6.11. LAMMPS DCD trajectory and DATA I/O — MDAnalysis.coordinates.LAMMPS

Classes to read and write LAMMPS DCD binary trajectories, LAMMPS DATA files and LAMMPS dump files. Trajectories can be read regardless of system-endianness as this is auto-detected.

LAMMPS can write DCD trajectories but unlike a CHARMM trajectory (which is often called a DCD even though CHARMM itself calls them “trj”) the time unit is not fixed to be the AKMA time unit (20 AKMA is 0.978 picoseconds or 1 AKMA = 4.888821e-14 s) but can depend on settings in LAMMPS. The most common case for biomolecular simulations appears to be that the time step is recorded in femtoseconds (command units real in the input file) and lengths in ångströms. Other cases are unit-less Lennard-Jones time units.

This presents a problem for MDAnalysis because it cannot autodetect the unit from the file. By default we are assuming that the unit for length is the ångström and for the time is the femtosecond. If this is not true then the user should supply the appropriate units in the keywords timeunit and/or lengthunit to DCDWriter and Universe (which then calls DCDReader).

6.11.1. Data file formats

By default either the atomic or full atom styles are expected, however this can be customised, see Atom styles.

6.11.2. Dump files

The DumpReader expects ascii dump files written with the default LAMMPS dump format of ‘atom’

6.11.3. Example: Loading a LAMMPS simulation

To load a LAMMPS simulation from a LAMMPS data file (using the DATAParser) together with a LAMMPS DCD with “real” provide the keyword format=”LAMMPS”:

>>> u = MDAnalysis.Universe("lammps.data", "lammps_real.dcd", format="LAMMPS")

If the trajectory uses units nano then use

>>> u = MDAnalysis.Universe("lammps.data", "lammps_nano.dcd", format="LAMMPS",
...                          lengthunit="nm", timeunit="ns")

To scan through a trajectory to find a desirable frame and write to a LAMMPS data file,

>>> for ts in u.trajectory:
...     # analyze frame
...     if take_this_frame == True:
...         with mda.Writer('frame.data') as W:
...             W.write(u.atoms)
...         break

Note

Lennard-Jones units are not implemented. See MDAnalysis.units for other recognized values and the documentation for the LAMMPS units command.

6.11.4. Classes

class MDAnalysis.coordinates.LAMMPS.DCDReader(dcdfilename, **kwargs)

Read a LAMMPS DCD trajectory.

The units can be set from the constructor with the keyword arguments timeunit and lengthunit. The defaults are “fs” and “Angstrom”, corresponding to LAMMPS units style “real”. See MDAnalysis.units for other recognized values.

Parameters

• filename (str) – trajectory filename

• convert_units (bool (optional)) – convert units to MDAnalysis units

• dt (float (optional)) – overwrite time delta stored in DCD

• **kwargs (dict) – General reader arguments.

Changed in version 0.17.0: Changed to use libdcd.pyx library and removed the correl function

OtherWriter(filename, **kwargs)

Returns a writer appropriate for filename.

Sets the default keywords start, step and dt (if available). n_atoms is always set from Reader.n_atoms.

See also

Reader.Writer()

Writer(filename, n_atoms=None, **kwargs)

Return writer for trajectory format

add_auxiliary(auxname, auxdata, format=None, **kwargs)

Add auxiliary data to be read alongside trajectory.

Auxiliary data may be any data timeseries from the trajectory additional to that read in by the trajectory reader. auxdata can be an AuxReader instance, or the data itself as e.g. a filename; in the latter case an appropriate AuxReader is guessed from the data/file format. An appropriate format may also be directly provided as a key word argument.

On adding, the AuxReader is initially matched to the current timestep of the trajectory, and will be updated when the trajectory timestep changes (through a call to next() or jumping timesteps with trajectory[i]).

The representative value(s) of the auxiliary data for each timestep (as calculated by the AuxReader) are stored in the current timestep in the ts.aux namespace under auxname; e.g. to add additional pull force data stored in pull-force.xvg:

u = MDAnalysis.Universe(PDB, XTC)
u.trajectory.add_auxiliary('pull', 'pull-force.xvg')

The representative value for the current timestep may then be accessed as u.trajectory.ts.aux.pull or u.trajectory.ts.aux['pull'].

See also

remove_auxiliary()

Note

Auxiliary data is assumed to be time-ordered, with no duplicates. See the Auxiliary API.

add_transformations(*transformations)

Add all transformations to be applied to the trajectory.

This function take as list of transformations as an argument. These transformations are functions that will be called by the Reader and given a Timestep object as argument, which will be transformed and returned to the Reader. The transformations can be part of the transformations module, or created by the user, and are stored as a list transformations. This list can only be modified once, and further calls of this function will raise an exception.

u = MDAnalysis.Universe(topology, coordinates)
workflow = [some_transform, another_transform, this_transform]
u.trajectory.add_transformations(*workflow)

The transformations are applied in the order given in the list transformations, i.e., the first transformation is the first or innermost one to be applied to the Timestep. The example above would be equivalent to

for ts in u.trajectory:
   ts = this_transform(another_transform(some_transform(ts)))

Parameters

transform_list (list) – list of all the transformations that will be applied to the coordinates in the order given in the list

See also

MDAnalysis.transformations

property aux_list

Lists the names of added auxiliary data.

check_slice_indices(start, stop, step)

Check frame indices are valid and clip to fit trajectory.

The usage follows standard Python conventions for range() but see the warning below.

Parameters

• start (int or None) – Starting frame index (inclusive). None corresponds to the default of 0, i.e., the initial frame.

