# [R] R for linear algebra

John Fox j|ox @end|ng |rom mcm@@ter@c@
Sat Jun 25 19:34:01 CEST 2022

Dear Avi,

The purpose of the matlib package is to *teach* linear algebra and
related topics, not to replace or even compete with similar
functionality in base R.

Consider, e.g., the following example for matlib::Inverse(), which
computes matrix inverses by Gaussian elimination (I've elided most of
the steps):

> example("Inverse")

Invers>   A <- matrix(c(2, 1, -1,
Invers+                -3, -1, 2,
Invers+                -2,  1, 2), 3, 3, byrow=TRUE)

Invers>   Inverse(A)
[,1] [,2] [,3]
[1,]    4    3   -1
[2,]   -2   -2    1
[3,]    5    4   -1

Invers>   Inverse(A, verbose=TRUE, fractions=TRUE)

Initial matrix:
[,1] [,2] [,3] [,4] [,5] [,6]
[1,]  2    1   -1    1    0    0
[2,] -3   -1    2    0    1    0
[3,] -2    1    2    0    0    1

row: 1

exchange rows 1 and 2
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] -3   -1    2    0    1    0
[2,]  2    1   -1    1    0    0
[3,] -2    1    2    0    0    1

multiply row 1 by -1/3
[,1] [,2] [,3] [,4] [,5] [,6]
[1,]    1  1/3 -2/3    0 -1/3    0
[2,]    2    1   -1    1    0    0
[3,]   -2    1    2    0    0    1

multiply row 1 by 2 and subtract from row 2
[,1] [,2] [,3] [,4] [,5] [,6]
[1,]    1  1/3 -2/3    0 -1/3    0
[2,]    0  1/3  1/3    1  2/3    0
[3,]   -2    1    2    0    0    1

. . .

multiply row 3 by 2/5 and subtract from row 2
[,1] [,2] [,3] [,4] [,5] [,6]
[1,]  1    0    0    4    3   -1
[2,]  0    1    0   -2   -2    1
[3,]  0    0    1    5    4   -1
[,1] [,2] [,3]
[1,]    4    3   -1
[2,]   -2   -2    1
[3,]    5    4   -1

And similarly for the other functions in the package. Moreover, the
functions in the package are transparently programmed in R rather than
calling (usually more efficient but relatively inaccessible) compiled
code, e.g., in a BLAS.

