Note
This documentation is for a development version. Click here for the latest stable release (v3.0.0).
Nengo frontend API¶
Nengo Objects¶
A network contains ensembles, nodes, connections, and other networks. 

A group of neurons that collectively represent a vector. 

An interface for making connections directly to an ensemble’s neurons. 

Provide nonneural inputs to Nengo objects and process outputs. 

Connects two objects together. 

An interface for making connections to a learning rule. 

A probe is an object that collects data from the simulation. 

class
nengo.
Network
(label=None, seed=None, add_to_container=None)[source]¶ A network contains ensembles, nodes, connections, and other networks.
A network is primarily used for grouping together related objects and connections for visualization purposes. However, you can also use networks as a nice way to reuse network creation code.
To group together related objects that you do not need to reuse, you can create a new
Network
and add objects in awith
block. For example:network = nengo.Network() with network: with nengo.Network(label="Vision"): v1 = nengo.Ensemble(n_neurons=100, dimensions=2) with nengo.Network(label="Motor"): sma = nengo.Ensemble(n_neurons=100, dimensions=2) nengo.Connection(v1, sma)
To reuse a group of related objects, you can create a new subclass of
Network
, and add objects in the__init__
method. For example:class OcularDominance(nengo.Network): def __init__(self): self.column = nengo.Ensemble(n_neurons=100, dimensions=2) network = nengo.Network() with network: left_eye = OcularDominance() right_eye = OcularDominance() nengo.Connection(left_eye.column, right_eye.column)
 Parameters
 labelstr, optional
Name of the network.
 seedint, optional
Random number seed that will be fed to the random number generator. Setting the seed makes the network’s build process deterministic.
 add_to_containerbool, optional
Determines if this network will be added to the current container. If None, this network will be added to the network at the top of the
Network.context
stack unless the stack is empty.
 Attributes
 connectionslist
Connection
instances in this network. ensembleslist
Ensemble
instances in this network. labelstr
Name of this network.
 networkslist
Network
instances in this network. nodeslist
Node
instances in this network. probeslist
Probe
instances in this network. seedint
Random seed used by this network.

property
all_objects
¶ (list) All objects in this network and its subnetworks.

property
all_ensembles
¶ (list) All ensembles in this network and its subnetworks.

property
all_nodes
¶ (list) All nodes in this network and its subnetworks.

property
all_networks
¶ (list) All networks in this network and its subnetworks.

property
all_connections
¶ (list) All connections in this network and its subnetworks.

property
all_probes
¶ (list) All probes in this network and its subnetworks.

property
n_neurons
¶ (int) Number of neurons in this network, including subnetworks.

class
nengo.
Ensemble
(n_neurons, dimensions, radius=Default, encoders=Default, intercepts=Default, max_rates=Default, eval_points=Default, n_eval_points=Default, neuron_type=Default, gain=Default, bias=Default, noise=Default, normalize_encoders=Default, label=Default, seed=Default)[source]¶ A group of neurons that collectively represent a vector.
 Parameters
 n_neuronsint
The number of neurons.
 dimensionsint
The number of representational dimensions.
 radiusint, optional
The representational radius of the ensemble.
 encodersDistribution or (n_neurons, dimensions) array_like, optional
The encoders used to transform from representational space to neuron space. Each row is a neuron’s encoder; each column is a representational dimension.
 interceptsDistribution or (n_neurons,) array_like, optional
The point along each neuron’s encoder where its activity is zero. If
e
is the neuron’s encoder, then the activity will be zero whendot(x, e) <= c
, wherec
is the given intercept. max_ratesDistribution or (n_neurons,) array_like, optional
The activity of each neuron when the input signal
x
is magnitude 1 and aligned with that neuron’s encodere
; i.e., whendot(x, e) = 1
. eval_pointsDistribution or (n_eval_points, dims) array_like, optional
The evaluation points used for decoder solving, spanning the interval (radius, radius) in each dimension, or a distribution from which to choose evaluation points.
 n_eval_pointsint, optional
The number of evaluation points to be drawn from the
eval_points
distribution. If None, then a heuristic is used to determine the number of evaluation points. neuron_type
NeuronType
, optional The model that simulates all neurons in the ensemble (see
NeuronType
). gainDistribution or (n_neurons,) array_like
The gains associated with each neuron in the ensemble. If None, then the gain will be solved for using
max_rates
andintercepts
. biasDistribution or (n_neurons,) array_like
The biases associated with each neuron in the ensemble. If None, then the gain will be solved for using
max_rates
andintercepts
. noiseProcess, optional
Random noise injected directly into each neuron in the ensemble as current. A sample is drawn for each individual neuron on every simulation step.
 normalize_encodersbool, optional
Indicates whether the encoders should be normalized.
 labelstr, optional
A name for the ensemble. Used for debugging and visualization.
 seedint, optional
The seed used for random number generation.
 Attributes
 biasDistribution or (n_neurons,) array_like or None
The biases associated with each neuron in the ensemble.
 dimensionsint
The number of representational dimensions.
 encodersDistribution or (n_neurons, dimensions) array_like
The encoders, used to transform from representational space to neuron space. Each row is a neuron’s encoder, each column is a representational dimension.
 eval_pointsDistribution or (n_eval_points, dims) array_like
The evaluation points used for decoder solving, spanning the interval (radius, radius) in each dimension, or a distribution from which to choose evaluation points.
 gainDistribution or (n_neurons,) array_like or None
The gains associated with each neuron in the ensemble.
 interceptsDistribution or (n_neurons) array_like or None
The point along each neuron’s encoder where its activity is zero. If
e
is the neuron’s encoder, then the activity will be zero whendot(x, e) <= c
, wherec
is the given intercept. labelstr or None
A name for the ensemble. Used for debugging and visualization.
 max_ratesDistribution or (n_neurons,) array_like or None
The activity of each neuron when
dot(x, e) = 1
, wheree
is the neuron’s encoder. n_eval_pointsint or None
The number of evaluation points to be drawn from the
eval_points
distribution. If None, then a heuristic is used to determine the number of evaluation points. n_neuronsint or None
The number of neurons.
 neuron_typeNeuronType
The model that simulates all neurons in the ensemble (see
nengo.neurons
). noiseProcess or None
Random noise injected directly into each neuron in the ensemble as current. A sample is drawn for each individual neuron on every simulation step.
 radiusint
The representational radius of the ensemble.
 seedint or None
The seed used for random number generation.

property
neurons
¶ A direct interface to the neurons in the ensemble.

property
size_in
¶ The dimensionality of the ensemble.

property
size_out
¶ The dimensionality of the ensemble.

class
nengo.ensemble.
Neurons
(ensemble)[source]¶ An interface for making connections directly to an ensemble’s neurons.
This should only ever be accessed through the
neurons
attribute of an ensemble, as a way to signal toConnection
that the connection should be made directly to the neurons rather than to the ensemble’s decoded value, e.g.:with nengo.Network(): a = nengo.Ensemble(10, 1) b = nengo.Ensemble(10, 1) nengo.Connection(a.neurons, b.neurons)

property
ensemble
¶ (Ensemble) The ensemble these neurons are part of.

property
probeable
¶ (tuple) Signals that can be probed in the neuron population.

property
size_in
¶ (int) The number of neurons in the population.

property
size_out
¶ (int) The number of neurons in the population.

property

class
nengo.
Node
(output=Default, size_in=Default, size_out=Default, label=Default, seed=Default)[source]¶ Provide nonneural inputs to Nengo objects and process outputs.
Nodes can accept input, and perform arbitrary computations for the purpose of controlling a Nengo simulation. Nodes are typically not part of a brain model per se, but serve to summarize the assumptions being made about sensory data or other environment variables that cannot be generated by a brain model alone.
Nodes can also be used to test models by providing specific input signals to parts of the model, and can simplify the input/output interface of a
Network
when used as a relay to/from its internal ensembles (seeEnsembleArray
for an example). Parameters
 outputcallable, array_like, or None
Function that transforms the Node inputs into outputs, a constant output value, or None to transmit signals unchanged.
 size_inint, optional
The number of dimensions of the input data parameter.
 size_outint, optional
The size of the output signal. If None, it will be determined based on the values of
output
andsize_in
. labelstr, optional
A name for the node. Used for debugging and visualization.
 seedint, optional
The seed used for random number generation. Note: no aspects of the node are random, so currently setting this seed has no effect.
 Attributes
 labelstr
The name of the node.
 outputcallable, array_like, or None
The given output.
 size_inint
The number of dimensions for incoming connection.
 size_outint
The number of output dimensions.

class
nengo.
Connection
(pre, post, synapse=Default, function=Default, transform=Default, solver=Default, learning_rule_type=Default, eval_points=Default, scale_eval_points=Default, label=Default, seed=Default)[source]¶ Connects two objects together.
The connection between the two object is unidirectional, transmitting information from the first argument,
pre
, to the second argument,post
.Almost any Nengo object can act as the pre or post side of a connection. Additionally, you can use Python slice syntax to access only some of the dimensions of the pre or post object.
For example, if
node
hassize_out=2
andensemble
hassize_in=1
:with nengo.Network() as net: node = nengo.Node(np.zeros(2)) ensemble = nengo.Ensemble(10, 1)
We could not create the following connection:
with net: nengo.Connection(node, ensemble)
But, we could create either of these two connections:
with net: nengo.Connection(node[0], ensemble) nengo.Connection(node[1], ensemble)
 Parameters
 preEnsemble or Neurons or Node
The source Nengo object for the connection.
 postEnsemble or Neurons or Node or LearningRule
The destination object for the connection.
 synapseSynapse or None, optional
Synapse model to use for filtering (see
Synapse
). If None, no synapse will be used and information will be transmitted without any delay (if supported by the backend—some backends may introduce a single time step delay).Note that at least one connection must have a synapse that is not None if components are connected in a cycle. Furthermore, a synaptic filter with a zero time constant is different from a None synapse as a synaptic filter will always add a delay of at least one time step.
 functioncallable or (n_eval_points, size_mid) array_like, optional
Function to compute across the connection. Note that
pre
must be an ensemble to apply a function across the connection. If an array is passed, the function is implicitly defined by the points in the array and the providedeval_points
, which have a onetoone correspondence. transform(size_out, size_mid) array_like, optional
Linear transform mapping the pre output to the post input. This transform is in terms of the sliced size; if either pre or post is a slice, the transform must be shaped according to the sliced dimensionality. Additionally, the function is applied before the transform, so if a function is computed across the connection, the transform must be of shape
(size_out, size_mid)
. solverSolver, optional
Solver instance to compute decoders or weights (see
Solver
). Ifsolver.weights
is True, a full connection weight matrix is computed instead of decoders. learning_rule_typeLearningRuleType or iterable of LearningRuleType, optional
Modifies the decoders or connection weights during simulation.
 eval_points(n_eval_points, size_in) array_like or int, optional
Points at which to evaluate
function
when computing decoders, spanning the interval (pre.radius, pre.radius) in each dimension. If None, will use the eval_points associated withpre
. scale_eval_pointsbool, optional
Indicates whether the evaluation points should be scaled by the radius of the pre Ensemble.
 labelstr, optional
A descriptive label for the connection.
 seedint, optional
The seed used for random number generation.
 Attributes
 is_decodedbool
True if and only if the connection is decoded. This will not occur when
solver.weights
is True or both pre and post areNeurons
. functioncallable
The given function.
 function_sizeint
The output dimensionality of the given function. If no function is specified, function_size will be 0.
 labelstr
A humanreadable connection label for debugging and visualization. If not overridden, incorporates the labels of the pre and post objects.
 learning_rule_typeinstance or list or dict of LearningRuleType, optional
The learning rule types.
 postEnsemble or Neurons or Node or Probe or ObjView
The given post object.
 post_objEnsemble or Neurons or Node or Probe
The underlying post object, even if
post
is anObjView
. post_sliceslice or list or None
The slice associated with
post
if it is an ObjView, or None. preEnsemble or Neurons or Node or ObjView
The given pre object.
 pre_objEnsemble or Neurons or Node
The underlying pre object, even if
post
is anObjView
. pre_sliceslice or list or None
The slice associated with
pre
if it is an ObjView, or None. seedint
The seed used for random number generation.
 solverSolver
The Solver instance that will be used to compute decoders or weights (see
nengo.solvers
). synapseSynapse
The Synapse model used for filtering across the connection (see
nengo.synapses
). transform(size_out, size_mid) array_like
Linear transform mapping the pre function output to the post input.

