<｜begin▁of▁sentence｜>### Instruction:
Given two matrices X (e.g., represented as a list of positions of vertices in graph X) and Y (the corresponding positions in graph Y), can you use OrthogonalProcrustes in graspologic to find an orthogonal matrix that most closely maps X to Y and then apply this transformation to X? Print the transformed X, the orthogonal matrix, and the objective function score.
### Response:
import numpy as np
from graspologic.align import OrthogonalProcrustes

# Sample data
X = np.array([[0, 0], [1, 0], [1, 1]])
Y = np.array([[0, 1], [0, 2], [1, 2]])

# Instantiate OrthogonalProcrustes
ortho = OrthogonalProcrustes()

# Fit the model
ortho.fit(X, Y)

# Transform the dataset
X_prime = ortho.transform(X)

# The dataset after transformation
print('Transformed X:', X_prime)

# The orthogonal matrix
print('Orthogonal matrix Q:', ortho.Q_array_)

# The final score
print('Objective function score:', ortho.score_)
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