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test_learning.py
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test_learning.py
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import numpy as np
import pytest
import psyneulink as pnl
# np.set_printoptions(suppress=True)
import numpy as np
import pytest
from psyneulink.core.compositions.composition import Composition, CompositionError, RunError
from psyneulink.core.components.mechanisms.processing.transfermechanism import TransferMechanism
from psyneulink.core.components.functions.learningfunctions import BackPropagation
class TestTargetSpecs:
def test_target_spec_default_assignment(self):
A = TransferMechanism(name="learning-process-mech-A")
B = TransferMechanism(name="learning-process-mech-B")
comp1 = Composition()
p1 = comp1.add_backpropagation_learning_pathway(pathway=[A,B])
# Call learn with default_variable specified for target (for comparison with missing target)
comp1.learn(inputs={A: 1.0,
p1.target: 0.0},
num_trials=2)
assert np.allclose(comp1.results, [[[1.]], [[0.9]]])
# Repeat with no target assignment (should use default_variable)
C = TransferMechanism(name="learning-process-mech-C")
D = TransferMechanism(name="learning-process-mech-D")
comp2 = Composition()
comp2.add_backpropagation_learning_pathway(pathway=[C,D])
# Call learn with no target specification
comp2.learn(inputs={C: 1.0},
num_trials=2)
# Should be same with default target specification
assert np.allclose(comp2.results, comp1.results)
def test_target_dict_spec_single_trial_scalar_and_lists_rl(self):
A = TransferMechanism(name="learning-process-mech-A")
B = TransferMechanism(name="learning-process-mech-B")
comp = Composition()
p = comp.add_reinforcement_learning_pathway(pathway=[A,B])
# Confirm that targets are ignored in run (vs learn)
comp.run(inputs={A: 1.0,
p.target:2.0})
assert np.allclose(comp.results, [[[1.]], [[1.]], [[1.]]])
comp.learn(inputs={A: 1.0,
p.target:2.0})
comp.learn(inputs={A: 1.0,
p.target:[2.0]})
comp.learn(inputs={A: 1.0,
p.target:[[2.0]]})
assert np.allclose(comp.results, [[[1.]], [[1.]], [[1.05]], [[1.0975]]])
def test_target_dict_spec_single_trial_scalar_and_lists_bp(self):
A = TransferMechanism(name="learning-process-mech-A")
B = TransferMechanism(name="learning-process-mech-B")
C = TransferMechanism(name="learning-process-mech-C")
comp = Composition()
p = comp.add_backpropagation_learning_pathway(pathway=[A,B,C])
# Confirm that targets are ignored in run (vs learn)
comp.run(inputs={A: 1.0,
p.target:2.0})
assert np.allclose(comp.results, [[[1.]]])
comp.learn(inputs={A: 1.0,
p.target:2.0})
comp.learn(inputs={A: 1.0,
p.target:[2.0]})
comp.learn(inputs={A: 1.0,
p.target:[[2.0]]})
assert np.allclose(comp.results, [[[1.]], [[1.]], [[1.21]], [[1.40873161]]])
def test_target_dict_spec_multi_trial_lists_rl(self):
A = TransferMechanism(name="learning-process-mech-A")
B = TransferMechanism(name="learning-process-mech-B")
comp = Composition()
p = comp.add_backpropagation_learning_pathway(pathway=[A,B])
comp.learn(inputs={A: [1.0, 2.0, 3.0],
p.target: [[4.0], [5.0], [6.0]]})
comp.learn(inputs={A: [1.0, 2.0, 3.0],
p.target: [[[4.0]], [[5.0]], [[6.0]]]})
assert np.allclose(comp.results,
[[[1.]], [[2.6]], [[5.34]],
[[1.978]], [[4.3604]], [[6.92436]]])
def test_target_dict_spec_multi_trial_lists_bp(self):
A = TransferMechanism(name="learning-process-mech-A")
B = TransferMechanism(name="learning-process-mech-B")
