def t_qps_pypower(quiet=False):
"""Tests of C{qps_pypower} QP solvers.
@author: Ray Zimmerman (PSERC Cornell)
"""
algs = [200, 250, 400, 500, 600, 700]
names = ['PIPS', 'sc-PIPS', 'IPOPT', 'CPLEX', 'MOSEK', 'Gurobi']
check = [None, None, 'ipopt', 'cplex', 'mosek', 'gurobipy']
n = 36
t_begin(n * len(algs), quiet)
for k in range(len(algs)):
if check[k] is not None and not have_fcn(check[k]):
t_skip(n, '%s not installed' % names[k])
else:
opt = {'verbose': 0, 'alg': algs[k]}
if names[k] == 'PIPS' or names[k] == 'sc-PIPS':
opt['pips_opt'] = {}
opt['pips_opt']['comptol'] = 1e-8
if names[k] == 'CPLEX':
# alg = 0 ## default uses barrier method with NaN bug in lower lim multipliers
alg = 2 ## use dual simplex
ppopt = ppoption(CPLEX_LPMETHOD = alg, CPLEX_QPMETHOD = min([4, alg]))
opt['cplex_opt'] = cplex_options([], ppopt)
if names[k] == 'MOSEK':
# alg = 5 ## use dual simplex
ppopt = ppoption()
# ppopt = ppoption(ppopt, MOSEK_LP_ALG = alg)
ppopt = ppoption(ppopt, MOSEK_GAP_TOL=1e-9)
opt['mosek_opt'] = mosek_options([], ppopt)
t = '%s - 3-d LP : ' % names[k]
## example from 'doc linprog'
c = array([-5, -4, -6], float)
A = sparse([[1, -1, 1],
[3, 2, 4],
[3, 2, 0]], dtype=float)
l = None
u = array([20, 42, 30], float)
xmin = array([0, 0, 0], float)
x0 = None
x, f, s, _, lam = qps_pypower(None, c, A, l, u, xmin, None, None, 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(shape(x)), 13, [t, 'lam.upper'])
t = '%s - unconstrained 3-d quadratic : ' % names[k]
## from http://www.akiti.ca/QuadProgEx0Constr.html
H = sparse([
[ 5, -2, -1],
[-2, 4, 3],
[-1, 3, 5]
], dtype=float)
c = array([2, -35, -47], float)
x0 = array([0, 0, 0], float)
x, f, s, _, lam = qps_pypower(H, c, opt=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(len(lam['mu_l']) == 0, [t, 'lam.mu_l'])
t_ok(len(lam['mu_u']) == 0, [t, 'lam.mu_u'])
t_is(lam['lower'], zeros(shape(x)), 13, [t, 'lam.lower'])
t_is(lam['upper'], zeros(shape(x)), 13, [t, 'lam.upper'])
t = '%s - constrained 2-d QP : ' % names[k]
## example from 'doc quadprog'
H = sparse([[ 1, -1],
[-1, 2]], dtype=float)
c = array([-2, -6], float)
A = sparse([[ 1, 1],
[-1, 2],
[ 2, 1]], dtype=float)
l = None
u = array([2, 2, 3], float)
xmin = array([0, 0])
x0 = None
x, f, s, _, lam = qps_pypower(H, c, A, l, u, xmin, None, x0, opt)
t_is(s, 1, 12, [t, 'success'])
t_is(x, array([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'], array([28., 4., 0.]) / 9, 7, [t, 'lam.mu_u'])
t_is(lam['lower'], zeros(shape(x)), 8, [t, 'lam.lower'])
t_is(lam['upper'], zeros(shape(x)), 13, [t, 'lam.upper'])
t = '%s - constrained 4-d QP : ' % names[k]
## from http://www.jmu.edu/docs/sasdoc/sashtml/iml/chap8/sect12.htm
H = sparse([[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, 10.0]])
c = zeros(4)
A = sparse([[ 1, 1, 1, 1],
[0.17, 0.11, 0.10, 0.18]])
l = array([1, 0.10])
u = array([1, Inf])
xmin = zeros(4)
x0 = array([1, 0, 0, 1], float)
x, f, s, _, lam = qps_pypower(H, c, A, l, u, xmin, None, x0, opt)
t_is(s, 1, 12, [t, 'success'])
t_is(x, array([0, 2.8, 0.2, 0]) / 3, 5, [t, 'x'])
t_is(f, 3.29 / 3, 6, [t, 'f'])
t_is(lam['mu_l'], array([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(shape(x)), 13, [t, 'lam.upper'])
t = '%s - (dict) constrained 4-d QP : ' % names[k]
p = {'H': H, 'A': A, 'l': l, 'u': u, 'xmin': xmin, 'x0': x0, 'opt': opt}
x, f, s, _, lam = qps_pypower(p)
t_is(s, 1, 12, [t, 'success'])
t_is(x, array([0, 2.8, 0.2, 0]) / 3, 5, [t, 'x'])
t_is(f, 3.29 / 3, 6, [t, 'f'])
t_is(lam['mu_l'], array([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(shape(x)), 13, [t, 'lam.upper'])
t = '%s - infeasible LP : ' % names[k]
p = {'A': sparse([1, 1]), 'c': array([1, 1]), 'u': array([-1]),
'xmin': array([0, 0]), 'opt': opt}
x, f, s, _, lam = qps_pypower(p)
t_ok(s <= 0, [t, 'no success'])
t_end()
def dcopf_solver(om, ppopt, out_opt=None):
"""Solves a DC optimal power flow.
Inputs are an OPF model object, a PYPOWER options dict and
a dict containing fields (can be empty) for each of the desired
optional output fields.
Outputs are a C{results} dict, C{success} flag and C{raw} output dict.
C{results} is a PYPOWER case dict (ppc) with the usual baseMVA, bus
branch, gen, gencost fields, along with the following additional
fields:
- C{order} see 'help ext2int' for details of this field
- C{x} final value of optimization variables (internal order)
- C{f} final objective function value
- C{mu} shadow prices on ...
- C{var}
- C{l} lower bounds on variables
- C{u} upper bounds on variables
- C{lin}
- C{l} lower bounds on linear constraints
- C{u} upper bounds on linear constraints
- C{g} (optional) constraint values
- C{dg} (optional) constraint 1st derivatives
- C{df} (optional) obj fun 1st derivatives (not yet implemented)
- C{d2f} (optional) obj fun 2nd derivatives (not yet implemented)
C{success} is C{True} if solver converged successfully, C{False} otherwise.
