Custom Factors

Julia's type inference allows overloading of member functions outside a module. Therefore new factors can be defined at any time. To better illustrate, in this example we will add new factors into the Main context after construction of the factor graph has already begun.

using IncrementalInference

# You must import this to later overload
import IncrementalInference: getSample

Let's start with some factor graph:

# empty factor graph object
fg = initfg()

# add a variable in 1 dimension
addVariable!(fg, :x0, ContinuousEuclid{1})
addVariable!(fg, :x1, ContinuousEuclid{1})

# and a basic IIF.Prior from existing factors and Distributions.jl
pr0 = Prior(Normal(0,1))
addFactor!(fg, [:x0], pr0)

# making fg slightly more interesting -- i.e. x0 and x1 are 10 units apart on 1D Euclidean space
addFactor!(fg, [:x0; :x1], LinearRelative(Normal(10,1)))

IIF is a convenient const alias of the module IncrementalInference, similarly AMP for ApproxManifoldProducts.

Defining a New Prior (Absolute / Gauge)

Now lets define in Main scope our own prior, MyPrior which allows for arbitrary distributions that inherit from <: IIF.SamplableBelief:

struct MyPrior{T <: SamplableBelief} <: IIF.AbstractPrior

# import IncrementalInference: getSample
# sampling function
getSample(cfo::CalcFactor{<:MyPrior}, N::Int=1) = (reshape(rand(cfo.factor.Z,N),1,:), )

Note the following critical aspects that allows IIF to use the new definition:

  • <:AbstractPrior as a unary factor that introduces absolute (or gauge) information about only one variable.
  • getSample is overloaded with dispatch on:
    • (cfo::CalcFactor{<:MyPrior}, ::Int)
  • getSample must return a ::Tuple, even if there is only stochastic value (as is the case above).
    • The first value in the tuple is special, and must be of type <:AbstractMatrix{<:Real}. We ensure that with the reshape.

IIF internally uses the number of rows in the first element of the getSample return tuple (i.e. the matrix) to extract the measurement dimension for this factor. In this case it is 1 dimensional.


getSample works similar for factors below. If the measurement dimension is 2D (i.e. zDim=2) then you should not use reshape(..., 1,N) which would force the samples into a 1 row matrix. The reshape(.., 1,N) in the above example is added as convenient way to convert from the rand return value a ::Array{Float64,1} to the required ::Array{Float64,2} type.

To recap, the new getSample function in this example factor returns a measurement which is of type ::Tuple{::Matrix{Float64}}. The ::Tuple is slightly clunky but was borne out of necessity to allow for versatility when multiple values from sampling are used during residual function evaluation. Previous uses include cases such as ::Tuple{<:Matrix, <:Vector, <:Function}.

Ready to Use

This new prior can now readily be added to an ongoing factor graph:

# lets generate a random nonparametric belief
pts = 8 .+ 2*rand(1,75)
someBelief = manikde!(pts, ContinuousEuclid{1})

# and build your new factor as an object
myprior = MyPrior(someBelief)

and add it to the existing factor graph from earlier, lets say:

addFactor!(fg, :x1, myprior)

Thats it, this factor is now part of the graph. This should be a solvable graph:

solveGraph!(fg); # exact alias of solveTree!(fg)

Later we will see how to ensure these new factors can be properly serialized to work with features like saveDFG and loadDFG.

What is CalcFactor

CalcFactor is part of the IIF interface to all factors. It contains metadata and other important bits of information that are useful in a wide swath of applications. As work requires more interesting features from the code base, it is likely that the cfo::CalcFactor object will contain such data. If not, please open an issue with Caesar.jl so that the necessary options may be added.

The cfo object contains the field .factor::T which is the type of the user factor being used, e.g. myprior from above example. That is cfo.factor::MyPrior. This is why getSample is using rand(cfo.factor.Z).

CalcFactor was introduced in IncrementalInference v0.20 to consolidate and standardize a variety of features that had previously been diseparate and unwieldy.


Many factors already exists in IncrementalInference, RoME, and Caesar. Please see their src directories for more details.

Relative Factors

One Dimension Roots Example

Previously we looked at adding a prior. This section demonstrates the first of two <:AbstractRelative factor types. These are factors that introduce only relative information between variables in the factor graph.

