def test_basic_complex(self):
import kvxopt
a = kvxopt.matrix([1, -2, 3])
b = kvxopt.matrix([1.0, -2.0, 3.0])
c = kvxopt.matrix([1.0 + 2j, 1 - 2j, 0 + 1j])
d = kvxopt.spmatrix(
[complex(1.0, 0.0),
complex(0.0, 1.0),
complex(2.0, -1.0)], [0, 1, 3], [0, 2, 3], (4, 4))
e = kvxopt.spmatrix(
[complex(1.0, 0.0),
complex(0.0, 1.0),
complex(2.0, -1.0)], [2, 3, 3], [1, 2, 3], (4, 4))
self.assertAlmostEqualLists(list(kvxopt.div(b, c)),
[0.2 - 0.4j, -0.4 - 0.8j, -3j])
self.assertAlmostEqualLists(list(kvxopt.div(b, 2.0j)),
[-0.5j, 1j, -1.5j])
self.assertAlmostEqualLists(list(kvxopt.div(a, c)),
[0.2 - 0.4j, -0.4 - 0.8j, -3j])
self.assertAlmostEqualLists(list(kvxopt.div(c, a)),
[(1 + 2j),
(-0.5 + 1j), 0.3333333333333333j])
self.assertAlmostEqualLists(list(kvxopt.div(c, c)), [1.0, 1.0, 1.0])
self.assertAlmostEqualLists(list(kvxopt.div(a, 2.0j)),
[-0.5j, 1j, -1.5j])
self.assertAlmostEqualLists(list(kvxopt.div(c, 1.0j)),
[2 - 1j, -2 - 1j, 1 + 0j])
self.assertAlmostEqualLists(list(kvxopt.div(1j, c)),
[0.4 + 0.2j, -0.4 + 0.2j, 1 + 0j])
self.assertTrue(len(d) + len(e) == len(kvxopt.sparse([d, e])))
self.assertTrue(len(d) + len(e) == len(kvxopt.sparse([[d], [e]])))
def test_get_det(self):
try:
import numpy as np
except ImportError:
self.skipTest("Numpy not available for determinant testing")
from kvxopt.klu import numeric, symbolic, get_det
from kvxopt import matrix, spmatrix
V = [2, 3, 3, -1, 4, 4, -3, 1, 2, 2, 6, 1]
Vc = list(map(lambda x: x + x * 1j, V))
I = [0, 1, 0, 2, 4, 1, 2, 3, 4, 2, 1, 4]
J = [0, 0, 1, 1, 1, 2, 2, 2, 2, 3, 4, 4]
B = matrix([1.0j] * 5)
A = spmatrix(V, I, J)
Ac = spmatrix(Vc, I, J)
# Double matrix case
Fs = symbolic(A)
Fn = numeric(A, Fs)
det1 = get_det(A, Fs, Fn)
det2 = np.linalg.det(np.array(matrix(A)))
self.assertAlmostEqual(det1, det2)
# Complex matrix case
Fs = symbolic(Ac)
Fn = numeric(Ac, Fs)
det1 = get_det(Ac, Fs, Fn)
det2 = np.linalg.det(np.array(matrix(Ac)))
self.assertAlmostEqual(det1, det2)
def test_basic(self):
import kvxopt
a = kvxopt.matrix([1.0, 2.0, 3.0])
assert list(a) == [1.0, 2.0, 3.0]
b = kvxopt.matrix([3.0, -2.0, -1.0])
c = kvxopt.spmatrix([1.0, -2.0, 3.0], [0, 2, 4], [1, 2, 4], (6, 5))
d = kvxopt.spmatrix([1.0, 2.0, 5.0], [0, 1, 2], [0, 0, 0], (3, 1))
e = kvxopt.mul(a, b)
self.assertEqualLists(e, [3.0, -4.0, -3.0])
self.assertAlmostEqualLists(list(kvxopt.div(a, b)),
[1.0 / 3.0, -1.0, -3.0])
self.assertAlmostEqual(kvxopt.div([1.0, 2.0, 0.25]), 2.0)
self.assertEqualLists(list(kvxopt.min(a, b)), [1.0, -2.0, -1.0])
self.assertEqualLists(list(kvxopt.max(a, b)), [3.0, 2.0, 3.0])
self.assertEqual(kvxopt.max([1.0, 2.0]), 2.0)
self.assertEqual(kvxopt.max(a), 3.0)
self.assertEqual(kvxopt.max(c), 3.0)
self.assertEqual(kvxopt.max(d), 5.0)
self.assertEqual(kvxopt.min([1.0, 2.0]), 1.0)
self.assertEqual(kvxopt.min(a), 1.0)
self.assertEqual(kvxopt.min(c), -2.0)
self.assertEqual(kvxopt.min(d), 1.0)
self.assertEqual(len(c.imag()), 0)
with self.assertRaises(OverflowError):
kvxopt.matrix(1.0, (32780 * 4, 32780))
with self.assertRaises(OverflowError):
kvxopt.spmatrix(1.0, (0, 32780 * 4), (0, 32780)) + 1
def F(x=None, z=None):
if x is None: return 5, matrix(17 * [0.0] + 5 * [1.0])
if min(x[17:]) <= 0.0: return None
f = -x[12:17] + div(Amin, x[17:])
Df = matrix(0.0, (5, 22))
