jmath package¶

Subpackages¶

Submodules¶

jmath.autodiff module¶

Automatic Differentiation

Examples

>>> from jmath.autodiff import x, y
>>> f = 6*x*y*2 + y + 9
>>> f_prime = f.d(x)
>>> f_prime(x = 2, y = 1)
6

>>> from jmath.autodiff import x, y
>>> f = x*y
>>> grad_f = f.d(x, y)
>>> grad_f(x = 3, y = 2)
Vector(2, 3)

class jmath.autodiff.Function(func, derivatives)¶

Bases: object

Automatic Differentiation Function Object

Parameters

func (Callable) – Represented function.
derivatives (Tuple[Callable]) – Tuple of partial derivatives of the function with respect to function variables. Note that derivatives may be numeric values or functions with built-in operations and Functions.

d(*wrt)¶

Differentiates the function with respect to a variable.

Parameters: wrt (Union[jmath.autodiff.Variable, str]) – The variable to differentiate with respect to.
Return type: Union[jmath.autodiff.Function, jmath.linearalgebra.vectors.Vector]

differentiate(*wrt)¶

Differentiates the function with respect to a variable.

Parameters: wrt (Union[jmath.autodiff.Variable, str]) – The variable to differentiate with respect to.
Return type: Union[jmath.autodiff.Function, jmath.linearalgebra.vectors.Vector]

register(*inputs)¶

Registers inputs to the function.

Parameters: inputs (jmath.autodiff.Function) – Args, the functions to register as inputs.

class jmath.autodiff.Variable(id=None)¶

Bases: jmath.autodiff.Function

Variables for function differentiation.

Parameters: id (str) – Unique identifier string.

differentiate(wrt)¶

Differentiates the function with respect to a variable.

Parameters: wrt (jmath.autodiff.Variable) – The variable to differentiate with respect to.
Return type: int

jmath.autodiff.analyse(f)¶

Automatically analyses the given function and produces a Function object.

Parameters: f (Callable) – The function to analyse
Returns: A differentiable function object representing the given function.
Return type: Function

jmath.complex module¶

Complex form of points.

class jmath.complex.Complex(real, imaginary)¶

Bases: jmath.linearalgebra.vectors.Point

Complex numbers based on vectors.

Parameters

real (float) – Real component of a complex number
imaginary (float) – Imaginary component of a complex number

argument()¶

Computes the argument of the complex number in radians.

Return type: float

imaginary()¶: Returns the imaginary component of the complex number.

modulus()¶

Rename of magnitude.

Return type: float

quadrant()¶

Returns which quadrant the number is in. Returns None if on a quadrant border.

Return type: Optional[int]

real()¶: Returns the real component of the complex number.

jmath.discrete module¶

jmath/discrete.py

Discrete mathematical tools.

class jmath.discrete.Graph¶

Bases: object

Graph object defined by a set of nodes.

add_nodes(*nodes)¶

Adds node/s to the graph

Parameters: *nodes – Graph nodes to be added.

get_node(id)¶

Returns a node object in the graph based upon its ID. Returns None if not found.

Parameters: id – The ID of the node
Return type: Optional[jmath.discrete.Node]

intersections()¶

Returns a list of nodes that have more than one connection

Return type: List[jmath.discrete.Node]

loops()¶

Finds loops in the graph

Return type: List[jmath.discrete.Loop]

relationships()¶

Prints a human readable description of the relationship between all nodes

Return type: str

walk(start, stop=None, neighbour=0, default_neighbour=0)¶

“Walks” a loop around the graph, intended for generating loops for self.loops()

Parameters

start (jmath.discrete.Node) – Node the walk starts at.
stop (Optional[jmath.discrete.Node]) – Node the walk stops at.
neighbour (int) – Initial neighbour to move to.
default_neighbour (int) – Neighbour to move to on consequential moves.

Return type

jmath.discrete.Loop

class jmath.discrete.Loop(nodes)¶

Bases: jmath.discrete.Graph

A sub-graph structure generated by Graph.loops(), represents a distinct path around the graph.

Parameters: nodes (List[jmath.discrete.Node]) – List of node objects that define the loop.

relationships()¶

Prints a human readable representation of the relationship between nodes

Return type: str

reorder(node)¶

Reorders the loop to start at the specified node.

Parameters: node (jmath.discrete.Node) – Node to reconfigure to start at.

class jmath.discrete.Node(id, weight=1)¶

Bases: object

Node of a graph.

