Comments (5)
Hi @cscherrer, I had a brief look at Stan but not sure I see the connection. The main point of this package is to provide types that implement in
, such as UnitDisk
(norm(x) ≤ 1
).
There are also maps between domains, maybe this is what you are interested in?
from domainsets.jl.
Yes, there are a few needs:
- Represent the support (set of nonzero densities) of a distribution. A few important ones are the unit interval, positive reals, and simplex
- Map between any continuous of these and ℝ^n
- Track Jacobian of this transformation
Is this not a good use case for your package? I had looked into using TransformVariables.jl which seems great, but may not have as much flexibility of representing different spaces as your approach.
from domainsets.jl.
I think this is a good use case for representing the domains. @daanhb might have comments about support for Jacobians.
from domainsets.jl.
In principle, the stance of the package is that the Jacobian of a map is itself a map.
The minimal amount of information about a map is which types it maps between (these are the type parameters S
and T
) and an implementation of applymap
: this should take an argument x
of type S
and return something of type T
. It is not assumed that maps are invertible, and there is support for specifying left and right inverses. (This flexibility helps to decide membership of a domain in case the dimensions of the spaces of a map differ.)
It is a pretty flexible framework. However, it hasn't been used much yet, and so there aren't many examples I'm afraid.
There is an example of a map in circle.jl. The AngleMap
and UnitCircleMap
describe the map from the interval to a circle and back. These do not (yet) have jacobians implemented.
An example of a Jacobian is in affine_maps.jl: the jacobian of any linear map is a constant map, see line 14. The affine maps are currently the most used and most developed ones. Compared to some other implementations in other Julia packages, it is not assumed that the matrix is square (i.e. it is not assumed that the map is uniquely invertible).
from domainsets.jl.
That should give me a good start. Thank you!
from domainsets.jl.
Related Issues (20)
- Support hyperfaces
- Write documentation HOT 5
- `UnitSimplex` HOT 11
- Incorrect statement in README? HOT 14
- Support `iterate` for finite-dimensional sets HOT 2
- rand() HOT 5
- tests fail in 1.8
- boundingbox does not work for 1-D Balls HOT 1
- boundingbox does not work for Balls with BigFloat StaticVectors HOT 1
- clamp() and clamp!() HOT 3
- Support `getindex` of `TupleProductDomain` and maybe add a `NamedTupleProductDomain`? HOT 2
- Domain as an interface HOT 3
- Define intersect between a Point and a Domain HOT 2
- use atol and rtol in approx_in HOT 1
- are there conflicting versions of isapprox in IntervalSets? HOT 14
- More Spaces HOT 18
- Can StaticArrays dependency be made optional? HOT 5
- Factor out Map's
- ℤ contains non-integers HOT 6
- export factors
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from domainsets.jl.