vector

mypackage.vector.vector

This module contains the Vector class and the NormError exception.

Attributes:

Name	Type	Description
MAX_NORM	float	Maximum norm allowed for a Vector instance.

Note

Imports should follow always the same order: import python_standard_library

import third_party_libraries

import local_librariess

NormError(norm)

Bases: ValueError

Exception raised when a vector's norm is greater than MAX_NORM.

Note

Custom exception classes are very useful for exception handling.

Parameters:

Name	Type	Description	Default
norm	float	The norm of the vector.	required

Attributes:

Name	Type	Description
message	str	The message to display when the exception is raised.

Source code in mypackage/vector/vector.py

def __init__(self, norm: float) -> None:
    message = f"Norm = {norm}, but it cannot be greater than {MAX_NORM}."
    super().__init__(message)

Vector(x, y)

Two dimensional vector.

Note

Remember that class docstrings in Google format should contain the arguments of the init method and the attributes of the class, but not the methods.

Parameters:

Name	Type	Description	Default
x	float	first component of the vector.	required
y	float	second component of the vector.	required

Attributes:

Name	Type	Description
x	float	first component of the vector.
y	float	second component of the vector.

Raises:

Type	Description
NormError	the norm of the vector is greater than MAX_NORM.

Source code in mypackage/vector/vector.py

def __init__(self, x: float, y: float) -> None:
    self.x: float = x
    self.y: float = y

    if self.norm > MAX_NORM:
        raise NormError(self.norm)

norm: float property

Returns the Euclidean norm of the vector.

Note

Since the method doesn't accept any input, we can treat it as an attribute. To do that we just have to add the @property decorator on top of the method.

Returns:

Name	Type	Description
float	float	the euclidean norm of the vector.

Examples:

>>> vector = Vector(1,0)
>>> vector.norm
1.0

__add__(other_vector)

Returns the addition vector of self and the other vector.

Parameters:

Name	Type	Description	Default
other_vector	Vector	Other vector (right hand side).	required

Raises:

Type	Description
TypeError	Not Vector passed in.

Returns:

Type	Description
Vector	The addition vector of self and the other vector.

Examples:

>>> Vector(1, 0) + Vector(0, 1)
Vector(1, 1)

Source code in mypackage/vector/vector.py

def __add__(self, other_vector: Vector) -> Vector:
    """Returns the addition vector of self and the other vector.

    Args:
        other_vector: Other vector (right hand side).

    Raises:
        TypeError: Not Vector passed in.

    Returns:
        The addition vector of self and the other vector.

    Examples:

        >>> Vector(1, 0) + Vector(0, 1)
        Vector(1, 1)

    """
    if not isinstance(other_vector, Vector):
        raise TypeError("You must pass in a Vector instance!")
    x = self.x + other_vector.x
    y = self.y + other_vector.y
    return Vector(x, y)

__eq__(other_vector)

Check if the vectors have the same values up to some tolerance.

Parameters:

Name	Type	Description	Default
other_vector	object	Other vector (right hand side).	required

Returns:

Type	Description
bool	True, if both vectors have the same values.
bool	False, else.

Examples:

>>> Vector(1, 0) == Vector(2, 0)
False

Source code in mypackage/vector/vector.py

def __eq__(self, other_vector: object) -> bool:
    """Check if the vectors have the same values up to some tolerance.

    Args:
        other_vector: Other vector (right hand side).

    Returns:
        True, if both vectors have the same values.
        False, else.

    Examples:

        >>> Vector(1, 0) == Vector(2, 0)
        False

    """
    if not isinstance(other_vector, Vector):
        return False
    # math.isclose returns true if the numbers are equal up to a small error
    equal_x: bool = math.isclose(self.x, other_vector.x, abs_tol=1e-10)
    equal_y: bool = math.isclose(self.y, other_vector.y, abs_tol=1e-10)
    return equal_x and equal_y

__mul__(other)

Return the multiplication of self and the other vector/number.

Parameters:

Name	Type	Description	Default
other	Vector | float	Other vector or scalar value (right hand side).	required

Raises:

Type	Description
TypeError	Not int/float passed in.

Returns:

Type	Description
Vector | float	The multiplication of self and the other vector/number.

Examples:

>>> Vector(1, 0) * 4
Vector(4, 0)

>>> Vector(1, 0) * Vector(1, 1)
1

Source code in mypackage/vector/vector.py

def __mul__(self, other: Vector | float) -> Vector | float:
    """Return the multiplication of self and the other vector/number.

    Args:
        other: Other vector or scalar value (right hand side).

    Raises:
        TypeError: Not int/float passed in.

    Returns:
        The multiplication of self and the other vector/number.

    Examples:

        >>> Vector(1, 0) * 4
        Vector(4, 0)

        >>> Vector(1, 0) * Vector(1, 1)
        1

    """
    if isinstance(other, Vector):
        return self.x * other.x + self.y * other.y

    if not isinstance(other, int | float):
        raise TypeError("You must pass in an int/float!")

    return Vector(self.x * other, self.y * other)

__repr__()

Return the vector representation.

Note

The idea behind representations is that, when we execute the output of this function, we should create an identical copy of this object.

Returns:

Type	Description
str	The representation of the vector.

Examples:

We type the following to output the vector representation:

>>> vector = Vector(1, 2)
>>> vector
Vector(1, 2)

Source code in mypackage/vector/vector.py

def __repr__(self) -> str:
    """Return the vector representation.

    Note:
        The idea behind representations is that, when we execute the output of this
        function, we should create an identical copy of this object.

    Returns:
        The representation of the vector.

    Examples:
        We type the following to output the vector representation:

        >>> vector = Vector(1, 2)
        >>> vector
        Vector(1, 2)

    """
    return f"Vector({self.x}, {self.y})"

__str__()

This method is called when we want to print our vector as a string.

Returns:

Type	Description
str	The vector instance as a string.

Examples:

To call str simply type

>>> vector = Vector(1, 2)
>>> print(vector)
(1, 2)

Source code in mypackage/vector/vector.py

def __str__(self) -> str:
    """This method is called when we want to print our vector as a string.

    Returns:
        The vector instance as a string.

    Examples:
        To call __str__ simply type

        >>> vector = Vector(1, 2)
        >>> print(vector)
        (1, 2)

    """
    return f"({self.x}, {self.y})"

projection(subspace=None)

By default projects the vector onto its first component. If a vector spanning a subspace is given, then the vector is projected along this subspace.

Parameters:

Name	Type	Description	Default
subspace	Vector	vector that spans the subspace onto which to project the vector. Defaults to None.	None

Returns:

Name	Type	Description
Vector	Vector	The projected vector.

Examples:

>>> Vector(1,1).projection(Vector(0,1))
Vector(0.0, 1.0)

Source code in mypackage/vector/vector.py

def projection(self, subspace: Vector | None = None) -> Vector:
    """By default projects the vector onto its first component. If a vector spanning
    a subspace is given, then the vector is projected along this subspace.

    Args:
        subspace (Vector, optional): vector that spans the subspace onto which to project
            the vector. Defaults to None.

    Returns:
        Vector: The projected vector.

    Examples:
        >>> Vector(1,1).projection(Vector(0,1))
        Vector(0.0, 1.0)

    """
    if subspace is None:
        warnings.warn(
            "No subspace given: the vector is projected onto the first component!", stacklevel=2
        )
        return Vector(self.x, 0)
    else:
        # Note that self is the instance of the Vector class
        projection_coef: float = (subspace * self) / subspace.norm**2
        return subspace * projection_coef