def GaussForm(AtomicData):
# At some point here, we need to add the portion that will find the scat factor based on atomtype
# but for now...
# scattering_params = etbl.get(at_type)
#step = 0
OutputArray = cp.zeros((BoxS,BoxS,BoxS))
OutputArray = cp.array(OutputArray, dtype = np.complex64)
scalefac = float(BoxS*apix)
for atom in AtomicData:
#step += 1
#t1 = time.time()
if(atom[0][0] == 'H'):
scattering_params = cp.array([1.0,3.15])
elif(atom[0] == 'OCbb'):
scattering_params = cp.array([1.35,4.15])
else:
scattering_params = cp.array([1.2,3.2])
scattering_params = (scattering_params/scalefac)
coords = atom[1:]
center = cp.array([cp.float(coords[0]/apix),coords[1]/apix,cp.float(coords[2]/apix)])
s = cp.float(1/scattering_params[1])
ampl = cp.float((1/cp.sqrt(cp.power(2*pi,3)))*(1/cp.power(s,3)))
coords = None
OutputArray += ((cp.float(scattering_params[0]) * cp.fft.ifftshift(ampl* cp.exp(-cp.power(pi,2)*(cp.power(ii,2)+cp.power(jj,2)+cp.power(kk,2))/(2*cp.power(s,2)) - ( (2*pi)*1j*(ii*center[0]+jj*center[1]+kk*center[2]) )) )))
center = None
#t2 = time.time()
#print('Atom Addition Time: ' + str(t2-t1))
#print('Current atom: ' + str(step))
ToAdd, Rem, ampl, s, center, coords, scattering_params,t1,t2 = None,None,None,None,None,None,None,None,None
OutputArray = cp.asnumpy(OutputArray)
#print('This is the size: ' + str(OutputArray.nbytes))
return OutputArray
def optimize(self, dw):
if self.opt == 'momentum':
return 0.6 * self.V - self.lr * dw
elif self.opt == 'adagrad':
self.Acc += dw * dw
return -self.lr * dw / (cp.sqrt(self.Acc) + 1e-7)
elif self.opt == 'rmsprop':
decay = 0.2
self.Acc = decay * self.Acc + (1 - decay) * dw * dw
return -self.lr * dw / (cp.sqrt(self.Acc) + 1e-7)
elif self.opt == 'adam':
beta1 = 0.6
beta2 = 0.2
self.mo = beta1 * self.mo + (1 - beta1) * dw
self.Acc = beta2 * self.Acc + (1 - beta2) * dw * dw
return -self.lr * self.mo / (cp.sqrt(self.Acc) + 1e-7)
elif self.opt == 'nadam':
self.t += 1
beta1 = 0.6
beta2 = 0.2
self.mo = beta1 * self.mo + (1 - beta1) * dw
self.mo = self.mo / (1 - cp.power(beta1, self.t))
self.Acc = beta2 * self.Acc + (1 - beta2) * dw * dw
self.Acc = self.Acc / (1 - cp.power(beta1, self.t))
return -self.lr * self.mo / (cp.sqrt(self.Acc) + 1e-7)
def yangDistributionDifference(aNeg, bNeg, aPos, bPos, p=1):
"""
Eq. (7) from :
Yang, R., Jiang, Y., Mathews, S. et al.
Data Min Knowl Disc (2019) 33: 995.
