Package: average-minimum-distance
average-minimum-distance: geometry based crystal descriptorsPyPI project:https://pypi.org/project/average-minimum-distanceDocumentation:https://average-minimum-distance.readthedocs.ioSource code:https://github.com/dwiddo/average-minimum-distanceReferences(bib references at the bottom of this page):Average minimum distances of periodic point sets - foundational invariants for mapping periodic crystals. MATCH Communications in Mathematical and in Computer Chemistry, 87(3):529-559 (2022).https://doi.org/10.46793/match.87-3.529WResolving the data ambiguity for periodic crystals. Advances in Neural Information Processing Systems (NeurIPS 2022), v.35.https://openreview.net/forum?id=4wrB7Mo9_OQ.What's amd?The typical representation of a crystal as a motif and unit cell is ambiguous, because many choices of cell and motif define the same crystal. This package implements crystal descriptors designed to beisometry invariants, meaning they are always the same for any two crystals which are geometrically equivalent, independent of the unit cell and motif. The descriptors can be compared to give a distance which is 0 for identical crystals, and close to 0 for similar crystals (acontinuous metric).Thepointwise distance distribution(PDD) is a descriptor that records the environment of each atom in the unit cell by listing distances to neighbouring atoms. Two PDDs are compared using an optimal matching algorithm (Earth Mover's distance). Taking the average of a PDD gives a vector called theaverage minimum distance(AMD), which are simpler and faster to compare (by several orders of magnitude) but can still identify crystals with similar geometry. Both have a parameter k, the number of neighbouring atoms considered for each atom in the unit cell.Getting startedUse pip to install average-minimum-distance:pipinstallaverage-minimum-distanceThen import average-minimum-distance withimport amd.amd.compare()compares crystals in cif files by AMD or PDD descriptors:importamd# compare items in file.cif pairwise by AMD, k=100dm=amd.compare('file.cif',by='AMD',k=100)# compare items in file1.cif vs file2.cif by PDD, k=100dm=amd.compare('file1.cif','file2.cif',by='PDD',k=100)The distance matrix returned is apandas DataFrame.amd.compare()can also accept paths to folders or lists of paths.amd.compare()reads crystals from CIFs, calculates their descriptors and compares them, but these steps can be done separately if needed (see below).amd.compare()accepts several optional parameters, seethe documentation for a full list.CSD Python API only:amd.compare()interfaces withcsd-python-api. It can accept one or more CSD refcodes if passedrefcode_families=Trueor other file formats instead of cifs if passedreader='ccdc'.Choosing a value of kThe parameter k is the number of neighbouring atoms considered for each atom in a unit cell. Two crystals with the same unit molecule will have a small AMD/PDD distance for small enough k (e.g. k = 5), and a larger k means the geometry must be similar up to a larger radius for the distance to be small. The default foramd.compare()is k = 100, but if this is significantly less than the number of atoms in the unit molecule, it may be better to choose a larger value. It is usually not useful to choose k too large (many times larger than the number of atoms in a unit cell).Reading crystals, calculating AMDs/PDDsThis code reads a cif file and computes the list of AMDs (k = 100):importamdreader=amd.CifReader('file.cif')amds=[amd.AMD(crystal,100)forcrystalinreader]# # To calculate the PDDs:# pdds = [amd.PDD(crystal, 100) for crystal in reader]CifReader accepts some optional parameters, e.g. for removing Hydrogen and handling disorder,see here for a full list.CSD Python API only:CSD entries can be accessed via the CSD Python API withamd.CSDReader,see the documentation for details. CifReader can accept file formats other than .cif by passingreader='ccdc'.Comparing by AMD or PDDTo compare all crystals in one collection with each other, useamd.AMD_pdist()oramd.PDD_pdist(), which accept a list of AMDs/PDDs and return acondensed distance matrixlike SciPy'spdist(). Here's a full example of reading crystals from a .cif, calculating the descriptors and comparing them:importamd# read and calculate AMDs and PDDs (k = 100)crystals=list(amd.CifReader('path/to/file.cif'))amds=[amd.AMD(crystal,100)forcrystalinreader]pdds=[amd.PDD(crystal,100)forcrystalinreader]amd_cdm=amd.AMD_pdist(amds)# compare AMDs pairwisepdd_cdm=amd.PDD_pdist(pdds)# compare PDDs pairwise# Use squareform for a symmetric 2D distance matrixfromscipy.distance.spatialimportsquareformamd_dm=squareform(amd_cdm)Note: AMDs can be quickly computed from PDDs withamd.PDD_to_AMD().The default metric for comparison ischebyshev(L-infinity), though it can be changed to anything accepted by SciPy'spdist, e.g.euclidean.To compare crystals in one set with those in another set, useamd.AMD_cdistoramd.PDD_cdist:importamdamds1=[amd.AMD(c,100)forcinamd.CifReader('set1.cif')]amds2=[amd.AMD(c,100)forcinamd.CifReader('set2.cif')]# dm[i][j] = AMD distance between amds1[i] & amds2[j]dm=amd.AMD_cdist(amds)Example: AMD-based dendrogramThis example compares some crystals in a cif by AMD (k = 100) and plots a single linkage dendrogram:importamdimportmatplotlib.pyplotaspltfromscipy.clusterimporthierarchycrystals=list(amd.CifReader('crystals.cif'))names=[crystal.nameforcrystalincrystals]amds=[amd.AMD(crystal,100)forcrystalincrystals]cdm=amd.AMD_pdist(amds)Z=hierarchy.linkage(cdm,'single')dn=hierarchy.dendrogram(Z,labels=names)plt.show()Cite usUse the following bib references to cite AMD or PDD.Average minimum distances of periodic point sets - foundational invariants for mapping periodic crystals. MATCH Communications in Mathematical and in Computer Chemistry, 87(3), 529-559 (2022).https://doi.org/10.46793/match.87-3.529W.@article{widdowson2022average,title={Average Minimum Distances of periodic point sets - foundational invariants for mapping periodic crystals},author={Widdowson, Daniel and Mosca, Marco M and Pulido, Angeles and Kurlin, Vitaliy and Cooper, Andrew I},journal={MATCH Communications in Mathematical and in Computer Chemistry},doi={10.46793/match.87-3.529W},volume={87},number={3},pages={529-559},year={2022}}Resolving the data ambiguity for periodic crystals. Advances in Neural Information Processing Systems (NeurIPS 2022), v.35.https://openreview.net/forum?id=4wrB7Mo9_OQ.@inproceedings{widdowson2022resolving,title={Resolving the data ambiguity for periodic crystals},author={Widdowson, Daniel and Kurlin, Vitaliy},booktitle={Advances in Neural Information Processing Systems},year={2022},url={https://openreview.net/forum?id=4wrB7Mo9_OQ}}