load_params_pr = False song_size = 2459 #filepath for saving parameters savefilename = '/vega/stats/users/sl3368/rnn_code/saves/params/neural/dual_single/'+brain_region+'_'+str(held_out_song)+'_'+str(neuron)+'.save' neurons_savefilename ='/vega/stats/users/sl3368/rnn_code/saves/params/neural/dual_single/'+brain_region+'_'+str(held_out_song)+'_'+str(neuron)+'.save_neurons' psth_savefilename ='/vega/stats/users/sl3368/rnn_code/saves/params/psth/dual_single/'+brain_region+'_'+str(held_out_song)+'_'+str(neuron)+'.psth' ################################################ # Load Data ################################################ dataset_info = load_all_data() stim = dataset_info[0] data_set_x = theano.shared(stim, borrow=True) n_batches = data_set_x.shape[0].eval()/song_size n_train_batches = n_batches print 'Number of songs in single matlab chunk: '+str(n_train_batches) print 'Getting neural data...' neural_data = load_neural_data() ntrials = theano.shared(neural_data[brain_region_index],borrow=True) responses = theano.shared(neural_data[brain_region_index+1],borrow=True)
song_size = 2459
#filepath for saving parameters
savefilename = '/vega/stats/users/sl3368/CLDNN/saves/neural/shallow/' + brain_region + '_' + str(
held_out_song) + '.save'
neurons_savefilename = '/vega/stats/users/sl3368/CLDNN/saves/neural/shallow/' + brain_region + '_' + str(
held_out_song) + '.save_neurons'
psth_savefilename = '/vega/stats/users/sl3368/CLDNN/saves/psth/shallow/' + brain_region + '_' + str(
held_out_song) + '.psth'
################################################
# Load Data
################################################
dataset_info = load_all_data()
stim = dataset_info[0]
data_set_x = theano.shared(stim, borrow=True)
n_batches = data_set_x.shape[0].eval() / song_size
n_train_batches = n_batches
print 'Number of songs in single matlab chunk: ' + str(n_train_batches)
print 'Getting neural data...'
neural_data = load_neural_data()
ntrials = theano.shared(neural_data[brain_region_index], borrow=True)
responses = theano.shared(neural_data[brain_region_index + 1], borrow=True)
def SGD_training(learning_rate=1, n_epochs=1000):
"""
stochastic gradient descent optimization
"""
dataset_info = load_all_data()
data_set_x = dataset_info[0]
maxBatchSize = numpy.int_(dataset_info[1])
batch_size = maxBatchSize
n_train_batches = 28
#n_valid_batches = 1
#n_test_batches = 1
######################
# BUILD ACTUAL MODEL #
######################
print '... building the model'
# allocate symbolic variables for the data
index = T.lscalar() # index to a [mini]batch
x = T.matrix('x') # the data is presented as a vector of inputs with many exchangeable examples of this vector
x = clip_gradient(x,1.0)
y = T.matrix('y') # the data is presented as a vector of inputs with many exchangeable examples of this vector
is_train = T.iscalar('is_train') # pseudo boolean for switching between training and prediction
rng = numpy.random.RandomState(1234)
################################################
# Architecture: input --> LSTM --> predict one-ahead
################################################
# The poisson regression layer gets as input the hidden units
# of the hidden layer
d_input = Dropout(rng, is_train, x)
n_hidden = 100
lstm_1 = LSTM(rng, d_input.output, n_in=data_set_x.get_value(borrow=True).shape[1], n_out=n_hidden)
#lstm_1 = RNN(rng, d_input.output, n_in=data_set_x.get_value(borrow=True).shape[1], n_out=n_hidden) #vanilla rnn
d_lstm_1 = Dropout(rng, is_train, lstm_1.output)
output = LinearRegression(input=d_lstm_1.output, n_in=n_hidden, n_out=data_set_x.get_value(borrow=True).shape[1])
#######################
# Objective function
#######################
print '... defining objective and compiling test and validate'
# the cost we minimize during training is the negative log likelihood of
# the model
cost = T.mean(output.negative_log_likelihood(y))
