def optimize(cost,lower,upper):
from mystic.tools import random_seed
from pyina.launchers import Mpi as Pool
random_seed(123)
# generate a set of random starting points
initial_values = samplepts(lower,upper,npts)
# run optimizer for each grid point
lb = [lower for i in range(len(initial_values))]
ub = [upper for i in range(len(initial_values))]
cf = [cost for i in range(len(initial_values))]
# map:: params, energy, func_evals = local_optimize(cost,x0,lb,ub)
results = Pool(nnodes).map(local_optimize, cf, initial_values, lb, ub)
#print "results = %s" % results
# get the results with the lowest energy
best = list(results[0][0]), results[0][1]
func_evals = results[0][2]
for result in results[1:]:
func_evals += result[2] # add function evaluations
if result[1] < best[1]: # compare energy
best = list(result[0]), result[1]
# return best
print "solved: %s" % best[0]
scale = 1.0
diameter_squared = -best[1] / scale #XXX: scale != 0
return diameter_squared, func_evals
def optimize(cost, lower, upper):
from mystic.tools import random_seed
from pyina.launchers import Mpi as Pool
random_seed(123)
# generate a set of random starting points
initial_values = samplepts(lower, upper, npts)
# run optimizer for each grid point
lb = [lower for i in range(len(initial_values))]
ub = [upper for i in range(len(initial_values))]
cf = [cost for i in range(len(initial_values))]
# map:: params, energy, func_evals = local_optimize(cost,x0,lb,ub)
results = Pool(nnodes).map(local_optimize, cf, initial_values, lb, ub)
#print("results = %s" % results)
# get the results with the lowest energy
best = list(results[0][0]), results[0][1]
func_evals = results[0][2]
for result in results[1:]:
func_evals += result[2] # add function evaluations
if result[1] < best[1]: # compare energy
best = list(result[0]), result[1]
# return best
print("solved: %s" % best[0])
scale = 1.0
diameter_squared = -best[1] / scale #XXX: scale != 0
return diameter_squared, func_evals
def test_calculate_methods(npts=2):
upper_bounds = [1.0]
lower_bounds = [0.0]
# -------------------------------------
# generate initial coordinates, weights
# -------------------------------------
# get a random distribution of points
if disp: print("generate random points and weights")
coordinates = samplepts(lower_bounds, upper_bounds, npts)
D0 = D = [i[0] for i in coordinates]
if disp: print("positions: %s" % D)
# calculate sample range
R0 = R = spread(D)
if disp: print("range: %s" % R)
# select weights randomly in [0,1], then normalize so sum(weights) = 1
wts = random_samples([0], [1], npts)[0]
weights = normalize(wts, 0.0, zsum=True)
if disp: print("weights (when normalized to 0.0): %s" % weights)
assert almostEqual(sum(weights), 0.0, tol=1e-15)
weights = normalize(wts, 1.0)
assert almostEqual(sum(weights), 1.0, tol=1e-15)
if disp: print("weights (when normalized to 1.0): %s" % weights)
w = norm(weights)
if disp: print("norm: %s" % w)
assert almostEqual(w, sum(weights) / npts)
# calculate sample mean
m0 = m = mean(D, weights)
if disp: print("mean: %s" % m)
if disp: print("")
# -------------------------------------
# modify coordinates, maintaining mean & range
# -------------------------------------
# get new random distribution
if disp: print("modify positions, maintaining mean and range")
coordinates = samplepts(lower_bounds, upper_bounds, npts)
D = [i[0] for i in coordinates]
# impose a range and mean on the points
D = impose_spread(R, D, weights)
D = impose_mean(m, D, weights)
# print results
if disp: print("positions: %s" % D)
R = spread(D)
if disp: print("range: %s" % R)
assert almostEqual(R, R0)
m = mean(D, weights)
if disp: print("mean: %s" % m)
assert almostEqual(m, m0)
if disp: print("")
# -------------------------------------
# modify weights, maintaining mean & norm
# -------------------------------------
# select weights randomly in [0,1]
if disp: print("modify weights, maintaining mean and range")
wts = random_samples([0], [1], npts)[0]
# print intermediate results
#print("weights: %s" % wts)
#sm = mean(D, wts)
#print("tmp mean: %s" % sm)
#print("")
# impose mean and weight norm on the points
D = impose_mean(m, D, wts)
DD, weights = impose_weight_norm(D, wts)
# print results
if disp: print("weights: %s" % weights)
w = norm(weights)
if disp: print("norm: %s" % w)