• stop (int or None) – Last frame index (exclusive). None corresponds to the default of n_frames, i.e., it includes the last frame of the trajectory.

• step (int or None) – step size of the slice, None corresponds to the default of 1, i.e, include every frame in the range start, stop.

Returns

start, stop, step – Integers representing the slice

Return type

tuple (int, int, int)

Warning

The returned values start, stop and step give the expected result when passed in range() but gives unexpected behavior when passed in a slice when stop=None and step=-1

This can be a problem for downstream processing of the output from this method. For example, slicing of trajectories is implemented by passing the values returned by check_slice_indices() to range()

range(start, stop, step)

and using them as the indices to randomly seek to. On the other hand, in MDAnalysis.analysis.base.AnalysisBase the values returned by check_slice_indices() are used to splice the trajectory by creating a slice instance

slice(start, stop, step)

This creates a discrepancy because these two lines are not equivalent:

range(10, -1, -1)             # [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]
range(10)[slice(10, -1, -1)]  # []

close()

close reader

convert_forces_from_native(force, inplace=True)

Conversion of forces array force from native to base units

Parameters

• force (array_like) – Forces to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input force is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

New in version 0.7.7.

convert_forces_to_native(force, inplace=True)

Conversion of force array force from base to native units.

Parameters

• force (array_like) – Forces to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input force is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

New in version 0.7.7.

convert_pos_from_native(x, inplace=True)

Conversion of coordinate array x from native units to base units.

Parameters

• x (array_like) – Positions to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input x is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

Changed in version 0.7.5: Keyword inplace can be set to False so that a modified copy is returned unless no conversion takes place, in which case the reference to the unmodified x is returned.

convert_pos_to_native(x, inplace=True)

Conversion of coordinate array x from base units to native units.

Parameters

• x (array_like) – Positions to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input x is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

Changed in version 0.7.5: Keyword inplace can be set to False so that a modified copy is returned unless no conversion takes place, in which case the reference to the unmodified x is returned.

convert_time_from_native(t, inplace=True)

Convert time t from native units to base units.

Parameters

• t (array_like) – Time values to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input t is modified in place and also returned (although note that scalar values t are passed by value in Python and hence an in-place modification has no effect on the caller.) In-place operations improve performance because allocating new arrays is avoided.

Changed in version 0.7.5: Keyword inplace can be set to False so that a modified copy is returned unless no conversion takes place, in which case the reference to the unmodified x is returned.

convert_time_to_native(t, inplace=True)

Convert time t from base units to native units.

Parameters

• t (array_like) – Time values to transform

• inplace (bool, optional) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input t is modified in place and also returned. (Also note that scalar values t are passed by value in Python and hence an in-place modification has no effect on the caller.)

Changed in version 0.7.5: Keyword inplace can be set to False so that a modified copy is returned unless no conversion takes place, in which case the reference to the unmodified x is returned.

convert_velocities_from_native(v, inplace=True)

Conversion of velocities array v from native to base units

Parameters

• v (array_like) – Velocities to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input v is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

New in version 0.7.5.

convert_velocities_to_native(v, inplace=True)

Conversion of coordinate array v from base to native units

Parameters

• v (array_like) – Velocities to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input v is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

New in version 0.7.5.

copy()

Return independent copy of this Reader.

New Reader will have its own file handle and can seek/iterate independently of the original.

Will also copy the current state of the Timestep held in the original Reader

property dimensions

unitcell dimensions (A, B, C, alpha, beta, gamma)

property dt

timestep between frames

property frame

Frame number of the current time step.

This is a simple short cut to Timestep.frame.

get_aux_attribute(auxname, attrname)

Get the value of attrname from the auxiliary auxname

Parameters

• auxname (str) – Name of the auxiliary to get value for

• attrname (str) – Name of gettable attribute in the auxiliary reader

See also

set_aux_attribute()

get_aux_descriptions(auxnames=None)

Get descriptions to allow reloading the specified auxiliaries.

If no auxnames are provided, defaults to the full list of added auxiliaries.

Passing the resultant description to add_auxiliary() will allow recreation of the auxiliary. e.g., to duplicate all auxiliaries into a second trajectory:

descriptions = trajectory_1.get_aux_descriptions()
for aux in descriptions:
    trajectory_2.add_auxiliary(**aux)

Returns

List of dictionaries of the args/kwargs describing each auxiliary.

Return type

list

See also

MDAnalysis.auxiliary.base.AuxReader.get_description()

iter_as_aux(auxname)

Iterate through timesteps for which there is at least one assigned step from the auxiliary auxname within the cutoff specified in auxname.

See also

next_as_aux(), iter_auxiliary()

iter_auxiliary(auxname, start=None, stop=None, step=None, selected=None)

Iterate through the auxiliary auxname independently of the trajectory.

Will iterate over the specified steps of the auxiliary (defaults to all steps). Allows to access all values in an auxiliary, including those out of the time range of the trajectory, without having to also iterate through the trajectory.

After interation, the auxiliary will be repositioned at the current step.

Parameters

• auxname (str) – Name of the auxiliary to iterate over.

• (start (optional) – Options for iterating over a slice of the auxiliary.

• stop (optional) – Options for iterating over a slice of the auxiliary.

• step) (optional) – Options for iterating over a slice of the auxiliary.

• selected (lst | ndarray, optional) – List of steps to iterate over.

Yields

AuxStep object

See also

iter_as_aux()

property n_frames

number of frames in trajectory

next()

Forward one step to next frame.

next_as_aux(auxname)

Move to the next timestep for which there is at least one step from the auxiliary auxname within the cutoff specified in auxname.

This allows progression through the trajectory without encountering NaN representative values (unless these are specifically part of the auxiliary data).

