Axis->new(10, 0., 1.), # x: 10 bins between 0 and 1
Math::Histogram::Axis->new([1, 2, 4, 8, 16]), # y: 5 bins of variable size
Math::Histogram::Axis->new(2, -1., 1.), # z: 2 bins: [-1, 0) and [0, 1)
);
my $hist = Math::Histogram->new(\@dimensions);
# FIXME cover make_histogram here, too
# Fill some primitive data
while (<>) {
chomp;
my @cols = split /\s+/, $_;
die "Invalid number of columns: " . scalar(@cols)
if @cols != 3;
# Insert new datum into histogram
$hist->fill(\@cols);
}
# Dump histogram content to screen (excluding overflow)
for my $iz (1 .. $hist->get_axis(2)->nbins) {
for my $iy (1 .. $hist->get_axis(1)->nbins) {
for my $ix (1 .. $hist->get_axis(0)->nbins) {
print $hist->get_bin_content([$ix, $iy, $iz]), " ";
}
print "\n";
}
print "\n";
}
DESCRIPTION
This Perl module wraps an n-dimensional histogramming library written in
C.
Beware, this is an early release. While the basic functionality is
rather well tested, the library has not been used in production. If you
intend to adopt it for production, please test your application well and
get in touch with the author.
On N-Dimensional Histogramming
If all you are looking for is a regular one dimensional histogram, then
consider other libraries such as Math::SimpleHisto::XS first for
simplicity and performance. Some care has been taken to optimize the
library for performance given a variable number of dimensions, but not
knowing the number of dimensions statically makes for both somewhat
inefficient algorithmic implementation as well as occasionally awkward
APIs. For example, simply iterating through all bins of a 2D histogram
-- a matrix -- is as simple as
# Pseudo-code
foreach my $ix (0..$nx-1) {
foreach my $iy (0..$ny-1) {
my $z = $matrix->get_bin_content([$ix, $iy]);
}
}
If you don't know the number of dimensions statically, you need to do
something like this (there are other ways to do it, too):
# Pseudo-code
my $coords = [(0) x $ndims];
foreach my $i (0..$unrolled_total_nbins-1) {
my $z = $ndimhisto->get_bin_content($coords);
my $i = 0;
++$coords->[$i];
while ($i < $ndims
&& $coords->[$i] >= $ndimhisto->get_axis($i)->nbins)
{
$coords->[$i] = 0;
++$coords->[++$i];
}
}
Not pretty, eh? Not fast either. So keep that in mind: Your application
knows the number of dimensions that you care about, this histogramming
library does not.
Overview
Generally speaking, a histogram object in the context of this library
contains N axis objects (axises 0 to N-1) that define the binning of
each dimension. Below and above its coordinate range, each axis has an
under- and an overflow bin. When you fill a histogram with data using
the "fill()" method, and the provided coordinates are outside the range
of the histogram, then the data will be filled into the correct under-
or overflow bin. For example, if you create a 2D histogram with the
following axises:
my $h = Math::Histogram->new([
Math::Histogram::Axis->new(2, 0., 1.),
Math::Histogram::Axis->new(3, 0., 3.),
]);
# Worst ASCII drawing ever:
# +-+-+-+-+
# |:|.|.|:|
# +-+-+-+-+
# |.| | |.|
# +-+-+-+-+
# |.| | |.| ^
# +-+-+-+-+ |
# |.| | |.| |
# +-+-+-+-+ dimension 1
# |:|.|.|:|
# +-+-+-+-+
# ---> dimension 0
#
# Bins marked with . are under- or overflow in one dimension.
# Bins marked with : are under- or overflow in BOTH dimensions.
Then you created a histogram with six regular bins: two bins in the X
direction and three bins in the Y direction for a total of "2 * 3 = 6".
On top of that, you get a ring of over- and underflow bins around your
ordinary bins. In this case, there are a grand total of 14 such over-
and underflow bins. As you increase the number of bins in your actual
histogram, the relative number of over- and underflow bins goes down.
You can access histogram content both by the N-dimensional bin numbers
(so, in the 2D example, an array reference containing two integers) or
by user coordinates (eg. an array reference of two floating point
numbers). The module provides facilities to determine the bin in which a
particular set of coordinates falls. The lower boundary of a bin is
always considered part of the bin, whereas the upper boundary is not.
