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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 the trained weights in an ensemble of neurons
On the function points branch of nengo
On the vision branch of nengo_extras
Step1:  Load the MNIST database
Step2:  Each digit is represented by a one hot vector where the index of the 1 represents the number
Step3:  Load the saved weight matrices that were created by trainging the model
Step4:  The network where the mental imagery and scaling occurs
The state, seed and ensemble parameters (including encoders) must all be the same for the saved weight matrices to work
The number of neurons (n_hid) must be the same as was used for training
The input must be shown for a short period of time to be able to view the scaling
The recurrent connection must be from the neurons because the weight matices were trained on the neuron activities
Step5:  The following is not part of the brain model, it is used to view the output for the ensemble
Since it's probing the neurons themselves, the output must be transformed from neuron activity to visual image
Step6:  Pickle the probe's output if it takes a long time to run
Step7:  Testing
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Python Code:
import nengo
import numpy as np
import cPickle
from nengo_extras.data import load_mnist
from nengo_extras.vision import Gabor, Mask
from matplotlib import pylab
import matplotlib.pyplot as plt
import matplotlib.animation as animation
Explanation: Using the trained weights in an ensemble of neurons
On the function points branch of nengo
On the vision branch of nengo_extras
End of explanation
# --- load the data
img_rows, img_cols = 28, 28
(X_train, y_train), (X_test, y_test) = load_mnist()
X_train = 2 * X_train - 1  # normalize to -1 to 1
X_test = 2 * X_test - 1  # normalize to -1 to 1
Explanation: Load the MNIST database
End of explanation
temp = np.diag([1]*10)
ZERO = temp[0]
ONE =  temp[1]
TWO =  temp[2]
THREE= temp[3]
FOUR = temp[4]
FIVE = temp[5]
SIX =  temp[6]
SEVEN =temp[7]
EIGHT= temp[8]
NINE = temp[9]
labels =[ZERO,ONE,TWO,THREE,FOUR,FIVE,SIX,SEVEN,EIGHT,NINE]
dim =28
Explanation: Each digit is represented by a one hot vector where the index of the 1 represents the number
End of explanation
label_weights = cPickle.load(open("label_weights1000.p", "rb"))
activity_to_img_weights = cPickle.load(open("activity_to_img_weights_scale1000.p", "rb"))
scale_up_after_encoder_weights =  cPickle.load(open("scale_up_after_encoder_weights1000.p", "r"))
scale_down_after_encoder_weights =  cPickle.load(open("scale_down_after_encoder_weights1000.p", "r"))
scale_up_weights = cPickle.load(open("scale_up_weights1000.p","rb"))
scale_down_weights = cPickle.load(open("scale_down_weights1000.p","rb"))
Explanation: Load the saved weight matrices that were created by trainging the model
End of explanation
rng = np.random.RandomState(9)
n_hid = 1000
model = nengo.Network(seed=3)
with model:
    #Stimulus only shows for brief period of time
    stim = nengo.Node(lambda t: ZERO if t < 0.1 else 0) #nengo.processes.PresentInput(labels,1))#
    
    ens_params = dict(
        eval_points=X_train,
        neuron_type=nengo.LIF(), #Why not use LIF?
        intercepts=nengo.dists.Choice([-0.5]),
        max_rates=nengo.dists.Choice([100]),
        )
        
    
    # linear filter used for edge detection as encoders, more plausible for human visual system
    encoders = Gabor().generate(n_hid, (11, 11), rng=rng)
    encoders = Mask((28, 28)).populate(encoders, rng=rng, flatten=True)
    ens = nengo.Ensemble(n_hid, dim**2, seed=3, encoders=encoders, **ens_params)
    
    #Recurrent connection on the neurons of the ensemble to perform the rotation
    nengo.Connection(ens.neurons, ens.neurons, transform = scale_down_after_encoder_weights.T, synapse=0.1)      
    #Connect stimulus to ensemble, transform using learned weight matrices
    nengo.Connection(stim, ens, transform = np.dot(label_weights,activity_to_img_weights).T, synapse=0.1)
    
    #Collect output, use synapse for smoothing
    probe = nengo.Probe(ens.neurons,synapse=0.1)
    
sim = nengo.Simulator(model)
sim.run(5)
Explanation: The network where the mental imagery and scaling occurs
The state, seed and ensemble parameters (including encoders) must all be the same for the saved weight matrices to work
The number of neurons (n_hid) must be the same as was used for training
The input must be shown for a short period of time to be able to view the scaling
The recurrent connection must be from the neurons because the weight matices were trained on the neuron activities
End of explanation
'''Animation for Probe output'''
fig = plt.figure()
output_acts = []
for act in sim.data[probe]:
    output_acts.append(np.dot(act,activity_to_img_weights))
def updatefig(i):
    im = pylab.imshow(np.reshape(output_acts[i],(dim, dim), 'F').T, cmap=plt.get_cmap('Greys_r'),animated=True)
    
    return im,
ani = animation.FuncAnimation(fig, updatefig, interval=0.1, blit=True)
plt.show()
Explanation: The following is not part of the brain model, it is used to view the output for the ensemble
Since it's probing the neurons themselves, the output must be transformed from neuron activity to visual image
End of explanation
#The filename includes the number of neurons and which digit is being rotated
filename = "mental_scaling_output_ZERO_"  + str(n_hid) + ".p"
cPickle.dump(sim.data[probe], open( filename , "wb" ) )
Explanation: Pickle the probe's output if it takes a long time to run
End of explanation
testing = np.dot(ZERO,np.dot(label_weights,activity_to_img_weights))
plt.subplot(121)
pylab.imshow(np.reshape(testing,(dim, dim), 'F').T, cmap=plt.get_cmap('Greys_r'))
#Get image
testing = np.dot(ZERO,np.dot(label_weights,activity_to_img_weights))
#Get activity of image
_, testing_act = nengo.utils.ensemble.tuning_curves(ens, sim, inputs=testing)
#Get rotated encoder outputs
testing_scale = np.dot(testing_act,scale_down_after_encoder_weights)
#Get activities
testing_scale = ens.neuron_type.rates(testing_scale, sim.data[ens].gain, sim.data[ens].bias)
for i in range(2):
    testing_scale = np.dot(testing_scale,scale_down_after_encoder_weights)
    testing_scale = ens.neuron_type.rates(testing_scale, sim.data[ens].gain, sim.data[ens].bias)
#testing_rotate = np.dot(testing_rotate,rotation_weights)
testing_scale = np.dot(testing_scale,activity_to_img_weights)
plt.subplot(122)
pylab.imshow(np.reshape(testing_scale,(dim, dim), 'F').T, cmap=plt.get_cmap('Greys_r'))
plt.show()
Explanation: Testing
End of explanation
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