If the auxiliary cutoff is not set, where auxiliary steps are less frequent (auxiliary.dt > trajectory.dt), this allows progression at the auxiliary pace (rounded to nearest timestep); while if the auxiliary steps are more frequent, this will work the same as calling next().

See the Auxiliary API.

See also

iter_as_aux()

static parse_n_atoms(filename, **kwargs)

Read the coordinate file and deduce the number of atoms

Returns

n_atoms – the number of atoms in the coordinate file

Return type

int

Raises

NotImplementedError – when the number of atoms can’t be deduced

remove_auxiliary(auxname)

Clear data and close the AuxReader for the auxiliary auxname.

See also

add_auxiliary()

rename_aux(auxname, new)

Change the name of the auxiliary auxname to new.

Provided there is not already an auxiliary named new, the auxiliary name will be changed in ts.aux namespace, the trajectory’s list of added auxiliaries, and in the auxiliary reader itself.

Parameters

• auxname (str) – Name of the auxiliary to rename

• new (str) – New name to try set

Raises

ValueError – If the name new is already in use by an existing auxiliary.

rewind()

Position at beginning of trajectory

set_aux_attribute(auxname, attrname, new)

Set the value of attrname in the auxiliary auxname.

Parameters

• auxname (str) – Name of the auxiliary to alter

• attrname (str) – Name of settable attribute in the auxiliary reader

• new – New value to try set attrname to

See also

get_aux_attribute(), rename_aux()

property time

Time of the current frame in MDAnalysis time units (typically ps).

This is either read straight from the Timestep, or calculated as time = Timestep.frame * Timestep.dt

timeseries(asel=None, start=None, stop=None, step=None, order='afc')

Return a subset of coordinate data for an AtomGroup

Parameters

• asel (AtomGroup) – The AtomGroup to read the coordinates from. Defaults to None, in which case the full set of coordinate data is returned.

• start (int (optional)) – Begin reading the trajectory at frame index start (where 0 is the index of the first frame in the trajectory); the default None starts at the beginning.

• stop (int (optional)) – End reading the trajectory at frame index stop-1, i.e, stop is excluded. The trajectory is read to the end with the default None.

• step (int (optional)) – Step size for reading; the default None is equivalent to 1 and means to read every frame.

• order (str (optional)) – the order/shape of the return data array, corresponding to (a)tom, (f)rame, (c)oordinates all six combinations of ‘a’, ‘f’, ‘c’ are allowed ie “fac” - return array where the shape is (frame, number of atoms, coordinates)

Changed in version 1.0.0: skip and format keywords have been removed.

property totaltime

Total length of the trajectory

The time is calculated as (n_frames - 1) * dt, i.e., we assume that the first frame no time as elapsed. Thus, a trajectory with two frames will be considered to have a length of a single time step dt and a “trajectory” with a single frame will be reported as length 0.

property transformations

Returns the list of transformations

class MDAnalysis.coordinates.LAMMPS.DCDWriter(*args, **kwargs)

Write a LAMMPS DCD trajectory.

The units can be set from the constructor with the keyword arguments timeunit and lengthunit. The defaults are “fs” and “Angstrom”. See MDAnalysis.units for other recognized values.

Parameters

• filename (str) – filename of trajectory

• n_atoms (int) – number of atoms to be written

• convert_units (bool (optional)) – convert from MDAnalysis units to format specific units

• step (int (optional)) – number of steps between frames to be written

• dt (float (optional)) – time between two frames. If None guess from first written TimeStep

• remarks (str (optional)) – remarks to be stored in DCD. Shouldn’t be more then 240 characters

• nsavc (int (optional)) – DCD files can also store the number of integrator time steps that correspond to the interval between two frames as nsavc (i.e., every how many MD steps is a frame saved to the DCD). By default, this number is just set to one and this should be sufficient for almost all cases but if required, nsavc can be changed.

• istart (int (optional)) – starting frame number in integrator timesteps. CHARMM defaults to nsavc, i.e., start at frame number 1 = istart / nsavc. The value None will set istart to nsavc (the CHARMM default). The MDAnalysis default is 0 so that the frame number and time of the first frame is 0.

• **kwargs (dict) – General writer arguments

close()

close trajectory

convert_dimensions_to_unitcell(ts, inplace=True)

Read dimensions from timestep ts and return appropriate unitcell.

The default is to return [A,B,C,alpha,beta,gamma]; if this is not appropriate then this method has to be overriden.

convert_forces_from_native(force, inplace=True)

Conversion of forces array force from native to base units

Parameters

• force (array_like) – Forces to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input force is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

New in version 0.7.7.

convert_forces_to_native(force, inplace=True)

Conversion of force array force from base to native units.

Parameters

• force (array_like) – Forces to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input force is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

New in version 0.7.7.

convert_pos_from_native(x, inplace=True)

Conversion of coordinate array x from native units to base units.

Parameters

• x (array_like) – Positions to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input x is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

Changed in version 0.7.5: Keyword inplace can be set to False so that a modified copy is returned unless no conversion takes place, in which case the reference to the unmodified x is returned.

convert_pos_to_native(x, inplace=True)

Conversion of coordinate array x from base units to native units.

Parameters

• x (array_like) – Positions to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input x is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

Changed in version 0.7.5: Keyword inplace can be set to False so that a modified copy is returned unless no conversion takes place, in which case the reference to the unmodified x is returned.

convert_time_from_native(t, inplace=True)

Convert time t from native units to base units.

Parameters

• t (array_like) – Time values to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input t is modified in place and also returned (although note that scalar values t are passed by value in Python and hence an in-place modification has no effect on the caller.) In-place operations improve performance because allocating new arrays is avoided.

