Fix type inconsistency in LDL factorization (#76)

* Generic eltype for S matrix in LDL factorization
* Add example validating Float32

examples/optimal_other_type.jl

@@ -0,0 +1,50 @@
+using Tulip
+import MathOptInterface
+const MOI = MathOptInterface
+using Test
+
+const T = Float32
+
+lp = Tulip.Optimizer{T}()
+
+# Create variables
+x = MOI.add_variable(lp)
+y = MOI.add_variable(lp)
+
+# Set variable bounds
+MOI.add_constraint(lp, MOI.SingleVariable(x), MOI.GreaterThan(T(0)))  # x >= 0
+MOI.add_constraint(lp, MOI.SingleVariable(y), MOI.GreaterThan(T(0)))  # y >= 0
+
+# Add constraints
+row1 = MOI.add_constraint(lp,
+    MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.(T[1.0, -1.0], [x, y]), T(0)),
+    MOI.GreaterThan(T(-2))
+)
+row2 = MOI.add_constraint(lp,
+    MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.(T[2.0, -1.0], [x, y]), T(0)),
+    MOI.LessThan(T(4))
+)
+row3 = MOI.add_constraint(lp,
+    MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.(T[1.0,  2.0], [x, y]), T(0)),
+    MOI.LessThan(T(7))
+) 
+
+# Set the objective
+MOI.set(lp,
+    MOI.ObjectiveFunction{MOI.ScalarAffineFunction{Float32}}(),
+    MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.(T[-2.0, -1.0], [x, y]), T(0))
+)
+MOI.set(lp, MOI.ObjectiveSense(), MOI.MIN_SENSE)
+
+MOI.optimize!(lp)
+
+objval = MOI.get(lp, MOI.ObjectiveValue())
+x_ = MOI.get(lp, MOI.VariablePrimal(), x)
+y_ = MOI.get(lp, MOI.VariablePrimal(), y)
+
+@test objval ≈ -8
+@test x_ ≈ 3
+@test y_ ≈ 2
+@test objval isa Float32
+@test x_ isa Float32
+@test y_ isa Float32

src/KKT/ldlfact.jl

@@ -42,7 +42,7 @@ mutable struct LDLFactSQD{T<:Real} <: AbstractKKTSolver{T}
 
         S = [
             spdiagm(0 => -θ)  A';
-            spzeros(T, m, n) spdiagm(0 => ones(m))
+            spzeros(T, m, n) spdiagm(0 => ones(T, m))
         ]
 
         # TODO: PSD-ness checks

test/examples.jl

@@ -30,3 +30,7 @@ end
         @testset "$T" begin ex_unbounded(T, OutputLevel=0) end
     end
 end
+
+@testset "Optimal Float32" begin
+    include(joinpath(examples_dir, "optimal_other_type.jl"))
+end

test/runtests.jl

@@ -8,7 +8,7 @@ TLP = Tulip
 
 import Convex
 
-const TvTYPES = [Float64, BigFloat]
+const TvTYPES = [Float32, Float64, BigFloat]
 
 # write your own tests here
 const testdir = dirname(@__FILE__)