The Vector Class

Vec

Bases: ndarray

A simple class to manipulate vectors in mouette. Basically, it inherits from a numpy array and implements some quality of life features for 2D and 3D vectors especially.

x: float property writable

First coordinate of the vector

Returns:

Name	Type	Description
float	float	vec[0]

xy property

First two coordinates of the vector

Returns:

Name	Type	Description
float		vec[:2]

y property writable

Second coordinate of the vector

Returns:

Name	Type	Description
float		vec[1]

z property writable

Third coordinate of the vector

Returns:

Name	Type	Description
float		vec[3]

X() classmethod

The [1,0,0] vector

Returns:

Name	Type	Description
Vec		[1,0,0]

Y() classmethod

The [0,1,0] vector

Returns:

Name	Type	Description
Vec		[0,1,0]

Z() classmethod

The [0,0,1] vector

Returns:

Name	Type	Description
Vec		[0,0,1]

dot(other)

Dot product between two vectors:

$ a \cdot b = \sum_i a[i]b[i]$

Parameters:

Name	Type	Description	Default
other	Vec	other vector to dot with	required

Returns:

Name	Type	Description
float	float	the dot product

from_complex(c) classmethod

2D vector from complex number

Parameters:

Name	Type	Description	Default
c	complex		required

Returns:

Name	Type	Description
Vec		Vec(c.real, c.imag)

norm(which='l2')

Vector norm. Three norms are implemented: the Euclidean l2 norm, the l1 norm or the l-infinite norm:

l2 : $ \sqrt{ \sum_i v[i]^2 } $

l1 : $ \sum_i |v[i]| $

linf : $ \max_i |v[i]| $

Parameters:

Name	Type	Description	Default
which	str	which norm to compute. Choices are "l2", "l1" and "linf". Defaults to "l2".	'l2'

Returns:

Name	Type	Description
float	float	the vector's norm

normalize(which='l2')

Normalizes the vector to have unit norm.

Parameters:

Name	Type	Description	Default
which	str	which norm to compute. Choices are "l2", "l1" and "linf". Defaults to "l2".	'l2'

normalized(vec, which='l2') staticmethod

Computes and returns a normalized vector of the input vector vec.

Parameters:

Name	Type	Description	Default
vec	Vec	the input vector	required
which	str	which norm to compute. Choices are "l2", "l1" and "linf". Defaults to "l2".	'l2'

Returns:

Name	Type	Description
Vec		the normalized vector

outer(other)

Outer product between two vectors:

\(a \otimes b = c \in \mathbb{R}^{n \times n}\) such that \(c[i,j] = a[i]b[j]\).

Parameters:

Name	Type	Description	Default
other	Vec	the second vector	required

Returns:

Type	Description
ndarray	np.array: an array of shape (n,n)

random(n) classmethod

Generates a random vector of size n with coefficients sampled uniformly and independently in [0;1)

Parameters:

Name	Type	Description	Default
n	int	size	required

Returns:

Name	Type	Description
Vec

zeros(n) classmethod

Generates a vector of size n full of zeros.

Parameters:

Name	Type	Description	Default
n	int	size	required

Returns:

Name	Type	Description
Vec