def _test_sample(self, kernel):
kern = kernel()
NUM = int(1e6)
bw = 1.0
pad = 4.0
xe, xc, dx = kale.utils.bins(-pad * bw, pad * bw, 100)
samp = kern.sample(NUM)
hist, _ = np.histogram(samp, xe, density=True)
pdf = kern.evaluate(xc)
cum_pdf = utils.trapz_dens_to_mass(pdf, xc)
cum_pdf = np.cumsum(cum_pdf)
cum_pdf = np.append([0.0], cum_pdf)
cdf = kern.cdf(xc)
# Compare 'analytic' PDF/CDF with distribution of samples
# CDF tend not to match as well, so use larger tolerance
for aa, bb, name, tol in zip([hist, cum_pdf], [pdf, cdf],
['pdf', 'cdf'], [1e-2, 1e-1]):
idx = (aa > 0.0) & (bb > 0.0)
dof = np.count_nonzero(idx) - 1
x2 = np.sum(np.square(aa[idx] - bb[idx]) / bb[idx]**2)
x2 = x2 / dof
print("Distribution: {} :: {} : x2/dof = {:.4e}".format(
kern.name(), name, x2))
print("\t" + kale.utils.array_str(aa[idx]))
print("\t" + kale.utils.array_str(bb[idx]))
utils.alltrue(x2 < tol)
return
def _test_evaluate(self, kernel):
print(kernel)
hh = 1.0
edges = np.linspace(-4 * hh, 4 * hh, 10000)
cents = kale.utils.midpoints(edges, 'lin')
yy = kernel.evaluate(cents)
# Make sure kernel is callable
# tools.assert_true(np.allclose(yy, kernel().evaluate(cents)))
# Make sure kernel is normalized
tot = np.trapz(yy, cents)
msg = "Kernel is {fail:} unitary"
utils.allclose(tot, 1.0, rtol=1e-3, msg=msg)
# Make sure kernels have expected support
tools.assert_true(np.all(yy >= 0.0))
if kernel._FINITE:
outside = (cents < -hh) | (hh < cents)
inside = (-hh < cents) & (cents < hh)
else:
outside = []
inside = np.ones_like(yy, dtype=bool)
utils.allclose(yy[outside], 0.0, rtol=1e-4, atol=1e-4)
utils.alltrue(yy[inside] > 0.0)
return
def _test_ndim_a2(self, ndim):
from kalepy import utils
BIN_SIZE_RANGE = [10, 30]
num_bins = np.random.randint(*BIN_SIZE_RANGE, ndim)
edges = []
for nb in num_bins:
ee = np.cumsum(np.random.uniform(0.0, 2.0, nb))
edges.append(ee)
grid = np.meshgrid(*edges, indexing='ij')
shp = np.array([len(ee) for ee in edges])
for axis in np.ndindex(*([ndim] * 2)):
if len(np.unique(axis)) != len(axis):
continue
axis = np.asarray(axis)
not_axis = np.array(list(set(range(ndim)) - set(axis)))
print("\nndim = {}, axis = {}, other = {}".format(
ndim, axis, not_axis))
bcast_norm = [np.newaxis for ii in range(ndim)]
for na in not_axis:
bcast_norm[na] = slice(None)
bcast_norm = tuple(bcast_norm)
norm = np.random.uniform(0.0, 10.0, shp[not_axis])[bcast_norm]
widths = []
for ii in range(ndim):
dim_len_inn = shp[ii]
if ii in axis:
wid = np.diff(edges[ii])
else:
wid = np.ones(dim_len_inn)
# Create new axes along all by the current dimension, slice along the current dimension
cut = [np.newaxis for ii in range(ndim)]
cut[ii] = slice(None)
temp = wid[tuple(cut)]
widths.append(temp)
wids = np.product(np.array(widths, dtype=object),
axis=0).astype(float)
pdf = np.ones_like(grid[0]) * norm
pmf = utils.trapz_dens_to_mass(pdf, edges, axis=axis)
new_shp = [ss for ss in shp]
for aa in axis:
new_shp[aa] -= 1
utils.alltrue(
np.shape(pmf) == np.array(new_shp),
"Output shape is {fail:}correct")
utils.alltrue(pmf == norm * wids, 'Values do {fail:}match')
return
def test_1d(self):
aa = np.random.uniform(*[-100, 100], 1000)
bounds = [-23, 43]
print(aa)
print(bounds)
for out in [False, True]:
idx = utils.bound_indices(aa, bounds, outside=out)
test_yes = aa[idx]
test_not = aa[~idx]
print("\n", out, idx)
for val, test in zip([out, not out], [test_yes, test_not]):
