def fillpts(lb,ub,npts,data=None,rtol=None,dist=None):
"""
takes lower and upper bounds (e.g. lb = [0,3], ub = [2,4])
finds npts that are at least rtol away from legacy data
produces a list of sample points s = [[1,3],[1,4],[2,3],[2,4]]
Inputs:
lb -- a list of the lower bounds
ub -- a list of the upper bounds
npts -- number of sample points
data -- a list of legacy sample points
rtol -- target radial distance from each point
dist -- a mystic.math.Distribution instance
Notes: if rtol is None, use max rtol; if rtol < 0, use quick-n-dirty method
"""
bounds = list(zip(lb,ub))
from mystic.math.distance import euclidean as metric
#XXX: expose solver settings to user? #XXX: better npop,ftol? faster?
###if rtol is None or type(rtol) in (int, float):
from mystic.solvers import diffev as solver
kwds = dict(npop=20, ftol=1e-4, gtol=None, disp=0, full_output=0)
###initial = lambda : bounds
###else: # assume it's a string
# from mystic.solvers import fmin_powell as solver
# kwds = dict(xtol=1e-8, ftol=1e-8, gtol=2, disp=0, full_output=0)
# if rtol == 'None': rtol = None
# else: rtol = float(rtol)
# import random as rd
# initial = lambda : [rd.randrange(l,u)+rd.random() for (l,u) in bounds]
#from numpy import round
#kwds['constraints'] = lambda x: round(x, 3)
# copy the legacy data points (e.g. monitor.x) #XXX: more efficient method?
pts = [] if data is None else list(data)
# 'min', 'np.sum()', 'np.min()' are also a choice of distance metric
if rtol and rtol < 0: # neg radius uses quick-n-dirty method
def holes(x):
return (metric(pts,x,axis=0).min(axis=0) < -rtol).sum()
elif rtol is None: # no radius finds max distance away
def holes(x):
res = metric(pts,x,axis=0).min()
return -res
else: # all points should be at least rtol away
def holes(x):
res = metric(pts,x,axis=0).min()
return -res if res < rtol else 0.0
# iteratively find a point away from all other points
for pt in range(npts):
res = solver(holes, x0=bounds, bounds=bounds, **kwds)
#res,cost = res[0],res[1]
pts.append(res.ravel().tolist())
pts = pts[-npts:]
# inject some randomness #XXX: what are alternatives? some sampling?
if dist is None: return pts
if not len(pts): return pts
pts += dist((len(pts),len(pts[0])))
return pts.tolist()
def fillpts(lb,ub,npts,data=None,rtol=None,dist=None):
"""
takes lower and upper bounds (e.g. lb = [0,3], ub = [2,4])
finds npts that are at least rtol away from legacy data
produces a list of sample points s = [[1,3],[1,4],[2,3],[2,4]]
Inputs:
lb -- a list of the lower bounds
ub -- a list of the upper bounds
npts -- number of sample points
data -- a list of legacy sample points
rtol -- target radial distance from each point
dist -- a mystic.math.Distribution instance
Notes: if rtol is None, use max rtol; if rtol < 0, use quick-n-dirty method
"""
bounds = list(zip(lb,ub))
from mystic.math.distance import euclidean as metric
#XXX: expose solver settings to user? #XXX: better npop,ftol? faster?
###if rtol is None or type(rtol) in (int, float):
from mystic.solvers import diffev as solver
kwds = dict(npop=20, ftol=1e-4, gtol=None, disp=0, full_output=0)
###initial = lambda : bounds
###else: # assume it's a string
# from mystic.solvers import fmin_powell as solver
# kwds = dict(xtol=1e-8, ftol=1e-8, gtol=2, disp=0, full_output=0)
# if rtol == 'None': rtol = None
# else: rtol = float(rtol)
# import random as rd
# initial = lambda : [rd.randrange(l,u)+rd.random() for (l,u) in bounds]
#from numpy import round
#kwds['constraints'] = lambda x: round(x, 3)
# copy the legacy data points (e.g. monitor.x) #XXX: more efficient method?
pts = [] if data is None else list(data)
# 'min', 'np.sum()', 'np.min()' are also a choice of distance metric
if rtol and rtol < 0: # neg radius uses quick-n-dirty method
def holes(x):
return (metric(pts,x,axis=0).min(axis=0) < -rtol).sum()
elif rtol is None: # no radius finds max distance away
def holes(x):
res = metric(pts,x,axis=0).min()
return -res
else: # all points should be at least rtol away
def holes(x):
res = metric(pts,x,axis=0).min()
return -res if res < rtol else 0.0
# iteratively find a point away from all other points
for pt in range(npts):
res = solver(holes, x0=bounds, bounds=bounds, **kwds)
#res,cost = res[0],res[1]
pts.append(res.ravel().tolist())
pts = pts[-npts:]
