def _conv(a):
if a is None: return None
# test depth:
v = a
d = 0
try:
while not isinstance(v,basestring):
v = v[0]
d += 1
except:
pass
if d != ndim:
raise ValueError("Expected array of %d dimensions, got %d" % (ndim,d))
if t is arg_id:
return array.array(a)
else:
return array.array(a,t)
def readeo(eofile):
"""
Read a .eo file and extract data.
The fileformat is:
--
numcon
numvar
numter
tercof[1]
...
tercof[numter]
consub[1]
...
consub[numter]
subb[1] subj[1] cof[1]
...
"""
f = open(eofile,'rb')
fiter = iter(f)
numcon = int(fiter.next())
numvar = int(fiter.next())
numter = int(fiter.next())
termcof = array([ float(fiter.next()) for i in range(numter) ])
subi = array([ int(fiter.next()) for i in range(numter) ])
terms = [ ([],[]) for i in range(numter) ]
subk,subj,cof = [],[],[]
for l in fiter:
if (l.strip()):
_k,_j,_c = re.split(r'[ \t]+', l)
subk.append(int(_k))
subj.append(int(_j))
cof.append(float(_c))
f.close()
subk = array(subk)
subj = array(subj)
cof = array(cof)
return numcon,numvar,termcof,subi,subk,subj,cof
def _conv(a):
if a is None: return None
# test depth:
v = a
d = 0
try:
while not isinstance(v,basestring):
v = v[0]
d += 1
except:
pass
if d != ndim:
raise ValueError("Expected array of %d dimensions, got %d" % (ndim,d))
if t is arg_id:
return array.array(a)
else:
return array.array(a,t)
def readeo(eofile):
"""
Read a .eo file and extract data.
The fileformat is:
--
numcon
numvar
numter
tercof[1]
...
tercof[numter]
consub[1]
...
consub[numter]
subb[1] subj[1] cof[1]
...
"""
f = open(eofile, 'rb')
fiter = iter(f)
numcon = int(fiter.next())
numvar = int(fiter.next())
numter = int(fiter.next())
termcof = array([float(fiter.next()) for i in range(numter)])
subi = array([int(fiter.next()) for i in range(numter)])
terms = [([], []) for i in range(numter)]
subk, subj, cof = [], [], []
for l in fiter:
if (l.strip()):
_k, _j, _c = re.split(r'[ \t]+', l)
subk.append(int(_k))
subj.append(int(_j))
cof.append(float(_c))
f.close()
subk = array(subk)
subj = array(subj)
cof = array(cof)
return numcon, numvar, termcof, subi, subk, subj, cof
def __init__(self,name,
foods,
nutrients,
daily_allowance,
nutritive_value):
Model.__init__(self,name)
finished = False
try:
self.foods = [ str(f) for f in foods ]
self.nutrients = [ str(n) for n in nutrients ]
self.dailyAllowance = array.array(daily_allowance, float)
self.nutrientValue = DenseMatrix(nutritive_value).transpose()
M = len(self.foods)
N = len(self.nutrients)
if len(self.dailyAllowance) != N:
raise ValueError("Length of daily_allowance does not match "
"the number of nutrients")
if self.nutrientValue.numColumns() != M:
raise ValueError("Number of rows in nutrient_value does not "
"match the number of foods")
if self.nutrientValue.numRows() != N:
raise ValueError("Number of columns in nutrient_value does "
"not match the number of nutrients")
self.__dailyPurchase = self.variable('Daily Purchase',
StringSet(self.foods),
Domain.greaterThan(0.0))
self.__dailyNutrients = \
self.constraint('Nutrient Balance',
StringSet(nutrients),
Expr.mul(self.nutrientValue,self.__dailyPurchase),
Domain.greaterThan(self.dailyAllowance))
self.objective(ObjectiveSense.Minimize, Expr.sum(self.__dailyPurchase))
finished = True
finally:
if not finished:
self.__del__()
def __init__(self, name, foods, nutrients, daily_allowance,
nutritive_value):
Model.__init__(self, name)
finished = False
try:
self.foods = [str(f) for f in foods]
self.nutrients = [str(n) for n in nutrients]
self.dailyAllowance = array.array(daily_allowance, float)
self.nutrientValue = DenseMatrix(nutritive_value).transpose()
M = len(self.foods)
N = len(self.nutrients)
if len(self.dailyAllowance) != N:
raise ValueError("Length of daily_allowance does not match "
"the number of nutrients")
if self.nutrientValue.numColumns() != M:
raise ValueError("Number of rows in nutrient_value does not "
"match the number of foods")
if self.nutrientValue.numRows() != N:
raise ValueError("Number of columns in nutrient_value does "
"not match the number of nutrients")
self.__dailyPurchase = self.variable('Daily Purchase',
StringSet(self.foods),
Domain.greaterThan(0.0))
self.__dailyNutrients = \
self.constraint('Nutrient Balance',
StringSet(nutrients),
Expr.mul(self.nutrientValue,self.__dailyPurchase),
Domain.greaterThan(self.dailyAllowance))
self.objective(ObjectiveSense.Minimize,
Expr.sum(self.__dailyPurchase))
finished = True
finally:
if not finished:
self.__del__()
def _vectorneg__3F(v): return array.array([ -i for i in v ])
def _vectorsub__3F_3F (v1,v2): return array.array([ v1[i]-v2[i] for i in xrange(len(v1)) ])
def ilp(c, G, h, A=None, b=None, I=None):
"""
Solves the mixed integer LP
minimize c'*x
subject to G*x + s = h
A*x = b
s >= 0
xi integer, forall i in I
using MOSEK 7.0.
solsta, x = ilp(c, G, h, A=None, b=None, I=None).
Input arguments
G is m x n, h is m x 1, A is p x n, b is p x 1. G and A must be
dense or sparse 'd' matrices. h and b are dense 'd' matrices
with one column. The default values for A and b are empty
matrices with zero rows.
I is a Python set with indices of integer elements of x. By
default all elements in x are constrained to be integer, i.e.,
the default value of I is I = set(range(n))
Dual variables are not returned for MOSEK.
Return values
solsta is a MOSEK solution status key.
If solsta is mosek.solsta.integer_optimal, then x contains
the solution.
If solsta is mosek.solsta.unknown, then x is None.
Other return values for solsta include:
mosek.solsta.near_integer_optimal
in which case the x value may not be well-defined,
c.f., section 17.48 of the MOSEK Python API manual.
x is the solution
Options are passed to MOSEK solvers via the msk.options dictionary,
e.g., the following turns off output from the MOSEK solvers
>>> msk.options = {mosek.iparam.log: 0}
see chapter 15 of the MOSEK Python API manual.
"""
if type(c) is not matrix or c.typecode != 'd' or c.size[1] != 1:
raise TypeError("'c' must be a dense column matrix")
n = c.size[0]
if n < 1: raise ValueError("number of variables must be at least 1")
if (type(G) is not matrix and type(G) is not spmatrix) or \
G.typecode != 'd' or G.size[1] != n:
raise TypeError("'G' must be a dense or sparse 'd' matrix "\
"with %d columns" %n)
m = G.size[0]
if m is 0: raise ValueError("m cannot be 0")
if type(h) is not matrix or h.typecode != 'd' or h.size != (m,1):
raise TypeError("'h' must be a 'd' matrix of size (%d,1)" %m)
if A is None: A = spmatrix([], [], [], (0,n), 'd')
if (type(A) is not matrix and type(A) is not spmatrix) or \
A.typecode != 'd' or A.size[1] != n:
raise TypeError("'A' must be a dense or sparse 'd' matrix "\
"with %d columns" %n)
p = A.size[0]
if b is None: b = matrix(0.0, (0,1))
if type(b) is not matrix or b.typecode != 'd' or b.size != (p,1):
raise TypeError("'b' must be a dense matrix of size (%d,1)" %p)
c = array(c)
if I is None: I = set(range(n))
if type(I) is not set:
raise TypeError("invalid argument for integer index set")
for i in I:
if type(i) is not int:
raise TypeError("invalid integer index set I")
if len(I) > 0 and min(I) < 0: raise IndexError(
"negative element in integer index set I")
if len(I) > 0 and max(I) > n-1: raise IndexError(
"maximum element in in integer index set I is larger than n-1")
bkc = m*[ mosek.boundkey.up ] + p*[ mosek.boundkey.fx ]
blc = m*[ -inf ] + [ bi for bi in b ]
buc = matrix([h, b])
bkx = n*[mosek.boundkey.fr]
blx = n*[ -inf ]
bux = n*[ +inf ]
colptr, asub, acof = sparse([G,A]).CCS
aptrb, aptre = colptr[:-1], colptr[1:]
task = env.Task(0,0)
task.set_Stream (mosek.streamtype.log, streamprinter)
# set MOSEK options
for (param, val) in options.items():
if str(param)[:6] == "iparam":
task.putintparam(param, val)
elif str(param)[:6] == "dparam":
task.putdouparam(param, val)
elif str(param)[:6] == "sparam":
task.putstrparam(param, val)
else:
raise ValueError("invalid MOSEK parameter: "+str(param))
task.inputdata (m+p, # number of constraints
n, # number of variables
array(c), # linear objective coefficients
0.0, # objective fixed value
array(aptrb),
array(aptre),
array(asub),
array(acof),
bkc,
blc,
buc,
bkx,
blx,
bux)
task.putobjsense(mosek.objsense.minimize)
# Define integer variables
if len(I) > 0:
task.putvartypelist(list(I), len(I)*[ mosek.variabletype.type_int ])
task.putintparam (mosek.iparam.mio_mode, mosek.miomode.satisfied)
task.optimize()
task.solutionsummary (mosek.streamtype.msg);
if len(I) > 0:
solsta = task.getsolsta(mosek.soltype.itg)
else:
solsta = task.getsolsta(mosek.soltype.bas)
x = zeros(n, float)
if len(I) > 0:
task.getsolutionslice(mosek.soltype.itg, mosek.solitem.xx, 0, n, x)
else:
task.getsolutionslice(mosek.soltype.bas, mosek.solitem.xx, 0, n, x)
x = matrix(x)
if (solsta is mosek.solsta.unknown):
return (solsta, None)
else:
return (solsta, x)
def qp(P, q, G=None, h=None, A=None, b=None):
"""
Solves a quadratic program
minimize (1/2)*x'*P*x + q'*x
subject to G*x <= h
A*x = b.