assert almostEqual(w, sum(weights) / npts)
if disp: print("positions: %s" % DD)
R = spread(DD)
if disp: print("range: %s" % R)
assert almostEqual(R, R0)
sm = mean(DD, weights)
if disp: print("mean: %s" % sm)
assert almostEqual(sm, m0)
sv = variance(DD, weights)
if disp: print("var: %s" % sv)
assert not almostEqual(sv, R)
assert almostEqual(sv, 0.0, tol=.3)
# -------------------------------------
# modify variance, maintaining mean
# -------------------------------------
if disp: print("\nmodify variance, maintaining mean")
DD = impose_variance(R, DD, weights)
sm = mean(DD, weights)
if disp: print("mean: %s" % sm)
assert almostEqual(sm, m0)
sv = variance(DD, weights)
if disp: print("var: %s" % sv)
assert almostEqual(sv, R)
def test_calculate_methods(npts=2):
upper_bounds = [1.0]
lower_bounds = [0.0]
# -------------------------------------
# generate initial coordinates, weights
# -------------------------------------
# get a random distribution of points
print "generate random points and weights"
coordinates = samplepts(lower_bounds, upper_bounds, npts)
D = [i[0] for i in coordinates]
print "positions: %s" % D
# calculate sample range
R = spread(D)
print "range: %s" % R
# select weights randomly in [0,1], then normalize so sum(weights) = 1
wts = random_samples([0], [1], npts)[0]
weights = normalize(wts, 0.0, zsum=True)
print "weights (when normalized to 0.0): %s" % weights
weights = normalize(wts)
print "weights (when normalized to 1.0): %s" % weights
w = norm(weights)
print "norm: %s" % w
# calculate sample mean
m = mean(D, weights)
print "mean: %s" % m
print ""
# -------------------------------------
# modify coordinates, maintaining mean & range
# -------------------------------------
# get new random distribution
print "modify positions, maintaining mean and range"
coordinates = samplepts(lower_bounds, upper_bounds, npts)
D = [i[0] for i in coordinates]
# impose a range and mean on the points
D = impose_spread(R, D, weights)
D = impose_mean(m, D, weights)
# print results
print "positions: %s" % D
R = spread(D)
print "range: %s" % R
m = mean(D, weights)
print "mean: %s" % m
print ""
# -------------------------------------
# modify weights, maintaining mean & norm
# -------------------------------------
# select weights randomly in [0,1]
print "modify weights, maintaining mean and range"
wts = random_samples([0], [1], npts)[0]
# print intermediate results
#print "weights: %s" % wts
#sm = mean(D, wts)
#print "tmp mean: %s" % sm
#print ""
# impose mean and weight norm on the points
D = impose_mean(m, D, wts)
DD, weights = impose_weight_norm(D, wts)
# print results
print "weights: %s" % weights
w = norm(weights)
print "norm: %s" % w
print "positions: %s" % DD
R = spread(DD)
print "range: %s" % R
sm = mean(DD, weights)
print "mean: %s" % sm
sv = variance(DD, weights)
print "var: %s" % sv
# -------------------------------------
# modify variance, maintaining mean
# -------------------------------------
print "\nmodify variance, maintaining mean"
DD = impose_variance(R, DD, weights)
sm = mean(DD, weights)
print "mean: %s" % sm
sv = variance(DD, weights)
print "var: %s" % sv
def test_calculate_methods(npts=2): upper_bounds = [1.0] lower_bounds = [0.0] # ------------------------------------- # generate initial coordinates, weights # ------------------------------------- # get a random distribution of points if disp: print "generate random points and weights" coordinates = samplepts(lower_bounds, upper_bounds, npts) D0 = D = [i[0] for i in coordinates] if disp: print "positions: %s" % D # calculate sample range R0 = R = spread(D) if disp: print "range: %s" % R # select weights randomly in [0,1], then normalize so sum(weights) = 1 wts = random_samples([0],[1], npts)[0] weights = normalize(wts, 0.0, zsum=True) if disp: print "weights (when normalized to 0.0): %s" % weights assert almostEqual(sum(weights), 0.0, tol=1e-15) weights = normalize(wts) assert almostEqual(sum(weights), 1.0, tol=1e-15) if disp: print "weights (when normalized to 1.0): %s" % weights w = norm(weights) if disp: print "norm: %s" % w assert almostEqual(w, sum(weights)/npts) # calculate sample mean m0 = m = mean(D,weights) if disp: print "mean: %s" % m if disp: print "" # ------------------------------------- # modify