property
learning_rule
¶ (LearningRule or iterable) Connectable learning rule object(s).

property
size_in
¶ (int) The number of output dimensions of the pre object.
Also the input size of the function, if one is specified.

property
size_mid
¶ (int) The number of output dimensions of the function, if specified.
If the function is not specified, then
size_in == size_mid
.

property
size_out
¶ (int) The number of input dimensions of the post object.
Also the number of output dimensions of the transform.

class
nengo.connection.
LearningRule
(connection, learning_rule_type)[source]¶ An interface for making connections to a learning rule.
Connections to a learning rule are to allow elements of the network to affect the learning rule. For example, learning rules that use error information can obtain that information through a connection.
Learning rule objects should only ever be accessed through the
learning_rule
attribute of a connection.
property
connection
¶ (Connection) The connection modified by the learning rule.

property
modifies
¶ (str) The variable modified by the learning rule.

property
probeable
¶ (tuple) Signals that can be probed in the learning rule.

property
size_out
¶ (int) Cannot connect from learning rules, so always 0.

property

class
nengo.
Probe
(target, attr=None, sample_every=Default, synapse=Default, solver=Default, label=Default, seed=Default)[source]¶ A probe is an object that collects data from the simulation.
This is to be used in any situation where you wish to gather simulation data (spike data, represented values, neuron voltages, etc.) for analysis.
Probes do not directly affect the simulation.
All Nengo objects can be probed (except Probes themselves). Each object has different attributes that can be probed. To see what is probeable for each object, print its
probeable
attribute.with nengo.Network(): ens = nengo.Ensemble(10, 1) print(ens.probeable)
('decoded_output', 'input', 'scaled_encoders')
 Parameters
 targetEnsemble, Neurons, Node, or Connection
The object to probe.
 attrstr, optional
The signal to probe. Refer to the target’s
probeable
list for details. If None, the first element in theprobeable
list will be used. sample_everyfloat, optional
Sampling period in seconds. If None, the
dt
of the simluation will be used. synapseSynapse, optional
A synaptic model to filter the probed signal.
 solverSolver, optional
Solver
to compute decoders for probes that require them. labelstr, optional
A name for the probe. Used for debugging and visualization.
 seedint, optional
The seed used for random number generation.
 Attributes
 attrstr or None
The signal that will be probed. If None, the first element of the target’s
probeable
list will be used. sample_everyfloat or None
Sampling period in seconds. If None, the
dt
of the simluation will be used. solverSolver or None
Solver
to compute decoders. Only used for probes of an ensemble’s decoded output. synapseSynapse or None
A synaptic model to filter the probed signal.
 targetEnsemble, Neurons, Node, or Connection
The object to probe.

property
obj
¶ (Nengo object) The underlying Nengo object target.

property
size_in
¶ (int) Dimensionality of the probed signal.

property
size_out
¶ (int) Cannot connect from probes, so always 0.

property
slice
¶ (slice) The slice associated with the Nengo object target.
Distributions¶
A base class for probability distributions. 

Convenience function to sample a distribution or return samples. 

An arbitrary distribution from a PDF. 

A uniform distribution. 

A Gaussian distribution. 

An exponential distribution (optionally with high values clipped). 

Uniform distribution on or in an ndimensional unit hypersphere. 

Discrete distribution across a set of possible values. 

A set of samples. 

Distribution of the square root of a Beta distributed random variable. 

Distribution of the length of a subvectors of a unit vector. 

Distribution of the cosine of the angle between two random vectors. 

class
nengo.dists.
Distribution
[source]¶ A base class for probability distributions.
The only thing that a probabilities distribution need to define is a
Distribution.sample
method. This base class ensures that all distributions accept the same arguments for the sample function.
sample
(self, n, d=None, rng=numpy.random)[source]¶ Samples the distribution.
 Parameters
 nint
Number samples to take.
 dint or None, optional
The number of dimensions to return. If this is an int, the return value will be of shape
(n, d)
. If None, the return value will be of shape(n,)
. rng
numpy.random.RandomState
, optional Random number generator state.
 Returns
 samples(n,) or (n, d) array_like
Samples as a 1d or 2d array depending on
d
. The second dimension enumerates the dimensions of the process.


nengo.dists.
get_samples
(dist_or_samples, n, d=None, rng=numpy.random)[source]¶ Convenience function to sample a distribution or return samples.
Use this function in situations where you accept an argument that could be a distribution, or could be an
array_like
of samples. Parameters
 dist_or_samples
Distribution
or (n, d) array_like Source of the samples to be returned.
 nint
Number samples to take.
 dint or None, optional
The number of dimensions to return.
 rngRandomState, optional
Random number generator.
 dist_or_samples
 Returns
 samples(n, d) array_like
Examples
from nengo.dists import get_samples rng = np.random.RandomState(seed=0) def mean(values, n=100): samples = get_samples(values, n=n, rng=rng) print("%.4f" % np.mean(samples)) mean([1, 2, 3, 4]) mean(nengo.dists.Gaussian(0, 1))
2.5000 0.0598

class
nengo.dists.
PDF
(x, p)[source]¶ An arbitrary distribution from a PDF.
 Parameters
 xvector_like (n,)
Values of the points to sample from (interpolated).
 pvector_like (n,)
Probabilities of the
x
points.

sample
(self, n, d=None, rng=numpy.random)[source]¶ Samples the distribution.
 Parameters
 nint
Number samples to take.
 dint or None, optional
The number of dimensions to return. If this is an int, the return value will be of shape
(n, d)
. If None, the return value will be of shape(n,)
. rng
numpy.random.RandomState
, optional Random number generator state.
 Returns
 samples(n,) or (n, d) array_like
Samples as a 1d or 2d array depending on
d
. The second dimension enumerates the dimensions of the process.

class
nengo.dists.
Uniform
(low, high, integer=False)[source]¶ A uniform distribution.
It’s equally likely to get any scalar between
low
andhigh
.Note that the order of
low
andhigh
doesn’t matter; iflow < high
this will still work, andlow
will still be a closed interval whilehigh
is open. Parameters
 lowNumber
The closed lower bound of the uniform distribution; samples >= low
 highNumber
The open upper bound of the uniform distribution; samples < high
 integerboolean, optional
If true, sample from a uniform distribution of integers. In this case, low and high should be integers.

sample
(self, n, d=None, rng=numpy.random)[source]¶ Samples the distribution.
 Parameters
 nint
Number samples to take.
 dint or None, optional
The number of dimensions to return. If this is an int, the return value will be of shape
(n, d)
. If None, the return value will be of shape(n,)
. rng
numpy.random.RandomState
, optional Random number generator state.
 Returns
 samples(n,) or (n, d) array_like
Samples as a 1d or 2d array depending on
d
. The second dimension enumerates the dimensions of the process.

class
nengo.dists.
Gaussian
(mean, std)[source]¶ A Gaussian distribution.
This represents a bellcurve centred at
mean
and with spread represented by the standard deviation,std
. Parameters
 meanNumber
The mean of the Gaussian.
 stdNumber
The standard deviation of the Gaussian.
 Raises
 ValidationError if std is <= 0

sample
(self, n, d=None, rng=numpy.random)[source]¶ Samples the distribution.
 Parameters
 nint
Number samples to take.
 dint or None, optional
The number of dimensions to return. If this is an int, the return value will be of shape
(n, d)
. If None, the return value will be of shape(n,)
. rng
numpy.random.RandomState
, optional Random number generator state.
 Returns
 samples(n,) or (n, d) array_like
Samples as a 1d or 2d array depending on
d
. The second dimension enumerates the dimensions of the process.

class
nengo.dists.
Exponential
(scale, shift=0.0, high=inf)[source]¶ An exponential distribution (optionally with high values clipped).
If
high
is left to its default value of infinity, this is a standard exponential distribution. Ifhigh
is set, then any sampled values at or abovehigh
will be clipped so they are slightly belowhigh
. This is useful for thresholding.The probability distribution function (PDF) is given by:
 0 if x < shift p(x) =  1/scale * exp((x  shift)/scale) if x >= shift and x < high  n if x == high  eps  0 if x >= high
where
n
is such that the PDF integrates to one, andeps
is an infinitesimally small number such that samples ofx
are strictly less thanhigh
(in practice,eps
depends on floating point precision). Parameters
 scalefloat
The scale parameter (inverse of the rate parameter lambda). Larger values make the distribution narrower (sharper peak).
 shiftfloat, optional
Amount to shift the distribution by. There will be no values smaller than this shift when sampling from the distribution.
 highfloat, optional
All values larger than or equal to this value will be clipped to slightly less than this value.

sample
(self, n, d=None, rng=numpy.random)[source]¶ Samples the distribution.
 Parameters
 nint
Number samples to take.
 dint or None, optional
The number of dimensions to return. If this is an int, the return value will be of shape
(n, d)
. If None, the return value will be of shape(n,)
. rng
numpy.random.RandomState
, optional Random number generator state.
 Returns
 samples(n,) or (n, d) array_like
Samples as a 1d or 2d array depending on
d
. The second dimension enumerates the dimensions of the process.

class
nengo.dists.
UniformHypersphere
(surface=False, min_magnitude=0)[source]¶ Uniform distribution on or in an ndimensional unit hypersphere.
Sample points are uniformly distributed across the volume (default) or surface of an ndimensional unit hypersphere.
 Parameters
 surfacebool, optional
Whether sample points should be distributed uniformly over the surface of the hyperphere (True), or within the hypersphere (False).
 min_magnitudeNumber, optional
Lower bound on the returned vector magnitudes (such that they are in the range
[min_magnitude, 1]
). Must be in the range [0, 1). Ignored ifsurface
isTrue
.

sample
(self, n, d=None, rng=numpy.random)[source]¶ Samples the distribution.
 Parameters
 nint
Number samples to take.
 dint or None, optional
The number of dimensions to return. If this is an int, the return value will be of shape
(n, d)
. If None, the return value will be of shape(n,)
. rng
numpy.random.RandomState
, optional Random number generator state.
 Returns
 samples(n,) or (n, d) array_like
Samples as a 1d or 2d array depending on
d
. The second dimension enumerates the dimensions of the process.

class
nengo.dists.
Choice
(options, weights=None)[source]¶ Discrete distribution across a set of possible values.
The same as Numpy random’s
choice
, except can take vector or matrix values for the choices. Parameters
 options(N, …) array_like
The options (choices) to choose between. The choice is always done along the first axis, so if
options
is a matrix, the options are the rows of that matrix. weights(N,) array_like, optional
Weights controlling the probability of selecting each option. Will automatically be normalized. If None, weights be uniformly distributed.

sample
(self, n, d=None, rng=numpy.random)[source]¶ Samples the distribution.
 Parameters
 nint
Number samples to take.
 dint or None, optional
The number of dimensions to return. If this is an int, the return value will be of shape
(n, d)
. If None, the return value will be of shape(n,)
. rng
numpy.random.RandomState
, optional Random number generator state.
 Returns
 samples(n,) or (n, d) array_like
Samples as a 1d or 2d array depending on
d
. The second dimension enumerates the dimensions of the process.

