def test_union(self):
self.message("Sparsity union")
nza = set([ (0,0),
(0,1),
(2,0),
(3,1)])
nzb = set([ (0,2),
(0,0),
(2,2)])
a = Sparsity(4,5)
for i in nza:
a.addNZ(i[0],i[1])
b = Sparsity(4,5)
for i in nzb:
b.addNZ(i[0],i[1])
c,w =a.patternUnion(b)
self.assertEquals(len(w),len(nza.union(nzb)))
for k in range(len(w)):
ind = (c.row(k),c.getCol()[k])
if (ind in nza and ind in nzb):
self.assertEquals(w[k],1 | 2)
elif (ind in nza):
self.assertEquals(w[k],1)
elif (ind in nzb):
self.assertEquals(w[k],2)
c = a + b
self.assertEquals(c.nnz(),len(nza.union(nzb)))
for k in range(c.nnz()):
ind = (c.row(k),c.getCol()[k])
self.assertTrue(ind in nza or ind in nzb)
def test_intersection(self):
self.message("Sparsity intersection")
nza = set([ (0,0),
(0,1),
(2,0),
(3,1),
(2,3)])
nzb = set([ (0,2),
(0,0),
(2,2),
(2,3)])
a = Sparsity(4,5)
for i in nza:
a.add_nz(i[0],i[1])
b = Sparsity(4,5)
for i in nzb:
b.add_nz(i[0],i[1])
c=a.intersect(b)
for k in range(c.nnz()):
ind = (c.row(k),c.get_col()[k])
self.assertTrue(ind in nza and ind in nzb)
c = a * b
self.assertEqual(c.nnz(),len(nza.intersection(nzb)))
for k in range(c.nnz()):
ind = (c.row(k),c.get_col()[k])
self.assertTrue(ind in nza and ind in nzb)
def test_intersection(self):
self.message("Sparsity intersection")
nza = set([ (0,0),
(0,1),
(2,0),
(3,1),
(2,3)])
nzb = set([ (0,2),
(0,0),
(2,2),
(2,3)])
a = Sparsity(4,5)
for i in nza:
a.add_nz(i[0],i[1])
b = Sparsity(4,5)
for i in nzb:
b.add_nz(i[0],i[1])
c=a.intersect(b)
for k in range(c.nnz()):
ind = (c.row(k),c.get_col()[k])
self.assertTrue(ind in nza and ind in nzb)
c = a * b
self.assertEqual(c.nnz(),len(nza.intersection(nzb)))
for k in range(c.nnz()):
ind = (c.row(k),c.get_col()[k])
self.assertTrue(ind in nza and ind in nzb)
def test_union(self):
self.message("Sparsity union")
nza = set([ (0,0),
(0,1),
(2,0),
(3,1)])
nzb = set([ (0,2),
(0,0),
(2,2)])
a = Sparsity(4,5)
for i in nza:
a.add_nz(i[0],i[1])
b = Sparsity(4,5)
for i in nzb:
b.add_nz(i[0],i[1])
c =a.unite(b)
c = a + b
self.assertEquals(c.nnz(),len(nza.union(nzb)))
for k in range(c.nnz()):
ind = (c.row(k),c.get_col()[k])
self.assertTrue(ind in nza or ind in nzb)
def test_sparsity_operation(self):
L = [DM(1), DM(Sparsity(1,1),1), DM(Sparsity(2,1),1), DM(Sparsity.dense(2,1),1)]
for a in L:
for b in L:
c = a*b
if a.nnz()==0 or b.nnz()==0:
self.assertTrue(c.nnz()==0)
else:
self.assertTrue(c.nnz()>0)
self.assertTrue(sum2(IM(Sparsity(1,1),1)).nnz()==0)
def test_sparsity_operation(self):
