def scirpus_regobj(preds, dtrain):
labels = dtrain.get_label()
x = (preds - labels)
from numpy import exp as npexp
grad = 2 * x * npexp(-(x**2)) * (npexp(x**2) + x**2 + 1)
hess = 2 * npexp(-(x**2)) * (npexp(x**2) - 2 * (x**4) + 5 * (x**2) - 1)
return grad, hess
def scirpus_regobj(preds, dtrain):
labels = dtrain.get_label()
x = (preds - labels)
from numpy import exp as npexp
grad = 2 * x * npexp(-(x ** 2)) * (npexp(x ** 2) + x ** 2 + 1)
hess = 2 * npexp(-(x ** 2)) * (npexp(x ** 2) - 2 * (x ** 4) + 5 * (x ** 2) - 1)
return grad, hess
def softmax_grad( theta, nclasses, dim, wdecay, data, labels ):
# unroll parameters from theta
theta = reshape(theta,(dim, nclasses)) # Do this
theta= theta.T
nsamp = data.shape[1]
# generate ground truth matrix
onevals = squeeze(ones((1,nsamp)))
rows = squeeze(labels)-1 # Here should -1 to align zero-indexing
cols = arange(nsamp)
ground_truth = csr_matrix((onevals,(rows,cols))).todense()
# plt.imshow(ground_truth,interpolation='nearest')
# plt.draw()
# print ground_truth
# compute hypothesis; use some in-place computations
theta_dot_prod = dot(theta,data)
theta_dot_prod = theta_dot_prod - numpy.amax(theta_dot_prod, axis=0) # This was wrong
soft_theta = npexp(theta_dot_prod)
soft_theta_sum = npsum(soft_theta,axis=0)
soft_theta_sum = tile(soft_theta_sum,(nclasses,1))
hyp = soft_theta/soft_theta_sum
# compute gradient
thetagrad = (-1.0/nsamp)*dot(ground_truth-hyp,transpose(data)) + wdecay*theta
thetagrad = asarray(thetagrad)
thetagrad = thetagrad.flatten(1)
return thetagrad
def scirpus_error(preds, dtrain):
labels = dtrain.get_label()
x = (labels - preds)
from numpy import exp as npexp
error = (x**2) * (1 - npexp(-(x**2)))
from numpy import mean
return 'error', mean(error)
def scirpus_error(preds, dtrain):
labels = dtrain.get_label()
x = (labels - preds)
from numpy import exp as npexp
error = (x ** 2) * (1 - npexp(-(x ** 2)))
from numpy import mean
return 'error', mean(error)
def asciiHistogram(histogram, log=False, width=60, label='length', maxLabelWidth=10):
(values,edges)=histogram[:2]
maxValue=max(values)
centers=[int(float(sum(edges[i:i+2]))/2.) for i in range(len(values))]
largestLabel = max(max([len(str(c)) for c in centers]),len(label))
if largestLabel<6:
largestLabel=6
elif largestLabel>maxLabelWidth:
largestLabel=maxLabelWidth
plotWidth=width-largestLabel+1
midPoint = npexp((nplog(maxValue)-nplog(.5))/2) if log else maxValue/2
output="%s|count%s%s|%s%s|\n" % (rightPad(label,largestLabel),
"".join([" " for i in range(plotWidth/2 - len(str(int(midPoint))) - len("count"))]),
str(int(midPoint)),
"".join([" " for i in range(int(ceil(plotWidth/2.)) - 1 - len(str(int(maxValue))))]),
str(int(maxValue)),
)
#output+="%s|%s\n" % ("".join(["_" for i in range(largestLabel)]),
# "".join(["_" for i in range(plotWidth)]),
# )
for i, v in enumerate(values):
output+="%s|%s\n" % (rightPad(str(centers[i]),largestLabel),getBarString(v, maxValue, plotWidth, log))
return output
def softmax_cost( theta, nclasses, dim, wdecay, data, labels ):
# unroll parameters from theta
theta = reshape(theta,(dim, nclasses)) # This was wrong
theta= theta.T
nsamp = data.shape[1]
# generate ground truth matrix
onevals = squeeze(ones((1,nsamp)))
rows = squeeze(labels)-1 # This was wrong
cols = arange(nsamp)
ground_truth = csr_matrix((onevals,(rows,cols))).todense()
# compute hypothesis; use some in-place computations
theta_dot_prod = dot(theta,data)
theta_dot_prod = theta_dot_prod - numpy.amax(theta_dot_prod, axis=0) # This was wrong
soft_theta = npexp(theta_dot_prod)
soft_theta_sum = npsum(soft_theta,axis=0)
soft_theta_sum = tile(soft_theta_sum,(nclasses,1))
hyp = soft_theta/soft_theta_sum
# compute cost
log_hyp = nplog(hyp)
temp = array(multiply(ground_truth,log_hyp))
temp = npsum(npsum(temp,axis=1),axis=0)
cost = (-1.0/nsamp)*temp + 0.5*wdecay*pow(norm(theta,'fro'),2)
return cost
def make_data(n=None, i=None, p=None):
from random import randint
from numpy import log, random as nprandom, arange as nparange, exp as npexp
n = n or randint(10,100)
i = i or randint(1,100)
p = p or randint(1,50) / 100
xx = nparange(1, n + 1)
yy_clean = npexp(xx * p) * i
yy = yy_clean + nprandom.normal(0, log(yy_clean).round() + (yy_clean//10), size=n)
return (xx,yy,yy_clean, n,i,p)
def _sigmoid(self, x):
"""
This method is separate from `forward` because it
will be used later with `backward` as well.
