In [2]:
# 1D
v1 = np.array([1.3])
v2 = np.array([3.6])
alpha = [0.1, 0.3, 0.8, 0.444]
interpolate_two_vectors(v1, v2, alpha, visualize=True)
Out[2]:
array([[1.53 ],
[1.99 ],
[3.14 ],
[2.3212]])
import numpy as np
import matplotlib.pyplot as plt
from typing import List
def interpolate_two_vectors(
v1: np.ndarray,
v2: np.ndarray,
alpha: List[float],
visualize: bool = False
) -> np.ndarray:
dash = "--"
black = "black"
gray = "gray"
red = "red"
data_legend = "data"
interpolated_legend = "interpolated"
interpolations = []
for a in alpha:
interpolation = v1 * (1 - a) + v2 * a
interpolations.append(interpolation)
if visualize is True:
_, axes = plt.subplots(
figsize=(len(alpha) * 5, 5),
nrows=1,
ncols=len(alpha),
subplot_kw={"projection": "3d"} if v1.size == 3 else None
)
axes_iter = [axes]
if len(alpha) > 1:
axes_iter = axes.flatten()
for a, interpolation, ax in zip(alpha, interpolations, axes_iter):
if interpolation.size == 1:
ax.plot([v1[0], v2[0]], [0, 0], gray, linestyle=dash)
ax.scatter(x=[v1[0], v2[0]], y=[0, 0], color=black, label=data_legend)
ax.scatter(x=[interpolation], y=[0], color=red, label=interpolated_legend)
ax.legend(loc="upper left")
ax.set_yticks([])
elif interpolation.size == 2:
ax.plot([v1[0], v2[0]], [v1[1], v2[1]], gray, linestyle=dash)
ax.scatter(x=[v1[0], v2[0]], y=[v1[1], v2[1]], color=black, label=data_legend)
ax.scatter(x=[interpolation[0]], y=[interpolation[1]], color=red, label=interpolated_legend)
ax.legend(loc="upper left")
ax.grid(True)
elif interpolation.size == 3:
ax.plot([v1[0], v2[0]], [v1[1], v2[1]], [v1[2], v2[2]], gray, linestyle=dash)
ax.scatter(xs=[v1[0], v2[0]], ys=[v1[1], v2[1]], zs=[v1[2], v2[2]], color=black, label=data_legend)
ax.scatter(xs=[v2[0]], ys=[v2[1]], zs=[v2[2]], color=black) # FIXME
ax.scatter(xs=[interpolation[0]], ys=[interpolation[1]], zs=[interpolation[2]], color=red, label=interpolated_legend)
ax.set_proj_type("ortho")
ax.legend(loc="upper left")
else:
return np.array(interpolations)
ax.set_title(f"alpha = {a:.3f} \n")
plt.show()
return np.array(interpolations)
# 1D
v1 = np.array([1.3])
v2 = np.array([3.6])
alpha = [0.1, 0.3, 0.8, 0.444]
interpolate_two_vectors(v1, v2, alpha, visualize=True)
array([[1.53 ],
[1.99 ],
[3.14 ],
[2.3212]])
# 2D
v1 = np.array([-1.3, -2.5])
v2 = np.array([2.7, -1.5])
alpha = [0.45, 0.6, 0.1, 0.333]
interpolate_two_vectors(v1, v2, alpha, visualize=True)
array([[ 0.5 , -2.05 ],
[ 1.1 , -1.9 ],
[-0.9 , -2.4 ],
[ 0.032, -2.167]])
# 3D
v1 = np.array([0, 1, 1])
v2 = np.array([-0.5, 1.2, 1])
alpha = [0.333, 0.15, 0.75, 0.9]
interpolate_two_vectors(v1, v2, alpha, visualize=True)
array([[-0.1665, 1.0666, 1. ],
[-0.075 , 1.03 , 1. ],
[-0.375 , 1.15 , 1. ],
[-0.45 , 1.18 , 1. ]])
# 4D or higher
import torch
import torch.nn as nn
# 32D
embeddings = nn.Embedding(2, 32)
v1 = embeddings(torch.tensor(0)).detach().numpy()
v2 = embeddings(torch.tensor(1)).detach().numpy()
alpha = [0.1, 0.5, 0.3, 0.2]
interpolate_two_vectors(v1, v2, alpha)
array([[ 7.62077093e-01, 1.29124343e+00, -6.84361160e-01,
-6.09649599e-01, -7.65964389e-01, -3.06535691e-01,
6.12711608e-01, 2.79399157e-01, 1.68153480e-01,
9.98653054e-01, -1.31590456e-01, -1.05776930e+00,
1.79577875e+00, -1.15841627e-03, -1.77378619e+00,
9.12473500e-01, 4.86587971e-01, -2.81786114e-01,
3.54215235e-01, -2.52348840e-01, 1.63696659e+00,
2.16303170e-01, -1.52252555e-01, 2.66019274e-02,
1.65617436e-01, 3.78290117e-01, -4.09932286e-01,
-1.19273856e-01, 3.98346931e-01, 2.52125412e-03,
7.34829307e-01, -2.54885375e-01],
[ 8.97734404e-01, 9.41371381e-01, -4.57736671e-01,
-1.02721095e+00, -5.21048546e-01, -3.03166986e-01,
8.73824835e-01, -4.12713766e-01, 4.51726988e-02,
7.84583569e-01, 9.73793343e-02, -9.31152463e-01,
1.55066681e+00, -2.34261766e-01, -5.64054489e-01,
6.25203848e-01, -8.09468925e-02, 1.10932827e-01,
1.83162302e-01, 9.39750910e-01, 9.19896305e-01,
-3.50714564e-01, -7.96270013e-01, 2.55016714e-01,
1.68526575e-01, 9.25441086e-01, -2.15743989e-01,
6.38548195e-01, 4.77876663e-01, 2.96972662e-01,
-2.15541422e-01, -5.91558993e-01],
[ 8.29905748e-01, 1.11630738e+00, -5.71048915e-01,
-8.18430305e-01, -6.43506467e-01, -3.04851353e-01,
7.43268251e-01, -6.66573048e-02, 1.06663086e-01,
8.91618371e-01, -1.71055645e-02, -9.94460881e-01,
1.67322278e+00, -1.17710099e-01, -1.16892028e+00,
7.68838704e-01, 2.02820539e-01, -8.54266137e-02,
2.68688768e-01, 3.43701065e-01, 1.27843153e+00,
-6.72056973e-02, -4.74261314e-01, 1.40809327e-01,
1.67071998e-01, 6.51865602e-01, -3.12838137e-01,
2.59637207e-01, 4.38111812e-01, 1.49746954e-01,
2.59643942e-01, -4.23222154e-01],
[ 7.95991480e-01, 1.20377541e+00, -6.27705038e-01,
-7.14039981e-01, -7.04735398e-01, -3.05693507e-01,
6.77989900e-01, 1.06370956e-01, 1.37408286e-01,
9.45135772e-01, -7.43480250e-02, -1.02611506e+00,
1.73450077e+00, -5.94342537e-02, -1.47135329e+00,
8.40656161e-01, 3.44704270e-01, -1.83606386e-01,
3.11452001e-01, 4.56760824e-02, 1.45769906e+00,
7.45487362e-02, -3.13256919e-01, 8.37056264e-02,
1.66344732e-01, 5.15077889e-01, -3.61385226e-01,
7.01816529e-02, 4.18229371e-01, 7.61341006e-02,
4.97236609e-01, -3.39053750e-01]], dtype=float32)