C = TransferMechanism(name="learning-process-mech-C",
default_variable=[[0.0, 0.0]])
comp = Composition()
p = comp.add_backpropagation_learning_pathway(pathway=[A,B,C])
comp.learn(inputs={A: 1.0,
p.target:[2.0, 3.0]})
comp.learn(inputs={A: 1.0,
p.target:[[2.0, 3.0]]})
comp.learn(inputs={A: [1.0, 2.0, 3.0],
p.target: [[3.0, 4.0], [5.0, 6.0], [7.0, 8.0]]})
comp.learn(inputs={A: [1.0, 2.0, 3.0],
p.target: [[[3.0, 4.0]], [[5.0, 6.0]], [[7.0, 8.0]]]})
assert np.allclose(comp.results,
[[[1., 1.]],
[[1.2075, 1.265]],
[[1.41003122, 1.54413183]], [[3.64504691, 4.13165454]], [[8.1607109 , 9.54419477]],
[[1.40021212, 1.56636511]], [[3.61629564, 4.17586792]], [[8.11241026, 9.57222535]]])
# DS: The following test fails the assert. The same value is returned whether a dict or function is used as input,
# which is not the same as the expected values. Are the expected values incorrect? If not, there is a problem
# at a deeper level than just the input handling. 5/18/2020
#
# def test_function_target_spec(self):
#
# from psyneulink.core.compositions.composition import Composition
# A = pnl.TransferMechanism(name="learning-process-mech-A")
# B = pnl.TransferMechanism(name="learning-process-mech-B",
# default_variable=np.array([[0.0, 0.0]]))
# comp = Composition()
# learning_pathway = comp.add_backpropagation_learning_pathway(pathway=[A,B], learning_rate=0.05)
# target = learning_pathway.target
# # global x
# # x = 1
#
# # def input_function(a,b):
# # global x
# # x = x + 1
# # y = 2 * x
# # z = 3 * x
# # target_value = {A:[x], target:[y,z]}
# # print('trial')
# # return target_value
# def input_function(trial):
# x = trial + 1
# y = 2 * x
# z = y + 2
# target_value = {A:[x], target:[y,z]}
# print(target_value)
# return target_value
#
# target.log.set_log_conditions('variable')
#
# comp.learn(inputs=input_function, num_trials=3)
# assert np.allclose(comp.results, [[[2., 2.]], [[2.4, 2.8]], [[2.72, 3.44]]])
def test_dict_target_spec_converging_pathways(self):
A = TransferMechanism(name="converging-learning-pathways-mech-A")
B = TransferMechanism(name="converging-learning-pathways-mech-B")
C = TransferMechanism(name="converging-learning-pathways-mech-C", size=2)
D = TransferMechanism(name="converging-learning-pathways-mech-D")
E = TransferMechanism(name="converging-learning-pathways-mech-E")
comp = Composition()
p1 = comp.add_backpropagation_learning_pathway(pathway=[A,B,C])
p2 = comp.add_backpropagation_learning_pathway(pathway=[D,E,C])
assert p1.target == p2.target
comp.learn(inputs={A: 1.0,
D: 2.0,
p1.target: [3.0, 4.0]
})
comp.learn(inputs={A: 5.0,
D: 6.0,
p1.target: [7.0, 8.0]
})
assert np.allclose(comp.results,[[[3., 3.]], [[11.85 , 12.7725]]])
def test_function_target_spec_converging_pathways(self):
A = TransferMechanism(name="converging-learning-pathways-mech-A")
B = TransferMechanism(name="converging-learning-pathways-mech-B")
C = TransferMechanism(name="converging-learning-pathways-mech-C", size=2)
D = TransferMechanism(name="converging-learning-pathways-mech-D")
E = TransferMechanism(name="converging-learning-pathways-mech-E")
comp = Composition()
p1 = comp.add_backpropagation_learning_pathway(pathway=[A,B,C])
p2 = comp.add_backpropagation_learning_pathway(pathway=[D,E,C])
assert p1.target == p2.target
inputs = {
A: [1.0, 5.0],
D: [2.0, 6.0],
p1.target: [[3.0, 4.0], [7.0, 8.0]]
}
def input_function(trial_num):
return {
A: inputs[A][trial_num],
D: inputs[D][trial_num],
