# Source code for MDAnalysis.analysis.density

# -*- Mode: python; tab-width: 4; indent-tabs-mode:nil; coding:utf-8 -*-
# vim: tabstop=4 expandtab shiftwidth=4 softtabstop=4
#
# MDAnalysis --- https://www.mdanalysis.org
# Copyright (c) 2006-2017 The MDAnalysis Development Team and contributors
# (see the file AUTHORS for the full list of names)
#
# Released under the GNU Public Licence, v2 or any higher version
#
#
# R. J. Gowers, M. Linke, J. Barnoud, T. J. E. Reddy, M. N. Melo, S. L. Seyler,
# D. L. Dotson, J. Domanski, S. Buchoux, I. M. Kenney, and O. Beckstein.
# MDAnalysis: A Python package for the rapid analysis of molecular dynamics
# simulations. In S. Benthall and S. Rostrup editors, Proceedings of the 15th
# Python in Science Conference, pages 102-109, Austin, TX, 2016. SciPy.
# doi: 10.25080/majora-629e541a-00e
#
# N. Michaud-Agrawal, E. J. Denning, T. B. Woolf, and O. Beckstein.
# MDAnalysis: A Toolkit for the Analysis of Molecular Dynamics Simulations.
# J. Comput. Chem. 32 (2011), 2319--2327, doi:10.1002/jcc.21787
#

# MDAnalysis -- density analysis
# Copyright (c) 2007-2011 Oliver Beckstein <[email protected]>
# (based on code from Hop --- a framework to analyze solvation dynamics from MD simulations)

r"""Generating densities from trajectories --- :mod:MDAnalysis.analysis.density
=============================================================================

:Author: Oliver Beckstein
:Year: 2011

The module provides classes and functions to generate and represent
volumetric data, in particular densities.

.. versionchanged:: 2.0.0
Deprecated :func:density_from_Universe, :func:density_from_PDB, and
:func:Bfactor2RMSF have now been removed.

Generating a density from a MD trajectory
-----------------------------------------

A common use case is to analyze the solvent density around a protein of
interest. The density is calculated with :class:DensityAnalysis in the
fixed coordinate system of the simulation unit cell. It is therefore necessary
to orient and fix the protein with respect to the box coordinate system. In
practice this means centering and superimposing the protein, frame by frame, on
a reference structure and translating and rotating all other components of the
simulation with the protein. In this way, the solvent will appear in the
reference frame of the protein.

An input trajectory must

1. have been centered on the protein of interest;
2. have all molecules made whole that have been broken across periodic
boundaries [#pbc]_;
3. have the solvent molecules remapped so that they are closest to the
solute (this is important when using triclinic unit cells such as
a dodecahedron or a truncated octahedron) [#pbc]_.
4. have a fixed frame of reference; for instance, by superimposing a protein
on a reference structure so that one can study the solvent density around
it [#fit]_.

To generate the density of water molecules around a protein (assuming that the
trajectory is already appropriately treated for periodic boundary artifacts and
is suitably superimposed to provide a fixed reference frame) [#testraj]_ ::

from MDAnalysis.analysis.density import DensityAnalysis
u = Universe(TPR, XTC)
ow = u.select_atoms("name OW")
D = DensityAnalysis(ow, delta=1.0)
D.run()
D.results.density.convert_density('TIP4P')
D.results.density.export("water.dx", type="double")

The positions of all water oxygens (the :class:AtomGroup ow) are
histogrammed on a grid with spacing *delta* = 1 Å. Initially the density is
measured in :math:\text{Å}^{-3}. With the :meth:Density.convert_density
method, the units of measurement are changed. In the example we are now
measuring the density relative to the literature value of the TIP4P water model
at ambient conditions (see the values in :data:MDAnalysis.units.water for
details). Finally, the density is written as an OpenDX_ compatible file that
can be read in VMD_, Chimera_, or PyMOL_.

The :class:Density object is accessible as the
:attr:DensityAnalysis.results.density attribute.  In particular, the data
for the density is stored as a NumPy array in :attr:Density.grid, which can
be processed in any manner.

Creating densities
------------------

The :class:DensityAnalysis class generates a :class:Density from an
atomgroup.

