def projection_cone_nosign(p, max_idx):
"""
Does not condition on sign!
Create a callable that projects onto one of two cones,
determined by which coordinate achieves the max in one
step of forward stepwise.
Parameters
----------
p : int
Dimension.
max_idx : int
Index achieving the max.
max_sign : [-1,1]
Sign of achieved max.
Returns
-------
projection : callable
A function to compute projection onto appropriate cone.
Takes one argument of shape (p,).
"""
P_plus = rr.linf_epigraph(p-1)
P_minus = rr.l1_epigraph_polar(p-1)
def _projection(state):
permuted_state = np.zeros_like(state)
permuted_state[-1] = state[max_idx]
permuted_state[:max_idx] = state[:max_idx]
permuted_state[max_idx:-1] = state[(max_idx+1):]
projected_state_plus = P_plus.cone_prox(permuted_state)
projected_state_minus = P_minus.cone_prox(permuted_state)
D_plus = np.linalg.norm(permuted_state - projected_state_plus)
D_minus = np.linalg.norm(permuted_state - projected_state_minus)
if D_plus < D_minus:
projected_state = projected_state_plus
else:
projected_state = projected_state_minus
new_state = np.zeros_like(state)
new_state[max_idx] = projected_state[-1]
new_state[:max_idx] = projected_state[:max_idx]
new_state[(max_idx+1):] = projected_state[max_idx:-1]
return new_state
return _projection
def projection_cone(p, max_idx, max_sign):
"""
Create a callable that projects onto one of two cones,
determined by which coordinate achieves the max in one
step of forward stepwise.
Parameters
----------
p : int
Dimension.
max_idx : int
Index achieving the max.
max_sign : [-1,1]
Sign of achieved max.
Returns
-------
projection : callable
A function to compute projection onto appropriate cone.
Takes one argument of shape (p,).
"""
if max_sign > 0:
P = rr.linf_epigraph(p-1)
else:
P = rr.l1_epigraph_polar(p-1)
def _projection(state):
permuted_state = np.zeros_like(state)
permuted_state[-1] = state[max_idx]
permuted_state[:max_idx] = state[:max_idx]
permuted_state[max_idx:-1] = state[(max_idx+1):]
projected_state = P.cone_prox(permuted_state)
new_state = np.zeros_like(state)
new_state[max_idx] = projected_state[-1]
new_state[:max_idx] = projected_state[:max_idx]
new_state[(max_idx+1):] = projected_state[max_idx:-1]
return new_state
return _projection