p1.target: inputs[p1.target][trial_num]
}
comp.learn(inputs=input_function,
num_trials=2)
assert np.allclose(comp.results,[[[3., 3.]], [[11.85 , 12.7725]]])
def test_dict_target_spec_diverging_pathways(self):
A = TransferMechanism(name="diverging-learning-pathways-mech-A")
B = TransferMechanism(name="diverging-learning-pathways-mech-B")
C = TransferMechanism(name="diverging-learning-pathways-mech-C")
D = TransferMechanism(name="diverging-learning-pathways-mech-D")
E = TransferMechanism(name="diverging-learning-pathways-mech-E")
comp = Composition()
p1 = comp.add_backpropagation_learning_pathway(pathway=[A,B,C])
p2 = comp.add_backpropagation_learning_pathway(pathway=[A,D,E])
inputs = {
A: [1.0, 2.0],
p1.target: [2.0, 2.0],
p2.target: [4.0, 4.0]
}
def input_function(trial_num):
return {
A: inputs[A][trial_num],
p1.target: inputs[p1.target][trial_num],
p2.target: inputs[p2.target][trial_num]
}
comp.learn(inputs=input_function,
num_trials=2)
assert np.allclose(comp.results,[[[1.], [1.]], [[2.42], [3.38]]])
def test_function_target_spec_divergin_pathways(self):
A = TransferMechanism(name="diverging-learning-pathways-mech-A")
B = TransferMechanism(name="diverging-learning-pathways-mech-B")
C = TransferMechanism(name="diverging-learning-pathways-mech-C")
D = TransferMechanism(name="diverging-learning-pathways-mech-D")
E = TransferMechanism(name="diverging-learning-pathways-mech-E")
comp = Composition()
p1 = comp.add_backpropagation_learning_pathway(pathway=[A,B,C])
p2 = comp.add_backpropagation_learning_pathway(pathway=[A,D,E])
comp.learn(inputs={A: 1.0,
p1.target: 2.0,
p2.target: 4.0
})
comp.learn(inputs={A: 2.0,
p1.target: 2.0,
p2.target: 4.0
})
assert np.allclose(comp.results,[[[1.], [1.]], [[2.42], [3.38]]])
def test_dict_target_spec_divering_pathways_with_only_one_target(self):
# First test with both targets (but use default_variale for second for comparison with missing target)
A = TransferMechanism(name="diverging-learning-pathways-mech-A")
B = TransferMechanism(name="diverging-learning-pathways-mech-B")
C = TransferMechanism(name="diverging-learning-pathways-mech-C")
D = TransferMechanism(name="diverging-learning-pathways-mech-D")
E = TransferMechanism(name="diverging-learning-pathways-mech-E")
comp1 = Composition()
p1 = comp1.add_backpropagation_learning_pathway(pathway=[A,B,C])
p2 = comp1.add_backpropagation_learning_pathway(pathway=[A,D,E])
comp1.learn(inputs={A: 1.0,
p1.target: 0.0,
p2.target: 2.0
},
num_trials=2)
assert np.allclose(comp1.results,[[[1.], [1.]], [[0.81], [1.21]]])
F = TransferMechanism(name="diverging-learning-pathways-mech-F")
G = TransferMechanism(name="diverging-learning-pathways-mech-G")
H = TransferMechanism(name="diverging-learning-pathways-mech-H")
I = TransferMechanism(name="diverging-learning-pathways-mech-I")
J = TransferMechanism(name="diverging-learning-pathways-mech-J")
comp2 = Composition()
p3 = comp2.add_backpropagation_learning_pathway(pathway=[F,G,H])
p4 = comp2.add_backpropagation_learning_pathway(pathway=[F,I,J])
# Call learn with missing spec for p3.target; should use default_variable
comp2.learn(inputs={F: 1.0,
p4.target: 2.0
},
num_trials=2)
assert np.allclose(comp2.results, comp1.results)
def test_target_spec_over_nesting_of_items_in_target_value_error(self):
A = TransferMechanism(name="learning-process-mech-A")
B = TransferMechanism(name="learning-process-mech-B")
C = TransferMechanism(name="learning-process-mech-C",
