Code

nablachem.alchemy

nablachem.alchemy.Monomial

A single monomial in the multi-dimensional Taylor expansion.

nablachem.alchemy.Monomial.__init__(prefactor, powers={})

Define the monomial.

Parameters:

Name	Type	Description	Default
prefactor	float	Weight or coefficient of the monomial.	required
powers	dict[str, int]	Involved variables as keys and the exponent as value, by default {}.	{}

nablachem.alchemy.Monomial.distance(pos, center)

Evaluate the distance term of the Taylor expansion.

Parameters:

Name	Type	Description	Default
pos	dict[str, float]	The position at which the Monomial is evaluated. Keys are the variable names, values are the positions.	required
center	dict[str, float]	The center of the Taylor expansion. Keys are the variable names, values are the positions.	required

Returns:

Type	Description
float	Distance

nablachem.alchemy.Monomial.prefactor()

Calculates the Taylor expansion prefactor.

Returns:

Type	Description
float	Prefactor for the summation in the Taylor expansion.

nablachem.alchemy.MultiTaylor

Multi-dimensional multi-variate arbitrary order Taylor expansion from any evenly spaced finite difference stencil.

Examples:

>>> import pandas as pd
>>> df = pd.read_csv("some_file.csv")
>>> df.columns
Index(['RX', 'RY', 'RZ', 'QX', 'QY', 'QZ', 'E', 'BETA1', 'BETA2',
   'SIGMA'],
  dtype='object')
>>> mt = MultiTaylor(df, outputs="BETA1 BETA2 SIGMA".split())
>>> spatial_center, electronic_center = 3, 2.5
>>> mt.reset_center(
    RX=spatial_center,
    RY=spatial_center,
    RZ=spatial_center,
    QX=electronic_center,
    QY=electronic_center,
    QZ=electronic_center,
)
>>> mt.reset_filter(E=4)
>>> mt.build_model(2)
>>> mt.query(RX=3.1, RY=3.1, RZ=3.1, QX=2.4, QY=2.4, QZ=2.4)
{'BETA1': 0.022412699999999976,
'BETA2': 0.014047600000000134,
'SIGMA': 0.0018744333333333316}

nablachem.alchemy.MultiTaylor.__init__(dataframe, outputs)

Initialize the Taylor expansion from a dataframe of data points forming the superset of stencils.

Parameters:

Name	Type	Description	Default
dataframe	DataFrame	Holds all data points available for the vicinity of the future center of the expansion.	required
outputs	list[str]	Those columns of the dataframe that are considered to be outputs rather than input coordinates.	required

nablachem.alchemy.MultiTaylor.build_model(orders, additional_terms=[])

Sets up the model for a specific expansion order or list of terms.

Parameters:

Name	Type	Description	Default
orders	int	All terms are included in the expansion up to this order.	required
additional_terms	list[tuple[str]]	The terms to ADDITIONALLY include, i.e. list of tuples of column names. To only include d/dx, give [('x',)] To only include d^2/dx^2, give [('x', 'x')] To only include d^2/dxdy, give [('x', 'y')] To include all three, give [('x',), ('x', 'x'), ('x', 'y')]	[]

Raises:

Type	Description
NotImplementedError	Center needs to be given in dataframe.
ValueError	Center is not unique.
ValueError	Duplicate points in the dataset.

nablachem.alchemy.MultiTaylor.maximize(target, bounds)

See _optimize.

Parameters:

Name	Type	Description	Default
target	str	Column name to maximize.	required
bounds	dict[str, tuple[float, float]]	Bounds for the search space.	required

Returns:

Type	Description
dict[str, float]	Optimal position found.

nablachem.alchemy.MultiTaylor.minimize(target, bounds)

See _optimize.

Parameters:

Name	Type	Description	Default
target	str	Column name to minimize.	required
bounds	dict[str, tuple[float, float]]	Bounds for the search space.	required

Returns:

Type	Description
dict[str, float]	Optimal position found.

nablachem.alchemy.MultiTaylor.query(**kwargs)

Evaluate the Taylor expansion at a given point.

Returns:

Type	Description
float	Value from all terms.

nablachem.alchemy.MultiTaylor.query_detail(output, **kwargs)

Breaks down the Taylor expansion into its monomials.

Parameters:

Name	Type	Description	Default
output	str	The output variable for which this analysis is done.	required

Returns:

Type	Description
dict[tuple[str, int], float]	Keys are the variable names and the exponents, values are the contributions from each monomial.

nablachem.alchemy.MultiTaylor.reset_center(**kwargs)

Sets the expansion center from named arguments for each column.

nablachem.alchemy.MultiTaylor.reset_filter(**kwargs)

Sets the filter for the dataframe from named arguments for each column.

All columns which are not filtered and not outputs are considered to be input coordinates.