BF-MATH - Basic Mathematics

Ver. 2.2.3 (2023-05-06)

This module provides basic mathematical classes.

class mlpro.bf.math.basics.Dimension(p_name_short, p_base_set='R', p_name_long='', p_name_latex='', p_unit='', p_unit_latex='', p_boundaries: list = [], p_description='', p_symmetrical: bool = False, p_logging=False, **p_kwargs)

Bases: EventManager

Objects of this type specify properties of a dimension of a set.

Parameters:

p_name_shortstr

Short name of dimension

p_base_set

Base set of dimension. See constants C_BASE_SET_*. Default = C_BASE_SET_R.

p_name_long :str

Long name of dimension (optional)

p_name_latexstr

LaTeX name of dimension (optional)

p_unitstr

Unit (optional)

p_unit_latexstr

LaTeX code of unit (optional)

p_boundarieslist

List with minimum and maximum value (optional)

p_descriptionstr

Description of dimension (optional)

p_symmetricalbool

Information about the symmetry of the dimension (optional, default is False)

p_logging

Log level (see constants of class Log). Default: Log.C_LOG_ALL

p_kwargsdict

Further optional keyword parameters.

C_TYPE = 'Dimension'

C_BASE_SET_R = 'R'

C_BASE_SET_N = 'N'

C_BASE_SET_Z = 'Z'

C_BASE_SET_DO = 'DO'

C_EVENT_BOUNDARIES = 'BOUNDARIES'

get_id()

get_name_short()

get_base_set()

get_name_long()

get_name_latex()

get_unit()

get_unit_latex()

get_boundaries()

set_boundaries(p_boundaries: list)

Sets new boundaries with respect to the symmmetry and raises event C_EVENT_BOUNDARIES.

Parameters:

p_boundaries (list) – New boundaries (lower and upper value)

get_description()

get_symmetrical() → bool

get_kwargs() → dict

copy()

class mlpro.bf.math.basics.Set

Bases: object

Objects of this type describe a (multivariate) set in a mathematical sense.

C_NUMERIC_BASE_SETS = ['N', 'Z', 'R']

add_dim(p_dim: Dimension, p_ignore_duplicates: bool = False)

Raises the dimensionality of the set by adding a new dimension.

Parameters:

• p_dim (Dimension) – Dimension to be added.

• p_ignore_duplicates (bool) – If True, duplicated short names of dimensions are accepted. Default = False.

is_numeric() → bool

Returns True if the set consists of numeric dimensions only.

get_dim(p_id) → Dimension

Returns the dimension specified by it’s unique id.

get_dim_by_name(p_name) → Dimension

get_dims() → list

” Returns all dimensions.

get_num_dim()

Returns the dimensionality of the set (=number of dimensions of the set).

get_dim_ids()

Returns the unique ids of the related dimensions.

spawn(p_id_list: list)

Spawns a new class with same type and a subset of dimensions specified by an index list.

Parameters:

adopted (p_id_list List of indices of dimensions to be)

Returns:

New object with subset of dimensions

copy(p_new_dim_ids: bool = True)

append(p_set, p_new_dim_ids: bool = True, p_ignore_duplicates: bool = False)

class mlpro.bf.math.basics.DataObject(p_data, *p_meta_data)

Bases: object

Container class for (big) data objects of any type with optional additional meta data.

get_data()

get_meta_data() → tuple

class mlpro.bf.math.basics.Element(p_set: Set)

Bases: object

Element of a (multivariate) set.

Parameters:

p_set (Set) – Underlying set.

get_related_set() → Set

set_related_set(p_set: Set)

get_dim_ids() → list

get_values() → list | ndarray

set_values(p_values: list | ndarray)

Overwrites the values of all components of the element.

Parameters:

dimensions. (p_values Something iterable with same length as number of element)

get_value(p_dim_id)

set_value(p_dim_id, p_value)

copy()

class mlpro.bf.math.basics.ElementList

Bases: object

List of Element objects.

add_elem(p_id, p_elem: Element)

Adds an element object under it’s id in the internal element list.

Parameters:

• element (p_id Unique id of the)

• added (p_elem Element object to be)

get_elem_ids() → list

get_elem(p_id) → Element

class mlpro.bf.math.basics.BatchElement(p_set: Set)

Bases: Element

class mlpro.bf.math.basics.MSpace

Bases: Set

Objects of this type represent a metric space. The method distance implements the metric of the space.

distance(p_e1: Element, p_e2: Element)

class mlpro.bf.math.basics.ESpace

Bases: MSpace

Objects of this type represent an Euclidian space. The distance method implements the Euclidian norm.

distance(p_e1: Element, p_e2: Element)

class mlpro.bf.math.basics.Function(p_input_space: ~mlpro.bf.math.basics.MSpace, p_output_space: ~mlpro.bf.math.basics.MSpace, p_output_elem_cls=<class 'mlpro.bf.math.basics.Element'>)

Bases: object

Model class for an elementary bi-multivariate mathematical function that maps elements of a multivariate input space to elements of a multivariate output space.

map(p_input: Element) → Element

Alternative method to map an input to an output. Actually, it refers to method __call__(). Redefining this method has no effect. See method __call__() and constructor for further details.

_map(p_input: Element, p_output: Element)

Custom method for own mapping algorithm. See methods __call__() and map() for further details.