This example is on <:IIF.AbstractRelativeRoots. First, lets create the factor as before

struct MyFactor{T <: SamplableBelief} <: IIF.AbstractRelativeRoots
getSample(cfo::CalcFactor{<:MyFactor}, N::Int=1) = (reshape(rand(cfo.factor.Z,N) ,1,N), )

function (cfo::CalcFactor{<:MyFactor})( measurement_z,
                                        x2  )
  res = measurement_z - (x2[1] - x1[1])
  return res

The selection of <:IIF.AbstractRelativeRoots, akin to earlier <:AbstractPrior, instructs IIF to find the roots of the provided residual function. That is the one dimensional residual function, res[1] = measurement - prediction, is used during inference to approximate the convolution of conditional beliefs from the approximate beliefs of the connected variables in the factor graph.

Important aspects to note, <:IIF.AbstractRelativeRoots requires all elements length(res) (the factor measurement dimension) to have a feasible zero crossing solution. A two dimensional system will solve for variables where both res[1]==0 and res[2]==0.


As of IncrementalInference v0.21, CalcResidual no longer takes a residual as input parameter and should return residual, see IIF#467.


Measurements and variables passed in to the factor residual function do not have the same type as when constructing the factor graph. It is recommended to leave these incoming types unrestricted. If you must define the types, these either are (or will be) of element type relating to the manifold on which the measurement or variable beliefs reside. Probably a vector or manifolds type. Usage can be very case specific, and hence better to let Julia type-inference automation do the hard work for you. The

Two Dimension Minimize Example

The second type is <:IIF.AbstractRelativeMinimize which simply minimizes the residual vector of the user factor. This type is useful for partial constraint situations where the residual function is not gauranteed to have zero crossings in all dimensions and the problem is converted into a minimization problem instead:

struct OtherFactor{T <: SamplableBelief} <: IIF.AbstractRelativeMinimize
  Z::T             # assuming something 2 dimensional
  userdata::String # or whatever is necessary

# just illustrating some arbitraty second value in tuple of different size
getSample(cfo::CalcFactor{<:OtherFactor}, N::Int=1) = (rand(cfo.factor.z,N), rand())

function (cfo::CalcFactor{<:OtherFactor})(res::AbstractVector{<:Real},
                                          x2 )
  # @assert length(z) == 2
  # not doing anything with `second_val` but illustrating
  # not doing anything with `cfo.factor.userdata` either
  # the broadcast operators with automatically vectorize
  res = z .- (x1[1:2] .- x1[1:2])
  return res

Special Considerations

Partial Factors

In some cases a factor only effects a partial set of dimensions of a variable. For example a magnetometer being added onto a Pose2 variable would look something like this:

struct MyMagnetoPrior{T<:SamplableBelief} <: AbstractPrior

# define a helper constructor
MyMagnetoPrior(z) = MyMagnetoPrior(z, (3,))

getSample(cfo::CalcFactor{<:MyMagnetoPrior}, N::Int=1) = (reshape(rand(cfo.factor.Z,N),1,N),)

Similarly for <:IIF.AbstractRelativeMinimize, and note that the Roots version currently does not support the .partial option.


The MM-iSAMv2 algorithm relies on the Kolmogorov-Criteria as well as uncorrelated factor sampling. This means that when generating fresh samples for a factor, those samples should not depend on values of variables in the graph or independent volatile variables. That said, if you are comfortable or have a valid reason for introducing correlation between the factor sampling process with values inside the factor graph then you can do so via the cfo.CalcFactor interface.

At present cfo contains three main fields:

  • cfo.factor::MyFactor the factor object as defined in the struct definition,
  • cfo.metadata::FactorMetadata, which is currently under development and likely to change.
    • This contains references to the connected variables to the factor and more, and is useful for large data retrieval such as used in Terrain Relative Navigation (TRN).
  • cfo._sampleIdx is the index of which computational sample is currently being calculated.

The old .specialSampler framework has been replaced with the standardized ::CalcFactor interface. See for details.

