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Some linear algebra algorithms used for computing statistics or storing datasets deal with matrices on a column-by-column basis. As such, they can be referred to as being columnar. What would be the equivalent adverb for algorithms that work on a row-by-row basis? A similar question on Answers.com seems to indicate that no such adverb exists, and all I can think of is really not satisfying (to say the least):

  • Rowar (neologism) looks and sounds ugly

  • Rownar isn't much better

  • Linear could be misconstrued

  • Linar (pronounced lahy-ner) might be the least worst of them

Any better idea?

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    Given that matrices are used throughout mathematics (they're not restricted to statistics!), and that this is a question of English usage of adverbs to refer to a mathematical object, you may get more traction on either math.SE or english.SE. I'd suggest flagging the question and asking the mods to move it. – Glen_b Dec 23 '14 at 22:46
  • Sounds good. I'll give it a shot. – Ismael Ghalimi Dec 23 '14 at 22:48
  • I think belongs better on the non-learner site, or on Math.SE. Or at least my answer does – shadowtalker Dec 24 '14 at 14:44
  • I 100% agree with @ssdecontrol - I am mystified why this was taken to ELL rather than english.stackexchange or math.stackexchange - either of which would be a better fit. – Glen_b Dec 24 '14 at 22:21
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    I agree with @ssdecontrol. We might even consider moving it back to stats.SE. – Ismael Ghalimi Dec 25 '14 at 3:53
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WARNING: this is my opinion, but I consider myself educated on the topic. I was a straight-A Latin student for most of a decade, and geeking out over language and etymology is one of my hobbies.

The correct counterpart is tabular.

tabulatum, tabulati N N 2 2 N [XXXCX]
floor, story; layer, row; tier formed by the horizontal branches of a tree;

source: http://www.archives.nd.edu/cgi-bin/wordz.pl?english=row

But the word you actually want, an adverb that means "operates on columns," is in fact column-wise, and its row-oriented counterpart is row-wise. The words "columnar" and "tabular," at least the way I see them used, more properly refer to data than to an algorithm.

This is because the suffix -ar (as in familiar) is derived from the Latin -aris, in turn derived from -alis (see, e.g. the "origin" section here) which is where we get the suffix -al (as in familial). Both suffixes mean the same thing as their Latin roots: "of or related to." Consider the difference in connotation between familiar, familial, and family-wise. Note also that, of these three, family-wise is the only one that makes sense as an adverb rather than an adjective.

Data

  • tabular: arranged in rows
  • columnar: arranged in columns

Algorithms:

  • row-wise: operates on rows
  • column-wise: operates on columns.

Also, my thanks to Glen_b for reminding me about the term "row-wise."

  • Where did you get the information that "-aris" derived from "-alis"? Can you provide a reference? Can't they be just parallel suffixes that existed in the language and happened to have the same meaning? – Giorgio Dec 24 '14 at 9:06
  • @Giorgio edited. I was always under the impression that they were in fact parallel suffixes, until I went to write this answer – shadowtalker Dec 24 '14 at 14:56
  • Since the question specifically asked about adverbs, not adjectives, and "tabular" and "columnar" are adjectival (as you point out), the correct adverb could not be tabular, and the one being sought would be row-wise. Further, while you describe well the origin of tabular, if we're to avoid the genetic fallacy, we'd have to consider how the word tabular is presently understood in statistical applications (where it means "organized as a table" -- i.e. into rows and columns).[1][2][3] ... (ctd) – Glen_b Dec 24 '14 at 22:14
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    @Glen_b good point about the adverb. I made an edit to reflect that – shadowtalker Dec 24 '14 at 22:17
  • (ctd)... As such tabular doesn't work - neither its present meaning nor its status as an adjective would let it qualify. Refs: 1. definition 1 here; 2. definition 2 here; 3. definition 3 here. None of those references include a meaning like row-wise. Good knowledge of Latin (and no doubt yours is better than mine) doesn't always help us when seeking present meanings. While I disagree with the conclusion I think this answer is very interesting. – Glen_b Dec 24 '14 at 22:18
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I'd suggest "row-wise" or "by rows". As in "R stores a matrix in columnar fashion, while some other languages store them row-wise" (though I usually wouldn't usually use 'columnar' myself; I'd more likely say "R stores a matrix column-by-column" or something equally descriptive).

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    In that case, would you also use "column-wise" for consistency purposes, or would you stick to "columnar"? – Ismael Ghalimi Dec 23 '14 at 22:42
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    It depends on the context. If I was responding to someone else's use of columnar, I would say it as above (not all English adverbs are regular, so they don't necessarily correspond to each other). If I was writing it from scratch I'd change 'columnar'. – Glen_b Dec 23 '14 at 22:43

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