<｜begin▁of▁sentence｜>### Instruction:
Imagine our client's organization is currently undergoing a strategic overhaul with the objective of enhancing their operational efficiency. They've put forward a business transformation blueprint represented by two sets of coordinates: the existing operational framework denoted as matrix X and the proposed future state framework represented as matrix Y. Each matrix illustrates respective positions of crucial operational touchpoints within the organizational structure.

Our task as management consultants is to devise a mathematically sound and optimally aligned transformation strategy, essentially an blueprint that realigns the current operations (X) to match the envisaged future state (Y) as closely as possible. This transformation must preserve the relational geometry of the operational touchpoints, meaning it has to be orthogonal.

For this purpose, we'll enlist the `OrthogonalProcrustes` function from the graspologic library. This powerful tool will aid us in computing the orthogonal matrix - let's refer to it as the realignment matrix - which will map the current operational framework X onto the new, desired framework Y with maximum fidelity.

To exemplify this: if the current state X consists of vertices at positions [(1, 3), (2, 5), ...] and the future state Y consists of vertices at positions [(4, 6), (7, 3), ...], our aim is to apply the `OrthogonalProcrustes` analysis to these data points. Upon doing so, we'll present our findings to the client including the optimized realignment matrix, the transformed coordinates of X after applying this matrix, and the score of the objective function, which quantifies how well the transformation aligns X to Y.

In conclusion, our deliverables will articulate the strategic realignment in a quantifiable and executable manner, ensuring that the client's blueprint for transformation is not only visionary but also firmly rooted in analytical precision.
### 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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