using MOSEK 7.0.
solsta, x, z, y = qp(P, q, G=None, h=None, A=None, b=None)
Return values
solsta is a MOSEK solution status key.
If solsta is mosek.solsta.optimal,
then (x, y, z) contains the primal-dual solution.
If solsta is mosek.solsta.prim_infeas_cer,
then (x, y, z) is a certificate of primal infeasibility.
If solsta is mosek.solsta.dual_infeas_cer,
then (x, y, z) is a certificate of dual infeasibility.
If solsta is mosek.solsta.unknown, then (x, y, z) are all None.
Other return values for solsta include:
mosek.solsta.dual_feas
mosek.solsta.near_dual_feas
mosek.solsta.near_optimal
mosek.solsta.near_prim_and_dual_feas
mosek.solsta.near_prim_feas
mosek.solsta.prim_and_dual_feas
mosek.solsta.prim_feas
in which case the (x,y,z) value may not be well-defined,
c.f., section 17.48 of the MOSEK Python API manual.
x, z, y the primal-dual solution.
Options are passed to MOSEK solvers via the msk.options dictionary,
e.g., the following turns off output from the MOSEK solvers
>>> msk.options = {mosek.iparam.log: 0}
see chapter 15 of the MOSEK Python API manual.
"""
if (type(P) is not matrix and type(P) is not spmatrix) or \
P.typecode != 'd' or P.size[0] != P.size[1]:
raise TypeError("'P' must be a square dense or sparse 'd' matrix ")
n = P.size[0]
if n < 1: raise ValueError("number of variables must be at least 1")
if type(q) is not matrix or q.typecode != 'd' or q.size != (n,1):
raise TypeError("'q' must be a 'd' matrix of size (%d,1)" %n)
if G is None: G = spmatrix([], [], [], (0,n), 'd')
if (type(G) is not matrix and type(G) is not spmatrix) or \
G.typecode != 'd' or G.size[1] != n:
raise TypeError("'G' must be a dense or sparse 'd' matrix "\
"with %d columns" %n)
m = G.size[0]
if h is None: h = matrix(0.0, (0,1))
if type(h) is not matrix or h.typecode != 'd' or h.size != (m,1):
raise TypeError("'h' must be a 'd' matrix of size (%d,1)" %m)
if A is None: A = spmatrix([], [], [], (0,n), 'd')
if (type(A) is not matrix and type(A) is not spmatrix) or \
A.typecode != 'd' or A.size[1] != n:
raise TypeError("'A' must be a dense or sparse 'd' matrix "\
"with %d columns" %n)
p = A.size[0]
if b is None: b = matrix(0.0, (0,1))
if type(b) is not matrix or b.typecode != 'd' or b.size != (p,1):
raise TypeError("'b' must be a dense matrix of size (%d,1)" %p)
if m+p is 0: raise ValueError("m + p must be greater than 0")
c = array(q)
bkc = m*[ mosek.boundkey.up ] + p*[ mosek.boundkey.fx ]
blc = m*[ -inf ] + [ bi for bi in b ]
buc = matrix([h, b])
bkx = n*[mosek.boundkey.fr]
blx = n*[ -inf ]
bux = n*[ +inf ]
colptr, asub, acof = sparse([G,A]).CCS
aptrb, aptre = colptr[:-1], colptr[1:]
task = env.Task(0,0)
task.set_Stream (mosek.streamtype.log, streamprinter)
# set MOSEK options
for (param, val) in options.items():
if str(param)[:6] == "iparam":
task.putintparam(param, val)
elif str(param)[:6] == "dparam":
task.putdouparam(param, val)
elif str(param)[:6] == "sparam":
task.putstrparam(param, val)
else:
raise ValueError("invalid MOSEK parameter: "+str(param))
task.inputdata (m+p, # number of constraints
n, # number of variables
array(c), # linear objective coefficients
0.0, # objective fixed value
array(aptrb),
array(aptre),
array(asub),
array(acof),
bkc,
blc,
buc,
bkx,
blx,
bux)
Ps = sparse(P)
I, J = Ps.I, Ps.J
tril = [ k for k in range(len(I)) if I[k] >= J[k] ]
task.putqobj(array(I[tril]), array(J[tril]), array(Ps.V[tril]))
task.putobjsense(mosek.objsense.minimize)
task.optimize()
task.solutionsummary (mosek.streamtype.msg);
solsta = task.getsolsta(mosek.soltype.itr)
x = zeros(n, float)
task.getsolutionslice(mosek.soltype.itr, mosek.solitem.xx, 0, n, x)
x = matrix(x)
if m is not 0:
z = zeros(m, float)
task.getsolutionslice(mosek.soltype.itr, mosek.solitem.suc, 0, m,
z)
z = matrix(z)
else:
z = matrix(0.0, (0,1))
if p is not 0:
yu, yl = zeros(p, float), zeros(p, float)
task.getsolutionslice(mosek.soltype.itr, mosek.solitem.suc, m, m+p,
yu)
task.getsolutionslice(mosek.soltype.itr, mosek.solitem.slc, m, m+p,
yl)
y = matrix(yu) - matrix(yl)
else:
y = matrix(0.0, (0,1))
if (solsta is mosek.solsta.unknown):
return (solsta, None, None, None)
else:
return (solsta, x, z, y)
def conelp(c, G, h, dims=None):
"""
Solves a pair of primal and dual SOCPs
minimize c'*x
subject to G*x + s = h
s >= 0
maximize -h'*z
subject to G'*z + c = 0
z >= 0
using MOSEK 7.0.
The inequalities are with respect to a cone C defined as the Cartesian
product of N + 1 cones:
C = C_0 x C_1 x .... x C_N x C_{N+1}.
The first cone C_0 is the nonnegative orthant of dimension ml.
The other cones are second order cones of dimension mq[0], ...,
mq[N-1]. The second order cone of dimension m is defined as
{ (u0, u1) in R x R^{m-1} | u0 >= ||u1||_2 }.
The formats of G and h are identical to that used in solvers.conelp(),
except that only componentwise and second order cone inequalities are
(dims['s'] must be zero, if defined).
Input arguments.
c is a dense 'd' matrix of size (n,1).
dims is a dictionary with the dimensions of the components of C.
It has three fields.
- dims['l'] = ml, the dimension of the nonnegative orthant C_0.
(ml >= 0.)
- dims['q'] = mq = [ mq[0], mq[1], ..., mq[N-1] ], a list of N
integers with the dimensions of the second order cones C_1, ...,
C_N. (N >= 0 and mq[k] >= 1.)
The default value of dims is {'l': G.size[0], 'q': []}.
G is a dense or sparse 'd' matrix of size (K,n), where
K = ml + mq[0] + ... + mq[N-1].
Each column of G describes a vector
v = ( v_0, v_1, ..., v_N, vec(v_{N+1}) )
in V = R^ml x R^mq[0] x ... x R^mq[N-1] stored as a column vector.
h is a dense 'd' matrix of size (K,1), representing a vector in V,
in the same format as the columns of G.