Df[:, 12:17] = spmatrix(-1.0, range(5), range(5))
Df[:, 17:] = spmatrix(-div(Amin, x[17:]**2), range(5), range(5))
if z is None: return f, Df
H = spmatrix(2.0 * mul(z, div(Amin, x[17::]**3)), range(17, 22),
range(17, 22))
return f, Df, H
def test_print(self):
from kvxopt import printing, matrix, spmatrix
printing.options['height'] = 2
A = spmatrix(1.0, range(3), range(3), tc='d')
print(printing.matrix_repr_default(matrix(A)))
print(printing.matrix_str_default(matrix(A)))
print(printing.spmatrix_repr_default(A))
print(printing.spmatrix_str_default(A))
print(printing.spmatrix_str_triplet(A))
A = spmatrix(1.0, range(3), range(3), tc='z')
print(printing.matrix_repr_default(matrix(A)))
print(printing.matrix_str_default(matrix(A)))
print(printing.spmatrix_repr_default(A))
print(printing.spmatrix_str_default(A))
print(printing.spmatrix_str_triplet(A))
A = spmatrix([], [], [], (3, 3))
print(printing.spmatrix_repr_default(A))
print(printing.spmatrix_str_default(A))
print(printing.spmatrix_str_triplet(A))
def read_mtx(self):
from kvxopt import spmatrix
fn = path.join(path.dirname(path.realpath(__file__)), self._matx_fn)
with open(fn, 'r') as fd:
size = None
for row in fd.readlines():
if row.startswith('%'):
continue
elif not size:
size = list(map(int, row.split(' ')))
I = [None] * size[2]
J = [None] * size[2]
V = [None] * size[2]
i = 0
continue
val = row.split(' ')
I[i] = int(val[0]) - 1
J[i] = int(val[1]) - 1
V[i] = float(val[2])
i += 1
return spmatrix(V, I, J, (size[0], size[1]))
def covsel(Y):
"""
Returns the solution of
minimize -log det K + tr(KY)
subject to K_ij = 0 if (i,j) not in zip(I, J).
Y is a symmetric sparse matrix with nonzero diagonal elements.
I = Y.I, J = Y.J.
"""
cholmod.options['supernodal'] = 2
I, J = Y.I, Y.J
n, m = Y.size[0], len(I)
# non-zero positions for one-argument indexing
N = I + J*n
# position of diagonal elements
D = [ k for k in range(m) if I[k]==J[k] ]
# starting point: symmetric identity with nonzero pattern I,J
K = spmatrix(0.0, I, J)
K[::n+1] = 1.0
# Kn is used in the line search
Kn = spmatrix(0.0, I, J)
# symbolic factorization of K
F = cholmod.symbolic(K)
# Kinv will be the inverse of K
Kinv = matrix(0.0, (n,n))
for iters in range(100):
# numeric factorization of K
cholmod.numeric(K, F)
d = cholmod.diag(F)
# compute Kinv by solving K*X = I
Kinv[:] = 0.0
Kinv[::n+1] = 1.0
cholmod.solve(F, Kinv)
# solve Newton system
grad = 2 * (Y.V - Kinv[N])
hess = 2 * ( mul(Kinv[I,J], Kinv[J,I]) +
mul(Kinv[I,I], Kinv[J,J]) )
v = -grad
lapack.posv(hess,v)
# stopping criterion
sqntdecr = -blas.dot(grad,v)
print("Newton decrement squared:%- 7.5e" %sqntdecr)
if (sqntdecr < 1e-12):
print("number of iterations: %d" %(iters+1))
break
# line search
dx = +v
dx[D] *= 2
f = -2.0*sum(log(d)) # f = -log det K
s = 1
for lsiter in range(50):
Kn.V = K.V + s*dx
try:
cholmod.numeric(Kn, F)
except ArithmeticError:
s *= 0.5
else:
d = cholmod.diag(F)
fn = -2.0 * sum(log(d)) + 2*s*blas.dot(v,Y.V)
if (fn < f - 0.01*s*sqntdecr): break
else: s *= 0.5
K.V = Kn.V
return K
def ilp(c, G, h, A=None, b=None, I=None, taskfile=None, **kwargs):
"""
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 8.
solsta, x = ilp(c, G, h, A=None, b=None, I=None, taskfile=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.