https://doi.org/10.1007/s10618-019-00622-6
"""
sampleSize = 1000
negSample = xp.random.beta(aNeg, bNeg, sampleSize)
posSample = xp.random.beta(aPos, bPos, sampleSize)
negPDF_NEG, posPDF_NEG, pdfDiffPos_NEG, pdfDiffNeg_NEG, pdfMax_NEG = calcDifference(
negSample, aNeg, bNeg, aPos, bPos)
negPDF_POS, posPDF_POS, pdfDiffPos_POS, pdfDiffPOS_POS, pdfMax_POS = calcDifference(
posSample, aNeg, bNeg, aPos, bPos)
numerator1 = xp.mean(pdfDiffNeg_NEG / negPDF_NEG)
numerator2 = xp.mean(pdfDiffPos_POS / posPDF_POS)
sumVecs = xp.power(numerator1,
xp.ones_like(numerator1) * p) + xp.power(
numerator2,
xp.ones_like(numerator2) * p)
dPHat = xp.power(sumVecs, xp.ones_like(sumVecs) * (1 / p))
dTermNeg = (posPDF_NEG * 0.5) + (negPDF_NEG * 0.5)
dTermPos = (posPDF_POS * 0.5) + (negPDF_POS * 0.5)
denominator = (xp.sum(pdfMax_NEG / dTermNeg) +
xp.sum(pdfMax_POS / dTermPos)) / (2 * sampleSize)
return dPHat / denominator
def update(self, w, grad_wrt_w):
# If not initialized
if self.w_updt is None:
self.w_updt = cupy.zeros(np.shape(w))
self.E_w_updt = cupy.zeros(np.shape(w))
self.E_grad = cupy.zeros(np.shape(grad_wrt_w))
# Update average of gradients at w
self.E_grad = self.rho * self.E_grad + (1 - self.rho) * cupy.power(
grad_wrt_w, 2)
RMS_delta_w = cupy.sqrt(self.E_w_updt + self.eps)
RMS_grad = cupy.sqrt(self.E_grad + self.eps)
# Adaptive learning rate
adaptive_lr = RMS_delta_w / RMS_grad
# Calculate the update
self.w_updt = adaptive_lr * grad_wrt_w
# Update the running average of w updates
self.E_w_updt = self.rho * self.E_w_updt + (1 - self.rho) * cupy.power(
self.w_updt, 2)
return w - self.w_updt
def compute_gain(sound, fs, min_db=-80.0, mode='A_weighting'):
if fs == 16000:
n_fft = 2048
elif fs == 44100:
n_fft = 4096
else:
raise Exception('Invalid fs {}'.format(fs))
stride = n_fft // 2
gain = None
for i in range(0, len(sound[0]) - n_fft + 1, stride):
if mode == 'RMSE':
g = cupy.mean(sound[i:i + n_fft]**2, axis=1)
elif mode == 'A_weighting':
spec = cupy.fft.rfft(
cupy.hanning(n_fft + 1)[:-1] * sound[:, i:i + n_fft])
power_spec = cupy.abs(spec)**2
a_weighted_spec = power_spec * cupy.power(10,
a_weight(fs, n_fft) / 10)
g = cupy.sum(a_weighted_spec, axis=1)
else:
raise Exception('Invalid mode {}'.format(mode))
if i == 0:
gain = g.reshape([-1, 1])
else:
gain = cupy.concatenate((gain, g.reshape([-1, 1])), axis=1)
gain = cupy.maximum(gain, cupy.power(10, min_db / 10))
gain_db = 10 * cupy.log10(gain)
return gain_db
def vander(x, N=None, increasing=False):
"""Returns a Vandermonde matrix.
Args:
x (array-like): 1-D array or array-like object.
N (int, optional): Number of columns in the output.
``N = len(x)`` by default.
increasing (bool, optional): Order of the powers of the columns.
If True, the powers increase from right to left,
if False (the default) they are reversed.
Returns:
cupy.ndarray: A Vandermonde matrix.
.. seealso:: :func:`numpy.vander`
"""
x = cupy.asarray(x)
if x.ndim != 1:
raise ValueError("x must be a one-dimensional array or sequence.")