# compiling a Theano function that computes the mistakes that are made
# by the model on a minibatch
# use cost or errors(y,tc,md) as output?
test_model = theano.function(inputs=[index],
outputs=[cost, output.E_y_given_x],
givens={
x: data_set_x[index * batch_size:((index + 1) * batch_size - 1)],
y: data_set_x[(index * batch_size + 1):(index + 1) * batch_size],
is_train: numpy.cast['int32'](0)})
# wanted to use below indexes and have different sized batches, but this didn't work
#[int(batchBreaks[index]-1):int(batchBreaks[(index+1)]-1)]
validate_model = theano.function(inputs=[index],
outputs=cost,
givens={
x: data_set_x[index * batch_size:((index + 1) * batch_size - 1)],
y: data_set_x[(index * batch_size + 1):(index + 1) * batch_size],
is_train: numpy.cast['int32'](0)})
#######################
# Parameters and gradients
#######################
print '... parameters and gradients'
# create a list (concatenated) of all model parameters to be fit by gradient descent
#order: [self.W, self.b]
params = lstm_1.params + output.params
params_helper = lstm_1.params_helper + output.params_helper
params_helper2 = lstm_1.params_helper2 + output.params_helper2
# compute the gradient of cost with respect to theta (sotred in params)
# the resulting gradients will be stored in a list gparams
gparams = []
for param in params:
gparam = T.grad(cost, param)
gparams.append(gparam)
# specify how to update the parameters of the model as a list of
# (variable, update expression) pairs
updates = []
# given two list the zip A = [a1, a2, a3, a4] and B = [b1, b2, b3, b4] of
# same length, zip generates a list C of same size, where each element
# is a pair formed from the two lists :
# C = [(a1, b1), (a2, b2), (a3, b3), (a4, b4)]
#for param, gparam in zip(params, gparams):
# updates.append((param, param - learning_rate * gparam))
#iter_count = theano.shared(1)
#L1_penalized = []
#larger_stepsize = []
#enforce_positive = [2, 3] #if recurrent
#enforce_positive = []
#zero_stepsize = []
param_index = 0
#rho = 1e-6
#for param, param_helper, param_helper2, gparam in zip(params, params_helper, params_helper2, gparams):
#updates.append((param_helper, param_helper + gparam ** 2)) #need sum of squares for learning rate
#updates.append((param_helper2, param_helper2 + gparam)) #need sum of gradients for L1 thresholding
#vanilla SGD
#for param, gparam in zip(params, gparams):
# updates.append((param, param - learning_rate * gparam))
# param_index += 1
#adadelta updates
rho = .95
eps_big = 1e-6
for param, param_helper, param_helper2, gparam in zip(params, params_helper, params_helper2, gparams):
updates.append((param_helper,rho * param_helper + (1. - rho) * (gparam ** 2))) #update decaying sum of previous gradients
dparam = - T.sqrt((param_helper2 + eps_big) / (rho * param_helper + (1. - rho) * (gparam ** 2) + eps_big)) *gparam # calculate step size
updates.append((param_helper2, rho * param_helper2 + (1. - rho) * (dparam ** 2))) #update decaying sum of previous step sizes
updates.append((param, param + dparam))
#updates.append((iter_count, iter_count + 1))
print '... compiling train'
# compiling a Theano function `train_model` that returns the cost, but
# in the same time updates the parameter of the model based on the rules
# defined in `updates`
train_model = theano.function(inputs=[index], outputs=cost,
updates=updates,
givens={
x: data_set_x[index * batch_size:((index + 1) * batch_size - 1)],
y: data_set_x[(index * batch_size + 1):(index + 1) * batch_size],
is_train: numpy.cast['int32'](0)})
###############
# TRAIN MODEL #
###############
print '... training'
# early-stopping parameters
patience = 5000 # look as this many examples regardless
#patience = train_set_x.get_value(borrow=True).shape[0] * n_epochs #no early stopping
patience_increase = 2 # wait this much longer when a new best is
# found
improvement_threshold = 0.99 # a relative improvement of this much is
# considered significant
validation_frequency = min(n_train_batches, patience / 2)
# go through this many
# minibatche before checking the network
# on the validation set; in this case we
# check every epoch
#best_params = None
best_validation_loss = numpy.inf
best_iter = 0
#test_score = 0.
