Change x->z

README.md

@@ -4,15 +4,15 @@
 
 $$
 \begin{align}
-\min_{x} &  ~\frac{1}{2}x^{T}Hx+(f+F \theta)^{T}x \\
-\text{s.t.} & ~A x \leq b + B \theta \\
+\min_{z} &  ~\frac{1}{2}z^{T}Hz+(f+F \theta)^{T}x \\
+\text{s.t.} & ~A z \leq b + B \theta \\
 & ~\theta \in \Theta
 \end{align}
 $$
 
 where $H \succ 0$ and $\Theta \triangleq \lbrace l \leq \theta \leq u : A_{\theta} \theta \leq b_{\theta}\rbrace$.
 
-The solution $x^*(\theta)$ is a piecewise-affine function over a polyhedral partition.
+The solution $z^*(\theta)$ is a piecewise-affine function over a polyhedral partition.
 
 ## Example
 The following code solves the mpQP in Section 7.1 in Bemporad et al. 2002

src/plot.jl

@@ -7,7 +7,7 @@ using RecipesBase
     vs=PolyDAQP.vrep_2d(minrep(slice(r.Ath,r.bth,collect(3:nth))...)...)
     nv = length(vs)
     x,y = first.(vs),last.(vs)
-    z = [r.x[:,1]'*[v;zeros(nth-2);1] for v in vs]
+    z = [r.z[:,1]'*[v;zeros(nth-2);1] for v in vs]
     connections--> (zeros(Int, nv-2),collect(1:nv-2),collect(2:nv-1))
     return x,y,z 
 end
@@ -27,8 +27,8 @@ end
             nv = length(vs)
             nv < 2 && continue
             x,y = first.(vs), last.(vs)
-            c = r.x[ids,uid]'*values + r.x[end,uid]
-            z = [r.x[free_ids,uid]'*v + c for v in vs]
+            c = r.z[ids,uid]'*values + r.z[end,uid]
+            z = [r.z[free_ids,uid]'*v + c for v in vs]
             @series begin
                 st --> :mesh3d 
                 legend --> false
@@ -42,12 +42,12 @@ end
 
 ## PGFPlotsX
 function plot_regions(sol::Solution;fix_ids=nothing,fix_vals=nothing,opts=Dict{Symbol,Any}())
-    pplot(get_critical_regions(sol);out_id=0,fix_ids,fix_vals,opts)
+    pplot(get_critical_regions(sol);z_id=0,fix_ids,fix_vals,opts)
 end
-function plot_solution(sol::Solution;out_id=1,fix_ids=nothing,fix_vals=nothing,opts=Dict{Symbol,Any}())
-    pplot(get_critical_regions(sol);out_id,fix_ids,fix_vals,opts)
+function plot_solution(sol::Solution;z_id=1,fix_ids=nothing,fix_vals=nothing,opts=Dict{Symbol,Any}())
+    pplot(get_critical_regions(sol);z_id,fix_ids,fix_vals,opts)
 end
-function pplot(rs::Vector{CriticalRegion};out_id=0, fix_ids = nothing, fix_vals=nothing,opts=Dict{Symbol,Any}())
+function pplot(rs::Vector{CriticalRegion};z_id=0, fix_ids = nothing, fix_vals=nothing,opts=Dict{Symbol,Any}())
     isempty(rs) && error("Cannot plot empty collection")
     nth = size(rs[1].Ath,1)
     ids = isnothing(fix_ids) ? collect(3:nth) : fix_ids
@@ -61,17 +61,17 @@ function pplot(rs::Vector{CriticalRegion};out_id=0, fix_ids = nothing, fix_vals=
         p = Polyhedron(slice(r.Ath,r.bth,ids;values)...)
         isempty(p) && continue
         push!(ps,p)
-        out_id == 0 && continue
-        c = r.x[ids,out_id]'*values + r.x[end,out_id]
-        push!(fs,v->c+r.x[free_ids,out_id]'*v[1:2])
+        z_id == 0 && continue
+        c = r.z[ids,z_id]'*values + r.z[end,z_id]
+        push!(fs,v->c+r.z[free_ids,z_id]'*v[1:2])
     end
     # Some plotting
     lopts = Dict(
                  :xlabel=>"\\large\$\\theta_{"*string(free_ids[1])*"}\$",
                  :ylabel=>"\\large\$\\theta_{"*string(free_ids[2])*"}\$",
                 )
-    if out_id != 0
-        push!(lopts,:zlabel=>"\\large\$x^*_{"*string(out_id[1])*"}\$")
+    if z_id != 0
+        push!(lopts,:zlabel=>"\\large\$z^*_{"*string(z_id[1])*"}\$")
 
         lopts = merge(Dict(:view=>(45,45),),lopts)
     else

src/tree.jl

@@ -47,22 +47,22 @@ end
 function get_feedbacks(CRs; tol=1e-6)
     isempty(CRs) && return nothing
     nth = size(CRs[1].Ath,1)
-    X,ids = [], []
+    Z,ids = [], []
     for cr in CRs 
         id = 0 
-        for (i,x) in enumerate(X)
-            if norm(cr.x-x) < tol
+        for (i,z) in enumerate(Z)
+            if norm(cr.z-z) < tol
                 id = i
                 push!(ids,id)
                 break
             end
         end
         if id == 0 # No duplicate
-            push!(X,cr.x)
-            push!(ids,length(X))
+            push!(Z,cr.z)
+            push!(ids,length(Z))
         end
     end
-    return X,ids
+    return Z,ids
 end
 
 # TODO: Can be cut in half by using points in CR 

src/types.jl

@@ -2,7 +2,7 @@ mutable struct CriticalRegion
     AS::Vector{Int16}
     Ath::Matrix{Float64}
     bth::Vector{Float64}
-    x::Matrix{Float64}
+    z::Matrix{Float64}
     lam::Matrix{Float64}
     th::Vector{Float64}
 end

src/utils.jl

@@ -88,7 +88,7 @@ function denormalize(cr::CriticalRegion,scaling,translation)
     else 
         An,bn = zeros(0,0),zeros(0)
     end
-    xn = !isempty(cr.x) ? denormalize(cr.x,scaling,translation) : zeros(0,0)
+    xn = !isempty(cr.z) ? denormalize(cr.z,scaling,translation) : zeros(0,0)
     lamn = !isempty(cr.lam) ? denormalize(cr.lam,scaling,translation) : zeros(0,0)
     thn = !isempty(cr.th) ? denormalize(cr.th,scaling,translation) : zeros(0)
     return CriticalRegion(cr.AS,An,bn,xn,lamn,thn)

test/runtests.jl

@@ -57,7 +57,7 @@ end
         inds = pointlocation(θ,sol.CRs);
         containment_inds[n]=length(inds)
         AS = sol.CRs[inds[1]].AS
-        xsol = sol.CRs[inds[1]].x'*[θ;1]
+        xsol = sol.CRs[inds[1]].z'*[θ;1]
         λsol = sol.CRs[inds[1]].lam'*[θ;1]
         f = mpQP.f[:,1]+mpQP.F*θ
         b = mpQP.b[:,1]+mpQP.B*θ