if N is None:
N = len(x)
v = cupy.empty((len(x), N), dtype=numpy.promote_types(x.dtype, int))
tmp = v[:, ::-1] if not increasing else v
cupy.power(x.reshape(-1, 1), cupy.arange(N), out=tmp)
return v
def gpu_gaussian(self, a, b, s):
km = cp.empty(shape=(a.shape[0], b.shape[0]), dtype=a.dtype)
km = cp.multiply(cp.dot(a, b.T, out=km), -2, out=km)
km += cp.power(a, 2).sum(axis=1).reshape(-1, 1)
km += cp.power(b, 2).sum(axis=1)
cp.multiply(km, -1 / (2 * s * s), out=km)
cp.exp(km, out=km)
return km
def _calc_offset(offset_map, region, parent_y, parent_x):
y0, y1, x0, x1 = region
x_area, y_area = offset_map[:, y0:y1, x0:x1]
x_vec = np.power(np.subtract(np.arange(x0, x1), parent_x), 2)
y_vec = np.power(np.subtract(np.arange(y0, y1), parent_y), 2)
xv, yv = np.meshgrid(x_vec, y_vec)
dist = np.sqrt(xv + yv) # sqrt(y^2 + x^2)
xv = np.divide(xv, dist) # normalize x
yv = np.divide(yv, dist) # normalize y
offset_map[0, y0:y1, x0:x1] = np.maximum(x_area, xv)
offset_map[1, y0:y1, x0:x1] = np.maximum(y_area, yv)
def create_col(self, num_rows, dtype=np.float32, min_val=0, max_val=1):
gamma = 1 - self.alpha
# range 1.0 - 2.0 to avoid using 0, which represents unknown, null, None
ser = _make_df(cupy.random.uniform(0.0, 1.0, size=num_rows))[0]
factor = cupy.power(max_val, gamma) - cupy.power(min_val, gamma)
ser = (ser * factor.item()) + cupy.power(min_val, gamma).item()
exp = 1.0 / gamma
ser = ser.pow(exp)
# replace zeroes saved for unknown
# add in nulls if requested
# select indexes
return ser.astype(dtype)
def weibull(self, a, size=None, dtype=float):
"""Returns an array of samples drawn from the weibull distribution.
.. seealso::
:func:`cupy.random.weibull` for full documentation,
:meth:`numpy.random.RandomState.weibull`
"""
a = cupy.asarray(a)
if cupy.any(a < 0):
raise ValueError("a < 0")
x = self.standard_exponential(size, dtype)
cupy.power(x, 1. / a, out=x)
return x
def getDistance(y1, x1, y2, x2):
"""
Get the average distance between two function
Parameters:
1. originalArr : Array of Y values of the baselineFunction
2. arr2 : Array of Y values of the test function
RETURN -> Float: dist
"""
res = np.sqrt( np.power((x1-x2), 2) + np.power((y1-y2), 2) )
res = np.asnumpy(res).tolist()
return res
def getBiasChange(DELTA, LayerIndex):
biasgradient = np.dot(np.ones((1, InputData.shape[0])),
DELTA[LayerIndex + 1])
biassquaresum[LayerIndex] += np.power(biasgradient, 2)
biaschange = -speed * biasgradient / (
np.sqrt(biassquaresum[LayerIndex]) + epsilon)
return biaschange
def backward(self):
grads = self.grads
if len(self.input_shape) == 4:
N, C, H, W = self.input_shape
grads = grads.transpose(0, 3, 2, 1).reshape((N * H * W, C))
gamma, beta = self.variables
xmu, sqrtvar, normalized_x = self.cache
if beta.require_grads:
beta.grads += cp.sum(grads, axis=0)
if gamma.require_grads:
gamma.grads += cp.sum(grads * normalized_x, axis=0)
N = normalized_x.shape[0]
dnormalized_x = grads * gamma.output_tensor
dvar = cp.sum(cp.power(-1. / sqrtvar, 3) * xmu * dnormalized_x * 0.5,
axis=0)
dmean = cp.sum(-dnormalized_x / sqrtvar,
axis=0) - 2 * dvar * cp.mean(xmu, axis=0)
outputs = dnormalized_x / sqrtvar + dvar * 2 * xmu / N + dmean / N
if len(self.input_shape) == 4:
N, C, H, W = self.input_shape
outputs = outputs.reshape(N, W, H, C).transpose(0, 3, 2, 1)
for layer in self.inbounds:
if layer.require_grads:
layer.grads += outputs
else:
layer.grads = grads
def test_randn(self):
ret = util.randn(int(1e6))
meanPower = xp.mean(xp.power(xp.abs(ret), 2))
self.assertAlmostEqual(meanPower,
1.0,
places=2,
msg="The mean power of randn differs from 1.0")
def binary_to_decimal(X):
"""
| This function takes :code:`X` of shape (n_images, L2, y, x) as an argument.
| Supporse that :code:`X[k]` (0 <= k < n_images) can be represented as
.. code-block:: none
X[k] = [map_k[0], map_k[1], ..., map_k[L2-1]]
where the shape of each map_k is (y, x).