start_time = time.clock()
epoch = 0
done_looping = False
while (epoch < n_epochs) and (not done_looping):
epoch = epoch + 1
for minibatch_index in xrange(n_train_batches):
minibatch_avg_cost = train_model(minibatch_index)
print minibatch_avg_cost
# iteration number
iter = (epoch - 1) * n_train_batches + minibatch_index
if (iter + 1) % validation_frequency == 0:
# compute absolute error loss on validation set
validation_losses = [validate_model(i) for i
in [28]]
this_validation_loss = numpy.mean(validation_losses) #mean over batches
print('epoch %i, minibatch %i, validation error %f' %
(epoch, minibatch_index + 1,
this_validation_loss))
# if we got the best validation score until now
if this_validation_loss < best_validation_loss:
#improve patience if loss improvement is good enough
if this_validation_loss < best_validation_loss * \
improvement_threshold:
patience = max(patience, iter * patience_increase)
best_validation_loss = this_validation_loss
best_iter = iter
# test it on the test set
#test_losses = [test_model(i) for i
# in [29]]
#test_score = numpy.mean(test_losses)
test_cost, test_pred = test_model(29)
#test_cost, test_costs_separate, test_pred_separate, test_actual_separate = test_model(29)
print((' epoch %i, minibatch %i, test error of '
'best model %f') %
(epoch, minibatch_index + 1,
numpy.sum(test_cost)))
if patience <= iter:
done_looping = True
break
end_time = time.clock()
print(('Optimization complete. Best validation score of %f'
'obtained at iteration %i, with test performance %f') %
(best_validation_loss, best_iter + 1, numpy.sum(test_cost)))
print >> sys.stderr, ('The code for file ' +
os.path.split(__file__)[1] +
' ran for %.2fm' % ((end_time - start_time) / 60.))
#store data
f = file('results/params.save', 'wb')
for obj in [params + [test_cost] + [test_pred]]:
cPickle.dump(obj, f, protocol=cPickle.HIGHEST_PROTOCOL)
f.close()
def SGD_training(learning_rate=1, n_epochs=1000):
"""
stochastic gradient descent optimization
"""
dataset_info = load_all_data()
data_set_x = dataset_info[0]
maxBatchSize = numpy.int_(dataset_info[1])
batch_size = maxBatchSize
n_train_batches = 28
#n_valid_batches = 1
#n_test_batches = 1
######################
# BUILD ACTUAL MODEL #
######################
print '... building the model'
# allocate symbolic variables for the data
index = T.lscalar() # index to a [mini]batch
x = T.matrix(
'x'
) # the data is presented as a vector of inputs with many exchangeable examples of this vector
x = clip_gradient(x, 1.0)
y = T.matrix(
'y'
) # the data is presented as a vector of inputs with many exchangeable examples of this vector
is_train = T.iscalar(
'is_train'
) # pseudo boolean for switching between training and prediction
rng = numpy.random.RandomState(1234)
################################################
# Architecture: input --> LSTM --> predict one-ahead
################################################
# The poisson regression layer gets as input the hidden units
# of the hidden layer
d_input = Dropout(rng, is_train, x)
n_hidden = 100
lstm_1 = LSTM(rng,
d_input.output,
n_in=data_set_x.get_value(borrow=True).shape[1],
n_out=n_hidden)
#lstm_1 = RNN(rng, d_input.output, n_in=data_set_x.get_value(borrow=True).shape[1], n_out=n_hidden) #vanilla rnn
d_lstm_1 = Dropout(rng, is_train, lstm_1.output)
output = LinearRegression(input=d_lstm_1.output,
n_in=n_hidden,
n_out=data_set_x.get_value(borrow=True).shape[1])
#######################
# Objective function
#######################
print '... defining objective and compiling test and validate'
# the cost we minimize during training is the negative log likelihood of
# the model
cost = T.mean(output.negative_log_likelihood(y))
