Announcement
MDArray version 0.5.3 has Just been released. MDArray is a multi
dimensional array implemented for JRuby inspired by NumPy
(www.numpy.org)
and Masahiro Tanakas Narray (narray.rubyforge.org). MDArray stands on
the
shoulders of JavaNetCDF and Parallel Colt. At this point MDArray has
libraries for mathematical, trigonometric and descriptive statistics
methods.
NetCDFJava Library is a Java interface to NetCDF
fileshttp://www.unidata.ucar.edu/software/netcdf/index.html,
as well as to many other types of scientific data formats. It is
developed
and distributed by Unidata (http://www.unidata.ucar.edu).
Parallel Colt (
http://grepcode.com/snapshot/repo1.maven.org/maven2/net.sourceforge.parallelcolt/parallelcolt/0.10.0/)
is a
multithreadedhttp://en.wikipedia.org/wiki/Thread_(computer_science)
version
of Colt http://dsd.lbl.gov/~hoschek/colt/ (
http://acs.lbl.gov/software/colt/). Colt provides a set of Open Source
Libraries for High Performance Scientific and Technical Computing in
Java.
Scientific and technical computing is characterized by demanding problem
sizes and a need for high performance at reasonably small memory
footprint.
Whats new*:*
Performance Improvement
On previous versions, array operations were done by passing a Ruby Proc
to
a loop for all elements of the given arrays. For instance, adding two
MDArrays was done by passing Proc.new { a, b a + b } and looping
through
all elements of the arrays. Procs are very flexible in Ruby; however,
from
my experience with MDArray, also very slow.
On this version, when available, instead of passing a Proc to the loop,
we
pass a native Java method. Available Java methods are those extracted
from
Parallel Colt and listed below. Note that Parallel Colt has native
methods
for the following types only: double, float, long and int. With
this change, there was a performance improvement of over 90%, and using
MDArray operations is close to native Java operations. We expect (but
have
not yet benchmarking data) that this brings MDArray performance close to
similar solutions such as NArray, NMatrix and NumPy (please try it, and
if
this assertion is false, Ill be glad to change it in future
announcements).
Methods not available in Parallel Colt but supported by Ruby, such as
sinh, tanh, and add for byte type, etc. are still supported by
MDArray. Again, to improve performance, instead of passing a Proc we
now
create a class as follows
class Add

*def self.apply(a, b) a + b end end
This change brought performance improvement of over 60% for MDArray
operations with Ruby methods.
Experimental Lazy Evaluation
Usual MDArray operations are done eagerly, i.e., if @a, @b, @c are three
MDArrays then the following:
@d = @a + @b + @c
will be evaluated as follows: first @a + @b is performed and stored in a
temporary variable, then this temporary variable is added to @c. For
large
expressions, temporary variables can have significant performance
impact.
This version of MDArray introduces lazy evaluation of expressions.
Thus,
when in lazy mode:
@lazy_d = @a + @b + @c
will not evaluate immediately. Rather, the expression is preprocessed
and
only executed when required. Since at execution time the whole
expression
is known, there is no need for temporary variables as the whole
expression
is executed at once. To put MDArray in lazy mode we only need to set
its
mode to lazy with the following command MDArray.lazy = true. All
expressions after that are by default lazy. In lazy mode, MDArray
resembles Numexpr, however, there is no need to write the expression as
a
string, and there is no compilation involved.
MDArray does not implement broadcasting rules as NumPy. As a result,
trying to operate on arrays of different shape raises an exception. On
lazy mode, this exception is raise only at evaluation time, so it is
possible to have an invalid lazy array. To evaluate a lazy array one
should use the [] method as follows:
@d = lazy_d[]
@d is now a normal MDArray.
Lazy MDArrays are really lazy, so lets assume that @a = [1, 2, 3, 4] and
@b = [5, 6, 7, 8]. Lets also have @l_c = @a + @b. Now doing @c =
@l_c[],
will evaluate @c to [6, 8, 10, 12]. Now, lets do @a[1] = 20 and then @d
@l_c[]. Now @d evaluates to [25, 8, 10, 12] as the new value of @a is
used.
Lazy arrays can be evaluated inside expressions:
@l_c = (@a + @b)[] + @c
In this example, @l_c is a lazy array, but (@a + @b) is evaluated when
the
[] method is called and then added to @c. If now the value of @a or @b
is changed, the evaluation of @l_c will not be changed as in the
previous
example.
Finally, laziness is contagious. So, lets assume that we have @l_c as
above, a lazy array and we do MDArray.lazy = false. From this point on
in
the code, operations will be done eagerly. Now doing: @e = @d + @l_c,
@e
is a lazy array as its construction involves a lazy array. One should
be
careful when in eager mode mixing lazy and eager arrays:
@c = @l_a + (@b + @c)
then, with parenthesis, first (@b + @c) is evaluated eagerly and then
added
lazily to @l_a, giving a lazy array.