Then we calculate
.. code-block:: none
a[0] * map_k[0] + a[1] * map_k[1] + ... + a[L2-1] * map_k[L2-1]
for each :code:`X[k]`, where :math:`a = [2^{L2-1}, 2^{L2-2}, ..., 2^{0}]`
Therefore, the output shape must be (n_images, y, x)
Parameters
----------
X: xp.ndarray
Feature maps
"""
a = xp.arange(X.shape[1])[::-1]
a = xp.power(2, a)
return xp.tensordot(X, a, axes=([1], [0]))
def predict_normalized(self, x): # x:shape=[2]
Psi = cp.exp(-cp.sum(self.theta * cp.power(
(cp.abs(self.X - x[cp.newaxis, :])), self.pl),
axis=1))
ccc = Psi.T.dot(self.bbb)
fff = self.mu + ccc
return fff
def mix(sound1, sound2, r, fs):
gain1 = cupy.max(compute_gain(sound1.data, fs), axis=1) # Decibel
gain2 = cupy.max(compute_gain(sound2.data, fs), axis=1)
t = 1.0 / (1 + cupy.power(10, (gain1 - gain2) / 20.) * (1 - r) / r)
sound = ((sound1 * t[:, None] + sound2 * (1 - t[:, None])) /
cupy.sqrt(t[:, None]**2 + (1 - t[:, None])**2))
return sound
def power(self, a, size=None, dtype=float):
"""Returns an array of samples drawn from the power distribution.
.. seealso::
:func:`cupy.random.power` for full documentation,
:meth:`numpy.random.RandomState.power`
"""
a = cupy.asarray(a)
if cupy.any(a < 0):
raise ValueError('a < 0')
if size is None:
size = a.shape
x = self.standard_exponential(size=size, dtype=dtype)
cupy.exp(-x, out=x)
cupy.add(1, -x, out=x)
cupy.power(x, 1. / a, out=x)
return x
def weibull(self, a, size=None, dtype=float):
"""Returns an array of samples drawn from the weibull distribution.
.. warning::
This function may synchronize the device.
.. seealso::
- :func:`cupy.random.weibull` for full documentation
- :meth:`numpy.random.RandomState.weibull`
"""
a = cupy.asarray(a)
if cupy.any(a < 0): # synchronize!
raise ValueError('a < 0')
x = self.standard_exponential(size, dtype)
cupy.power(x, 1. / a, out=x)
return x
def update(self, layers):
#없으면 init 해줌
if not len(self.m) or not len(self.v):
for i, layer in enumerate(layers):
g = layer.get_gradient()
if not g:
continue
dw, db = g
dw_idx = "dw" + str(i)
db_idx = "db" + str(i)
self.m[dw_idx] = np.zeros_like(dw)
self.m[db_idx] = np.zeros_like(db)
self.v[dw_idx] = np.zeros_like(dw)
self.v[db_idx] = np.zeros_like(db)
#받아온다
for i, layer in enumerate(layers):
weights, gradients = layer.get_weight(), layer.get_gradient()
if weights is None or gradients is None:
continue
(w, b) = weights
(dw, db) = gradients
#key 값
dw_idx = "dw" + str(i)
db_idx = "db" + str(i)
self.m[dw_idx] = self.beta_1 * self.m[dw_idx] + (1 -
self.beta_1) * dw
self.m[db_idx] = self.beta_1 * self.m[db_idx] + (1 -
self.beta_1) * db
self.v[dw_idx] = self.beta_2 * self.v[dw_idx] + (
1 - self.beta_2) * np.power(dw, 2)
self.v[db_idx] = self.beta_2 * self.v[db_idx] + (
1 - self.beta_2) * np.power(db, 2)
# 나중에 가중치 편향이 일어나면 step 고려해줘야함
dw = self.m[dw_idx] / (np.sqrt(self.v[dw_idx]) + self.eps)
db = self.m[db_idx] / (np.sqrt(self.v[db_idx]) + self.eps)
weight = layer.weights - self.lr * dw
bias = layer.bias - self.lr * db
layer.set_weight(weight, bias)
