Shapes as collective Variables¶

Overview

`pysages.colvars.shape.RadiusOfGyration`(indices)	Collective Variable that calculates the unweighted radius of gyration as CV.
`pysages.colvars.shape.PrincipalMoment`(...[, ...])	Calculate the principal moment as collective variable.
`pysages.colvars.shape.Asphericity`(indices[, ...])	Collective Variable that calculates the Asphericity.
`pysages.colvars.shape.Acylindricity`(indices)	Collective Variable that calculates the Acylindricity CV.
`pysages.colvars.shape.ShapeAnisotropy`(indices)	Collective Variable that calculates the Shape Anisotropy CV.

Details

Collective Variables that are calculated from the shape of group of atoms.

class pysages.colvars.shape.RadiusOfGyration(indices, group_length=None)¶

Collective Variable that calculates the unweighted radius of gyration as CV.

Parameters:

indices (list[int], list[tuple(int)]) – Must be a list or tuple of atoms (integers or ranges) or groups of atoms. A group is specified as a nested list or tuple of atoms.
group_length (int, optional) – Specify if a fixed group length is expected.

property function¶: returns: See pysages.colvars.shape.radius_of_gyration for details. :rtype: Callable

pysages.colvars.shape.radius_of_gyration(positions)¶

Calculate the radius of gyration for a group of atoms.

Parameters:: positions (jax.Array) – Array of particle positions used to calculate the radius of gyration.
Returns:: Radius of gyration vector
Return type:: jax.Array

pysages.colvars.shape.weighted_radius_of_gyration(positions, weights)¶

Calculate the radius of gyration for a group of atoms weighted by arbitrary weights.

Parameters:

positions (jax.Array) – Array of particle positions used to calculate the radius of gyration.
weights (jax.Array) – Array of weights for the positions.

Returns:

Weighted radius of gyration vector

Return type:

jax.Array

class pysages.colvars.shape.PrincipalMoment(indices, axis, group_length=None)¶

Calculate the principal moment as collective variable.

Parameters:

indices (list[int], list[tuple(int)]) – Must be a list or tuple of atoms (integers or ranges) or groups of atoms. A group is specified as a nested list or tuple of atoms.
axis (int) – Index of the Cartesian coordinate: 0 (X), 1 (Y), 2 (Z)
group_length (Optional[int]) – Specify if a fixed group length is expected.

property function¶: returns: Function to calculate the eigenvalue with the specified axis index of the gyration tensor. See pysages.colvars.shape.principal_moments and pysages.colvars.shape.gyration_tensor for details. :rtype: Callable

pysages.colvars.shape.gyration_tensor(positions)¶

Calculate the gyration tensor for a collection of points in space.

Parameters:: positions (jax.Array) – Points in space that are equally weighted to calculate the gyration tensor.
Returns:: Gyration tensor
Return type:: jax.Array

pysages.colvars.shape.weighted_gyration_tensor(positions, weights)¶

Calculate the gyration tensor for a collection of points in space weighted by arbitrary weights.

Parameters:

positions (jax.Array) – Points in space that are weighted by weight to calculate the gyration tensor.
weights (jax.Array) – Weights for the points in space e.g. particle masses

Returns:

Gyration tensor

Return type:

jax.Array

pysages.colvars.shape.principal_moments(positions)¶

Calculate the principal moments for positions. The principal moments are the eigenvalues of the gyration tensor. See pysages.colvars.shape.gyration_tensor for details.

Parameters:: positions (jax.Array) – Points in space that are equally weighted to calculate the gyration tensor.
Returns:: Eigenvalues of the gyration tensor
Return type:: jax.Array

class pysages.colvars.shape.Asphericity(indices, group_length=None)¶

Collective Variable that calculates the Asphericity.

Parameters:

indices (list[int], list[tuple(int)]) – Must be a list or tuple of atoms (integers or ranges) or groups of atoms. A group is specified as a nested list or tuple of atoms.
group_length (Optional[int]) – Specify if a fixed group length is expected.

property function¶: returns: See pysages.colvars.shape.asphericity for details. :rtype: Callable

pysages.colvars.shape.asphericity(positions)¶

Calculate the Asphericity from a group of atoms. It is defined as \(\lambda_3 - (\lambda_1 + \lambda_2) / 2\), where \(\lambda_i\) specifies the principal moments of the group of atoms.

See pysages.colvars.shape.principal_moments for details.

Parameters:: positions (jax.Array) – Points in space that are equally weighted to calculate the principal moments.
Returns:: Asphericity
Return type:: float

class pysages.colvars.shape.Acylindricity(indices, axes='xy', group_length=None)¶

Collective Variable that calculates the Acylindricity CV.

Parameters:

indices (list[int], list[tuple(int)]) – Must be a list or tuple of atoms (integers or ranges) or groups of atoms. A group is specified as a nested list or tuple of atoms.
group_length (Optional[int]) – Specify if a fixed group length is expected.
axes (str) – Axis combination around which the particles are symmetric. Options are: xy, yz, xz

property function¶: returns: See pysages.colvars.shape.acylindricity for details. :rtype: Callable

pysages.colvars.shape.acylindricity(positions, axes)¶

Calculate the Acylindricity from a group of atoms. It is defined as \(\lambda_k - \lambda_j\), where \(\lambda_i\) specifies the principal moments of the group of atoms, and j and k are the axes around which the particles are symmetric.

See pysages.colvars.shape.principal_moments for details.

Parameters:

positions (jax.Array) – Points in space that are equally weighted to calculate the principal moments from.
axes (Tuple[int, int]) – Indices of the axes around which the particles are symmetric.

Returns:

Acylindricity

Return type:

float

class pysages.colvars.shape.ShapeAnisotropy(indices, group_length=None)¶

Collective Variable that calculates the Shape Anisotropy CV.

Parameters:

indices (list[int], list[tuple(int)]) – Must be a list or tuple of atoms (integers or ranges) or groups of atoms. A group is specified as a nested list or tuple of atoms.
group_length (Optional[int]) – Specify if a fixed group length is expected.

property function¶: returns: See pysages.colvars.shape.shape_anisotropy for details. :rtype: Callable

pysages.colvars.shape.shape_anisotropy(positions)¶

Calculate the shape anisotropy from a group of atoms, defined as:

\[\frac{3}{2} \frac{\lambda_1^2 + \lambda_2^2 + \lambda_3^2} {(\lambda_1 + \lambda_2 + \lambda_3)^2} - \frac{1}{2}\]

where \(\lambda_i\) specifies the principal moments of the group of atoms.

See pysages.colvars.shape.principal_moments for details.

Parameters:: positions (jax.Array) – Points in space that are equally weighted to calculate the principal moments from.
Returns:: Shape Anisotropy
Return type:: float