From: Michael Orlitzky <michael@orlitzky.com>
Date: Mon, 14 Jun 2010 08:14:09 +0000 (-0400)
Subject: Added the SimplexIteration class to the LinearProgramming module.
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=9e873928a42a91b468e56bf95217f8504c12dad2;p=dead%2Fcensus-tools.git

Added the SimplexIteration class to the LinearProgramming module.
---

diff --git a/src/LinearProgramming.py b/src/LinearProgramming.py
index d779dc0..ceb2e5f 100644
--- a/src/LinearProgramming.py
+++ b/src/LinearProgramming.py
@@ -4,6 +4,7 @@ integration with lp_solve.
 """
 
 import fractions
+from numpy import *
 import os
 import site
 import sys
@@ -11,8 +12,10 @@ import sys
 # Add LP_SOLVE_PATH to our path. There is no point to this variable
 # other than to make the site.addsitedir() line fit within 80
 # characters.
-LP_SOLVE_PATH = '/../../lib/lp_solve'
-site.addsitedir(os.path.dirname(os.path.abspath(sys.argv[0])) + LP_SOLVE_PATH)
+LP_SOLVE_PATH1 = '/../../lib/lp_solve'
+LP_SOLVE_PATH2 = '/../lib/lp_solve'
+site.addsitedir(os.path.dirname(os.path.abspath(sys.argv[0])) + LP_SOLVE_PATH1)
+site.addsitedir(os.path.dirname(os.path.abspath(sys.argv[0])) + LP_SOLVE_PATH2)
 
 from lpsolve55 import *
 
@@ -335,3 +338,152 @@ class LinearProgram(object):
         Return the GCD of all objective function coefficients.
         """
         return reduce(fractions.gcd, self.objective_coefficients)
+
+
+
+class SimplexIteration(object):
+    """
+    Represents the 'current' iteration of the simplex method at some
+    point. It needs an A,b,x, and c corresponding to the linear
+    program in standard form. It can then determine whether or not the
+    current vertex (x) is optimal, and possible move to a better one.
+    """
+
+    @property
+    def constraint_matrix(self):
+        return self._constraint_matrix.tolist()
+
+    @constraint_matrix.setter
+    def constraint_matrix(self, value):
+        self._constraint_matrix = matrix(value)
+
+    @property
+    def rhs(self):
+        return self._rhs
+
+    @rhs.setter
+    def rhs(self, value):
+        self._rhs = value
+
+    @property
+    def objective_coefficients(self):
+        return self._objective_coefficients
+
+    @objective_coefficients.setter
+    def objective_coefficients(self, value):
+        self._objective_coefficients = value
+
+    @property
+    def solution_vector(self):
+        return self._solution_vector.tolist()
+
+    @solution_vector.setter
+    def solution_vector(self, value):
+        self._solution_vector = array(value)
+
+
+    @property
+    def basic_variables(self):
+        # The current set of basic variables. Constructed from the
+        # "true" source, our list of basic indices.
+        idxs = self.basic_indices
+        return map(lambda x: "x" + str(x+1), idxs)
+
+
+    @basic_variables.setter
+    def basic_variables(self, value):
+        """
+        Syntactic sugar to set the basic indices. We take a string
+        of the form x1,x2,...xn, and subtract one from each of the
+        subscripts to get the basic indices.
+        """
+        basic_indices = []
+        vars = value.split(',')
+
+        for var in vars:
+            var = var.strip()
+            var = var.replace('x', '')
+            basic_indices.append(int(var)-1)
+
+        self.basic_indices = basic_indices
+
+
+    @property
+    def nonbasic_variables(self):
+        # All elements of the solution vector that have value zero.
+        idxs = self.nonbasic_indices
+        return map(lambda x: "x" + str(x+1), idxs)
+
+
+    @property
+    def basic_indices(self):
+        return self._basic_indices
+
+
+    @basic_indices.setter
+    def basic_indices(self, value):
+        self._basic_indices = value
+
+
+    @property
+    def nonbasic_indices(self):
+        all_indices = range(0, len(self.solution_vector))
+        return list(set(all_indices) - set(self.basic_indices))
+
+
+    @property
+    def optimal(self):
+        # True if the current solution is optimal, false if not.
+        for idx in self.nonbasic_indices:
+            if self.reduced_cost(idx) < 0.0:
+                return False
+
+        return True
+
+
+    def constraint_column(self, idx):
+        # Return the column of the constraint matrix corresponding
+        # to index idx.
+        bm = matrix(self.constraint_matrix).transpose().tolist()
+        return bm[idx]
+
+    def negative_constraint_column(self, idx):
+        # Return the column of the constraint matrix corresponding
+        # to index idx, multiplied by negative one.
+        bm = (-matrix(self.constraint_matrix).transpose()).tolist()
+        return bm[idx]
+
+    def basis_matrix(self):
+        # Return the columns of our constraint matrix corresponding
+        # to the basic variables.
+        idxs = self.nonbasic_indices
+        bm = matrix(self.constraint_matrix)
+        bm = delete(bm, idxs, axis=1)
+        return bm.tolist()
+
+    def reduced_cost(self, idx):
+        # Find the reduced cost ofthe variable whose column has index
+        # idx.
+        dx = array(self.delta_x(idx))
+        c = array(self.objective_coefficients)
+        return dot(dx, c)
+
+    def delta_x(self, idx):
+        # Return the array of deltas that would result from increasing
+        # the variable with index idx by one.
+        A = matrix(self.basis_matrix())
+        b = array(self.negative_constraint_column(idx))
+        x = linalg.solve(A,b).tolist()
+
+        # Now we get to add back the nonbasic columns. The 'idx' column
+        # should have a value of 1, and the other two non-basics should
+        # have a value of 0.
+        xfull = [0.0] * len(self.solution_vector)
+        bidxs = self.basic_indices
+
+        for bidx in bidxs:
+            xfull[bidx] = x.pop(0)
+
+        xfull[idx] = 1.0
+
+        return xfull