Changed in version 0.7.5: Keyword inplace can be set to False so that a modified copy is returned unless no conversion takes place, in which case the reference to the unmodified x is returned.

convert_time_to_native(t, inplace=True)

Convert time t from base units to native units.

Parameters

• t (array_like) – Time values to transform

• inplace (bool, optional) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input t is modified in place and also returned. (Also note that scalar values t are passed by value in Python and hence an in-place modification has no effect on the caller.)

Changed in version 0.7.5: Keyword inplace can be set to False so that a modified copy is returned unless no conversion takes place, in which case the reference to the unmodified x is returned.

convert_velocities_from_native(v, inplace=True)

Conversion of velocities array v from native to base units

Parameters

• v (array_like) – Velocities to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input v is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

New in version 0.7.5.

convert_velocities_to_native(v, inplace=True)

Conversion of coordinate array v from base to native units

Parameters

• v (array_like) – Velocities to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input v is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

New in version 0.7.5.

has_valid_coordinates(criteria, x)

Returns True if all values are within limit values of their formats.

Due to rounding, the test is asymmetric (and min is supposed to be negative):

min < x <= max

Parameters

• criteria (dict) – dictionary containing the max and min values in native units

• x (numpy.ndarray) – (x, y, z) coordinates of atoms selected to be written out

Return type

bool

write(obj)

Write current timestep, using the supplied obj.

Parameters

obj (AtomGroup or Universe) – write coordinate information associate with obj

Note

The size of the obj must be the same as the number of atoms provided when setting up the trajectory.

Changed in version 2.0.0: Deprecated support for Timestep argument to write has now been removed. Use AtomGroup or Universe as an input instead.

class MDAnalysis.coordinates.LAMMPS.DATAReader(filename, **kwargs)

Reads a single frame of coordinate information from a LAMMPS DATA file.

New in version 0.9.0.

Changed in version 0.11.0: Frames now 0-based instead of 1-based

OtherWriter(filename, **kwargs)

Returns a writer appropriate for filename.

Sets the default keywords start, step and dt (if available). n_atoms is always set from Reader.n_atoms.

See also

Reader.Writer()

Writer(filename, **kwargs)

A trajectory writer with the same properties as this trajectory.

add_auxiliary(auxname, auxdata, format=None, **kwargs)

Add auxiliary data to be read alongside trajectory.

Auxiliary data may be any data timeseries from the trajectory additional to that read in by the trajectory reader. auxdata can be an AuxReader instance, or the data itself as e.g. a filename; in the latter case an appropriate AuxReader is guessed from the data/file format. An appropriate format may also be directly provided as a key word argument.

On adding, the AuxReader is initially matched to the current timestep of the trajectory, and will be updated when the trajectory timestep changes (through a call to next() or jumping timesteps with trajectory[i]).

The representative value(s) of the auxiliary data for each timestep (as calculated by the AuxReader) are stored in the current timestep in the ts.aux namespace under auxname; e.g. to add additional pull force data stored in pull-force.xvg:

u = MDAnalysis.Universe(PDB, XTC)
u.trajectory.add_auxiliary('pull', 'pull-force.xvg')

The representative value for the current timestep may then be accessed as u.trajectory.ts.aux.pull or u.trajectory.ts.aux['pull'].

See also

remove_auxiliary()

Note

Auxiliary data is assumed to be time-ordered, with no duplicates. See the Auxiliary API.

add_transformations(*transformations)

Add all transformations to be applied to the trajectory.

This function take as list of transformations as an argument. These transformations are functions that will be called by the Reader and given a Timestep object as argument, which will be transformed and returned to the Reader. The transformations can be part of the transformations module, or created by the user, and are stored as a list transformations. This list can only be modified once, and further calls of this function will raise an exception.

u = MDAnalysis.Universe(topology, coordinates)
workflow = [some_transform, another_transform, this_transform]
u.trajectory.add_transformations(*workflow)

Parameters

transform_list (list) – list of all the transformations that will be applied to the coordinates

See also

MDAnalysis.transformations

property aux_list

Lists the names of added auxiliary data.

check_slice_indices(start, stop, step)

Check frame indices are valid and clip to fit trajectory.

The usage follows standard Python conventions for range() but see the warning below.

Parameters

• start (int or None) – Starting frame index (inclusive). None corresponds to the default of 0, i.e., the initial frame.

• stop (int or None) – Last frame index (exclusive). None corresponds to the default of n_frames, i.e., it includes the last frame of the trajectory.

• step (int or None) – step size of the slice, None corresponds to the default of 1, i.e, include every frame in the range start, stop.

Returns

start, stop, step – Integers representing the slice

Return type

tuple (int, int, int)

Warning

The returned values start, stop and step give the expected result when passed in range() but gives unexpected behavior when passed in a slice when stop=None and step=-1

This can be a problem for downstream processing of the output from this method. For example, slicing of trajectories is implemented by passing the values returned by check_slice_indices() to range()

range(start, stop, step)

and using them as the indices to randomly seek to. On the other hand, in MDAnalysis.analysis.base.AnalysisBase the values returned by check_slice_indices() are used to splice the trajectory by creating a slice instance

slice(start, stop, step)

This creates a discrepancy because these two lines are not equivalent:

range(10, -1, -1)             # [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]
range(10)[slice(10, -1, -1)]  # []

close()

Close the trajectory file.

convert_forces_from_native(force, inplace=True)

Conversion of forces array force from native to base units

Parameters

• force (array_like) – Forces to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input force is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

New in version 0.7.7.

convert_forces_to_native(force, inplace=True)

Conversion of force array force from base to native units.

