Source code for naginterfaces.library.examples.opt.handle_solve_pennon_lmi_ex

#!/usr/bin/env python
"""
``naginterfaces.library.opt.handle_solve_pennon`` Python Example,
with linear matrix inequality constraints.
"""

# NAG Copyright 2018-2019.

# pylint: disable=invalid-name,too-many-arguments,too-many-locals,too-many-statements

import numpy as np

from naginterfaces.library import opt

[docs]def main(): """ Example for :func:`naginterfaces.library.opt.handle_solve_pennon`, with linear matrix inequality constraints. Semidefinite programming using Pennon. >>> main() naginterfaces.library.opt.handle_solve_pennon Python Example Results. Find the Lovasz theta number for a Petersen Graph. Lovasz theta number of the given graph is 4.00. """ print( 'naginterfaces.library.opt.handle_solve_pennon Python Example Results.' ) print('Find the Lovasz theta number for a Petersen Graph.') # The graph structure: # Number of vertices in the graph: nv = 10 # Number of edges in the graph: ne = 15 va = np.empty(ne, dtype=int) vb = np.empty(ne, dtype=int) maxe = ne ne = 0 ij = [ (1, 2), (2, 3), (3, 4), (4, 5), (1, 5), (1, 6), (2, 7), (3, 8), (4, 9), (5, 10), (6, 8), (6, 9), (7, 9), (7, 10), (8, 10), ] for idx in range(maxe): i = ij[idx][0] j = ij[idx][1] if 1 <= i < j <= nv: va[ne] = i vb[ne] = j ne += 1 # Initial estimate of the solution: nvar = ne + 1 x = [0.]*nvar # Create a handle for the problem: handle = opt.handle_init(nvar) # Define the quadratic objective: opt.handle_set_quadobj( handle, idxc=[1], c=[1.], ) # Define the linear matrix constraint: nnzasum = ne + nv + (nv + 1) * nv // 2 nnza = np.empty(nvar + 1, dtype=int) irowa = np.empty(nnzasum, dtype=int) icola = np.empty(nnzasum, dtype=int) a = np.empty(nnzasum) idx = 0 nnza[0] = (nv + 1) * nv // 2 for i in range(1, nv+1): for j in range(i, nv+1): irowa[idx] = i icola[idx] = j a[idx] = 1.0 idx += 1 nnza[1] = nv for i in range(1, nv+1): irowa[idx] = i icola[idx] = i a[idx] = 1.0 idx += 1 for i in range(0, ne): nnza[2 + i] = 1 irowa[idx] = va[i] icola[idx] = vb[i] a[idx] = 1.0 idx += 1 opt.handle_set_linmatineq( handle, nv, nnza, irowa, icola, a, ) opt.handle_opt_set( handle, 'Initial X = Automatic', ) opt.handle_opt_set( handle, 'Print Level = 0', ) opt.handle_opt_set( handle, 'Print Options = No', ) # Solve the problem: theta = opt.handle_solve_pennon(handle, x, inform=0).rinfo[0] print( 'Lovasz theta number of the given graph is {:7.2f}.'.format(theta) ) # Destroy the handle: opt.handle_free(handle)
if __name__ == '__main__': import doctest import sys sys.exit( doctest.testmod( None, verbose=True, report=False, optionflags=doctest.ELLIPSIS | doctest.REPORT_NDIFF, ).failed )