def test_expect(constrain=False):
G = marc_surr #XXX: uses the above-provided test function
function_name = G.__name__
_mean = 06.0 #NOTE: SET THE mean HERE!
_range = 00.5 #NOTE: SET THE range HERE!
nx = 3 #NOTE: SET THE NUMBER OF 'h' POINTS HERE!
ny = 3 #NOTE: SET THE NUMBER OF 'a' POINTS HERE!
nz = 3 #NOTE: SET THE NUMBER OF 'v' POINTS HERE!
h_lower = [60.0]
a_lower = [0.0]
v_lower = [2.1]
h_upper = [105.0]
a_upper = [30.0]
v_upper = [2.8]
lower_bounds = (nx * h_lower) + (ny * a_lower) + (nz * v_lower)
upper_bounds = (nx * h_upper) + (ny * a_upper) + (nz * v_upper)
bounds = (lower_bounds, upper_bounds)
if debug:
print(" model: f(x) = %s(x)" % function_name)
print(" mean: %s" % _mean)
print(" range: %s" % _range)
print("..............\n")
if debug:
param_string = "["
for i in range(nx):
param_string += "'x%s', " % str(i + 1)
for i in range(ny):
param_string += "'y%s', " % str(i + 1)
for i in range(nz):
param_string += "'z%s', " % str(i + 1)
param_string = param_string[:-2] + "]"
print(" parameters: %s" % param_string)
print(" lower bounds: %s" % lower_bounds)
print(" upper bounds: %s" % upper_bounds)
# print(" ...")
wx = [1.0 / float(nx)] * nx
wy = [1.0 / float(ny)] * ny
wz = [1.0 / float(nz)] * nz
from mystic.math.measures import _pack, _unpack
wts = _pack([wx, wy, wz])
weights = [i[0] * i[1] * i[2] for i in wts]
if not constrain:
constraints = None
else: # impose a mean constraint on 'thickness'
h_mean = (h_upper[0] + h_lower[0]) / 2.0
h_error = 1.0
v_mean = (v_upper[0] + v_lower[0]) / 2.0
v_error = 0.05
if debug:
print("impose: mean[x] = %s +/- %s" % (str(h_mean), str(h_error)))
print("impose: mean[z] = %s +/- %s" % (str(v_mean), str(v_error)))
def constraints(x, w):
from mystic.math.discrete import compose, decompose
c = compose(x, w)
E = float(c[0].mean)
if not (E <= float(h_mean + h_error)) or not (
float(h_mean - h_error) <= E):
c[0].mean = h_mean
E = float(c[2].mean)
if not (E <= float(v_mean + v_error)) or not (
float(v_mean - v_error) <= E):
c[2].mean = v_mean
return decompose(c)[0]
from mystic.math.measures import mean, expectation, impose_expectation
samples = impose_expectation(_mean, G, (nx,ny,nz), bounds, weights, \
tol=_range, constraints=constraints)
smp = _unpack(samples, (nx, ny, nz))
if debug:
from numpy import array
# rv = [xi]*nx + [yi]*ny + [zi]*nz
print("\nsolved [x]: %s" % array(smp[0]))
print("solved [y]: %s" % array(smp[1]))
print("solved [z]: %s" % array(smp[2]))
#print("solved: %s" % smp)
mx = mean(smp[0])
my = mean(smp[1])
mz = mean(smp[2])
if debug:
print("\nmean[x]: %s" % mx) # weights are all equal
print("mean[y]: %s" % my) # weights are all equal
print("mean[z]: %s\n" % mz) # weights are all equal
if constrain:
assert almostEqual(mx, h_mean, tol=h_error)
assert almostEqual(mz, v_mean, tol=v_error)
Ex = expectation(G, samples, weights)
cost = (Ex - _mean)**2
if debug:
print("expect: %s" % Ex)
print("cost = (E[G] - m)^2: %s" % cost)
assert almostEqual(cost, 0.0, 0.01)
def __set_positions(self, positions):
from mystic.math.measures import _unpack
positions = _unpack(positions, self.pts)
for i in range(len(positions)):
self[i].positions = positions[i]
return
def test_pack_unpack():
x = [[1, 2, 3], [4, 5], [6, 7, 8, 9]]
n = [len(i) for i in x]
assert x == _unpack(_pack(x), n)
return
c = compose(x,w)
E = float(c[0].mean)
if not (E <= float(h_mean+h_error)) or not (float(h_mean-h_error) <= E):
c[0].mean = h_mean
E = float(c[2].mean)
if not (E <= float(v_mean+v_error)) or not (float(v_mean-v_error) <= E):
c[2].mean = v_mean
return decompose(c)[0]
from mystic.math.measures import mean, expectation, impose_expectation
samples = impose_expectation((_mean,_range), G, (nx,ny,nz), bounds, \
weights, constraints=constraints)
if debug:
from numpy import array
# rv = [xi]*nx + [yi]*ny + [zi]*nz
smp = _unpack(samples,(nx,ny,nz))
print "\nsolved [x]: %s" % array( smp[0] )
print "solved [y]: %s" % array( smp[1] )
print "solved [z]: %s" % array( smp[2] )
#print "solved: %s" % smp
print "\nmean[x]: %s" % mean(smp[0]) # weights are all equal
print "mean[y]: %s" % mean(smp[1]) # weights are all equal
print "mean[z]: %s\n" % mean(smp[2]) # weights are all equal
Ex = expectation(G, samples, weights)
print "expect: %s" % Ex
print "cost = (E[G] - m)^2: %s" % (Ex - _mean)**2
# EOF
def test_pack_unpack(): x = [[1,2,3],[4,5],[6,7,8,9]] n = [len(i) for i in x] assert x == _unpack(_pack(x),n) return
def test_expect(constrain=False):
G = marc_surr #XXX: uses the above-provided test function
function_name = G.__name__
_mean = 06.0 #NOTE: SET THE mean HERE!