C{raw} is a raw output dict in form returned by MINOS
- C{xr} final value of optimization variables
- C{pimul} constraint multipliers
- C{info} solver specific termination code
- C{output} solver specific output information
@see: L{opf}, L{qps_pypower}
@author: Ray Zimmerman (PSERC Cornell)
@author: Carlos E. Murillo-Sanchez (PSERC Cornell & Universidad
Autonoma de Manizales)
@author: Richard Lincoln
"""
if out_opt is None:
out_opt = {}
## options
verbose = ppopt['VERBOSE']
alg = ppopt['OPF_ALG_DC']
if alg == 0:
if have_fcn('cplex'): ## use CPLEX by default, if available
alg = 500
elif have_fcn('mosek'): ## if not, then MOSEK, if available
alg = 600
elif have_fcn('gurobi'): ## if not, then Gurobi, if available
alg = 700
else: ## otherwise PIPS
alg = 200
## unpack data
ppc = om.get_ppc()
baseMVA, bus, gen, branch, gencost = \
ppc["baseMVA"], ppc["bus"], ppc["gen"], ppc["branch"], ppc["gencost"]
cp = om.get_cost_params()
N, H, Cw = cp["N"], cp["H"], cp["Cw"]
fparm = array(c_[cp["dd"], cp["rh"], cp["kk"], cp["mm"]])
Bf = om.userdata('Bf')
Pfinj = om.userdata('Pfinj')
vv, ll, _, _ = om.get_idx()
## problem dimensions
ipol = find(gencost[:, MODEL] == POLYNOMIAL) ## polynomial costs
ipwl = find(gencost[:, MODEL] == PW_LINEAR) ## piece-wise linear costs
nb = bus.shape[0] ## number of buses
nl = branch.shape[0] ## number of branches
nw = N.shape[0] ## number of general cost vars, w
ny = om.getN('var', 'y') ## number of piece-wise linear costs
nxyz = om.getN('var') ## total number of control vars of all types
## linear constraints & variable bounds
A, l, u = om.linear_constraints()
x0, xmin, xmax = om.getv()
## set up objective function of the form: f = 1/2 * X'*HH*X + CC'*X
## where X = [x;y;z]. First set up as quadratic function of w,
## f = 1/2 * w'*HHw*w + CCw'*w, where w = diag(M) * (N*X - Rhat). We
## will be building on the (optionally present) user supplied parameters.
## piece-wise linear costs
any_pwl = int(ny > 0)
if any_pwl:
# Sum of y vars.
Npwl = sparse(
(ones(ny), (zeros(ny), arange(vv["i1"]["y"], vv["iN"]["y"]))),
(1, nxyz))
Hpwl = sparse((1, 1))
Cpwl = array([1])
fparm_pwl = array([[1, 0, 0, 1]])
else:
Npwl = None #zeros((0, nxyz))
Hpwl = None #array([])
Cpwl = array([])
fparm_pwl = zeros((0, 4))
## quadratic costs
npol = len(ipol)
if any(find(gencost[ipol, NCOST] > 3)):
stderr.write('DC opf cannot handle polynomial costs with higher '
'than quadratic order.\n')
iqdr = find(gencost[ipol, NCOST] == 3)
ilin = find(gencost[ipol, NCOST] == 2)
polycf = zeros((npol, 3)) ## quadratic coeffs for Pg
if len(iqdr) > 0:
polycf[iqdr, :] = gencost[ipol[iqdr], COST:COST + 3]
if npol:
polycf[ilin, 1:3] = gencost[ipol[ilin], COST:COST + 2]
polycf = dot(polycf, diag([baseMVA**2, baseMVA, 1])) ## convert to p.u.
if npol:
Npol = sparse((ones(npol), (arange(npol), vv["i1"]["Pg"] + ipol)),
(npol, nxyz)) # Pg vars
Hpol = sparse((2 * polycf[:, 0], (arange(npol), arange(npol))),
(npol, npol))
else:
Npol = None
Hpol = None
Cpol = polycf[:, 1]
fparm_pol = ones((npol, 1)) * array([[1, 0, 0, 1]])
## combine with user costs
NN = vstack(
[n for n in [Npwl, Npol, N] if n is not None and n.shape[0] > 0],
"csr")
# FIXME: Zero dimension sparse matrices.
if (Hpwl is not None) and any_pwl and (npol + nw):
Hpwl = hstack([Hpwl, sparse((any_pwl, npol + nw))])
if Hpol is not None:
if any_pwl and npol:
Hpol = hstack([sparse((npol, any_pwl)), Hpol])
if npol and nw:
Hpol = hstack([Hpol, sparse((npol, nw))])
if (H is not None) and nw and (any_pwl + npol):
H = hstack([sparse((nw, any_pwl + npol)), H])
HHw = vstack(
[h for h in [Hpwl, Hpol, H] if h is not None and h.shape[0] > 0],
"csr")
CCw = r_[Cpwl, Cpol, Cw]
ffparm = r_[fparm_pwl, fparm_pol, fparm]
## transform quadratic coefficients for w into coefficients for X
nnw = any_pwl + npol + nw
M = sparse((ffparm[:, 3], (range(nnw), range(nnw))))
MR = M * ffparm[:, 1]
HMR = HHw * MR
MN = M * NN
HH = MN.T * HHw * MN
CC = MN.T * (CCw - HMR)
C0 = 0.5 * dot(MR, HMR) + sum(polycf[:, 2]) # Constant term of cost.
