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Using_AMDs.rst

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Using AMDs

Calculation

The average minimum distance (AMD) of a crystal is given by :func:`amd.AMD() <amd.calculate.AMD>`. It accepts a crystal and an integer k, returning \text{AMD}_k as a 1D NumPy array.

If you have a .cif file, use :class:`amd.CifReader <amd.io.CifReader>` to read the crystals (see :doc:`Reading_cifs`). If csd-python-api is installed, :class:`amd.CSDReader <amd.io.CSDReader>` accepts CSD refcodes (see :doc:`Reading_from_the_CSD`).

# get AMDs of crystals in a .cif
crystals = list(amd.CifReader('file.cif'))
amds = [amd.AMD(crystal, 100) for crystal in crystals]

# get AMDs of crystals in DEBXIT family
csd_reader = amd.CSDReader('DEBXIT', families=True)
amds = [amd.AMD(crystal, 100) for crystal in csd_reader]

You can also give the coordinates of motif points and unit cell as a tuple of numpy arrays, in Cartesian form:

# AMD (k=10) of 3D cubic lattice
motif = np.array([[0,0,0]])
cell = np.identity(3)
cubic_lattice = (motif, cell)
cubic_amd = amd.AMD(cubic_lattice, 10)

The object returned by amd.AMD(crystal, k) is a vector with k elements.

Note: The AMD of a crystal can be calculated from its PDD with :func:`amd.PDD_to_AMD() <amd.calculate.PDD_to_AMD>`, which is faster if both are needed.

Comparison

AMDs are just vectors that can be compared with any metric, but the :mod:`amd.compare <amd.compare>` module has functions to compare collections of AMDs for you.

:func:`amd.AMD_pdist() <amd.compare.AMD_pdist>` and :func:`amd.AMD_cdist() <amd.compare.AMD_cdist>` are like SciPy's functions pdist and cdist. pdist takes a set and compares all elements pairwise, whereas cdist takes two sets and compares elements in one with the other. cdist returns a 2D distance matrix, but pdist returns a condensed distance matrix (see SciPy's pdist). The default metric for AMD comparisons is L-infinity (aka Chebyshev), but it can be changed to any metric accepted by SciPy's pdist/cdist.

# compare crystals in file1.cif with those in file2.cif by AMD, k=100
amds1 = [amd.AMD(crystal, 100) for crystal in amd.CifReader('file1.cif')]
amds2 = [amd.AMD(crystal, 100) for crystal in amd.CifReader('file2.cif')]
distance_matrix = amd.AMD_cdist(amds1, amds2)

# compare everything in file1.cif with each other (using L-infinity)
condensed_dm = amd.AMD_pdist(amds1)

Comparison options

:func:`amd.AMD_pdist() <amd.compare.AMD_pdist>` and :func:`amd.AMD_cdist() <amd.compare.AMD_cdist>` share the following optional arguments:

  • metric (default chebyshev) chooses the metric used for comparison, see SciPy's cdist/pdist for a list of accepted metrics.
  • low_memory (default False, requires metric='chebyshev') uses a slower algorithm with a smaller memory footprint, for larger inputs.