def connect(self, prev_layer: Layer):
if prev_layer is not None:
self.input_shape = prev_layer.output_shape
else:
assert self.input_shape is not None
assert cp.prod(self.input_shape[1:]) == cp.prod(self.output_shape[1:]), "can not change the element's number"
Layer.connect(self, prev_layer)
def __call__(self, layer: Layer)-> Layer:
if layer is not None:
self.input_shape = layer.output_shape
else:
assert self.input_shape is not None
assert cp.prod(self.input_shape[1:]) == cp.prod(self.output_shape[1:]),"can not change the element's number"
super(Reshape, self).__call__(layer)
return self
def decompose_size(self, size):
size = cp.array(size)
if size.ndim == 2:
fan_in, fan_out = size
elif size.ndim == 4 or size.ndim == 5:
respective_field_size = cp.prod(size[2:])
fan_in = size[1] * respective_field_size
fan_out = size[0] * respective_field_size
else:
fan_in = fan_out = int(cp.sqrt(cp.prod(size)))
return fan_in, fan_out
def wiener(im, mysize=None, noise=None):
"""
Perform a Wiener filter on an N-dimensional array.
Apply a Wiener filter to the N-dimensional array `im`.
Parameters
----------
im : ndarray
An N-dimensional array.
mysize : int or array_like, optional
A scalar or an N-length list giving the size of the Wiener filter
window in each dimension. Elements of mysize should be odd.
If mysize is a scalar, then this scalar is used as the size
in each dimension.
noise : float, optional
The noise-power to use. If None, then noise is estimated as the
average of the local variance of the input.
Returns
-------
out : ndarray
Wiener filtered result with the same shape as `im`.
"""
im = asarray(im)
if mysize is None:
mysize = [3] * im.ndim
mysize = np.asarray(mysize)
if mysize.shape == ():
mysize = cp.repeat(mysize.item(), im.ndim)
mysize = np.asarray(mysize)
# Estimate the local mean
lMean = correlate(im, ones(mysize), "same") / prod(mysize, axis=0)
# Estimate the local variance
lVar = (
correlate(im ** 2, ones(mysize), "same") / prod(mysize, axis=0)
- lMean ** 2
)
# Estimate the noise power if needed.
if noise is None:
noise = mean(ravel(lVar), axis=0)
res = im - lMean
res *= 1 - noise / lVar
res += lMean
out = where(lVar < noise, lMean, res)
return out
def downsample_gpu(image, size_out):
"""
Use Fourier methods to change the sample interval and/or aspect ratio
of any dimensions of the input image. Uses CuPy.
"""
x = cp.fft.fftshift(cp.fft.fft2(image))
# crop x:
nx, ny = x.shape
nsx = int(cp.floor(nx/2) - cp.floor(size_out[1]/2))
nsy = int(cp.floor(ny/2) - cp.floor(size_out[0]/2))
fx = x[nsx : nsx + size_out[1], nsy : nsy + size_out[0]]
output = cp.fft.ifft2(cp.fft.ifftshift(fx)) * (cp.prod(cp.array(size_out)) / cp.prod(cp.array(image.shape)))
return cp.asnumpy(output.real)
def normal_density_cupy(x, mean, stddev, from_axis=None, eps=1e-8, gpu=0):
import cupy as cp
with cp.cuda.Device(gpu):
variance = cp.maximum(stddev ** 2, eps)
stddev = cp.maximum(stddev, eps)
density = cp.exp(-cp.square(x - mean) / (2 * variance)) / (stddev * math.sqrt(2 * math.pi))
if (from_axis is not None) and (from_axis >= 0):
shape = tuple(density.shape[:from_axis]) + (cp.prod(density.shape[from_axis:]),)
density = cp.reshape(density, shape)
density = cp.prod(density, axis=from_axis)
return density
def __init__(self,
name,
observables,
binning=None,
interpolation=None,
value=None):
self.systematics = [
syst for dim_systs in zip(observables.scales, observables.shifts,
observables.resolutions)
for syst in dim_systs
]
# Should be linked to something that loads MC when called (DataLoader)
self.mc_param = observables.analysis.add_parameter(name + '_mc',
fixed=False)
self.cur_mc = None
self.interpolation = interpolation
self.binning = binning
self.bin_edges = binning_to_edges(binning,
lows=observables.lows,
highs=observables.highs)
self.indexes = [np.arange(len(edges)) for edges in self.bin_edges]