.. autoclass:: DensityAnalysis
:members:
:inherited-members: run

.. attribute:: results.density

After the analysis (see the :meth:~DensityAnalysis.run method), the
resulting density is stored in the :attr:results.density attribute as
a :class:Density instance. Note: this replaces the now deprecated
:attr:density attribute.

.. automethod:: _set_user_grid

Density object
--------------

The main output of the density creation functions is a :class:Density
instance, which is derived from a :class:gridData.core.Grid. A
:class:Density is essentially a 3D array with origin and lengths.

.. See Also:: :mod:gridData

.. autoclass:: Density
:members:
:inherited-members:
:show-inheritance:

.. rubric:: Footnotes

.. [#pbc] Making molecules whole can be accomplished with the
:meth:MDAnalysis.core.groups.AtomGroup.wrap of
:attr:Universe.atoms (use compound="fragments").  or the
PBC-wrapping transformations in
:mod:MDAnalysis.transformations.wrap.

.. [#fit] Superposition can be performed with
:class:MDAnalysis.analysis.align.AlignTraj or the fitting
transformations in :mod:MDAnalysis.transformations.fit.

.. [#testraj] Note that the trajectory in the example (XTC) is *not*
properly made whole and fitted to a reference structure;
these steps were omitted to clearly show the steps necessary
for the actual density calculation.

.. -----

.. _OpenDX: http://www.opendx.org/
.. _VMD:   http://www.ks.uiuc.edu/Research/vmd/
.. _Chimera: https://www.cgl.ucsf.edu/chimera/
.. _PyMOL: http://www.pymol.org/
.. _Gromacs: http://www.gromacs.org
.. _gmx trjconv: http://manual.gromacs.org/programs/gmx-trjconv.html

"""
import numpy as np
import sys
import os
import os.path
import errno
import warnings

from gridData import Grid

import MDAnalysis
from MDAnalysis.core import groups
from MDAnalysis.lib.util import (fixedwidth_bins, iterable, asiterable,
deprecate,)
from MDAnalysis.lib import NeighborSearch as NS
from MDAnalysis import NoDataError, MissingDataWarning
from .. import units
from ..lib import distances
from MDAnalysis.lib.log import ProgressBar

from .base import AnalysisBase

import logging

logger = logging.getLogger("MDAnalysis.analysis.density")

[docs]class DensityAnalysis(AnalysisBase):
r"""Volumetric density analysis.

The trajectory is read, frame by frame, and the atoms in atomgroup are
histogrammed on a 3D grid with spacing delta.

Parameters
----------
atomgroup : AtomGroup or UpdatingAtomGroup
Group of atoms (such as all the water oxygen atoms) being analyzed.
This can be an :class:~MDAnalysis.core.groups.UpdatingAtomGroup for
selections that change every time step.
delta : float (optional)
Bin size for the density grid in ångström (same in x,y,z).
Increase histogram dimensions by padding (on top of initial box
size) in ångström. Padding is ignored when setting a user defined
grid.
gridcenter : numpy ndarray, float32 (optional)
3 element numpy array detailing the x, y and z coordinates of the
center of a user defined grid box in ångström.
xdim : float (optional)
User defined x dimension box edge in ångström.
ydim : float (optional)
User defined y dimension box edge in ångström.
zdim : float (optional)
User defined z dimension box edge in ångström.

Attributes
----------
results.density : :class:Density
A :class:Density instance containing a physical density of units
:math:Angstrom^{-3}.

density : :class:Density
Alias to the :attr:results.density.

.. deprecated:: 2.0.0
Will be removed in MDAnalysis 3.0.0. Please use
:attr:results.density instead.

Raises
------
ValueError
if AtomGroup is empty and no user defined grid is provided, or
if the user defined grid is not or incorrectly provided
UserWarning
if AtomGroup is empty and a user defined grid is provided

--------
pmda.density.DensityAnalysis for a parallel version

Notes
-----
If the gridcenter and x/y/zdim arguments are not provided,
:class:DensityAnalysis will attempt to automatically generate
a gridbox from the atoms in 'atomgroup' (See Examples).

