def projection_solver(M, constraints, rank=2, maxiter=100, tol=1e-6):
"""
does projection, so that L.T L is closest to M(y)
and y is the projection of cloest to L.T L what satisfies the contraints
any fixed point is a valid solution
"""
lenys = len(M.matrix_monos)
rowsM = len(M.row_monos)
lenLs = rank*rowsM
L = np.random.randn(rank, len(M.row_monos))
L = np.array([[1,1,1,1],[1,2,4,8]])/np.sqrt(2) + np.random.randn(2,4)*0.3
Bf = M.get_Bflat()
A,b = M.get_Ab(constraints, cvxoptmode = False)
weightone = 1
A = A*weightone; b = b*weightone
for i in xrange(maxiter):
yL = Bf.dot(L.T.dot(L).flatten()[:, np.newaxis])/np.sum(Bf,1)[:,np.newaxis]
y = util.project_nullspace(A,b,yL, randomize =0/np.sqrt(i+100))
My = M.numeric_instance(y)
objyconstrs = scipy.linalg.norm(L.T.dot(L) - M.numeric_instance(y)) + scipy.linalg.norm(A.dot(y)-b)
U,D,V=scipy.linalg.svd(My)
L = V[0:rank,:]*np.sqrt(D[0:rank, np.newaxis])
objprojL = scipy.linalg.norm(L.T.dot(L) - M.numeric_instance(y)) + scipy.linalg.norm(A.dot(y)-b)
print '%d:\t%f\t%f' % (i, objyconstrs, objprojL)
if objprojL < tol:
break
return y,L
def convex_projection_solver(M, constraints, rank=2, tau=1, delta = 0.1, maxiter=100, tol=1e-6):
"""
does projection, so that L.T L is closest to M(y)
and y is the projection of cloest to L.T L what satisfies the contraints
any fixed point is a valid solution
"""
lenys = len(M.matrix_monos)
rowsM = len(M.row_monos)
lenLs = rank*rowsM
Bf = M.get_Bflat()
A,b = M.get_Ab(constraints, cvxoptmode = False)
weightone = 1
A = A*weightone; b = b*weightone
X = np.random.randn(rowsM, rowsM)
for i in xrange(maxiter):
yX = Bf.dot(X.flatten()[:, np.newaxis])/np.sum(Bf,1)[:,np.newaxis]
yproj = util.project_nullspace(A,b,yX, randomize =0)
y = yproj #yX + delta*(yproj - yX)
My = M.numeric_instance(y)
objyconstrs = scipy.linalg.norm(X- M.numeric_instance(y)) + scipy.linalg.norm(A.dot(y)-b)
U,D,V=scipy.linalg.svd(My)
D = np.fmax(D - tau, 0)
X = U.dot(np.diag(D)).dot(V)
objprojL = scipy.linalg.norm(X - M.numeric_instance(y)) + scipy.linalg.norm(A.dot(y)-b)
print '%d:\t%f\t%f' % (i, objyconstrs, objprojL)
if objprojL < tol:
break
return y,X
