0
$\begingroup$

I have a list of integers dims and a list of SparseArrays bdrs (representing a chain complex $\mathbb{Z}^{d_0}\overset{\partial_1}{\leftarrow}\mathbb{Z}^{d_1}\overset{\partial_2}{\leftarrow}\mathbb{Z}^{d_2}\leftarrow\ldots$).

I wish to import/export such data from/to a file.txt (each line should be a matrix entry). For instance, the data $$\mathbb{Z}^{2}\xleftarrow{\left[\begin{smallmatrix}5&0&0\\0&6&7\end{smallmatrix}\right]} \mathbb{Z}^{3}\xleftarrow{\left[\begin{smallmatrix}0&8&0&0\\9&0&0&0\\0&0&-1&-2\end{smallmatrix}\right]}\mathbb{Z}^{4}$$ corresponds to a file

2 3 4

1 1 5
2 2 6
2 3 7

1 2 8
2 1 9
3 3 -1
3 4 -2

and $$ \mathbb{Z}^{7}\xleftarrow{0} \mathbb{Z}^{0}\xleftarrow{0} \mathbb{Z}^{5} \xleftarrow{\left[\begin{smallmatrix}0&0\\0&0\\0&0\\0&0\\0&0\\\end{smallmatrix}\right]} \mathbb{Z}^{2}\xleftarrow{\left[\begin{smallmatrix}0&0&0&15\\21&0&0&0\\\end{smallmatrix}\right]} \mathbb{Z}^{4}$$ corresponds to a file

7 0 5 2 4




1 4 14
2 1 21

My solution is:

chcxIn[file_]:= Module[{s,dims,bdrs={},k=1,i=1}, s=Import["/home/"<>file,"List"]; 
   s=Map[If[#=="",{},ImportString[#,"Table"][[1]]]&,s];   dims=s[[1]];   s=ParallelMap[If[#=={},{},#[[;;2]]->#[[3]]]&,s[[3;;]],{1}]; 
   Do[ If[s[[j]]=={}, AppendTo[bdrs,SparseArray[s[[i;;j-1]], dims[[k;;k+1]]]]; k+=1; i=j+1;],{j,Length@s}];   Return@{bdrs,dims}]; 
chcxOut[bdrs_,dims_,file_]:= Export["/home/"<>file, {StringReplace[ ToString@dims, {"{"->"","}"->"",","->""}],""}~Join~
   Flatten[Table[ArrayRules[b][[;; -2]]~Join~{""} /.({u_,v_}->w_):>(ToString[u]<>" "<>ToString[v]<>" "<>ToString[w]), {b,bdrs}],1]~Join~{""}, "List"]; 

However, this is hopelessly inefficient (time and memory wise). For 50MB of data, chcxOut needs 65 seconds and 700MB of RAM. This seems excessive. I wish to deal with files of size 10GB. Is there an efficient way of doing this?


Edit: With the help of @HenrikSchumacher, here is an improvement.

chcxIn[fileName_] := Module[{s=OpenRead[fileName],r(*read*), l(*line*), dims,bdrs={},k=0,e={}}, 
   dims=ImportString[Read[s,String],"Table"][[1]];  
   r:=Read[s,Record,NullRecords->True]; Monitor[If[s=!=$Failed, While[l=!=EndOfFile, l=r;   
   Which[l=="0", , l=="", k+=1; AppendTo[bdrs,SparseArray[e,dims[[k;;k+1]]]]; e={}, True, 
   l=ImportString[l,"Table"][[1]]; AppendTo[e,l[[1;;2]]->l[[3]]]]; ]], k];  Close[s]; {bdrs,dims}]; 
chcxOut[bdrs_,dims_,fileName_] := Module[{f=OpenWrite[fileName], w(*write*)}, 
   w=WriteString[f,ExportString[#,"Table"]]&; w@{dims}; WriteString[f,"\n\n"]; 
   Monitor[ Do[ If[Times@@dims[[k;;k+1]]==0 || bdrs[[k]]["Density"]==0, w@{0}, 
      w@Join[bdrs[[k]]["NonzeroPositions"],Partition[bdrs[[k]]["NonzeroValues"], 1], 2]];   
     WriteString[f,"\n\n"],{k,Length@bdrs}],k];     Close[f];]; 

For a 2MB file, the time and memory performance is: Export 0.1sec 4MB, Import 0.2sec 8MB, chcxOut 1.1sec 12MB, chcxIn 265sec 9MB. As we can see, importing from my custom format is still much slower. Hopefully, there is a better way to do this.

$\endgroup$
  • 1
    $\begingroup$ Use a sparse matrix format like MAT, MTX, or "HarwellBoeing". MAT is a binary format and should produce the smallest files. $\endgroup$ – Henrik Schumacher Jul 1 at 20:34
  • $\begingroup$ @HenrikSchumacher These files will also be read in Python, C++, SageMath, GAP, so I'd like to stick to this format. Also, my data is a sequence of matrices, not just one. $\endgroup$ – Leo Jul 1 at 21:35
  • 2
    $\begingroup$ Even more a reason to use a standard format. Otherwise you will have to reimplement import/export in all these languages. Btw.: MAT can handle sequences of matrices. $\endgroup$ – Henrik Schumacher Jul 1 at 21:40
  • $\begingroup$ And all aforementioned programs support this format? Hmm, give me a bit of time to try import/export using .mat. $\endgroup$ – Leo Jul 1 at 22:06
  • $\begingroup$ Yes, have a look. I am pretty sure that there must be APIs for Python (alone for migration reasons from MATLAB to SciPy) and C++. SageMath has MAT support through SciPy, too. So if you call GAP from SageMath, this should also be covered. $\endgroup$ – Henrik Schumacher Jul 2 at 6:52
3
$\begingroup$

Something like this should work.

dims = Prepend[(Dimensions /@ bndrs)[[All, 2]], Dimensions[bndrs[[1]]][[1]]];
file = OpenWrite["a.txt"];
WriteString[file, ExportString[{dims}, "Table"]];
Do[
  WriteString[file, "\n\n"];
  WriteString[
   file,
   ExportString[
    Join[A["NonzeroPositions"], Partition[A["NonzeroValues"], 1], 2],
    "Table"
    ]],
  {A, bndrs}];
Close[file]

The result is a human-readible file, so it is not really super compressed.

| improve this answer | |
$\endgroup$
  • $\begingroup$ Thank you, but this does not work when some of the matrices have height or width 0. $\endgroup$ – Leo Jul 29 at 18:33
  • 3
    $\begingroup$ Then you have to write an ecxeption for that case... $\endgroup$ – Henrik Schumacher Jul 29 at 18:36

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.