# Dot-product operators and strides for linear algebra **URL:** \ **Category:** Ruby\ **Created:** [February 17, 2006, 12:02am UTC](https://www.ruby-forum.com/t/dot-product-operators-and-strides-for-linear-algebra/69464 "2006-02-17T00:02:26Z")\ **Posts on this page:** 5\ **Page:** 1
**Author:** ![unknown](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/u/4bbf92/32.png) [@unknown](https://www.ruby-forum.com/u/unknown)\ **Post date:** [February 17, 2006, 12:02am UTC](https://www.ruby-forum.com/t/dot-product-operators-and-strides-for-linear-algebra/69464/1 "2006-02-17T00:02:26Z")
Hi, I am looking for the suitability of ruby for numerical applications. I am currently using MATLAB and Octave for this purpose (see [www.octave.org](http://www.octave.org), [www.mathworks.com](http://www.mathworks.com)). For vectors and matrices a single “_" or “/” operator is not sufficient to implement the necessary matrix/vector arithmetic in a convinient and consistent operator notation. In OOPS languages like C++ which support operator overloading, Matrix class libraries usually resort to a mixed functional/operator notation and assign the matrix product to the "_” and implement the dot-product by a function e.g as dot(A, B). ``` Besides product and division operators for matrix/vector operations ``` it is necessary to introduce a transpose and hermite operator which is of no interest in scalar arithmetic. In MATLAB the transpose of a matrix X is expressed as X.’ and the conjugate transpose is X’. ``` A simple and compact example of how this notation can be used is in ``` computing the 2-norm of a vector: x = 1:1:10 % Vector counting from 1 to 10 norm2 = sqrt( x_x’ ) % use matrix multiplication to compute the squared sum norm2 = sqrt(sum(x ._ x)) % use elementwise multiplication norm2 = sqrt(sum(x .^ 2)) % square element by element ``` In standart programming languages with an OOPS library this might ``` look like: x = [1 2 3 4 … 10] ; norm2 = sqrt( x\*x.transpose()) ; // use matrix multiplication norm2 = sqrt(sum(dot(x, x))) ; // use dot-product auxiliary function ``` While for such a simple example, there is not so much difference in ``` readability, but for real world examples, the matrix operator notation makes the code more compact and readable. Conceptionally it lacks consistency, if the maybe more often used dot-product is implemented as function and the matrix product as operator. My assumption is that is might be possible to extend ruby with reasonable effort to add the additional “.\*” “./” and “.^2” binary operators and the transpose / conjugate transpose operators. For the standard ruby this function would just do the same as their scalar conterparts, however, when implementing a matrix class these additional operators can become alive and be used to implement the elementwise dot operations. ``` Aside from the operators a second concept is quite essential for a ``` scripting matrix and vector class. This requires a new data-type to express strides. Suppose one wants to access only every second element of a vector or reverse a vector, then usually this has to be done in a loop. Since looping over elements is prohibitively expensive in a scripting language, the preferred solution for doing such common indexing operation is to use strides. For ruby, it would be possible to define a stride class, which stores the index of the first, last and stepsize. Reversing a vector might look like: ``` vector x=stride(1, 3) // use a stride to construct a new vector ``` from 1 to 3. reverse\_x = x( stride(3, 1, -1) ) ``` More elegantly, if strides are natively supported by the scripting ``` language, then the example could be implemented as ``` x = 1:3 ; reverse_x = x(3:-1:1) ; Has anybody implemented a patch to include dot-operators or index ``` strides to ruby? Are there any plans / discussion to include MATLAB/Octave-alike features in the future? ``` Regards, よろしくおねがいします Roderick Koehle References: * http://en.wikipedia.org/wiki/Matlab * http://en.wikipedia.org/wiki/IDL_programming_language ``` ---
**Author:** ![unknown](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/u/4bbf92/32.png) [@unknown](https://www.ruby-forum.com/u/unknown)\ **Post date:** [February 17, 2006, 12:20am UTC](https://www.ruby-forum.com/t/dot-product-operators-and-strides-for-linear-algebra/69464/2 "2006-02-17T00:20:41Z")
On Feb 16, 2006, at 5:59 PM, [removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid) wrote: > My assumption is that is might be possible to extend ruby with > reasonable effort to add the additional “.\*” “./” and “.^2” binary > operators and the transpose / conjugate transpose operators. For > the standard ruby this function would just do the same as their > scalar conterparts, however, when implementing a matrix class > these additional operators can become alive and be used to > implement the elementwise dot operations. That’s an especially poor choice of operator name 😉 a \* b == a.\*(b) You could add a method called ._, but you couldn’t call it in the normal manner, you’d have to say: a.send("._", b) which I don’t think is what you were looking for. As for “strides”, have you seen ranges? 0…9 # 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 1…10 # 1, 2, 3, 4, 5, 6, 7, 8, 9 As for having an alternative step, you can use #step, 1.step(10, 2) { |x| p x } 1 3 5 7 9 To turn a step into a range-like object (instead of a method) use an enumerator: require ‘enumerator’ zero\_to\_twentyfive\_by\_five = 0.to\_enum(:step, 25, 5) zero\_to\_twentyfive\_by\_five.each { |x| p x } 0 5 10 15 20 25 In 1.9 you don’t even need to use the to\_enum, ie you could simply write zero\_to\_twentyfive\_by\_five = 0.step(25,5) ---