`x`: A numpy array-like object.
Return the result of the sigmoid function.
Your code here!
"""
from numpy import exp as npexp
return 1 / (1 + npexp(-x))
def stetson_jindex(ftimes, fmags, ferrs, weightbytimediff=False):
'''This calculates the Stetson index for the magseries, based on consecutive
pairs of observations. Based on Nicole Loncke's work for her Planets and
Life certificate at Princeton.
This requires finite times, mags, and errs.
If weightbytimediff is True, the Stetson index for any pair of mags will be
reweighted by the difference in times between them using the scheme in
Fruth+ 2012 and Zhange+ 2003 (as seen in Sokolovsky+ 2017).
w_i = exp(- (t_i+1 - t_i)/ delta_t )
'''
ndet = len(fmags)
if ndet > 9:
# get the median and ndet
medmag = npmedian(fmags)
# get the stetson index elements
delta_prefactor = (ndet / (ndet - 1))
sigma_i = delta_prefactor * (fmags - medmag) / ferrs
sigma_j = nproll(sigma_i,
1) # Nicole's clever trick to advance indices
# by 1 and do x_i*x_(i+1)
if weightbytimediff:
time_i = ftimes
time_j = nproll(ftimes, 1)
difft = npdiff(ftimes)
deltat = npmedian(difft)
weights_i = npexp(-difft / deltat)
products = (weights_i * sigma_i[1:] * sigma_j[1:])
else:
# ignore first elem since it's actually x_0*x_n
products = (sigma_i * sigma_j)[1:]
stetsonj = (npsum(npsign(products) * npsqrt(npabs(products)))) / ndet
return stetsonj
else:
LOGERROR('not enough detections in this magseries '
'to calculate stetson J index')
return npnan
def kRegression(self, point, k, weight):
""" Performs a locally weighted kernel regression
Args
---
`point : np.array` the point to be classified
`k : int` the number of nearest neighbors
`weight : float` how strongly the closeness of the neighbor is taken into consideration
Returns
---
`classification : float` the classification label of the given point
"""
distances = []
weights = []
for i in range(self.N):
distance = lrDistance(point, self.X[:, i], self.dim)
distances.append(distance)
weights.append(npexp(-distance / weight))
# Find indices of nearest neighbors
ind_neighbors = argpartition(distances, k)[:k]
# Sort neighbors by weight
neigbor_weights = []
for i in ind_neighbors:
neigbor_weights.append((i, weights[i]))
nw = reversed(sorted(neigbor_weights, key=itemgetter(1)))
# Matrix of nearest points
P = zeros((self.dim, k))
# Diagonal matrix of weights
K = zeros((k, k))
# Labels vector
f = zeros(k)
column = 0
for i, weight in nw:
P[:, column] = self.X[:, i]
K[column][column] = weight
f[column] = self.y[i]
column += 1
w = inverse(P @ K @ P.T) @ (P @ K) @ f
classification = w.T @ point
return classification
def softmax_predict( theta, nclasses, dim, data ):
# unroll parameters from theta
theta = reshape(theta,(dim, nclasses)) # Do this
theta= theta.T
# compute hypothesis; use some in-place computations
theta_dot_prod = dot(theta,data)
theta_dot_prod = theta_dot_prod - numpy.amax(theta_dot_prod, axis=0) # This was wrong
soft_theta = npexp(theta_dot_prod)
soft_theta_sum = npsum(soft_theta,axis=0)
soft_theta_sum = tile(soft_theta_sum,(nclasses,1))
hyp = soft_theta/soft_theta_sum
print "hyp.shape"
print hyp.shape
pred=numpy.argmax(hyp, axis=0)
