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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:
 Analyzing the flexible path length simulation
Step1:  Load the file, and from the file pull our the engine (which tells us what the timestep was) and the move scheme (which gives us a starting point for much of the analysis).
Step2:  That tell us a little about the file we're dealing with. Now we'll start analyzing the contents of that file. We used a very simple move scheme (only shooting), so the main information that the move_summary gives us is the acceptance of the only kind of move in that scheme. See the MSTIS examples for more complicated move schemes, where you want to make sure that frequency at which the move runs is close to what was expected.
Step3:  Replica history tree and decorrelated trajectories
The ReplicaHistoryTree object gives us both the history tree (often called the "move tree") and the number of decorrelated trajectories.
A ReplicaHistoryTree is made for a certain set of Monte Carlo steps. First, we make a tree of only the first 25 steps in order to visualize it. (All 10000 steps would be unwieldy.) 
After the visualization, we make a second PathTree of all the steps. We won't visualize that; instead we use it to count the number of decorrelated trajectories.
Step4:  Path length distribution
Flexible length TPS gives a distribution of path lengths. Here we calculate the length of every accepted trajectory, then histogram those lengths, and calculate the maximum and average path lengths.
We also use engine.snapshot_timestep to convert the count of frames to time, including correct units.
Step5:  Path density histogram
Next we will create a path density histogram. Calculating the histogram itself is quite easy
Step6:  Now we've built the path density histogram, and we want to visualize it. We have a convenient plot_2d_histogram function that works in this case, and takes the histogram, desired plot tick labels and limits, and additional matplotlib named arguments to plt.pcolormesh.
Step7:  Convert to MDTraj for analysis by external tools
The trajectory can be converted to an MDTraj trajectory, and then used anywhere that MDTraj can be used. This includes writing it to a file (in any number of file formats) or visualizing the trajectory using, e.g., NGLView.
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Python Code:
from __future__ import print_function
%matplotlib inline
import openpathsampling as paths
import numpy as np
import matplotlib.pyplot as plt
import os
import openpathsampling.visualize as ops_vis
from IPython.display import SVG
Explanation: Analyzing the flexible path length simulation
End of explanation
# note that this log will overwrite the log from the previous notebook
#import logging.config
#logging.config.fileConfig("logging.conf", disable_existing_loggers=False)
%%time
flexible = paths.AnalysisStorage("ad_tps.nc")
# opening as AnalysisStorage is a little slower, but speeds up the move_summary
engine = flexible.engines[0]
flex_scheme = flexible.schemes[0]
print("File size: {0} for {1} steps, {2} snapshots".format(
    flexible.file_size_str,
    len(flexible.steps),
    len(flexible.snapshots)
))
Explanation: Load the file, and from the file pull our the engine (which tells us what the timestep was) and the move scheme (which gives us a starting point for much of the analysis).
End of explanation
flex_scheme.move_summary(flexible.steps)
Explanation: That tell us a little about the file we're dealing with. Now we'll start analyzing the contents of that file. We used a very simple move scheme (only shooting), so the main information that the move_summary gives us is the acceptance of the only kind of move in that scheme. See the MSTIS examples for more complicated move schemes, where you want to make sure that frequency at which the move runs is close to what was expected.
End of explanation
replica_history = ops_vis.ReplicaEvolution(replica=0)
tree = ops_vis.PathTree(
    flexible.steps[0:25],
    replica_history
)
tree.options.css['scale_x'] = 3
SVG(tree.svg())
# can write to svg file and open with programs that can read SVG
with open("flex_tps_tree.svg", 'w') as f:
    f.write(tree.svg())
print("Decorrelated trajectories:", len(tree.generator.decorrelated_trajectories))
%%time
full_history = ops_vis.PathTree(
    flexible.steps,
    ops_vis.ReplicaEvolution(
        replica=0
    )
)
n_decorrelated = len(full_history.generator.decorrelated_trajectories)
print("All decorrelated trajectories:", n_decorrelated)
Explanation: Replica history tree and decorrelated trajectories
The ReplicaHistoryTree object gives us both the history tree (often called the "move tree") and the number of decorrelated trajectories.
A ReplicaHistoryTree is made for a certain set of Monte Carlo steps. First, we make a tree of only the first 25 steps in order to visualize it. (All 10000 steps would be unwieldy.) 
After the visualization, we make a second PathTree of all the steps. We won't visualize that; instead we use it to count the number of decorrelated trajectories.
End of explanation
path_lengths = [len(step.active[0].trajectory) for step in flexible.steps]
plt.hist(path_lengths, bins=40, alpha=0.5);
print("Maximum:", max(path_lengths), 
      "("+(max(path_lengths)*engine.snapshot_timestep).format("%.3f")+")")
print ("Average:", "{0:.2f}".format(np.mean(path_lengths)),
       "("+(np.mean(path_lengths)*engine.snapshot_timestep).format("%.3f")+")")
Explanation: Path length distribution
Flexible length TPS gives a distribution of path lengths. Here we calculate the length of every accepted trajectory, then histogram those lengths, and calculate the maximum and average path lengths.
We also use engine.snapshot_timestep to convert the count of frames to time, including correct units.
End of explanation
from openpathsampling.numerics import HistogramPlotter2D
psi = flexible.cvs['psi']
phi = flexible.cvs['phi']
deg = 180.0 / np.pi
path_density = paths.PathDensityHistogram(cvs=[phi, psi],
                                          left_bin_edges=(-180/deg,-180/deg),
                                          bin_widths=(2.0/deg,2.0/deg))
path_dens_counter = path_density.histogram([s.active[0].trajectory for s in flexible.steps])
Explanation: Path density histogram
Next we will create a path density histogram. Calculating the histogram itself is quite easy: first we reload the collective variables we want to plot it in (we choose the phi and psi angles). Then we create the empty path density histogram, by telling it which CVs to use and how to make the histogram (bin sizes, etc). Finally, we build the histogram by giving it the list of active trajectories to histogram.
End of explanation
tick_labels = np.arange(-np.pi, np.pi+0.01, np.pi/4)
plotter = HistogramPlotter2D(path_density, 
                             xticklabels=tick_labels,
                             yticklabels=tick_labels, 
                             label_format="{:4.2f}")
ax = plotter.plot(cmap="Blues")
Explanation: Now we've built the path density histogram, and we want to visualize it. We have a convenient plot_2d_histogram function that works in this case, and takes the histogram, desired plot tick labels and limits, and additional matplotlib named arguments to plt.pcolormesh.
End of explanation
ops_traj = flexible.steps[1000].active[0].trajectory
traj = ops_traj.to_mdtraj()
traj
# Here's how you would then use NGLView:
#import nglview as nv
#view = nv.show_mdtraj(traj)
#view
flexible.close()
Explanation: Convert to MDTraj for analysis by external tools
The trajectory can be converted to an MDTraj trajectory, and then used anywhere that MDTraj can be used. This includes writing it to a file (in any number of file formats) or visualizing the trajectory using, e.g., NGLView.
End of explanation
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