Parameters

• force (array_like) – Forces to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input force is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

New in version 0.7.7.

convert_pos_from_native(x, inplace=True)

Conversion of coordinate array x from native units to base units.

Parameters

• x (array_like) – Positions to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input x is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

Changed in version 0.7.5: Keyword inplace can be set to False so that a modified copy is returned unless no conversion takes place, in which case the reference to the unmodified x is returned.

convert_pos_to_native(x, inplace=True)

Conversion of coordinate array x from base units to native units.

Parameters

• x (array_like) – Positions to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input x is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

Changed in version 0.7.5: Keyword inplace can be set to False so that a modified copy is returned unless no conversion takes place, in which case the reference to the unmodified x is returned.

convert_time_from_native(t, inplace=True)

Convert time t from native units to base units.

Parameters

• t (array_like) – Time values to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input t is modified in place and also returned (although note that scalar values t are passed by value in Python and hence an in-place modification has no effect on the caller.) In-place operations improve performance because allocating new arrays is avoided.

Changed in version 0.7.5: Keyword inplace can be set to False so that a modified copy is returned unless no conversion takes place, in which case the reference to the unmodified x is returned.

convert_time_to_native(t, inplace=True)

Convert time t from base units to native units.

Parameters

• t (array_like) – Time values to transform

• inplace (bool, optional) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input t is modified in place and also returned. (Also note that scalar values t are passed by value in Python and hence an in-place modification has no effect on the caller.)

Changed in version 0.7.5: Keyword inplace can be set to False so that a modified copy is returned unless no conversion takes place, in which case the reference to the unmodified x is returned.

convert_velocities_from_native(v, inplace=True)

Conversion of velocities array v from native to base units

Parameters

• v (array_like) – Velocities to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input v is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

New in version 0.7.5.

convert_velocities_to_native(v, inplace=True)

Conversion of coordinate array v from base to native units

Parameters

• v (array_like) – Velocities to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input v is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

New in version 0.7.5.

copy()

Return independent copy of this Reader.

New Reader will have its own file handle and can seek/iterate independently of the original.

Will also copy the current state of the Timestep held in the original Reader

property dt

Time between two trajectory frames in picoseconds.

property frame

Frame number of the current time step.

This is a simple short cut to Timestep.frame.

get_aux_attribute(auxname, attrname)

Get the value of attrname from the auxiliary auxname

Parameters

• auxname (str) – Name of the auxiliary to get value for

• attrname (str) – Name of gettable attribute in the auxiliary reader

See also

set_aux_attribute()

get_aux_descriptions(auxnames=None)

Get descriptions to allow reloading the specified auxiliaries.

If no auxnames are provided, defaults to the full list of added auxiliaries.

Passing the resultant description to add_auxiliary() will allow recreation of the auxiliary. e.g., to duplicate all auxiliaries into a second trajectory:

descriptions = trajectory_1.get_aux_descriptions()
for aux in descriptions:
    trajectory_2.add_auxiliary(**aux)

Returns

List of dictionaries of the args/kwargs describing each auxiliary.

Return type

list

See also

MDAnalysis.auxiliary.base.AuxReader.get_description()

iter_as_aux(auxname)

Iterate through timesteps for which there is at least one assigned step from the auxiliary auxname within the cutoff specified in auxname.

See also

next_as_aux(), iter_auxiliary()

iter_auxiliary(auxname, start=None, stop=None, step=None, selected=None)

Iterate through the auxiliary auxname independently of the trajectory.

Will iterate over the specified steps of the auxiliary (defaults to all steps). Allows to access all values in an auxiliary, including those out of the time range of the trajectory, without having to also iterate through the trajectory.

After interation, the auxiliary will be repositioned at the current step.

Parameters

• auxname (str) – Name of the auxiliary to iterate over.

• (start (optional) – Options for iterating over a slice of the auxiliary.

• stop (optional) – Options for iterating over a slice of the auxiliary.

• step) (optional) – Options for iterating over a slice of the auxiliary.

• selected (lst | ndarray, optional) – List of steps to iterate over.

Yields

AuxStep object

See also

iter_as_aux()

next()

Forward one step to next frame.

next_as_aux(auxname)

Move to the next timestep for which there is at least one step from the auxiliary auxname within the cutoff specified in auxname.

This allows progression through the trajectory without encountering NaN representative values (unless these are specifically part of the auxiliary data).

If the auxiliary cutoff is not set, where auxiliary steps are less frequent (auxiliary.dt > trajectory.dt), this allows progression at the auxiliary pace (rounded to nearest timestep); while if the auxiliary steps are more frequent, this will work the same as calling next().

See the Auxiliary API.

See also

iter_as_aux()

classmethod parse_n_atoms(filename, **kwargs)

Read the coordinate file and deduce the number of atoms

Returns

n_atoms – the number of atoms in the coordinate file

Return type

int

Raises

NotImplementedError – when the number of atoms can’t be deduced

remove_auxiliary(auxname)

Clear data and close the AuxReader for the auxiliary auxname.

See also

add_auxiliary()

rename_aux(auxname, new)

Change the name of the auxiliary auxname to new.

Provided there is not already an auxiliary named new, the auxiliary name will be changed in ts.aux namespace, the trajectory’s list of added auxiliaries, and in the auxiliary reader itself.

Parameters

• auxname (str) – Name of the auxiliary to rename

• new (str) – New name to try set

Raises

ValueError – If the name new is already in use by an existing auxiliary.

rewind()

Position at beginning of trajectory

set_aux_attribute(auxname, attrname, new)

Set the value of attrname in the auxiliary auxname.