## set up input for QP solver
opt = {'alg': alg, 'verbose': verbose}
if (alg == 200) or (alg == 250):
## try to select an interior initial point
Varefs = bus[bus[:, BUS_TYPE] == REF, VA] * (pi / 180.0)
lb, ub = xmin.copy(), xmax.copy()
lb[xmin == -Inf] = -1e10 ## replace Inf with numerical proxies
ub[xmax == Inf] = 1e10
x0 = (lb + ub) / 2
# angles set to first reference angle
x0[vv["i1"]["Va"]:vv["iN"]["Va"]] = Varefs[0]
if ny > 0:
ipwl = find(gencost[:, MODEL] == PW_LINEAR)
# largest y-value in CCV data
c = gencost.flatten('F')[sub2ind(gencost.shape, ipwl,
NCOST + 2 * gencost[ipwl, NCOST])]
x0[vv["i1"]["y"]:vv["iN"]["y"]] = max(c) + 0.1 * abs(max(c))
## set up options
feastol = ppopt['PDIPM_FEASTOL']
gradtol = ppopt['PDIPM_GRADTOL']
comptol = ppopt['PDIPM_COMPTOL']
costtol = ppopt['PDIPM_COSTTOL']
max_it = ppopt['PDIPM_MAX_IT']
max_red = ppopt['SCPDIPM_RED_IT']
if feastol == 0:
feastol = ppopt['OPF_VIOLATION'] ## = OPF_VIOLATION by default
opt["pips_opt"] = {
'feastol': feastol,
'gradtol': gradtol,
'comptol': comptol,
'costtol': costtol,
'max_it': max_it,
'max_red': max_red,
'cost_mult': 1
}
elif alg == 400:
opt['ipopt_opt'] = ipopt_options([], ppopt)
elif alg == 500:
opt['cplex_opt'] = cplex_options([], ppopt)
elif alg == 600:
opt['mosek_opt'] = mosek_options([], ppopt)
elif alg == 700:
opt['grb_opt'] = gurobi_options([], ppopt)
else:
raise ValueError("Unrecognised solver [%d]." % alg)
##----- run opf -----
x, f, info, output, lmbda = \
qps_pypower(HH, CC, A, l, u, xmin, xmax, x0, opt)
success = (info == 1)
##----- calculate return values -----
if not any(isnan(x)):
## update solution data
Va = x[vv["i1"]["Va"]:vv["iN"]["Va"]]
Pg = x[vv["i1"]["Pg"]:vv["iN"]["Pg"]]
f = f + C0
## update voltages & generator outputs
bus[:, VA] = Va * 180 / pi
gen[:, PG] = Pg * baseMVA
## compute branch flows
branch[:, [QF, QT]] = zeros((nl, 2))
branch[:, PF] = (Bf * Va + Pfinj) * baseMVA
branch[:, PT] = -branch[:, PF]
## package up results
mu_l = lmbda["mu_l"]
mu_u = lmbda["mu_u"]
muLB = lmbda["lower"]
muUB = lmbda["upper"]
## update Lagrange multipliers
il = find((branch[:, RATE_A] != 0) & (branch[:, RATE_A] < 1e10))
bus[:, [LAM_P, LAM_Q, MU_VMIN, MU_VMAX]] = zeros((nb, 4))
gen[:, [MU_PMIN, MU_PMAX, MU_QMIN, MU_QMAX]] = zeros((gen.shape[0], 4))
branch[:, [MU_SF, MU_ST]] = zeros((nl, 2))
bus[:, LAM_P] = (mu_u[ll["i1"]["Pmis"]:ll["iN"]["Pmis"]] -
mu_l[ll["i1"]["Pmis"]:ll["iN"]["Pmis"]]) / baseMVA
branch[il, MU_SF] = mu_u[ll["i1"]["Pf"]:ll["iN"]["Pf"]] / baseMVA
branch[il, MU_ST] = mu_u[ll["i1"]["Pt"]:ll["iN"]["Pt"]] / baseMVA
gen[:, MU_PMIN] = muLB[vv["i1"]["Pg"]:vv["iN"]["Pg"]] / baseMVA
gen[:, MU_PMAX] = muUB[vv["i1"]["Pg"]:vv["iN"]["Pg"]] / baseMVA
pimul = r_[mu_l - mu_u, -ones(
(ny > 0)), ## dummy entry corresponding to linear cost row in A
muLB - muUB]
mu = {'var': {'l': muLB, 'u': muUB}, 'lin': {'l': mu_l, 'u': mu_u}}
results = deepcopy(ppc)
results["bus"], results["branch"], results["gen"], \
results["om"], results["x"], results["mu"], results["f"] = \
bus, branch, gen, om, x, mu, f
raw = {'xr': x, 'pimul': pimul, 'info': info, 'output': output}
return results, success, raw
def dcopf_solver(om, ppopt, out_opt=None):
"""Solves a DC optimal power flow.
Inputs are an OPF model object, a PYPOWER options dict and
a dict containing fields (can be empty) for each of the desired
optional output fields.
Outputs are a C{results} dict, C{success} flag and C{raw} output dict.
C{results} is a PYPOWER case dict (ppc) with the usual baseMVA, bus
branch, gen, gencost fields, along with the following additional
fields:
- C{order} see 'help ext2int' for details of this field
- C{x} final value of optimization variables (internal order)
- C{f} final objective function value
- C{mu} shadow prices on ...
- C{var}
- C{l} lower bounds on variables
- C{u} upper bounds on variables
- C{lin}
- C{l} lower bounds on linear constraints
- C{u} upper bounds on linear constraints
- C{g} (optional) constraint values
- C{dg} (optional) constraint 1st derivatives
- C{df} (optional) obj fun 1st derivatives (not yet implemented)
- C{d2f} (optional) obj fun 2nd derivatives (not yet implemented)
C{success} is C{True} if solver converged successfully, C{False} otherwise.
C{raw} is a raw output dict in form returned by MINOS
- C{xr} final value of optimization variables
- C{pimul} constraint multipliers
- C{info} solver specific termination code
- C{output} solver specific output information
@see: L{opf}, L{qps_pypower}
@author: Ray Zimmerman (PSERC Cornell)
@author: Carlos E. Murillo-Sanchez (PSERC Cornell & Universidad
Autonoma de Manizales)
"""
if out_opt is None:
out_opt = {}
## options
verbose = ppopt['VERBOSE']
alg = ppopt['OPF_ALG_DC']
if alg == 0:
if have_fcn('cplex'): ## use CPLEX by default, if available
alg = 500
elif have_fcn('mosek'): ## if not, then MOSEK, if available
alg = 600
elif have_fcn('gurobi'): ## if not, then Gurobi, if available
alg = 700
else: ## otherwise PIPS
alg = 200
## unpack data
ppc = om.get_ppc()
baseMVA, bus, gen, branch, gencost = \
ppc["baseMVA"], ppc["bus"], ppc["gen"], ppc["branch"], ppc["gencost"]
cp = om.get_cost_params()
N, H, Cw = cp["N"], cp["H"], cp["Cw"]
fparm = array(c_[cp["dd"], cp["rh"], cp["kk"], cp["mm"]])
Bf = om.userdata('Bf')
Pfinj = om.userdata('Pfinj')
vv, ll, _, _ = om.get_idx()
## problem dimensions
ipol = find(gencost[:, MODEL] == POLYNOMIAL) ## polynomial costs
ipwl = find(gencost[:, MODEL] == PW_LINEAR) ## piece-wise linear costs
nb = bus.shape[0] ## number of buses
nl = branch.shape[0] ## number of branches
nw = N.shape[0] ## number of general cost vars, w
ny = om.getN('var', 'y') ## number of piece-wise linear costs
nxyz = om.getN('var') ## total number of control vars of all types
## linear constraints & variable bounds
A, l, u = om.linear_constraints()
x0, xmin, xmax = om.getv()