# inject some randomness #XXX: what are alternatives? some sampling?
if dist is None: return pts
if not len(pts): return pts
pts += dist((len(pts),len(pts[0])))
return pts.tolist()
def fmin_powell(cost, x0, full=1, disp=1, monitor=0):
""" change default behavior for selected optimizers """
from mystic.solvers import fmin_powell as solver
from mystic.monitors import Monitor, VerboseMonitor
if monitor: mon = VerboseMonitor(10)
else: mon = Monitor()
npop = 10*len(x0)
solved = solver(cost, x0, npop=npop, full_output=full,
disp=disp, itermon=mon, handler=0)
# return: solution, energy, generations, fevals
return solved[0], solved[1], solved[2], solved[3]
def fmin_powell(cost, x0, full=1, disp=1, monitor=0):
""" change default behavior for selected optimizers """
from mystic.solvers import fmin_powell as solver
from mystic.monitors import Monitor, VerboseMonitor
if monitor: mon = VerboseMonitor(10)
else: mon = Monitor()
npop = 10*len(x0)
solved = solver(cost, x0, npop=npop, full_output=full,
disp=disp, itermon=mon, handler=0)
# return: solution, energy, generations, fevals
return solved[0], solved[1], solved[3], solved[4]
def impose_reweighted_variance(v, samples, weights=None, solver=None):
"""impose a variance on a list of points by reweighting weights"""
ndim = len(samples)
if weights is None:
weights = [1.0 / ndim] * ndim
if solver is None or solver == 'fmin':
from mystic.solvers import fmin as solver
elif solver == 'fmin_powell':
from mystic.solvers import fmin_powell as solver
elif solver == 'diffev':
from mystic.solvers import diffev as solver
elif solver == 'diffev2':
from mystic.solvers import diffev2 as solver
norm = sum(weights)
m = mean(samples, weights)
inequality = ""
equality = ""
equality2 = ""
equality3 = ""
for i in range(ndim):
inequality += "x%s >= 0.0\n" % (i) # positive
equality += "x%s + " % (i) # normalized
equality2 += "%s * x%s + " % (float(samples[i]), (i)) # mean
equality3 += "x%s*(%s-%s)**2 + " % ((i), float(samples[i]), m) # var
equality += "0.0 = %s\n" % float(norm)
equality += equality2 + "0.0 = %s*%s\n" % (float(norm), m)
equality += equality3 + "0.0 = %s*%s\n" % (float(norm), v)
penalties = generate_penalty(generate_conditions(inequality))
constrain = generate_constraint(generate_solvers(solve(equality)))
def cost(x):
return sum(x)
results = solver(cost, weights, constraints=constrain, \
penalty=penalties, disp=False, full_output=True)
wts = list(results[0])
_norm = results[1] # should have _norm == norm
warn = results[4] # nonzero if didn't converge
#XXX: better to fail immediately if xlo < m < xhi... or the below?
if warn or not almostEqual(_norm, norm):
print "Warning: could not impose mean through reweighting"
return None #impose_variance(v, samples, weights), weights
return wts #samples, wts # "mean-preserving"
def impose_reweighted_variance(v, samples, weights=None, solver=None):
"""impose a variance on a list of points by reweighting weights"""
ndim = len(samples)
if weights is None:
weights = [1.0/ndim] * ndim
if solver is None or solver == 'fmin':
from mystic.solvers import fmin as solver
elif solver == 'fmin_powell':
from mystic.solvers import fmin_powell as solver
elif solver == 'diffev':
from mystic.solvers import diffev as solver
elif solver == 'diffev2':
from mystic.solvers import diffev2 as solver
norm = sum(weights)
m = mean(samples, weights)
inequality = ""
equality = ""; equality2 = ""; equality3 = ""
for i in range(ndim):
inequality += "x%s >= 0.0\n" % (i) # positive
equality += "x%s + " % (i) # normalized
equality2 += "%s * x%s + " % (float(samples[i]),(i)) # mean
equality3 += "x%s*(%s-%s)**2 + " % ((i),float(samples[i]),m) # var
equality += "0.0 = %s\n" % float(norm)
equality += equality2 + "0.0 = %s*%s\n" % (float(norm),m)
equality += equality3 + "0.0 = %s*%s\n" % (float(norm),v)
penalties = generate_penalty(generate_conditions(inequality))
constrain = generate_constraint(generate_solvers(solve(equality)))
def cost(x): return sum(x)
results = solver(cost, weights, constraints=constrain, \
penalty=penalties, disp=False, full_output=True)
wts = list(results[0])
_norm = results[1] # should have _norm == norm
warn = results[4] # nonzero if didn't converge
#XXX: better to fail immediately if xlo < m < xhi... or the below?
if warn or not almostEqual(_norm, norm):
print "Warning: could not impose mean through reweighting"
return None #impose_variance(v, samples, weights), weights
return wts #samples, wts # "mean-preserving"