Return values
solsta is a MOSEK solution status key.
If solsta is mosek.solsta.optimal,
then (x, zl, zq) contains the primal-dual solution.
If solsta is moseksolsta.prim_infeas_cer,
then (x, zl, zq) is a certificate of dual infeasibility.
If solsta is moseksolsta.dual_infeas_cer,
then (x, zl, zq) is a certificate of primal infeasibility.
If solsta is mosek.solsta.unknown,
then (x, zl, zq) are all None
Other return values for solsta include:
mosek.solsta.dual_feas
mosek.solsta.near_dual_feas
mosek.solsta.near_optimal
mosek.solsta.near_prim_and_dual_feas
mosek.solsta.near_prim_feas
mosek.solsta.prim_and_dual_feas
mosek.solsta.prim_feas
in which case the (x,y,z) value may not be well-defined,
c.f., section 17.48 of the MOSEK Python API manual.
x, z the primal-dual solution.
Options are passed to MOSEK solvers via the msk.options dictionary,
e.g., the following turns off output from the MOSEK solvers
>>> msk.options = {mosek.iparam.log:0}
see chapter 15 of the MOSEK Python API manual.
"""
if dims is None:
(solsta, x, y, z) = lp(c, G, h)
return (solsta, x, z, None)
try:
if len(dims['s']) > 0: raise ValueError("dims['s'] must be zero")
except:
pass
N, n = G.size
ml, mq = dims['l'], dims['q']
cdim = ml + sum(mq)
if cdim is 0: raise ValueError("ml+mq cannot be 0")
# Data for kth 'q' constraint are found in rows indq[k]:indq[k+1] of G.
indq = [dims['l']]
for k in dims['q']:
indq = indq + [indq[-1] + k]
if type(h) is not matrix or h.typecode != 'd' or h.size[1] != 1:
raise TypeError("'h' must be a 'd' matrix with 1 column")
if type(G) is matrix or type(G) is spmatrix:
if G.typecode != 'd' or G.size[0] != cdim:
raise TypeError("'G' must be a 'd' matrix with %d rows " % cdim)
if h.size[0] != cdim:
raise TypeError("'h' must have %d rows" % cdim)
else:
raise TypeError("'G' must be a matrix")
if min(dims['q']) < 1:
raise TypeError("dimensions of quadratic cones must be positive")
bkc = n * [mosek.boundkey.fx]
blc = array(-c)
buc = array(-c)
bkx = ml * [mosek.boundkey.lo] + sum(mq) * [mosek.boundkey.fr]
blx = ml * [0.0] + sum(mq) * [-inf]
bux = N * [+inf]
c = array(-h)
colptr, asub, acof = sparse([G.T]).CCS
aptrb, aptre = colptr[:-1], colptr[1:]
task = env.Task(0, 0)
task.set_Stream(mosek.streamtype.log, streamprinter)
# set MOSEK options
for (param, val) in options.items():
if str(param)[:6] == "iparam":
task.putintparam(param, val)
elif str(param)[:6] == "dparam":
task.putdouparam(param, val)
elif str(param)[:6] == "sparam":
task.putstrparam(param, val)
else:
raise ValueError("invalid MOSEK parameter: " + str(param))
task.inputdata(
n, # number of constraints
N, # number of variables
c, # linear objective coefficients
0.0, # objective fixed value
array(aptrb),
array(aptre),
array(asub),
array(acof),
bkc,
blc,
buc,
bkx,
blx,
bux)
task.putobjsense(mosek.objsense.maximize)
for k in range(len(mq)):
task.appendcone(mosek.conetype.quad, 0.0,
array(range(ml + sum(mq[:k]), ml + sum(mq[:k + 1]))))
task.optimize()
task.solutionsummary(mosek.streamtype.msg)
solsta = task.getsolsta(mosek.soltype.itr)
xu, xl, zq = zeros(n, float), zeros(n, float), zeros(sum(mq), float)
task.getsolutionslice(mosek.soltype.itr, mosek.solitem.slc, 0, n, xl)
task.getsolutionslice(mosek.soltype.itr, mosek.solitem.suc, 0, n, xu)
task.getsolutionslice(mosek.soltype.itr, mosek.solitem.xx, ml, N, zq)
x = matrix(xu - xl)
zq = matrix(zq)
if ml:
zl = zeros(ml, float)
task.getsolutionslice(mosek.soltype.itr, mosek.solitem.xx, 0, ml, zl)
zl = matrix(zl)
else:
zl = matrix(0.0, (0, 1))
if (solsta is mosek.solsta.unknown):
return (solsta, None, None)
else:
return (solsta, x, matrix([zl, zq]))
def _vectorneg__3F(v): return array.array([ -i for i in v ])
def conelp(c, G, h, dims = None):
"""
Solves a pair of primal and dual SOCPs
minimize c'*x
subject to G*x + s = h
s >= 0
maximize -h'*z
subject to G'*z + c = 0
z >= 0
using MOSEK 7.0.
The inequalities are with respect to a cone C defined as the Cartesian
product of N + 1 cones:
C = C_0 x C_1 x .... x C_N x C_{N+1}.
The first cone C_0 is the nonnegative orthant of dimension ml.
The other cones are second order cones of dimension mq[0], ...,
mq[N-1]. The second order cone of dimension m is defined as
{ (u0, u1) in R x R^{m-1} | u0 >= ||u1||_2 }.
The formats of G and h are identical to that used in solvers.conelp(),
except that only componentwise and second order cone inequalities are
(dims['s'] must be zero, if defined).
Input arguments.
c is a dense 'd' matrix of size (n,1).
dims is a dictionary with the dimensions of the components of C.
It has three fields.
- dims['l'] = ml, the dimension of the nonnegative orthant C_0.
(ml >= 0.)
- dims['q'] = mq = [ mq[0], mq[1], ..., mq[N-1] ], a list of N
integers with the dimensions of the second order cones C_1, ...,
C_N. (N >= 0 and mq[k] >= 1.)
The default value of dims is {'l': G.size[0], 'q': []}.
G is a dense or sparse 'd' matrix of size (K,n), where
K = ml + mq[0] + ... + mq[N-1].
Each column of G describes a vector
v = ( v_0, v_1, ..., v_N, vec(v_{N+1}) )
in V = R^ml x R^mq[0] x ... x R^mq[N-1] stored as a column vector.
h is a dense 'd' matrix of size (K,1), representing a vector in V,
in the same format as the columns of G.
Return values
solsta is a MOSEK solution status key.
If solsta is mosek.solsta.optimal,
then (x, zl, zq) contains the primal-dual solution.
If solsta is moseksolsta.prim_infeas_cer,
then (x, zl, zq) is a certificate of dual infeasibility.
If solsta is moseksolsta.dual_infeas_cer,
then (x, zl, zq) is a certificate of primal infeasibility.
If solsta is mosek.solsta.unknown,
then (x, zl, zq) are all None
Other return values for solsta include:
mosek.solsta.dual_feas
mosek.solsta.near_dual_feas
mosek.solsta.near_optimal
mosek.solsta.near_prim_and_dual_feas
mosek.solsta.near_prim_feas
mosek.solsta.prim_and_dual_feas
mosek.solsta.prim_feas
in which case the (x,y,z) value may not be well-defined,
c.f., section 17.48 of the MOSEK Python API manual.
x, z the primal-dual solution.
Options are passed to MOSEK solvers via the msk.options dictionary,
e.g., the following turns off output from the MOSEK solvers
>>> msk.options = {mosek.iparam.log:0}
see chapter 15 of the MOSEK Python API manual.