self.a_kj, self.b_kj = edges_to_points(self.bin_edges)
self.bin_centers = [(edges[:-1] + edges[1:]) / 2
for edges in self.bin_edges]
self.bin_vol = cp.prod(self.b_kj - self.a_kj, axis=1)
super().__init__(name,
observables, [self.mc_param] + self.systematics,
value=value)
def integrate_mc_gpu(func, limits, num):
xs = sample_from(limits, num, cp.random.uniform)
ys = func(xs)
integral = cp.prod(cp.array([i[1] - i[0]
for i in limits])) * cp.sum(ys) / num
return integral
def prob(self, sample, **kwargs):
if _GPU_ENABLED:
prob = cp.prod(
cp.asarray([self[key].prob(sample[key]) for key in sample]),
**kwargs)
return prob
else:
return super(PriorDict, self).prob(sample, **kwargs)
def __call__(self, layers):
super(Flatten, self).__call__(layers)
flatten_shape = cp.prod(cp.array(self.input_shape[self.out_dim -
1:])).tolist()
flatten_shape = self.input_shape[:self.out_dim - 1] + (flatten_shape, )
self.output_shape = flatten_shape
return self
def connect(self, prev_layer):
assert len(prev_layer.output_shape) >= 3
flatten_shape = cp.prod(
cp.array(prev_layer.output_shape[self.out_dim - 1:])).tolist()
flatten_shape = prev_layer.output_shape[:self.out_dim -
1] + (flatten_shape, )
self.output_shape = flatten_shape
Layer.connect(self, prev_layer)
def _get_region(im_height, im_width, center_x, center_y, sigma, bbox):
radius = math.sqrt(np.prod(np.array(bbox[2:])) / np.pi) * sigma
# top-left corner
x0 = int(max(0, center_x - radius + 0.5))
y0 = int(max(0, center_y - radius + 0.5))
# bottom-right corner
x1 = int(min(im_width - 1, center_x + radius + 0.5)) + 1
y1 = int(min(im_height - 1, center_y + radius + 0.5)) + 1
return y0, y1, x0, x1
def __call__(self, size):
size = cp.array(size)
flat_shape = (size[0].tolist(), cp.prod(size[1:]).tolist())
a = Normal(1.)(flat_shape)
u, _, v = cp.linalg.svd(a, full_matrices=False)
q = u if u.shape == flat_shape else v
q = q.reshape(size.tolist())
q = self.gain * q
return q
def repeat_to_match_shape(g, shape, dtype, axis, keepdims):
"""Returns the array g repeated along axis to fit vector space vs.
Also returns the number of repetitions of the array."""
if shape == ():
return g, 1
axis = list(axis) if isinstance(axis, tuple) else axis
new_shape = ocp.array(shape)
new_shape[axis] = 1
new_shape = tuple([int(i) for i in new_shape])
num_reps = ocp.prod(ocp.array(shape)[axis])
return acp.reshape(g, new_shape) + ocp.zeros(shape, dtype=dtype), num_reps
def _kdpdf0(x_j, t_ij, h_j, w_i):
'''
x_j is the j-dimensional point to evaluate the PDF at
t_ij are the i events in the PDF at j-dimensional points
h_j are the bandwidths for all PDF events in dimension j
'''
w = cp.sum(w_i)
h_j_prod = cp.prod(KernelDensityPDF._inv_sqrt_2pi / h_j)
res = h_j_prod * cp.sum(
w_i * cp.exp(-0.5 * cp.sum(cp.square(
(x_j - t_ij) / h_j), axis=1))) / w
return res if np == cp else res.get()
def __init__(self,name,pdf,binning):
from .signal import BinnedPDF
super().__init__(name,[pdf])
self.pdf = pdf
if isinstance(pdf,BinnedPDF) and pdf.binning == binning:
self.binned_correctly = True
else:
self.binned_correctly = False
self.bin_edges = binning_to_edges(binning)
self.a_kj, self.b_kj = edges_to_points(self.bin_edges)
self.bin_vol = cp.ascontiguousarray(cp.prod(self.b_kj-self.a_kj,axis=1))
self.last_systs = None
self.bin_ints = None
def calc_loss(self, y_hat, y_true):
to_sum_shape = cp.asarray(y_hat.shape[:-1])
avg = cp.prod(to_sum_shape)
loss = 0
if y_hat.ndim == 2:
for m in range(y_hat.shape[0]):
loss -= cp.log(y_hat[m, y_true[m]])
elif y_hat.ndim == 3:
for m in range(y_hat.shape[0]):
for n in range(y_hat.shape[1]):
loss -= cp.log(y_hat[m, n, y_true[m, n]])
loss /= avg
return loss
def _kdpdf1(x_j, t_ij, h_ij, w_i):
'''
Evaluate a the normalized PDF at a single point using generic NumPy/CuPy
code instead of a dedicated CUDA kernel.
