def setup_solver_cvx(self):
c = self.constvars
imagedims = c['imagedims']
n_image = c['n_image']
d_image = c['d_image']
l_labels = c['l_labels']
l_shm = c['l_shm']
self.cvx_x = Variable(
('p', (l_shm, d_image, n_image)),
('q0', (n_image, )),
('q1', (l_labels, n_image)),
('q2', (l_labels, n_image)),
)
self.cvx_y = Variable(
('u1', (n_image, l_labels)),
('v', (n_image, l_shm)),
('misc', (n_image, )),
)
p, q0, q1, q2 = [cvxVariable(*a['shape']) for a in self.cvx_x.vars()]
self.cvx_vars = p + [q0, q1, q2]
fid_fun_dual = 0
for i in range(n_image):
for k in range(l_labels):
fid_fun_dual += -1.0/c['b'][k]*(cvx.power(q2[k,i],2)/2 \
+ cvx.maximum(q2[k,i]*c['b'][k]*c['f1'][i,k],
q2[k,i]*c['b'][k]*c['f2'][i,k]))
self.cvx_obj = cvx.Maximize(fid_fun_dual - cvx.sum(q0))
div_op = sparse_div_op(imagedims)
self.cvx_dual = True
self.cvx_constr = []
# u1_constr
for i in range(n_image):
self.cvx_constr.append(c['b'] * q0[i] - q1[:, i] >= 0)
# v_constr
for i in range(n_image):
for k in range(l_shm):
Yk = cvx.vec(c['Y'][:, k])
self.cvx_constr.append(
Yk.T*(c['M'][k]*q2[:,i] + q1[:,i]) \
- cvxOp(div_op, p[k], i) == 0)
# additional inequality constraints
for i in range(n_image):
self.cvx_constr.append(sum(cvx.sum_squares(p[k][:,i]) \
for k in range(l_shm)) <= c['lbd']**2)
def setup_solver_cvx(self):
c = self.constvars
imagedims = c['imagedims']
n_image = c['n_image']
d_image = c['d_image']
l_labels = c['l_labels']
m_gradients = c['m_gradients']
s_manifold = c['s_manifold']
l_shm = c['l_shm']
self.cvx_x = Variable(
('p', (l_shm, d_image, n_image)),
('g', (n_image, m_gradients, s_manifold, d_image)),
('q0', (n_image, )),
('q1', (l_labels, n_image)),
('q2', (l_labels, n_image)),
)
self.cvx_y = Variable(
('u1', (n_image, l_labels)),
('v', (n_image, l_shm)),
('w', (m_gradients, n_image, d_image, s_manifold)),
('misc', (n_image * m_gradients, )),
)
p, g, q0, q1, q2 = [
cvxVariable(*a['shape']) for a in self.cvx_x.vars()
]
self.cvx_vars = p + sum(g, []) + [q0, q1, q2]
self.cvx_obj = cvx.Maximize(
0.5 * cvx.sum(cvx.diag(c['b']) * cvx.square(c['f'].T)) -
0.5 * cvx.sum(
cvx.diag(1.0 / c['b']) *
cvx.square(q2 + cvx.diag(c['b']) * c['f'].T)) - cvx.sum(q0))
div_op = sparse_div_op(imagedims)
self.cvx_dual = True
self.cvx_constr = []
# u1_constr
for i in range(n_image):
self.cvx_constr.append(c['b'] * q0[i] - q1[:, i] >= 0)
# v_constr
for i in range(n_image):
for k in range(l_shm):
Yk = cvx.vec(c['Y'][:, k])
self.cvx_constr.append(
Yk.T*(c['M'][k]*q2[:,i] + q1[:,i]) \
- cvxOp(div_op, p[k], i) == 0)
# w_constr
for j in range(m_gradients):
Gj = c['G'][j, :, :]
for i in range(n_image):
for t in range(d_image):
for l in range(s_manifold):
self.cvx_constr.append(
g[i][j][l,t] == sum([Gj[l,k]*p[k][t,i] \
for k in range(l_shm)]))
# additional inequality constraints
for i in range(n_image):