default_variable=[[0.0, 0.0]])
comp = Composition()
p = comp.add_backpropagation_learning_pathway(pathway=[A,B,C])
# Elicit error with run
with pytest.raises(RunError) as error_text:
comp.run(inputs={A: [1.0, 2.0, 3.0],
p.target: [[[3.0], [4.0]], [[5.0], [6.0]], [[7.0], [8.0]]]})
assert ("Input stimulus" in str(error_text.value) and
"for Target is incompatible with its external_input_values" in str(error_text.value))
# Elicit error with learn
with pytest.raises(RunError) as error_text:
comp.learn(inputs={A: [1.0, 2.0, 3.0],
p.target: [[[3.0], [4.0]], [[5.0], [6.0]], [[7.0], [8.0]]]})
assert ("Input stimulus" in str(error_text.value) and
"for Target is incompatible with its external_input_values" in str(error_text.value))
# The input sizes were picked because the lengths conflict in set:
# >>> print({10, 2}, {2, 10})
# {10, 2} {2, 10}
# whereas:
# >>> print({4, 2}, {2, 4})
# {2, 4} {2, 4}
@pytest.mark.parametrize("input_A, target_B", [
([[[1.0]], [[2.0]]], [[1.0], [2.0], [3.0], [4.0], [5.0], [6.0], [7.0], [8.0], [9.0], [10.0]]),
([[[1.0]], [[2.0]], [[3.0]], [[4.0]], [[5.0]], [[6.0]], [[7.0]], [[8.0]], [[9.0]], [[10.0]]], [[1.0], [2.0]])],
ids=["2,10", "10,2"])
def test_different_number_of_stimuli_for_targets_and_other_input_mech_error(self, input_A, target_B):
A = TransferMechanism(name="learning-process-mech-A")
B = TransferMechanism(name="learning-process-mech-B")
comp = Composition()
p = comp.add_backpropagation_learning_pathway(pathway=[A,B])
with pytest.raises(CompositionError) as error:
comp.run(inputs={A: input_A, p.target: target_B})
error_text = str(error.value)
assert 'The input dictionary' in error_text
assert 'contains input specifications of different lengths ({10, 2})' in error_text or \
'contains input specifications of different lengths ({2, 10})' in error_text
assert 'The same number of inputs must be provided for each node in a Composition' in error_text
class TestLearningPathwayMethods:
def test_multiple_of_same_learning_pathway(self):
in_to_hidden_matrix = np.random.rand(2,10)
hidden_to_out_matrix = np.random.rand(10,1)
input_comp = pnl.TransferMechanism(name='input_comp',
default_variable=np.zeros(2))
hidden_comp = pnl.TransferMechanism(name='hidden_comp',
default_variable=np.zeros(10),
function=pnl.Logistic())
output_comp = pnl.TransferMechanism(name='output_comp',
default_variable=np.zeros(1),
function=pnl.Logistic())
in_to_hidden_comp = pnl.MappingProjection(name='in_to_hidden_comp',
matrix=in_to_hidden_matrix.copy(),
sender=input_comp,
receiver=hidden_comp)
hidden_to_out_comp = pnl.MappingProjection(name='hidden_to_out_comp',
matrix=hidden_to_out_matrix.copy(),
sender=hidden_comp,
receiver=output_comp)
xor_comp = pnl.Composition()
backprop_pathway = xor_comp.add_backpropagation_learning_pathway([input_comp,
in_to_hidden_comp,
hidden_comp,
hidden_to_out_comp,
output_comp],
learning_rate=10)
# Try readd the same learning pathway (shouldn't error)
backprop_pathway = xor_comp.add_backpropagation_learning_pathway([input_comp,
in_to_hidden_comp,
hidden_comp,
hidden_to_out_comp,
output_comp],
learning_rate=10)
def test_run_no_targets(self):
in_to_hidden_matrix = np.random.rand(2,10)
hidden_to_out_matrix = np.random.rand(10,1)
input_comp = pnl.TransferMechanism(name='input_comp',
default_variable=np.zeros(2))
hidden_comp = pnl.TransferMechanism(name='hidden_comp',
default_variable=np.zeros(10),
function=pnl.Logistic())