## set up objective function of the form: f = 1/2 * X'*HH*X + CC'*X
## where X = [x;y;z]. First set up as quadratic function of w,
## f = 1/2 * w'*HHw*w + CCw'*w, where w = diag(M) * (N*X - Rhat). We
## will be building on the (optionally present) user supplied parameters.
## piece-wise linear costs
any_pwl = int(ny > 0)
if any_pwl:
# Sum of y vars.
Npwl = sparse((ones(ny), (zeros(ny), arange(vv["i1"]["y"], vv["iN"]["y"]))), (1, nxyz))
Hpwl = sparse((1, 1))
Cpwl = array([1])
fparm_pwl = array([[1, 0, 0, 1]])
else:
Npwl = None#zeros((0, nxyz))
Hpwl = None#array([])
Cpwl = array([])
fparm_pwl = zeros((0, 4))
## quadratic costs
npol = len(ipol)
if any(find(gencost[ipol, NCOST] > 3)):
stderr.write('DC opf cannot handle polynomial costs with higher '
'than quadratic order.\n')
iqdr = find(gencost[ipol, NCOST] == 3)
ilin = find(gencost[ipol, NCOST] == 2)
polycf = zeros((npol, 3)) ## quadratic coeffs for Pg
if len(iqdr) > 0:
polycf[iqdr, :] = gencost[ipol[iqdr], COST:COST + 3]
if npol:
polycf[ilin, 1:3] = gencost[ipol[ilin], COST:COST + 2]
polycf = dot(polycf, diag([ baseMVA**2, baseMVA, 1])) ## convert to p.u.
if npol:
Npol = sparse((ones(npol), (arange(npol), vv["i1"]["Pg"] + ipol)),
(npol, nxyz)) # Pg vars
Hpol = sparse((2 * polycf[:, 0], (arange(npol), arange(npol))),
(npol, npol))
else:
Npol = None
Hpol = None
Cpol = polycf[:, 1]
fparm_pol = ones((npol, 1)) * array([[1, 0, 0, 1]])
## combine with user costs
NN = vstack([n for n in [Npwl, Npol, N] if n is not None and n.shape[0] > 0], "csr")
# FIXME: Zero dimension sparse matrices.
if (Hpwl is not None) and any_pwl and (npol + nw):
Hpwl = hstack([Hpwl, sparse((any_pwl, npol + nw))])
if Hpol is not None:
if any_pwl and npol:
Hpol = hstack([sparse((npol, any_pwl)), Hpol])
if npol and nw:
Hpol = hstack([Hpol, sparse((npol, nw))])
if (H is not None) and nw and (any_pwl + npol):
H = hstack([sparse((nw, any_pwl + npol)), H])
HHw = vstack([h for h in [Hpwl, Hpol, H] if h is not None and h.shape[0] > 0], "csr")
CCw = r_[Cpwl, Cpol, Cw]
ffparm = r_[fparm_pwl, fparm_pol, fparm]
## transform quadratic coefficients for w into coefficients for X
nnw = any_pwl + npol + nw
M = sparse((ffparm[:, 3], (range(nnw), range(nnw))))
MR = M * ffparm[:, 1]
HMR = HHw * MR
MN = M * NN
HH = MN.T * HHw * MN
CC = MN.T * (CCw - HMR)
C0 = 0.5 * dot(MR, HMR) + sum(polycf[:, 2]) # Constant term of cost.
## set up input for QP solver
opt = {'alg': alg, 'verbose': verbose}
if (alg == 200) or (alg == 250):
## try to select an interior initial point
Varefs = bus[bus[:, BUS_TYPE] == REF, VA] * (pi / 180.0)
lb, ub = xmin.copy(), xmax.copy()
lb[xmin == -Inf] = -1e10 ## replace Inf with numerical proxies
ub[xmax == Inf] = 1e10
x0 = (lb + ub) / 2;
# angles set to first reference angle
x0[vv["i1"]["Va"]:vv["iN"]["Va"]] = Varefs[0]
if ny > 0:
ipwl = find(gencost[:, MODEL] == PW_LINEAR)
# largest y-value in CCV data
c = gencost.flatten('F')[sub2ind(gencost.shape, ipwl,
NCOST + 2 * gencost[ipwl, NCOST])]
x0[vv["i1"]["y"]:vv["iN"]["y"]] = max(c) + 0.1 * abs(max(c))
## set up options
feastol = ppopt['PDIPM_FEASTOL']
gradtol = ppopt['PDIPM_GRADTOL']
comptol = ppopt['PDIPM_COMPTOL']
costtol = ppopt['PDIPM_COSTTOL']
max_it = ppopt['PDIPM_MAX_IT']
max_red = ppopt['SCPDIPM_RED_IT']
if feastol == 0:
feastol = ppopt['OPF_VIOLATION'] ## = OPF_VIOLATION by default
opt["pips_opt"] = { 'feastol': feastol,
'gradtol': gradtol,
'comptol': comptol,
'costtol': costtol,
'max_it': max_it,
'max_red': max_red,
'cost_mult': 1 }
elif alg == 400:
opt['ipopt_opt'] = ipopt_options([], ppopt)
elif alg == 500:
opt['cplex_opt'] = cplex_options([], ppopt)
elif alg == 600:
opt['mosek_opt'] = mosek_options([], ppopt)
elif alg == 700:
opt['grb_opt'] = gurobi_options([], ppopt)
else:
raise ValueError("Unrecognised solver [%d]." % alg)
##----- run opf -----
x, f, info, output, lmbda = \
qps_pypower(HH, CC, A, l, u, xmin, xmax, x0, opt)
success = (info == 1)
##----- calculate return values -----
if not any(isnan(x)):
## update solution data
Va = x[vv["i1"]["Va"]:vv["iN"]["Va"]]
Pg = x[vv["i1"]["Pg"]:vv["iN"]["Pg"]]
f = f + C0
## update voltages & generator outputs
bus[:, VA] = Va * 180 / pi
gen[:, PG] = Pg * baseMVA
## compute branch flows
branch[:, [QF, QT]] = zeros((nl, 2))
branch[:, PF] = (Bf * Va + Pfinj) * baseMVA
branch[:, PT] = -branch[:, PF]
## package up results
mu_l = lmbda["mu_l"]
mu_u = lmbda["mu_u"]