Normal :class:AtomGroup instances represent a static selection of
atoms. If you want *dynamically changing selections* (such as "name OW and
around 4.0 (protein and not name H*)", i.e., the water oxygen atoms that
are within 4 Å of the protein heavy atoms) then create an
:class:~MDAnalysis.core.groups.UpdatingAtomGroup (see Examples).

:class:DensityAnalysis will fail when the :class:AtomGroup instance
does not contain any selection of atoms, even when updating is set to
True. In such a situation, user defined box limits can be provided to
generate a Density. Although, it remains the user's responsibility
to ensure that the provided grid limits encompass atoms to be selected
on all trajectory frames.

Examples
--------
A common use case is to analyze the solvent density around a protein of
interest. The density is calculated with :class:DensityAnalysis in the
fixed coordinate system of the simulation unit cell. It is therefore
necessary to orient and fix the protein with respect to the box coordinate
system. In practice this means centering and superimposing the protein,
frame by frame, on a reference structure and translating and rotating all
other components of the simulation with the protein. In this way, the
solvent will appear in the reference frame of the protein.

An input trajectory must

1. have been centered on the protein of interest;
2. have all molecules made whole that have been broken across periodic
boundaries [#pbc]_;
3. have the solvent molecules remapped so that they are closest to the
solute (this is important when using triclinic unit cells such as
a dodecahedron or a truncated octahedron) [#pbc]_;
4. have a fixed frame of reference; for instance, by superimposing a
protein on a reference structure so that one can study the solvent
density around it [#fit]_.

.. rubric:: Generate the density

To generate the density of water molecules around a protein (assuming that
the trajectory is already appropriately treated for periodic boundary
artifacts and is suitably superimposed to provide a fixed reference frame)
[#testraj]_, first  create the :class:DensityAnalysis object by
supplying an AtomGroup, then use  the :meth:run method::

from MDAnalysis.analysis import density
u = Universe(TPR, XTC)
ow = u.select_atoms("name OW")
D = density.DensityAnalysis(ow, delta=1.0)
D.run()
D.results.density.convert_density('TIP4P')

The positions of all water oxygens are histogrammed on a grid with spacing
*delta* = 1 Å and stored as a :class:Density object in the attribute
:attr:DensityAnalysis.results.density.

.. rubric:: Working with a density

A :class:Density contains a large number of methods and attributes that
are listed in the documentation. Here we use the
:meth:Density.convert_density to convert the density from inverse cubic
ångström to a density relative to the bulk density of TIP4P water at
standard conditions. (MDAnalysis stores a number of literature values in
:data:MDAnalysis.units.water.)

One can directly access the density as a 3D NumPy array through
:attr:Density.grid.

By default, the :class:Density object returned contains a physical
density in units of Å\ :sup:-3. If you are interested in recovering the
underlying **probability density**, simply divide by the sum::

probability_density = D.results.density.grid / D.results.density.grid.sum()

Similarly, if you would like to recover a grid containing a **histogram of
atom counts**, simply multiply by the volume dV of each bin (or voxel);
in this case you need to ensure that the physical density is measured in
Å\ :sup:-3 by converting it::

import numpy as np

# ensure that the density is A^{-3}
D.results.density.convert_density("A^{-3}")

dV = np.prod(D.results.density.delta)
atom_count_histogram = D.results.density.grid * dV

.. rubric:: Writing the density to a file

A density can be exported to different formats
<https://www.mdanalysis.org/GridDataFormats/gridData/formats.html>_ with
:meth:Density.export (thanks to the fact that :class:Density is a
subclass :class:gridData.core.Grid, which provides the functionality).
For example, to write a DX file
<https://www.mdanalysis.org/GridDataFormats/gridData/basic.html#writing-out-data>_
water.dx that can be read with VMD, PyMOL, or Chimera::

D.results.density.export("water.dx", type="double")

.. rubric:: Example: Water density in the whole simulation

Basic use for creating a water density (just using the water oxygen
atoms "OW")::

D = DensityAnalysis(universe.select_atoms('name OW')).run()

.. rubric:: Example: Water in a binding site (updating selection)

If you are only interested in water within a certain region, e.g., within
a vicinity around a binding site, you can use a selection that updates
every step by using an :class:~MDAnalysis.core.groups.UpdatingAtomGroup::

near_waters = universe.select_atoms('name OW and around 5 (resid 156 157 305)',
updating=True)
D_site = DensityAnalysis(near_waters).run()

