Extract the space group generators from Bilbao Crystallographic Server.

Fri Jul 15 05:11:36 EDT 2022

On Friday, July 15, 2022 at 11:08:55 AM UTC+8, avi.e... at gmail.com wrote:
> I guess Dan, that he may not be seeing what he is working on as a list of 
> lists of lists with each terminal sublist being of cardinality 4. Maybe 
> Zhao could look up what methods a list object has that allow you to place 
> additional items, such as a list of 4 numbers, at the beginning or end or in 
> middle and select a method that does what he wants. 
> 
> But I have to ask where exactly he wants to place this: "[0, 0, 0, 1]" 

Yes. This must be appended to each of the subsists to construct an affine transformation matrix, as described here [1-3].

[1] https://www.cryst.ehu.es/cgi-bin/cryst/programs/nph-doc-trmat
[2] https://www.gap-system.org/Manuals/pkg/crystcat/htm/CHAP001.htm#SECT002
[3] https://www.gap-system.org/Manuals/pkg/cryst/htm/CHAP002.htm

> Unfortunately, we got no before and after picture, just after. I will 
> explain what that means at the end but for now, I am making believe what you 
> show is the before and see what that would mean. 
> 
> The list seems to be a representation for a matrix that is 8 by 4 by 4. 
> Where do you place just the foursome above just once without breaking the 
> matrix? I mean you can extend it at the bottom by adding four of the above 
> as in 
> [ [0, 0, 0, 1], 
> [0, 0, 0, 1], 
> [0, 0, 0, 1], 
> [0, 0, 0, 1] ] 
> 
> Or you can take each internal four partner like the first one:
> [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0,1, 0], [0, 0, 0, 1]]
> And extend each one at the right end by adding a fifth: 
> 
> [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0,1, 0], [0, 0, 0, 1], [0, 0, 0, 1]] 
> 
> I can think of other transformations albeit I have no idea why this is being 
> done and what makes sense. 
> 
> So first he needs to be clear on where and what he is adding and then think 
> of a method. 
> 
> And BTW, this problem may also be looked at under a transformation. If 
> allowed to use some modules, it might make sense to feed the data structure 
> into something that returns a 3-D matrix directly and then use methods that 
> allow you to tack on parts of other matrices of various dimensions including 
> one. You can then flip it back into nested list format, if you wish. 
> 
> OK, as mentioned earlier, if this is the AFTER then I have to look and see 
> if it is obvious where the "[0, 0, 0, 1]" was placed to make this:
> [[[1, 0, 0, 0], [0, 1, 0, 0], [0, 0,1, 0], [0, 0, 0, 1]], 
> [[-1, 0, 0, 1], [0,-1, 0, 1/2], [0, 0, 1, 1/2], [0, 0, 0, 1]], 
> [[-1, 0, 0, 1/2], [0, 1, 0, 1/2], [0, 0,-1, 1], [0, 0, 0, 1]], 
> [[0, 0, 1, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1]], 
> [[0, 1, 0, 3/4], [1, 0, 0, 1/4], [0, 0, -1, 3/4], [0, 0, 0, 1]], 
> [[-1, 0, 0, 1/4], [0, -1, 0, 1/4], [0, 0, -1, 1/4], [0, 0, 0, 1]], 
> [[1, 0, 0, 0], [0, 1, 0, 1/2], [0, 0, 1, 1/2], [0, 0, 0, 1 ]], 
> [[1, 0, 0, 1/2], [0, 1, 0, 0], [0, 0, 1, 1/2], [0, 0, 0, 1]]]
> It looks like you are adding not once copy but eight copies with one each at 
> the end of the lists within the main list. 
> 
> That makes this easy enough so think about what it means to deal with lists 
> and NOT matrices. 
> 
> Your top list contains what I will call an a,b,c,d,e,f,g,h so if you wrote 
> code like 
> 
> Mylist = [ "a", "b", ..., "g", "h"] 
> 
> Then you can use a loop to iterate over those or perhaps a construct like 
> this: 
> 
> [ item for item in Mylist ] 
> 
> Wil gather them together and place them back in a list, which is useless but 
> it could be something applied to item like changing to upper case. In your 
> case, each item will be something like this: 
> 
> [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0,1, 0]] 
> 
> And you want to extend it by attaching this [0, 0, 0, 1] 
> 
> So how do you attach something to a list? Whatever that method is, call it 
> append and look it up and consider a line of code like: 
> 
> [ item.append(something) for item in Mylist ] 
> 
> If done right, the above list comprehension loops over one dimension of your 
> list version of a matrix and adds [0, 0, 0, 1] to the end and then 
> eventually put the a/b/d/..h components back together to look like what I 
> THINK you are asking. 
> 
> You can make some of the other possible changes using other tricks and 
> gimmicks like a nested comprehension but at some point, if you work well 
> with matrices, you may be better off converting your nested list into a 
> numpy matrix and make your addition another matrix and then use 
> numpy.concatenate, numpy.vstack and numpy.hstack with proper care with 
> multiple dimensions to specify what axis they will combine on. 
> 
> But doing the full (home)work for you is ...