muLB = lmbda["lower"]
muUB = lmbda["upper"]
## update Lagrange multipliers
il = find((branch[:, RATE_A] != 0) & (branch[:, RATE_A] < 1e10))
bus[:, [LAM_P, LAM_Q, MU_VMIN, MU_VMAX]] = zeros((nb, 4))
gen[:, [MU_PMIN, MU_PMAX, MU_QMIN, MU_QMAX]] = zeros((gen.shape[0], 4))
branch[:, [MU_SF, MU_ST]] = zeros((nl, 2))
bus[:, LAM_P] = (mu_u[ll["i1"]["Pmis"]:ll["iN"]["Pmis"]] -
mu_l[ll["i1"]["Pmis"]:ll["iN"]["Pmis"]]) / baseMVA
branch[il, MU_SF] = mu_u[ll["i1"]["Pf"]:ll["iN"]["Pf"]] / baseMVA
branch[il, MU_ST] = mu_u[ll["i1"]["Pt"]:ll["iN"]["Pt"]] / baseMVA
gen[:, MU_PMIN] = muLB[vv["i1"]["Pg"]:vv["iN"]["Pg"]] / baseMVA
gen[:, MU_PMAX] = muUB[vv["i1"]["Pg"]:vv["iN"]["Pg"]] / baseMVA
pimul = r_[
mu_l - mu_u,
-ones(int(ny > 0)), ## dummy entry corresponding to linear cost row in A
muLB - muUB
]
mu = { 'var': {'l': muLB, 'u': muUB},
'lin': {'l': mu_l, 'u': mu_u} }
results = deepcopy(ppc)
results["bus"], results["branch"], results["gen"], \
results["om"], results["x"], results["mu"], results["f"] = \
bus, branch, gen, om, x, mu, f
raw = {'xr': x, 'pimul': pimul, 'info': info, 'output': output}
return results, success, raw
def qps_mosek(H, c=None, A=None, l=None, u=None, xmin=None, xmax=None,
x0=None, opt=None):
"""Quadratic Program Solver based on MOSEK.
A wrapper function providing a PYPOWER standardized interface for using
MOSEKOPT to solve the following QP (quadratic programming) problem::
min 1/2 x'*H*x + c'*x
x
subject to::
l <= A*x <= u (linear constraints)
xmin <= x <= xmax (variable bounds)
Inputs (all optional except C{H}, C{C}, C{A} and C{L}):
- C{H} : matrix (possibly sparse) of quadratic cost coefficients
- C{C} : vector of linear cost coefficients
- C{A, l, u} : define the optional linear constraints. Default
values for the elements of L and U are -Inf and Inf, respectively.
- xmin, xmax : optional lower and upper bounds on the
C{x} variables, defaults are -Inf and Inf, respectively.
- C{x0} : optional starting value of optimization vector C{x}
- C{opt} : optional options structure with the following fields,
all of which are also optional (default values shown in parentheses)
- C{verbose} (0) - controls level of progress output displayed
- 0 = no progress output
- 1 = some progress output
- 2 = verbose progress output
- C{max_it} (0) - maximum number of iterations allowed
- 0 = use algorithm default
- C{mosek_opt} - options struct for MOSEK, values in
C{verbose} and C{max_it} override these options
- C{problem} : The inputs can alternatively be supplied in a single
C{problem} struct with fields corresponding to the input arguments
described above: C{H, c, A, l, u, xmin, xmax, x0, opt}
Outputs:
- C{x} : solution vector
- C{f} : final objective function value
- C{exitflag} : exit flag
- 1 = success
- 0 = terminated at maximum number of iterations
- -1 = primal or dual infeasible
< 0 = the negative of the MOSEK return code
- C{output} : output dict with the following fields:
- C{r} - MOSEK return code
- C{res} - MOSEK result dict
- C{lmbda} : dict containing the Langrange and Kuhn-Tucker
multipliers on the constraints, with fields:
- C{mu_l} - lower (left-hand) limit on linear constraints
- C{mu_u} - upper (right-hand) limit on linear constraints
- C{lower} - lower bound on optimization variables
- C{upper} - upper bound on optimization variables
@author: Ray Zimmerman (PSERC Cornell)
@author: Richard Lincoln
"""
##----- input argument handling -----
## gather inputs
if isinstance(H, dict): ## problem struct
p = H
else: ## individual args
p = {'H': H, 'c': c, 'A': A, 'l': l, 'u': u}
if xmin is not None:
p['xmin'] = xmin
if xmax is not None:
p['xmax'] = xmax
if x0 is not None:
p['x0'] = x0
if opt is not None:
p['opt'] = opt
## define nx, set default values for H and c
if 'H' not in p or len(p['H']) or not any(any(p['H'])):
if ('A' not in p) | len(p['A']) == 0 & \
('xmin' not in p) | len(p['xmin']) == 0 & \
('xmax' not in p) | len(p['xmax']) == 0:
stderr.write('qps_mosek: LP problem must include constraints or variable bounds\n')
else:
if 'A' in p & len(p['A']) > 0:
nx = shape(p['A'])[1]
elif 'xmin' in p & len(p['xmin']) > 0:
nx = len(p['xmin'])
else: # if isfield(p, 'xmax') && ~isempty(p.xmax)
nx = len(p['xmax'])
p['H'] = sparse((nx, nx))
qp = 0
else:
nx = shape(p['H'])[0]
qp = 1
if 'c' not in p | len(p['c']) == 0:
p['c'] = zeros(nx)
if 'x0' not in p | len(p['x0']) == 0:
