Matrix Examples

This section includes source code for all of the Gurobi matrix examples. The same source code can be found in the examples directory of the Gurobi distribution.

matrix1

#!/usr/bin/env python3.11

# Copyright 2024, Gurobi Optimization, LLC

# This example formulates and solves the following simple MIP model
# using the matrix API:
#  maximize
#        x +   y + 2 z
#  subject to
#        x + 2 y + 3 z <= 4
#        x +   y       >= 1
#        x, y, z binary

import gurobipy as gp
from gurobipy import GRB
import numpy as np
import scipy.sparse as sp

try:
    # Create a new model
    m = gp.Model("matrix1")

    # Create variables
    x = m.addMVar(shape=3, vtype=GRB.BINARY, name="x")

    # Set objective
    obj = np.array([1.0, 1.0, 2.0])
    m.setObjective(obj @ x, GRB.MAXIMIZE)

    # Build (sparse) constraint matrix
    val = np.array([1.0, 2.0, 3.0, -1.0, -1.0])
    row = np.array([0, 0, 0, 1, 1])
    col = np.array([0, 1, 2, 0, 1])

    A = sp.csr_matrix((val, (row, col)), shape=(2, 3))

    # Build rhs vector
    rhs = np.array([4.0, -1.0])

    # Add constraints
    m.addConstr(A @ x <= rhs, name="c")

    # Optimize model
    m.optimize()

    print(x.X)
    print(f"Obj: {m.ObjVal:g}")

except gp.GurobiError as e:
    print(f"Error code {e.errno}: {e}")

except AttributeError:
    print("Encountered an attribute error")

matrix2

#!/usr/bin/env python3.11

# Copyright 2024, Gurobi Optimization, LLC

# This example uses the matrix friendly API to formulate the n-queens
# problem; it maximizes the number queens placed on an n x n
# chessboard without threatening each other.
#
# This example demonstrates slicing on MVar objects.

import numpy as np
import gurobipy as gp
from gurobipy import GRB

n = 8

m = gp.Model("nqueens")

# n-by-n binary variables; x[i, j] decides whether a queen is placed at
# position (i, j)
x = m.addMVar((n, n), vtype=GRB.BINARY, name="x")

# Maximize the number of placed queens
m.setObjective(x.sum(), GRB.MAXIMIZE)

# At most one queen per row; this adds n linear constraints
m.addConstr(x.sum(axis=1) <= 1, name="row")

# At most one queen per column; this adds n linear constraints
m.addConstr(x.sum(axis=0) <= 1, name="col")

for i in range(-n + 1, n):
    # At most one queen on diagonal i
    m.addConstr(x.diagonal(i).sum() <= 1, name=f"diag{i:d}")

    # At most one queen on anti-diagonal i
    m.addConstr(x[:, ::-1].diagonal(i).sum() <= 1, name=f"adiag{i:d}")

# Solve the problem
m.optimize()

print(x.X)
print(f"Queens placed: {m.ObjVal:.0f}")