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function t_qps_matpower(quiet)
%T_QPS_MATPOWER Tests of QPS_MATPOWER QP solvers.
% MATPOWER
% $Id: t_qps_matpower.m,v 1.12 2011/07/05 20:34:59 cvs Exp $
% by Ray Zimmerman, PSERC Cornell
% Copyright (c) 2010-2011 by Power System Engineering Research Center (PSERC)
%
% This file is part of MATPOWER.
% See http://www.pserc.cornell.edu/matpower/ for more info.
%
% MATPOWER is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published
% by the Free Software Foundation, either version 3 of the License,
% or (at your option) any later version.
%
% MATPOWER is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with MATPOWER. If not, see <http://www.gnu.org/licenses/>.
%
% Additional permission under GNU GPL version 3 section 7
%
% If you modify MATPOWER, or any covered work, to interface with
% other modules (such as MATLAB code and MEX-files) available in a
% MATLAB(R) or comparable environment containing parts covered
% under other licensing terms, the licensors of MATPOWER grant
% you additional permission to convey the resulting work.
if nargin < 1
quiet = 0;
end
algs = [100 200 250 400 300 500 600 700];
names = {'BPMPD_MEX', 'MIPS', 'sc-MIPS', 'IPOPT', 'quadprog', 'CPLEX', 'MOSEK', 'Gurobi'};
check = {'bpmpd', [], [], 'ipopt', 'quadprog', 'cplex', 'mosek', 'gurobi'};
n = 36;
t_begin(n*length(algs), quiet);
for k = 1:length(algs)
if ~isempty(check{k}) && ~have_fcn(check{k})
t_skip(n, sprintf('%s not installed', names{k}));
else
opt = struct('verbose', 0, 'alg', algs(k));
if strcmp(names{k}, 'MIPS') || strcmp(names{k}, 'sc-MIPS')
opt.mips_opt.comptol = 1e-8;
end
% if strcmp(names{k}, 'quadprog')
% end
if strcmp(names{k}, 'CPLEX')
% alg = 0; %% default uses barrier method with NaN bug in lower lim multipliers
alg = 2; %% use dual simplex
mpopt = mpoption('CPLEX_LPMETHOD', alg, 'CPLEX_QPMETHOD', min([4 alg]));
opt.cplex_opt = cplex_options([], mpopt);
end
if strcmp(names{k}, 'MOSEK')
% alg = 5; %% use dual simplex
mpopt = mpoption;
% mpopt = mpoption(mpopt, 'MOSEK_LP_ALG', alg );
mpopt = mpoption(mpopt, 'MOSEK_GAP_TOL', 1e-9);
opt.mosek_opt = mosek_options([], mpopt);
end
t = sprintf('%s - 3-d LP : ', names{k});
%% example from 'doc linprog'
c = [-5; -4; -6];
A = [1 -1 1;
3 2 4;
3 2 0];
l = [];
u = [20; 42; 30];
xmin = [0; 0; 0];
x0 = [];
[x, f, s, out, lam] = qps_matpower([], c, A, l, u, xmin, [], [], opt);
t_is(s, 1, 12, [t 'success']);
t_is(x, [0; 15; 3], 6, [t 'x']);
t_is(f, -78, 6, [t 'f']);
t_is(lam.mu_l, [0;0;0], 13, [t 'lam.mu_l']);
t_is(lam.mu_u, [0;1.5;0.5], 9, [t 'lam.mu_u']);
