Source Code for Module pypower.t.t_qps_pypower

  1  # Copyright (C) 2010-2011 Power System Engineering Research Center (PSERC) 
  2  # Copyright (C) 2011 Richard Lincoln 
  3  # 
  4  # PYPOWER is free software: you can redistribute it and/or modify 
  5  # it under the terms of the GNU General Public License as published 
  6  # by the Free Software Foundation, either version 3 of the License, 
  7  # or (at your option) any later version. 
  8  # 
  9  # PYPOWER is distributed in the hope that it will be useful, 
 10  # but WITHOUT ANY WARRANTY], without even the implied warranty of 
 11  # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 
 12  # GNU General Public License for more details. 
 13  # 
 14  # You should have received a copy of the GNU General Public License 
 15  # along with PYPOWER. If not, see <http://www.gnu.org/licenses/>. 
 16   
 17  """Tests of C{qps_pypower} QP solvers. 
 18  """ 
 19   
 20  from numpy import array, zeros, shape, Inf 
 21   
 22  from scipy.sparse import csr_matrix as sparse 
 23   
 24  from pypower.ppoption import ppoption 
 25  from pypower.cplex_options import cplex_options 
 26  from pypower.mosek_options import mosek_options 
 27  from pypower.qps_pypower import qps_pypower 
 28   
 29  from pypower.t.t_begin import t_begin 
 30  from pypower.t.t_is import t_is 
 31  from pypower.t.t_end import t_end 
 32  from pypower.t.t_ok import t_ok 
 33  from pypower.t.t_skip import t_skip 
 34   
 35   
 36 -def t_qps_pypower(quiet=False): 
 37      """Tests of C{qps_pypower} QP solvers. 
 38   
 39      @author: Ray Zimmerman (PSERC Cornell) 
 40      @author: Richard Lincoln 
 41      """ 
 42      algs = [200, 250, 400, 500, 600] 
 43      names = ['PIPS', 'sc-PIPS', 'IPOPT', 'CPLEX', 'MOSEK'] 
 44      check = [None, None, 'ipopt', 'cplex', 'mosek'] 
 45   
 46      n = 36 
 47      t_begin(n * len(algs), quiet) 
 48   
 49      for k in range(len(algs)): 
 50          if check[k] is not None and not have_fcn(check[k]): 
 51              t_skip(n, '%s not installed' % names[k]) 
 52          else: 
 53              opt = {'verbose': 0, 'alg': algs[k]} 
 54   
 55              if names[k] == 'PIPS' or names[k] == 'sc-PIPS': 
 56                  opt['pips_opt'] = {} 
 57                  opt['pips_opt']['comptol'] = 1e-8 
 58              if names[k] == 'CPLEX': 
 59  #               alg = 0        ## default uses barrier method with NaN bug in lower lim multipliers 
 60                  alg = 2        ## use dual simplex 
 61                  ppopt = ppoption(CPLEX_LPMETHOD = alg, CPLEX_QPMETHOD = min([4, alg])) 
 62                  opt['cplex_opt'] = cplex_options([], ppopt) 
 63   
 64              if names[k] == 'MOSEK': 
 65  #                alg = 5        ## use dual simplex 
 66                  ppopt = ppoption() 
 67  #                ppopt = ppoption(ppopt, MOSEK_LP_ALG = alg) 
 68                  ppopt = ppoption(ppopt, MOSEK_GAP_TOL=1e-9) 
 69                  opt['mosek_opt'] = mosek_options([], ppopt) 
 70   
 71              t = '%s - 3-d LP : ' % names[k] 
 72              ## example from 'doc linprog' 
 73              c = array([-5, -4, -6], float) 
 74              A = sparse([[1, -1,  1], 
 75                          [3,  2,  4], 
 76                          [3,  2,  0]], dtype=float) 
 77              l = None 
 78              u = array([20, 42, 30], float) 
 79              xmin = array([0, 0, 0], float) 
 80              x0 = None 
 81              x, f, s, _, lam = qps_pypower(None, c, A, l, u, xmin, None, None, opt) 
 82              t_is(s, 1, 12, [t, 'success']) 
 83              t_is(x, [0, 15, 3], 6, [t, 'x']) 
 84              t_is(f, -78, 6, [t, 'f']) 
 85              t_is(lam['mu_l'], [0, 0, 0], 13, [t, 'lam.mu_l']) 
 86              t_is(lam['mu_u'], [0, 1.5, 0.5], 9, [t, 'lam.mu_u']) 
 87              t_is(lam['lower'], [1, 0, 0], 9, [t, 'lam.lower']) 
 88              t_is(lam['upper'], zeros(shape(x)), 13, [t, 'lam.upper']) 
 89   
 90              t = '%s - unconstrained 3-d quadratic : ' % names[k] 
 91              ## from http://www.akiti.ca/QuadProgEx0Constr.html 
 92              H = sparse([ 
 93                  [ 5, -2, -1], 
 94                  [-2,  4,  3], 
 95                  [-1,  3,  5] 