Best,
John

On 2022-06-24 9:57 p.m., Avi Gross via R-help wrote:
> Yes, Michael, packages like matlib will extend the basic support within base R and I was amused at looking at what the package supported that I had not thought about in years!
> https://www.rdocumentation.org/packages/matlib/versions/0.9.5
> However, once you through in packages/modules/libraries and other add-ons, I suggest many languages share such gifts that then allow a serious amount of what we call linear Algebra to be done, albeit with some work.
> In some ways my review of Linear Algebra in recent years showed me that some things have changed from when I took it as part of a math degree in college but a big change has been in finding so many uses of it now that computers can do complicated things fast and even faster when using vectors and matrices as a way to organize and consolidate operations, sometimes even in parallel.
> Packages can be nice and especially if they gather together lots of related functions to teach a subject but anyone doing serious work should first make sure they know what is in the base.
> If your matrix is A, you could load a package like psych to get a trace of A:
> psych::tr(A)
> Or install  matlib with oodles of dependencies
>
> matlib::tr(A)
> Or without worrying if the user had installed and made available a library, use built-ins like diag() and sum():
> sum(diag(A))
> And what does  matlib::Det(A) gain you most of the time that det(A) does not tell you?
> A policy of this forum is to point out mostly what is part of standard R and obviously there can  be specialized functionality in packages, albeit some functions  in that package are unlikely to be taught in a first undergraduate Linear Algebra course. I note matlib is billed as also being for learning Multivariate Statistics, and that is fine, just perhaps a tad of overkill.
> If the users have a question about the base R functionality, they can ask about it here. But if they want to know why the cholesky function in matlib is not working for them, ...
>
>
>
> -----Original Message-----
> From: Michael L Friendly <friendly using yorku.ca>
> To: org (R-help using r-project.org) <r-help using r-project.org>
> Cc: Avi Gross <avigross using verizon.net>; abouelmakarim1962 using gmail.com>, <abouelmakarim1962 using gmail.com>
> Sent: Fri, Jun 24, 2022 9:12 pm
> Subject: Re: R for linear algebra
>
>   <!--#yiv2977149432 _filtered {} _filtered {}#yiv2977149432 #yiv2977149432 p.yiv2977149432MsoNormal, #yiv2977149432 li.yiv2977149432MsoNormal, #yiv2977149432 div.yiv2977149432MsoNormal {margin:0in;font-size:11.0pt;font-family:"Calibri", sans-serif;}#yiv2977149432 a:link, #yiv2977149432 span.yiv2977149432MsoHyperlink {color:#0563C1;text-decoration:underline;}#yiv2977149432 p.yiv2977149432MsoPlainText, #yiv2977149432 li.yiv2977149432MsoPlainText, #yiv2977149432 div.yiv2977149432MsoPlainText {margin:0in;font-size:11.0pt;font-family:"Calibri", sans-serif;}#yiv2977149432 span.yiv2977149432EmailStyle17 {font-family:"Calibri", sans-serif;color:windowtext;}#yiv2977149432 span.yiv2977149432PlainTextChar {font-family:"Calibri", sans-serif;}#yiv2977149432 .yiv2977149432MsoChpDefault {font-family:"Calibri", sans-serif;} _filtered {}#yiv2977149432 div.yiv2977149432WordSection1 {}-->Hello    The {matlib} package was developed for just this purpose – teaching and illustrating linear algebra concepts and techniques. In my old 6140 Multivariate Data Analysis course, I spent ~5-6 weeks on linear algebra.    CRAN: https://cran.r-project.org/web/packages/matlib/index.html GitHub: https://github.com/friendly/matlib 6140: http://euclid.psych.yorku.ca/www/psy6140/    There are quite a few vignettes    --- Michael Friendly     Email: friendly AT yorku DOT ca Professor, Psychology Dept York University      Voice: 416 736-2100 x66249 4700 Keele Street    Web:http://www.datavis.ca | @datavisFriendly Toronto, ONT  M3J 1P3 CANADA          Message: 11 Date: Fri, 24 Jun 2022 02:31:24 +0000 (UTC) From: Avi Gross <avigross using verizon.net> To: "abouelmakarim1962 using gmail.com" <abouelmakarim1962 using gmail.com>,                "r-help using r-project.org" <r-help using r-project.org> Subject: Re: [R] R for Linear Algebra Message-ID: <1658548037.4476854.1656037884865 using mail.yahoo.com> Content-Type: text/plain; charset="utf-8"    R is a language specially made to do many things with vectors and matrices and arrays with any reasonable number of dimensions and also has a host of functions that do things like make diagonal matrices, calculate determinants and multiply them in several ways,  invert them, get eigenvalues and much more if you look for packages. So the question becomes, what else do you feel you need for a Linear Algebra course that a simple web search would not have found like this: https://towardsdatascience.com/intro-to-r-linear-algebra-2a4de2506c93    https://towardsdatascience.com/intro-to-r-linear-algebra-2a4de2506c93#:~:text=R%20is%20especially%20handy%20with,solvers%20and%20dynamic%20indexing%20capabilities. Unless I missed something, yes, R is more easily able to be used to do such things than many other languages albeit just about any language tends to have access to a variety of functions that may do these things but are not built in.       -----Original Message----- From: AbouEl-Makarim Aboueissa <abouelmakarim1962 using gmail.com> To: R mailing list <r-help using r-project.org> Sent: Thu, Jun 23, 2022 10:39 am Subject: [R] R for Linear Algebra    Re: R for Linear Algebra          Dear All:                In my STA 591 topics in Biostatistics Fall 2022, I am planning to spend about 5 weeks on Linear Algebra.          I am wondering if someone has or knows the source for some R functions/programs written for linear algebra calculations.          Also if you know a book in Linear Algebra with R, will be a good help too.       Any help in this matter is highly appreciated in advance.
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