# Uses the xpress.Dot() operator to formulate constraints simply.
#
# Note that the NumPy dot operator is not suitable here as the
# result is an expression in the Xpress variables.
#
# (C) 1983-2025 Fair Isaac Corporation

import xpress as xp
import numpy as np

A = np.random.random(30).reshape(6, 5)  # A is a 6x5 matrix.
Q = np.random.random(25).reshape(5, 5)  # Q is a 5x5 matrix.

p = xp.problem()

# Add a NumPy array of variables.
x = p.addVariables(5)
x0 = np.random.random(5)  # Random vector.

Q += 4 * np.eye(5)  # Add 5 * the identity matrix.

# 6 constraints (rows of A).
Lin_sys = xp.Dot(A, x) <= np.array([3, 4, 1, 4, 8, 7])

# One quadratic constraint.
Conv_c = xp.Dot(x, Q, x) <= 1

p.addConstraint(Lin_sys, Conv_c)
p.setObjective(xp.Dot(x-x0, x-x0))

p.optimize()