Parameters

• auxname (str) – Name of the auxiliary to alter

• attrname (str) – Name of settable attribute in the auxiliary reader

• new – New value to try set attrname to

See also

get_aux_attribute(), rename_aux()

property time

Time of the current frame in MDAnalysis time units (typically ps).

This is either read straight from the Timestep, or calculated as time = Timestep.frame * Timestep.dt

property totaltime

Total length of the trajectory

The time is calculated as (n_frames - 1) * dt, i.e., we assume that the first frame no time as elapsed. Thus, a trajectory with two frames will be considered to have a length of a single time step dt and a “trajectory” with a single frame will be reported as length 0.

property transformations

Returns the list of transformations

class MDAnalysis.coordinates.LAMMPS.DATAWriter(filename, convert_units=True, **kwargs)

Write out the current time step as a LAMMPS DATA file.

This writer supports the sections Atoms, Masses, Velocities, Bonds, Angles, Dihedrals, and Impropers. This writer will write the header and these sections (if applicable). Atoms section is written in the “full” sub-style if charges are available or “molecular” sub-style if they are not. Molecule id is set to 0 for all atoms.

Note

This writer assumes “conventional” or “real” LAMMPS units where length is measured in Angstroms and velocity is measured in Angstroms per femtosecond. To write in different units, specify lengthunit

If atom types are not already positive integers, the user must set them to be positive integers, because the writer will not automatically assign new types.

To preserve numerical atom types when writing a selection, the Masses section will have entries for each atom type up to the maximum atom type. If the universe does not contain atoms of some type in {1, … max(atom_types)}, then the mass for that type will be set to 1.

In order to write bonds, each selected bond type must be explicitly set to an integer >= 1.

Set up a DATAWriter

Parameters

• filename (str) – output filename

• convert_units (bool, optional) – units are converted to the MDAnalysis base format; [True]

close()

Close the trajectory file.

convert_dimensions_to_unitcell(ts, inplace=True)

Read dimensions from timestep ts and return appropriate unitcell.

The default is to return [A,B,C,alpha,beta,gamma]; if this is not appropriate then this method has to be overriden.

convert_forces_from_native(force, inplace=True)

Conversion of forces array force from native to base units

Parameters

• force (array_like) – Forces to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input force is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

New in version 0.7.7.

convert_forces_to_native(force, inplace=True)

Conversion of force array force from base to native units.

Parameters

• force (array_like) – Forces to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input force is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

New in version 0.7.7.

convert_pos_from_native(x, inplace=True)

Conversion of coordinate array x from native units to base units.

Parameters

• x (array_like) – Positions to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input x is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

Changed in version 0.7.5: Keyword inplace can be set to False so that a modified copy is returned unless no conversion takes place, in which case the reference to the unmodified x is returned.

convert_pos_to_native(x, inplace=True)

Conversion of coordinate array x from base units to native units.

Parameters

• x (array_like) – Positions to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input x is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

Changed in version 0.7.5: Keyword inplace can be set to False so that a modified copy is returned unless no conversion takes place, in which case the reference to the unmodified x is returned.

convert_time_from_native(t, inplace=True)

Convert time t from native units to base units.

Parameters

• t (array_like) – Time values to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input t is modified in place and also returned (although note that scalar values t are passed by value in Python and hence an in-place modification has no effect on the caller.) In-place operations improve performance because allocating new arrays is avoided.

Changed in version 0.7.5: Keyword inplace can be set to False so that a modified copy is returned unless no conversion takes place, in which case the reference to the unmodified x is returned.

convert_time_to_native(t, inplace=True)

Convert time t from base units to native units.

Parameters

• t (array_like) – Time values to transform

• inplace (bool, optional) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input t is modified in place and also returned. (Also note that scalar values t are passed by value in Python and hence an in-place modification has no effect on the caller.)

Changed in version 0.7.5: Keyword inplace can be set to False so that a modified copy is returned unless no conversion takes place, in which case the reference to the unmodified x is returned.

convert_velocities_from_native(v, inplace=True)

Conversion of velocities array v from native to base units

Parameters

• v (array_like) – Velocities to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input v is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

New in version 0.7.5.

convert_velocities_to_native(v, inplace=True)

Conversion of coordinate array v from base to native units

Parameters

• v (array_like) – Velocities to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input v is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

New in version 0.7.5.

has_valid_coordinates(criteria, x)

Returns True if all values are within limit values of their formats.

Due to rounding, the test is asymmetric (and min is supposed to be negative):

min < x <= max

Parameters

• criteria (dict) – dictionary containing the max and min values in native units

• x (numpy.ndarray) – (x, y, z) coordinates of atoms selected to be written out

Return type

bool

write(selection, frame=None)

Write selection at current trajectory frame to file.

The sections for Atoms, Masses, Velocities, Bonds, Angles, Dihedrals, and Impropers (if these are defined) are written. The Atoms section is written in the “full” sub-style if charges are available or “molecular” sub-style if they are not. Molecule id in atoms section is set to to 0.

No other sections are written to the DATA file. As of this writing, other sections are not parsed into the topology by the DATAReader.

Note

If the selection includes a partial fragment, then only the bonds, angles, etc. whose atoms are contained within the selection will be included.