class
nengo.dists.
Samples
(samples)[source]¶ A set of samples.
This class is a subclass of
Distribution
so that it can be used in any situation that calls for aDistribution
. However, the call toDistribution.sample
must match the dimensions of the samples or aValidationError
will be raised. Parameters
 samples(n, d) array_like
n
andd
must match what is eventually passed to

sample
(self, n, d=None, rng=numpy.random)[source]¶ Samples the distribution.
 Parameters
 nint
Number samples to take.
 dint or None, optional
The number of dimensions to return. If this is an int, the return value will be of shape
(n, d)
. If None, the return value will be of shape(n,)
. rng
numpy.random.RandomState
, optional Random number generator state.
 Returns
 samples(n,) or (n, d) array_like
Samples as a 1d or 2d array depending on
d
. The second dimension enumerates the dimensions of the process.

class
nengo.dists.
SqrtBeta
(n, m=1)[source]¶ Distribution of the square root of a Beta distributed random variable.
Given
n + m
dimensional random unit vectors, the length of subvectors withm
elements will be distributed according to this distribution. Parameters
 n: int
Number of subvectors.
 m: int, optional
Length of each subvector.
See also

sample
(self, num, d=None, rng=numpy.random)[source]¶ Samples the distribution.
 Parameters
 nint
Number samples to take.
 dint or None, optional
The number of dimensions to return. If this is an int, the return value will be of shape
(n, d)
. If None, the return value will be of shape(n,)
. rng
numpy.random.RandomState
, optional Random number generator state.
 Returns
 samples(n,) or (n, d) array_like
Samples as a 1d or 2d array depending on
d
. The second dimension enumerates the dimensions of the process.

cdf
(x)[source]¶ Cumulative distribution function.
Note
Requires SciPy.
 Parameters
 xarray_like
Evaluation points in [0, 1].
 Returns
 cdfarray_like
Probability that
X <= x
.

class
nengo.dists.
SubvectorLength
(dimensions, subdimensions=1)[source]¶ Distribution of the length of a subvectors of a unit vector.
 Parameters
 dimensionsint
Dimensionality of the complete unit vector.
 subdimensionsint, optional
Dimensionality of the subvector.
See also

class
nengo.dists.
CosineSimilarity
(dimensions)[source]¶ Distribution of the cosine of the angle between two random vectors.
The “cosine similarity” is the cosine of the angle between two vectors, which is equal to the dot product of the vectors, divided by the L2norms of the individual vectors. When these vectors are unit length, this is then simply the distribution of their dot product.
This is also equivalent to the distribution of a single coefficient from a unit vector (a single dimension of
UniformHypersphere(surface=True)
). Furthermore,CosineSimilarity(d+2)
is equivalent to the distribution of a single coordinate from points uniformly sampled from the ddimensional unit ball (a single dimension ofUniformHypersphere(surface=False).sample(n, d)
). These relationships have been detailed in [Voelker2017].This can be used to calculate an intercept
c = ppf(1  p)
such thatdot(u, v) >= c
with probabilityp
, for random unit vectorsu
andv
. In other words, a neuron with interceptppf(1  p)
will fire with probabilityp
for a random unit length input. Parameters
 dimensions: int
Dimensionality of the complete unit vector.
See also

sample
(self, num, d=None, rng=numpy.random)[source]¶ Samples the distribution.
 Parameters
 nint
Number samples to take.
 dint or None, optional
The number of dimensions to return. If this is an int, the return value will be of shape
(n, d)
. If None, the return value will be of shape(n,)
. rng
numpy.random.RandomState
, optional Random number generator state.
 Returns
 samples(n,) or (n, d) array_like
Samples as a 1d or 2d array depending on
d
. The second dimension enumerates the dimensions of the process.

cdf
(x)[source]¶ Cumulative distribution function.
Note
Requires SciPy.
 Parameters
 xarray_like
Evaluation points in [0, 1].
 Returns
 cdfarray_like
Probability that
X <= x
.
Learning rule types¶
Base class for all learning rule objects. 

Prescribed Error Sensitivity learning rule. 

BienenstockCooperMunroe learning rule. 

Oja learning rule. 

Vector Oja learning rule. 

class
nengo.learning_rules.
LearningRuleTypeSizeInParam
(name, default=Unconfigurable, low=None, high=None, low_open=False, high_open=False, optional=False, readonly=None)[source]¶

class
nengo.learning_rules.
LearningRuleType
(learning_rate=Default<1e06>, size_in=0)[source]¶ Base class for all learning rule objects.
To use a learning rule, pass it as a
learning_rule_type
keyword argument to theConnection
on which you want to do learning.Each learning rule exposes two important pieces of metadata that the builder uses to determine what information should be stored.
The
size_in
is the dimensionality of the incoming error signal. It can either take an integer or one of the following string values:'pre'
: vector error signal in preobject space'post'
: vector error signal in postobject space'mid'
: vector error signal in theconn.size_mid
space'pre_state'
: vector error signal in presynaptic ensemble space'post_state'
: vector error signal in presynaptic ensemble space
The difference between
'post_state'
and'post'
is that with the former, if aNeurons
object is passed, it will use the dimensionality of the correspondingEnsemble
, whereas the latter simply uses thepost
objectsize_in
. Similarly with'pre_state'
and'pre'
.The
modifies
attribute denotes the signal targeted by the rule. Options are:'encoders'
'decoders'
'weights'
 Parameters
 learning_ratefloat, optional
A scalar indicating the rate at which
modifies
will be adjusted. size_inint, str, optional
Dimensionality of the error signal (see above).
 Attributes
 learning_ratefloat
A scalar indicating the rate at which
modifies
will be adjusted. size_inint, str
Dimensionality of the error signal.
 modifiesstr
The signal targeted by the learning rule.

class
nengo.
PES
(learning_rate=Default<0.0001>, pre_synapse=Default<Lowpass(tau=0.005)>)[source]¶ Prescribed Error Sensitivity learning rule.
Modifies a connection’s decoders to minimize an error signal provided through a connection to the connection’s learning rule.
 Parameters
 learning_ratefloat, optional
A scalar indicating the rate at which weights will be adjusted.
 pre_synapse
Synapse
, optional Synapse model used to filter the presynaptic activities.
 Attributes
 learning_ratefloat
A scalar indicating the rate at which weights will be adjusted.
 pre_synapse
Synapse
Synapse model used to filter the presynaptic activities.

class
nengo.
BCM
(learning_rate=Default<1e09>, pre_synapse=Default<Lowpass(tau=0.005)>, post_synapse=Default<None>, theta_synapse=Default<Lowpass(tau=1.0)>)[source]¶ BienenstockCooperMunroe learning rule.
Modifies connection weights as a function of the presynaptic activity and the difference between the postsynaptic activity and the average postsynaptic activity.
 Parameters
 learning_ratefloat, optional
A scalar indicating the rate at which weights will be adjusted.
 pre_synapse
Synapse
, optional Synapse model used to filter the presynaptic activities.
 post_synapse
Synapse
, optional Synapse model used to filter the postsynaptic activities. If None,
post_synapse
will be the same aspre_synapse
. theta_synapse
Synapse
, optional Synapse model used to filter the theta signal.
Notes
The BCM rule is dependent on pre and post neural activities, not decoded values, and so is not affected by changes in the size of pre and post ensembles. However, if you are decoding from the post ensemble, the BCM rule will have an increased effect on larger post ensembles because more connection weights are changing. In these cases, it may be advantageous to scale the learning rate on the BCM rule by
1 / post.n_neurons
. Attributes
 learning_ratefloat
A scalar indicating the rate at which weights will be adjusted.
 post_synapse
Synapse
Synapse model used to filter the postsynaptic activities.
 pre_synapse
Synapse
Synapse model used to filter the presynaptic activities.
 theta_synapse
Synapse
Synapse model used to filter the theta signal.

class
nengo.
Oja
(learning_rate=Default<1e06>, pre_synapse=Default<Lowpass(tau=0.005)>, post_synapse=Default<None>, beta=Default<1.0>)[source]¶ Oja learning rule.
Modifies connection weights according to the Hebbian Oja rule, which augments typically Hebbian coactivity with a “forgetting” term that is proportional to the weight of the connection and the square of the postsynaptic activity.
 Parameters
 learning_ratefloat, optional
A scalar indicating the rate at which weights will be adjusted.
 pre_synapse
Synapse
, optional Synapse model used to filter the presynaptic activities.
 post_synapse
Synapse
, optional Synapse model used to filter the postsynaptic activities. If None,
post_synapse
will be the same aspre_synapse
. betafloat, optional
A scalar weight on the forgetting term.
Notes
The Oja rule is dependent on pre and post neural activities, not decoded values, and so is not affected by changes in the size of pre and post ensembles. However, if you are decoding from the post ensemble, the Oja rule will have an increased effect on larger post ensembles because more connection weights are changing. In these cases, it may be advantageous to scale the learning rate on the Oja rule by
1 / post.n_neurons
.

class
nengo.
Voja
(learning_rate=Default<0.01>, post_synapse=Default<Lowpass(tau=0.005)>)[source]¶ Vector Oja learning rule.
Modifies an ensemble’s encoders to be selective to its inputs.
A connection to the learning rule will provide a scalar weight for the learning rate, minus 1. For instance, 0 is normal learning, 1 is no learning, and less than 1 causes antilearning or “forgetting”.
 Parameters
 post_taufloat, optional
Filter constant on activities of neurons in post population.
 learning_ratefloat, optional
A scalar indicating the rate at which encoders will be adjusted.
 post_synapse
Synapse
, optional Synapse model used to filter the postsynaptic activities.
 Attributes
 learning_ratefloat
A scalar indicating the rate at which encoders will be adjusted.
 post_synapse
Synapse
Synapse model used to filter the postsynaptic activities.
Neuron types¶
Compute firing rates (in Hz) for given vector input, 

Base class for Nengo neuron models. 

Signifies that an ensemble should simulate in direct mode. 

A rectified linear neuron model. 

A rectified integrate and fire neuron model. 

A nonspiking neuron model whose response curve is a sigmoid. 

A nonspiking neuron model whose response curve is a hyperbolic tangent. 

Nonspiking version of the leaky integrateandfire (LIF) neuron model. 

Spiking version of the leaky integrateandfire (LIF) neuron model. 

Adaptive nonspiking version of the LIF neuron model. 

Adaptive spiking version of the LIF neuron model. 

Izhikevich neuron model. 

Base class for neuron types that turn rate types into spiking ones. 

Turn a rate neuron type into a spiking one with regular interspike intervals. 

Turn a rate neuron type into a spiking one using stochastic rounding. 