# compiling a Theano function that computes the mistakes that are made
# by the model on a minibatch
# use cost or errors(y,tc,md) as output?
test_model = theano.function(
inputs=[index],
outputs=[cost, output.E_y_given_x],
givens={
x: data_set_x[index * batch_size:((index + 1) * batch_size - 1)],
y: data_set_x[(index * batch_size + 1):(index + 1) * batch_size],
is_train: numpy.cast['int32'](0)
})
# wanted to use below indexes and have different sized batches, but this didn't work
#[int(batchBreaks[index]-1):int(batchBreaks[(index+1)]-1)]
validate_model = theano.function(
inputs=[index],
outputs=cost,
givens={
x: data_set_x[index * batch_size:((index + 1) * batch_size - 1)],
y: data_set_x[(index * batch_size + 1):(index + 1) * batch_size],
is_train: numpy.cast['int32'](0)
})
#######################
# Parameters and gradients
#######################
print '... parameters and gradients'
# create a list (concatenated) of all model parameters to be fit by gradient descent
#order: [self.W, self.b]
params = lstm_1.params + output.params
params_helper = lstm_1.params_helper + output.params_helper
params_helper2 = lstm_1.params_helper2 + output.params_helper2
# compute the gradient of cost with respect to theta (sotred in params)
# the resulting gradients will be stored in a list gparams
gparams = []
for param in params:
gparam = T.grad(cost, param)
gparams.append(gparam)
# specify how to update the parameters of the model as a list of
# (variable, update expression) pairs
updates = []
# given two list the zip A = [a1, a2, a3, a4] and B = [b1, b2, b3, b4] of
# same length, zip generates a list C of same size, where each element
# is a pair formed from the two lists :
# C = [(a1, b1), (a2, b2), (a3, b3), (a4, b4)]
#for param, gparam in zip(params, gparams):
# updates.append((param, param - learning_rate * gparam))
#iter_count = theano.shared(1)
#L1_penalized = []
#larger_stepsize = []
#enforce_positive = [2, 3] #if recurrent
#enforce_positive = []
#zero_stepsize = []
param_index = 0
#rho = 1e-6
#for param, param_helper, param_helper2, gparam in zip(params, params_helper, params_helper2, gparams):
#updates.append((param_helper, param_helper + gparam ** 2)) #need sum of squares for learning rate
#updates.append((param_helper2, param_helper2 + gparam)) #need sum of gradients for L1 thresholding
#vanilla SGD
#for param, gparam in zip(params, gparams):
# updates.append((param, param - learning_rate * gparam))
# param_index += 1
#adadelta updates
rho = .95
eps_big = 1e-6
for param, param_helper, param_helper2, gparam in zip(
params, params_helper, params_helper2, gparams):
updates.append(
(param_helper, rho * param_helper + (1. - rho) *
(gparam**2))) #update decaying sum of previous gradients
dparam = -T.sqrt(
(param_helper2 + eps_big) /
(rho * param_helper + (1. - rho) *
(gparam**2) + eps_big)) * gparam # calculate step size
updates.append(
(param_helper2, rho * param_helper2 + (1. - rho) *
(dparam**2))) #update decaying sum of previous step sizes
updates.append((param, param + dparam))
#updates.append((iter_count, iter_count + 1))
print '... compiling train'
# compiling a Theano function `train_model` that returns the cost, but
# in the same time updates the parameter of the model based on the rules
# defined in `updates`
train_model = theano.function(
inputs=[index],
outputs=cost,
updates=updates,
givens={
x: data_set_x[index * batch_size:((index + 1) * batch_size - 1)],
y: data_set_x[(index * batch_size + 1):(index + 1) * batch_size],
is_train: numpy.cast['int32'](0)
})
###############
# TRAIN MODEL #
###############
print '... training'
# early-stopping parameters
patience = 5000 # look as this many examples regardless
#patience = train_set_x.get_value(borrow=True).shape[0] * n_epochs #no early stopping
patience_increase = 2 # wait this much longer when a new best is
# found
improvement_threshold = 0.99 # a relative improvement of this much is
# considered significant
validation_frequency = min(n_train_batches, patience / 2)
# go through this many
# minibatche before checking the network
# on the validation set; in this case we
# check every epoch
#best_params = None
best_validation_loss = numpy.inf
best_iter = 0
#test_score = 0.