"""
if dims is None:
(solsta, x, y, z) = lp(c, G, h)
return (solsta, x, z, None)
try:
if len(dims['s']) > 0: raise ValueError("dims['s'] must be zero")
except:
pass
N, n = G.size
ml, mq = dims['l'], dims['q']
cdim = ml + sum(mq)
if cdim is 0: raise ValueError("ml+mq cannot be 0")
# Data for kth 'q' constraint are found in rows indq[k]:indq[k+1] of G.
indq = [ dims['l'] ]
for k in dims['q']: indq = indq + [ indq[-1] + k ]
if type(h) is not matrix or h.typecode != 'd' or h.size[1] != 1:
raise TypeError("'h' must be a 'd' matrix with 1 column")
if type(G) is matrix or type(G) is spmatrix:
if G.typecode != 'd' or G.size[0] != cdim:
raise TypeError("'G' must be a 'd' matrix with %d rows " %cdim)
if h.size[0] != cdim:
raise TypeError("'h' must have %d rows" %cdim)
else:
raise TypeError("'G' must be a matrix")
if min(dims['q'])<1: raise TypeError(
"dimensions of quadratic cones must be positive")
bkc = n*[ mosek.boundkey.fx ]
blc = array(-c)
buc = array(-c)
bkx = ml*[ mosek.boundkey.lo ] + sum(mq)*[ mosek.boundkey.fr ]
blx = ml*[ 0.0 ] + sum(mq)*[ -inf ]
bux = N*[ +inf ]
c = array(-h)
colptr, asub, acof = sparse([G.T]).CCS
aptrb, aptre = colptr[:-1], colptr[1:]
task = env.Task(0,0)
task.set_Stream (mosek.streamtype.log, streamprinter)
# set MOSEK options
for (param, val) in options.items():
if str(param)[:6] == "iparam":
task.putintparam(param, val)
elif str(param)[:6] == "dparam":
task.putdouparam(param, val)
elif str(param)[:6] == "sparam":
task.putstrparam(param, val)
else:
raise ValueError("invalid MOSEK parameter: "+str(param))
task.inputdata (n, # number of constraints
N, # number of variables
c, # linear objective coefficients
0.0, # objective fixed value
array(aptrb),
array(aptre),
array(asub),
array(acof),
bkc,
blc,
buc,
bkx,
blx,
bux)
task.putobjsense(mosek.objsense.maximize)
for k in range(len(mq)):
task.appendcone(mosek.conetype.quad, 0.0,
array(range(ml+sum(mq[:k]),ml+sum(mq[:k+1]))))
task.optimize()
task.solutionsummary (mosek.streamtype.msg);
solsta = task.getsolsta(mosek.soltype.itr)
xu, xl, zq = zeros(n, float), zeros(n, float), zeros(sum(mq), float)
task.getsolutionslice(mosek.soltype.itr, mosek.solitem.slc, 0, n, xl)
task.getsolutionslice(mosek.soltype.itr, mosek.solitem.suc, 0, n, xu)
task.getsolutionslice(mosek.soltype.itr, mosek.solitem.xx, ml, N, zq)
x = matrix(xu-xl)
zq = matrix(zq)
if ml:
zl = zeros(ml, float)
task.getsolutionslice(mosek.soltype.itr, mosek.solitem.xx, 0, ml,
zl)
zl = matrix(zl)
else:
zl = matrix(0.0, (0,1))
if (solsta is mosek.solsta.unknown):
return (solsta, None, None)
else:
return (solsta, x, matrix([zl, zq]))
def main(eofile):
# Open MOSEK and create an environment and task
# Create a handle to MOSEK
mskhandle = mosek.mosek()
# Make a MOSEK environment
env = mskhandle.Env()
# Attach a printer to the environment
env.set_Stream(mosek.streamtype.log, streamprinter)
# Initialize the environment
env.init()
task = env.Task()
task.set_Stream(mosek.streamtype.log, streamprinter) # log
numcon, numvar, termcof, subi, subk, subj, cof = readeo(eofile)
numter = len(termcof)
oprjo = []
opric = []
oprjc = []
for i in range(len(termcof)):
if subi[i] == 0:
# objective term
oprjo.append(i)
else:
opric.append(subi[i] - 1)
oprjc.append(i)
numobjterm = len(oprjo)
if numobjterm > 0:
opro = [mosek.scopr.exp for i in range(numobjterm)]
oprjo = array(oprjo)
oprfo = ones(numobjterm, Float)
oprgo = ones(numobjterm, Float)
oprho = zeros(numobjterm, Float)
else:
opro = None
oprjo = None
oprfo = None
oprgo = None
oprho = None
numconterm = len(opric)
if numconterm > 0:
oprc = [mosek.scopr.exp for i in range(numconterm)]
opric = array(opric)
oprjc = array(oprjc)
oprfc = ones(numconterm, Float)
oprgc = ones(numconterm, Float)
oprhc = zeros(numconterm, Float)
else:
oprc = None
opric = None
oprjc = None
oprfc = None
oprgc = None
oprhc = None
# Define:
# var[0..numter-1] are the new variables
# var[numter..numter+numvar-1] are the original variables
# con[0..numcon-1] are the non-linear ("original") constraints
# con[numcon..numcon+numter] is the affine transformation
task.append(mosek.accmode.var, numvar + numter)
task.append(mosek.accmode.con, numcon + numter)
for i in range(numter):
task.putname(mosek.problemitem.var, i, 'v%d' % i)
for i in range(numvar):
task.putname(mosek.problemitem.var, i + numter, 'x%d' % i)
for i in range(numcon):
task.putname(mosek.problemitem.con, i, 'con%d' % i)
for i in range(numter):
task.putname(mosek.problemitem.con, i + numcon, 'fx%d' % i)
task.putobjname('obj')
task.putboundslice(mosek.accmode.var, 0, numvar + numter,
[mosek.boundkey.fr for i in range(numvar + numter)],
zeros(numvar + numter, Float),
zeros(numvar + numter, Float))
# Non-linear objective and constraints
task.putSCeval(opro=opro,
oprjo=oprjo,
oprfo=oprfo,
oprgo=oprgo,
oprho=oprho,
oprc=oprc,
opric=opric,
oprjc=oprjc,
oprfc=oprfc,
oprgc=oprgc,
oprhc=oprhc)
task.putboundslice(mosek.accmode.con, 0, numcon,
[mosek.boundkey.up for i in range(numcon)],
-inf * ones(numcon, Float), ones(numcon, Float))
# Linear constraints
task.putaijlist(
array(range(numcon, numcon + numter)), # row
array(range(numter)), # var
-ones(numter, Float)) # cof
task.putaijlist(
subk + numcon, # row
subj + numter, # var
cof)
task.putboundslice(mosek.accmode.con, numcon, numcon + numter,
[mosek.boundkey.fx for i in range(numter)],
-log(termcof), -log(termcof))
task.putobjsense(mosek.objsense.minimize)
task.optimize()
print "Solution summary"
task.solutionsummary(mosek.streamtype.log)
xx = zeros(numvar, Float)
task.getsolutionslice(mosek.soltype.itr, mosek.solitem.xx, numter,
numter + numvar, xx)
print "x =", xx
return None
def ilp(c, G, h, A=None, b=None, I=None):
"""
Solves the mixed integer LP
minimize c'*x
subject to G*x + s = h
A*x = b
s >= 0
xi integer, forall i in I
using MOSEK 7.0.
solsta, x = ilp(c, G, h, A=None, b=None, I=None).
Input arguments
G is m x n, h is m x 1, A is p x n, b is p x 1. G and A must be
dense or sparse 'd' matrices. h and b are dense 'd' matrices
with one column. The default values for A and b are empty
matrices with zero rows.
I is a Python set with indices of integer elements of x. By
default all elements in x are constrained to be integer, i.e.,
the default value of I is I = set(range(n))
Dual variables are not returned for MOSEK.
Return values
solsta is a MOSEK solution status key.
If solsta is mosek.solsta.integer_optimal, then x contains
the solution.
If solsta is mosek.solsta.unknown, then x is None.
Other return values for solsta include:
mosek.solsta.near_integer_optimal
in which case the x value may not be well-defined,
c.f., section 17.48 of the MOSEK Python API manual.
x is the solution
Options are passed to MOSEK solvers via the msk.options dictionary,
e.g., the following turns off output from the MOSEK solvers
>>> msk.options = {mosek.iparam.log: 0}
see chapter 15 of the MOSEK Python API manual.