Turn a rate neuron type into a spiking one with Poisson spiking statistics. 

nengo.neurons.
settled_firingrate
(step, J, state, dt=0.001, settle_time=0.1, sim_time=1.0)[source]¶ Compute firing rates (in Hz) for given vector input,
x
.Unlike the default naive implementation, this approach takes into account some characteristics of spiking neurons. We start by simulating the neurons for a short amount of time, to let any initial transients settle. Then, we run the neurons for a second and find the average (which should approximate the firing rate).
 Parameters
 stepfunction
the step function of the neuron type
 Jndarray
a vector of currents to generate firing rates from
 statedict of ndarrays
additional state needed by the step function

class
nengo.neurons.
NeuronType
(initial_state=None)[source]¶ Base class for Nengo neuron models.
 Parameters
 initial_state{str: Distribution or array_like}
Mapping from state variables names to their desired initial value. These values will override the defaults set in the class’s state attribute.
 Attributes
 state{str: Distribution}
State variables held by the neuron type during simulation. Values in the dict indicate their initial values, or how to obtain those initial values. These elements can also be probed in the neuron population.
 negativebool
Whether the neurons can emit negative outputs (i.e. negative spikes or rates).

current
(x, gain, bias)[source]¶ Compute current injected in each neuron given input, gain and bias.
Note that
x
is assumed to be already projected onto the encoders associated with the neurons and normalized to radius 1, so the maximum expected current for a neuron occurs when input for that neuron is 1. Parameters
 x(n_samples,) or (n_samples, n_neurons) array_like
Scalar inputs for which to calculate current.
 gain(n_neurons,) array_like
Gains associated with each neuron.
 bias(n_neurons,) array_like
Bias current associated with each neuron.
 Returns
 current(n_samples, n_neurons)
Current to be injected in each neuron.

gain_bias
(max_rates, intercepts)[source]¶ Compute the gain and bias needed to satisfy max_rates, intercepts.
This takes the neurons, approximates their response function, and then uses that approximation to find the gain and bias value that will give the requested intercepts and max_rates.
Note that this default implementation is very slow! Whenever possible, subclasses should override this with a neuronspecific implementation.
 Parameters
 max_rates(n_neurons,) array_like
Maximum firing rates of neurons.
 intercepts(n_neurons,) array_like
Xintercepts of neurons.
 Returns
 gain(n_neurons,) array_like
Gain associated with each neuron. Sometimes denoted alpha.
 bias(n_neurons,) array_like
Bias current associated with each neuron.

max_rates_intercepts
(gain, bias)[source]¶ Compute the max_rates and intercepts given gain and bias.
Note that this default implementation is very slow! Whenever possible, subclasses should override this with a neuronspecific implementation.
 Parameters
 gain(n_neurons,) array_like
Gain associated with each neuron. Sometimes denoted alpha.
 bias(n_neurons,) array_like
Bias current associated with each neuron.
 Returns
 max_rates(n_neurons,) array_like
Maximum firing rates of neurons.
 intercepts(n_neurons,) array_like
Xintercepts of neurons.

rates
(x, gain, bias)[source]¶ Compute firing rates (in Hz) for given input
x
.This default implementation takes the naive approach of running the step function for a second. This should suffice for most ratebased neuron types; for spiking neurons it will likely fail (those models should override this function).
Note that
x
is assumed to be already projected onto the encoders associated with the neurons and normalized to radius 1, so the maximum expected rate for a neuron occurs when input for that neuron is 1. Parameters
 x(n_samples,) or (n_samples, n_neurons) array_like
Scalar inputs for which to calculate rates.
 gain(n_neurons,) array_like
Gains associated with each neuron.
 bias(n_neurons,) array_like
Bias current associated with each neuron.
 Returns
 rates(n_samples, n_neurons) ndarray
The firing rates at each given value of
x
.

step
(dt, J, output, **state)[source]¶ Implements the differential equation for this neuron type.
At a minimum, NeuronType subclasses must implement this method. That implementation should modify the
output
parameter rather than returning anything, for efficiency reasons. Parameters
 dtfloat
Simulation timestep.
 J(n_neurons,) array_like
Input currents associated with each neuron.
 output(n_neurons,) array_like
Output activity associated with each neuron (e.g., spikes or firing rates).
 state{str: array_like}
State variables associated with the population.

class
nengo.neurons.
NeuronTypeParam
(name, default=Unconfigurable, optional=False, readonly=None)[source]¶

class
nengo.
Direct
(initial_state=None)[source]¶ Signifies that an ensemble should simulate in direct mode.
In direct mode, the ensemble represents and transforms signals perfectly, rather than through a neural approximation. Note that direct mode ensembles with recurrent connections can easily diverge; most other neuron types will instead saturate at a certain high firing rate.

class
nengo.
RectifiedLinear
(amplitude=1, initial_state=None)[source]¶ A rectified linear neuron model.
Each neuron is modeled as a rectified line. That is, the neuron’s activity scales linearly with current, unless it passes below zero, at which point the neural activity will stay at zero.
 Parameters
 amplitudefloat
Scaling factor on the neuron output. Corresponds to the relative amplitude of the output of the neuron.
 initial_state{str: Distribution or array_like}
Mapping from state variables names to their desired initial value. These values will override the defaults set in the class’s state attribute.

class
nengo.
SpikingRectifiedLinear
(amplitude=1, initial_state=None)[source]¶ A rectified integrate and fire neuron model.
Each neuron is modeled as a rectified line. That is, the neuron’s activity scales linearly with current, unless the current is less than zero, at which point the neural activity will stay at zero. This is a spiking version of the RectifiedLinear neuron model.
 Parameters
 amplitudefloat
Scaling factor on the neuron output. Corresponds to the relative amplitude of the output spikes of the neuron.
 initial_state{str: Distribution or array_like}
Mapping from state variables names to their desired initial value. These values will override the defaults set in the class’s state attribute.

class
nengo.
Sigmoid
(tau_ref=0.0025, initial_state=None)[source]¶ A nonspiking neuron model whose response curve is a sigmoid.
Since the tuning curves are strictly positive, the
intercepts
correspond to the inflection point of each sigmoid. That is,f(intercept) = 0.5
wheref
is the pure sigmoid function. Parameters
 tau_reffloat
The neuron refractory period, in seconds. The maximum firing rate of the neurons is
1 / tau_ref
. Must be positive (i.e.tau_ref > 0
). initial_state{str: Distribution or array_like}
Mapping from state variables names to their desired initial value. These values will override the defaults set in the class’s state attribute.

class
nengo.
Tanh
(tau_ref=0.0025, initial_state=None)[source]¶ A nonspiking neuron model whose response curve is a hyperbolic tangent.
 Parameters
 tau_reffloat
The neuron refractory period, in seconds. The maximum firing rate of the neurons is
1 / tau_ref
. Must be positive (i.e.tau_ref > 0
). initial_state{str: Distribution or array_like}
Mapping from state variables names to their desired initial value. These values will override the defaults set in the class’s state attribute.

class
nengo.
LIFRate
(tau_rc=0.02, tau_ref=0.002, amplitude=1, initial_state=None)[source]¶ Nonspiking version of the leaky integrateandfire (LIF) neuron model.
 Parameters
 tau_rcfloat
Membrane RC time constant, in seconds. Affects how quickly the membrane voltage decays to zero in the absence of input (larger = slower decay).
 tau_reffloat
Absolute refractory period, in seconds. This is how long the membrane voltage is held at zero after a spike.
 amplitudefloat
Scaling factor on the neuron output. Corresponds to the relative amplitude of the output spikes of the neuron.
 initial_state{str: Distribution or array_like}
Mapping from state variables names to their desired initial value. These values will override the defaults set in the class’s state attribute.

class
nengo.
LIF
(tau_rc=0.02, tau_ref=0.002, min_voltage=0, amplitude=1, initial_state=None)[source]¶ Spiking version of the leaky integrateandfire (LIF) neuron model.
 Parameters
 tau_rcfloat
Membrane RC time constant, in seconds. Affects how quickly the membrane voltage decays to zero in the absence of input (larger = slower decay).
 tau_reffloat
Absolute refractory period, in seconds. This is how long the membrane voltage is held at zero after a spike.
 min_voltagefloat
Minimum value for the membrane voltage. If
np.inf
, the voltage is never clipped. amplitudefloat
Scaling factor on the neuron output. Corresponds to the relative amplitude of the output spikes of the neuron.
 initial_state{str: Distribution or array_like}
Mapping from state variables names to their desired initial value. These values will override the defaults set in the class’s state attribute.

class
nengo.
AdaptiveLIFRate
(tau_n=1, inc_n=0.01, tau_rc=0.02, tau_ref=0.002, amplitude=1, initial_state=None)[source]¶ Adaptive nonspiking version of the LIF neuron model.
Works as the LIF model, except with adapation state
n
, which is subtracted from the input current. Its dynamics are:tau_n dn/dt = n
where
n
is incremented byinc_n
when the neuron spikes. Parameters
 tau_nfloat
Adaptation time constant. Affects how quickly the adaptation state decays to zero in the absence of spikes (larger = slower decay).
 inc_nfloat
Adaptation increment. How much the adaptation state is increased after each spike.
 tau_rcfloat
Membrane RC time constant, in seconds. Affects how quickly the membrane voltage decays to zero in the absence of input (larger = slower decay).
 tau_reffloat
Absolute refractory period, in seconds. This is how long the membrane voltage is held at zero after a spike.
 amplitudefloat
Scaling factor on the neuron output. Corresponds to the relative amplitude of the output spikes of the neuron.
 initial_state{str: Distribution or array_like}
Mapping from state variables names to their desired initial value. These values will override the defaults set in the class’s state attribute.
References
 1
Camera, Giancarlo La, et al. “Minimal models of adapted neuronal response to in VivoLike input currents.” Neural computation 16.10 (2004): 21012124.

class
nengo.
AdaptiveLIF
(tau_n=1, inc_n=0.01, tau_rc=0.02, tau_ref=0.002, min_voltage=0, amplitude=1, initial_state=None)[source]¶ Adaptive spiking version of the LIF neuron model.
Works as the LIF model, except with adapation state
n
, which is subtracted from the input current. Its dynamics are:tau_n dn/dt = n
where
n
is incremented byinc_n
when the neuron spikes. Parameters
 tau_nfloat
Adaptation time constant. Affects how quickly the adaptation state decays to zero in the absence of spikes (larger = slower decay).
 inc_nfloat
Adaptation increment. How much the adaptation state is increased after each spike.
 tau_rcfloat
Membrane RC time constant, in seconds. Affects how quickly the membrane voltage decays to zero in the absence of input (larger = slower decay).
 tau_reffloat
Absolute refractory period, in seconds. This is how long the membrane voltage is held at zero after a spike.
 min_voltagefloat
Minimum value for the membrane voltage. If
np.inf
, the voltage is never clipped. amplitudefloat
Scaling factor on the neuron output. Corresponds to the relative amplitude of the output spikes of the neuron.
 initial_state{str: Distribution or array_like}
Mapping from state variables names to their desired initial value. These values will override the defaults set in the class’s state attribute.
References
 1
Camera, Giancarlo La, et al. “Minimal models of adapted neuronal response to in VivoLike input currents.” Neural computation 16.10 (2004): 21012124.

class
nengo.
Izhikevich
(tau_recovery=0.02, coupling=0.2, reset_voltage= 65.0, reset_recovery=8.0, initial_state=None)[source]¶ Izhikevich neuron model.
This implementation is based on the original paper [1]; however, we rename some variables for clarity. What was originally ‘v’ we term ‘voltage’, which represents the membrane potential of each neuron. What was originally ‘u’ we term ‘recovery’, which represents membrane recovery, “which accounts for the activation of K+ ionic currents and inactivation of Na+ ionic currents.” The ‘a’, ‘b’, ‘c’, and ‘d’ parameters are also renamed (see the parameters below).
We use default values that correspond to regular spiking (‘RS’) neurons. For other classes of neurons, set the parameters as follows.
Intrinsically bursting (IB):
reset_voltage=55, reset_recovery=4
Chattering (CH):
reset_voltage=50, reset_recovery=2
Fast spiking (FS):
tau_recovery=0.1
Lowthreshold spiking (LTS):
coupling=0.25
Resonator (RZ):
tau_recovery=0.1, coupling=0.26
 Parameters
 tau_recoveryfloat, optional
(Originally ‘a’) Time scale of the recovery variable.
 couplingfloat, optional
(Originally ‘b’) How sensitive recovery is to subthreshold fluctuations of voltage.
 reset_voltagefloat, optional
(Originally ‘c’) The voltage to reset to after a spike, in millivolts.
 reset_recoveryfloat, optional
(Originally ‘d’) The recovery value to reset to after a spike.
 initial_state{str: Distribution or array_like}
Mapping from state variables names to their desired initial value. These values will override the defaults set in the class’s state attribute.
References
 1
E. M. Izhikevich, “Simple model of spiking neurons.” IEEE Transactions on Neural Networks, vol. 14, no. 6, pp. 15691572. (http://www.izhikevich.org/publications/spikes.pdf)

class
nengo.neurons.
RatesToSpikesNeuronType
(base_type, amplitude=1.0, initial_state=None)[source]¶ Base class for neuron types that turn rate types into spiking ones.