for j in range(m_gradients):
self.cvx_constr.append(cvx.norm(g[i][j], 2) <= c['lbd'])
def setup_solver_cvx(self):
c = self.constvars
imagedims = c['imagedims']
n_image = c['n_image']
d_image = c['d_image']
l_labels = c['l_labels']
m_gradients = c['m_gradients']
s_manifold = c['s_manifold']
l_shm = c['l_shm']
self.cvx_x = Variable(
('p', (l_labels, d_image, n_image)),
('g', (n_image, m_gradients, s_manifold, d_image)),
('q0', (n_image, )),
('q1', (l_labels, n_image)),
('q2', (l_labels, n_image)),
)
self.cvx_y = Variable(
('u1', (n_image, l_labels)),
('v', (n_image, l_shm)),
('w', (m_gradients, n_image, d_image, s_manifold)),
('misc', (n_image * m_gradients, )),
)
p, g, q0, q1, q2 = [
cvxVariable(*a['shape']) for a in self.cvx_x.vars()
]
self.cvx_vars = p + sum(g, []) + [q0, q1, q2]
fid_fun_dual = 0
for i in range(n_image):
for k in range(l_labels):
fid_fun_dual += -cvx.power(q2[k,i],2)/2 \
- cvx.maximum(q2[k,i]*c['f1'][i,k],
q2[k,i]*c['f2'][i,k])
self.cvx_obj = cvx.Maximize(fid_fun_dual - cvx.sum(q0))
div_op = sparse_div_op(imagedims)
self.cvx_dual = True
self.cvx_constr = []
# u1_constr
for i in range(n_image):
for k in range(l_labels):
self.cvx_constr.append(
c['b'][k] *
(q0[i] - cvxOp(div_op, p[k], i)) - q1[k, i] >= 0)
# v_constr
for i in range(n_image):
for k in range(l_shm):
Yk = cvx.vec(c['Y'][:, k])
self.cvx_constr.append(Yk.T *
(c['M'][k] * q2[:, i] + q1[:, i]) == 0)
# w_constr
for j in range(m_gradients):
Aj = c['A'][j, :, :]
Bj = c['B'][j, :, :]
Pj = c['P'][j, :]
for i in range(n_image):
for t in range(d_image):
for l in range(s_manifold):
self.cvx_constr.append(Aj * g[i][j][l, t] == sum(
[Bj[l, m] * p[Pj[m]][t, i] for m in range(3)]))
# additional inequality constraints
for i in range(n_image):
for j in range(m_gradients):
self.cvx_constr.append(cvx.norm(g[i][j], 2) <= c['lbd'])
def setup_solver_cvx(self):
c = self.constvars
imagedims = c['imagedims']
n_image = c['n_image']
d_image = c['d_image']
l_labels = c['l_labels']
l_shm = c['l_shm']
self.cvx_x = Variable(
('p', (l_shm, d_image, n_image)),
('q0', (n_image, )),
('q1', (l_labels, n_image)),
('q2', (l_labels, n_image)),
('q3', (l_labels, n_image)),
('q4', (l_labels, n_image)),
)
self.cvx_y = Variable(
('u1', (n_image, l_labels)),
('v', (n_image, l_shm)),
('misc', (n_image * l_labels * 5 + n_image, )),
)
p, q0, q1, q2, q3, q4 = [
cvxVariable(*a['shape']) for a in self.cvx_x.vars()
]
self.cvx_vars = p + [q0, q1, q2, q3, q4]
self.cvx_obj = cvx.Maximize(
cvx.vec(q3).T * cvx.vec(cvx.diag(c['b']) * c['f1'].T) -
cvx.vec(q4).T * cvx.vec(cvx.diag(c['b']) * c['f2'].T) -
cvx.sum(q0))
div_op = sparse_div_op(imagedims)
self.cvx_dual = True
self.cvx_constr = []
# u1_constr
for i in range(n_image):
self.cvx_constr.append(c['b'][:] * q0[i] - q1[:, i] >= 0)
