@amoeba: A good thing that people don't really appreciate is that the dawn of ML caused a lot of trained coders (CS graduates) to start writing Statistics code and use best practices when developing statistical open-source software. This caused statisticians (and core science graduates in general) to up their coding game!

@whuber hence my use of the word dog twice in reference to them in previous comments

@usεr11852 On the other hand statisticians had been complaining vociferoulsly and literally for decades about the quality of the stats functionality in Excel (including the RNGs we've been discussing above) ... it took a good 30 years to get Microsoft to really take that seriously. I was showing people bad problems in the 80s... (a number of papers listed problems as well) and there are still some serious problems (though far fewer) now. Microsoft is filled with professional programmers.

It drives me crazy how many questions on Stack Exchange are titled "How to X?" instead of "How to X" or "How can I X?" or simply "X".

@Glen_b: I fully appreciate the point but I have little sympathy for people doing surgery using cutlery. It is a spreadsheet program; not a statistics/numerics program. MATLAB was out since 1984 and SPSS since 1963...

@Kodiologist That's interesting. I usually add "?" to the title "How to X" if I edit. Why do you think it's wrong?

@gung Re Lenna: I am not sure. I edited the post to add a link to where you can download color and grayscale version of the file, so no need to crop. In any case, I assume when you display the original file it displays fine? And after PCA reconstruction it's all black? It is strange because even the mean itself ("reconstruction" from 0 components) is already not black, it should have vertical grey stripes.

I added a link to another answer that gives R code for image pca compression, including how to display it. Perhaps it will help. If not, share your code and I will try too!

@amoeba Why, "How to X?" is not grammatical. Formally, I guess this could be explained by saying that "How to X" is a fragment, not a complete sentence, so it can't be a question. But no native speaker would say out loud "How to X?" even by accident, I think.

@Kodiologist It depends on what "X" stands for. If it is a verb phrase, like "generate a random number," then "How to X?" is perfectly grammatical as well as being a common rhetorical device--it's just not a complete sentence. I'm not aware of any requirement that question titles be complete sentences (although usually that's a good thing to do). What, then, do you mean by "X"?

I am more concerned with the form "I don't understand". I am happy to believe it's genuine, every time, but a statement is not a question, and it could often mean a problem at almost any level. I remember being asked to teach someone the very first steps in programming (this was Fortran, ~1976) and writing down X = 1 as an example. What is X? It's just like algebra... What is algebra? (The other person's mathematical education had stopped with arithmetic, supposedly.)

@whuber Does "How to generate a random number?" sound grammatical to you? If I heard someone say it, I would assume they were a non-native speaker, or had misspoke.

Although, in natural speech, "How do I…" and "How to…" could sound very similar.

@Kodiologist It depends on whether you are talking about normative or descriptive grammar. The normative grammarians eschew splitting infinitives, ending sentences with prepositions, and using anything other than a nominative case with forms of "is" (e.g., "it was her" is bad; "it was she" is correct)--but anybody who follows those rules would rightly be accused of stilted speech.

In that sense, "how to generate a random number?" is the sort of thing heard every day in speech and it's perfectly well understood. The omission of the subject ("I" or "one") is a rhetorical device. If you want to call it ungrammatical (in the normative sense) I would have to agree but I don't think that's going to be a useful criticism.

@whuber I am talking descriptively, and I can't say I've ever heard a native speaker say that.

@Kodiologist perhaps the most famous example of a split infinitive is "to boldly go where no man has gone before." historically, split infinitives were very common, then there was a grammarian counterrevolution which swung the pendulum the other way, but these kinds of pointless battles are part of why I decided to study math instead of Enlgihs

@GeneralAbrial I am trying to work out if that last word is a deliberate mistake :-)

@GeneralAbrial Let the record show that I have never been against split infinitives.

Can more native English speakers please comment on whether "How to generate a random number?" sounds like a grammatical or an ungrammatical title to them, and whether native speakers would actually say that when talking? @Silverfish @NickCox

I've used "How to" four times in paper titles in the Stata Journal stata-journal.com/sjsearch.html?choice=author&q=Cox e.g. How to repeat yourself without going mad Titles can be incomplete sentences. I'd call myself fussy about language, yet chose all those titles freely.

Thanks @Nick. I have to say I am relieved.

@amoeba Yes it sounds perfectly natural to me too.

@Kodiologist See above...

I'm originally from the UK. "How To Generate A Random Number." sounds completely fine to me.

Though one could never honestly call me fussy over language and grammar, so most everything is fine with me.

EXCEPT ALL CAPS.

+1

@amoeba Guys, I specifically said that "How to X" is a a perfectly good alternative to "How to X?".

There's nothing wrong with using a fragment as a title. The problem is using a fragment as a question (without appropriate context).