return numpy.asarray(pred)
def ascii_histogram(histogram,
log=False,
width=60,
label='length',
maxLabelWidth=10):
(values, edges) = histogram[:2]
maxValue = max(values)
centers = [
int(float(sum(edges[i:i + 2])) / 2.) for i in range(len(values))
]
largestLabel = max(max([len(str(c)) for c in centers]), len(label))
if largestLabel < 6:
largestLabel = 6
elif largestLabel > maxLabelWidth:
largestLabel = maxLabelWidth
plotWidth = width - largestLabel + 1
midPoint = npexp((nplog(maxValue) - nplog(.5)) / 2) \
if log else maxValue / 2
midPointStr = str(int(midPoint))
padding_a_width = int(plotWidth / 2) - len(midPointStr) - len("count")
padding_a = "".join([" " for i in range(padding_a_width)])
maxValueStr = str(int(maxValue))
padding_b_width = int(ceil(plotWidth / 2.)) - 1 - len(maxValueStr)
padding_b = "".join([" " for i in range(padding_b_width)])
output = "%s|count%s%s|%s%s|\n" % (
rightPad(label, largestLabel),
padding_a,
midPointStr,
padding_b,
maxValueStr,
)
# output+="%s|%s\n" % ("".join(["_" for i in range(largestLabel)]),
# "".join(["_" for i in range(plotWidth)]),
# )
for i, v in enumerate(values):
output += "%s|%s\n" % (rightPad(str(centers[i]), largestLabel),
getBarString(v, maxValue, plotWidth, log))
return output
def cost(self, theta):
"""
This function computes the cost associated to the softmax classifier.
:param data: data matrix :math:`D_1\in\mathbb{R}^{d \\times n}`, where
:math:`d` is the dimensionality and
:math:`n` is the number of training samples
:type data: numpy array
"""
# unroll parameters from theta
theta = reshape(theta, (self.dim, self.nclasses))
theta = theta.T
nsamp = self.data.shape[1]
# generate ground truth matrix
onevals = squeeze(ones((1, nsamp)))
rows = squeeze(self.labels) - 1
cols = arange(nsamp)
ground_truth = csr_matrix((onevals, (rows, cols))).todense()
# compute hypothesis; use some in-place computations
theta_dot_prod = dot(theta, self.data)
theta_dot_prod = theta_dot_prod - numpy.amax(theta_dot_prod, axis=0)
soft_theta = npexp(theta_dot_prod)
soft_theta_sum = npsum(soft_theta, axis=0)
soft_theta_sum = tile(soft_theta_sum, (self.nclasses, 1))
hyp = soft_theta / soft_theta_sum
# compute cost
log_hyp = nplog(hyp)
temp = array(multiply(ground_truth, log_hyp))
temp = npsum(npsum(temp, axis=1), axis=0)
cost = (-1.0 / nsamp) * temp + 0.5 * self.wdecay * pow(norm(theta, "fro"), 2)
thetagrad = (-1.0 / nsamp) * dot(ground_truth - hyp, transpose(self.data)) + self.wdecay * theta
thetagrad = thetagrad.flatten(1)
return cost, thetagrad
def exp(x):
return npexp(x)
def sigmoid(self, x):
return (1 / (1 + npexp(-x)))
def munchetal(im, args):
"""Process a sinogram image with the Munch et al. de-striping algorithm.
Parameters
----------
im : array_like
Image data as numpy array.
wlevel : int
Levels of the wavelet decomposition.
sigma : float
Smoothing effect.
Example (using tiffile.py)
--------------------------
>>> im = imread('sino_orig.tif')
>>> im = munchetal(im, 4, 1.0)
>>> imsave('sino_flt.tif', im)
References
----------
B. Munch, P. Trtik, F. Marone, M. Stampanoni, Stripe and ring artifact removal with
combined wavelet-Fourier filtering, Optics Express 17(10):8567-8591, 2009.