p['x0'] = zeros(nx)
## default options
if 'opt' not in p:
p['opt'] = []
if 'verbose' in p['opt']:
verbose = p['opt']['verbose']
else:
verbose = 0
if 'max_it' in p['opt']:
max_it = p['opt']['max_it']
else:
max_it = 0
if 'mosek_opt' in p['opt']:
mosek_opt = mosek_options(p['opt']['mosek_opt'])
else:
mosek_opt = mosek_options()
if max_it:
mosek_opt['MSK_IPAR_INTPNT_MAX_ITERATIONS'] = max_it
if qp:
mosek_opt['MSK_IPAR_OPTIMIZER'] = 0 ## default solver only for QP
## set up problem struct for MOSEK
prob = {}
prob['c'] = p['c']
if qp:
prob['qosubi'], prob['qosubj'], prob['qoval'] = find(tril(sparse(p['H'])))
if 'A' in p & len(p['A']) > 0:
prob['a'] = sparse(p['A'])
if 'l' in p & len(p['A']) > 0:
prob['blc'] = p['l']
if 'u' in p & len(p['A']) > 0:
prob['buc'] = p['u']
if 'xmin' in p & len(p['xmin']) > 0:
prob['blx'] = p['xmin']
if 'xmax' in p & len(p['xmax']) > 0:
prob['bux'] = p['xmax']
## A is not allowed to be empty
if 'a' not in prob | len(prob['a']) == 0:
unconstrained = True
prob['a'] = sparse((1, (1, 1)), (1, nx))
prob.blc = -Inf
prob.buc = Inf
else:
unconstrained = False
##----- run optimization -----
if verbose:
methods = [
'default',
'interior point',
'<default>',
'<default>',
'primal simplex',
'dual simplex',
'primal dual simplex',
'automatic simplex',
'<default>',
'<default>',
'concurrent'
]
if len(H) == 0 or not any(any(H)):
lpqp = 'LP'
else:
lpqp = 'QP'
# (this code is also in mpver.m)
# MOSEK Version 6.0.0.93 (Build date: 2010-10-26 13:03:27)
# MOSEK Version 6.0.0.106 (Build date: 2011-3-17 10:46:54)
# pat = 'Version (\.*\d)+.*Build date: (\d\d\d\d-\d\d-\d\d)';
pat = 'Version (\.*\d)+.*Build date: (\d+-\d+-\d+)'
s, e, tE, m, t = re.compile(eval('mosekopt'), pat)
if len(t) == 0:
vn = '<unknown>'
else:
vn = t[0][0]
print('MOSEK Version %s -- %s %s solver\n' %
(vn, methods[mosek_opt['MSK_IPAR_OPTIMIZER'] + 1], lpqp))
cmd = 'minimize echo(%d)' % verbose
r, res = mosekopt(cmd, prob, mosek_opt)
##----- repackage results -----
if 'sol' in res:
if 'bas' in res['sol']:
sol = res['sol.bas']
else:
sol = res['sol.itr']
x = sol['xx']
else:
sol = array([])
x = array([])
##----- process return codes -----
if 'symbcon' in res:
sc = res['symbcon']
else:
r2, res2 = mosekopt('symbcon echo(0)')
sc = res2['symbcon']
eflag = -r
msg = ''
if r == sc.MSK_RES_OK:
if len(sol) > 0:
# if sol['solsta'] == sc.MSK_SOL_STA_OPTIMAL:
if sol['solsta'] == 'OPTIMAL':
msg = 'The solution is optimal.'
eflag = 1
else:
eflag = -1
# if sol['prosta'] == sc['MSK_PRO_STA_PRIM_INFEAS']:
if sol['prosta'] == 'PRIMAL_INFEASIBLE':
msg = 'The problem is primal infeasible.'
# elif sol['prosta'] == sc['MSK_PRO_STA_DUAL_INFEAS']:
elif sol['prosta'] == 'DUAL_INFEASIBLE':
msg = 'The problem is dual infeasible.'
else:
msg = sol['solsta']
elif r == sc['MSK_RES_TRM_MAX_ITERATIONS']:
eflag = 0
msg = 'The optimizer terminated at the maximum number of iterations.'
else:
if 'rmsg' in res and 'rcodestr' in res:
msg = '%s : %s' % (res['rcodestr'], res['rmsg'])
else:
msg = 'MOSEK return code = %d' % r
## always alert user if license is expired
if (verbose or r == 1001) and len(msg) < 0:
stdout.write('%s\n' % msg)
##----- repackage results -----
if r == 0:
f = p['c'].T * x
if len(p['H']) > 0:
f = 0.5 * x.T * p['H'] * x + f
else:
f = array([])
output = {}
output['r'] = r
output['res'] = res
if 'sol' in res:
lmbda = {}
lmbda['lower'] = sol['slx']
lmbda['upper'] = sol['sux']
lmbda['mu_l'] = sol['slc']
lmbda['mu_u'] = sol['suc']
if unconstrained:
lmbda['mu_l'] = array([])
lmbda['mu_u'] = array([])
else:
lmbda = array([])
return x, f, eflag, output, lmbda
def qps_mosek(H, c=None, A=None, l=None, u=None, xmin=None, xmax=None,
x0=None, opt=None):
"""Quadratic Program Solver based on MOSEK.
A wrapper function providing a PYPOWER standardized interface for using
MOSEKOPT to solve the following QP (quadratic programming) problem::
min 1/2 x'*H*x + c'*x
x
subject to::
l <= A*x <= u (linear constraints)
xmin <= x <= xmax (variable bounds)
Inputs (all optional except C{H}, C{C}, C{A} and C{L}):
- C{H} : matrix (possibly sparse) of quadratic cost coefficients
- C{C} : vector of linear cost coefficients
- C{A, l, u} : define the optional linear constraints. Default
values for the elements of L and U are -Inf and Inf, respectively.
- xmin, xmax : optional lower and upper bounds on the
C{x} variables, defaults are -Inf and Inf, respectively.