x_j is the j-dimensional point to evaluate the PDF at
t_ij are the i events in the PDF at j-dimensional points
h_ij are the bandwidths of each PDF event i in dimension j
w_i are the weights of each PDF event
'''
res = cp.sum(
w_i * cp.prod(KernelDensityPDF._inv_sqrt_2pi / h_ij, axis=1) *
cp.exp(-0.5 * cp.sum(cp.square((x_j - t_ij) / h_ij), axis=1)))
return res if np == cp else res.get()
def normal_log_density_cupy(x, mean, stddev, from_axis=None, eps=1e-8, gpu=0):
import cupy as cp
with cp.cuda.Device(gpu):
variance = cp.maximum(stddev ** 2, eps)
log_stddev = cp.log(cp.maximum(stddev, eps))
log_density = -0.5 * (math.log(2 * math.pi) + 2 * log_stddev + ((x - mean)**2 / variance))
if (from_axis is not None) and (from_axis >= 0):
shape = tuple(log_density.shape[:from_axis]) + (cp.prod(log_density.shape[from_axis:]),)
log_density = cp.reshape(log_density, shape)
log_density = cp.sum(log_density, axis=from_axis)
return log_density
def prod(tensor, axis=None, dtype=None, out=None, keepdims=False):
"""Returns the product of an array along a given axis.
Args:
tensor (ndarray): Array to take the maximum.
axis (int): Along which axis to take the maximum. The flattened array
is used by default. Defaults to None.
dtype: Data type specifier.
out (ndarray): Output array. Default to None.
keepdims (bool): If ``True``, the axis is kept as an axis of
size one. Default to False.
Returns:
ndarray: The maximum of ``tensor``, along the axis if specified.
"""
return cp.prod(tensor, axis=axis, out=out, keepdims=keepdims, dtype=dtype)
def add_water(self, atom_histograms_gpu):
vacs = cp.prod(cp.where(atom_histograms_gpu == 0, True, False), axis=0)
# average number of water molecules in a voxel
vox_wat_num = water_num_dens * self.d1 * self.d2 * self.dz
box = (self.n_slice, self.n1, self.n2)
oxygens = cp.where(vacs, cp.random.poisson(vox_wat_num, box),
0).astype(cp.int)
hydrogens = cp.where(vacs, cp.random.poisson(vox_wat_num * 2, box),
0).astype(cp.int)
unique_elements_list = list(self.unique_elements)
for z, hist in [(1, hydrogens), (8, oxygens)]:
idx = unique_elements_list.index(z)
atom_histograms_gpu[idx] += hist
return atom_histograms_gpu
def _int_kdpdf1(a_j, b_j, t_ij, h_ij, w_i, get=True):
'''
Integrates the PDF evaluated by _kdpdf1 and _kdpdf1_multi.
a_j and b_j are the j-dimensional points represneting the lower and
upper bounds of integration
t_ij are the i events in the PDF at j-dimensional points
h_ij are the bandwidths of each PDF event i in dimension j
w_i are the weights of each PDF event
'''
w = cp.sum(w_i)
n = t_ij.shape[0]
d = t_ij.shape[1]
res = cp.sum(w_i * cp.prod(erf(
(b_j - t_ij) / h_ij / KernelDensityPDF._sqrt2) - erf(
(a_j - t_ij) / h_ij / KernelDensityPDF._sqrt2),
axis=1)) / w / (2**d)
return res.get() if get else res
def wiener(im, mysize=None, noise=None):
"""
Perform a Wiener filter on an N-dimensional array.