def GaussForm(AtomicData, HParams):
OutputArray = cp.zeros((340, 340, 340))
OutputArray = cp.array(OutputArray, dtype=np.complex64)
for atom in AtomicData:
if (atom[0][0] == 'H'):
scattering_params = cp.array(HParams)
else:
scattering_params = cp.array([1, 3])
coords = atom[1:]
center = cp.array([
cp.float(coords[0] / apix), coords[1] / apix,
cp.float(coords[2] / apix)
])
s = cp.float(1 / scattering_params[1])
ampl = cp.float(
(1 / cp.sqrt(cp.power(2 * pi, 3))) * (1 / cp.power(s, 3)))
coords = None
OutputArray += ((cp.float(scattering_params[0]) * cp.fft.ifftshift(
ampl *
cp.exp(-cp.power(pi, 2) *
(cp.power(ii, 2) + cp.power(jj, 2) + cp.power(kk, 2)) /
(2 * cp.power(s, 2)) -
((2 * pi) * 1j *
(ii * center[0] + jj * center[1] + kk * center[2]))))))
center = None
ToAdd, Rem, ampl, s, center, coords, scattering_params, t1, t2 = None, None, None, None, None, None, None, None, None
OutputArray = cp.asnumpy(OutputArray)
return OutputArray
def GaussForm(AtomicData, Params):
#step = 0
OutputArray = cp.zeros((340, 340, 340))
OutputArray = cp.array(OutputArray, dtype=np.complex64)
scattering_params = cp.array(Params)
for atom in AtomicData:
#step += 1
#t1 = time.time()
coords = atom[1:]
center = cp.array([
cp.float(coords[0] / apix), coords[1] / apix,
cp.float(coords[2] / apix)
])
s = cp.float(1 / scattering_params[1])
ampl = cp.float(
(1 / cp.sqrt(cp.power(2 * pi, 3))) * (1 / cp.power(s, 3)))
coords = None
OutputArray += ((cp.float(scattering_params[0]) * cp.fft.ifftshift(
ampl *
cp.exp(-cp.power(pi, 2) *
(cp.power(ii, 2) + cp.power(jj, 2) + cp.power(kk, 2)) /
(2 * cp.power(s, 2)) -
((2 * pi) * 1j *
(ii * center[0] + jj * center[1] + kk * center[2]))))))
center = None
#t2 = time.time()
#print('Atom Addition Time: ' + str(t2-t1))
#print('Current atom: ' + str(step))
ToAdd, Rem, ampl, s, center, coords, t1, t2 = None, None, None, None, None, None, None, None
OutputArray = cp.asnumpy(OutputArray)
#print('This is the size: ' + str(OutputArray.nbytes))
return OutputArray
def update(self, w, grad_wrt_w):
# If not initialized
if self.G is None:
self.G = cupy.zeros(np.shape(w))
# Add the square of the gradient of the loss function at w
self.G += cupy.power(grad_wrt_w, 2)
# Adaptive gradient with higher learning rate for sparse data
return w - self.learning_rate * grad_wrt_w / cupy.sqrt(self.G +
self.eps)
def _calc_gaussian(heatmap,
region,
center_x,
center_y,
theta=2.,
threshold=4.605):
# [theta, radius]: [1.0, 3.5px]; [2.0, 6.5px], and [0.5, 2.0px]
y0, y1, x0, x1 = region
# fast way
heat_area = heatmap[y0:y1, x0:x1]
factor = 1 / 2.0 / theta / theta
x_vec = np.power(np.subtract(np.arange(x0, x1), center_x), 2)
y_vec = np.power(np.subtract(np.arange(y0, y1), center_y), 2)
xv, yv = np.meshgrid(x_vec, y_vec)
_sum = factor * (xv + yv)
_exp = np.exp(-_sum)
_exp[_sum > threshold] = 0
heatmap[y0:y1, x0:x1] = np.maximum(heat_area, _exp)
def f(n):
tot = 0
num_range = np.arange(0, n, dtype=cp.uint32)
for p in ittr.product(num_range, repeat=6):