start_time = time.clock()
epoch = 0
done_looping = False
while (epoch < n_epochs) and (not done_looping):
epoch = epoch + 1
for minibatch_index in xrange(n_train_batches):
minibatch_avg_cost = train_model(minibatch_index)
print minibatch_avg_cost
# iteration number
iter = (epoch - 1) * n_train_batches + minibatch_index
if (iter + 1) % validation_frequency == 0:
# compute absolute error loss on validation set
validation_losses = [validate_model(i) for i in [28]]
this_validation_loss = numpy.mean(
validation_losses) #mean over batches
print('epoch %i, minibatch %i, validation error %f' %
(epoch, minibatch_index + 1, this_validation_loss))
# if we got the best validation score until now
if this_validation_loss < best_validation_loss:
#improve patience if loss improvement is good enough
if this_validation_loss < best_validation_loss * \
improvement_threshold:
patience = max(patience, iter * patience_increase)
best_validation_loss = this_validation_loss
best_iter = iter
# test it on the test set
#test_losses = [test_model(i) for i
# in [29]]
#test_score = numpy.mean(test_losses)
test_cost, test_pred = test_model(29)
#test_cost, test_costs_separate, test_pred_separate, test_actual_separate = test_model(29)
print((' epoch %i, minibatch %i, test error of '
'best model %f') %
(epoch, minibatch_index + 1, numpy.sum(test_cost)))
if patience <= iter:
done_looping = True
break
end_time = time.clock()
print(('Optimization complete. Best validation score of %f'
'obtained at iteration %i, with test performance %f') %
(best_validation_loss, best_iter + 1, numpy.sum(test_cost)))
print >> sys.stderr, ('The code for file ' + os.path.split(__file__)[1] +
' ran for %.2fm' % ((end_time - start_time) / 60.))
#store data
f = file('results/params.save', 'wb')
for obj in [params + [test_cost] + [test_pred]]:
cPickle.dump(obj, f, protocol=cPickle.HIGHEST_PROTOCOL)
f.close()
def generate_visualization_on_section(region,heldout,neuron_no,training_iterations,hidden,song_section,previous):
region_dict = {'L1':0,'L2':2,'L3':4,'NC':6,'MLd':8}
held_out_song = heldout
brain_region = region
brain_region_index = region_dict[brain_region]
neuron = neuron_no
prev_trained_size = previous.shape[0]
n_epochs= training_iterations
n_hidden = hidden
song_depth = song_section
print 'Running CV for held out song '+str(held_out_song)+' for brain region '+brain_region+' index at '+str(brain_region_index)+' iteration:'+str(song_depth)
#Filepath for printing results
results_filename='/vega/stats/users/sl3368/rnn_code/results/neural/dual_'+str(n_hidden)+'/visualizations/'+brain_region+'_'+str(held_out_song)+'_'+str(neuron)+'.out'
#check if exists already, then load or not load
load_params_pr_filename = '/vega/stats/users/sl3368/rnn_code/saves/params/neural/dual_'+str(n_hidden)+'/'+brain_region+'_'+str(held_out_song)+'.save'
if path.isfile(load_params_pr_filename):
#print 'Will load previous regression parameters...'
load_params_pr = True
else:
load_params_pr = False
song_size = 2459
#filepath for saving parameters
savefilename = '/vega/stats/users/sl3368/rnn_code/saves/params/neural/dual_'+str(n_hidden)+'/visualizations/'+brain_region+'_'+str(held_out_song)+'_'+str(neuron)+'.visualization'
if path.isfile(savefilename):
load_visualize = True
else:
load_visualize = False
################################################
# Load Data
################################################
dataset_info = load_all_data()
stim = dataset_info[0]
data_set_x = theano.shared(stim, borrow=True)
#print 'Getting neural data...'
neural_data = load_neural_data()
ntrials = theano.shared(neural_data[brain_region_index],borrow=True)
responses = theano.shared(neural_data[brain_region_index+1],borrow=True)
######################
# BUILD ACTUAL MODEL #
######################
#print 'building the model...'
# allocate symbolic variables for the data
index = T.lscalar() # index to a [mini]batch
section = T.lscalar()
init = numpy.zeros((song_depth,60)).astype('f')
init[:prev_trained_size] = previous
x = shared(init,borrow=True)
y = T.matrix('y') # the data is presented as a vector of inputs with many exchangeable examples of this vector
trial_no = T.matrix('trial_no')
rng = numpy.random.RandomState(1234)
# Architecture: input --> LSTM --> predict one-ahead
lstm_1 = LSTM(rng, x, n_in=data_set_x.get_value(borrow=True).shape[1], n_out=n_hidden)
output = PoissonRegression(input=lstm_1.output, n_in=n_hidden, n_out=1)
pred = output.E_y_given_x.T * trial_no[:,neuron]
nll = output.negative_log_likelihood(y[:,neuron],trial_no[:,neuron],single=True)
################################
# Objective function and GD
################################
#print 'defining cost, parameters, and learning function...'