"""
# Disable a warning:
simplefilter("ignore", ComplexWarning)
# Get args:
wlevel, sigma = args.split(";")
wlevel = int(wlevel)
sigma = float(sigma)
# The wavelet transform to use : {'haar', 'db1'-'db20', 'sym2'-'sym20', 'coif1'-'coif5', 'dmey'}
wname = "db2"
# Wavelet decomposition:
coeffs = wavedec2(im.astype(float32), wname, level=wlevel)
coeffsFlt = [coeffs[0]]
# FFT transform of horizontal frequency bands:
for i in range(1, wlevel + 1):
# FFT:
fcV = fftshift(fft(coeffs[i][1], axis=0))
my, mx = fcV.shape
# Damping of vertical stripes:
damp = 1 - npexp(-(arange(-floor(my / 2.),-floor(my / 2.) + my) ** 2) / (2 * (sigma ** 2)))
dampprime = kron(ones((1,mx)), damp.reshape((damp.shape[0],1)))
fcV = fcV * dampprime
# Inverse FFT:
fcVflt = ifft(ifftshift(fcV), axis=0)
cVHDtup = (coeffs[i][0], fcVflt, coeffs[i][2])
coeffsFlt.append(cVHDtup)
# Get wavelet reconstruction:
im_f = real(waverec2(coeffsFlt, wname))
# Return image according to input type:
if (im.dtype == 'uint16'):
# Check extrema for uint16 images:
im_f[im_f < iinfo(uint16).min] = iinfo(uint16).min
im_f[im_f > iinfo(uint16).max] = iinfo(uint16).max
# Return filtered image (an additional row and/or column might be
# present):
return im_f[0:im.shape[0],0:im.shape[1]].astype(uint16)
else:
return im_f[0:im.shape[0],0:im.shape[1]]
def homomorphic(im, args):
"""Process the input image with an homomorphic filtering.
Parameters
----------
im : array_like
Image data as numpy array.
d0 : float
Cutoff in the range [0.01, 0.99] of the high pass Gaussian filter.
Higher values means more high pass effect. [Suggested for default: 0.80].
alpha : float
Offset to preserve the zero frequency where. Higher values means less
high pass effect. [Suggested for default: 0.2]
(Parameters d0 and alpha have to passed as a string separated by ;)
Example (using tiffile.py)
--------------------------
>>> im = imread('im_orig.tif')
>>> im = homomorphic(im, '0.5;0.2')
>>> imsave('im_flt.tif', im)
References
----------
"""
# Get args:
param1, param2 = args.split(";")
d0 = (1.0 - float(param1)) # Simpler for user
alpha = float(param2)
# Internal parameters for Gaussian low-pass filtering:
d0 = d0 * (im.shape[1] / 2.0)
# Take the log:
im = nplog(1 + im)
# Compute FFT:
n_byte_align(im, simd_alignment)
im = rfft2(im, threads=2)
# Prepare the frequency coordinates:
u = arange(0, im.shape[0], dtype=float32)
v = arange(0, im.shape[1], dtype=float32)
# Compute the indices for meshgrid:
u[(u > im.shape[0] / 2.0)] = u[(u > im.shape[0] / 2.0)] - im.shape[0]
v[(v > im.shape[1] / 2.0)] = v[(v > im.shape[1] / 2.0)] - im.shape[1]
# Compute the meshgrid arrays:
V, U = meshgrid(v, u)
# Compute the distances D(U, V):
D = sqrt(U ** 2 + V ** 2)
# Prepare Guassian filter:
H = npexp(-(D ** 2) / (2 * (d0 ** 2)))
H = (1 - H) + alpha
# Do the filtering:
im = H * im
# Compute inverse FFT of the filtered data:
n_byte_align(im, simd_alignment)
#im = real(irfft2(im, threads=2))
im = irfft2(im, threads=2)
# Take the exp:
im = npexp(im) - 1
# Return image according to input type:
return im.astype(float32)
def homomorphic(im, args):
"""Process the input image with an homomorphic filtering.
Parameters
----------
im : array_like
Image data as numpy array.
d0 : float
Cutoff in the range [0.01, 0.99] of the high pass Gaussian filter.