"""
if type(c) is not matrix or c.typecode != 'd' or c.size[1] != 1:
raise TypeError("'c' must be a dense column matrix")
n = c.size[0]
if n < 1: raise ValueError("number of variables must be at least 1")
if (type(G) is not matrix and type(G) is not spmatrix) or \
G.typecode != 'd' or G.size[1] != n:
raise TypeError("'G' must be a dense or sparse 'd' matrix "\
"with %d columns" %n)
m = G.size[0]
if m is 0: raise ValueError("m cannot be 0")
if type(h) is not matrix or h.typecode != 'd' or h.size != (m, 1):
raise TypeError("'h' must be a 'd' matrix of size (%d,1)" % m)
if A is None: A = spmatrix([], [], [], (0, n), 'd')
if (type(A) is not matrix and type(A) is not spmatrix) or \
A.typecode != 'd' or A.size[1] != n:
raise TypeError("'A' must be a dense or sparse 'd' matrix "\
"with %d columns" %n)
p = A.size[0]
if b is None: b = matrix(0.0, (0, 1))
if type(b) is not matrix or b.typecode != 'd' or b.size != (p, 1):
raise TypeError("'b' must be a dense matrix of size (%d,1)" % p)
c = array(c)
if I is None: I = set(range(n))
if type(I) is not set:
raise TypeError("invalid argument for integer index set")
for i in I:
if type(i) is not int:
raise TypeError("invalid integer index set I")
if len(I) > 0 and min(I) < 0:
raise IndexError("negative element in integer index set I")
if len(I) > 0 and max(I) > n - 1:
raise IndexError(
"maximum element in in integer index set I is larger than n-1")
bkc = m * [mosek.boundkey.up] + p * [mosek.boundkey.fx]
blc = m * [-inf] + [bi for bi in b]
buc = matrix([h, b])
bkx = n * [mosek.boundkey.fr]
blx = n * [-inf]
bux = n * [+inf]
colptr, asub, acof = sparse([G, A]).CCS
aptrb, aptre = colptr[:-1], colptr[1:]
task = env.Task(0, 0)
task.set_Stream(mosek.streamtype.log, streamprinter)
# set MOSEK options
for (param, val) in options.items():
if str(param)[:6] == "iparam":
task.putintparam(param, val)
elif str(param)[:6] == "dparam":
task.putdouparam(param, val)
elif str(param)[:6] == "sparam":
task.putstrparam(param, val)
else:
raise ValueError("invalid MOSEK parameter: " + str(param))
task.inputdata(
m + p, # number of constraints
n, # number of variables
array(c), # linear objective coefficients
0.0, # objective fixed value
array(aptrb),
array(aptre),
array(asub),
array(acof),
bkc,
blc,
buc,
bkx,
blx,
bux)
task.putobjsense(mosek.objsense.minimize)
# Define integer variables
if len(I) > 0:
task.putvartypelist(list(I), len(I) * [mosek.variabletype.type_int])
task.putintparam(mosek.iparam.mio_mode, mosek.miomode.satisfied)
task.optimize()
task.solutionsummary(mosek.streamtype.msg)
if len(I) > 0:
solsta = task.getsolsta(mosek.soltype.itg)
else:
solsta = task.getsolsta(mosek.soltype.bas)
x = zeros(n, float)
if len(I) > 0:
task.getsolutionslice(mosek.soltype.itg, mosek.solitem.xx, 0, n, x)
else:
task.getsolutionslice(mosek.soltype.bas, mosek.solitem.xx, 0, n, x)
x = matrix(x)
if (solsta is mosek.solsta.unknown):
return (solsta, None)
else:
return (solsta, x)
def qp(P, q, G=None, h=None, A=None, b=None):
"""
Solves a quadratic program
minimize (1/2)*x'*P*x + q'*x
subject to G*x <= h
A*x = b.
using MOSEK 7.0.
solsta, x, z, y = qp(P, q, G=None, h=None, A=None, b=None)
Return values
solsta is a MOSEK solution status key.
If solsta is mosek.solsta.optimal,
then (x, y, z) contains the primal-dual solution.
If solsta is mosek.solsta.prim_infeas_cer,
then (x, y, z) is a certificate of primal infeasibility.
If solsta is mosek.solsta.dual_infeas_cer,
then (x, y, z) is a certificate of dual infeasibility.
If solsta is mosek.solsta.unknown, then (x, y, z) are all None.
Other return values for solsta include:
mosek.solsta.dual_feas
mosek.solsta.near_dual_feas
mosek.solsta.near_optimal
mosek.solsta.near_prim_and_dual_feas
mosek.solsta.near_prim_feas
mosek.solsta.prim_and_dual_feas
mosek.solsta.prim_feas
in which case the (x,y,z) value may not be well-defined,
c.f., section 17.48 of the MOSEK Python API manual.
x, z, y the primal-dual solution.
Options are passed to MOSEK solvers via the msk.options dictionary,
e.g., the following turns off output from the MOSEK solvers
>>> msk.options = {mosek.iparam.log: 0}
see chapter 15 of the MOSEK Python API manual.
"""
if (type(P) is not matrix and type(P) is not spmatrix) or \
P.typecode != 'd' or P.size[0] != P.size[1]:
raise TypeError("'P' must be a square dense or sparse 'd' matrix ")
n = P.size[0]
if n < 1: raise ValueError("number of variables must be at least 1")
if type(q) is not matrix or q.typecode != 'd' or q.size != (n, 1):
raise TypeError("'q' must be a 'd' matrix of size (%d,1)" % n)
if G is None: G = spmatrix([], [], [], (0, n), 'd')
if (type(G) is not matrix and type(G) is not spmatrix) or \
G.typecode != 'd' or G.size[1] != n:
raise TypeError("'G' must be a dense or sparse 'd' matrix "\
"with %d columns" %n)
m = G.size[0]
if h is None: h = matrix(0.0, (0, 1))
if type(h) is not matrix or h.typecode != 'd' or h.size != (m, 1):
raise TypeError("'h' must be a 'd' matrix of size (%d,1)" % m)
if A is None: A = spmatrix([], [], [], (0, n), 'd')
if (type(A) is not matrix and type(A) is not spmatrix) or \
A.typecode != 'd' or A.size[1] != n:
raise TypeError("'A' must be a dense or sparse 'd' matrix "\
"with %d columns" %n)
p = A.size[0]
if b is None: b = matrix(0.0, (0, 1))
if type(b) is not matrix or b.typecode != 'd' or b.size != (p, 1):
raise TypeError("'b' must be a dense matrix of size (%d,1)" % p)
if m + p is 0: raise ValueError("m + p must be greater than 0")
c = array(q)
bkc = m * [mosek.boundkey.up] + p * [mosek.boundkey.fx]
blc = m * [-inf] + [bi for bi in b]
buc = matrix([h, b])
bkx = n * [mosek.boundkey.fr]
blx = n * [-inf]
bux = n * [+inf]
colptr, asub, acof = sparse([G, A]).CCS
aptrb, aptre = colptr[:-1], colptr[1:]
task = env.Task(0, 0)
task.set_Stream(mosek.streamtype.log, streamprinter)
# set MOSEK options
for (param, val) in options.items():
if str(param)[:6] == "iparam":
task.putintparam(param, val)
elif str(param)[:6] == "dparam":
task.putdouparam(param, val)
elif str(param)[:6] == "sparam":
task.putstrparam(param, val)
else:
raise ValueError("invalid MOSEK parameter: " + str(param))
task.inputdata(
m + p, # number of constraints
n, # number of variables
array(c), # linear objective coefficients
0.0, # objective fixed value
array(aptrb),
array(aptre),
array(asub),
array(acof),
bkc,
blc,
buc,
bkx,
blx,
bux)
Ps = sparse(P)
I, J = Ps.I, Ps.J
tril = [k for k in range(len(I)) if I[k] >= J[k]]
task.putqobj(array(I[tril]), array(J[tril]), array(Ps.V[tril]))
task.putobjsense(mosek.objsense.minimize)
task.optimize()
task.solutionsummary(mosek.streamtype.msg)
solsta = task.getsolsta(mosek.soltype.itr)
x = zeros(n, float)
task.getsolutionslice(mosek.soltype.itr, mosek.solitem.xx, 0, n, x)
x = matrix(x)
if m is not 0:
z = zeros(m, float)
task.getsolutionslice(mosek.soltype.itr, mosek.solitem.suc, 0, m, z)
z = matrix(z)
else:
z = matrix(0.0, (0, 1))
if p is not 0:
yu, yl = zeros(p, float), zeros(p, float)
task.getsolutionslice(mosek.soltype.itr, mosek.solitem.suc, m, m + p,
yu)
task.getsolutionslice(mosek.soltype.itr, mosek.solitem.slc, m, m + p,
yl)
y = matrix(yu) - matrix(yl)
else:
y = matrix(0.0, (0, 1))
if (solsta is mosek.solsta.unknown):
return (solsta, None, None, None)
else:
return (solsta, x, z, y)
def lp(c, G, h, A=None, b=None):
"""
Solves a pair of primal and dual LPs
minimize c'*x maximize -h'*z - b'*y
subject to G*x + s = h subject to G'*z + A'*y + c = 0
A*x = b z >= 0.
s >= 0
using MOSEK 7.0.
(solsta, x, z, y) = lp(c, G, h, A=None, b=None).
Input arguments
c is n x 1, G is m x n, h is m x 1, A is p x n, b is p x 1. G and
A must be dense or sparse 'd' matrices. c, h and b are dense 'd'
matrices with one column. The default values for A and b are
empty matrices with zero rows.
Return values
solsta is a MOSEK solution status key.
If solsta is mosek.solsta.optimal, then (x, y, z) contains the
primal-dual solution.
If solsta is mosek.solsta.prim_infeas_cer, then (x, y, z) is a
certificate of primal infeasibility.
If solsta is mosek.solsta.dual_infeas_cer, then (x, y, z) is a
certificate of dual infeasibility.
If solsta is mosek.solsta.unknown, then (x, y, z) are all None.
