John Woods merged my last pull request to NMatrix recently and I wanted to write about why we created these shortcuts and what can be done with them.
The need for shortcuts
The first iteration of NMatrix shortcuts was written by Daniel Carrera and sent to the mailing list, where I started working with them. Some discussions, decisions and two pull requests later, we have a working set of methods to create common matrices (zeros, ones, random, etc) and do some cool stuff (column and linspace) very easily.
There are at least two good reasons to have these shortcuts: MATLAB users are going to feel at home, and the shortcuts allow us to prototype and experiment more rapidly. For example, it’s dead simple to create an identify matrix when you need one:
>> require 'nmatrix'
>> matrix = NMatrix.identity(3) # 3x3
=> #<NMatrix:0x007faa5b8cda40shape:[3,3] dtype:float64 stype:dense>
>> matrix.pp
# [1.0, 0.0, 0.0]
# [0.0, 1.0, 0.0]
# [0.0, 0.0, 1.0]
And a random matrix to test some operation:
>> rand_matrix = NMatrix.random(4) # 4x4
=> #<NMatrix:0x007faa5b01cdd8shape:[4,4] dtype:float64 stype:dense>
>> rand_matrix.pp
# [0.5933103148378577, 0.8556103970281977, 0.7176768395610358, 0.07160353964395305]
# [0.8566365570076784, 0.33925854948960343, 0.5994298479703805, 0.6906794137948586]
# [0.5684593743073485, 0.10273166792035393, 0.46187577773882293, 0.586085963973687]
# [0.8944982538369494, 0.9896291945923837, 0.8787034784673503, 0.5933103148378577]
Shortcuts available
The following list is taken from NMatrix’s wiki. All are class methods on NMatrix.
ones(3,3) # A 3x3 matrix of ones.
zeros(4,4) or zeroes(4,4) # Creates a matrix of zeros with dimensions as parameters.
identity(5,5) or eye(5,5) # A 5x5 identity matrix. Only works with NMatrix.
seq(8) # An 8-vector with a sequence of values from 0 to 7.
random(6,6) # A 6x6 matrix of random values between 0 and 1.
column(2) # Return the 2nd column of the original matrix. Only works with NMatrix.
indgen(8) # To make IDL users happy. Same as `seq(8, :int32)`.
findgen(8) # Same as `seq(8, :float32)`.
bindgen(8) # Same as `seq(8, :byte)`.
cindgen(8) # Same as `seq(8, :complex64)`.
linspace(0, pi, 100) # A vector of 100 values from 0 to pi, inclusive. Only works with NVector.
The method names are mostly from MATLAB. In the future, when more functionality is added, we’ll try to create a more “Ruby-like” feel to the API. But as these shortcuts do very primitive tasks, there isn’t any obvious room for improvement. (Feel free to prove us wrong, however!)
I’ll create a separate wiki page for the shortcuts to be able to organize and put more information about how to use them. But I want to create a better RDoc documentation for NMatrix — so the full API will probably be referenced there. I’ll write a new blog post here when something along these lines is done.
Examples
First, let’s try normalizing the columns of an NMatrix.
require 'nmatrix'
m = NMatrix.seq(3, :float32)
m.pp
# [0.0, 1.0, 2.0]
# [3.0, 4.0, 5.0]
# [6.0, 7.0, 8.0]
(0 .. m.shape[1] - 1).each do |j|
col = m.column(j)
norm = Math.sqrt(col.transpose.dot(col)[0, 0])
(0 .. m.shape[0] - 1).each { |i| m[i,j] /= norm }
end
m.pp
# [0.0, 0.12309148907661438, 0.20739033818244934]
# [0.4472135901451111, 0.4923659563064575, 0.5184758305549622]
# [0.8944271802902222, 0.861640453338623, 0.8295613527297974]
(0 .. m.shape[1] - 1).each do |j|
col = m.column(j)
puts Math.sqrt(col.transpose.dot(col)[0,0])
end
# 0.9999999701976772
# 1.0
# 1.0
Unfortunately, slice by reference isn’t working on HEAD, or we could make a few additional improvements (see issue #51).
The other thing that I’ve wanted to do is to use linspace to generate points for plotting sines, cosines, etc. Here is an example:
require 'nmatrix'
vector = NVector.linspace(0, Math::PI, 10)
vector.pretty_print
# 0.0
# 0.3490658503988659
# 0.6981317007977318
# 1.0471975511965976
# 1.3962634015954636
# 1.7453292519943295
# 2.0943951023931953
# 2.443460952792061
# 2.792526803190927
# 3.141592653589793
10.times do |i|
vector[k, 0] = Math::sin(vector[k, 0])
end
vector.pretty_print
# 0.0
# 0.3420201433256687
# 0.6427876096865393
# 0.8660254037844386
# 0.984807753012208
# 0.984807753012208
# 0.8660254037844388
# 0.6427876096865395
# 0.3420201433256689
# 1.2246467991473532e-16
These results show a happy result, in that we are able to use NMatrix for simple tasks already. Of course, there are problems to be solved, e.g. slice by reference, inversion for all dtypes, eigenvalues. But it’s going somewhere, it’s growing.
I hope that by this time next year we’ll have a very mature linear algebra library (and much more).
]]>
