Evaluating Expressions

Evaluation using a list of pairs

The value of an expression can be computed by providing an assignment of values to all variables as a list of (variable, value) pairs.

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

import pyqbpp as qbpp

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

print("f(0,1,1) =", f([(x, 0), (y, 1), (z, 1)]))

In this program, a list of pairs [(x, 0), (y, 1), (z, 1)] defines the assignment $x=0$, $y=1$, $z=1$. Then f(...) 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(f) returns the value of the expression f under the assignment stored in sol.

import pyqbpp as qbpp

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

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

print("f(0,1,1) =", sol(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 property:

import pyqbpp as qbpp

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

solver = qbpp.EasySolver(f)
sol = solver.search({"target_energy": 0})

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)