gain_bias
(max_rates, intercepts)[source]¶ Compute the gain and bias needed to satisfy max_rates, intercepts.
This takes the neurons, approximates their response function, and then uses that approximation to find the gain and bias value that will give the requested intercepts and max_rates.
Note that this default implementation is very slow! Whenever possible, subclasses should override this with a neuronspecific implementation.
 Parameters
 max_rates(n_neurons,) array_like
Maximum firing rates of neurons.
 intercepts(n_neurons,) array_like
Xintercepts of neurons.
 Returns
 gain(n_neurons,) array_like
Gain associated with each neuron. Sometimes denoted alpha.
 bias(n_neurons,) array_like
Bias current associated with each neuron.

max_rates_intercepts
(gain, bias)[source]¶ Compute the max_rates and intercepts given gain and bias.
Note that this default implementation is very slow! Whenever possible, subclasses should override this with a neuronspecific implementation.
 Parameters
 gain(n_neurons,) array_like
Gain associated with each neuron. Sometimes denoted alpha.
 bias(n_neurons,) array_like
Bias current associated with each neuron.
 Returns
 max_rates(n_neurons,) array_like
Maximum firing rates of neurons.
 intercepts(n_neurons,) array_like
Xintercepts of neurons.

rates
(x, gain, bias)[source]¶ Compute firing rates (in Hz) for given input
x
.This default implementation takes the naive approach of running the step function for a second. This should suffice for most ratebased neuron types; for spiking neurons it will likely fail (those models should override this function).
Note that
x
is assumed to be already projected onto the encoders associated with the neurons and normalized to radius 1, so the maximum expected rate for a neuron occurs when input for that neuron is 1. Parameters
 x(n_samples,) or (n_samples, n_neurons) array_like
Scalar inputs for which to calculate rates.
 gain(n_neurons,) array_like
Gains associated with each neuron.
 bias(n_neurons,) array_like
Bias current associated with each neuron.
 Returns
 rates(n_samples, n_neurons) ndarray
The firing rates at each given value of
x
.

step
(dt, J, output, **state)[source]¶ Implements the differential equation for this neuron type.
At a minimum, NeuronType subclasses must implement this method. That implementation should modify the
output
parameter rather than returning anything, for efficiency reasons. Parameters
 dtfloat
Simulation timestep.
 J(n_neurons,) array_like
Input currents associated with each neuron.
 output(n_neurons,) array_like
Output activity associated with each neuron (e.g., spikes or firing rates).
 state{str: array_like}
State variables associated with the population.


class
nengo.
RegularSpiking
(base_type, amplitude=1.0, initial_state=None)[source]¶ Turn a rate neuron type into a spiking one with regular interspike intervals.
Spikes at regular intervals based on the rates of the base neuron type. [1]
 Parameters
 base_typeNeuronType
A ratebased neuron type to convert to a regularly spiking neuron.
 amplitudefloat
Scaling factor on the neuron output. Corresponds to the relative amplitude of the output spikes of the neuron.
 initial_state{str: Distribution or array_like}
Mapping from state variables names to their desired initial value. These values will override the defaults set in the class’s state attribute.
References
 1
Voelker, A. R., Rasmussen, D., & Eliasmith, C. (2020). A Spike in Performance: Training HybridSpiking Neural Networks with Quantized Activation Functions. arXiv preprint arXiv:2002.03553. (https://arxiv.org/abs/2002.03553)

step
(dt, J, output, voltage)[source]¶ Implements the differential equation for this neuron type.
At a minimum, NeuronType subclasses must implement this method. That implementation should modify the
output
parameter rather than returning anything, for efficiency reasons. Parameters
 dtfloat
Simulation timestep.
 J(n_neurons,) array_like
Input currents associated with each neuron.
 output(n_neurons,) array_like
Output activity associated with each neuron (e.g., spikes or firing rates).
 state{str: array_like}
State variables associated with the population.

class
nengo.
StochasticSpiking
(base_type, amplitude=1.0, initial_state=None)[source]¶ Turn a rate neuron type into a spiking one using stochastic rounding.
The expected number of spikes per timestep
e = dt * r
is determined by the base type firing rater
and the timestepdt
. Given the fractional partf
and integer partq
ofe
, the number of generated spikes isq
with probability1  f
andq + 1
with probabilityf
. Fore
much less than one, this is very similar to Poisson statistics. Parameters
 base_typeNeuronType
A ratebased neuron type to convert to a Poisson spiking neuron.
 amplitudefloat
Scaling factor on the neuron output. Corresponds to the relative amplitude of the output spikes of the neuron.
 initial_state{str: Distribution or array_like}
Mapping from state variables names to their desired initial value. These values will override the defaults set in the class’s state attribute.

step
(dt, J, output, rng, **base_state)[source]¶ Implements the differential equation for this neuron type.
At a minimum, NeuronType subclasses must implement this method. That implementation should modify the
output
parameter rather than returning anything, for efficiency reasons. Parameters
 dtfloat
Simulation timestep.
 J(n_neurons,) array_like
Input currents associated with each neuron.
 output(n_neurons,) array_like
Output activity associated with each neuron (e.g., spikes or firing rates).
 state{str: array_like}
State variables associated with the population.

class
nengo.
PoissonSpiking
(base_type, amplitude=1.0, initial_state=None)[source]¶ Turn a rate neuron type into a spiking one with Poisson spiking statistics.
Spikes with Poisson probability based on the rates of the base neuron type.
 Parameters
 base_typeNeuronType
A ratebased neuron type to convert to a Poisson spiking neuron.
 amplitudefloat
Scaling factor on the neuron output. Corresponds to the relative amplitude of the output spikes of the neuron.
 initial_state{str: Distribution or array_like}
Mapping from state variables names to their desired initial value. These values will override the defaults set in the class’s state attribute.

step
(dt, J, output, rng, **base_state)[source]¶ Implements the differential equation for this neuron type.
At a minimum, NeuronType subclasses must implement this method. That implementation should modify the
output
parameter rather than returning anything, for efficiency reasons. Parameters
 dtfloat
Simulation timestep.
 J(n_neurons,) array_like
Input currents associated with each neuron.
 output(n_neurons,) array_like
Output activity associated with each neuron (e.g., spikes or firing rates).
 state{str: array_like}
State variables associated with the population.
Processes¶
A general system with input, output, and state. 

Fullspectrum white noise process. 

Filtered white noise process. 

Brown noise process (aka Brownian noise, red noise, Wiener process). 

An ideal lowpass filtered white noise process. 

Present a series of inputs, each for the same fixed length of time. 

A piecewise function with different options for interpolation. 

class
nengo.processes.
WhiteNoise
(dist=Gaussian(mean=0, std=1), scale=True, **kwargs)[source]¶ Fullspectrum white noise process.
 Parameters
 distDistribution, optional
The distribution from which to draw samples.
 scalebool, optional
Whether to scale the white noise for integration. Integrating white noise requires using a time constant of
sqrt(dt)
instead ofdt
on the noise term [1], to ensure the magnitude of the integrated noise does not change withdt
. seedint, optional
Random number seed. Ensures noise will be the same each run.
References
 1
Gillespie, D.T. (1996) Exact numerical simulation of the Ornstein Uhlenbeck process and its integral. Phys. Rev. E 54, pp. 208491.

make_step
(shape_in, shape_out, dt, rng, state)[source]¶ Create function that advances the process forward one time step.
This must be implemented by all custom processes. The parameters below indicate what information is provided by the builder.
 Parameters
 shape_intuple
The shape of the input signal.
 shape_outtuple
The shape of the output signal.
 dtfloat
The simulation timestep.
 rng
numpy.random.RandomState
A random number generator.
 state{string:
numpy.ndarray
} A dictionary mapping keys to signals, where the signals fully represent the state of the process. The signals are initialized by
Process.make_state
.New in version 3.0.0.

class
nengo.processes.
FilteredNoise
(synapse=Lowpass(tau=0.005), dist=Gaussian(mean=0, std=1), scale=True, **kwargs)[source]¶ Filtered white noise process.
This process takes white noise and filters it using the provided synapse.
 Parameters
 synapseSynapse, optional
The synapse to use to filter the noise.
 distDistribution, optional
The distribution used to generate the white noise.
 scalebool, optional
Whether to scale the white noise for integration, making the output signal invariant to
dt
. seedint, optional
Random number seed. Ensures noise will be the same each run.

make_state
(shape_in, shape_out, dt, dtype=None)[source]¶ Get a dictionary of signals to represent the state of this process.
The builder uses this to allocate memory for the process state, so that the state can be represented as part of the whole simulator state.
New in version 3.0.0.
 Parameters
 shape_intuple
The shape of the input signal.
 shape_outtuple
The shape of the output signal.
 dtfloat
The simulation timestep.
 dtype
numpy.dtype
The data type requested by the builder. If
None
, then this function is free to choose the best type for the signals involved.
 Returns
 initial_state{string:
numpy.ndarray
} A dictionary mapping keys to arrays containing the initial state values. The keys will be used to identify the signals in
Process.make_step
.
 initial_state{string:

make_step
(shape_in, shape_out, dt, rng, state)[source]¶ Create function that advances the process forward one time step.
This must be implemented by all custom processes. The parameters below indicate what information is provided by the builder.
 Parameters
 shape_intuple
The shape of the input signal.
 shape_outtuple
The shape of the output signal.
 dtfloat
The simulation timestep.
 rng
numpy.random.RandomState
A random number generator.
 state{string:
numpy.ndarray
} A dictionary mapping keys to signals, where the signals fully represent the state of the process. The signals are initialized by
Process.make_state
.New in version 3.0.0.

class
nengo.processes.
BrownNoise
(dist=Gaussian(mean=0, std=1), **kwargs)[source]¶ Brown noise process (aka Brownian noise, red noise, Wiener process).
This process is the integral of white noise.
 Parameters
 distDistribution, optional
The distribution used to generate the white noise.
 seedint, optional
Random number seed. Ensures noise will be the same each run.

class
nengo.processes.
WhiteSignal
(period, high, rms=0.5, y0=None, **kwargs)[source]¶ An ideal lowpass filtered white noise process.
This signal is created in the frequency domain, and designed to have exactly equal power at all frequencies below the cutoff frequency, and no power above the cutoff.
The signal is naturally periodic, so it can be used beyond its period while still being continuous with continuous derivatives.
 Parameters
 periodfloat
A white noise signal with this period will be generated. Samples will repeat after this duration.
 highfloat
The cutoff frequency of the lowpass filter, in Hz. Must not exceed the Nyquist frequency for the simulation timestep, which is
0.5 / dt
. rmsfloat, optional
The root mean square power of the filtered signal
 y0float, optional
Align the phase of each output dimension to begin at the value that is closest (in absolute value) to y0.
 seedint, optional
Random number seed. Ensures noise will be the same each run.

make_step
(shape_in, shape_out, dt, rng, state)[source]¶ Create function that advances the process forward one time step.
This must be implemented by all custom processes. The parameters below indicate what information is provided by the builder.
 Parameters
 shape_intuple
The shape of the input signal.
 shape_outtuple
The shape of the output signal.
 dtfloat
The simulation timestep.
 rng
numpy.random.RandomState
A random number generator.
 state{string:
numpy.ndarray
} A dictionary mapping keys to signals, where the signals fully represent the state of the process. The signals are initialized by
Process.make_state
.New in version 3.0.0.

class
nengo.processes.
PresentInput
(inputs, presentation_time, **kwargs)[source]¶ Present a series of inputs, each for the same fixed length of time.
 Parameters
 inputsarray_like
Inputs to present, where each row is an input. Rows will be flattened.
 presentation_timefloat
Show each input for this amount of time (in seconds).