Parameters

id (str) – Unique ID string describing the object.
weight (float) – Weighting of node.

add_neighbour(neighbour, weight=1, two_way=False)¶

Adds a neighbouring node

Parameters

neighbour (jmath.discrete.Node) – Node object describing the neighbour.
weight (float) – The weighting of the relationship.
two_way (bool) – Whether the relationship goes both ways.

neighbours_list()¶

Returns the IDs of the neighbouring nodes

Return type: list

relationships()¶

Returns human readable string of relationships between node and neighbours.

Return type: str

remove_neighbour(neighbour)¶

Removes the relationship between the nodes.

Parameters: neighbour (jmath.discrete.Node) – Node object describing the neighbour node

Notes

Only removes the neighbourship from THIS NODE.

jmath.exceptions module¶

Defines exceptions for jmath.

exception jmath.exceptions.NoConversion(from_unit, to_unit, message='')¶

Bases: Exception

Exception thrown if there is no way to convert between two given units.

Parameters

from_unit (Unit) – The unit to convert from.
to_unit (Unit) – The unit to convert to.
message (str) – Appended additional message

exception jmath.exceptions.OutOfRange(num_input, lower_bound, upper_bound, message='')¶

Bases: Exception

Exception thrown for values that are not within expected bounds.

Parameters

num_input (float) – The input number
lower_bound (float) – The lower boundary
upper_bound (float) – The upper boundary
message (str) – Appended additional message

exception jmath.exceptions.VectorsNotSameSize(message='Operation invalid for vectors of different sizes.')¶

Bases: Exception

Exception thrown for operations on vectors of different sizes

exception jmath.exceptions.ZeroDistance(message='Invalid operation! Zero distance between objects.')¶

Bases: Exception

Exception thrown for calculations with zero distance between objects.

jmath.modular module¶

Tools for modular arithmetic

jmath.modular.extended_gcd(a, b)¶

Recursive extended euclidean algorithm to find the greatest common denominator and its linear combination Returns g, m, n such that gcd(a, b) = g = m*a + n*b

Parameters

a (int) – Number to find the greatest common denominator of with b
b (int) – Number to find the greatest common denominator of with a

Return type

Tuple[int, int, int]

jmath.modular.modular_inverse(a, set_size)¶

Finds the modular inverse of a number in a set.

Parameters

a (int) – The number to find the modular inverse of
set_size (int) – The size of the set to find the inverse in

Return type

Optional[int]

jmath.uncertainties module¶

Provides a class to deal with values with associated uncertainty.

class jmath.uncertainties.Uncertainty(value, uncertainty)¶

Bases: object

A value with an associated uncertainty.

Parameters

value (float) – The value associated with an uncertainty
uncertainty (float) – Uncertainty associated with the value

Examples

>>> Uncertainty(3, 1) + Uncertainty(4, 2)
Uncertainty(7, 3)

>>> Uncertainty(10, 1) - Uncertainty(2, 1)
Uncertainty(8, 2)

>>> 2 * Uncertainty(2, 1)
Uncertainty(4, 2.0)

>>> Uncertainty(2, 1) + Uncertainty(4, 1)
Uncertainty(8, 6.0)

>>> Uncertainty(20, 2) / Uncertainty(2, 0.5)
Uncertainty(10.0, 3.5)

abs_uncertainty()¶

Returns the absolute uncertainty.

Return type: float

apply(func, *args)¶

Applies a mathematical function to the value using the bruteforce method to calculate the new uncertainty.

Parameters

func (Callable[[float], float]) – The function to apply.
args – Additional arguments to send to the function.

Return type

jmath.uncertainties.Uncertainty

rel_uncertainty()¶

Returns the relative uncertainty as proportion.

Return type: float

jmath.uncertainties.half_range(data)¶

Calculates the absolute uncertainty associated with a set of data.

Parameters: data (List[float]) – List/tuple of the data
Return type: float

jmath.uncertainties.mean(data)¶

Calculates the mean of a set of data and it’s uncertainty by the half range rule.

Parameters: data (List[float]) – List/tuple of data to take the mean of.
Return type: jmath.uncertainties.Uncertainty

Module contents¶

The jmath top level package. Provides a set of default and optional sub-packages for doing maths in Python.

Testing¶

Testing can be performed upon the entire jmath codebase using

$ pytest

when in the jmath root directory.

Documentation¶

Upon addition of a new sub-module the documentation must be updated with

$ sphinx-apidoc -o ./docs/source/ ./jmath –force

when in the jmath root directory.

Documentation is automatically built by a workflow in github and published to https://jmath.jordanhay.com/