def test_var(func, vals):
x = pb.Variable('x', vtype=float)
y = pb.Variable('y', vtype=float)
a = pb.Variable('a', vtype=float)
b = pb.Variable('b', vtype=float)
xy = x & y
ab = a & b
functional = pb.Functional(ab, xy)
functional.add_func(a, func[0](x[:]))
functional.add_func(b, func[1](y[:]))
eval_a = functional[a](vals[0])
eval_b = functional[b](vals[1])
assert np.isclose(eval_a, vals[1])
assert np.isclose(eval_b, vals[0])
def test_inc(inp, out):
# Sympy
x = pb.Variable('x', vtype=float, vset=[zero, inf])
x.set_ufun(x[:] + 1.)
output = x.ufun[0](inp)
assert ismatch(out, output), \
"Observed/expected match {}/{}".format(output, out)
output = x.ufun[-1](output)
assert ismatch(inp, output), \
"Observed/expected match {}/{}".format(output, inp)
# Numpy
y = pb.Variable('y', vtype=float, vset=[zero, inf])
y.set_ufun((lambda z: z + 1, lambda z: z - 1))
output = y.ufun[0](inp)
assert ismatch(out, output), \
"Observed/expected match {}/{}".format(output, out)
output = y.ufun[-1](output)
assert ismatch(inp, output), \
"Observed/expected match {}/{}".format(output, inp)
def test_log(inp, out):
# Sympy
x = pb.Variable('x', vtype=float, vset=[zero, inf])
x.set_ufun(sympy.log(~x))
output = x.ufun[0](inp)
assert ismatch(out, output), \
"Observed/expected match {}/{}".format(output, out)
output = x.ufun[-1](output)
assert ismatch(inp, output), \
"Observed/expected match {}/{}".format(output, inp)
# Numpy
y = pb.Variable('y', vtype=float, vset=[zero, inf])
y.set_ufun((np.log, np.exp))
output = y.ufun[0](inp)
assert ismatch(out, output), \
"Observed/expected match {}/{}".format(output, out)
output = y.ufun[-1](output)
assert ismatch(inp, output), \
"Observed/expected match {}/{}".format(output, inp)
def test_ran(ran, val):
# Sympy
x = pb.Variable('x', vtype=float, vset=ran)
x.set_ufun(sympy.log(x[:]))
vals = x(val)[x.name]
assert np.max(vals) <= x.vlims[1] and np.min(vals) >= x.vlims[0]
# Numpy
y = pb.Variable('y', vtype=float, vset=ran)
y.set_ufun((np.log, np.exp))
vals = y(val)[y.name]
assert np.max(vals) <= x.vlims[1] and np.min(vals) >= x.vlims[0]
# Delta
steps = int(abs(list(val)[0]))
value = np.mean(vals)
y.set_delta([1], bound=True)
vals = np.empty(steps, dtype=float)
for i in range(steps):
vals[i] = y.apply_delta(value)
value = vals[i]
assert np.max(vals) <= x.vlims[1] and np.min(vals) >= x.vlims[0]
def test_log(inp, out):
for use_variable in False, True:
if not use_variable:
x = sy.Symbol('x')
x_expr = pb.Expr(sy.log(x))
output = x_expr({'x': inp})
else:
y = pb.Variable('y', vtype=float)
y_expr = pb.Expr(sy.log(~y))
output = y_expr({'y': inp})
close = np.isclose(output, out)
if isinstance(inp, np.ndarray):
assert np.all(close), "Output values not as expected"
else:
assert close, "Output value {} not as expected {}".format(
output, out)
# Change of variables example
import collections
import probayes as pb
import numpy as np
from pylab import *
ion()
num_samples = 500
x = pb.Variable('x', vtype=float, vset=[0, 1])
y = pb.Variable('y', vtype=float, vset=[0, 1])
s = pb.Variable('s', vtype=float)
d = pb.Variable('d', vtype=float)
xy = x & y
sd = s & d
sd_from_xy = sd | xy
sd_from_xy.func.add_func(s[:], x[:] + y[:])
sd_from_xy.func.add_func(d[:], x[:] - y[:])
# Example of sampling from a Zipfian probability density function
import numpy as np
from pylab import *
ion()
import probayes as pb
zipf_range = [0.1, 10.]
set_size = {-10000} # size negation denotes random sampling
var = pb.Variable("var", zipf_range)
var.set_ufun((np.log, np.exp))
samples = var(set_size)
figure()
hist(samples[var.name], 100)