t_is(lam.lower, [1;0;0], 9, [t 'lam.lower']);
t_is(lam.upper, zeros(size(x)), 13, [t 'lam.upper']);
t = sprintf('%s - unconstrained 3-d quadratic : ', names{k});
%% from http://www.akiti.ca/QuadProgEx0Constr.html
H = [5 -2 -1; -2 4 3; -1 3 5];
c = [2; -35; -47];
x0 = [0; 0; 0];
[x, f, s, out, lam] = qps_matpower(H, c, [], [], [], [], [], [], opt);
t_is(s, 1, 12, [t 'success']);
t_is(x, [3; 5; 7], 8, [t 'x']);
t_is(f, -249, 13, [t 'f']);
t_ok(isempty(lam.mu_l), [t 'lam.mu_l']);
t_ok(isempty(lam.mu_u), [t 'lam.mu_u']);
t_is(lam.lower, zeros(size(x)), 13, [t 'lam.lower']);
t_is(lam.upper, zeros(size(x)), 13, [t 'lam.upper']);
t = sprintf('%s - constrained 2-d QP : ', names{k});
%% example from 'doc quadprog'
H = [ 1 -1;
-1 2 ];
c = [-2; -6];
A = [ 1 1;
-1 2;
2 1 ];
l = [];
u = [2; 2; 3];
xmin = [0; 0];
x0 = [];
[x, f, s, out, lam] = qps_matpower(H, c, A, l, u, xmin, [], x0, opt);
t_is(s, 1, 12, [t 'success']);
t_is(x, [2; 4]/3, 7, [t 'x']);
t_is(f, -74/9, 6, [t 'f']);
t_is(lam.mu_l, [0;0;0], 13, [t 'lam.mu_l']);
t_is(lam.mu_u, [28;4;0]/9, 7, [t 'lam.mu_u']);
t_is(lam.lower, zeros(size(x)), 8, [t 'lam.lower']);
t_is(lam.upper, zeros(size(x)), 13, [t 'lam.upper']);
t = sprintf('%s - constrained 4-d QP : ', names{k});
%% from http://www.jmu.edu/docs/sasdoc/sashtml/iml/chap8/sect12.htm
H = [ 1003.1 4.3 6.3 5.9;
4.3 2.2 2.1 3.9;
6.3 2.1 3.5 4.8;
5.9 3.9 4.8 10 ];
c = zeros(4,1);
A = [ 1 1 1 1;
0.17 0.11 0.10 0.18 ];
l = [1; 0.10];
u = [1; Inf];
xmin = zeros(4,1);
x0 = [1; 0; 0; 1];
[x, f, s, out, lam] = qps_matpower(H, c, A, l, u, xmin, [], x0, opt);
t_is(s, 1, 12, [t 'success']);
t_is(x, [0; 2.8; 0.2; 0]/3, 5, [t 'x']);
t_is(f, 3.29/3, 6, [t 'f']);
t_is(lam.mu_l, [6.58;0]/3, 6, [t 'lam.mu_l']);
t_is(lam.mu_u, [0;0], 13, [t 'lam.mu_u']);
t_is(lam.lower, [2.24;0;0;1.7667], 4, [t 'lam.lower']);
t_is(lam.upper, zeros(size(x)), 13, [t 'lam.upper']);
t = sprintf('%s - (struct) constrained 4-d QP : ', names{k});
p = struct('H', H, 'A', A, 'l', l, 'u', u, 'xmin', xmin, 'x0', x0, 'opt', opt);
[x, f, s, out, lam] = qps_matpower(p);
t_is(s, 1, 12, [t 'success']);
t_is(x, [0; 2.8; 0.2; 0]/3, 5, [t 'x']);
t_is(f, 3.29/3, 6, [t 'f']);
t_is(lam.mu_l, [6.58;0]/3, 6, [t 'lam.mu_l']);
t_is(lam.mu_u, [0;0], 13, [t 'lam.mu_u']);
t_is(lam.lower, [2.24;0;0;1.7667], 4, [t 'lam.lower']);
t_is(lam.upper, zeros(size(x)), 13, [t 'lam.upper']);
t = sprintf('%s - infeasible LP : ', names{k});
p = struct('A', sparse([1 1]), 'c', [1;1], 'u', -1, 'xmin', [0;0], 'opt', opt);
[x, f, s, out, lam] = qps_matpower(p);
t_ok(s <= 0, [t 'no success']);
end
end
t_end;