k = cp.square(cp.array(p, dtype=cp.uint32))
nn = cp.power(p, 2)
if gcd(k.sum(), nn) == 1:
tot += 1
return tot
def update(self, trainable_variables):
if self.ms is None:
self.ms = [cp.zeros_like(g.grads) for g in trainable_variables]
if self.delta_x is None:
self.delta_x = [
cp.zeros_like(g.grads) for g in trainable_variables
]
for i, (s, var,
x) in enumerate(zip(self.ms, trainable_variables,
self.delta_x)):
s = self.beta1 * s + (1 - self.beta1) * cp.power(var.grads, 2)
g_ = cp.sqrt((x + self.epsilon) / (s + self.epsilon)) * var.grads
var.output_tensor -= g_
x = self.beta1 * x + (1 - self.beta1) * cp.power(g_, 2)
self.ms[i] = s
self.delta_x[i] = x
super(AdaDelta, self).update(trainable_variables)
def update(self, trainable_variables):
if self.ms is None:
self.ms = [cp.zeros_like(g.grads) for g in trainable_variables]
for i, (s, var) in enumerate(zip(self.ms, trainable_variables)):
s += cp.power(var.grads, 2)
var.output_tensor -= self.lr * var.grads / cp.sqrt(s +
self.epsilon)
self.ms[i] = s
super(AdaGrad, self).update(trainable_variables)
def generate_q_u_matrix(x_coordinate: cp.array,
y_coordinate: cp.array) -> tuple:
flatten_flag = x_coordinate.ndim > 1
if flatten_flag:
x_coordinate = x_coordinate.flatten()
y_coordinate = y_coordinate.flatten()
t, u = cp.modf(y_coordinate)
u = u.astype(int)
uy = cp.vstack([
cp.minimum(cp.maximum(u - 1, 0), h - 1),
cp.minimum(cp.maximum(u, 0), h - 1),
cp.minimum(cp.maximum(u + 1, 0), h - 1),
cp.minimum(cp.maximum(u + 2, 0), h - 1),
]).astype(int)
Qy = cp.dot(
coeff,
cp.vstack([
cp.ones_like(t, dtype=cp.float32), t,
cp.power(t, 2),
cp.power(t, 3)
]))
t, u = cp.modf(x_coordinate)
u = u.astype(int)
ux = cp.vstack([
cp.minimum(cp.maximum(u - 1, 0), w - 1),
cp.minimum(cp.maximum(u, 0), w - 1),
cp.minimum(cp.maximum(u + 1, 0), w - 1),
cp.minimum(cp.maximum(u + 2, 0), w - 1),
])
Qx = cp.dot(
coeff,
cp.vstack([
cp.ones_like(t, dtype=cp.float32), t,
cp.power(t, 2),
cp.power(t, 3)
]))
if flatten_flag:
Qx = Qx.reshape(4, frame_n, int(w * mag)).transpose(1, 0, 2).copy()
Qy = Qy.reshape(4, frame_n, int(h * mag)).transpose(1, 0, 2).copy()
ux = ux.reshape(4, frame_n, int(w * mag)).transpose(1, 0, 2).copy()
uy = uy.reshape(4, frame_n, int(h * mag)).transpose(1, 0, 2).copy()
return Qx, Qy, ux, uy
def getWeightChange(DJDW, LayerIndex):
weightm[LayerIndex] = (beta1) * weightm[LayerIndex] + (
1 - beta1) * DJDW[LayerIndex]
weightv[LayerIndex] = (beta2) * weightv[LayerIndex] + (
1 - beta2) * np.power(DJDW[LayerIndex], 2)
weightmfinal = weightm[LayerIndex] / (1 - beta1**t)
weightvfinal = weightv[LayerIndex] / (1 - beta2**t)
weightchange = -speed * weightmfinal / (np.sqrt(weightvfinal) +
epsilon)
return weightchange
def ncc_single(X, Y):
if isinstance(X, np.ndarray):
X = cp.array(X)
if isinstance(Y, np.ndarray):
Y = cp.array(Y)
n = int(np.prod(X.shape))
NCC = (cp.sum(X * Y) - (cp.sum(X) * cp.sum(Y) / n)) / cp.power(
(cp.sum(X * X) - cp.sum(X)**2 / n) *
(cp.sum(Y * Y) - cp.sum(Y)**2 / n), 0.5)
return NCC