coordinates, maintaining mean & range # ------------------------------------- # get new random distribution if disp: print "modify positions, maintaining mean and range" coordinates = samplepts(lower_bounds, upper_bounds, npts) D = [i[0] for i in coordinates] # impose a range and mean on the points D = impose_spread(R, D, weights) D = impose_mean(m, D, weights) # print results if disp: print "positions: %s" % D R = spread(D) if disp: print "range: %s" % R assert almostEqual(R, R0) m = mean(D, weights) if disp: print "mean: %s" % m assert almostEqual(m, m0) if disp: print "" # ------------------------------------- # modify weights, maintaining mean & norm # ------------------------------------- # select weights randomly in [0,1] if disp: print "modify weights, maintaining mean and range" wts = random_samples([0],[1], npts)[0] # print intermediate results #print "weights: %s" % wts #sm = mean(D, wts) #print "tmp mean: %s" % sm #print "" # impose mean and weight norm on the points D = impose_mean(m, D, wts) DD, weights = impose_weight_norm(D, wts) # print results if disp: print "weights: %s" % weights w = norm(weights) if disp: print "norm: %s" % w assert almostEqual(w, sum(weights)/npts) if disp: print "positions: %s" % DD R = spread(DD) if disp: print "range: %s" % R assert almostEqual(R, R0) sm = mean(DD, weights) if disp: print "mean: %s" % sm assert almostEqual(sm, m0) sv = variance(DD, weights) if disp: print "var: %s" % sv assert not almostEqual(sv, R) assert almostEqual(sv, 0.0, tol=.2) # ------------------------------------- # modify variance, maintaining mean # ------------------------------------- if disp: print "\nmodify variance, maintaining mean" DD = impose_variance(R, DD, weights) sm = mean(DD, weights) if disp: print "mean: %s" % sm assert almostEqual(sm, m0) sv = variance(DD, weights) if disp: print "var: %s" % sv assert almostEqual(sv, R)
def test_calculate_methods(npts=2): upper_bounds = [1.0] lower_bounds = [0.0] # ------------------------------------- # generate initial coordinates, weights # ------------------------------------- # get a random distribution of points print "generate random points and weights" coordinates = samplepts(lower_bounds, upper_bounds, npts) D = [i[0] for i in coordinates] print "positions: %s" % D # calculate sample range R = spread(D) print "range: %s" % R # select weights randomly in [0,1], then normalize so sum(weights) = 1 wts = random_samples([0],[1], npts)[0] weights = normalize(wts, 0.0, zsum=True) print "weights (when normalized to 0.0): %s" % weights weights = normalize(wts) print "weights (when normalized to 1.0): %s" % weights w = norm(weights) print "norm: %s" % w # calculate sample mean m = mean(D,weights) print "mean: %s" % m print "" # ------------------------------------- # modify coordinates, maintaining mean & range # ------------------------------------- # get new random distribution print "modify positions, maintaining mean and range" coordinates = samplepts(lower_bounds, upper_bounds, npts) D = [i[0] for i in coordinates] # impose a range and mean on the points D = impose_spread(R, D, weights) D = impose_mean(m, D, weights) # print results print "positions: %s" % D R = spread(D) print "range: %s" % R m = mean(D, weights) print "mean: %s" % m print "" # ------------------------------------- # modify weights, maintaining mean & norm # ------------------------------------- # select weights randomly in [0,1] print "modify weights, maintaining mean and range" wts = random_samples([0],[1], npts)[0] # print intermediate results #print "weights: %s" % wts #sm = mean(D, wts) #print "tmp mean: %s" % sm #print "" # impose mean and weight norm on the points D = impose_mean(m, D, wts) DD, weights = impose_weight_norm(D, wts) # print results print "weights: %s" % weights w = norm(weights) print "norm: %s" % w print "positions: %s" % DD R = spread(DD) print "range: %s" % R sm = mean(DD, weights) print "mean: %s" % sm sv = variance(DD, weights) print "var: %s" % sv # ------------------------------------- # modify variance, maintaining mean # ------------------------------------- print "\nmodify variance, maintaining mean" DD = impose_variance(R, DD, weights) sm = mean(DD, weights) print "mean: %s" % sm sv = variance(DD, weights) print "var: %s" % sv