output_comp = pnl.TransferMechanism(name='output_comp',
default_variable=np.zeros(1),
function=pnl.Logistic())
in_to_hidden_comp = pnl.MappingProjection(name='in_to_hidden_comp',
matrix=in_to_hidden_matrix.copy(),
sender=input_comp,
receiver=hidden_comp)
hidden_to_out_comp = pnl.MappingProjection(name='hidden_to_out_comp',
matrix=hidden_to_out_matrix.copy(),
sender=hidden_comp,
receiver=output_comp)
xor_comp = pnl.Composition()
backprop_pathway = xor_comp.add_backpropagation_learning_pathway([input_comp,
in_to_hidden_comp,
hidden_comp,
hidden_to_out_comp,
output_comp],
learning_rate=10)
# Try to run without any targets (non-learning
xor_inputs = np.array( # the inputs we will provide to the model
[[0, 0],
[0, 1],
[1, 0],
[1, 1]])
xor_comp.run(inputs={input_comp:xor_inputs})
def test_indepedence_of_learning_pathways_using_same_mechs_in_different_comps(self):
A = TransferMechanism(name="Mech A")
B = TransferMechanism(name="Mech B")
comp1 = Composition(pathways=([A,B], BackPropagation))
comp1.learn(inputs={A: 1.0,
comp1.pathways[0].target: 0.0},
num_trials=2)
assert np.allclose(comp1.results, [[[1.]], [[0.9]]])
comp2 = Composition()
comp2.add_backpropagation_learning_pathway(pathway=[A,B], name='P1')
comp2.learn(inputs={A: 1.0},
targets={B: 0.0},
num_trials=2)
assert np.allclose(comp2.results, comp1.results)
class TestNoLearning:
def test_multilayer(self):
Input_Layer = pnl.TransferMechanism(
name='Input Layer',
function=pnl.Logistic,
default_variable=np.zeros((2,)),
)
Hidden_Layer_1 = pnl.TransferMechanism(
name='Hidden Layer_1',
function=pnl.Logistic(),
default_variable=np.zeros((5,)),
)
Hidden_Layer_2 = pnl.TransferMechanism(
name='Hidden Layer_2',
function=pnl.Logistic(),
default_variable=[0, 0, 0, 0],
)
Output_Layer = pnl.TransferMechanism(
name='Output Layer',
function=pnl.Logistic,
default_variable=[0, 0, 0],
)
Input_Weights_matrix = (np.arange(2 * 5).reshape((2, 5)) + 1) / (2 * 5)
# TEST LEARNING WITH:
# CREATION OF FREE STANDING PROJECTIONS THAT HAVE NO LEARNING (Input_Weights, Middle_Weights and Output_Weights)
# INLINE CREATION OF PROJECTIONS (Input_Weights, Middle_Weights and Output_Weights)
# NO EXPLICIT CREATION OF PROJECTIONS (Input_Weights, Middle_Weights and Output_Weights)
# This projection will be used by the process below by referencing it in the process' pathway;
# note: sender and receiver args don't need to be specified
Input_Weights = pnl.MappingProjection(
name='Input Weights',
matrix=Input_Weights_matrix,
)
c = pnl.Composition()
learning_pathway = c.add_backpropagation_learning_pathway(pathway=[Input_Layer,
Input_Weights,
Hidden_Layer_1,
Hidden_Layer_2,
Output_Layer])
target = learning_pathway.target
stim_list = {Input_Layer: [[-1, 30]],
target: [0, 0, 1]}
c.run(num_trials=10, inputs=stim_list, clamp_input=pnl.SOFT_CLAMP)
expected_Output_Layer_output = [np.array([0.97988347, 0.97988347, 0.97988347])]
np.testing.assert_allclose(expected_Output_Layer_output, Output_Layer.get_output_values(c))
class TestHebbian:
def test_simple_hebbian(self):
Hebb_C = pnl.Composition()
size = 9
Hebb2 = pnl.RecurrentTransferMechanism(
size=size,
function=pnl.Linear,
enable_learning=True,
hetero=0.,
auto=0.,
name='Hebb2',
)
Hebb_C.add_node(Hebb2)
src = [1, 0, 0, 1, 0, 0, 1, 0, 0]
inputs_dict = {Hebb2: np.array(src)}
output = Hebb_C.learn(num_trials=5,
inputs=inputs_dict)
activity = Hebb2.value
assert np.allclose(activity, [[1.86643089, 0., 0., 1.86643089, 0., 0., 1.86643089, 0., 0.]])