Higher values means more high pass effect. [Suggested for default: 0.80].
alpha : float
Offset to preserve the zero frequency where. Higher values means less
high pass effect. [Suggested for default: 0.2]
(Parameters d0 and alpha have to passed as a string separated by ;)
Example (using tiffile.py)
--------------------------
>>> im = imread('im_orig.tif')
>>> im = homomorphic(im, '0.5;0.2')
>>> imsave('im_flt.tif', im)
References
----------
"""
# Get args:
param1, param2 = args.split(";")
d0 = (1.0 - float(param1)) # Simpler for user
alpha = float(param2)
# Internal parameters for Gaussian low-pass filtering:
d0 = d0 * (im.shape[1] / 2.0)
# Take the log:
im = nplog(1 + im)
# Compute FFT:
n_byte_align(im, simd_alignment)
im = rfft2(im, threads=2)
# Prepare the frequency coordinates:
u = arange(0, im.shape[0], dtype=float32)
v = arange(0, im.shape[1], dtype=float32)
# Compute the indices for meshgrid:
u[(u > im.shape[0] / 2.0)] = u[(u > im.shape[0] / 2.0)] - im.shape[0]
v[(v > im.shape[1] / 2.0)] = v[(v > im.shape[1] / 2.0)] - im.shape[1]
# Compute the meshgrid arrays:
V, U = meshgrid(v, u)
# Compute the distances D(U, V):
D = sqrt(U**2 + V**2)
# Prepare Guassian filter:
H = npexp(-(D**2) / (2 * (d0**2)))
H = (1 - H) + alpha
# Do the filtering:
im = H * im
# Compute inverse FFT of the filtered data:
n_byte_align(im, simd_alignment)
#im = real(irfft2(im, threads=2))
im = irfft2(im, threads=2)
# Take the exp:
im = npexp(im) - 1
# Return image according to input type:
return im.astype(float32)
def exp(m):
m = to_nparray(m)
m = npexp(m)
m = from_nparray(m)
return m
def softmax(x):
""" Softmax function with input vector x """
exp_x = npexp(x)
exp_sum = sum(exp_x)
smax = exp_x / exp_sum
return smax
def muenchetal(im, args):
"""Process a sinogram image with the Munch et al. de-striping algorithm.
Parameters
----------
im : array_like
Image data as numpy array.
wlevel : int
Levels of the wavelet decomposition.
sigma : float
Smoothing effect.
(Parameters wlevel and sigma have to passed as a string separated by ;)
Example (using tiffile.py)
--------------------------
>>> im = imread('sino_orig.tif')
>>> im = munchetal(im, '4;1.0')
>>> imsave('sino_flt.tif', im)
References
----------
B. Munch, P. Trtik, F. Marone, M. Stampanoni, Stripe and ring artifact removal with
combined wavelet-Fourier filtering, Optics Express 17(10):8567-8591, 2009.
"""
# Disable a warning:
simplefilter("ignore", ComplexWarning)
# Get args:
wlevel, sigma = args.split(";")
wlevel = int(wlevel)
sigma = float(sigma)
# The wavelet transform to use : {'haar', 'db1'-'db20', 'sym2'-'sym20', 'coif1'-'coif5', 'dmey'}
wname = "db5"
# Wavelet decomposition:
coeffs = wavedec2(im.astype(float32), wname, level=wlevel)
coeffsFlt = [coeffs[0]]
# FFT transform of horizontal frequency bands:
for i in range(1, wlevel + 1):
# Padding and windowing of input signal:
n_byte_align(coeffs[i][1], simd_alignment)
siz = coeffs[i][1].shape
tmp = pad(coeffs[i][1], pad_width=((coeffs[i][1].shape[0] / 2, coeffs[i][1].shape[0] / 2), (0,0)), mode='constant') # or 'constant' for zero padding
tmp = pad(tmp, pad_width=((0,0) ,(coeffs[i][1].shape[1] / 2, coeffs[i][1].shape[1] / 2)), mode='constant') # or 'constant' for zero padding
tmp = _windowing_lr(tmp, siz[1])
tmp = _windowing_lr(tmp.T, siz[0]).T
# FFT:
fcV = fftshift(fft(tmp, axis=0, threads=2))
my, mx = fcV.shape
# Damping of vertical stripes:
damp = 1 - npexp(-(arange(-floor(my / 2.),-floor(my / 2.) + my) ** 2) / (2 * (sigma ** 2)))
dampprime = kron(ones((1,mx)), damp.reshape((damp.shape[0],1)))
fcV = fcV * dampprime
# Inverse FFT:
fcV = ifftshift(fcV)
n_byte_align(fcV, simd_alignment)
fcVflt = ifft(fcV, axis=0, threads=2)
## Crop image:
tmp = fcVflt[fcVflt.shape[0] / 4:(fcVflt.shape[0] / 4 + siz[0]), fcVflt.shape[1] / 4:(fcVflt.shape[1] / 4 + siz[1])]
# Dump back coefficients:
cVHDtup = (coeffs[i][0], tmp, coeffs[i][2])
coeffsFlt.append(cVHDtup)
# Get wavelet reconstruction:
im_f = real(waverec2(coeffsFlt, wname))
# Return filtered image (an additional row and/or column might be present):
return im_f[0:im.shape[0],0:im.shape[1]].astype(float32)
def invsp(x):
return nplog(npexp(x) - 1)
def tansig(x):
""" Tansig function with input vector x """
tsig = 2 / (1 + npexp(-2 * x)) - 1
return tsig
def stetson_jindex(ftimes, fmags, ferrs, weightbytimediff=False):
'''This calculates the Stetson index for the magseries, based on consecutive
pairs of observations.