Thank you for your analysis and comments.

Best,
Zhao

> -----Original Message----- 
> From: Python-list <python-list-bounces+avi.e.gross=gmai... at python.org> On 
> Behalf Of Dan Stromberg 
> Sent: Thursday, July 14, 2022 10:07 PM 
> To: hongy... at gmail.com <hongy... at gmail.com> 
> Cc: Python List <pytho... at python.org> 
> Subject: Re: Extract the space group generators from Bilbao Crystallographic 
> Server. 
> 
> It's good to include what you want to see as output, but it's important to 
> also include what you have as input. 
> 
> It's also good to include what you've coded so far. It's considered good 
> etiquette to give it a try yourself before asking the list. 
> 
> On Thu, Jul 14, 2022 at 1:03 PM hongy... at gmail.com <hongy... at gmail.com> 
> wrote:
> > I'm trying to extract the matrix data of "ITA-Setting F d -3 m [origin 1]" 
> > listed here [1], and then building an augmented matrix for each of 
> > them by adding the last row as "[0, 0, 0, 1]". In short, the following 
> > form is the ultimate-desired result: 
> > 
> > [[[1, 0, 0, 0], [0, 1, 0, 0], [0, 0,1, 0], [0, 0, 0, 1]], 
> > [[-1, 0, 0, 1], [0,-1, 0, 1/2], [0, 0, 1, 1/2], [0, 0, 0, 1]], 
> > [[-1, 0, 0, 1/2], [0, 1, 0, 1/2], [0, 0,-1, 1], [0, 0, 0, 1]], 
> > [[0, 0, 1, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1]], 
> > [[0, 1, 0, 3/4], [1, 0, 0, 1/4], [0, 0, -1, 3/4], [0, 0, 0, 1]], 
> > [[-1, 0, 0, 1/4], [0, -1, 0, 1/4], [0, 0, -1, 1/4], [0, 0, 0, 1]], 
> > [[1, 0, 0, 0], [0, 1, 0, 1/2], [0, 0, 1, 1/2], [0, 0, 0, 1 ]], 
> > [[1, 0, 0, 1/2], [0, 1, 0, 0], [0, 0, 1, 1/2], [0, 0, 0, 1]]] 
> > 
> > Any hints/tips/tricks for achieving this aim will be appreciated. 
> > 
> > [1] 
> > https://www.cryst.ehu.es/cgi-bin/cryst/programs//nph-trgen?gnum=227&wh
> > at=gen&trmat=a-1/8,b-1/8,c-1/8&unconv=F%20d%20-3%20m%20:1&from=ita 
> > 
> > Regards, 
> > Zhao 
> > -- 
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> >
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