Parameters

• selection (AtomGroup or Universe) – MDAnalysis AtomGroup (selection or Universe.atoms) or also Universe

• frame (int (optional)) – optionally move to frame number frame

class MDAnalysis.coordinates.LAMMPS.DumpReader(filename, lammps_coordinate_convention='auto', **kwargs)

Reads the default LAMMPS dump format

Supports coordinates in the LAMMPS “unscaled” (x,y,z), “scaled” (xs,ys,zs), “unwrapped” (xu,yu,zu) and “scaled_unwrapped” (xsu,ysu,zsu) coordinate conventions (see https://docs.lammps.org/dump.html for more details). If lammps_coordinate_convention=’auto’ (default), one will be guessed. Guessing checks whether the coordinates fit each convention in the order “unscaled”, “scaled”, “unwrapped”, “scaled_unwrapped” and whichever set of coordinates is detected first will be used. If coordinates are given in the scaled coordinate convention (xs,ys,zs) or scaled unwrapped coordinate convention (xsu,ysu,zsu) they will automatically be converted from their scaled/fractional representation to their real values.

Changed in version 2.0.0: Now parses coordinates in multiple lammps conventions (x,xs,xu,xsu)

New in version 0.19.0.

OtherWriter(filename, **kwargs)

Returns a writer appropriate for filename.

Sets the default keywords start, step and dt (if available). n_atoms is always set from Reader.n_atoms.

See also

Reader.Writer()

Writer(filename, **kwargs)

A trajectory writer with the same properties as this trajectory.

add_auxiliary(auxname, auxdata, format=None, **kwargs)

Add auxiliary data to be read alongside trajectory.

Auxiliary data may be any data timeseries from the trajectory additional to that read in by the trajectory reader. auxdata can be an AuxReader instance, or the data itself as e.g. a filename; in the latter case an appropriate AuxReader is guessed from the data/file format. An appropriate format may also be directly provided as a key word argument.

On adding, the AuxReader is initially matched to the current timestep of the trajectory, and will be updated when the trajectory timestep changes (through a call to next() or jumping timesteps with trajectory[i]).

The representative value(s) of the auxiliary data for each timestep (as calculated by the AuxReader) are stored in the current timestep in the ts.aux namespace under auxname; e.g. to add additional pull force data stored in pull-force.xvg:

u = MDAnalysis.Universe(PDB, XTC)
u.trajectory.add_auxiliary('pull', 'pull-force.xvg')

The representative value for the current timestep may then be accessed as u.trajectory.ts.aux.pull or u.trajectory.ts.aux['pull'].

See also

remove_auxiliary()

Note

Auxiliary data is assumed to be time-ordered, with no duplicates. See the Auxiliary API.

add_transformations(*transformations)

Add all transformations to be applied to the trajectory.

This function take as list of transformations as an argument. These transformations are functions that will be called by the Reader and given a Timestep object as argument, which will be transformed and returned to the Reader. The transformations can be part of the transformations module, or created by the user, and are stored as a list transformations. This list can only be modified once, and further calls of this function will raise an exception.

u = MDAnalysis.Universe(topology, coordinates)
workflow = [some_transform, another_transform, this_transform]
u.trajectory.add_transformations(*workflow)

The transformations are applied in the order given in the list transformations, i.e., the first transformation is the first or innermost one to be applied to the Timestep. The example above would be equivalent to

for ts in u.trajectory:
   ts = this_transform(another_transform(some_transform(ts)))

Parameters

transform_list (list) – list of all the transformations that will be applied to the coordinates in the order given in the list

See also

MDAnalysis.transformations

property aux_list

Lists the names of added auxiliary data.

check_slice_indices(start, stop, step)

Check frame indices are valid and clip to fit trajectory.

The usage follows standard Python conventions for range() but see the warning below.

Parameters

• start (int or None) – Starting frame index (inclusive). None corresponds to the default of 0, i.e., the initial frame.

• stop (int or None) – Last frame index (exclusive). None corresponds to the default of n_frames, i.e., it includes the last frame of the trajectory.

• step (int or None) – step size of the slice, None corresponds to the default of 1, i.e, include every frame in the range start, stop.

Returns

start, stop, step – Integers representing the slice

Return type

tuple (int, int, int)

Warning

The returned values start, stop and step give the expected result when passed in range() but gives unexpected behavior when passed in a slice when stop=None and step=-1

This can be a problem for downstream processing of the output from this method. For example, slicing of trajectories is implemented by passing the values returned by check_slice_indices() to range()

range(start, stop, step)

and using them as the indices to randomly seek to. On the other hand, in MDAnalysis.analysis.base.AnalysisBase the values returned by check_slice_indices() are used to splice the trajectory by creating a slice instance

slice(start, stop, step)

This creates a discrepancy because these two lines are not equivalent:

range(10, -1, -1)             # [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]
range(10)[slice(10, -1, -1)]  # []

close()

Close the trajectory file.

convert_forces_from_native(force, inplace=True)

Conversion of forces array force from native to base units

Parameters

• force (array_like) – Forces to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input force is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

New in version 0.7.7.

convert_forces_to_native(force, inplace=True)

Conversion of force array force from base to native units.

Parameters

• force (array_like) – Forces to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input force is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

New in version 0.7.7.

convert_pos_from_native(x, inplace=True)

Conversion of coordinate array x from native units to base units.

Parameters

• x (array_like) – Positions to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input x is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

Changed in version 0.7.5: Keyword inplace can be set to False so that a modified copy is returned unless no conversion takes place, in which case the reference to the unmodified x is returned.

convert_pos_to_native(x, inplace=True)

Conversion of coordinate array x from base units to native units.

Parameters

• x (array_like) – Positions to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input x is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

Changed in version 0.7.5: Keyword inplace can be set to False so that a modified copy is returned unless no conversion takes place, in which case the reference to the unmodified x is returned.

convert_time_from_native(t, inplace=True)

Convert time t from native units to base units.

