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#934 - Add exact projection method #935

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merged 5 commits into from Dec 11, 2018
Merged

#934 - Add exact projection method #935

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8e12af5
Added lazy projection and exact decompose
kpotomkin Dec 5, 2018
28e57ba
adding decomposition of exact projections
kpotomkin Dec 6, 2018
01af155
refactoring according to @schillic comments
kpotomkin Dec 7, 2018
5331bc5
fixed doc for new projection
kpotomkin Dec 10, 2018
a39919d
use new method at other places
schillic Dec 10, 2018
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39 changes: 36 additions & 3 deletions src/Approximations/decompositions.jl
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Expand Up @@ -217,7 +217,7 @@ julia> [typeof(ai) for ai in array(decompose(S, block_types=bt, ε=0.01))]
```
"""
function decompose(S::LazySet{N};
set_type::Type{<:Union{HPolygon, Hyperrectangle, Interval}}=Hyperrectangle,
set_type::Type{<:Union{HPolygon, Hyperrectangle, Interval, LinearMap}}=Hyperrectangle,
ε::Real=Inf,
blocks::AbstractVector{Int}=default_block_structure(S, set_type),
block_types=Dict{Type{<:LazySet}, AbstractVector{<:AbstractVector{Int}}}(),
Expand All @@ -226,9 +226,15 @@ function decompose(S::LazySet{N};
n = dim(S)
result = Vector{LazySet{N}}()

if directions != nothing
if set_type == LinearMap
block_start = 1
@inbounds for bi in blocks
push!(result, project(S, block_start:(block_start + bi - 1), n))
block_start += bi
end
elseif directions != nothing
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# template directions
# potentially defined option set_type is *ignored*
# potentially defined option set_type is *ignored*
block_start = 1
@inbounds for bi in blocks
push!(result, project(S, block_start:(block_start + bi - 1), directions(bi), n))
Expand Down Expand Up @@ -268,6 +274,7 @@ function decompose(S::LazySet{N};
return CartesianProductArray(result)
end


"""
project(S::LazySet{N},
block::AbstractVector{Int},
Expand Down Expand Up @@ -442,3 +449,29 @@ The template direction approximation of the projection of `S`.
M = sparse(1:length(block), block, ones(N, length(block)), length(block), n)
return overapproximate(M * S, directions)
end

"""
project(S::LazySet{N},
block::AbstractVector{Int},
n::Int
)::LinearMap where {N<:Real}

Project a high-dimensional set to a low-dimensional set.
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### Input

- `S` -- set
- `block` -- block structure - a vector with the dimensions of interest
- `n` -- (optional, default: `dim(S)`) ambient dimension of the set `S`

### Output

The lazy linear map of the projection of `S`.
"""
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@inline function project(S::LazySet{N},
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block::AbstractVector{Int},
n::Int=dim(S)
)::LinearMap where {N<:Real}
M = sparse(1:length(block), block, ones(N, length(block)), length(block), n)
return M * S
end