# the cost we minimize during training is the negative log likelihood of
# the model
cost = T.mean(nll)
#Defining params
params = [x]
# updates from ADAM
updates = Adam(cost, params)
#######################
# Objective function
#######################
#print 'compiling train....'
train_model = theano.function(inputs=[index,section], outputs=cost,
updates=updates,
givens={
trial_no: ntrials[index * song_size:((index * song_size)+section)],
y: responses[index * song_size:((index * song_size)+section)]})
#validate_model = theano.function(inputs=[index,section],
# outputs=[cost,nll.shape,pred.shape],
# givens={
# trial_no: ntrials[index * song_size:((index * song_size)+section)],
# y: responses[index * song_size:((index * song_size)+section)]})
#######################
# Parameters and gradients
#######################
#print 'parameters and gradients...'
if load_params_pr:
#print 'loading LSTM parameters from file...'
f = open( load_params_pr_filename)
old_p = cPickle.load(f)
lstm_1.W_i.set_value(old_p[0].get_value(), borrow=True)
lstm_1.W_f.set_value(old_p[1].get_value(), borrow=True)
lstm_1.W_c.set_value(old_p[2].get_value(), borrow=True)
lstm_1.W_o.set_value(old_p[3].get_value(), borrow=True)
lstm_1.U_i.set_value(old_p[4].get_value(), borrow=True)
lstm_1.U_f.set_value(old_p[5].get_value(), borrow=True)
lstm_1.U_c.set_value(old_p[6].get_value(), borrow=True)
lstm_1.U_o.set_value(old_p[7].get_value(), borrow=True)
lstm_1.V_o.set_value(old_p[8].get_value(), borrow=True)
lstm_1.b_i.set_value(old_p[9].get_value(), borrow=True)
lstm_1.b_f.set_value(old_p[10].get_value(), borrow=True)
lstm_1.b_c.set_value(old_p[11].get_value(), borrow=True)
lstm_1.b_o.set_value(old_p[12].get_value(), borrow=True)
f.close()
if load_params_pr:
#print 'loading PR parameters from file...'
f = open( load_params_pr_filename)
old_p = cPickle.load(f)
output.W.set_value(old_p[13].get_value(), borrow=True)
output.b.set_value(old_p[14].get_value(), borrow=True)
f.close()
#if load_visualize:
# print 'loading visualization from file...'
# f = open(savefilename)
# old_v = cPickle.load(f)
# x.set_value(old_v, borrow=True)
# f.close()
###############
# TRAIN MODEL #
###############
#print 'training...'
best_validation_loss = numpy.inf
epoch = 0
last_e = time.time()
r_log=open(results_filename,'a')
r_log.write('Starting training...\n')
r_log.close()
while (epoch < n_epochs):
#print str(epoch)+' epoch took: '+str(time.time()-last_e)
#r_log=open(results_filename, 'a')
#r_log.write(str(epoch)+ ' epoch took: '+str(time.time()-last_e)+'\n')
#r_log.close()
last_e = time.time()
epoch = epoch + 1
mb_costs = []
heldout = 0
for minibatch_index in xrange(14):
if(heldout==held_out_song):
minibatch_avg_cost = train_model(minibatch_index,song_depth)
#print minibatch_avg_cost
mb_costs.append(minibatch_avg_cost)
heldout=heldout+1
for minibatch_index in xrange(24,30):
if(heldout==held_out_song):
minibatch_avg_cost = train_model(minibatch_index,song_depth)
#print minibatch_avg_cost
mb_costs.append(minibatch_avg_cost)
heldout=heldout+1
avg_cost = numpy.mean(mb_costs)
# if we got the best validation score until now
if avg_cost < best_validation_loss:
best_validation_loss = avg_cost
visualization = numpy.asarray(x.eval())
#store data
f = file(savefilename, 'wb')
for obj in [visualization]:
cPickle.dump(obj, f, protocol=cPickle.HIGHEST_PROTOCOL)
f.close()
print('epoch %i, training error %f' % (epoch, avg_cost))
r_log=open(results_filename, 'a')
r_log.write('epoch %i, training error %f' % (epoch, avg_cost))
r_log.close()
return numpy.asarray(x.eval())