Internally, the histogram data is stored in a flat array since the
dimensionality is unknown at compile time. The linear index into this
array is what may be referred to as the "flat" or "linear" bin number.
In a 1D histogram, it corresponds to the bin numbers of the only axis in
the histogram.
METHODS
new
Class method, constructor. Takes an array reference as first parameter.
The array reference must contain one or more Math::Histogram::Axis
objects that define the binning in one dimension each. The number of
axises determines the dimensionality of the histogram.
clone
Returns an exact clone of the histogram.
new_alike
Returns a clone of the histogram, but without its content.
get_axis
Given a dimension number (starting at 0), returns the axis object of
that dimension.
ndim
Returns the number of dimensions in the histogram.
total
Returns the total content of the histogram. (The sum over all bins,
except this is cached.)
nfills
Returns the number of fill operations that have been performed on the
histogram so far. This is not the same as total unless all fills have a
weight of 1.
fill
Given a reference to an array of coordinates, adds 1 to the content of
the bin that the coordinates belong to.
fill_w
Same as "fill()", except that the second argument needs to be a weight,
the number to add to the bin content (instead of incrementing by 1).
fill_n
Same as "fill()", except that the first parameter needs to be a
reference to a nested array, each of the inner arrays containing a set
of coordinates. In other words, this method works the same as calling
"fill()" repeatedly for each element in the outer array:
my @coords = (
[0.1, 0.2],
[3.8, -1.2],
...
);
$h->fill_n(\@coords);
# Is the same as:
$h->fill($_) for @coords;
# Except a teeny bit faster.
fill_nw
This is to "fill_w(\@coord, $weight)" what "fill_n(\@coords)" is to
"fill(\@coord)". In other words, the first argument is the same as for
"fill_n()", the second is an array reference containing as many weights
as the first had coordinate sets.
fill_bin
Same as "fill()", but takes an array reference containing bin numbers as
argument (instead of a reference to an array of coordinates).
fill_bin_w
This is to "fill_w" what "fill_bin" is to "fill".
fill_bin_n
This is to "fill_n" what "fill_bin" is to "fill".
fill_bin_nw
This is to "fill_nw" what "fill_bin" is to "fill".
get_bin_content
Given a reference to an array of bin numbers, returns the content of the
specified bin. Throws an exception when out of bounds.
find_bin_numbers
Given a reference to an array of coordinates, returns a reference to an
array of (the same number of) bin numbers that correspond to the bin
that the coordinates fall into.
contract_dimension
Given a dimension number (starting at 0), creates an N-1 dimensional
histogram that contains the original data, but with the specified
dimension contracted. The original histogram is untouched. Throws an
exception if the dimension is out of bounds.
cumulate
Given a dimension number (starting at 0), cumulates along that
dimension, modifying the input histogram. Throws an exception if the
dimension is out of bounds. Example:
X ->
1 2 3 ^
4 5 6 |
7 8 9 Y
Cumulated along X, the result is:
1 3 6
4 9 15
7 15 24
Cumulated along Y instead, the result is (note direction of Y axis in
example):
12 15 18
11 13 15
7 8 9
data_equal_to
Given another histogram, returns true if the data content is equal to
the invocant's data. Uses your machine "DBL_EPSILON" for floating point
comparisons.
is_overflow_bin
Given a set of bin numbers, returns true if the bin is an under- or
overflow bin, false otherwise. This is O(n) in the number of dimensions,
but O(1) in the number of bins in the histogram.
is_overflow_bin_linear
Given a linear bin number, returns true if the bin is an under- or
overflow bin, false otherwise. This is O(1) in the number of dimensions
and the number of bins in the histogram.
serialize
Returns a JSON string that represents this histogram object.
deserialize
Class method. Given a JSON string as generated by "serialize()",
recreates the histogram object that it represents. Also accepts a scalar
reference to a JSON string.
SEE ALSO
Math::Histogram::Axis, which is part of this distribution, implements
the binning for a histogram in a single dimension.
Math::SimpleHisto::XS is a fast 1D histogramming module.
SOOT is a dynamic wrapper around the ROOT C++ library which does
histogramming and much more. Beware, it is experimental software.
AUTHOR
Steffen Mueller,
COPYRIGHT AND LICENSE
Copyright (C) 2012 by Steffen Mueller
This library is free software; you can redistribute it and/or modify it
under the same terms as Perl itself, either Perl version 5.8.1 or, at
your option, any later version of Perl 5 you may have available.