.. rubric:: Example: Small region around a ligand (manual box selection)

If you are interested in explicitly setting a grid box of a given edge size
and origin, you can use the gridcenter and xdim/ydim/zdim
arguments.  For example to plot the density of waters within 5 Å of a
ligand (in this case the ligand has been assigned the residue name "LIG")
in a cubic grid with 20 Å edges which is centered on the center of mass
(COM) of the ligand::

# Create a selection based on the ligand
ligand_selection = universe.select_atoms("resname LIG")

# Extract the COM of the ligand
ligand_COM = ligand_selection.center_of_mass()

# Create a density of waters on a cubic grid centered on the ligand COM
# In this case, we update the atom selection as shown above.
ligand_waters = universe.select_atoms('name OW and around 5 resname LIG',
updating=True)
D_water = DensityAnalysis(ligand_waters,
delta=1.0,
gridcenter=ligand_COM,
xdim=20, ydim=20, zdim=20)

(It should be noted that the padding keyword is not used when a user
defined grid is assigned).

.. versionchanged:: 2.0.0
:func:_set_user_grid is now a method of :class:DensityAnalysis.
:class:Density results are now stored in a
:class:MDAnalysis.analysis.base.Results instance.
"""

def __init__(self, atomgroup, delta=1.0,
gridcenter=None,
xdim=None, ydim=None, zdim=None):
u = atomgroup.universe
super(DensityAnalysis, self).__init__(u.trajectory)
self._atomgroup = atomgroup
self._delta = delta
self._gridcenter = gridcenter
self._xdim = xdim
self._ydim = ydim
self._zdim = zdim

def _prepare(self):
coord = self._atomgroup.positions
if (self._gridcenter is not None or
any([self._xdim, self._ydim, self._zdim])):
# Issue 2372: padding is ignored, defaults to 2.0 therefore warn
f"is not used in user defined grids.")
warnings.warn(msg)
logger.warning(msg)
# Generate a copy of smin/smax from coords to later check if the
# defined box might be too small for the selection
try:
smin = np.min(coord, axis=0)
smax = np.max(coord, axis=0)
except ValueError as err:
msg = ("No atoms in AtomGroup at input time frame. "
"This may be intended; please ensure that "
"your grid selection covers the atomic "
"positions you wish to capture.")
warnings.warn(msg)
logger.warning(msg)
smin = self._gridcenter     #assigns limits to be later -
smax = self._gridcenter     #overwritten by _set_user_grid
# Overwrite smin/smax with user defined values
smin, smax = self._set_user_grid(self._gridcenter, self._xdim,
self._ydim, self._zdim, smin,
smax)
else:
# Make the box bigger to avoid as much as possible 'outlier'. This
# is important if the sites are defined at a high density: in this
# case the bulk regions don't have to be close to 1 * n0 but can
# be less. It's much more difficult to deal with outliers.  The
# ideal solution would use images: implement 'looking across the
# periodic boundaries' but that gets complicated when the box
# rotates due to RMS fitting.
try:
smin = np.min(coord, axis=0) - self._padding
smax = np.max(coord, axis=0) + self._padding
except ValueError as err:
errmsg = ("No atoms in AtomGroup at input time frame. "
"Grid for density could not be automatically"
" generated. If this is expected, a user"
" defined grid will need to be "
raise ValueError(errmsg) from err
BINS = fixedwidth_bins(self._delta, smin, smax)
arange = np.transpose(np.vstack((BINS['min'], BINS['max'])))
bins = BINS['Nbins']
# create empty grid with the right dimensions (and get the edges)
grid, edges = np.histogramdd(np.zeros((1, 3)), bins=bins,
range=arange, normed=False)
grid *= 0.0
self._grid = grid
self._edges = edges
self._arange = arange
self._bins = bins

def _single_frame(self):
h, _ = np.histogramdd(self._atomgroup.positions,
bins=self._bins, range=self._arange,
normed=False)
# reduce (proposed change #2542 to match the parallel version in pmda.density)
# return self._reduce(self._grid, h)
#
# serial code can simply do
self._grid += h

def _conclude(self):
# average:
self._grid /= float(self.n_frames)
density = Density(grid=self._grid, edges=self._edges,
units={'length': "Angstrom"},
parameters={'isDensity': False})
density.make_density()
self.results.density = density