Other return values for solsta include:
mosek.solsta.dual_feas
mosek.solsta.near_dual_feas
mosek.solsta.near_optimal
mosek.solsta.near_prim_and_dual_feas
mosek.solsta.near_prim_feas
mosek.solsta.prim_and_dual_feas
mosek.solsta.prim_feas
in which case the (x,y,z) value may not be well-defined,
c.f., section 17.48 of the MOSEK Python API manual.
x, y, z the primal-dual solution.
Options are passed to MOSEK solvers via the msk.options dictionary.
For example, the following turns off output from the MOSEK solvers
>>> msk.options = {mosek.iparam.log: 0}
see chapter 15 of the MOSEK Python API manual.
"""
if type(c) is not matrix or c.typecode != 'd' or c.size[1] != 1:
raise TypeError("'c' must be a dense column matrix")
n = c.size[0]
if n < 1: raise ValueError("number of variables must be at least 1")
if (type(G) is not matrix and type(G) is not spmatrix) or \
G.typecode != 'd' or G.size[1] != n:
raise TypeError("'G' must be a dense or sparse 'd' matrix "\
"with %d columns" %n)
m = G.size[0]
if m is 0: raise ValueError("m cannot be 0")
if type(h) is not matrix or h.typecode != 'd' or h.size != (m, 1):
raise TypeError("'h' must be a 'd' matrix of size (%d,1)" % m)
if A is None: A = spmatrix([], [], [], (0, n), 'd')
if (type(A) is not matrix and type(A) is not spmatrix) or \
A.typecode != 'd' or A.size[1] != n:
raise TypeError("'A' must be a dense or sparse 'd' matrix "\
"with %d columns" %n)
p = A.size[0]
if b is None: b = matrix(0.0, (0, 1))
if type(b) is not matrix or b.typecode != 'd' or b.size != (p, 1):
raise TypeError("'b' must be a dense matrix of size (%d,1)" % p)
bkc = m * [mosek.boundkey.up] + p * [mosek.boundkey.fx]
blc = m * [-inf] + [bi for bi in b]
buc = matrix([h, b])
bkx = n * [mosek.boundkey.fr]
blx = n * [-inf]
bux = n * [+inf]
colptr, asub, acof = sparse([G, A]).CCS
aptrb, aptre = colptr[:-1], colptr[1:]
task = env.Task(0, 0)
task.set_Stream(mosek.streamtype.log, streamprinter)
# set MOSEK options
for (param, val) in options.items():
if str(param)[:6] == "iparam":
task.putintparam(param, val)
elif str(param)[:6] == "dparam":
task.putdouparam(param, val)
elif str(param)[:6] == "sparam":
task.putstrparam(param, val)
else:
raise ValueError("invalid MOSEK parameter: " + str(param))
task.inputdata(
m + p, # number of constraints
n, # number of variables
array(c), # linear objective coefficients
0.0, # objective fixed value
array(aptrb),
array(aptre),
array(asub),
array(acof),
bkc,
blc,
buc,
bkx,
blx,
bux)
task.putobjsense(mosek.objsense.minimize)
task.optimize()
task.solutionsummary(mosek.streamtype.msg)
solsta = task.getsolsta(mosek.soltype.bas)
x, z = zeros(n, float), zeros(m, float)
task.getsolutionslice(mosek.soltype.bas, mosek.solitem.xx, 0, n, x)
task.getsolutionslice(mosek.soltype.bas, mosek.solitem.suc, 0, m, z)
x, z = matrix(x), matrix(z)
if p is not 0:
yu, yl = zeros(p, float), zeros(p, float)
task.getsolutionslice(mosek.soltype.bas, mosek.solitem.suc, m, m + p,
yu)
task.getsolutionslice(mosek.soltype.bas, mosek.solitem.slc, m, m + p,
yl)
y = matrix(yu) - matrix(yl)
else:
y = matrix(0.0, (0, 1))
if (solsta is mosek.solsta.unknown):
return (solsta, None, None, None)
else:
return (solsta, x, z, y)
def socp(c, Gl=None, hl=None, Gq=None, hq=None):
"""
Solves a pair of primal and dual SOCPs
minimize c'*x
subject to Gl*x + sl = hl
Gq[k]*x + sq[k] = hq[k], k = 0, ..., N-1
sl >= 0,
sq[k] >= 0, k = 0, ..., N-1
maximize -hl'*zl - sum_k hq[k]'*zq[k]
subject to Gl'*zl + sum_k Gq[k]'*zq[k] + c = 0
zl >= 0, zq[k] >= 0, k = 0, ..., N-1.
using MOSEK 7.0.
solsta, x, zl, zq = socp(c, Gl = None, hl = None, Gq = None, hq = None)
Return values
solsta is a MOSEK solution status key.
If solsta is mosek.solsta.optimal,
then (x, zl, zq) contains the primal-dual solution.
If solsta is mosek.solsta.prim_infeas_cer,
then (x, zl, zq) is a certificate of dual infeasibility.
If solsta is mosek.solsta.dual_infeas_cer,
then (x, zl, zq) is a certificate of primal infeasibility.
If solsta is mosek.solsta.unknown,
then (x, zl, zq) are all None
Other return values for solsta include:
mosek.solsta.dual_feas
mosek.solsta.near_dual_feas
mosek.solsta.near_optimal
mosek.solsta.near_prim_and_dual_feas
mosek.solsta.near_prim_feas
mosek.solsta.prim_and_dual_feas
mosek.solsta.prim_feas
in which case the (x,y,z) value may not be well-defined,
c.f., section 17.48 of the MOSEK Python API manual.
x, zl, zq the primal-dual solution.
Options are passed to MOSEK solvers via the msk.options dictionary,
e.g., the following turns off output from the MOSEK solvers
>>> msk.options = {mosek.iparam.log: 0}
see chapter 15 of the MOSEK Python API manual.
"""
if type(c) is not matrix or c.typecode != 'd' or c.size[1] != 1:
raise TypeError("'c' must be a dense column matrix")
n = c.size[0]
if n < 1: raise ValueError("number of variables must be at least 1")
if Gl is None: Gl = spmatrix([], [], [], (0, n), tc='d')
if (type(Gl) is not matrix and type(Gl) is not spmatrix) or \
Gl.typecode != 'd' or Gl.size[1] != n:
raise TypeError("'Gl' must be a dense or sparse 'd' matrix "\
"with %d columns" %n)
ml = Gl.size[0]
if hl is None: hl = matrix(0.0, (0, 1))
if type(hl) is not matrix or hl.typecode != 'd' or \
hl.size != (ml,1):
raise TypeError("'hl' must be a dense 'd' matrix of " \
"size (%d,1)" %ml)
if Gq is None: Gq = []
if type(Gq) is not list or [
G
for G in Gq if (type(G) is not matrix and type(G) is not spmatrix)
or G.typecode != 'd' or G.size[1] != n
]:
raise TypeError("'Gq' must be a list of sparse or dense 'd' "\
"matrices with %d columns" %n)
mq = [G.size[0] for G in Gq]
a = [k for k in range(len(mq)) if mq[k] == 0]
if a: raise TypeError("the number of rows of Gq[%d] is zero" % a[0])
if hq is None: hq = []
if type(hq) is not list or len(hq) != len(mq) or [
h
for h in hq if (type(h) is not matrix and type(h) is not spmatrix)
or h.typecode != 'd'
]:
raise TypeError("'hq' must be a list of %d dense or sparse "\
"'d' matrices" %len(mq))
a = [k for k in range(len(mq)) if hq[k].size != (mq[k], 1)]
if a:
k = a[0]
raise TypeError("'hq[%d]' has size (%d,%d). Expected size "\
"is (%d,1)." %(k, hq[k].size[0], hq[k].size[1], mq[k]))
N = ml + sum(mq)
h = matrix(0.0, (N, 1))
if type(Gl) is matrix or [Gk for Gk in Gq if type(Gk) is matrix]:
G = matrix(0.0, (N, n))
else:
G = spmatrix([], [], [], (N, n), 'd')
h[:ml] = hl
G[:ml, :] = Gl
ind = ml
for k in range(len(mq)):
h[ind:ind + mq[k]] = hq[k]
G[ind:ind + mq[k], :] = Gq[k]
