def grad_dense(R_hat, U_hat, rows, cols, D, P):
X = build_dense(D, P, rows, cols)
W = la.inv(X)
# print 'W eis:', (min(la.eigvalsh(W)),max(la.eigvalsh(W)))
R = W.diagonal()
U = W[rows, cols]
return (-R + R_hat, 2 * (-U + U_hat))
def hessian_dir_dense(R_hat, U_hat, rows, cols, D, P):
""" Newton step seems to work now?
"""
X = build_dense(D, P, rows, cols)
W = la.inv(X)
n = len(D)
A = n * np.arange(n) + np.arange(n)
B = n * rows + cols
K = np.kron(W, W)
# todo: finish here
H = np.vstack(
(np.hstack((K[np.ix_(A, A)], 2 * K[np.ix_(A, B)])), np.hstack((2 * K[np.ix_(A, B)].T, 4 * K[np.ix_(B, B)])))
)
(g_D, g_P) = grad_dense(R_hat, U_hat, rows, cols, D, P)
g = np.hstack((g_D, g_P))
v = la.solve(H, g)
v_D = v[:n]
v_P = v[n:]
return (-v_D, -v_P)
def covsel_quick(R,U,rows,cols,lbda=1e6):
min_ei = smallest_ev_arpack(R, U, rows, cols)
if min_ei < 0:
print "min_ei is %f"%min_ei
R0 = R - min_ei + 1e-3
else:
R0 = R
n = len(R)
m = len(U)
S = build_dense(R0, U, rows, cols)
L=lbda * np.ones((n,n),dtype=np.double)
L[np.arange(n),np.arange(n)] = 0
L[rows,cols]=0
L[cols,rows]=0
(X_, W_, opt, time) = run_quic(S, L)
D = X_.diagonal()
P = X_[rows,cols]
R2 = W_.diagonal()
U2 = W_[rows,cols]
print "Quic: Error is %f diag, %f outer"%(linalg.norm(R0-R2),linalg.norm(U-U2))
return (D,P)
def is_psd_dense(R,U,rows,cols,tolerance=1e-4): """ Simple check using dense matrices. """ X = build_dense(R, U, rows, cols) return np.all(linalg.eigvalsh(X)>tolerance)
from mm.arterial_hkt.gmrf_learning.cvx import run_cvx_dense, covsel_cvx_dense,\ covsel_cvx_cholmod from mm.arterial_hkt.gmrf_learning.quic_cpp.low_rank import random_projection_cholmod,\ random_projection_cholmod_csc from scikits.sparse.cholmod import analyze def star(n,diag): m = n-1 D = diag*np.ones(n,dtype=np.double)+np.arange(n)/float(n) P = np.arange(m)/float(m)+1 rows = np.zeros((n-1,),dtype=np.int) cols = np.arange(1,n,dtype=np.int) return (D,P,rows,cols) (D,P,rows,cols) = star(5,4) X = build_dense(D, P, rows, cols) Xs = build_sparse(D, P, rows, cols) l1 = logdet_dense(D, P, rows, cols) l2 = logdet_dense_chol(D, P, rows, cols) l3 = logdet_cholmod(D, P, rows, cols) (M,Dn,Pn) = normalized_problem(D, P, rows, cols) test_data(D, P, rows, cols) W = la.inv(X) #Q = random_projection_cholmod(D, U, rows, cols, k, factor) Q = random_projection_cholmod_csc(Xs, k=1000) A = Q.T print A.shape R = np.sum(A*A,axis=1)
def inv_dense(R,U,rows,cols): X = build_dense(R, U, rows, cols) Y = linalg.inv(X) D = Y.diagonal() P = Y[rows,cols] return (D,P)
def logdet_dense_chol(R,U,rows,cols):
if not is_psd_dense(R, U, rows, cols):
return -np.Inf
X = build_dense(R, U, rows, cols)
C = linalg.cholesky(X).diagonal()
return np.sum(np.log(C))*2
def logdet_dense(R,U,rows,cols):
if not is_psd_dense(R, U, rows, cols):
return -np.Inf
X = build_dense(R, U, rows, cols)
eis = linalg.eigvalsh(X)
return np.sum(np.log(eis))