Parameters

• t (array_like) – Time values to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input t is modified in place and also returned (although note that scalar values t are passed by value in Python and hence an in-place modification has no effect on the caller.) In-place operations improve performance because allocating new arrays is avoided.

Changed in version 0.7.5: Keyword inplace can be set to False so that a modified copy is returned unless no conversion takes place, in which case the reference to the unmodified x is returned.

convert_time_to_native(t, inplace=True)

Convert time t from base units to native units.

Parameters

• t (array_like) – Time values to transform

• inplace (bool, optional) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input t is modified in place and also returned. (Also note that scalar values t are passed by value in Python and hence an in-place modification has no effect on the caller.)

Changed in version 0.7.5: Keyword inplace can be set to False so that a modified copy is returned unless no conversion takes place, in which case the reference to the unmodified x is returned.

convert_velocities_from_native(v, inplace=True)

Conversion of velocities array v from native to base units

Parameters

• v (array_like) – Velocities to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input v is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

New in version 0.7.5.

convert_velocities_to_native(v, inplace=True)

Conversion of coordinate array v from base to native units

Parameters

• v (array_like) – Velocities to transform

• inplace (bool (optional)) – Whether to modify the array inplace, overwriting previous data

Note

By default, the input v is modified in place and also returned. In-place operations improve performance because allocating new arrays is avoided.

New in version 0.7.5.

copy()

Return independent copy of this Reader.

New Reader will have its own file handle and can seek/iterate independently of the original.

Will also copy the current state of the Timestep held in the original Reader

property dt

Time between two trajectory frames in picoseconds.

property frame

Frame number of the current time step.

This is a simple short cut to Timestep.frame.

get_aux_attribute(auxname, attrname)

Get the value of attrname from the auxiliary auxname

Parameters

• auxname (str) – Name of the auxiliary to get value for

• attrname (str) – Name of gettable attribute in the auxiliary reader

See also

set_aux_attribute()

get_aux_descriptions(auxnames=None)

Get descriptions to allow reloading the specified auxiliaries.

If no auxnames are provided, defaults to the full list of added auxiliaries.

Passing the resultant description to add_auxiliary() will allow recreation of the auxiliary. e.g., to duplicate all auxiliaries into a second trajectory:

descriptions = trajectory_1.get_aux_descriptions()
for aux in descriptions:
    trajectory_2.add_auxiliary(**aux)

Returns

List of dictionaries of the args/kwargs describing each auxiliary.

Return type

list

See also

MDAnalysis.auxiliary.base.AuxReader.get_description()

iter_as_aux(auxname)

Iterate through timesteps for which there is at least one assigned step from the auxiliary auxname within the cutoff specified in auxname.

See also

next_as_aux(), iter_auxiliary()

iter_auxiliary(auxname, start=None, stop=None, step=None, selected=None)

Iterate through the auxiliary auxname independently of the trajectory.

Will iterate over the specified steps of the auxiliary (defaults to all steps). Allows to access all values in an auxiliary, including those out of the time range of the trajectory, without having to also iterate through the trajectory.

After interation, the auxiliary will be repositioned at the current step.

Parameters

• auxname (str) – Name of the auxiliary to iterate over.

• (start (optional) – Options for iterating over a slice of the auxiliary.

• stop (optional) – Options for iterating over a slice of the auxiliary.

• step) (optional) – Options for iterating over a slice of the auxiliary.

• selected (lst | ndarray, optional) – List of steps to iterate over.

Yields

AuxStep object

See also

iter_as_aux()

next()

Forward one step to next frame.

next_as_aux(auxname)

Move to the next timestep for which there is at least one step from the auxiliary auxname within the cutoff specified in auxname.

This allows progression through the trajectory without encountering NaN representative values (unless these are specifically part of the auxiliary data).

If the auxiliary cutoff is not set, where auxiliary steps are less frequent (auxiliary.dt > trajectory.dt), this allows progression at the auxiliary pace (rounded to nearest timestep); while if the auxiliary steps are more frequent, this will work the same as calling next().

See the Auxiliary API.

See also

iter_as_aux()

classmethod parse_n_atoms(filename, **kwargs)

Read the coordinate file and deduce the number of atoms

Returns

n_atoms – the number of atoms in the coordinate file

Return type

int

Raises

NotImplementedError – when the number of atoms can’t be deduced

remove_auxiliary(auxname)

Clear data and close the AuxReader for the auxiliary auxname.

See also

add_auxiliary()

rename_aux(auxname, new)

Change the name of the auxiliary auxname to new.

Provided there is not already an auxiliary named new, the auxiliary name will be changed in ts.aux namespace, the trajectory’s list of added auxiliaries, and in the auxiliary reader itself.

Parameters

• auxname (str) – Name of the auxiliary to rename

• new (str) – New name to try set

Raises

ValueError – If the name new is already in use by an existing auxiliary.

rewind()

Position at beginning of trajectory

set_aux_attribute(auxname, attrname, new)

Set the value of attrname in the auxiliary auxname.

Parameters

• auxname (str) – Name of the auxiliary to alter

• attrname (str) – Name of settable attribute in the auxiliary reader

• new – New value to try set attrname to

See also

get_aux_attribute(), rename_aux()

property time

Time of the current frame in MDAnalysis time units (typically ps).

This is either read straight from the Timestep, or calculated as time = Timestep.frame * Timestep.dt

property totaltime

Total length of the trajectory

The time is calculated as (n_frames - 1) * dt, i.e., we assume that the first frame no time as elapsed. Thus, a trajectory with two frames will be considered to have a length of a single time step dt and a “trajectory” with a single frame will be reported as length 0.

property transformations

Returns the list of transformations