PPLBackend: Add support for integer variables

src/sage/numerical/backends/ppl_backend.pyx

@@ -20,7 +20,7 @@ AUTHORS:
 #*****************************************************************************
 
 from sage.numerical.mip import MIPSolverException
-from sage.libs.ppl import MIP_Problem, Variable, Linear_Expression, Constraint, Generator
+from sage.libs.ppl import MIP_Problem, Variable, Variables_Set, Linear_Expression, Constraint, Generator
 from sage.rings.integer cimport Integer
 from sage.rings.rational cimport Rational
 
@@ -36,6 +36,8 @@ cdef class PPLBackend(GenericBackend):
     cdef list col_name_var
     cdef int is_maximize
     cdef str name
+    cdef object integer_variables
+
     # Common denominator for objective function in self.mip (not for the constant term)
     cdef Integer obj_denominator
 
@@ -59,6 +61,7 @@ cdef class PPLBackend(GenericBackend):
         self.name = ''
         self.obj_constant_term = Rational(0)
         self.obj_denominator = Integer(1)
+        self.integer_variables = set()
 
         if maximization:
             self.set_sense(+1)
@@ -94,6 +97,13 @@ cdef class PPLBackend(GenericBackend):
 
         self.mip.add_space_dimensions_and_embed(len(self.objective_function))
 
+        # Integrality
+
+        ivar = Variables_Set()
+        for i in self.integer_variables:
+            ivar.insert(Variable(i))
+        self.mip.add_to_integer_space_dimensions(ivar)
+
         # Objective function
         mip_obj = Linear_Expression(0)
         denom = Integer(1)
@@ -133,7 +143,7 @@ cdef class PPLBackend(GenericBackend):
         else:
             self.mip.set_optimization_mode('minimization')
 
-    cpdef int add_variable(self, lower_bound=0, upper_bound=None, binary=False, continuous=True, integer=False, obj=0, name=None) except -1:
+    cpdef int add_variable(self, lower_bound=0, upper_bound=None, binary=False, continuous=False, integer=False, obj=0, name=None) except -1:
         """
         Add a variable.
 
@@ -179,19 +189,28 @@ cdef class PPLBackend(GenericBackend):
             sage: p.objective_coefficient(2)
             2/3
             sage: p.add_variable(integer=True)
-            Traceback (most recent call last):
-            ...
-            NotImplementedError: The PPL backend in Sage only supports continuous variables
+            3
         """
-        if binary or integer:
-            raise NotImplementedError("The PPL backend in Sage only supports continuous variables")
+        cdef int vtype = int(bool(binary)) + int(bool(continuous)) + int(bool(integer))
+        if  vtype == 0:
+            continuous = True
+        elif vtype != 1:
+            raise ValueError("Exactly one parameter of 'binary', 'integer' and 'continuous' must be 'True'.")
+
         for i in range(len(self.Matrix)):
             self.Matrix[i].append(0)
         self.col_lower_bound.append(lower_bound)
         self.col_upper_bound.append(upper_bound)
         self.objective_function.append(obj)
         self.col_name_var.append(name)
-        return len(self.objective_function) - 1
+
+        n = len(self.objective_function) - 1
+        if binary:
+            self.set_variable_type(n,0)
+        elif integer:
+            self.set_variable_type(n,1)
+
+        return n
 
     cpdef int add_variables(self, int n, lower_bound=0, upper_bound=None, binary=False, continuous=True, integer=False, obj=0, names=None) except -1:
         """
@@ -264,20 +283,54 @@ cdef class PPLBackend(GenericBackend):
         """
         Set the type of a variable.
 
+        INPUT:
+
+        - ``variable`` (integer) -- the variable's id
+
+        - ``vtype`` (integer) :
+
+            *  1  Integer
+            *  0  Binary
+            *  -1  Continuous
+
         EXAMPLE::
 
             sage: from sage.numerical.backends.generic_backend import get_solver
             sage: p = get_solver(solver = "PPL")
             sage: p.add_variables(5)
             4
+            sage: p.set_variable_type(0,1)
+            sage: p.is_variable_integer(0)
+            True
+            sage: p.set_variable_type(3,0)
+            sage: p.is_variable_integer(3) or p.is_variable_binary(3)
+            True
+            sage: p.col_bounds(3) # tol 1e-6
+            (0, 1)
             sage: p.set_variable_type(3, -1)
+            sage: p.is_variable_continuous(3)
+            True
+
+        TESTS:
+
+        Test that an exception is raised when an invalid type is passed::
+
             sage: p.set_variable_type(3, -2)
             Traceback (most recent call last):
             ...
-            Exception: ...
+            ValueError: ...
         """
-        if vtype != -1:
-            raise Exception('This backend does not handle integer variables ! Read the doc !')
+        if vtype == -1:
+            if variable in self.integer_variables:
+                self.integer_variables.remove(variable)
+        elif vtype == 0:
+            self.integer_variables.add(variable)
+            self.variable_lower_bound(variable, 0)
+            self.variable_upper_bound(variable, 1)
+        elif vtype == 1:
+            self.integer_variables.add(variable)
+        else:
+            raise ValueError("Invalid variable type: {}".format(vtype))
 
     cpdef set_sense(self, int sense):
         """
@@ -524,28 +577,44 @@ cdef class PPLBackend(GenericBackend):
                 self.row_name_var.append(None)
 
     cpdef int solve(self) except -1:
+        # integer example copied from cplex_backend.pyx
         """
         Solve the problem.
 
         .. NOTE::
 
             This method raises ``MIPSolverException`` exceptions when
             the solution can not be computed for any reason (none
-            exists, or the LP solver was not able to find it, etc...)
+            exists, or the solver was not able to find it, etc...)
 
-        EXAMPLE::
+        EXAMPLES:
+
+        A linear optimization problem::
 
             sage: from sage.numerical.backends.generic_backend import get_solver
             sage: p = get_solver(solver = "PPL")
             sage: p.add_linear_constraints(5, 0, None)
             sage: p.add_col(range(5), range(5))
             sage: p.solve()
             0
+
+        An unbounded problem::
+
             sage: p.objective_coefficient(0,1)
             sage: p.solve()
             Traceback (most recent call last):
             ...
             MIPSolverException: ...
+
+        An integer optimization problem::
+
+            sage: p = MixedIntegerLinearProgram(solver='PPL')
+            sage: x = p.new_variable(integer=True, nonnegative=True)
+            sage: p.add_constraint(2*x[0] + 3*x[1], max = 6)
+            sage: p.add_constraint(3*x[0] + 2*x[1], max = 6)
+            sage: p.set_objective(x[0] + x[1] + 7)
+            sage: p.solve()
+            9
         """
         self.init_mip()
 
@@ -809,7 +878,7 @@ cdef class PPLBackend(GenericBackend):
             sage: p.is_variable_binary(0)
             False
         """
-        return False
+        return index in self.integer_variables and self.col_bounds(index) == (0, 1)
 
     cpdef bint is_variable_integer(self, int index):
         """
@@ -830,7 +899,7 @@ cdef class PPLBackend(GenericBackend):
             sage: p.is_variable_integer(0)
             False
         """
-        return False
+        return index in self.integer_variables and self.col_bounds(index) != (0, 1)
 
     cpdef bint is_variable_continuous(self, int index):
         """
@@ -851,7 +920,7 @@ cdef class PPLBackend(GenericBackend):
             sage: p.is_variable_continuous(0)
             True
         """
-        return True
+        return index not in self.integer_variables
 
     cpdef row_name(self, int index):
         """