ind += mq[k]
bkc = n * [mosek.boundkey.fx]
blc = array(-c)
buc = array(-c)
bkx = ml * [mosek.boundkey.lo] + sum(mq) * [mosek.boundkey.fr]
blx = ml * [0.0] + sum(mq) * [-inf]
bux = N * [+inf]
c = -h
colptr, asub, acof = sparse([G.T]).CCS
aptrb, aptre = colptr[:-1], colptr[1:]
task = env.Task(0, 0)
task.set_Stream(mosek.streamtype.log, streamprinter)
# set MOSEK options
for (param, val) in options.items():
if str(param)[:6] == "iparam":
task.putintparam(param, val)
elif str(param)[:6] == "dparam":
task.putdouparam(param, val)
elif str(param)[:6] == "sparam":
task.putstrparam(param, val)
else:
raise ValueError("invalid MOSEK parameter: " + str(param))
task.inputdata(
n, # number of constraints
N, # number of variables
array(c), # linear objective coefficients
0.0, # objective fixed value
array(aptrb),
array(aptre),
array(asub),
array(acof),
bkc,
blc,
buc,
bkx,
blx,
bux)
task.putobjsense(mosek.objsense.maximize)
for k in range(len(mq)):
task.appendcone(mosek.conetype.quad, 0.0,
array(range(ml + sum(mq[:k]), ml + sum(mq[:k + 1]))))
task.optimize()
task.solutionsummary(mosek.streamtype.msg)
solsta = task.getsolsta(mosek.soltype.itr)
xu, xl, zq = zeros(n, float), zeros(n, float), zeros(sum(mq), float)
task.getsolutionslice(mosek.soltype.itr, mosek.solitem.slc, 0, n, xl)
task.getsolutionslice(mosek.soltype.itr, mosek.solitem.suc, 0, n, xu)
task.getsolutionslice(mosek.soltype.itr, mosek.solitem.xx, ml, N, zq)
x = matrix(xu) - matrix(xl)
zq = [matrix(zq[sum(mq[:k]):sum(mq[:k + 1])]) for k in range(len(mq))]
if ml:
zl = zeros(ml, float)
task.getsolutionslice(mosek.soltype.itr, mosek.solitem.xx, 0, ml, zl)
zl = matrix(zl)
else:
zl = matrix(0.0, (0, 1))
if (solsta is mosek.solsta.unknown):
return (solsta, None, None, None)
else:
return (solsta, x, zl, zq)
def _vectorsub__3F_3F (v1,v2): return array.array([ v1[i]-v2[i] for i in xrange(len(v1)) ])
def main (eofile):
# Open MOSEK and create an environment and task
# Create a handle to MOSEK
mskhandle = mosek.mosek ()
# Make a MOSEK environment
env = mskhandle.Env ()
# Attach a printer to the environment
env.set_Stream (mosek.streamtype.log, streamprinter)
# Initialize the environment
env.init ()
task = env.Task()
task.set_Stream (mosek.streamtype.log,streamprinter)# log
numcon,numvar,termcof,subi,subk,subj,cof = readeo(eofile)
numter = len(termcof)
oprjo = []
opric = []
oprjc = []
for i in range(len(termcof)):
if subi[i] == 0:
# objective term
oprjo.append(i)
else:
opric.append(subi[i]-1)
oprjc.append(i)
numobjterm = len(oprjo)
if numobjterm > 0:
opro = [ mosek.scopr.exp for i in range(numobjterm) ]
oprjo = array(oprjo)
oprfo = ones(numobjterm,Float)
oprgo = ones(numobjterm,Float)
oprho = zeros(numobjterm,Float)
else:
opro = None
oprjo = None
oprfo = None
oprgo = None
oprho = None
numconterm = len(opric)
if numconterm > 0:
oprc = [ mosek.scopr.exp for i in range(numconterm) ]
opric = array(opric)
oprjc = array(oprjc)
oprfc = ones(numconterm,Float)
oprgc = ones(numconterm,Float)
oprhc = zeros(numconterm,Float)
else:
oprc = None
opric = None
oprjc = None
oprfc = None
oprgc = None
oprhc = None
# Define:
# var[0..numter-1] are the new variables
# var[numter..numter+numvar-1] are the original variables
# con[0..numcon-1] are the non-linear ("original") constraints
# con[numcon..numcon+numter] is the affine transformation
task.append(mosek.accmode.var, numvar + numter)
task.append(mosek.accmode.con, numcon + numter)
for i in range(numter):
task.putname(mosek.problemitem.var,i,'v%d' % i)
for i in range(numvar):
task.putname(mosek.problemitem.var,i+numter,'x%d' % i)
for i in range(numcon):
task.putname(mosek.problemitem.con,i,'con%d' % i)
for i in range(numter):
task.putname(mosek.problemitem.con,i+numcon,'fx%d' % i)
task.putobjname('obj')
task.putboundslice(mosek.accmode.var,
0, numvar + numter,
[ mosek.boundkey.fr for i in range(numvar + numter)],
zeros(numvar + numter, Float),
zeros(numvar + numter, Float))
# Non-linear objective and constraints
task.putSCeval(opro = opro,
oprjo = oprjo,
oprfo = oprfo,
oprgo = oprgo,
oprho = oprho,
oprc = oprc,
opric = opric,
oprjc = oprjc,
oprfc = oprfc,
oprgc = oprgc,
oprhc = oprhc)
task.putboundslice(mosek.accmode.con,
0, numcon,
[ mosek.boundkey.up for i in range(numcon)],
-inf * ones(numcon,Float),
ones(numcon,Float))
# Linear constraints
task.putaijlist(array(range(numcon, numcon + numter)), # row
array(range(numter)), # var
-ones(numter,Float)) # cof
task.putaijlist(subk + numcon, # row
subj + numter, # var
cof)
task.putboundslice(mosek.accmode.con,
numcon, numcon+numter,
[ mosek.boundkey.fx for i in range(numter) ],
-log(termcof),
-log(termcof))
task.putobjsense(mosek.objsense.minimize)
task.optimize ()
print "Solution summary"
task.solutionsummary(mosek.streamtype.log)
xx = zeros(numvar, Float)
task.getsolutionslice(mosek.soltype.itr,
mosek.solitem.xx,
numter, numter+numvar,
xx)
print "x =", xx
return None
def lp(c, G, h, A=None, b=None):
"""
Solves a pair of primal and dual LPs
minimize c'*x maximize -h'*z - b'*y
subject to G*x + s = h subject to G'*z + A'*y + c = 0
A*x = b z >= 0.
s >= 0
using MOSEK 7.0.
(solsta, x, z, y) = lp(c, G, h, A=None, b=None).
Input arguments
c is n x 1, G is m x n, h is m x 1, A is p x n, b is p x 1. G and
A must be dense or sparse 'd' matrices. c, h and b are dense 'd'
matrices with one column. The default values for A and b are
empty matrices with zero rows.
Return values
solsta is a MOSEK solution status key.
If solsta is mosek.solsta.optimal, then (x, y, z) contains the
primal-dual solution.
If solsta is mosek.solsta.prim_infeas_cer, then (x, y, z) is a
certificate of primal infeasibility.
If solsta is mosek.solsta.dual_infeas_cer, then (x, y, z) is a
certificate of dual infeasibility.
If solsta is mosek.solsta.unknown, then (x, y, z) are all None.
Other return values for solsta include:
mosek.solsta.dual_feas
mosek.solsta.near_dual_feas
mosek.solsta.near_optimal
mosek.solsta.near_prim_and_dual_feas
mosek.solsta.near_prim_feas
mosek.solsta.prim_and_dual_feas
mosek.solsta.prim_feas
in which case the (x,y,z) value may not be well-defined,
c.f., section 17.48 of the MOSEK Python API manual.
x, y, z the primal-dual solution.
Options are passed to MOSEK solvers via the msk.options dictionary.
For example, the following turns off output from the MOSEK solvers
>>> msk.options = {mosek.iparam.log: 0}
see chapter 15 of the MOSEK Python API manual.