class TestReinforcement:
def test_rl(self):
input_layer = pnl.TransferMechanism(size=2,
name='Input Layer')
input_layer.log.set_log_conditions(items=pnl.VALUE)
action_selection = pnl.DDM(input_format=pnl.ARRAY,
function=pnl.DriftDiffusionAnalytical(),
output_ports=[pnl.SELECTED_INPUT_ARRAY],
name='DDM')
action_selection.log.set_log_conditions(items=pnl.SELECTED_INPUT_ARRAY)
comp = pnl.Composition(name='comp')
learning_pathway = comp.add_reinforcement_learning_pathway(pathway=[input_layer, action_selection],
learning_rate=0.05)
learned_projection = learning_pathway.learning_components[pnl.LEARNED_PROJECTIONS]
learning_mechanism = learning_pathway.learning_components[pnl.LEARNING_MECHANISMS]
target_mechanism = learning_pathway.target
comparator_mechanism = learning_pathway.learning_objective
learned_projection.log.set_log_conditions(items=["matrix", "mod_matrix"])
inputs_dict = {input_layer: [[1., 1.], [1., 1.]],
target_mechanism: [[10.], [10.]]
}
learning_mechanism.log.set_log_conditions(items=[pnl.VALUE])
comparator_mechanism.log.set_log_conditions(items=[pnl.VALUE])
target_mechanism.log.set_log_conditions(items=pnl.VALUE)
comp.learn(inputs=inputs_dict)
assert np.allclose(learning_mechanism.value, [np.array([0.4275, 0.]), np.array([0.4275, 0.])])
assert np.allclose(action_selection.value, [[1.], [2.30401336], [0.97340301], [0.02659699], [2.30401336],
[2.08614798], [1.85006765], [2.30401336], [2.08614798],
[1.85006765]])
def test_reinforcement_fixed_targets(self):
input_layer = pnl.TransferMechanism(size=2,
name='Input Layer',
)
action_selection = pnl.DDM(input_format=pnl.ARRAY,
function=pnl.DriftDiffusionAnalytical(),
output_ports=[pnl.SELECTED_INPUT_ARRAY],
name='DDM')
c = pnl.Composition()
c.add_reinforcement_learning_pathway([input_layer, action_selection], learning_rate=0.05)
# LEARN:
c.learn(inputs={input_layer: [[1, 1], [1, 1]]},
targets={action_selection: [[10.], [10.]]})
assert np.allclose(action_selection.value, [[1.], [2.30401336], [0.97340301], [0.02659699], [2.30401336],
[2.08614798], [1.85006765], [2.30401336], [2.08614798], [1.85006765]])
def test_prediction_error_delta_first_run(self):
learning_rate = 0.3
stimulus_onset = 41
sample = np.zeros(60)
sample[stimulus_onset:] = 1
reward_onset = 54
target = np.zeros(60)
target[reward_onset] = 1
delta_function = pnl.PredictionErrorDeltaFunction()
delta_vals = np.zeros((60, 60))
weights = np.zeros(60)
for t in range(60):
print("Timestep {}".format(t))
new_sample = sample * weights
# print("sample = {}".format(new_sample))
delta_vals[t] = delta_function(variable=[new_sample, target])
print("delta: {}".format(delta_vals[t]))
for i in range(59):
weights[i] = weights[i] + learning_rate * sample[i] * \
delta_vals[t][i + 1]
validation_array = np.array([[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
1.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.3,
0.7, 0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.09,
0.42000000000000004, 0.49, 0.0, 0.0, 0.0, 0.0,
0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.027, 0.189,
0.44100000000000006, 0.34299999999999997, 0.0,
0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0081, 0.0756,