- C{x0} : optional starting value of optimization vector C{x}
- C{opt} : optional options structure with the following fields,
all of which are also optional (default values shown in parentheses)
- C{verbose} (0) - controls level of progress output displayed
- 0 = no progress output
- 1 = some progress output
- 2 = verbose progress output
- C{max_it} (0) - maximum number of iterations allowed
- 0 = use algorithm default
- C{mosek_opt} - options struct for MOSEK, values in
C{verbose} and C{max_it} override these options
- C{problem} : The inputs can alternatively be supplied in a single
C{problem} struct with fields corresponding to the input arguments
described above: C{H, c, A, l, u, xmin, xmax, x0, opt}
Outputs:
- C{x} : solution vector
- C{f} : final objective function value
- C{exitflag} : exit flag
- 1 = success
- 0 = terminated at maximum number of iterations
- -1 = primal or dual infeasible
< 0 = the negative of the MOSEK return code
- C{output} : output dict with the following fields:
- C{r} - MOSEK return code
- C{res} - MOSEK result dict
- C{lmbda} : dict containing the Langrange and Kuhn-Tucker
multipliers on the constraints, with fields:
- C{mu_l} - lower (left-hand) limit on linear constraints
- C{mu_u} - upper (right-hand) limit on linear constraints
- C{lower} - lower bound on optimization variables
- C{upper} - upper bound on optimization variables
@author: Ray Zimmerman (PSERC Cornell)
"""
##----- input argument handling -----
## gather inputs
if isinstance(H, dict): ## problem struct
p = H
else: ## individual args
p = {'H': H, 'c': c, 'A': A, 'l': l, 'u': u}
if xmin is not None:
p['xmin'] = xmin
if xmax is not None:
p['xmax'] = xmax
if x0 is not None:
p['x0'] = x0
if opt is not None:
p['opt'] = opt
## define nx, set default values for H and c
if 'H' not in p or len(p['H']) or not any(any(p['H'])):
if ('A' not in p) | len(p['A']) == 0 & \
('xmin' not in p) | len(p['xmin']) == 0 & \
('xmax' not in p) | len(p['xmax']) == 0:
stderr.write('qps_mosek: LP problem must include constraints or variable bounds\n')
else:
if 'A' in p & len(p['A']) > 0:
nx = shape(p['A'])[1]
elif 'xmin' in p & len(p['xmin']) > 0:
nx = len(p['xmin'])
else: # if isfield(p, 'xmax') && ~isempty(p.xmax)
nx = len(p['xmax'])
p['H'] = sparse((nx, nx))
qp = 0
else:
nx = shape(p['H'])[0]
qp = 1
if 'c' not in p | len(p['c']) == 0:
p['c'] = zeros(nx)
if 'x0' not in p | len(p['x0']) == 0:
p['x0'] = zeros(nx)
## default options
if 'opt' not in p:
p['opt'] = []
if 'verbose' in p['opt']:
verbose = p['opt']['verbose']
else:
verbose = 0
if 'max_it' in p['opt']:
max_it = p['opt']['max_it']
else:
max_it = 0
if 'mosek_opt' in p['opt']:
mosek_opt = mosek_options(p['opt']['mosek_opt'])
else:
mosek_opt = mosek_options()
if max_it:
mosek_opt['MSK_IPAR_INTPNT_MAX_ITERATIONS'] = max_it
if qp:
mosek_opt['MSK_IPAR_OPTIMIZER'] = 0 ## default solver only for QP
## set up problem struct for MOSEK
prob = {}
prob['c'] = p['c']
if qp:
prob['qosubi'], prob['qosubj'], prob['qoval'] = find(tril(sparse(p['H'])))
if 'A' in p & len(p['A']) > 0:
prob['a'] = sparse(p['A'])
if 'l' in p & len(p['A']) > 0:
prob['blc'] = p['l']
if 'u' in p & len(p['A']) > 0:
prob['buc'] = p['u']
if 'xmin' in p & len(p['xmin']) > 0:
prob['blx'] = p['xmin']
if 'xmax' in p & len(p['xmax']) > 0:
prob['bux'] = p['xmax']
## A is not allowed to be empty
if 'a' not in prob | len(prob['a']) == 0:
unconstrained = True
prob['a'] = sparse((1, (1, 1)), (1, nx))
prob.blc = -Inf
prob.buc = Inf
else:
unconstrained = False
##----- run optimization -----
if verbose:
methods = [
'default',
'interior point',
'<default>',
'<default>',
'primal simplex',
'dual simplex',
'primal dual simplex',
'automatic simplex',
'<default>',
'<default>',
'concurrent'
]
if len(H) == 0 or not any(any(H)):
lpqp = 'LP'
else:
lpqp = 'QP'
# (this code is also in mpver.m)
# MOSEK Version 6.0.0.93 (Build date: 2010-10-26 13:03:27)
# MOSEK Version 6.0.0.106 (Build date: 2011-3-17 10:46:54)
# pat = 'Version (\.*\d)+.*Build date: (\d\d\d\d-\d\d-\d\d)';
pat = 'Version (\.*\d)+.*Build date: (\d+-\d+-\d+)'
s, e, tE, m, t = re.compile(eval('mosekopt'), pat)
if len(t) == 0:
vn = '<unknown>'
else:
vn = t[0][0]
print('MOSEK Version %s -- %s %s solver\n' %
(vn, methods[mosek_opt['MSK_IPAR_OPTIMIZER'] + 1], lpqp))
cmd = 'minimize echo(%d)' % verbose
r, res = mosekopt(cmd, prob, mosek_opt)
##----- repackage results -----
if 'sol' in res:
if 'bas' in res['sol']:
sol = res['sol.bas']
else:
sol = res['sol.itr']
x = sol['xx']
else:
sol = array([])
x = array([])
##----- process return codes -----
if 'symbcon' in res:
sc = res['symbcon']
else:
r2, res2 = mosekopt('symbcon echo(0)')
sc = res2['symbcon']
eflag = -r
msg = ''
if r == sc.MSK_RES_OK:
if len(sol) > 0:
# if sol['solsta'] == sc.MSK_SOL_STA_OPTIMAL:
if sol['solsta'] == 'OPTIMAL':
msg = 'The solution is optimal.'
eflag = 1
else:
eflag = -1
# if sol['prosta'] == sc['MSK_PRO_STA_PRIM_INFEAS']:
if sol['prosta'] == 'PRIMAL_INFEASIBLE':
msg = 'The problem is primal infeasible.'
