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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 This example demonstrates one possible way to cluster data sets that are too large to fit into memory using MDTraj and scipy.cluster. The idea for the algorithim is that we'll cluster every N-th frame directly, and then, considering the clusters fixed "assign" the remaining frames to the nearest cluster. It's not the most sophisticated algorithm, but it's a good demonstration of how MDTraj can be integrated with other data science tools.
Step1:  Compute the pairwise RMSD between all of the frames. This requires
N^2 memory, which is why we might need to stride.
Step2:  Now that we have the distances, we can use out favorite clustering
algorithm. I like ward.
Step3:  Now, we need to extract n_leaders random samples from each of the clusters.
One way to do this is by building a map from each of the cluster labels
to the list of the indices of the subsampled confs which belong to it.
Step4:  Now we can iterate through the mapping and select n_leaders random
samples from each list. As we select them, we'll extract the
conformation and append it to a new trajectory called leaders, which
will start empty.
Step5:  Now our leaders trajectory contains a set of representitive conformations
for each cluster. Here comes the second pass of the two-pass clustering.
Let's now consider these clusters as fixed objects and iterate through
every frame in our data set, assigning each frame to the cluster
it's closest to. We take the simple approach here of computing the distance
from each frame to each leader and assigning the frame to the cluster whose
leader is closest.
Note that this whole algorithm never requires having the entire
dataset in memory at once
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Python Code:
from __future__ import print_function
import random
from collections import defaultdict
import mdtraj as md
import numpy as np
import scipy.cluster.hierarchy
stride = 5
subsampled = md.load('ala2.h5', stride=stride)
print(subsampled)
Explanation: This example demonstrates one possible way to cluster data sets that are too large to fit into memory using MDTraj and scipy.cluster. The idea for the algorithim is that we'll cluster every N-th frame directly, and then, considering the clusters fixed "assign" the remaining frames to the nearest cluster. It's not the most sophisticated algorithm, but it's a good demonstration of how MDTraj can be integrated with other data science tools.
End of explanation
distances = np.empty((subsampled.n_frames, subsampled.n_frames))
for i in range(subsampled.n_frames):
    distances[i] = md.rmsd(subsampled, subsampled, i)
Explanation: Compute the pairwise RMSD between all of the frames. This requires
N^2 memory, which is why we might need to stride.
End of explanation
n_clusters = 3
linkage = scipy.cluster.hierarchy.ward(distances)
labels = scipy.cluster.hierarchy.fcluster(linkage, t=n_clusters, criterion='maxclust')
labels
Explanation: Now that we have the distances, we can use out favorite clustering
algorithm. I like ward.
End of explanation
mapping = defaultdict(lambda : [])
for i, label in enumerate(labels):
    mapping[label].append(i)
mapping
Explanation: Now, we need to extract n_leaders random samples from each of the clusters.
One way to do this is by building a map from each of the cluster labels
to the list of the indices of the subsampled confs which belong to it.
End of explanation
n_leaders_per_cluster = 2
leaders = md.Trajectory(xyz=np.empty((0, subsampled.n_atoms, 3)),
                        topology=subsampled.topology)
leader_labels = []
for label, indices in mapping.items():
    leaders = leaders.join(subsampled[np.random.choice(indices, n_leaders_per_cluster)])
    leader_labels.extend([label] * n_leaders_per_cluster)
print(leaders)
print(leader_labels)
Explanation: Now we can iterate through the mapping and select n_leaders random
samples from each list. As we select them, we'll extract the
conformation and append it to a new trajectory called leaders, which
will start empty.
End of explanation
labels = []
for frame in md.iterload('ala2.h5', chunk=1):
    labels.append(leader_labels[np.argmin(md.rmsd(leaders, frame, 0))])
labels = np.array(labels)
print(labels)
print(labels.shape)
Explanation: Now our leaders trajectory contains a set of representitive conformations
for each cluster. Here comes the second pass of the two-pass clustering.
Let's now consider these clusters as fixed objects and iterate through
every frame in our data set, assigning each frame to the cluster
it's closest to. We take the simple approach here of computing the distance
from each frame to each leader and assigning the frame to the cluster whose
leader is closest.
Note that this whole algorithm never requires having the entire
dataset in memory at once
End of explanation
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