Evaluating Expressions

Evaluation using MapList

The value of an expression can be computed by providing an assignment of values to all variables as a list of pairs. A list can be defined as a MapList object.

The following program computes the function $f(x,y,z)$ for $(x,y,z)=(0,1,1)$:

from pyqbpp import var, sqr, MapList

x = var("x")
y = var("y")
z = var("z")
f = sqr(x + 2 * y + 3 * z - 3)

ml = MapList([(x, 0), (y, 1), (z, 1)])
print("f(0,1,1) =", f.eval(ml))

In this program, a MapList object ml is defined with the assignment $x=0$, $y=1$, $z=1$. Then f.eval(ml) returns the value of $f(0,1,1)$. This program displays the following output:

f(0,1,1) = 4

Evaluation using Sol

A solution object (Sol) can also be used to evaluate the value of an expression. To do this, we first construct a Sol object associated with a given expression. The newly created Sol object is initialized with the all-zero assignment.

Using the set() method, we can assign values to individual variables. Then sol.eval(f) returns the value of the expression f under the assignment stored in sol.

from pyqbpp import var, sqr, Sol

x = var("x")
y = var("y")
z = var("z")
f = sqr(x + 2 * y + 3 * z - 3)
f.simplify_as_binary()

sol = Sol(f)
sol.set(y, 1)
sol.set(z, 1)

print("f(0,1,1) =", sol.eval(f))

The method comp_energy() computes the energy value and caches it internally. A solution object returned by a solver already has its energy cached. To retrieve the cached energy, use the energy() method:

from pyqbpp import var, sqr, EasySolver

x = var("x")
y = var("y")
z = var("z")
f = sqr(x + 2 * y + 3 * z - 4)
f.simplify_as_binary()

solver = EasySolver(f)
solver.target_energy(0)
sol = solver.search()

print(sol)
print("energy =", sol.energy())

This program produces the following output:

Sol(energy=0, x=1, y=0, z=1)
energy = 0

After modifying a solution (e.g., using flip()), the cached energy becomes invalid. You must explicitly recompute it by calling comp_energy():

sol.flip(z)
print("comp_energy =", sol.comp_energy())
print("energy =", sol.energy())