In this version, Lazy evaluation is around 40% less efficient in one
machine I tested up to approximately the same performance in another
equipment than eager evaluation when only native Java methods (Parallel
Colt methods described below) are used in the expression. If expression
involves any Ruby method, evaluation of lazy expressions becomes much
slower than eager evaluation. In order to improve performance, I
believe
that compilation of expression will be necessary.
MDArray and SciRuby*:*
MDArray subscribes fully to the SciRuby Manifesto (http://sciruby.com/).
Ruby http://www.rubylang.org/ has for some time had no
equivalent
to the beautifully constructed *NumPy http://numpy.scipy.org/,
SciPyhttp://www.scipy.org/,
and matplotlib http://matplotlib.sourceforge.net/ libraries for **
Pytho http://www.python.org/n.*
We believe that the time for a Ruby science and visualization package
has
come. Sometimes when a solution of sugar and water becomes
supersaturated,
from it precipitates a pure, delicious, and diabetesinducing crystal of
sweetness, induced by no more than the tap of a finger. So is occurring
now, we believe, with numeric and visualization libraries for Ruby.
MDArray main properties are*:*
Homogeneous multidimensional array, a table of elements
(usually
numbers), all of the same type, indexed by a tuple of positive integers;
Easy calculation for large numerical multi dimensional arrays;
Basic types are: boolean, byte, short, int, long, float,
double,
string, structure;
Based on JRuby, which allows importing Java libraries;
Operator: +,,*,/,%,**, >, >=, etc.;
Functions: abs, ceil, floor, truncate, is_zero, square, cube,
fourth;
Binary Operators: &, , ^, ~ (binary_ones_complement), <<, >>;
Ruby Math functions: acos, acosh, asin, asinh, atan, atan2,
atanh, cbrt, cos, erf, exp, gamma, hypot, ldexp, log, log10, log2, sin,
sinh, sqrt, tan, tanh, neg;
Boolean operations on boolean arrays: and, or, not;
Fast descriptive statistics from Parallel Colt (complete list
found bellow);
Easy manipulation of arrays: reshape, reduce dimension,
permute,
section, slice, etc.;
Reading of two dimensional arrays from CSV files (mainly for
debugging and simple testing purposes);
StatList: a list that can grow/shrink and that can compute
Parallel Colt descriptive statistics;
Experimental lazy evaluation (still slower than eager
evaluation).
Descriptive statistics methods imported from Parallel Colt*:*
auto_correlation, correlation, covariance, durbin_watson, frequencies,
geometric_mean, harmonic_mean, kurtosis, lag1, max, mean,
mean_deviation,
median, min, moment, moment3, moment4, pooled_mean, pooled_variance,
product, quantile, quantile_inverse, rank_interpolated, rms,
sample_covariance, sample_kurtosis, sample_kurtosis_standard_error,
sample_skew, sample_skew_standard_error, sample_standard_deviation,
sample_variance, sample_weighted_variance, skew,
split, standard_deviation, standard_error, sum, sum_of_inversions,
sum_of_logarithms, sum_of_powers, sum_of_power_deviations,
sum_of_squares,
sum_of_squared_deviations, trimmed_mean, variance, weighted_mean,
weighted_rms, weighted_sums, winsorized_mean.
Double and Float methods from Parallel Colt:
acos, asin, atan, atan2, ceil, cos, exp, floor, greater, IEEEremainder,
inv, less, lg, log, log2, rint, sin, sqrt, tan.
Double, Float, Long and Int methods from Parallel Colt:
abs, compare, div, divNeg, equals, isEqual (is_equal), isGreater
(is_greater), isles (is_less), max, min, minus, mod, mult, multNeg
(mult_neg), multSquare (mult_square), neg, plus (add), plusAbs
(plus_abs),
pow (power), sign, square.
Long and Int methods from Parallel Colt
and, dec, factorial, inc, not, or, shiftLeft (shift_left),
shiftRightSigned
(shift_right_signed), shiftRightUnsigned (shift_right_unsigned), xor.
MDArray installation and download*:*
Install Jruby
jruby S gem install mdarray
MDArray Homepages*:*
http://rubygems.org/gems/mdarray
https://github.com/rbotafogo/mdarray/wiki
Contributors*:*
Contributors are welcome.
MDArray History*:*
24/05/2013: Version 0.5.0 Over 90% Performance improvements for
methods imported from Parallel Colt and over 40% performance
improvements
for all other methods (implemented in Ruby);
16/05/2013: Version 0.5.0  All loops transferred to Java with over
50% performance improvements. Descriptive statistics from Parallel
Colt;
19/04/2013: Version 0.4.3  Fixes a simple, but fatal bug in
0.4.2. No new features;
17/04/2013: Version 0.4.2  Adds simple statistics and boolean
operators;
05/04/2013: Version 0.4.0 Initial release.