0.2646, 0.4116, 0.24009999999999998, 0.0, 0.0,
0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.00243, 0.02835, 0.1323,
0.3087, 0.3601500000000001,
0.16806999999999994, 0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0007289999999999999,
0.010206, 0.05953499999999999, 0.18522,
0.32413500000000006, 0.30252599999999996,
0.117649, 0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.00021869999999999998, 0.0035721,
0.025004699999999998, 0.09724049999999998,
0.2268945, 0.31765230000000005,
0.24706289999999997, 0.08235429999999999, 0.0,
0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 6.560999999999999e-05,
0.0012247199999999999, 0.01000188, 0.04667544,
0.1361367, 0.25412184, 0.29647548,
0.19765032000000005, 0.05764800999999997, 0.0,
0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
1.9682999999999998e-05, 0.000413343,
0.003857868, 0.021003947999999998,
0.073513818, 0.171532242, 0.26682793199999993,
0.2668279320000001, 0.15564962699999996,
0.040353607000000014, 0.0, 0.0, 0.0, 0.0,
0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
5.904899999999999e-06, 0.000137781,
0.0014467005, 0.009001692,
0.036756909000000004, 0.1029193452,
0.200120949, 0.26682793199999993,
0.2334744405000001, 0.12106082099999993,
0.028247524900000043, 0.0, 0.0, 0.0, 0.0,
0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
1.7714699999999997e-06,
4.5467729999999994e-05, 0.00053045685,
0.0037131979500000002, 0.0173282571,
0.05660563986, 0.13207982633999998,
0.2201330439, 0.25682188454999993,
0.19975035465000013, 0.09321683216999987,
0.019773267430000074, 0.0, 0.0, 0.0, 0.0,
0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
5.314409999999999e-07, 1.4880347999999997e-05,
0.00019096446599999996, 0.00148527918,
0.0077977156950000005, 0.029111471928000003,
0.07924789580399999, 0.15849579160799998,
0.23113969609499996, 0.23970042558000004,
0.16779029790600009, 0.07118376274799987,
0.013841287201000085, 0.0, 0.0, 0.0, 0.0,
0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0,
1.5943229999999994e-07, 4.8361131e-06,
6.770558339999998e-05, 0.0005792588802,
0.0033790101345, 0.014191842564900003,
0.044152399090799994, 0.1030222645452,
0.18028896295409996, 0.23370791494049992,
0.21812738727780012, 0.1388083373586,
0.05398102008389993, 0.009688901040700082,
0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 1.61026623e-06,
2.3696954189999994e-05, 0.00022117157244,
0.00141918425649, 0.006622859863620001,
0.023180009522670002, 0.06181335872711999,
0.12620227406787, 0.19631464855001995,
0.22903375664168996, 0.19433167230204007,
0.11336014217619006, 0.040693384370939945,
0.006782230728490046, 0.0, 0.0, 0.0, 0.0,
0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0,
8.719352486999997e-06, 8.2939339665e-05,
0.000580575377655, 0.002980286938629,
0.011590004761335003, 0.034770014284004995,
0.08113003332934499, 0.14723598641251498,
0.20613038097752096, 0.218623131339795,
0.1700402132642851, 0.09156011483461501,
0.03052003827820493, 0.0047475615099430435,
0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0,
3.3601154386499996e-05,
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