From dc02abaa4aaf0cd7e8da391d565e813c5860bdea Mon Sep 17 00:00:00 2001
From: Chris Brown <chris@thebrown.net>
Date: Thu, 26 Jun 2014 21:19:41 +0100
Subject: [PATCH] Pivoting

---
 js/simplex.js       | 44 +++++++++++++++++++++++-
 test/simplexSpec.js | 82 +++++++++++++++++++++++++++++++++++++++++++--
 2 files changed, 123 insertions(+), 3 deletions(-)

diff --git a/js/simplex.js b/js/simplex.js
index b52a14b..fe61742 100644
--- a/js/simplex.js
+++ b/js/simplex.js
@@ -1,4 +1,4 @@
-function initialSol(prob, mat) {
+function solution(prob, mat) {
     var sol = {};
     var constraints = prob.constraints;
     if (constraints) {
@@ -12,3 +12,45 @@ function initialSol(prob, mat) {
     }
     return sol;
 }
+
+function pivotVar(mat) {
+    var p = {
+        sym: mat.vars[0],
+        index: 0
+    };
+    var obj = mat.rows[mat.rows.length - 1] ;
+    var min = obj[0];
+    for (var i = 1; i < mat.vars.length; i++) {
+        if (obj[i] < min) {
+            p = {
+                sym: mat.vars[i],
+                index: i
+            }
+            min = obj[i];
+        }
+    }
+    if (min < 0) {
+        return p;
+    } else {
+        return null;
+    }
+}
+
+function pivotRow(mat, pivotVar) {
+    var index = null;
+    var min = null;
+
+    for (var i = 0; i < mat.rows.length - 1; i++) {
+        var v = mat.rows[i][pivotVar.index];
+        if (v <= 0) {
+            continue;
+        }
+        var r = mat.rhs[i] / v;
+        if (min === null || r < min) {
+            min = r;
+            index = i;
+        }
+    }
+
+    return index;
+}
diff --git a/test/simplexSpec.js b/test/simplexSpec.js
index 676c658..589406d 100644
--- a/test/simplexSpec.js
+++ b/test/simplexSpec.js
@@ -1,5 +1,5 @@
 describe('simplex', function () {
-    describe('initialSol', function () {
+    describe('solution', function () {
         it('should set up the initial solution', function () {
             var prob = {
                 constraints: [
@@ -23,7 +23,7 @@ describe('simplex', function () {
             };
 
             var mat = toMatrix(prob);
-            var sol = initialSol(prob, mat);
+            var sol = solution(prob, mat);
 
             expect(sol).toEqual({
                 '_s0': -14,
@@ -31,4 +31,82 @@ describe('simplex', function () {
             });
         });
     });
+
+    describe('pivotVar', function () {
+        it('should select the correct pivot variable', function () {
+            var mat = {
+                vars: ['a', 'b', 'c', 'd', 'e'],
+                varIndices: {},
+                rows: [
+                    [],
+                    [1, -4, 2, -1, 5]
+                ],
+                rhs: []
+            };
+
+            var pv = pivotVar(mat);
+            expect(pv).toEqual({
+                sym: 'b',
+                index: 1
+            });
+        });
+
+        it('should return null if there is no appropriate pivot variable', function () {
+            var mat = {
+                vars: ['a', 'b', 'c', 'd', 'e'],
+                varIndices: {},
+                rows: [
+                    [],
+                    [1, 0, 2, 1, 0]
+                ],
+                rhs: []
+            };
+
+            var pv = pivotVar(mat);
+            expect(pv).toBe(null);
+        });
+    });
+
+    describe('pivotRow', function () {
+        it('should select the correct pivot row', function () {
+            var mat = {
+                vars: ['a'],
+                varIndices: {},
+                rows: [
+                    [1],
+                    [0],
+                    [2],
+                    [3],
+                    [-1]
+                ],
+                rhs: [4, 1, 6, 10, 1]
+            };
+
+            var pv = {
+                sym: 'a',
+                index: 0
+            };
+            var pr = pivotRow(mat, pv);
+            expect(pr).toBe(2);
+        });
+
+        it('should return null if no pivot row candidates', function () {
+            var mat = {
+                vars: ['a'],
+                varIndices: {},
+                rows: [
+                    [0],
+                    [-1]
+                ],
+                rhs: [1, 1]
+            };
+
+            var pv = {
+                sym: 'a',
+                index: 0
+            };
+            var pr = pivotRow(mat, pv);
+            expect(pr).toBe(null);
+        });
+    });
 });