def __init__(self,x,y,λ=0.1,W=None):
# W = list of matricies
n = x.shape[0]
m = y.shape[0]
q = x.shape[1]
assert y.shape[1] == q
Q = zeros(m*n,m*n)
c = zeros(m*n)
for i in range(q):
if W is None:
Q += np.kron(eye(m), x[:,i] * x[:,i].T)
c += np.kron(eye(m), x[:,i]) *y[:,i]
else:
Q += np.kron(eye(m), x[:,i] * W[i].T * W[i]* x[:,i].T)
c += np.kron(eye(m), x[:,i]) * W[i].T * W[i] * y[:,i]
Q *= 2
c *= -2
vec_A = norm.linear_QP_reg_l_1( Q, c ).solve()
A = mat( vec_A, m, n )
t = np.mean(np.abs(vec_A))
for i in range(m):
for j in range(n):
if abs(A[i,j]) < t:
A[i,j] = 0
self.A = sparse(A)
def __init__(self,A, λ = 0.1):
m = A.shape[0]
n = A.shape[1]
x = norm.linear_l_p_reg_q( np.kron(eye(n),A.T), vec(eye(n)), λ, 2, 1).solve()
mu = np.mean(x)
for i in range(len(x)):
if abs(x[i]) < mu:
x[i]=0
self.pinv_A = mat(x,n,m)
self.spinv_A = sparse(self.pinv_A)
def __init__(self,s):
"""
x ∈ R^n
"""
s = sampled_convex_set.remove_interior_points(s)
n = s.shape[0]
m = s.shape[1]
A_ub = np.bmat([[zeros(m,n),-eye(m)],[zeros(m,n),eye(m)]])
b_ub = np.bmat([[zeros(m)],[ones(m)]])
A_eq = np.bmat([[-eye(n),s],[zeros(1,n),ones(1,m)]])
b_eq = np.bmat([[zeros(n)],[ones(1)]])
self.P = poly(A_ub,b_ub,A_eq,b_eq)
def __init__(self, P1, P2, q):
n = P1.n
assert P2.n is n
A = np.bmat([[eye(n),-eye(n)]])
b = zeros(n,1)
P = poly.diag(P1,P2)
if q is 1:
self.problem = norm.linear_l_1(A,b,P)
elif q is 2:
self.problem = norm.linear_l_2(A,b,P)
elif q is 'inf':
self.problem = norm.linear_l_inf(A,b,P)
else:
assert False, "q must be 1, 2, or \'inf\'"
self.P1 = P1
self.P2 = P2
self.P = P
self.n = n
self.q = q
self.sol = None
def full_rank_right_pseudo_inverse(self, A, b):
"""
min J = f( A x - b ) 🠊 min J = f( A y )
x ∈ R^n y ∈ R^n
s.t. x ∈ POLYHEDRON_self s.t. y ∈ POLYHEDRON_out
y + A^+ b ∈ POLYHEDRON_self 🠊 y ∈ POLYHEDRON_out
"""
m = A.shape[0]
n = A.shape[1]
if is_full_rank(A) and min(m, n) is m:
return self.affine_transform(eye(n), pinv(A) * b)
else:
print("warning: full_rank_right_pseudo_inverse")
return None
def init_E(EA, Ex, Eb, EAx, EAoA, EAox, EAoAx, EAob, W, m ,n):
if W is None:
M = eye(m)
else:
M = W.T * W
if EA is None:
EA = zeros(m,n)
if Ex is None:
Ex = zeros(n,1)
if Eb is None:
Eb = zeros(m,1)
if EAx is None:
EAx = zeros(m,1)
if EAoA is None:
EAoA = zeros(m*m,n*n)
if EAox is None:
EAox = zeros(m*n,n*1)
if EAoAx is None:
EAoAx = zeros(m*m,n*1)
if EAob is None:
EAob = zeros(m*m,n*1)
return (EA, Ex, Eb, EAx, EAoA, EAox, EAoAx, EAob, M)
def dz_j_dvec_A_j(self, j):
return self.Ds(self.A[j]*self.z[j-1]-self.b[j])\
* np.kron( eye(self.m[j]), self.z[j-1].T )
def test():
P1 = poly.rand(2,4,0,1).affine_transform(eye(2),2*ones(2,1))
P2 = poly.rand(2,4,0,1).affine_transform(eye(2),-2*ones(2,1))
problem = interset(P1,P2,2)
problem.solve()
print(problem)
