Interval set type. #277

mforets · 2018-03-05T17:30:11Z

Closes #270.

schillic · 2018-03-05T18:21:36Z

src/Interval.jl

@@ -0,0 +1,148 @@
+@require IntervalArithmetic begin
+
+import IntervalArithmetic.AbstractInterval


I know that I proposed this, but since you need more from this package, better remove this import again.

schillic · 2018-03-05T18:22:21Z

src/Interval.jl

+Support vector in the given direction.
+"""
+function σ(d::AbstractVector{N}, x::Interval{N, IN})::AbstractVector{N} where {N, IN <: IA.AbstractInterval{N}}
+    return d[1] > 0 ? [x.dat.hi] : [x.dat.lo]


It might be problematic that you can ask for σ([1., 2., 3.], x).

do you mean that we don't check dimensions? it's not yet global, but yes, some types have an assertion.

julia> B LazySets.Ball1{Float64}([0.0, 0.0], 1.0) julia> σ(rand(4), B) # support vector of dim 4 over a dim 2 set 2-element Array{Float64,1}: 0.0 1.0

but

julia> v = VPolygon([rand(2) for i in 1:5]) LazySets.VPolygon{Float64}(Array{Float64,1}[[0.142884, 0.0902304], [0.973041, 0.0771555], [0.973452, 0.282573], [0.685435, 0.738067]]) julia> σ(rand(4), v) ERROR: DimensionMismatch("dot product arguments have lengths 4 and 2") Stacktrace: [1] dot(::Array{Float64,1}, ::Array{Float64,1}) at ./linalg/blas.jl:311 [2] σ(::Array{Float64,1}, ::LazySets.VPolygon{Float64}) at /Users/forets/.julia/v0.6/LazySets/src/VPolygon.jl:139

Yes, that is what I meant.

schillic · 2018-03-05T18:22:58Z

src/Interval.jl

+"""
+    center(x::Interval)
+
+Return the center of ther interval.


schillic · 2018-03-05T18:24:11Z

src/Interval.jl

+
+julia> center(x)
+0.5
+```


Maybe add some computation example x + y * z - w.

schillic · 2018-03-05T18:25:32Z

src/Interval.jl

+
+The list of vertices of the interval represented as two one-dimensional vectors.
+"""
+vertices_list(x::Interval) = [[low(x::Interval)], [high(x::Interval)]]


You can omit the types on the r.h.s.

schillic · 2018-03-05T18:27:54Z

test/unit_Interval.jl

+p = x * y
+@test dim(p) == 1
+@test σ([1.0], p) == [0.5]
+@test σ([-1.0], p) == [-2.0]


Add a test for -, high, low, and vertices_list.

done. any other method that we would like to have?

Those are all functions that are defined here 👍

i really meant: do we want some other new method for the Interval type? i can think of overapproximate.

there is also ∈ and ⊆.

Ah yes, we definitely want to have overapproximate to be a no-op.

function ∈(x::AbstractVector{N}, I::LazySets.Interval{N, IN}) where ... @assert length(x) == dim(I) return low(I) <= x[1] <= high(I) end

function ⊆(X::LazySet{N}, I::LazySets.Interval{N, IN}) where ... @assert dim(X) == dim(I) return low(I) <= σ(X, [-one(N)]) && σ(X, [one(N)]) <= high(I) end function ⊆(I::LazySets.Interval{N, IN}, X::LazySet{N}) where ... @assert dim(X) == dim(I) return σ(X, [-one(N)]) <= low(I) && high(I) <= σ(X, [one(N)]) end function ⊆(I1::LazySets.Interval{N, IN}, I2::LazySets.Interval{N, IN}) where ... return low(I2) <= low(I1) && high(I2) <= high(l1) end

(no witness production)

that is all good. while we don't extend for witness production i've just called the interval arithmetic backend for these.

mforets · 2018-03-05T18:51:43Z

actually, for consistency with all other symbolic set types, + should trigger a fresh MinkowskiSum instance. minkowski_sum should behave like my current +. thoughts?

schillic · 2018-03-05T18:54:32Z

actually, for consistency with all other symbolic set types, + should trigger a fresh MinkowskiSum instance.

