def _init_data(self):
"""Override `Sample_Grid._init_data()` to avoid calculating `idx` and `csum`, not needed yet
"""
if self._mass is None:
self._mass = utils.trapz_dens_to_mass(self._dens,
self._edges,
axis=None)
if (self._scalar_mass is None) and (self._scalar_dens is not None):
self._scalar_mass = utils.trapz_dens_to_mass(self._scalar_dens,
self._edges,
axis=None)
return
def _init_data(self):
if self._mass is None:
self._mass = utils.trapz_dens_to_mass(self._dens,
self._edges,
axis=None)
if (self._scalar_mass is None) and (self._scalar_dens is not None):
self._scalar_mass = utils.trapz_dens_to_mass(self._scalar_dens,
self._edges,
axis=None)
idx, csum = _data_to_cumulative(self._mass)
self._idx = idx
self._csum = csum
return
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_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_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_ndim(self, ndim):
from kalepy import utils
print("`ndim` = {}".format(ndim))
BIN_SIZE_RANGE = [10, 30]
extr = [[0.0, np.random.uniform(0.0, 2.0)] for ii in range(ndim)]
norm = np.random.uniform(0.0, 10.0)
# extr = [[0.0, 1.0] for ii in range(ndim)]
# norm = 1.0
edges = [
np.linspace(*ex, np.random.randint(*BIN_SIZE_RANGE)) for ex in extr
]
grid = np.meshgrid(*edges, indexing='ij')
lengths = np.max(extr, axis=-1)
xx = np.min(np.moveaxis(grid, 0, -1) / lengths, axis=-1)
pdf = norm * xx
area = np.product(lengths)
pmf = utils.trapz_dens_to_mass(pdf, edges)
# Known area of a pyramid in ndim
vol = area * norm / (ndim + 1)
tot = np.sum(pmf)
print("Volume = {:.4e}, Total Mass = {:.4e}; ratio = {:.4e}".format(
vol, tot, tot / vol))
utils.allclose(vol,
tot,
rtol=1e-2,
msg="total volume does {fail:}match analytic value")
test = utils.trapz_nd(pdf, edges)
print("Volume = {:.4e}, Total Mass = {:.4e}; ratio = {:.4e}".format(
test, tot, tot / test))
utils.allclose(vol,
tot,
rtol=1e-2,
msg="total volume does {fail:}match `trapz_nd` value")
return
def sample(self, nsamp=None, interpolate=True, return_scalar=None):
"""Sample from the probability distribution.
Arguments
---------
nsamp : scalar or None
interpolate : bool
return_scalar : bool
Returns
-------
vals : (D, N) ndarray of scalar
"""
dens = self._dens
scalar_dens = self._scalar_dens
edges = self._edges
ndim = self._ndim
# ---- initialize parameters
if interpolate and (dens is None):
logging.info("`dens` is None, cannot interpolate sampling")
interpolate = False
# If no number of samples are given, assume that the units of `self._mass` are number of samples, and choose
# the total numbe of samples to be the total of this
if nsamp is None:
nsamp = self._mass.sum()
nsamp = int(nsamp)
if return_scalar is None:
return_scalar = (scalar_dens is not None)
elif return_scalar and (scalar_dens is None):
return_scalar = False
logging.warning(
"WARNING: no `scalar` initialized, but `return_scalar`=True!")
# ---- Get generalized sampling locations
# Choose random bins, proportionally to `mass`, and positions within bins (uniformly distributed)
# `bin_numbers_flat` (N*D,) are the index numbers for bins in flattened 1D array of length N*D
# `intrabin_locs` (D, N) are position [0.0, 1.0] within each bin for each sample in each dimension
bin_numbers_flat, intrabin_locs = self._random_bins(nsamp)
# Convert from flat (N,) indices into ND indices; (D, N) for D dimensions, N samples (`nsamp`)
bin_numbers = np.unravel_index(bin_numbers_flat, self._shape_bins)
# If scalars are also being sampled: find scalar value for bin centers (i.e. bin averages)
# this will be updated/improved if `interpolation=True`
if return_scalar:
scalar_mass = self._scalar_mass
scalar_values = scalar_mass[bin_numbers]
# ---- Place samples in each dimension
vals = np.zeros_like(intrabin_locs)
for dim, (edge, bidx) in enumerate(zip(edges, bin_numbers)):
# Width of bins in this dimension
wid = np.diff(edge)
# Random location, in this dimension, for each bin. Relative position, i.e. between [0.0, 1.0]
loc = intrabin_locs[dim]
# Uniform / no-interpolation :: random-uniform within each bin
if (not interpolate):
vals[dim, :] = edge[bidx] + wid[bidx] * loc
# Interpolated :: random-linear proportional to bin gradients (i.e. slope across bin in each dimension)
else:
# Calculate normalization for gradients; needs to be done for each dimension specifically
# This normalization is needed to ensure that the pdf values are unitary when integrating in each dim
norm = utils.trapz_dens_to_mass(dens, edges, axis=dim)
others = np.arange(ndim).tolist()
others.pop(dim)
norm = utils.midpoints(norm, axis=others)
edge = np.asarray(edge)
# Find the gradient along this dimension (using center-values in other dimensions)
grad = _grad_along(dens, dim) / norm
# get the gradient for each sample
grad = grad.flat[bin_numbers_flat] * wid[bidx]
# interpolate edge values in this dimension (returns values [0.0, 1.0])
temp = _intrabin_linear_interp(loc, grad)
# convert from intrabin positions to overall positions by linearly rescaling
vals[dim, :] = edge[bidx] + temp * wid[bidx]
# interpolate scalar values also
if return_scalar and interpolate:
grad = _grad_along(scalar_dens, dim)
grad = grad.flat[bin_numbers_flat]
# shift `loc` (location within bin) to center point
scalar_values += grad * (loc - 0.5)
if return_scalar:
return vals, scalar_values
return vals