make_step
(shape_in, shape_out, dt, rng, state)[source]¶ Create function that advances the process forward one time step.
This must be implemented by all custom processes. The parameters below indicate what information is provided by the builder.
 Parameters
 shape_intuple
The shape of the input signal.
 shape_outtuple
The shape of the output signal.
 dtfloat
The simulation timestep.
 rng
numpy.random.RandomState
A random number generator.
 state{string:
numpy.ndarray
} A dictionary mapping keys to signals, where the signals fully represent the state of the process. The signals are initialized by
Process.make_state
.New in version 3.0.0.

class
nengo.processes.
PiecewiseDataParam
(name, default=Unconfigurable, optional=False, readonly=None)[source]¶ Piecewisespecific validation for the data dictionary.
In the
Piecewise
data dict, the keys are points in time (float) and values are numerical constants or callables of the same dimensionality.

class
nengo.processes.
Piecewise
(data, interpolation='zero', **kwargs)[source]¶ A piecewise function with different options for interpolation.
Given an input dictionary of
{0: 0, 0.5: 1, 0.75: 0.5, 1: 0}
, this process will emit the numerical values (0, 1, 0.5, 0) starting at the corresponding time points (0, 0.5, 0.75, 1).The keys in the input dictionary must be times (float or int). The values in the dictionary can be floats, lists of floats, or numpy arrays. All lists or numpy arrays must be of the same length, as the output shape of the process will be determined by the shape of the values.
Interpolation on the data points using
scipy.interpolate
is also supported. The default interpolation is ‘zero’, which creates a piecewise function whose values change at the specified time points. So the above example would be shortcut for:def function(t): if t < 0.5: return 0 elif t < 0.75: return 1 elif t < 1: return 0.5 else: return 0
For times before the first specified time, an array of zeros (of the correct length) will be emitted. This means that the above can be simplified to:
from nengo.processes import Piecewise Piecewise({0.5: 1, 0.75: 0.5, 1: 0})
 Parameters
 datadict
A dictionary mapping times to the values that should be emitted at those times. Times must be numbers (ints or floats), while values can be numbers, lists of numbers, numpy arrays of numbers, or callables that return any of those options.
 interpolationstr, optional
One of ‘linear’, ‘nearest’, ‘slinear’, ‘quadratic’, ‘cubic’, or ‘zero’. Specifies how to interpolate between times with specified value. ‘zero’ creates a plain piecewise function whose values begin at corresponding time points, while all other options interpolate as described in
scipy.interpolate
.
Examples
from nengo.processes import Piecewise process = Piecewise({0.5: 1, 0.75: 1, 1: 0}) with nengo.Network() as model: u = nengo.Node(process, size_out=process.default_size_out) up = nengo.Probe(u) with nengo.Simulator(model, progress_bar=False) as sim: sim.run(1.5) f = sim.data[up] t = sim.trange() print(f[t == 0.2]) print(f[t == 0.58])
[[ 0.]] [[ 1.]]
 Attributes
 datadict
A dictionary mapping times to the values that should be emitted at those times. Times are numbers (ints or floats), while values can be numbers, lists of numbers, numpy arrays of numbers, or callables that return any of those options.
 interpolationstr
One of ‘linear’, ‘nearest’, ‘slinear’, ‘quadratic’, ‘cubic’, or ‘zero’. Specifies how to interpolate between times with specified value. ‘zero’ creates a plain piecewise function whose values change at corresponding time points, while all other options interpolate as described in
scipy.interpolate
.

make_step
(shape_in, shape_out, dt, rng, state)[source]¶ Create function that advances the process forward one time step.
This must be implemented by all custom processes. The parameters below indicate what information is provided by the builder.
 Parameters
 shape_intuple
The shape of the input signal.
 shape_outtuple
The shape of the output signal.
 dtfloat
The simulation timestep.
 rng
numpy.random.RandomState
A random number generator.
 state{string:
numpy.ndarray
} A dictionary mapping keys to signals, where the signals fully represent the state of the process. The signals are initialized by
Process.make_state
.New in version 3.0.0.

class
nengo.
Process
(default_size_in=0, default_size_out=1, default_dt=0.001, seed=None)[source]¶ A general system with input, output, and state.
For more details on how to use processes and make custom process subclasses, see Processes and how to use them.
 Parameters
 default_size_inint
Sets the default size in for nodes using this process.
 default_size_outint
Sets the default size out for nodes running this process. Also, if
d
is not specified inrun
orrun_steps
, this will be used. default_dtfloat
If
dt
is not specified inrun
,run_steps
,ntrange
, ortrange
, this will be used. seedint, optional
Random number seed. Ensures random factors will be the same each run.
 Attributes
 default_dtfloat
If
dt
is not specified inrun
,run_steps
,ntrange
, ortrange
, this will be used. default_size_inint
The default size in for nodes using this process.
 default_size_outint
The default size out for nodes running this process. Also, if
d
is not specified inrun
orrun_steps
, this will be used. seedint or None
Random number seed. Ensures random factors will be the same each run.

apply
(self, x, d=None, dt=None, rng=numpy.random, copy=True, **kwargs)[source]¶ Run process on a given input.
Keyword arguments that do not appear in the parameter list below will be passed to the
make_step
function of this process. Parameters
 xndarray
The input signal given to the process.
 dint, optional
Output dimensionality. If None,
default_size_out
will be used. dtfloat, optional
Simulation timestep. If None,
default_dt
will be used. rng
numpy.random.RandomState
Random number generator used for stochstic processes.
 copybool, optional
If True, a new output array will be created for output. If False, the input signal
x
will be overwritten.

get_rng
(rng)[source]¶ Get a properly seeded independent RNG for the process step.
 Parameters
 rng
numpy.random.RandomState
The parent random number generator to use if the seed is not set.
 rng

make_state
(shape_in, shape_out, dt, dtype=None)[source]¶ Get a dictionary of signals to represent the state of this process.
The builder uses this to allocate memory for the process state, so that the state can be represented as part of the whole simulator state.
New in version 3.0.0.
 Parameters
 shape_intuple
The shape of the input signal.
 shape_outtuple
The shape of the output signal.
 dtfloat
The simulation timestep.
 dtype
numpy.dtype
The data type requested by the builder. If
None
, then this function is free to choose the best type for the signals involved.
 Returns
 initial_state{string:
numpy.ndarray
} A dictionary mapping keys to arrays containing the initial state values. The keys will be used to identify the signals in
Process.make_step
.
 initial_state{string:

make_step
(shape_in, shape_out, dt, rng, state)[source]¶ Create function that advances the process forward one time step.
This must be implemented by all custom processes. The parameters below indicate what information is provided by the builder.
 Parameters
 shape_intuple
The shape of the input signal.
 shape_outtuple
The shape of the output signal.
 dtfloat
The simulation timestep.
 rng
numpy.random.RandomState
A random number generator.
 state{string:
numpy.ndarray
} A dictionary mapping keys to signals, where the signals fully represent the state of the process. The signals are initialized by
Process.make_state
.New in version 3.0.0.

run
(self, t, d=None, dt=None, rng=numpy.random, **kwargs)[source]¶ Run process without input for given length of time.
Keyword arguments that do not appear in the parameter list below will be passed to the
make_step
function of this process. Parameters
 tfloat
The length of time to run.
 dint, optional
Output dimensionality. If None,
default_size_out
will be used. dtfloat, optional
Simulation timestep. If None,
default_dt
will be used. rng
numpy.random.RandomState
Random number generator used for stochstic processes.

run_steps
(self, n_steps, d=None, dt=None, rng=numpy.random, **kwargs)[source]¶ Run process without input for given number of steps.
Keyword arguments that do not appear in the parameter list below will be passed to the
make_step
function of this process. Parameters
 n_stepsint
The number of steps to run.
 dint, optional
Output dimensionality. If None,
default_size_out
will be used. dtfloat, optional
Simulation timestep. If None,
default_dt
will be used. rng
numpy.random.RandomState
Random number generator used for stochstic processes.
Solvers¶
Classes concerned with solving for decoders or full weight matrices.
Decoder or weight solver. 

Unregularized leastsquares solver. 

Leastsquares solver with additive Gaussian white noise. 

Leastsquares solver with multiplicative white noise. 

Leastsquares solver with L2 regularization. 

Leastsquares solver with L2 regularization on nonzero components. 

Leastsquares solver with L1 and L2 regularization (elastic net). 

Find sparser decoders/weights by dropping small values. 

Nonnegative leastsquares solver without regularization. 

Nonnegative leastsquares solver with L2 regularization. 

Nonnegative leastsquares with L2 regularization on nonzero components. 

Manually pass in weights, bypassing the decoder solver. 

class
nengo.solvers.
Solver
(weights=False)[source]¶ Decoder or weight solver.
A solver can have the
weights
parameter equal toTrue
orFalse
.Weight solvers are used to form neurontoneuron weight matrices. They can be compositional or noncompositional. Noncompositional solvers must operate on the whole neurontoneuron weight matrix (i.e., each target is a separate postsynaptic current, without the bias term), while compositional solvers operate in the decoded statespace (i.e., each target is a dimension in statespace). Compositional solvers then combine the returned
X
with the transform and/or encoders to generate the full weight matrix.For a solver to be compositional, the following property must be true:
X = solver(A, Y) if and only if L(X) = solver(A, L(Y))
where
L
is some arbitrary linear operator (i.e., the transform and/or encoders for the postsynaptic population). This property can then be leveraged by the backend for efficiency. See the solver’scompositional
class attribute to determine if it is compositional.Nonweight solvers always operate in the decoded statespace regardless of whether they are compositional or noncompositional.

class
nengo.solvers.
SolverParam
(name, default=Unconfigurable, optional=False, readonly=None)[source]¶ A parameter in which the value is a
Solver
instance.

class
nengo.solvers.
Lstsq
(weights=False, rcond=0.01)[source]¶ Unregularized leastsquares solver.
 Parameters
 weightsbool, optional
If False, solve for decoders. If True, solve for weights.
 rcondfloat, optional
Cutoff ratio for small singular values (see
numpy.linalg.lstsq
).
 Attributes
 rcondfloat
Cutoff ratio for small singular values (see
numpy.linalg.lstsq
). weightsbool
If False, solve for decoders. If True, solve for weights.

class
nengo.solvers.
LstsqNoise
(weights=False, noise=0.1, solver=Cholesky())[source]¶ Leastsquares solver with additive Gaussian white noise.
 Parameters
 weightsbool, optional
If False, solve for decoders. If True, solve for weights.
 noisefloat, optional
Amount of noise, as a fraction of the neuron activity.
 solver
LeastSquaresSolver
, optional Subsolver to use for solving the least squares problem.
 Attributes
 noisefloat
Amount of noise, as a fraction of the neuron activity.
 solver
LeastSquaresSolver
Subsolver to use for solving the least squares problem.
 weightsbool
If False, solve for decoders. If True, solve for weights.

class
nengo.solvers.
LstsqMultNoise
(weights=False, noise=0.1, solver=Cholesky())[source]¶ Leastsquares solver with multiplicative white noise.
 Parameters
 weightsbool, optional
If False, solve for decoders. If True, solve for weights.
 noisefloat, optional
Amount of noise, as a fraction of the neuron activity.
 solver
LeastSquaresSolver
, optional Subsolver to use for solving the least squares problem.
 Attributes
 noisefloat
Amount of noise, as a fraction of the neuron activity.
 solver
LeastSquaresSolver
Subsolver to use for solving the least squares problem.
 weightsbool
If False, solve for decoders. If True, solve for weights.

