orthogonality check added

CHANGELOG.md

@@ -1,6 +1,9 @@
 LaplacianOpt.jl Change Log
 =========================
 
+### v0.6.2 
+- Minor fix for testing eigen cut orthogonality if `projected_eigen_cuts` is active
+
 ### v0.6.1
 - Readme update for dark/light theme logo display
 - Fixed Docs compile issue

Project.toml

@@ -1,7 +1,7 @@
 name = "LaplacianOpt"
 uuid = "bb20392f-64fb-4001-92e8-14b3aedd5a9e"
 authors = ["Harsha Nagarajan"]
-version = "0.6.1"
+version = "0.6.2"
 
 [deps]
 DataStructures = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"

examples/plots/plot_5.dot

@@ -0,0 +1,9 @@
+graph G { 
+layout=neato; 
+size="10,5"; 
+node [fontname="Helvetica", fontsize=7, shape = circle, width=0.15, fixedsize=true, style="filled", fillcolor="cyan"]; 
+1 -- 4 [fontsize=9, fontname="Helvetica", len=0.5]; 
+2 -- 4 [fontsize=9, fontname="Helvetica", len=0.5]; 
+3 -- 4 [fontsize=9, fontname="Helvetica", len=0.5]; 
+3 -- 5 [fontsize=9, fontname="Helvetica", len=0.5]; 
+}

examples/plots/plot_5.tex

@@ -0,0 +1,52 @@
+\documentclass[tikz]{standalone}
+\usepackage{fontspec}
+\setmainfont{Latin Modern Math}
+\usetikzlibrary{arrows}
+\usetikzlibrary{graphs}
+\usetikzlibrary{graphdrawing}
+
+% from: https://tex.stackexchange.com/questions/453132/fresh-install-of-tl2018-no-tikz-graph-drawing-libraries-found
+\usepackage{luacode}
+\begin{luacode*}
+	function pgf_lookup_and_require(name)
+	local sep = package.config:sub(1,1)
+	local function lookup(name)
+	local sub = name:gsub('%.',sep)  
+	if kpse.find_file(sub, 'lua') then
+	require(name)
+	elseif kpse.find_file(sub, 'clua') then
+	collectgarbage('stop') 
+	require(name)
+	collectgarbage('restart')
+	else
+	return false
+	end
+	return true
+	end
+	return
+	lookup('pgf.gd.' .. name .. '.library') or
+	lookup('pgf.gd.' .. name) or
+	lookup(name .. '.library') or
+	lookup(name) 
+	end
+\end{luacode*}
+
+\usegdlibrary{force}
+\begin{document}
+\begin{tikzpicture}[]
+\graph [spring electrical layout, random seed = 42, electric charge=1.0,, ] {
+1/"1" [draw, rounded corners, fill=blue!10],
+2/"2" [draw, rounded corners, fill=blue!10],
+3/"3" [draw, rounded corners, fill=blue!10],
+4/"4" [draw, rounded corners, fill=blue!10],
+5/"5" [draw, rounded corners, fill=blue!10],
+;
+1 -- [,edge label={11.27},] 4;
+2 -- [,edge label={13.67},] 4;
+3 -- [,edge label={29.12},] 4;
+3 -- [,edge label={27.75},] 5;
+};
+
+\end{tikzpicture}
+
+\end{document}

src/constraints.jl

@@ -163,11 +163,13 @@ function _add_eigen_cut_lazy(
 
     violated_eigen_vec =
         LOpt._violated_eigen_vector(W_val[idx, idx], tol = lom.options.tol_psd)
+
     if violated_eigen_vec !== nothing
         # Projected eigen-cuts in (x, gamma) space
         if lom.options.projected_eigen_cuts
             # NxN matrix
-            if length(idx) == num_nodes
+            if (length(idx) == num_nodes) &&
+               (isapprox(abs(sum(violated_eigen_vec)), 0, atol = 1E-6))
                 con = JuMP.@build_constraint(
                     sum(
                         adjacency[i, j] *