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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:
 Using OPSPiggybacker to stub in test data for analysis
One of the main uses of OPSPiggybacker is to make data from one source readable for OPS analysis tools. In this example, we'll create some fake data and use it to do OPS analysis.
Creating the fake dataset
The first stage is, of course, to create our fake data.
We're going to create trajectories which correspond to flexible length shooting moves. The approach we're going to take isn't actually to directly build those trajectories. Instead, we'll take an easier to code, but more roundabout path. It looks like this
Step1:  Now we join the two trajectories together. The approach we use is a little complicated, but the basic idea is this
Step2:  Note, importantly, that the trajectory we'll use as input for the piggybacker is the whole trajectory, not just the segment generated by one-way shooting.
Step3:  OPS objects that must be created
This approach isn't quite as simple as a straightforward file converter, because you still need to create a few OPS objects (Volumes, Ensembles, etc.) -- although you could, in principle, create other converters to automatically generate those.
Now we're going to create those objects.
Step4:  Create the MoveStub and PseudoSimulator
Next we create the objects from OPSPiggybacker. Essentially, this boils down to creating something that can stub in for a move scheme in OPS, and feed back the results of the simulation.
Step5:  Feed the fake data to the PseudoSimulator
Now we actually run this to create our desired .nc file, which should be largely indistinguishable from one created by OPS! This is the primary "production" step of the process.
Step6:  Use OPS analysis tools on the faked data
Finally, let's show that it works
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Python Code:
from openpathsampling.tests.test_helpers import make_1d_traj
left_state_edge = 0.0
right_state_edge = 10.0
def make_traj(suffix, stride=1):
    frame = left_state_edge -1.0 + suffix
    coords = [frame]
    while frame < right_state_edge:
        frame += 1.0*stride
        coords.append(frame)
        
    return make_1d_traj(coords)
traj1 = make_traj(suffix=0.1)
traj2 = make_traj(suffix=0.2, stride=2)
traj3 = make_traj(suffix=0.3, stride=3)
traj4 = make_traj(suffix=0.4, stride=2)
traj5 = make_traj(suffix=0.5, stride=1)
mytrajs = [traj1, traj2, traj3, traj4, traj5]
for traj in mytrajs:
    plt.plot([s.xyz[0][0] for s in traj], 'o')
    plt.plot([0.0]*13, 'r')
    plt.plot([10.0]*13, 'r')
Explanation: Using OPSPiggybacker to stub in test data for analysis
One of the main uses of OPSPiggybacker is to make data from one source readable for OPS analysis tools. In this example, we'll create some fake data and use it to do OPS analysis.
Creating the fake dataset
The first stage is, of course, to create our fake data.
We're going to create trajectories which correspond to flexible length shooting moves. The approach we're going to take isn't actually to directly build those trajectories. Instead, we'll take an easier to code, but more roundabout path. It looks like this:
Make a bunch of (full) trajectories that satisfy the ensemble, with different strides (to get different pathlength) and different values (to identify which trajectories they came from)
Select shooting points. Join two trajectories prev_traj and new_traj in a way that mimics one-way shooting (details below). The resulting trajectory is the input to the piggybacker.
End of explanation
def join_as_shooting(prev_traj, new_traj, shooting_point, direction):
    sp_index = prev_traj.index(shooting_point)
    if direction == 1:
        prev_seg = prev_traj[:sp_index+1]
        new_seg = [snap for snap in new_traj if snap.xyz[0][0] > shooting_point.xyz[0][0]]
        result = prev_seg + new_seg
    elif direction == -1:
        prev_seg = prev_traj[sp_index:]
        new_seg = [snap for snap in new_traj if snap.xyz[0][0] < shooting_point.xyz[0][0]]
        result = new_seg + prev_seg
    else:
        raise RuntimeError("Bad direction")
    return paths.Trajectory(result)
# simple function to plot the traj and show where the snapshots originated
def simple_plot(traj, origin_trajs):
    plt.plot([s.xyz[0][0] for s in traj], 'k')
    for (otraj, style) in zip(origin_trajs, ['bo', 'go', 'ro', 'co', 'mo']):
        in_style = zip(*[(traj.index(s), s.xyz[0][0]) for s in traj if s in otraj])
        if len(in_style) == 2:
            plt.plot(in_style[0], in_style[1], style)
Explanation: Now we join the two trajectories together. The approach we use is a little complicated, but the basic idea is this:
We give a certain shooting_point: this is a frame from prev_traj
The new_traj finds the first snapshot for which snapshot.xyz[0][0] is on the other side of shooting_point.xyz[0][0], where "other side" means "greater than" if direction==1 or "less than" if direction==-1.
