def test_bfgs_madsen(self):
from ch import SumOfSquares
import scipy.optimize
obj = Ch(lambda x: SumOfSquares(Madsen(x=x)))
def errfunc(x):
obj.x = Ch(x)
return obj.r
def gradfunc(x):
obj.x = Ch(x)
return obj.dr_wrt(obj.x).ravel()
x0 = np.array((3., 1.))
# Optimize with built-in bfgs.
# Note: with 8 iters, this actually requires 14 gradient evaluations.
# This can be verified by setting "disp" to 1.
#tm = time.time()
x1 = scipy.optimize.fmin_bfgs(errfunc,
x0,
fprime=gradfunc,
maxiter=8,
disp=0)
#print 'forward: took %.es' % (time.time() - tm,)
self.assertTrue(obj.r / 2. < 0.386599528247)
# Optimize with chumpy's minimize (which uses scipy's bfgs).
obj.x = x0
minimize(fun=obj, x0=[obj.x], method='bfgs', options={'maxiter': 8})
self.assertTrue(obj.r / 2. < 0.386599528247)
def minimize(fun,
x0,
method='dogleg',
bounds=None,
constraints=(),
tol=None,
callback=None,
options=None):
if method == 'dogleg':
if options is None: options = {}
return minimize_dogleg(fun,
free_variables=x0,
on_step=callback,
**options)
if isinstance(fun, list) or isinstance(fun, tuple):
fun = ch.concatenate([f.ravel() for f in fun])
if isinstance(fun, dict):
fun = ch.concatenate([f.ravel() for f in fun.values()])
obj = fun
free_variables = x0
from ch import SumOfSquares
hessp = None
hess = None
if obj.size == 1:
obj_scalar = obj
else:
obj_scalar = SumOfSquares(obj)
def hessp(vs, p, obj, obj_scalar, free_variables):
changevars(vs, obj, obj_scalar, free_variables)
if not hasattr(hessp, 'vs'):
hessp.vs = vs * 0 + 1e16
if np.max(np.abs(vs - hessp.vs)) > 0:
J = ns_jacfunc(vs, obj, obj_scalar, free_variables)
hessp.J = J
hessp.H = 2. * J.T.dot(J)
hessp.vs = vs
return np.array(hessp.H.dot(p)).ravel()
#return 2*np.array(hessp.J.T.dot(hessp.J.dot(p))).ravel()
if method.lower() != 'newton-cg':
def hess(vs, obj, obj_scalar, free_variables):
changevars(vs, obj, obj_scalar, free_variables)
if not hasattr(hessp, 'vs'):
hessp.vs = vs * 0 + 1e16
if np.max(np.abs(vs - hessp.vs)) > 0:
J = ns_jacfunc(vs, obj, obj_scalar, free_variables)
hessp.H = 2. * J.T.dot(J)
return hessp.H
def changevars(vs, obj, obj_scalar, free_variables):
cur = 0
changed = False
for idx, freevar in enumerate(free_variables):
sz = freevar.r.size
newvals = vs[cur:cur + sz].copy().reshape(
free_variables[idx].shape)
if np.max(np.abs(newvals - free_variables[idx]).ravel()) > 0:
free_variables[idx][:] = newvals
changed = True
cur += sz
methods_without_callback = ('anneal', 'powell', 'cobyla', 'slsqp')
if callback is not None and changed and method.lower(
) in methods_without_callback:
callback(None)
return changed
def residuals(vs, obj, obj_scalar, free_variables):
changevars(vs, obj, obj_scalar, free_variables)
residuals = obj_scalar.r.ravel()[0]
return residuals
def scalar_jacfunc(vs, obj, obj_scalar, free_variables):
if not hasattr(scalar_jacfunc, 'vs'):
scalar_jacfunc.vs = vs * 0 + 1e16
if np.max(np.abs(vs - scalar_jacfunc.vs)) == 0:
return scalar_jacfunc.J
changevars(vs, obj, obj_scalar, free_variables)
if True: # faster, at least on some problems
result = np.concatenate([
np.array(obj_scalar.lop(wrt, np.array([[1]]))).ravel()
for wrt in free_variables
])
else:
jacs = [obj_scalar.dr_wrt(wrt) for wrt in free_variables]
for idx, jac in enumerate(jacs):
if sp.issparse(jac):
jacs[idx] = jacs[idx].todense()
result = np.concatenate([jac.ravel() for jac in jacs])
scalar_jacfunc.J = result
scalar_jacfunc.vs = vs
return result.ravel()
def ns_jacfunc(vs, obj, obj_scalar, free_variables):
if not hasattr(ns_jacfunc, 'vs'):
ns_jacfunc.vs = vs * 0 + 1e16
if np.max(np.abs(vs - ns_jacfunc.vs)) == 0:
return ns_jacfunc.J
changevars(vs, obj, obj_scalar, free_variables)
jacs = [obj.dr_wrt(wrt) for wrt in free_variables]
result = hstack(jacs)
ns_jacfunc.J = result
ns_jacfunc.vs = vs
return result
x1 = scipy.optimize.minimize(method=method,
fun=residuals,
callback=callback,
x0=np.concatenate([
free_variable.r.ravel()
for free_variable in free_variables
]),
jac=scalar_jacfunc,
hessp=hessp,
hess=hess,
args=(obj, obj_scalar, free_variables),
bounds=bounds,
constraints=constraints,
tol=tol,
options=options).x
changevars(x1, obj, obj_scalar, free_variables)
return free_variables