L = [DM(1), DM(Sparsity(1,1),1), DM(Sparsity(2,1),1), DM(Sparsity.dense(2,1),1)]
for a in L:
for b in L:
c = a*b
if a.nnz()==0 or b.nnz()==0:
self.assertTrue(c.nnz()==0)
else:
self.assertTrue(c.nnz()>0)
self.assertTrue(sum2(IM(Sparsity(1,1),1)).nnz()==0)
def test_mxnull(self):
a = SX(5,0)
b = SX(0,3)
c = mtimes(a,b)
self.assertEqual(c.nnz(),0)
a = SX(5,3)
b = SX(3,4)
c = mtimes(a,b)
self.assertEqual(c.nnz(),0)
def test_mxnull(self):
a = SX(5,0)
b = SX(0,3)
c = mtimes(a,b)
self.assertEqual(c.nnz(),0)
a = SX(5,3)
b = SX(3,4)
c = mtimes(a,b)
self.assertEqual(c.nnz(),0)
def test_union(self):
self.message("Sparsity union")
nza = set([(0, 0), (0, 1), (2, 0), (3, 1)])
nzb = set([(0, 2), (0, 0), (2, 2)])
a = Sparsity(4, 5)
for i in nza:
a.add_nz(i[0], i[1])
b = Sparsity(4, 5)
for i in nzb:
b.add_nz(i[0], i[1])
c = a.unite(b)
c = a + b
self.assertEquals(c.nnz(), len(nza.union(nzb)))
for k in range(c.nnz()):
ind = (c.row(k), c.get_col()[k])
self.assertTrue(ind in nza or ind in nzb)
def test_example1(self):
self.message("Example1")
# Originates from http://sdpa.indsys.chuo-u.ac.jp/sdpa/files/sdpa-c.6.2.0.manual.pdf
c = DMatrix([48, -8, 20])
A = DMatrix(0, 3)
Fi = [-DMatrix([[10, 4], [4, 0]]), -DMatrix([[0, 0], [0, -8]]), -DMatrix([[0, -8], [-8, -2]])]
F = horzcat(Fi)
F = sparsify(F)
print F
G = -DMatrix([[-11, 0], [0, 23]])
G = sparsify(G)
for sdpsolver, sdp_options in sdpsolvers:
sdp = SdpSolver(sdpsolver, sdpStruct(a=A.sparsity(), g=G.sparsity(), f=F.sparsity()))
sdp.setOption(sdp_options)
sdp.init()
sdp.setInput(G, "g")
sdp.setInput(c, "c")
sdp.setInput(F, "f")
sdp.evaluate()
self.checkarray(sdp.getOutput("cost"), DMatrix(-41.9), digits=5)
self.checkarray(sdp.getOutput("dual_cost"), DMatrix(-41.9), digits=5)
self.checkarray(sdp.getOutput("x"), DMatrix([-1.1, -2.7375, -0.55]), digits=5)
self.checkarray(sdp.getOutput("dual"), DMatrix([[5.9, -1.375], [-1.375, 1]]), digits=5)
self.checkarray(sdp.getOutput("p"), DMatrix.zeros(2, 2), digits=5)
try:
NlpSolver.loadPlugin("ipopt")
except:
return
V = struct_symSX([entry("L", shape=G.shape), entry("x", shape=c.nnz())])
L = V["L"]
x = V["x"]
P = mul(L, L.T)
g = []
g.append(sum([-Fi[i] * x[i] for i in range(3)]) + G - P)
nlp = SXFunction(nlpIn(x=V), nlpOut(f=mul(c.T, x), g=veccat(g)))
sol = NlpSolver("ipopt", nlp)
sol.init()
sol.setInput(0, "lbg")
sol.setInput(0, "ubg")
V(sol.input("x0"))["x"] = -1
V(sol.input("x0"))["L"] = 0.1
sol.evaluate()
sol_ = V(sol.getOutput())
self.checkarray(sol_["x"], DMatrix([-1.1, -2.7375, -0.55]), digits=5)