Apply a Wiener filter to the N-dimensional array `im`.
Parameters
----------
im : ndarray
An N-dimensional array.
mysize : int or array_like, optional
A scalar or an N-length list giving the size of the Wiener filter
window in each dimension. Elements of mysize should be odd.
If mysize is a scalar, then this scalar is used as the size
in each dimension.
noise : float, optional
The noise-power to use. If None, then noise is estimated as the
average of the local variance of the input.
Returns
-------
out : ndarray
Wiener filtered result with the same shape as `im`.
"""
im = cp.asarray(im)
if mysize is None:
mysize = [3] * im.ndim
mysize = np.asarray(mysize)
if mysize.shape == ():
mysize = cp.repeat(mysize.item(), im.ndim)
mysize = np.asarray(mysize)
lprod = cp.prod(mysize, axis=0)
lMean = correlate(im, cp.ones(mysize), "same")
lVar = correlate(im**2, cp.ones(mysize), "same")
lMean, lVar = _wiener_prep_kernel(lMean, lVar, lprod)
# Estimate the noise power if needed.
if noise is None:
noise = cp.mean(cp.ravel(lVar), axis=0)
return _wiener_post_kernel(im, lMean, lVar, noise)
def _adapt_bandwidth(self, w_i=None):
'''
Calculates and returns bandwidths for all pdf events.
'''
n = self.t_ij.shape[0]
d = len(self.observables.dimensions)
sigma = cp.prod(self.sigma_j)**(1 / d)
estimates = self._estimate_pdf_multi(self.t_ij, w_i=w_i, get=False)
h_i = (4/(d+2))**(1/(d+4)) \
* n**(-1/(d+4)) \
/ sigma \
/ estimates**(1/d)
h_ij = cp.outer(h_i, self.rho * self.sigma_j)
if cp.any(cp.isnan(h_ij)):
print('d:', d, 'n:', n, 'sigma:', sigma)
print('sigma_j:', self.sigma_j)
print('small_estimates', estimates[estimates < 1e-8])
raise Exception('NaN bandwidths in ' + self.name)
cp.cuda.Stream.null.synchronize()
return cp.ascontiguousarray(h_ij)
def _arg_min_or_max(self, axis, out, op, compare):
if out is not None:
raise ValueError("Sparse matrices do not support "
"an 'out' parameter.")
sputils.validateaxis(axis)
if axis is None:
if 0 in self.shape:
raise ValueError("Can't apply the operation to "
"an empty matrix.")
if self.nnz == 0:
return 0
else:
zero = self.dtype.type(0)
mat = self.tocoo()
mat.sum_duplicates()
am = op(mat.data)
m = mat.data[am]
if compare(m, zero):
return mat.row[am] * mat.shape[1] + mat.col[am]
else:
size = cupy.prod(mat.shape)
if size == mat.nnz:
return am
else:
ind = mat.row * mat.shape[1] + mat.col
zero_ind = _find_missing_index(ind, size)
if m == zero:
return min(zero_ind, am)
else:
return zero_ind
if axis < 0:
axis += 2
return self._arg_min_or_max_axis(axis, op)
def __init__(self,
name,
signals,
observables,
binning=21,
nan_behavior='unlikely'):
self.nan_behavior = nan_behavior
self.bin_edges = binning_to_edges(binning,
lows=observables.lows,
highs=observables.highs)
self.a_kj, self.b_kj = edges_to_points(self.bin_edges)
self.bin_vol = cp.ascontiguousarray(
cp.prod(self.b_kj - self.a_kj, axis=1))
self.signals = signals
self.observables = observables
n_evs = [s.nev_param for s in signals]
binned_signals = [
PDFBinner(s.name + '_binner', s, binning=binning) for s in signals
]
super().__init__(name, n_evs + binned_signals + [observables])