End of explanation
# tuples of shooting point (frame number), direction, and acceptance
sp_index = [4, 4, 6, 5]
directions = [-1, +1, -1, -1]
acceptance = [True, True, False, True]
long_trials = mytrajs[1:]
sp_dir_acc_traj = zip(sp_index, directions, acceptance, long_trials)
#sp_dir_acc_traj = [(4, -1, True, traj2), (4, +1, True, traj3), (6, -1, False, traj4), (5, -1, True, traj5)]
inp_trajs = [traj1]
last_accepted = 0
for i in range(len(sp_dir_acc_traj)):
    move = sp_dir_acc_traj[i]
    prev_traj = inp_trajs[last_accepted]
    sp = move[0]
    direction = move[1]
    accept = move[2]
    long_trial = move[3]
    trial = join_as_shooting(prev_traj, long_trial, prev_traj[sp], direction)
    inp_trajs.append(trial)
    if accept:
        last_accepted = i+1
simple_plot(inp_trajs[0], mytrajs)
simple_plot(inp_trajs[1], mytrajs)
simple_plot(inp_trajs[2], mytrajs)
simple_plot(inp_trajs[3], mytrajs) # REJECTED PATH!
simple_plot(inp_trajs[4], mytrajs)
Explanation: Note, importantly, that the trajectory we'll use as input for the piggybacker is the whole trajectory, not just the segment generated by one-way shooting.
End of explanation
# volumes
cv = paths.FunctionCV("x", lambda snap: snap.xyz[0][0])
left_state = paths.CVDefinedVolume(cv, float("-inf"), 0.0)
right_state = paths.CVDefinedVolume(cv, 10.0, float("inf"))
# network
network = paths.TPSNetwork(left_state, right_state)
ensemble = network.sampling_ensembles[0]  # the only one
Explanation: OPS objects that must be created
This approach isn't quite as simple as a straightforward file converter, because you still need to create a few OPS objects (Volumes, Ensembles, etc.) -- although you could, in principle, create other converters to automatically generate those.
Now we're going to create those objects.
End of explanation
initial_conditions = paths.SampleSet([
        paths.Sample(replica=0,
                     trajectory=inp_trajs[0],
                     ensemble=ensemble)
])
template = initial_conditions[0].trajectory[0]
shoot = oink.ShootingStub(ensemble)
sim = oink.ShootingPseudoSimulator(storage=paths.Storage('pseudoshoot.nc', 'w', template=template),
                                   initial_conditions=initial_conditions,
                                   mover=shoot,
                                   network=network)
Explanation: Create the MoveStub and PseudoSimulator
Next we create the objects from OPSPiggybacker. Essentially, this boils down to creating something that can stub in for a move scheme in OPS, and feed back the results of the simulation.
End of explanation
trial_trajectories = inp_trajs[1:]
replicas = [0]*len(sp_index)
move_inputs = zip(replicas, trial_trajectories, sp_index, acceptance)
for move in move_inputs:
    print move
sim.run(move_inputs)
sim.storage.close()
Explanation: Feed the fake data to the PseudoSimulator
Now we actually run this to create our desired .nc file, which should be largely indistinguishable from one created by OPS! This is the primary "production" step of the process.
End of explanation
analysis_file = paths.AnalysisStorage("pseudoshoot.nc")
scheme = analysis_file.schemes[0]
scheme.move_summary(analysis_file.steps)
import openpathsampling.visualize as ops_vis
from IPython.display import SVG
history = ops_vis.PathTree(
    analysis_file.steps,
    ops_vis.ReplicaEvolution(replica=0)
)
# switch to the "boxcar" look for the trajectories
history.options.movers['default']['new'] = 'single'
history.options.css['horizontal_gap'] = True
SVG(history.svg())
path_lengths = [len(step.active[0].trajectory) for step in analysis_file.steps]
plt.hist(path_lengths, alpha=0.5);
Explanation: Use OPS analysis tools on the faked data
Finally, let's show that it works: we'll load that file and analyze it with the tools we would use for OPS.
End of explanation
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