[OPTIONAL] Standardized Serialization

To take advantage of features like DFG.saveDFG and DFG.loadDFG a user specified type should be able to serialize via JSON standards. The decision was taken to require bespoke factor types to always be converted into a JSON friendly struct which must be prefixed as type name with PackedMyPrior{T}. Similarly, the user must also overload Base.convert as follows:

# necessary for overloading Base.convert
import Base: convert

struct PackedMyPrior <: PackedInferenceType

# IIF provides convert methods for `SamplableBelief` types
convert(::Type{PackedMyPrior}, pr::MyPrior{<:SamplableBelief}) = PackedMyPrior(convert(PackedSamplableBelief, pr.Z))
convert(::Type{MyPrior}, pr::PackedMyPrior) = MyPrior(IIF.convert(SamplableBelief, pr.Z))

Now you should be able to saveDFG and loadDFG your own factor graph types to Caesar.jl / FileDFG standard .tar.gz format.

fg = initfg()
addVariable!(fg, :x0, ContinuousScalar)
addFactor!(fg, [:x0], MyPrior(Normal()))

# generate /tmp/myfg.tar.gz
saveDFG("/tmp/myfg", fg)

# test loading the .tar.gz (extension optional)
fg2 = loadDFG("/tmp/myfg")

# list the contents
ls(fg2), lsf(fg2)
# should see :x0 and :x0f1 listed

Factors supporting a Parametric Solution

See the parametric solve section


All factors inherit from one of the following types, depending on their function:

  • AbstractPrior: AbstractPrior are priors (unary factors) that provide an absolute constraint for a single variable. A simple example of this is an absolute GPS prior, or equivalently a (0, 0, 0) starting location in a Pose2 scenario.
    • Requires: A getSample function
  • IIF.AbstractRelativeMinimize: IIF.AbstractRelativeMinimize are relative factors that introduce an algebraic relationship between two or more variables. A simple example of this is an odometry factor between two pose variables, or a range factor indicating the range between a pose and another variable.
    • Requires: A getSample function and a residual function definition
    • The minimize suffix specifies that the residual function of this factor will be enforced by numerical minimization (find me the minimum of this function)
  • IIF.AbstractRelativeRoots: IIF.AbstractRelativeRoots are relative factors that introduce algebraic relationships between two or more variables. They are the same as IIF.AbstractRelativeMinimize, however they use root finding to find the zero crossings (rather than numerical minimization).
    • Requires: A getSample function and a residual function definition

How do you decide which to use?

  • If you are creating factors for world-frame information that will be tied to a single variable, inherit from <:AbstractPrior
    • GPS coordinates should be priors
  • If you are creating factors for local-frame relationships between variables, inherit from IIF.AbstractRelativeMinimize
    • Odometry and bearing deltas should be introduced as pairwise factors and should be local frame

TBD: Users should start with IIF.AbstractRelativeMinimize, discuss why and when they should promote their factors to IIF.AbstractRelativeRoots.


IIF.AbstractRelativeMinimize does not imply that the overall inference algorithm only minimizes an objective function. The Multi-model iSAM algorithm is built around fixed-point analysis. Minimization is used here to locally enforce the residual function.

What you need to build in the new factor:

  • A struct for the factor itself
  • A sampler function to return measurements from the random ditributions
  • If you are building a IIF.AbstractRelativeMinimize or a IIF.AbstractRelativeRoots you need to define a residual function to introduce the relative algebraic relationship between the variables
    • Minimization function should be lower-bounded and smooth
  • A packed type of the factor which must be named Packed[Factor name], and allows the factor to be packed/transmitted/unpacked
  • Serialization and deserialization methods
    • These are convert functions that pack and unpack the factor (which may be highly complex) into serialization-compatible formats
    • As the factors are mostly comprised of distributions (of type SamplableBelief), functions are provided to pack and unpack the distributions:
      • Packing: To convert from a SamplableBelief to a serializable obhect, use convert(PackedSamplableBelief, ::SamplableBelief)
      • Unpacking: To convert from string back to a SamplableBelief, use convert(SamplableBelief, ::PackedSamplableBelief)

An example of this is the Pose2Point2BearingRange, which provides a bearing+range relationship between a 2D pose and a 2D point.

Missing docstring.

Missing docstring for IIF.AbstractRelativeMinimize. Check Documenter's build log for details.

Missing docstring.

Missing docstring for IIF.AbstractRelativeRoots. Check Documenter's build log for details.