self.last_x_kj = None
def backward(self, y_hat, y_true):
# to_sum_shape = cp.asarray(y_hat.shape[:-1])
# avg = cp.prod(to_sum_shape)
# idx = []
# for s in to_sum_shape:
# idx.append(cp.arange(s).tolist())
# idx.append(y_true.flatten().tolist())
#
# y_hat[idx]-=1
# return y_hat/avg
to_sum_shape = cp.asarray(y_hat.shape[:-1])
avg = cp.prod(to_sum_shape)
output = y_hat
if y_hat.ndim == 2:
for m in range(y_hat.shape[0]):
output[m, y_true[m]] -= 1
elif y_hat.ndim == 3:
for m in range(y_hat.shape[0]):
for n in range(y_hat.shape[1]):
output[m, n, y_true[m, n]] -= 1
output /= avg
return output
def backward(self):
grads=self.grads
gamma,beta=self.variables
outputs=cp.zeros_like(grads)
for k in range(grads.shape[self.axis]):
xmu,sqrtvar,normalzied_x=self.cache[k]
if beta.require_grads:
beta.grads[k]+=cp.sum(grads[:,k])
if gamma.require_grads:
gamma.grads[k]+=cp.sum(grads[:,k]*normalzied_x)
dnormalized_x=grads[:,k]*gamma.output_tensor[k]
# equals to var^-3/2,where sqrtvar=var^1/2
dvar=cp.sum(cp.power(-1./sqrtvar,3)*xmu*dnormalized_x*0.5)
dmean=cp.sum(-dnormalized_x/sqrtvar)-dvar*2*cp.mean(xmu)
m=cp.prod(cp.asarray(xmu.shape)).tolist()
outputs[:,k]=dnormalized_x/sqrtvar+dvar*2*xmu/m+dmean/m
for layer in self.inbound_layers:
if layer.require_grads:
layer.grads+=outputs
else:
layer.grads=grads
def ts_product(x, window):
if window > len(x):
return cp.full(len(x), cp.nan)
# # 增加对溢出的处理
# max_element = cp.max(cp.abs(x))
# if max_element**window == cp.inf:
# return cp.nan
# 对于有空值的地方，开方再取幂
# exp_nan_inf = window / ts_count_not_nan_inf(x, window)
# 空值，填充为1
x = cp.where(cp.isinf(x), cp.nan, x)
pre_fix = cp.full(window - 1, cp.nan)
x_rolling_array = cp_rolling_window(x, window)
result = cp.prod(x_rolling_array, axis=1)
# 指数放缩, 有一个奇怪的现象就是1^nan = 1
# result = cp.sign(result) * (cp.abs(result)**exp_nan_inf)
# 当window内均为nan时，处理为nan
# result[cp.isnan(exp_nan_inf)] = cp.nan
return cp.concatenate((pre_fix, result))
def __init__(self,
name,
observables,
reflect_axes=None,
value=None,
bootstrap_binning=None,
rho=1.0):
self.rho = rho
self.bootstrap_binning = bootstrap_binning
if bootstrap_binning is not None:
self.bin_edges = binning_to_edges(bootstrap_binning,
lows=observables.lows,
highs=observables.highs)
self.indexes = [np.arange(len(edges)) for edges in self.bin_edges]
self.a_kj, self.b_kj = edges_to_points(self.bin_edges)
self.bin_centers = [(edges[:-1] + edges[1:]) / 2
for edges in self.bin_edges]
self.bin_vol = cp.ascontiguousarray(
cp.prod(self.b_kj - self.a_kj, axis=1))
self.reflect_axes = reflect_axes if reflect_axes is not None else [
False for _ in range(len(observables.dimensions))
]
self.a = cp.asarray([l for l in observables.lows])
self.b = cp.asarray([h for h in observables.highs])
self.systematics = [
syst for dim_systs in zip(observables.scales, observables.shifts,
observables.resolutions)
for syst in dim_systs
]
# Should be linked to something that loads MC when called (DataLoader)
self.mc_param = observables.analysis.add_parameter(name + '_mc',
fixed=False)
self.cur_mc = None
super().__init__(name,
observables, [self.mc_param] + self.systematics,
value=value)