# Minimize a polynomial constructed with the Dot product
#
# (C) Fair Isaac Corp., 1983-2021
from __future__ import print_function
import xpress as xp
import numpy as np
#
# Generate a random coefficient tensor T of dimension k + 1 and sizes
# n+1 for each dimension except for the first, which is h, then use it
# to create h polynomial constraints. The lhs of each constraint has a
# polynomial of degree k, and not homogeneous as we amend the vector
# of variable with the constant 1. This is accomplished via a single
# dot product.
#
n = 10 # dimension of variable space
h = 3 # number of polynomial constraints
k = 4 # degree of each polynomial
# Vector of n elements: (1, x1, ..., x_{n-1}), declared with NumPy's
# dtype notation for Xpress expressions (to guarantee Xpress
# operations will be used).
x = np.array([1] + [xp.var(lb=-10, ub=10) for _ in range(n-1)], dtype=xp.npexpr)
sizes = [n]*k # creates list [n,n,...,n] of k elements
# Operator * before a list translates the list into its
# (unparenthesized) tuple, i.e., the result is a reshape list of
# argument that looks like (h, n, n, ..., n)
T = np.random.random(h * n ** k).reshape(h, *sizes)
print(T)
T2list = [x]*k
compact = xp.Dot(T, *T2list) <= 0
p = xp.problem()
p.addVariable(x[1:])
p.addConstraint(compact)
p.write('polynomial', 'lp')