if len(test) == 0:
continue
outside = (test < bounds[0]) | (bounds[1] < test)
inside = (bounds[0] < test) & (test < bounds[1])
print("outside = {}, out = {}, val = {}".format(
np.all(outside), out, val))
utils.alltrue(outside == val)
print("inside = {}, out = {}, val = {}".format(
np.all(inside), out, val))
utils.alltrue(inside == (not val))
return
def _test_ndim_a1(self, ndim):
from kalepy import utils
BIN_SIZE_RANGE = [10, 30]
num_bins = np.random.randint(*BIN_SIZE_RANGE, ndim)
# num_bins = [3, 4]
edges = []
for nb in num_bins:
ee = np.cumsum(np.random.uniform(0.0, 2.0, nb))
edges.append(ee)
grid = np.meshgrid(*edges, indexing='ij')
shp = [len(ee) for ee in edges]
for axis in range(ndim):
not_axis = (axis + 1) % ndim
print("\nndim = {}, axis = {}, other = {}".format(
ndim, axis, not_axis))
bcast_norm = [np.newaxis for ii in range(ndim)]
bcast_norm[not_axis] = slice(None)
bcast_norm = tuple(bcast_norm)
norm = np.random.uniform(0.0, 10.0, shp[not_axis])[bcast_norm]
bcast_wids = [np.newaxis for ii in range(ndim)]
bcast_wids[axis] = slice(None)
bcast_wids = tuple(bcast_wids)
wids = np.diff(edges[axis])[bcast_wids]
pdf = np.ones_like(grid[0]) * norm
pmf = utils.trapz_dens_to_mass(pdf, edges, axis=axis)
new_shp = [ss for ss in shp]
new_shp[axis] -= 1
utils.alltrue(
np.shape(pmf) == np.array(new_shp),
"Output shape is {fail:}correct")
utils.alltrue(pmf == norm * wids, 'Values do {fail:}match')
# print(pdf)
# print(wids)
# print(pmf)
return
def test_parse(self):
from kalepy.kernels import Distribution
ndim_max = 5
for ndim in range(ndim_max):
# Use `ndim` to make sure that a scalar (non-array) is valid, but this still counts
# as a "one-dimensional" value (i.e. a single-variate distribution), so set ndim=1
if ndim == 0:
xx = 0.5
ndim = 1
else:
nvals = np.random.randint(2, 10)
# Squeeze this array to test that (N,) will be expanded to (1, N)
xx = np.random.uniform(-10.0, 10.0,
nvals * ndim).reshape(ndim,
nvals).squeeze()
yy, _ndim, squeeze = Distribution._parse(xx)
# Make sure number of dimensions are accurate
utils.alltrue(_ndim == ndim)
# Squeeze should be true for less than 2D
utils.alltrue(squeeze == (ndim < 2))
# Make sure values are the same, but 2d
utils.allclose(yy, xx)
utils.alltrue(np.ndim(yy) == 2)
return
def _test_evaluate(self, kernel):
print("\n|Test_Kernels_Generic:_test_evaluate()|")
print(kernel)
# bandwidth should always be scaled to 1.0
# yy, ndim, nval, squeeze = kernel.scale(hh, 0.0, hh)
# tools.assert_true(np.isclose(yy, 1.0))
# tools.assert_true(ndim == 1)
# tools.assert_true(nval == 1)
hh = 1.0
edges = np.linspace(-10 * hh, 10 * hh, 10000)
cents = kale.utils.midpoints(edges, 'lin')
# width = np.diff(edges)
yy = kernel.evaluate(cents[np.newaxis, :], 1).squeeze()
# Make sure kernel is callable
# tools.assert_true(np.allclose(yy, kernel().evaluate(cents)))
# Make sure kernel is normalized
# tot = np.sum(yy*width)
tot = np.trapz(yy, cents)
# print("\t\ttot = {:.4e}".format(tot))
tools.assert_almost_equal(tot, 1.0, delta=1e-3)
# Make sure kernels have expected support
tools.assert_true(np.all(yy >= 0.0))
if kernel._FINITE:
outside = (cents < -hh) | (hh < cents)
inside = (-hh < cents) & (cents < hh)
else:
outside = []
inside = np.ones_like(yy, dtype=bool)
utils.allclose(yy[outside], 0.0, rtol=1e-4, atol=1e-4)
utils.alltrue(yy[inside] > 0.0)
return