@property
def density(self):
wmsg = ("The density attribute was deprecated in MDAnalysis 2.0.0 "
"and will be removed in MDAnalysis 3.0.0. Please use "
"results.density instead")
warnings.warn(wmsg, DeprecationWarning)
return self.results.density

[docs]    @staticmethod
def _set_user_grid(gridcenter, xdim, ydim, zdim, smin, smax):
"""Helper function to set the grid dimensions to user defined values

Parameters
----------
gridcenter : numpy ndarray, float32
3 element ndarray containing the x, y and z coordinates of the
grid box center
xdim : float
Box edge length in the x dimension
ydim : float
Box edge length in the y dimension
zdim : float
Box edge length in the y dimension
smin : numpy ndarray, float32
Minimum x,y,z coordinates for the input selection
smax : numpy ndarray, float32
Maximum x,y,z coordinates for the input selection

Returns
-------
umin : numpy ndarray, float32
Minimum x,y,z coordinates of the user defined grid
umax : numpy ndarray, float32
Maximum x,y,z coordinates of the user defined grid

.. versionchanged:: 2.0.0
Now a staticmethod of :class:DensityAnalysis.
"""
# Check user inputs
if any(x is None for x in [gridcenter, xdim, ydim, zdim]):
errmsg = ("Gridcenter or grid dimensions are not provided")
raise ValueError(errmsg)
try:
gridcenter = np.asarray(gridcenter, dtype=np.float32).reshape(3,)
except ValueError as err:
raise ValueError("Gridcenter must be a 3D coordinate") from err
try:
xyzdim = np.array([xdim, ydim, zdim], dtype=np.float32)
except ValueError as err:
raise ValueError("xdim, ydim, and zdim must be numbers") from err
if any(np.isnan(gridcenter)) or any(np.isnan(xyzdim)):
raise ValueError("Gridcenter or grid dimensions have NaN element")

# Set min/max by shifting by half the edge length of each dimension
umin = gridcenter - xyzdim/2
umax = gridcenter + xyzdim/2

# Here we test if coords of selection fall outside of the defined grid
# if this happens, we warn users they may want to resize their grids
if any(smin < umin) or any(smax > umax):
msg = ("Atom selection does not fit grid --- "
"you may want to define a larger box")
warnings.warn(msg)
logger.warning(msg)
return umin, umax

# _reduce is not strictly necessary for the serial version but is necessary for
# pmda-style parallelism (see #2542)
# @staticmethod
# def _reduce(res, result_single_frame):
#     """'accumulate' action for a time series
#
#     If res is a numpy array, the result_single_frame is added to it
#     element-wise. If res and result_single_frame are lists then
#     result_single_frame is appended to res.
#     """
#     if isinstance(res, list) and len(res) == 0:
#         res = result_single_frame
#     else:
#         res += result_single_frame
#     return res

[docs]class Density(Grid):
r"""Class representing a density on a regular cartesian grid.

Parameters
----------
grid : array_like
histogram or density, typically a :class:numpy.ndarray
edges : list
list of arrays, the lower and upper bin edges along the axes
parameters : dict
dictionary of class parameters; saved with
:meth:Density.save. The following keys are meaningful to
the class. Meaning of the values are listed:

*isDensity*

- False: grid is a histogram with counts [default]
- True: a density

Applying :meth:Density.make_density sets it to True.
units : dict
A dict with the keys

- *length*:  physical unit of grid edges (Angstrom or nm) [Angstrom]
- *density*: unit of the density if isDensity=True or None
otherwise; the default is "Angstrom^{-3}" for densities
(meaning :math:\text{Å}^{-3}).
a user defined dictionary of arbitrary values associated with the
density; the class does not touch :attr:Density.metadata but
stores it with :meth:Density.save

Attributes
----------
grid : array
counts or density
edges : list of 1d-arrays
The boundaries of each cell in grid along all axes (equivalent
to what :func:numpy.histogramdd returns).
delta : array
Cell size in each dimension.
origin : array
Coordinates of the *center* of the cell at index grid[0, 0, 0, ...,
0], which is considered to be the front lower left corner.
units : dict
The units for lengths and density; change units with the method
:meth:~Density.convert_length or :meth:~Density.convert_density.