_range = 00.5 #NOTE: SET THE range HERE!
nx = 3 #NOTE: SET THE NUMBER OF 'h' POINTS HERE!
ny = 3 #NOTE: SET THE NUMBER OF 'a' POINTS HERE!
nz = 3 #NOTE: SET THE NUMBER OF 'v' POINTS HERE!
h_lower = [60.0]; a_lower = [0.0]; v_lower = [2.1]
h_upper = [105.0]; a_upper = [30.0]; v_upper = [2.8]
lower_bounds = (nx * h_lower) + (ny * a_lower) + (nz * v_lower)
upper_bounds = (nx * h_upper) + (ny * a_upper) + (nz * v_upper)
bounds = (lower_bounds,upper_bounds)
if debug:
print(" model: f(x) = %s(x)" % function_name)
print(" mean: %s" % _mean)
print(" range: %s" % _range)
print("..............\n")
if debug:
param_string = "["
for i in range(nx):
param_string += "'x%s', " % str(i+1)
for i in range(ny):
param_string += "'y%s', " % str(i+1)
for i in range(nz):
param_string += "'z%s', " % str(i+1)
param_string = param_string[:-2] + "]"
print(" parameters: %s" % param_string)
print(" lower bounds: %s" % lower_bounds)
print(" upper bounds: %s" % upper_bounds)
# print(" ...")
wx = [1.0 / float(nx)] * nx
wy = [1.0 / float(ny)] * ny
wz = [1.0 / float(nz)] * nz
from mystic.math.measures import _pack, _unpack
wts = _pack([wx,wy,wz])
weights = [i[0]*i[1]*i[2] for i in wts]
if not constrain:
constraints = None
else: # impose a mean constraint on 'thickness'
h_mean = (h_upper[0] + h_lower[0]) / 2.0
h_error = 1.0
v_mean = (v_upper[0] + v_lower[0]) / 2.0
v_error = 0.05
if debug:
print("impose: mean[x] = %s +/- %s" % (str(h_mean),str(h_error)))
print("impose: mean[z] = %s +/- %s" % (str(v_mean),str(v_error)))
def constraints(x, w):
from mystic.math.discrete import compose, decompose
c = compose(x,w)
E = float(c[0].mean)
if not (E <= float(h_mean+h_error)) or not (float(h_mean-h_error) <= E):
c[0].mean = h_mean
E = float(c[2].mean)
if not (E <= float(v_mean+v_error)) or not (float(v_mean-v_error) <= E):
c[2].mean = v_mean
return decompose(c)[0]
from mystic.math.measures import mean, expectation, impose_expectation
samples = impose_expectation(_mean, G, (nx,ny,nz), bounds, weights, \
tol=_range, constraints=constraints)
smp = _unpack(samples,(nx,ny,nz))
if debug:
from numpy import array
# rv = [xi]*nx + [yi]*ny + [zi]*nz
print("\nsolved [x]: %s" % array( smp[0] ))
print("solved [y]: %s" % array( smp[1] ))
print("solved [z]: %s" % array( smp[2] ))
#print("solved: %s" % smp)
mx = mean(smp[0])
my = mean(smp[1])
mz = mean(smp[2])
if debug:
print("\nmean[x]: %s" % mx) # weights are all equal
print("mean[y]: %s" % my) # weights are all equal
print("mean[z]: %s\n" % mz) # weights are all equal
if constrain:
assert almostEqual(mx, h_mean, tol=h_error)
assert almostEqual(mz, v_mean, tol=v_error)
Ex = expectation(G, samples, weights)
cost = (Ex - _mean)**2
if debug:
print("expect: %s" % Ex)
print("cost = (E[G] - m)^2: %s" % cost)
assert almostEqual(cost, 0.0, 0.01)
def __set_positions(self, positions):
from mystic.math.measures import _unpack
positions = _unpack(positions, self.pts)
for i in range(len(positions)):
self[i].positions = positions[i]
return
if not (E <= float(h_mean + h_error)) or not (
float(h_mean - h_error) <= E):
c[0].mean = h_mean
E = float(c[2].mean)
if not (E <= float(v_mean + v_error)) or not (
float(v_mean - v_error) <= E):
c[2].mean = v_mean
return decompose(c)[0]
from mystic.math.measures import mean, expectation, impose_expectation
samples = impose_expectation((_mean,_range), G, (nx,ny,nz), bounds, \
weights, constraints=constraints)
if debug:
from numpy import array
# rv = [xi]*nx + [yi]*ny + [zi]*nz
smp = _unpack(samples, (nx, ny, nz))
print "\nsolved [x]: %s" % array(smp[0])
print "solved [y]: %s" % array(smp[1])
print "solved [z]: %s" % array(smp[2])
#print "solved: %s" % smp
print "\nmean[x]: %s" % mean(smp[0]) # weights are all equal
print "mean[y]: %s" % mean(smp[1]) # weights are all equal
print "mean[z]: %s\n" % mean(smp[2]) # weights are all equal
Ex = expectation(G, samples, weights)
print "expect: %s" % Ex
print "cost = (E[G] - m)^2: %s" % (Ex - _mean)**2
# EOF