Optionally, the interface can write a .task file, required for
support questions on the MOSEK solver.
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 the MOSEK Python API manual.
"""
with mosek.Env() as env:
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 == 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)
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 = list(h) + list(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:]
with env.Task(0, 0) as task:
task.set_Stream(mosek.streamtype.log, streamprinter)
# set MOSEK options
options = kwargs.get('options', globals()['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
list(c), # linear objective coefficients
0.0, # objective fixed value
list(aptrb),
list(aptre),
list(asub),
list(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)
if taskfile:
task.writetask(taskfile)
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 = n * [0.0]
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, taskfile=None, **kwargs):
"""
Solves a quadratic program
minimize (1/2)*x'*P*x + q'*x
subject to G*x <= h
A*x = b.
using MOSEK 8.
solsta, x, z, y = qp(P, q, G=None, h=None, A=None, b=None, taskfile=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.
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 the MOSEK Python API manual.
Optionally, the interface can write a .task file, required for
support questions on the MOSEK solver.
"""
with mosek.Env() as env:
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 == 0: raise ValueError("m + p must be greater than 0")
c = list(q)
bkc = m * [mosek.boundkey.up] + p * [mosek.boundkey.fx]
blc = m * [-inf] + [bi for bi in b]
buc = list(h) + list(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:]
with env.Task(0, 0) as task:
task.set_Stream(mosek.streamtype.log, streamprinter)
# set MOSEK options
options = kwargs.get('options', globals()['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
c, # linear objective coefficients
0.0, # objective fixed value
list(aptrb),
list(aptre),
list(asub),
list(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(list(I[tril]), list(J[tril]), list(Ps.V[tril]))
task.putobjsense(mosek.objsense.minimize)
if taskfile:
task.writetask(taskfile)
task.optimize()
task.solutionsummary(mosek.streamtype.msg)
solsta = task.getsolsta(mosek.soltype.itr)
x = n * [0.0]
task.getsolutionslice(mosek.soltype.itr, mosek.solitem.xx, 0, n, x)
x = matrix(x)
if m != 0:
z = m * [0.0]
task.getsolutionslice(mosek.soltype.itr, mosek.solitem.suc, 0,
m, z)
z = matrix(z)
else:
z = matrix(0.0, (0, 1))
if p != 0:
yu, yl = p * [0.0], p * [0.0]
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 socp(c, Gl=None, hl=None, Gq=None, hq=None, taskfile=None, **kwargs):
"""
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 8.
solsta, x, zl, zq = socp(c, Gl = None, hl = None, Gq = None, hq = None, taskfile=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.
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 the MOSEK Python API manual.
Optionally, the interface can write a .task file, required for
support questions on the MOSEK solver.
"""
with mosek.Env() as env:
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 = list(-c)
buc = list(-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:]
with env.Task(0, 0) as task:
task.set_Stream(mosek.streamtype.log, streamprinter)
# set MOSEK options
options = kwargs.get('options', globals()['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
list(c), # linear objective coefficients
0.0, # objective fixed value
list(aptrb),
list(aptre),
list(asub),
list(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,
list(range(ml + sum(mq[:k]), ml + sum(mq[:k + 1]))))
if taskfile:
task.writetask(taskfile)
task.optimize()
task.solutionsummary(mosek.streamtype.msg)
solsta = task.getsolsta(mosek.soltype.itr)
xu, xl, zq = n * [0.0], n * [0.0], sum(mq) * [0.0]
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 = ml * [0.0]
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 lp(c, G, h, A=None, b=None, taskfile=None, **kwargs):
"""
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 8.
(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.
Optionally, the interface can write a .task file, required for
support questions on the MOSEK solver.
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.
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 the MOSEK Python API manual.
"""
with mosek.Env() as env:
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 == 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 = list(h) + list(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:]
with env.Task(0, 0) as task:
task.set_Stream(mosek.streamtype.log, streamprinter)
# set MOSEK options
options = kwargs.get('options', globals()['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
list(c), # linear objective coefficients
0.0, # objective fixed value
list(aptrb),
list(aptre),
list(asub),
list(acof),
bkc,
blc,
buc,
bkx,
blx,
bux)
task.putobjsense(mosek.objsense.minimize)
if taskfile:
task.writetask(taskfile)
task.optimize()
task.solutionsummary(mosek.streamtype.msg)
solsta = task.getsolsta(mosek.soltype.bas)
x, z = n * [0.0], m * [0.0]
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 != 0:
yu, yl = p * [0.0], p * [0.0]
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)