Notes
-----
The data (:attr:Density.grid) can be manipulated as a standard numpy
array. Changes can be saved to a file using the :meth:Density.save method. The
grid can be restored using the :meth:Density.load method or by supplying the
filename to the constructor.

The attribute :attr:Density.metadata holds a user-defined dictionary that
can be used to annotate the data. It is also saved with :meth:Density.save.

The :meth:Density.export method always exports a 3D object (written in
such a way to be readable in VMD_, Chimera_, and PyMOL_), the rest should
work for an array of any dimension. Note that PyMOL_ only understands DX
files with the DX data type "double" in the "array" object (see known
issues when writing OpenDX files_ and issue
MDAnalysis/GridDataFormats#35_ for details). Using the keyword
type="double" for the method :meth:Density.export, the user can
ensure that the DX file is written in a format suitable for PyMOL_.

If the input histogram consists of counts per cell then the
:meth:Density.make_density method converts the grid to a physical density. For
a probability density, divide it by :meth:Density.grid.sum or use normed=True
right away in :func:~numpy.histogramdd.

The user *should* set the *parameters* keyword (see docs for the
constructor); in particular, if the data are already a density, one must
set isDensity=True because there is no reliable way to detect if
data represent counts or a density. As a special convenience, if data are
read from a file and the user has not set isDensity then it is assumed
that the data are in fact a density.

.. _MDAnalysis/GridDataFormats#35:
https://github.com/MDAnalysis/GridDataFormats/issues/35
.. _known issues when writing OpenDX files:
https://www.mdanalysis.org/GridDataFormats/gridData/formats/OpenDX.html#known-issues-for-writing-opendx-files

--------
gridData.core.Grid is the base class of :class:Density.

Examples
--------
Typical use:

1. From a histogram (i.e. counts on a grid)::

h,edges = numpy.histogramdd(...)
D = Density(h, edges, parameters={'isDensity': False}, units={'length': 'A'})
D.make_density()

2. From a saved density file (e.g. in OpenDX format), where the lengths are
in Angstrom and the density in 1/A**3::

D = Density("density.dx")

3. From a saved density file (e.g. in OpenDX format), where the lengths are
in Angstrom and the density is measured relative to the density of water
at ambient conditions::

D = Density("density.dx", units={'density': 'water'})

4. From a saved *histogram* (less common, but in order to demonstrate the
*parameters* keyword) where the lengths are in nm::

D = Density("counts.dx", parameters={'isDensity': False}, units={'length': 'nm'})
D.make_density()
D.convert_length('Angstrom^{-3}')
D.convert_density('water')

After the final step, D will contain a density on a grid measured in
ångström, with the density values itself measured relative to the
density of water.

:class:Density objects can be algebraically manipulated (added,
subtracted, multiplied, ...)  but there are *no sanity checks* in place to
make sure that units, metadata, etc are compatible!

.. Note::

It is suggested to construct the Grid object from a histogram,
to supply the appropriate length unit, and to use
:meth:Density.make_density to obtain a density. This ensures
that the length- and the density unit correspond to each other.

"""

def __init__(self, *args, **kwargs):
length_unit = 'Angstrom'

parameters = kwargs.pop('parameters', {})
if (len(args) > 0 and isinstance(args[0], str) or
isinstance(kwargs.get('grid', None), str)):
# try to be smart: when reading from a file then it is likely that
# this is a density
parameters.setdefault('isDensity', True)
else:
parameters.setdefault('isDensity', False)
units = kwargs.pop('units', {})
units.setdefault('length', length_unit)
if parameters['isDensity']:
units.setdefault('density', length_unit)
else:
units.setdefault('density', None)

super(Density, self).__init__(*args, **kwargs)

self.parameters = parameters  # isDensity: set by make_density()
self.units = units

def _check_set_unit(self, u):
"""Check and set units.

First check that all units and their values in the dict u are valid
and then set the object's units attribute.