 96              ], dtype=float) 
 97              c = array([2, -35, -47], float) 
 98              x0 = array([0, 0, 0], float) 
 99              x, f, s, _, lam = qps_pypower(H, c, opt=opt) 
100              t_is(s, 1, 12, [t, 'success']) 
101              t_is(x, [3, 5, 7], 8, [t, 'x']) 
102              t_is(f, -249, 13, [t, 'f']) 
103              t_ok(len(lam['mu_l']) == 0, [t, 'lam.mu_l']) 
104              t_ok(len(lam['mu_u']) == 0, [t, 'lam.mu_u']) 
105              t_is(lam['lower'], zeros(shape(x)), 13, [t, 'lam.lower']) 
106              t_is(lam['upper'], zeros(shape(x)), 13, [t, 'lam.upper']) 
107   
108              t = '%s - constrained 2-d QP : ' % names[k] 
109              ## example from 'doc quadprog' 
110              H = sparse([[ 1, -1], 
111                          [-1,  2]], dtype=float) 
112              c = array([-2, -6], float) 
113              A = sparse([[ 1, 1], 
114                          [-1, 2], 
115                          [ 2, 1]], dtype=float) 
116              l = None 
117              u = array([2, 2, 3], float) 
118              xmin = array([0, 0]) 
119              x0 = None 
120              x, f, s, _, lam = qps_pypower(H, c, A, l, u, xmin, None, x0, opt) 
121              t_is(s, 1, 12, [t, 'success']) 
122              t_is(x, array([2., 4.]) / 3, 7, [t, 'x']) 
123              t_is(f, -74. / 9, 6, [t, 'f']) 
124              t_is(lam['mu_l'], [0., 0., 0.], 13, [t, 'lam.mu_l']) 
125              t_is(lam['mu_u'], array([28., 4., 0.]) / 9, 7, [t, 'lam.mu_u']) 
126              t_is(lam['lower'], zeros(shape(x)), 8, [t, 'lam.lower']) 
127              t_is(lam['upper'], zeros(shape(x)), 13, [t, 'lam.upper']) 
128   
129              t = '%s - constrained 4-d QP : ' % names[k] 
130              ## from http://www.jmu.edu/docs/sasdoc/sashtml/iml/chap8/sect12.htm 
131              H = sparse([[1003.1,  4.3,     6.3,     5.9], 
132                          [4.3,     2.2,     2.1,     3.9], 
133                          [6.3,     2.1,     3.5,     4.8], 
134                          [5.9,     3.9,     4.8,    10.0]]) 
135              c = zeros(4) 
136              A = sparse([[   1,       1,       1,       1], 
137                          [0.17,    0.11,    0.10,    0.18]]) 
138              l = array([1, 0.10]) 
139              u = array([1, Inf]) 
140              xmin = zeros(4) 
141              x0 = array([1, 0, 0, 1], float) 
142              x, f, s, _, lam = qps_pypower(H, c, A, l, u, xmin, None, x0, opt) 
143              t_is(s, 1, 12, [t, 'success']) 
144              t_is(x, array([0, 2.8, 0.2, 0]) / 3, 5, [t, 'x']) 
145              t_is(f, 3.29 / 3, 6, [t, 'f']) 
146              t_is(lam['mu_l'], array([6.58, 0]) / 3, 6, [t, 'lam.mu_l']) 
147              t_is(lam['mu_u'], [0, 0], 13, [t, 'lam.mu_u']) 
148              t_is(lam['lower'], [2.24, 0, 0, 1.7667], 4, [t, 'lam.lower']) 
149              t_is(lam['upper'], zeros(shape(x)), 13, [t, 'lam.upper']) 
150   
151              t = '%s - (dict) constrained 4-d QP : ' % names[k] 
152              p = {'H': H, 'A': A, 'l': l, 'u': u, 'xmin': xmin, 'x0': x0, 'opt': opt} 
153              x, f, s, _, lam = qps_pypower(p) 
154              t_is(s, 1, 12, [t, 'success']) 
155              t_is(x, array([0, 2.8, 0.2, 0]) / 3, 5, [t, 'x']) 
156              t_is(f, 3.29 / 3, 6, [t, 'f']) 
157              t_is(lam['mu_l'], array([6.58, 0]) / 3, 6, [t, 'lam.mu_l']) 
158              t_is(lam['mu_u'], [0, 0], 13, [t, 'lam.mu_u']) 
159              t_is(lam['lower'], [2.24, 0, 0, 1.7667], 4, [t, 'lam.lower']) 
160              t_is(lam['upper'], zeros(shape(x)), 13, [t, 'lam.upper']) 
161   
162              t = '%s - infeasible LP : ' % names[k] 
163              p = {'A': sparse([1, 1]), 'c': array([1, 1]), 'u': array([-1]), 
164                   'xmin': array([0, 0]), 'opt': opt} 
165              x, f, s, _, lam = qps_pypower(p) 
166              t_ok(s <= 0, [t, 'no success']) 
167   
168      t_end() 
169   
170   
171 -def have_fcn(name): 
172      try: 
173          __import__(name) 
174          return True 
175      except ImportError: 
176          return False 
177   
178   
179  if __name__ == '__main__': 
180      t_qps_pypower(quiet=False) 
181