Okay, or make a difference between ⊕ and +, like for × and *.

mforets · 2018-03-05T19:01:57Z

.. yes * should be a new CartesianProduct.

then i take back my suggestion and propose that for intervals, + and * are NOT symbolic.

schillic · 2018-03-05T19:08:35Z

I am fine with either way.

schillic · 2018-03-05T19:26:30Z

test/unit_Interval.jl

+@test low(r) == -5.5 && high(r) == 4.0
+
+# Minkowski sum
+


Something missing?

#278 and the unit test :)

mforets · 2018-03-05T20:05:01Z

just saw that center(x::Interval) should return a vector (not a scalar), so that Interval works smoothly with other interface methods, eg. an_element(x).

mforets · 2018-03-05T20:41:45Z

having added the new overapproximate(S::LazySets.Interval{N, IN}, ::Type{Hyperrectangle}) where {N, IN <: IntervalArithmetic.AbstractInterval{N}} i stumble upon some compilation error and i'm clueless.

in a fresh session:

julia> using LazySets # so far so good
INFO: Precompiling module LazySets.
julia> using IntervalArithmetic  # boom
WARNING: Error requiring IntervalArithmetic from LazySets.Approximations:
UndefVarError: Interval not defined
Stacktrace:
 [1] err(::LazySets.Approximations.##6#13, ::Module, ::String) at /Users/forets/.julia/v0.6/Requires/src/require.jl:42
 [2] withpath(::LazySets.Approximations.##5#12, ::String) at /Users/forets/.julia/v0.6/Requires/src/require.jl:32
 [3] (::LazySets.Approximations.##4#11)() at /Users/forets/.julia/v0.6/Requires/src/require.jl:53
 [4] _collect(::Array{Function,1}, ::Base.Generator{Array{Function,1},Requires.##3#4}, ::Base.EltypeUnknown, ::Base.HasShape) at ./array.jl:488
 [5] loadmod(::Symbol) at /Users/forets/.julia/v0.6/Requires/src/require.jl:20
 [6] require(::Symbol) at ./loading.jl:408
 [7] eval(::Module, ::Any) at ./boot.jl:235
 [8] eval_user_input(::Any, ::Base.REPL.REPLBackend) at ./REPL.jl:66
 [9] macro expansion at ./REPL.jl:97 [inlined]
 [10] (::Base.REPL.##1#2{Base.REPL.REPLBackend})() at ./event.jl:73

schillic · 2018-03-05T20:59:26Z

Confirmed here. Replacing @require IntervalArithmetic begin [...] end by using IntervalArithmetic solves the error, but we want to use @require.
My guess was that Interval is not exported correctly (the export is only inside the @reexport). But adding export Interval outside did not help.

schillic · 2018-03-05T22:22:56Z

The problem is that Requires stores the things to execute by the module name and in Julia LazySets.Approximations comes before LazySets.

You can wrap the Interval.jl inside a new module that comes before Approximations, e.g., module a. But then you always need to write LazySets.a.Interval and you have to spell out IA.

schillic approved these changes Mar 5, 2018

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schillic reviewed Mar 5, 2018

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mforets added 7 commits March 5, 2018 16:42

add Interval type

919be25

add common methods

ef0b3f9

add unit tests

d17b0ae

add more constructors, update docstring

5bcb278

update tests

6dd7648

add docstring comment

96eedb2

update tests

c5ee0f6

mforets force-pushed the mforets/270 branch from a4f1a3a to c5ee0f6 Compare March 5, 2018 19:44

typo

cf4fae9

mforets added 3 commits March 5, 2018 17:26

add ∈, ⊆ ops

dc10e9e

add conversion to Hyperrectangle

1dace06

add new overapproximate method

0cfe9c1

update script with IntervalArithmetic requirement

e5940a6

remove require IntervalArithmetic

d71da71

update Interval.jl

71c8270

mforets merged commit 0d74723 into master Mar 6, 2018

schillic deleted the mforets/270 branch March 6, 2018 20:41

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Interval set type. #277

Interval set type. #277

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schillic commented Mar 5, 2018

		@@ -0,0 +1,148 @@
		@require IntervalArithmetic begin

		import IntervalArithmetic.AbstractInterval

Interval set type. #277

Interval set type. #277

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