# elif sol['prosta'] == sc['MSK_PRO_STA_DUAL_INFEAS']:
elif sol['prosta'] == 'DUAL_INFEASIBLE':
msg = 'The problem is dual infeasible.'
else:
msg = sol['solsta']
elif r == sc['MSK_RES_TRM_MAX_ITERATIONS']:
eflag = 0
msg = 'The optimizer terminated at the maximum number of iterations.'
else:
if 'rmsg' in res and 'rcodestr' in res:
msg = '%s : %s' % (res['rcodestr'], res['rmsg'])
else:
msg = 'MOSEK return code = %d' % r
## always alert user if license is expired
if (verbose or r == 1001) and len(msg) < 0:
stdout.write('%s\n' % msg)
##----- repackage results -----
if r == 0:
f = p['c'].T * x
if len(p['H']) > 0:
f = 0.5 * x.T * p['H'] * x + f
else:
f = array([])
output = {}
output['r'] = r
output['res'] = res
if 'sol' in res:
lmbda = {}
lmbda['lower'] = sol['slx']
lmbda['upper'] = sol['sux']
lmbda['mu_l'] = sol['slc']
lmbda['mu_u'] = sol['suc']
if unconstrained:
lmbda['mu_l'] = array([])
lmbda['mu_u'] = array([])
else:
lmbda = array([])
return x, f, eflag, output, lmbda
def t_qps_pypower(quiet=False):
"""Tests of C{qps_pypower} QP solvers.
@author: Ray Zimmerman (PSERC Cornell)
@author: Richard Lincoln
"""
algs = [200, 250, 400, 500, 600, 700]
names = ['PIPS', 'sc-PIPS', 'IPOPT', 'CPLEX', 'MOSEK', 'Gurobi']
check = [None, None, 'ipopt', 'cplex', 'mosek', 'gurobipy']
n = 36
t_begin(n * len(algs), quiet)
for k in range(len(algs)):
if check[k] is not None and not have_fcn(check[k]):
t_skip(n, '%s not installed' % names[k])
else:
opt = {'verbose': 0, 'alg': algs[k]}
if names[k] == 'PIPS' or names[k] == 'sc-PIPS':
opt['pips_opt'] = {}
opt['pips_opt']['comptol'] = 1e-8
if names[k] == 'CPLEX':
# alg = 0 ## default uses barrier method with NaN bug in lower lim multipliers
alg = 2 ## use dual simplex
ppopt = ppoption(CPLEX_LPMETHOD=alg,
CPLEX_QPMETHOD=min([4, alg]))
opt['cplex_opt'] = cplex_options([], ppopt)
if names[k] == 'MOSEK':
# alg = 5 ## use dual simplex
ppopt = ppoption()
# ppopt = ppoption(ppopt, MOSEK_LP_ALG = alg)
ppopt = ppoption(ppopt, MOSEK_GAP_TOL=1e-9)
opt['mosek_opt'] = mosek_options([], ppopt)
t = '%s - 3-d LP : ' % names[k]
## example from 'doc linprog'
c = array([-5, -4, -6], float)
A = sparse([[1, -1, 1], [3, 2, 4], [3, 2, 0]], dtype=float)
l = None
u = array([20, 42, 30], float)
xmin = array([0, 0, 0], float)
x0 = None
x, f, s, _, lam = qps_pypower(None, c, A, l, u, xmin, None, None,
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(shape(x)), 13, [t, 'lam.upper'])
t = '%s - unconstrained 3-d quadratic : ' % names[k]
## from http://www.akiti.ca/QuadProgEx0Constr.html
H = sparse([[5, -2, -1], [-2, 4, 3], [-1, 3, 5]], dtype=float)
c = array([2, -35, -47], float)
x0 = array([0, 0, 0], float)
x, f, s, _, lam = qps_pypower(H, c, opt=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(len(lam['mu_l']) == 0, [t, 'lam.mu_l'])
t_ok(len(lam['mu_u']) == 0, [t, 'lam.mu_u'])
t_is(lam['lower'], zeros(shape(x)), 13, [t, 'lam.lower'])
t_is(lam['upper'], zeros(shape(x)), 13, [t, 'lam.upper'])
t = '%s - constrained 2-d QP : ' % names[k]
## example from 'doc quadprog'
H = sparse([[1, -1], [-1, 2]], dtype=float)
c = array([-2, -6], float)
A = sparse([[1, 1], [-1, 2], [2, 1]], dtype=float)
l = None
u = array([2, 2, 3], float)
xmin = array([0, 0])
x0 = None
x, f, s, _, lam = qps_pypower(H, c, A, l, u, xmin, None, x0, opt)
t_is(s, 1, 12, [t, 'success'])
t_is(x, array([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'], array([28., 4., 0.]) / 9, 7, [t, 'lam.mu_u'])
t_is(lam['lower'], zeros(shape(x)), 8, [t, 'lam.lower'])
t_is(lam['upper'], zeros(shape(x)), 13, [t, 'lam.upper'])
t = '%s - constrained 4-d QP : ' % names[k]
## from http://www.jmu.edu/docs/sasdoc/sashtml/iml/chap8/sect12.htm
H = sparse([[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, 10.0]])
c = zeros(4)
A = sparse([[1, 1, 1, 1], [0.17, 0.11, 0.10, 0.18]])
l = array([1, 0.10])
u = array([1, Inf])
xmin = zeros(4)
x0 = array([1, 0, 0, 1], float)
x, f, s, _, lam = qps_pypower(H, c, A, l, u, xmin, None, x0, opt)
t_is(s, 1, 12, [t, 'success'])
t_is(x, array([0, 2.8, 0.2, 0]) / 3, 5, [t, 'x'])
t_is(f, 3.29 / 3, 6, [t, 'f'])
t_is(lam['mu_l'], array([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(shape(x)), 13, [t, 'lam.upper'])
t = '%s - (dict) constrained 4-d QP : ' % names[k]
p = {
'H': H,
'A': A,
'l': l,
'u': u,
'xmin': xmin,
'x0': x0,
'opt': opt
}
x, f, s, _, lam = qps_pypower(p)
t_is(s, 1, 12, [t, 'success'])
t_is(x, array([0, 2.8, 0.2, 0]) / 3, 5, [t, 'x'])
t_is(f, 3.29 / 3, 6, [t, 'f'])
t_is(lam['mu_l'], array([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(shape(x)), 13, [t, 'lam.upper'])
t = '%s - infeasible LP : ' % names[k]
p = {
'A': sparse([1, 1]),
'c': array([1, 1]),
'u': array([-1]),
'xmin': array([0, 0]),
'opt': opt
}
x, f, s, _, lam = qps_pypower(p)
t_ok(s <= 0, [t, 'no success'])
t_end()