"""
if type(c) is not matrix or c.typecode != 'd' or c.size[1] != 1:
raise TypeError("'c' must be a dense column matrix")
n = c.size[0]
if n < 1: raise ValueError("number of variables must be at least 1")
if (type(G) is not matrix and type(G) is not spmatrix) or \
G.typecode != 'd' or G.size[1] != n:
raise TypeError("'G' must be a dense or sparse 'd' matrix "\
"with %d columns" %n)
m = G.size[0]
if m is 0: raise ValueError("m cannot be 0")
if type(h) is not matrix or h.typecode != 'd' or h.size != (m,1):
raise TypeError("'h' must be a 'd' matrix of size (%d,1)" %m)
if A is None: A = spmatrix([], [], [], (0,n), 'd')
if (type(A) is not matrix and type(A) is not spmatrix) or \
A.typecode != 'd' or A.size[1] != n:
raise TypeError("'A' must be a dense or sparse 'd' matrix "\
"with %d columns" %n)
p = A.size[0]
if b is None: b = matrix(0.0, (0,1))
if type(b) is not matrix or b.typecode != 'd' or b.size != (p,1):
raise TypeError("'b' must be a dense matrix of size (%d,1)" %p)
bkc = m*[ mosek.boundkey.up ] + p*[ mosek.boundkey.fx ]
blc = m*[ -inf ] + [ bi for bi in b ]
buc = matrix([h, b])
bkx = n*[mosek.boundkey.fr]
blx = n*[ -inf ]
bux = n*[ +inf ]
colptr, asub, acof = sparse([G,A]).CCS
aptrb, aptre = colptr[:-1], colptr[1:]
task = env.Task(0,0)
task.set_Stream (mosek.streamtype.log, streamprinter)
# set MOSEK options
for (param, val) in options.items():
if str(param)[:6] == "iparam":
task.putintparam(param, val)
elif str(param)[:6] == "dparam":
task.putdouparam(param, val)
elif str(param)[:6] == "sparam":
task.putstrparam(param, val)
else:
raise ValueError("invalid MOSEK parameter: " + str(param))
task.inputdata (m+p, # number of constraints
n, # number of variables
array(c), # linear objective coefficients
0.0, # objective fixed value
array(aptrb),
array(aptre),
array(asub),
array(acof),
bkc,
blc,
buc,
bkx,
blx,
bux)
task.putobjsense(mosek.objsense.minimize)
task.optimize()
task.solutionsummary (mosek.streamtype.msg);
solsta = task.getsolsta(mosek.soltype.bas)
x, z = zeros(n, float), zeros(m, float)
task.getsolutionslice(mosek.soltype.bas, mosek.solitem.xx, 0, n, x)
task.getsolutionslice(mosek.soltype.bas, mosek.solitem.suc, 0, m, z)
x, z = matrix(x), matrix(z)
if p is not 0:
yu, yl = zeros(p, float), zeros(p, float)
task.getsolutionslice(mosek.soltype.bas, mosek.solitem.suc, m,
m+p, yu)
task.getsolutionslice(mosek.soltype.bas, mosek.solitem.slc, m,
m+p, yl)
y = matrix(yu) - matrix(yl)
else:
y = matrix(0.0, (0,1))
if (solsta is mosek.solsta.unknown):
return (solsta, None, None, None)
else:
return (solsta, x, z, y)
def socp(c, Gl = None, hl = None, Gq = None, hq = None):
"""
Solves a pair of primal and dual SOCPs
minimize c'*x
subject to Gl*x + sl = hl
Gq[k]*x + sq[k] = hq[k], k = 0, ..., N-1
sl >= 0,
sq[k] >= 0, k = 0, ..., N-1
maximize -hl'*zl - sum_k hq[k]'*zq[k]
subject to Gl'*zl + sum_k Gq[k]'*zq[k] + c = 0
zl >= 0, zq[k] >= 0, k = 0, ..., N-1.
using MOSEK 7.0.
solsta, x, zl, zq = socp(c, Gl = None, hl = None, Gq = None, hq = None)
Return values
solsta is a MOSEK solution status key.
If solsta is mosek.solsta.optimal,
then (x, zl, zq) contains the primal-dual solution.
If solsta is mosek.solsta.prim_infeas_cer,
then (x, zl, zq) is a certificate of dual infeasibility.
If solsta is mosek.solsta.dual_infeas_cer,
then (x, zl, zq) is a certificate of primal infeasibility.
If solsta is mosek.solsta.unknown,
then (x, zl, zq) are all None
Other return values for solsta include:
mosek.solsta.dual_feas
mosek.solsta.near_dual_feas
mosek.solsta.near_optimal
mosek.solsta.near_prim_and_dual_feas
mosek.solsta.near_prim_feas
mosek.solsta.prim_and_dual_feas
mosek.solsta.prim_feas
in which case the (x,y,z) value may not be well-defined,
c.f., section 17.48 of the MOSEK Python API manual.
x, zl, zq the primal-dual solution.
Options are passed to MOSEK solvers via the msk.options dictionary,
e.g., the following turns off output from the MOSEK solvers
>>> msk.options = {mosek.iparam.log: 0}
see chapter 15 of the MOSEK Python API manual.
"""
if type(c) is not matrix or c.typecode != 'd' or c.size[1] != 1:
raise TypeError("'c' must be a dense column matrix")
n = c.size[0]
if n < 1: raise ValueError("number of variables must be at least 1")
if Gl is None: Gl = spmatrix([], [], [], (0,n), tc='d')
if (type(Gl) is not matrix and type(Gl) is not spmatrix) or \
Gl.typecode != 'd' or Gl.size[1] != n:
raise TypeError("'Gl' must be a dense or sparse 'd' matrix "\
"with %d columns" %n)
ml = Gl.size[0]
if hl is None: hl = matrix(0.0, (0,1))
if type(hl) is not matrix or hl.typecode != 'd' or \
hl.size != (ml,1):
raise TypeError("'hl' must be a dense 'd' matrix of " \
"size (%d,1)" %ml)
if Gq is None: Gq = []
if type(Gq) is not list or [ G for G in Gq if (type(G) is not matrix
and type(G) is not spmatrix) or G.typecode != 'd' or
G.size[1] != n ]:
raise TypeError("'Gq' must be a list of sparse or dense 'd' "\
"matrices with %d columns" %n)
mq = [ G.size[0] for G in Gq ]
a = [ k for k in range(len(mq)) if mq[k] == 0 ]
if a: raise TypeError("the number of rows of Gq[%d] is zero" %a[0])
if hq is None: hq = []
if type(hq) is not list or len(hq) != len(mq) or [ h for h in hq if
(type(h) is not matrix and type(h) is not spmatrix) or
h.typecode != 'd' ]:
raise TypeError("'hq' must be a list of %d dense or sparse "\
"'d' matrices" %len(mq))
a = [ k for k in range(len(mq)) if hq[k].size != (mq[k], 1) ]
if a:
k = a[0]
raise TypeError("'hq[%d]' has size (%d,%d). Expected size "\
"is (%d,1)." %(k, hq[k].size[0], hq[k].size[1], mq[k]))
N = ml + sum(mq)
h = matrix(0.0, (N,1))
if type(Gl) is matrix or [ Gk for Gk in Gq if type(Gk) is matrix ]:
G = matrix(0.0, (N, n))
else:
G = spmatrix([], [], [], (N, n), 'd')
h[:ml] = hl
G[:ml,:] = Gl
ind = ml
for k in range(len(mq)):
h[ind : ind + mq[k]] = hq[k]
G[ind : ind + mq[k], :] = Gq[k]
ind += mq[k]
bkc = n*[ mosek.boundkey.fx ]
blc = array(-c)
buc = array(-c)
bkx = ml*[ mosek.boundkey.lo ] + sum(mq)*[ mosek.boundkey.fr ]
blx = ml*[ 0.0 ] + sum(mq)*[ -inf ]
bux = N*[ +inf ]
c = -h
colptr, asub, acof = sparse([G.T]).CCS
aptrb, aptre = colptr[:-1], colptr[1:]
task = env.Task(0,0)
task.set_Stream (mosek.streamtype.log, streamprinter)
# set MOSEK options
for (param, val) in options.items():
if str(param)[:6] == "iparam":
task.putintparam(param, val)
elif str(param)[:6] == "dparam":
task.putdouparam(param, val)
elif str(param)[:6] == "sparam":
task.putstrparam(param, val)
else:
raise ValueError("invalid MOSEK parameter: "+str(param))
task.inputdata (n, # number of constraints
N, # number of variables
array(c), # linear objective coefficients
0.0, # objective fixed value
array(aptrb),
array(aptre),
array(asub),
array(acof),
bkc,
blc,
buc,
bkx,
blx,
bux)
task.putobjsense(mosek.objsense.maximize)
for k in range(len(mq)):
task.appendcone(mosek.conetype.quad, 0.0,
array(range(ml+sum(mq[:k]),ml+sum(mq[:k+1]))))
task.optimize()
task.solutionsummary (mosek.streamtype.msg);
solsta = task.getsolsta(mosek.soltype.itr)
xu, xl, zq = zeros(n, float), zeros(n, float), zeros(sum(mq), float)
task.getsolutionslice(mosek.soltype.itr, mosek.solitem.slc, 0, n, xl)
task.getsolutionslice(mosek.soltype.itr, mosek.solitem.suc, 0, n, xu)
task.getsolutionslice(mosek.soltype.itr, mosek.solitem.xx, ml, N, zq)
x = matrix(xu) - matrix(xl)
zq = [ matrix(zq[sum(mq[:k]):sum(mq[:k+1])]) for k in range(len(mq)) ]
if ml:
zl = zeros(ml, float)
task.getsolutionslice(mosek.soltype.itr, mosek.solitem.xx, 0, ml,
zl)
zl = matrix(zl)
else:
zl = matrix(0.0, (0,1))
if (solsta is mosek.solsta.unknown):
return (solsta, None, None, None)
else:
return (solsta, x, zl, zq)
