def test_projected_inverse(self):
Y = cp.cspmatrix(self.symb) + self.A
Am = Y.spmatrix(symmetric=True,reordered=False)
cp.cholesky(Y)
cp.projected_inverse(Y)
Ym = Y.spmatrix(symmetric=True,reordered=False)
self.assertAlmostEqual((Ym.V.T*(Am.V))[0], self.symb.n)
def test_projected_inverse(self):
Y = cp.cspmatrix(self.symb) + self.A
Am = Y.spmatrix(symmetric=True, reordered=False)
cp.cholesky(Y)
cp.projected_inverse(Y)
Ym = Y.spmatrix(symmetric=True, reordered=False)
self.assertAlmostEqual((Ym.V.T * (Am.V))[0], self.symb.n)
def test_completion_fu(self):
L = cp.cspmatrix(self.symb) + self.A
cp.cholesky(L)
L2 = L.copy()
cp.projected_inverse(L2)
cp.completion(L2, factored_updates = True)
diff = list((L.spmatrix()-L2.spmatrix()).V)
self.assertAlmostEqualLists(diff, len(diff)*[0.0])
def test_completion_fu(self):
L = cp.cspmatrix(self.symb) + self.A
cp.cholesky(L)
L2 = L.copy()
cp.projected_inverse(L2)
cp.completion(L2, factored_updates=True)
diff = list((L.spmatrix() - L2.spmatrix()).V)
self.assertAlmostEqualLists(diff, len(diff) * [0.0])
def test_hessian_fu(self):
L = cp.cspmatrix(self.symb) + self.A
cp.cholesky(L)
Y = L.copy()
cp.projected_inverse(Y)
U = cp.cspmatrix(self.symb) + 0.1*self.A
cp.hessian(L, Y, U, adj = False, inv = False, factored_updates = True)
cp.hessian(L, Y, U, adj = True, inv = False, factored_updates = True)
cp.hessian(L, Y, U, adj = True, inv = True, factored_updates = True)
cp.hessian(L, Y, U, adj = False, inv = True, factored_updates = True)
diff = list((0.1*self.A-U.spmatrix(reordered=False,symmetric=False)).V)
self.assertAlmostEqualLists(diff, len(diff)*[0.0])
def test_hessian_fu(self):
L = cp.cspmatrix(self.symb) + self.A
cp.cholesky(L)
Y = L.copy()
cp.projected_inverse(Y)
U = cp.cspmatrix(self.symb) + 0.1 * self.A
cp.hessian(L, Y, U, adj=False, inv=False, factored_updates=True)
cp.hessian(L, Y, U, adj=True, inv=False, factored_updates=True)
cp.hessian(L, Y, U, adj=True, inv=True, factored_updates=True)
cp.hessian(L, Y, U, adj=False, inv=True, factored_updates=True)
diff = list(
(0.1 * self.A - U.spmatrix(reordered=False, symmetric=False)).V)
self.assertAlmostEqualLists(diff, len(diff) * [0.0])
print("Largest clique : %i\n" % (symb.clique_number))
A = cspmatrix(symb) # create new cspmatrix from symbolic factorization
A += As # add spmatrix 'As' to cspmatrix 'A'; this ignores the upper triangular entries in As
print("Computing Cholesky factorization..")
L = A.copy() # make a copy of A
cholesky(L) # compute Cholesky factorization; overwrites L
print("Computing Cholesky product..")
At = L.copy() # make a copy of L
llt(At) # compute Cholesky product; overwrites At
print("Computing projected inverse..")
Y = L.copy() # make a copy of L
projected_inverse(Y) # compute projected inverse; overwrites Y
print("Computing completion..")
Lc = Y.copy() # make a copy of Y
completion(Lc, factored_updates = False) # compute completion; overwrites Lc
print("Computing completion with factored updates..")
Lc2 = Y.copy() # make a copy of Y
completion(Lc2, factored_updates = True) # compute completion (with factored updates); overwrites Lc2
print("Applying Hessian factors..")
U = At.copy()
fupd = False
hessian(L, Y, U, adj = False, inv = False, factored_updates = fupd)
hessian(L, Y, U, adj = True, inv = False, factored_updates = fupd)
hessian(L, Y, U, adj = True, inv = True, factored_updates = fupd)