# v_constr
for i in range(n_image):
for k in range(l_shm):
Yk = cvx.vec(c['Y'][:, k])
self.cvx_constr.append(
Yk.T*(c['M'][k]*q2[:,i] + q1[:,i]) \
- cvxOp(div_op, p[k], i) == 0)
# additional inequality constraints
for i in range(n_image):
for k in range(l_labels):
self.cvx_constr.append(0 <= q3[k, i])
self.cvx_constr.append(q3[k, i] <= 1)
self.cvx_constr.append(0 <= q4[k, i])
self.cvx_constr.append(q4[k, i] <= 1)
self.cvx_constr.append(q4[k, i] - q3[k, i] - q2[k, i] == 0)
for i in range(n_image):
self.cvx_constr.append(sum(cvx.sum_squares(p[k][:,i]) \
for k in range(l_shm)) <= c['lbd']**2)
def setup_solver_cvx(self):
if self.dataterm != "W1":
raise Exception("Only W1 dataterm is implemented in CVX")
c = self.constvars
imagedims = c['imagedims']
n_image = c['n_image']
d_image = c['d_image']
l_labels = c['l_labels']
m_gradients = c['m_gradients']
s_manifold = c['s_manifold']
l_shm = c['l_shm']
f_flat = self.data.odf.reshape(-1, l_labels).T
f = np.array(f_flat.reshape((l_labels, ) + imagedims), order='C')
normalize_odf(f, c['b'])
f_flat = f.reshape(l_labels, n_image)
self.cvx_x = Variable(
('p', (l_labels, d_image, n_image)),
('g', (n_image, m_gradients, s_manifold, d_image)),
('q0', (n_image, )),
('q1', (l_labels, n_image)),
('p0', (l_labels, n_image)),
('g0', (n_image, m_gradients, s_manifold)),
)
self.cvx_y = Variable(
('u', (n_image, l_labels)),
('v', (n_image, l_shm)),
('w', (m_gradients, n_image, d_image, s_manifold)),
('w0', (m_gradients, n_image, s_manifold)),
('misc', (n_image * m_gradients, )),
)
p, g, q0, q1, p0, g0 = [
cvxVariable(*a['shape']) for a in self.cvx_x.vars()
]
self.cvx_vars = p + sum(g, []) + [q0, q1, p0] + g0
self.cvx_obj = cvx.Maximize(-cvx.vec(f_flat).T *
cvx.vec(cvx.diag(c['b']) * p0) -
cvx.sum(q0))
div_op = sparse_div_op(imagedims)
self.cvx_dual = True
self.cvx_constr = []
# u_constr
for i in range(n_image):
for k in range(l_labels):
self.cvx_constr.append(
c['b'][k]*(q0[i] + p0[k,i] \
- cvxOp(div_op, p[k], i)) - q1[k,i] >= 0)
# v_constr
for i in range(n_image):
for k in range(l_shm):
Yk = cvx.vec(c['Y'][:, k])
self.cvx_constr.append(-Yk.T * q1[:, i] == 0)
# w_constr
for j in range(m_gradients):
Aj = c['A'][j, :, :]
Bj = c['B'][j, :, :]
Pj = c['P'][j, :]
for i in range(n_image):
for t in range(d_image):
for l in range(s_manifold):
self.cvx_constr.append(
Aj*g[i][j][l,t] == sum([Bj[l,m]*p[Pj[m]][t,i] \
for m in range(3)]))
# w0_constr
for j in range(m_gradients):
Aj = c['A'][j, :, :]
Bj = c['B'][j, :, :]
Pj = c['P'][j, :]
for i in range(n_image):
self.cvx_constr.append(Aj * g0[i][j, :].T == Bj * p0[Pj, i])
# additional inequality constraints
for i in range(n_image):
for j in range(m_gradients):
self.cvx_constr.append(cvx.norm(g[i][j], 2) <= c['lbd'])
self.cvx_constr.append(cvx.norm(g0[i][j, :], 2) <= 1.0)