class
nengo.solvers.
LstsqL2
(weights=False, reg=0.1, solver=Cholesky())[source]¶ Leastsquares solver with L2 regularization.
 Parameters
 weightsbool, optional
If False, solve for decoders. If True, solve for weights.
 regfloat, optional
Amount of regularization, as a fraction of the neuron activity.
 solver
LeastSquaresSolver
, optional Subsolver to use for solving the least squares problem.
 Attributes
 regfloat
Amount of regularization, as a fraction of the neuron activity.
 solver
LeastSquaresSolver
Subsolver to use for solving the least squares problem.
 weightsbool
If False, solve for decoders. If True, solve for weights.

class
nengo.solvers.
LstsqL2nz
(weights=False, reg=0.1, solver=Cholesky())[source]¶ Leastsquares solver with L2 regularization on nonzero components.
 Parameters
 weightsbool, optional
If False, solve for decoders. If True, solve for weights.
 regfloat, optional
Amount of regularization, as a fraction of the neuron activity.
 solver
LeastSquaresSolver
, optional Subsolver to use for solving the least squares problem.
 Attributes
 regfloat
Amount of regularization, as a fraction of the neuron activity.
 solver
LeastSquaresSolver
Subsolver to use for solving the least squares problem.
 weightsbool
If False, solve for decoders. If True, solve for weights.

class
nengo.solvers.
LstsqL1
(weights=False, l1=0.0001, l2=1e06, max_iter=1000)[source]¶ Leastsquares solver with L1 and L2 regularization (elastic net).
This method is well suited for creating sparse decoders or weight matrices.
Note
Requires scikitlearn.
 Parameters
 weightsbool, optional
If False, solve for decoders. If True, solve for weights.
 l1float, optional
Amount of L1 regularization.
 l2float, optional
Amount of L2 regularization.
 max_iterint, optional
Maximum number of iterations for the underlying elastic net.
 Attributes
 l1float
Amount of L1 regularization.
 l2float
Amount of L2 regularization.
 weightsbool
If False, solve for decoders. If True, solve for weights.
 max_iterint
Maximum number of iterations for the underlying elastic net.

class
nengo.solvers.
LstsqDrop
(weights=False, drop=0.25, solver1=LstsqL2(reg=0.001), solver2=LstsqL2())[source]¶ Find sparser decoders/weights by dropping small values.
This solver first solves for coefficients (decoders/weights) with L2 regularization, drops those nearest to zero, and retrains remaining.
 Parameters
 weightsbool, optional
If False, solve for decoders. If True, solve for weights.
 dropfloat, optional
Fraction of decoders or weights to set to zero.
 solver1Solver, optional
Solver for finding the initial decoders.
 solver2Solver, optional
Used for resolving for the decoders after dropout.
 Attributes
 dropfloat
Fraction of decoders or weights to set to zero.
 solver1Solver
Solver for finding the initial decoders.
 solver2Solver
Used for resolving for the decoders after dropout.
 weightsbool
If False, solve for decoders. If True, solve for weights.

class
nengo.solvers.
Nnls
(weights=False)[source]¶ Nonnegative leastsquares solver without regularization.
Similar to
Lstsq
, except the output values are nonnegative.If solving for nonnegative weights, it is important that the intercepts of the postpopulation are also nonnegative, since neurons with negative intercepts will never be silent, affecting output accuracy.
Note
Requires SciPy.
 Parameters
 weightsbool, optional
If False, solve for decoders. If True, solve for weights.
 Attributes
 weightsbool
If False, solve for decoders. If True, solve for weights.

class
nengo.solvers.
NnlsL2
(weights=False, reg=0.1)[source]¶ Nonnegative leastsquares solver with L2 regularization.
Similar to
LstsqL2
, except the output values are nonnegative.If solving for nonnegative weights, it is important that the intercepts of the postpopulation are also nonnegative, since neurons with negative intercepts will never be silent, affecting output accuracy.
Note
Requires SciPy.
 Parameters
 weightsbool, optional
If False, solve for decoders. If True, solve for weights.
 regfloat, optional
Amount of regularization, as a fraction of the neuron activity.
 Attributes
 regfloat
Amount of regularization, as a fraction of the neuron activity.
 weightsbool
If False, solve for decoders. If True, solve for weights.

class
nengo.solvers.
NnlsL2nz
(weights=False, reg=0.1)[source]¶ Nonnegative leastsquares with L2 regularization on nonzero components.
Similar to
LstsqL2nz
, except the output values are nonnegative.If solving for nonnegative weights, it is important that the intercepts of the postpopulation are also nonnegative, since neurons with negative intercepts will never be silent, affecting output accuracy.
Note
Requires SciPy.
 Parameters
 weightsbool, optional
If False, solve for decoders. If True, solve for weights.
 regfloat, optional
Amount of regularization, as a fraction of the neuron activity.
 Attributes
 regfloat
Amount of regularization, as a fraction of the neuron activity.
 weightsbool
If False, solve for decoders. If True, solve for weights.

class
nengo.solvers.
NoSolver
(values=None, weights=False)[source]¶ Manually pass in weights, bypassing the decoder solver.
 Parameters
 values(n_neurons, size_out) array_like, optional
The array of decoders to use.
size_out
is the dimensionality of the decoded signal (determined by the connection function). IfNone
, which is the default, the solver will return an appropriately sized array of zeros. weightsbool, optional
If False, connection will use factored weights (decoders from this solver, transform, and encoders). If True, connection will use a full weight matrix (created by linearly combining decoder, transform, and encoders).
 Attributes
 values(n_neurons, size_out) array_like, optional
The array of decoders to use.
size_out
is the dimensionality of the decoded signal (determined by the connection function). IfNone
, which is the default, the solver will return an appropriately sized array of zeros. weightsbool, optional
If False, connection will use factored weights (decoders from this solver, transform, and encoders). If True, connection will use a full weight matrix (created by linearly combining decoder, transform, and encoders).
Solver methods¶
These solvers are to be passed as arguments to Solver
objects.
For example:
from nengo.solvers import LstsqL2
from nengo.utils.least_squares_solvers import SVD
with nengo.Network():
ens_a = nengo.Ensemble(10, 1)
ens_b = nengo.Ensemble(10, 1)
nengo.Connection(ens_a, ens_b, solver=LstsqL2(solver=SVD()))
Extract data from A/Y matrices. 

Returns the rootmeansquared error (RMSE) of the solution X. 

Linear least squares system solver. 

Solve a leastsquares system using the Cholesky decomposition. 

Solve a leastsquares system using Scipy’s conjugate gradient. 

Solve a leastsquares system using Scipy’s LSMR. 

Solve a leastsquares system using conjugate gradient. 

Solve a multipleRHS leastsquares system using block conj. 

Solve a leastsquares system using full SVD. 

Solve a leastsquares system using a randomized (partial) SVD. 

A parameter where the value is a LeastSquaresSolver. 

nengo.utils.least_squares_solvers.
rmses
(A, X, Y)[source]¶ Returns the rootmeansquared error (RMSE) of the solution X.

class
nengo.utils.least_squares_solvers.
LeastSquaresSolver
[source]¶ Linear least squares system solver.

class
nengo.utils.least_squares_solvers.
Cholesky
(transpose=None)[source]¶ Solve a leastsquares system using the Cholesky decomposition.

class
nengo.utils.least_squares_solvers.
ConjgradScipy
(tol=0.0001, atol=1e08)[source]¶ Solve a leastsquares system using Scipy’s conjugate gradient.
 Parameters
References
 1(1,2)
scipy.sparse.linalg.cg documentation, https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.cg.html

class
nengo.utils.least_squares_solvers.
LSMRScipy
(tol=0.0001)[source]¶ Solve a leastsquares system using Scipy’s LSMR.

class
nengo.utils.least_squares_solvers.
Conjgrad
(tol=0.01, maxiters=None, X0=None)[source]¶ Solve a leastsquares system using conjugate gradient.

class
nengo.utils.least_squares_solvers.
BlockConjgrad
(tol=0.01, X0=None)[source]¶ Solve a multipleRHS leastsquares system using block conj. gradient.

class
nengo.utils.least_squares_solvers.
RandomizedSVD
(n_components=60, n_oversamples=10, n_iter=0)[source]¶ Solve a leastsquares system using a randomized (partial) SVD.
Useful for solving large matrices quickly, but nonoptimally.
 Parameters
 n_componentsint, optional
The number of SVD components to compute. A small survey of activity matrices suggests that the first 60 components capture almost all the variance.
 n_oversamplesint, optional
The number of additional samples on the range of A.
 n_iterint, optional
The number of power iterations to perform (can help with noisy data).
See also
sklearn.utils.extmath.randomized_svd
Function used by this class
Synapse models¶
Abstract base class for synapse models. 

General linear timeinvariant (LTI) system synapse. 

Standard firstorder lowpass filter synapse. 

Alphafunction filter synapse. 

Triangular finite impulse response (FIR) synapse. 

class
nengo.synapses.
Synapse
(default_size_in=1, default_size_out=None, default_dt=0.001, seed=None)[source]¶ Abstract base class for synapse models.
Conceptually, a synapse model emulates a biological synapse, taking in input in the form of released neurotransmitter and opening ion channels to allow more or less current to flow into the neuron.
In Nengo, the implementation of a synapse is as a specific case of a
Process
in which the input and output shapes are the same. The input is the current across the synapse, and the output is the current that will be induced in the postsynaptic neuron.Synapses also contain the
Synapse.filt
andSynapse.filtfilt
methods, which make it easy to use Nengo’s synapse models outside of Nengo simulations. Parameters
 default_size_inint, optional
The size_in used if not specified.
 default_size_outint
The size_out used if not specified. If None, will be the same as default_size_in.
 default_dtfloat
The simulation timestep used if not specified.
 seedint, optional
Random number seed. Ensures random factors will be the same each run.
 Attributes
 default_dtfloat
The simulation timestep used if not specified.
 default_size_inint
The size_in used if not specified.
 default_size_outint
The size_out used if not specified.
 seedint, optional
Random number seed. Ensures random factors will be the same each run.

make_state
(shape_in, shape_out, dt, dtype=None, y0=None)[source]¶ Get a dictionary of signals to represent the state of this process.
The builder uses this to allocate memory for the process state, so that the state can be represented as part of the whole simulator state.
New in version 3.0.0.
 Parameters
 shape_intuple
The shape of the input signal.
 shape_outtuple
The shape of the output signal.
 dtfloat
The simulation timestep.
 dtype
numpy.dtype
The data type requested by the builder. If
None
, then this function is free to choose the best type for the signals involved.
 Returns
 initial_state{string:
numpy.ndarray
} A dictionary mapping keys to arrays containing the initial state values. The keys will be used to identify the signals in
Process.make_step
.
 initial_state{string:

filt
(x, dt=None, axis=0, y0=0, copy=True, filtfilt=False)[source]¶ Filter
x
with this synapse model. Parameters
 xarray_like
The signal to filter.
 dtfloat, optional
The timestep of the input signal. If None,
default_dt
will be used. axisint, optional
The axis along which to filter.
 y0array_like, optional
The starting state of the filter output. Must be zero for unstable linear systems.
 copybool, optional
Whether to copy the input data, or simply work inplace.
 filtfiltbool, optional
If True, runs the process forward then backward on the signal, for zerophase filtering (like Matlab’s
filtfilt
).

filtfilt
(x, **kwargs)[source]¶ Zerophase filtering of
x
using this filter.Equivalent to
filt(x, filtfilt=True, **kwargs)
.

class
nengo.
LinearFilter
(num, den, analog=True, method='zoh', **kwargs)[source]¶ General linear timeinvariant (LTI) system synapse.
This class can be used to implement any linear filter, given the filter’s transfer function. [1]
 Parameters
 numarray_like
Numerator coefficients of transfer function.
 denarray_like
Denominator coefficients of transfer function.
 analogboolean, optional
Whether the synapse coefficients are analog (i.e. continuoustime), or discrete. Analog coefficients will be converted to discrete for simulation using the simulator
dt
. methodstring
The method to use for discretization (if
analog
is True). Seescipy.signal.cont2discrete
for information about the options.New in version 3.0.0.
References
 Attributes
 analogboolean
Whether the synapse coefficients are analog (i.e. continuoustime), or discrete. Analog coefficients will be converted to discrete for simulation using the simulator
dt
. denndarray
Denominator coefficients of transfer function.
 numndarray
Numerator coefficients of transfer function.
 methodstring
The method to use for discretization (if
analog
is True). Seescipy.signal.cont2discrete
for information about the options.