**Author:** ![unknown](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/u/4bbf92/32.png) [@unknown](https://www.ruby-forum.com/u/unknown)\ **Post date:** [February 17, 2006, 5:11pm UTC](https://www.ruby-forum.com/t/dot-product-operators-and-strides-for-linear-algebra/69464/3 "2006-02-17T17:11:38Z")
On Feb 17, 2006, at 3:37 AM, [removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid) [removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid) wrote: > The steps method, constructs an array immediately, this is not > necessary for strides. Not true, step does not construct an array. ---
**Author:** ![unknown](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/u/4bbf92/32.png) [@unknown](https://www.ruby-forum.com/u/unknown)\ **Post date:** [February 17, 2006, 9:40am UTC](https://www.ruby-forum.com/t/dot-product-operators-and-strides-for-linear-algebra/69464/4 "2006-02-17T09:40:50Z")
1. Operator/Method Abiguity: Clearly, this is a problem. I don’t think “.\*” or the like operators would hurt too much though. It would be necessary to forbid “class.\*method” style of methods and therefore a major design issue. 2. Ranges: This is a good suggestion, but how to extend it to possibly n-dimensional matrices? I am not an expert on the implementation of ranges, by I suspect that ranges are executed by the interpreter. Strides can be executed by the matrix library and implemented more efficiently in C. The steps method, constructs an array immediately, this is not necessary for strides. If a stride is used for indexing it is only necessary to hand over the start, step and end index. Only if a stride is assigned to a vector, then it is necessary to convert it to an array. Regards, Roderick Logan C. [removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid) schrieb: On Feb 16, 2006, at 5:59 PM, wrote: > My assumption is that is might be possible to extend ruby with > reasonable effort to add the additional “.\*” “./” and “.^2” binary > operators and the transpose / conjugate transpose operators. For > the standard ruby this function would just do the same as their > scalar conterparts, however, when implementing a matrix class > these additional operators can become alive and be used to > implement the elementwise dot operations. That’s an especially poor choice of operator name 😉 a \* b == a.\*(b) You could add a method called ._, but you couldn’t call it in the normal manner, you’d have to say: a.send("._", b) which I don’t think is what you were looking for. As for “strides”, have you seen ranges? 0…9 # 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 1…10 # 1, 2, 3, 4, 5, 6, 7, 8, 9 As for having an alternative step, you can use #step, 1.step(10, 2) { |x| p x } 1 3 5 7 9 To turn a step into a range-like object (instead of a method) use an enumerator: require ‘enumerator’ zero\_to\_twentyfive\_by\_five = 0.to\_enum(:step, 25, 5) zero\_to\_twentyfive\_by\_five.each { |x| p x } 0 5 10 15 20 25 In 1.9 you don’t even need to use the to\_enum, ie you could simply write zero\_to\_twentyfive\_by\_five = 0.step(25,5) ---
**Author:** ![unknown](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/u/4bbf92/32.png) [@unknown](https://www.ruby-forum.com/u/unknown)\ **Post date:** [February 18, 2006, 5:31pm UTC](https://www.ruby-forum.com/t/dot-product-operators-and-strides-for-linear-algebra/69464/5 "2006-02-18T17:31:42Z")
I guess a lot depends on what your performance requirements are. Octave interfaces to LAPACK and the BLAS for its core numerical operations, whereas Ruby currently uses either interpreted Ruby code or the built-in primitives implemented in C. If your LAPACK and BLAS are backed by the Automatically Tuned Linear Algebra Subroutines (ATLAS) you can do numerical linear algebra on decent-sized problems at near peak hardware speeds. From reading the Pickaxe book, it doesn’t look like it would be too difficult to interface Ruby to LAPACK and the BLAS. There is also a primitive Ruby package on RAA that interfaces with the R language math library. I got the Ruby/Rmath package working a few weeks ago but had to drop the project to get some paid work done :). If anybody on the list wants to pick this up, let me know and I’ll get you going on it. I don’t know enough Ruby to even begin to design a math library. I have played with the combination of Matrix, Mathn, Rational and Complex and for small problems, they work well. My guess is that they would be hopelessly slow for larger problems. I personally use R for all of my numerical work and have no plans to move to another language – R is designed for that and has a collection of library packages that do 98 percent of what I need. By the way, what platform are you on? A lot of the GPL magic for numerical computation works best on Linux and Solaris and second-best on Windows and Macs. I’m on Gentoo Linux and I’ve got the works – R, Octave, LAPACK and BLAS, both with the Atlas high-speed linear algebra backing, TeXmacs, LyX, (wx)Maxima, Axiom, Ruby, Rails, etc. removed\_email\_address@domain.invalid wrote: > ``` > norm2 = sqrt( x*x' ) % use matrix multiplication to compute the squared sum > > ``` > > My assumption is that is might be possible to extend ruby with reasonable effort to add the additional “.\*” “./” and “.^2” binary operators and the transpose / conjugate transpose operators. For the standard ruby this function would just do the same as their scalar conterparts, however, when implementing a matrix class these additional operators can become alive and be used to implement the elementwise dot operations. > x = 1:3 ; > References: > \* [http://en.wikipedia.org/wiki/Matlab](http://en.wikipedia.org/wiki/Matlab) > \* [IDL (programming language) - Wikipedia](http://en.wikipedia.org/wiki/IDL_programming_language) > > * * * > > Telefonieren Sie ohne weitere Kosten mit Ihren Freunden von PC zu PC! > Jetzt Yahoo! Messenger installieren! – M. Edward (Ed) Borasky > **[世界杯竞猜彩票-世界杯官网竞猜（集团）有限公司](http://www.linuxcapacityplanning.com/)** > > 世界杯竞猜彩票一直以来遵守商业道德，世界杯官网竞猜坚持诚信为本，保证诚实经营。世界杯竞猜彩票先后成为安徽省电子商务协会理事单位、安徽省网商协会会员单位、合肥市电子商务协会理事单位、合肥市服务外包行业协会会员单位、安徽省云计算产业促进会会员单位。世界杯官网竞猜一直保持良好的技术及服务态度，更好地为客户服务。