Using mypackage.linearmap¶

Importing¶

In [2]:

from sys import path
from os.path import abspath

# Tell python to search for the files and modules starting from the working directory
module_path = abspath("..")
if module_path not in path:
    path.append(module_path)

from sys import path from os.path import abspath # Tell python to search for the files and modules starting from the working directory module_path = abspath("..") if module_path not in path: path.append(module_path)

Note: If we don't want to be telling Python where to search for our library, we can install it (in editable mode) in our conda environment using

pip install -e .

In [3]:

import numpy as np

from mypackage import Vector, LinearMap, Rotation, Shear

import numpy as np from mypackage import Vector, LinearMap, Rotation, Shear

To make plots, we import matplotlib and adjust the style

In [4]:

import matplotlib.pyplot as plt

plt.style.use("seaborn-whitegrid")

import matplotlib.pyplot as plt plt.style.use("seaborn-whitegrid")

/var/folders/fg/9xcyj6451md237pczr54fr6c0000gn/T/ipykernel_27868/1055582722.py:3: MatplotlibDeprecationWarning: The seaborn styles shipped by Matplotlib are deprecated since 3.6, as they no longer correspond to the styles shipped by seaborn. However, they will remain available as 'seaborn-v0_8-<style>'. Alternatively, directly use the seaborn API instead.
  plt.style.use("seaborn-whitegrid")

Transforming vectors¶

As a first example, we will see what happens if we try to initialize the abstract class LinearMap

In [5]:

matrix = [[1, 0], [1, 2]]
matrix_map = LinearMap(matrix)

matrix = [[1, 0], [1, 2]] matrix_map = LinearMap(matrix)

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In[5], line 2
      1 matrix = [[1, 0], [1, 2]]
----> 2 matrix_map = LinearMap(matrix)

TypeError: Can't instantiate abstract class LinearMap with abstract method _get_inverse

As we can see, since the method _get_inverse() is not defined, the class cannot be instantiated.

On the contrary, there is no problem initializing a Rotation object:

In [9]:

angle = np.pi / 4
rotation = Rotation(angle)

angle = np.pi / 4 rotation = Rotation(angle)

We can see what happens if we apply this rotation and its inverse to a vector

In [10]:

vector = Vector(1, 1)
rot_vector = rotation(vector)
inv_rot_vector = rotation.inverse(vector)

vector = Vector(1, 1) rot_vector = rotation(vector) inv_rot_vector = rotation.inverse(vector)

In [11]:

fig, ax = plt.subplots(figsize=(6, 6))
arrow_kwargs = {
    "width": 0.01,
    "head_width": 0.05,
    "length_includes_head": True,
}
ax.arrow(0, 0, rot_vector.x, rot_vector.y, color="teal", label="rot_vector", **arrow_kwargs)
ax.arrow(0, 0, vector.x, vector.y, color="crimson", label="vector", **arrow_kwargs)
ax.arrow(
    0,
    0,
    inv_rot_vector.x,
    inv_rot_vector.y,
    color="goldenrod",
    label="inv_rot_vector",
    **arrow_kwargs,
)

ax.legend(loc="lower left", fontsize=14)
ax.set_title(r"Rotating a vector an angle $\pi/4$", fontsize=16)
ax.set_xlim(-1.5, 1.5)
ax.set_ylim(-1.5, 1.5)

plt.show()

fig, ax = plt.subplots(figsize=(6, 6)) arrow_kwargs = { "width": 0.01, "head_width": 0.05, "length_includes_head": True, } ax.arrow(0, 0, rot_vector.x, rot_vector.y, color="teal", label="rot_vector", **arrow_kwargs) ax.arrow(0, 0, vector.x, vector.y, color="crimson", label="vector", **arrow_kwargs) ax.arrow( 0, 0, inv_rot_vector.x, inv_rot_vector.y, color="goldenrod", label="inv_rot_vector", **arrow_kwargs, ) ax.legend(loc="lower left", fontsize=14) ax.set_title(r"Rotating a vector an angle $\pi/4$", fontsize=16) ax.set_xlim(-1.5, 1.5) ax.set_ylim(-1.5, 1.5) plt.show()

In a similar fashion, we can apply a shear transformation and its inverse to a vector

In [12]:

angle = np.pi / 4
shear_map = Shear(angle)

vector = Vector(1, 1)
shear_vector = shear_map(vector)
inv_shear_vector = shear_map.inverse(vector)

angle = np.pi / 4 shear_map = Shear(angle) vector = Vector(1, 1) shear_vector = shear_map(vector) inv_shear_vector = shear_map.inverse(vector)

In [13]:

fig, ax = plt.subplots(figsize=(6, 6))
arrow_kwargs = {
    "width": 0.01,
    "head_width": 0.05,
    "length_includes_head": True,
}
ax.arrow(0, 0, shear_vector.x, shear_vector.y, color="teal", label="shear_vector", **arrow_kwargs)
ax.arrow(0, 0, vector.x, vector.y, color="crimson", label="vector", **arrow_kwargs)
ax.arrow(
    0,
    0,
    inv_shear_vector.x,
    inv_shear_vector.y,
    color="goldenrod",
    label="inv_shear_vector",
    **arrow_kwargs,
)

ax.legend(loc="lower left", fontsize=14)
ax.set_title(r"Rotating a vector an angle $\pi/4$", fontsize=16)
ax.set_xlim(-2, 2)
ax.set_ylim(-2, 2)

plt.show()

fig, ax = plt.subplots(figsize=(6, 6)) arrow_kwargs = { "width": 0.01, "head_width": 0.05, "length_includes_head": True, } ax.arrow(0, 0, shear_vector.x, shear_vector.y, color="teal", label="shear_vector", **arrow_kwargs) ax.arrow(0, 0, vector.x, vector.y, color="crimson", label="vector", **arrow_kwargs) ax.arrow( 0, 0, inv_shear_vector.x, inv_shear_vector.y, color="goldenrod", label="inv_shear_vector", **arrow_kwargs, ) ax.legend(loc="lower left", fontsize=14) ax.set_title(r"Rotating a vector an angle $\pi/4$", fontsize=16) ax.set_xlim(-2, 2) ax.set_ylim(-2, 2) plt.show()