evaluate
(frequencies)[source]¶ Evaluate the transfer function at the given frequencies.
Examples
Using the
evaluate
function to make a Bode plot:import matplotlib.pyplot as plt synapse = nengo.synapses.LinearFilter([1], [0.02, 1]) f = np.logspace(1, 3, 100) y = synapse.evaluate(f) plt.subplot(211); plt.semilogx(f, 20*np.log10(np.abs(y))) plt.xlabel('frequency [Hz]'); plt.ylabel('magnitude [dB]') plt.subplot(212); plt.semilogx(f, np.angle(y)) plt.xlabel('frequency [Hz]'); plt.ylabel('phase [radians]')

make_state
(shape_in, shape_out, dt, dtype=None, y0=0)[source]¶ Get a dictionary of signals to represent the state of this process.
The builder uses this to allocate memory for the process state, so that the state can be represented as part of the whole simulator state.
New in version 3.0.0.
 Parameters
 shape_intuple
The shape of the input signal.
 shape_outtuple
The shape of the output signal.
 dtfloat
The simulation timestep.
 dtype
numpy.dtype
The data type requested by the builder. If
None
, then this function is free to choose the best type for the signals involved.
 Returns
 initial_state{string:
numpy.ndarray
} A dictionary mapping keys to arrays containing the initial state values. The keys will be used to identify the signals in
Process.make_step
.
 initial_state{string:

make_step
(shape_in, shape_out, dt, rng, state)[source]¶ Returns a
Step
instance that implements the linear filter.

class
OneXScalar
(A, B, C, D, X)[source]¶ Step for systems with one state element, no passthrough, and a size1 input.
Using the builtin float math improves performance.

class
nengo.
Lowpass
(tau, **kwargs)[source]¶ Standard firstorder lowpass filter synapse.
The impulseresponse function is given by:
f(t) = (1 / tau) * exp(t / tau)
 Parameters
 taufloat
The time constant of the filter in seconds.
 Attributes
 taufloat
The time constant of the filter in seconds.

class
nengo.
Alpha
(tau, **kwargs)[source]¶ Alphafunction filter synapse.
The impulseresponse function is given by:
alpha(t) = (t / tau**2) * exp(t / tau)
and was found by [1] to be a good basic model for synapses.
 Parameters
 taufloat
The time constant of the filter in seconds.
References
 1
Mainen, Z.F. and Sejnowski, T.J. (1995). Reliability of spike timing in neocortical neurons. Science (New York, NY), 268(5216):15036.
 Attributes
 taufloat
The time constant of the filter in seconds.

class
nengo.synapses.
Triangle
(t, **kwargs)[source]¶ Triangular finite impulse response (FIR) synapse.
This synapse has a triangular and finite impulse response. The length of the triangle is
t
seconds; thus the digital filter will havet / dt + 1
taps. Parameters
 tfloat
Length of the triangle, in seconds.
 Attributes
 tfloat
Length of the triangle, in seconds.

make_state
(shape_in, shape_out, dt, dtype=None, y0=0)[source]¶ Get a dictionary of signals to represent the state of this process.
The builder uses this to allocate memory for the process state, so that the state can be represented as part of the whole simulator state.
New in version 3.0.0.
 Parameters
 shape_intuple
The shape of the input signal.
 shape_outtuple
The shape of the output signal.
 dtfloat
The simulation timestep.
 dtype
numpy.dtype
The data type requested by the builder. If
None
, then this function is free to choose the best type for the signals involved.
 Returns
 initial_state{string:
numpy.ndarray
} A dictionary mapping keys to arrays containing the initial state values. The keys will be used to identify the signals in
Process.make_step
.
 initial_state{string:

make_step
(shape_in, shape_out, dt, rng, state)[source]¶ Create function that advances the process forward one time step.
This must be implemented by all custom processes. The parameters below indicate what information is provided by the builder.
 Parameters
 shape_intuple
The shape of the input signal.
 shape_outtuple
The shape of the output signal.
 dtfloat
The simulation timestep.
 rng
numpy.random.RandomState
A random number generator.
 state{string:
numpy.ndarray
} A dictionary mapping keys to signals, where the signals fully represent the state of the process. The signals are initialized by
Process.make_state
.New in version 3.0.0.
Transforms¶
A base class for connection transforms. 

A dense matrix transformation between an input and output signal. 

Represents a sparse matrix. 

A sparse matrix transformation between an input and output signal. 

An Ndimensional convolutional transform. 

Represents shape information with variable channel position. 

Directly pass the signal through without any transform operations. 

class
nengo.transforms.
Transform
[source]¶ A base class for connection transforms.
New in version 3.0.0.

sample
(self, rng=numpy.random)[source]¶ Returns concrete weights to implement the specified transform.
 Parameters
 rng
numpy.random.RandomState
, optional Random number generator state.
 rng
 Returns
 array_like
Transform weights

property
size_in
¶ Expected size of input to transform.

property
size_out
¶ Expected size of output from transform.


class
nengo.transforms.
ChannelShapeParam
(name, default=Unconfigurable, length=None, low=0, optional=False, readonly=None)[source]¶ A parameter where the value must be a shape with channels.
New in version 3.0.0.

class
nengo.
Dense
(shape, init=1.0)[source]¶ A dense matrix transformation between an input and output signal.
New in version 3.0.0.
 Parameters
 shapetuple of int
The shape of the dense matrix:
(size_out, size_in)
. init
Distribution
or array_like, optional A Distribution used to initialize the transform matrix, or a concrete instantiation for the matrix. If the matrix is square we also allow a scalar (equivalent to
np.eye(n) * init
) or a vector (equivalent tonp.diag(init)
) to represent the matrix more compactly.

sample
(self, rng=numpy.random)[source]¶ Returns concrete weights to implement the specified transform.
 Parameters
 rng
numpy.random.RandomState
, optional Random number generator state.
 rng
 Returns
 array_like
Transform weights

property
init_shape
¶ The shape of the initial value.

property
size_in
¶ Expected size of input to transform.

property
size_out
¶ Expected size of output from transform.

class
nengo.transforms.
SparseInitParam
(name, default=Unconfigurable, optional=False, readonly=None)[source]¶

class
nengo.transforms.
SparseMatrix
(indices, data, shape)[source]¶ Represents a sparse matrix.
New in version 3.0.0.
 Parameters
 indicesarray_like of int
An Nx2 array of integers indicating the (row,col) coordinates for the N nonzero elements in the matrix.
 dataarray_like or
Distribution
An Nx1 array defining the value of the nonzero elements in the matrix (corresponding to
indices
), or aDistribution
that will be used to initialize the nonzero elements. shapetuple of int
Shape of the full matrix.

allocate
()[source]¶ Return a
scipy.sparse.csr_matrix
or dense matrix equivalent.We mark this data as readonly to be consistent with how other data associated with signals are allocated. If this allocated data is to be modified, it should be copied first.

sample
(self, rng=numpy.random)[source]¶ Convert
Distribution
data to fixed array. Parameters
 rng
numpy.random.RandomState
Random number generator that will be used when sampling distribution.
 rng
 Returns
 matrix
SparseMatrix
A new
SparseMatrix
instance withDistribution
converted to array ifself.data
is aDistribution
, otherwise simply returnsself
.
 matrix

class
nengo.
Sparse
(shape, indices=None, init=1.0)[source]¶ A sparse matrix transformation between an input and output signal.
New in version 3.0.0.
 Parameters
 shapetuple of int
The full shape of the sparse matrix:
(size_out, size_in)
. indicesarray_like of int
An Nx2 array of integers indicating the (row,col) coordinates for the N nonzero elements in the matrix.
 init
Distribution
or array_like, optional A Distribution used to initialize the transform matrix, or a concrete instantiation for the matrix. If the matrix is square we also allow a scalar (equivalent to
np.eye(n) * init
) or a vector (equivalent tonp.diag(init)
) to represent the matrix more compactly.

sample
(self, rng=numpy.random)[source]¶ Returns concrete weights to implement the specified transform.
 Parameters
 rng
numpy.random.RandomState
, optional Random number generator state.
 rng
 Returns
 array_like
Transform weights

property
size_in
¶ Expected size of input to transform.

property
size_out
¶ Expected size of output from transform.

class
nengo.
Convolution
(n_filters, input_shape, kernel_size=3, 3, strides=1, 1, padding='valid', channels_last=True, init=Uniform(low= 1, high=1))[source]¶ An Ndimensional convolutional transform.
The dimensionality of the convolution is determined by the input shape.
New in version 3.0.0.
 Parameters
 n_filtersint
The number of convolutional filters to apply
 input_shapetuple of int or
ChannelShape
Shape of the input signal to the convolution; e.g.,
(height, width, channels)
for a 2D convolution withchannels_last=True
. kernel_sizetuple of int, optional
Size of the convolutional kernels (1 element for a 1D convolution, 2 for a 2D convolution, etc.).
 stridestuple of int, optional
Stride of the convolution (1 element for a 1D convolution, 2 for a 2D convolution, etc.).
 padding
"same"
or"valid"
, optional Padding method for input signal. “Valid” means no padding, and convolution will only be applied to the fullyoverlapping areas of the input signal (meaning the output will be smaller). “Same” means that the input signal is zeropadded so that the output is the same shape as the input.
 channels_lastbool, optional
If
True
(default), the channels are the last dimension in the input signal (e.g., a 28x28 image with 3 channels would have shape(28, 28, 3)
).False
means that channels are the first dimension (e.g.,(3, 28, 28)
). init
Distribution
orndarray
, optional A predefined kernel with shape
kernel_size + (input_channels, n_filters)
, or aDistribution
that will be used to initialize the kernel.
Notes
As is typical in neural networks, this is technically correlation rather than convolution (because the kernel is not flipped).

sample
(self, rng=numpy.random)[source]¶ Returns concrete weights to implement the specified transform.
 Parameters
 rng
numpy.random.RandomState
, optional Random number generator state.
 rng
 Returns
 array_like
Transform weights

property
kernel_shape
¶ Full shape of kernel.

property
size_in
¶ Expected size of input to transform.

property
size_out
¶ Expected size of output from transform.

property
dimensions
¶ Dimensionality of convolution.

property
output_shape
¶ Output shape after applying convolution to input.

class
nengo.transforms.
ChannelShape
(shape, channels_last=True)[source]¶ Represents shape information with variable channel position.
New in version 3.0.0.
 Parameters
 shapetuple of int
Signal shape
 channels_lastbool, optional
If True (default), the last item in
shape
represents the channels, and the rest are spatial dimensions. Otherwise, the first item inshape
is the channel dimension.

property
spatial_shape
¶ The spatial part of the shape (omitting channels).

property
size
¶ The total number of elements in the represented signal.

property
n_channels
¶ The number of channels in the represented signal.

property
dimensions
¶ The spatial dimensionality of the represented signal.

class
nengo.transforms.
NoTransform
(size_in)[source]¶ Directly pass the signal through without any transform operations.
New in version 3.1.0.
 Parameters
 size_inint
Dimensionality of transform input and output.

sample
(self, rng=numpy.random)[source]¶ Returns concrete weights to implement the specified transform.
 Parameters
 rng
numpy.random.RandomState
, optional Random number generator state.
 rng
 Raises
 TypeError
There is nothing to sample for NoTransform, so it is an error if this is called.

property
size_in
¶ Expected size of input to transform.

property
size_out
¶ Expected size of output from transform.