Parameters
----------
u : dict
{unit_type : value, ...}

Raises
------
ValueError
if unit types or unit values are not recognized or if required
unit types are not in :attr:units
"""
# all this unit crap should be a class...
try:
for unit_type, value in u.items():
if value is None:  # check here, too iffy to use dictionary[None]=None
self.units[unit_type] = None
continue
try:
units.conversion_factor[unit_type][value]
self.units[unit_type] = value
except KeyError:
errmsg = (f"Unit {value} of type {unit_type} is not "
f"recognized.")
raise ValueError(errmsg) from None
except AttributeError:
errmsg = '"unit" must be a dictionary with keys "length" and "density.'
logger.fatal(errmsg)
raise ValueError(errmsg) from None
# need at least length and density (can be None)
if 'length' not in self.units:
raise ValueError('"unit" must contain a unit for "length".')
if 'density' not in self.units:
self.units['density'] = None

[docs]    def make_density(self):
"""Convert the grid (a histogram, counts in a cell) to a density (counts/volume).

This method changes the grid irrevocably.

For a probability density, manually divide by :meth:grid.sum.

If this is already a density, then a warning is issued and nothing is
done, so calling make_density multiple times does not do any harm.
"""
# Make it a density by dividing by the volume of each grid cell
# (from numpy.histogramdd, which is for general n-D grids)

if self.parameters['isDensity']:
msg = "Running make_density() makes no sense: Grid is already a density. Nothing done."
logger.warning(msg)
warnings.warn(msg)
return

dedges = [np.diff(edge) for edge in self.edges]
D = len(self.edges)
for i in range(D):
shape = np.ones(D, int)
shape[i] = len(dedges[i])
self.grid /= dedges[i].reshape(shape)
self.parameters['isDensity'] = True
# see units.densityUnit_factor for units
self.units['density'] = self.units['length'] + "^{-3}"

[docs]    def convert_length(self, unit='Angstrom'):
"""Convert Grid object to the new unit.

Parameters
----------
unit : str (optional)
unit that the grid should be converted to: one of
"Angstrom", "nm"

Notes
-----
This changes the edges but will not change the density; it is the
user's responsibility to supply the appropriate unit if the Grid object
is constructed from a density. It is suggested to start from a
histogram and a length unit and use :meth:make_density.

"""
if unit == self.units['length']:
return
cvnfact = units.get_conversion_factor('length', self.units['length'], unit)
self.edges = [x * cvnfact for x in self.edges]
self.units['length'] = unit
self._update()  # needed to recalculate midpoints and origin

[docs]    def convert_density(self, unit='Angstrom'):
"""Convert the density to the physical units given by unit.

Parameters
----------
unit : str (optional)
The target unit that the density should be converted to.

unit can be one of the following:

=============  ===============================================================
name           description of the unit
=============  ===============================================================
Angstrom^{-3}  particles/A**3
nm^{-3}        particles/nm**3
SPC            density of SPC water at standard conditions
TIP3P          ... see :data:MDAnalysis.units.water
TIP4P          ... see :data:MDAnalysis.units.water
water          density of real water at standard conditions (0.997 g/cm**3)
Molar          mol/l
=============  ===============================================================

Raises
------
RuntimeError
If the density does not have a unit associated with it to begin
with (i.e., is not a density) then no conversion can take place.
ValueError
for unknown unit.

Notes
-----

(1) This method only works if there is already a length unit associated with the
density; otherwise raises :exc:RuntimeError
(2) Conversions always go back to unity so there can be rounding
and floating point artifacts for multiple conversions.

"""
if not self.parameters['isDensity']:
errmsg = 'The grid is not a density so converty_density() makes no sense.'
logger.fatal(errmsg)
raise RuntimeError(errmsg)
if unit == self.units['density']:
return
try:
self.grid *= units.get_conversion_factor('density',
self.units['density'], unit)
except KeyError:
errmsg = (f"The name of the unit ({unit} supplied) must be one "
f"of:\n{units.conversion_factor['density'].keys()}")
raise ValueError(errmsg) from None
self.units['density'] = unit

def __repr__(self):
if self.parameters['isDensity']:
grid_type = 'density'
else:
grid_type = 'histogram'
return '<Density ' + grid_type + ' with ' + str(self.grid.shape) + ' bins>'
`