Based on Nicole Loncke's work for her Planets and Life certificate at
Princeton in 2014.
Parameters
----------
ftimes,fmags,ferrs : np.array
The input mag/flux time-series with all non-finite elements removed.
weightbytimediff : bool
If this is True, the Stetson index for any pair of mags will be
reweighted by the difference in times between them using the scheme in
Fruth+ 2012 and Zhange+ 2003 (as seen in Sokolovsky+ 2017)::
w_i = exp(- (t_i+1 - t_i)/ delta_t )
Returns
-------
float
The calculated Stetson J variability index.
'''
ndet = len(fmags)
if ndet > 9:
# get the median and ndet
medmag = npmedian(fmags)
# get the stetson index elements
delta_prefactor = (ndet / (ndet - 1))
sigma_i = delta_prefactor * (fmags - medmag) / ferrs
# Nicole's clever trick to advance indices by 1 and do x_i*x_(i+1)
sigma_j = nproll(sigma_i, 1)
if weightbytimediff:
difft = npdiff(ftimes)
deltat = npmedian(difft)
weights_i = npexp(-difft / deltat)
products = (weights_i * sigma_i[1:] * sigma_j[1:])
else:
# ignore first elem since it's actually x_0*x_n
products = (sigma_i * sigma_j)[1:]
stetsonj = (npsum(npsign(products) * npsqrt(npabs(products)))) / ndet
return stetsonj
else:
LOGERROR('not enough detections in this magseries '
'to calculate stetson J index')
return npnan
def _settling_flux(X, v_max, v_max_practical, X_min, rh, rp, n0):
X_star = npmax(X-X_min, n0)
v = npmin(v_max_practical, v_max*(npexp(-rh*X_star) - npexp(-rp*X_star)))
return X*npmax(v, n0)
def muenchetal(im, args):
"""Process a sinogram image with the Munch et al. de-striping algorithm.
Parameters
----------
im : array_like
Image data as numpy array.
wlevel : int
Levels of the wavelet decomposition.
sigma : float
Smoothing effect.
(Parameters wlevel and sigma have to passed as a string separated by ;)
Example (using tiffile.py)
--------------------------
>>> im = imread('sino_orig.tif')
>>> im = munchetal(im, '4;1.0')
>>> imsave('sino_flt.tif', im)
References
----------
B. Munch, P. Trtik, F. Marone, M. Stampanoni, Stripe and ring artifact removal with
combined wavelet-Fourier filtering, Optics Express 17(10):8567-8591, 2009.
"""
# Disable a warning:
simplefilter("ignore", ComplexWarning)
# Get args:
wlevel, sigma = args.split(";")
wlevel = int(wlevel)
sigma = float(sigma)
# The wavelet transform to use : {'haar', 'db1'-'db20', 'sym2'-'sym20', 'coif1'-'coif5', 'dmey'}
wname = "db5"
# Wavelet decomposition:
coeffs = wavedec2(im.astype(float32), wname, level=wlevel)
coeffsFlt = [coeffs[0]]
# FFT transform of horizontal frequency bands:
for i in range(1, wlevel + 1):
# Padding and windowing of input signal:
n_byte_align(coeffs[i][1], simd_alignment)
siz = coeffs[i][1].shape
tmp = pad(coeffs[i][1],
pad_width=((coeffs[i][1].shape[0] / 2,
coeffs[i][1].shape[0] / 2), (0, 0)),
mode='constant') # or 'constant' for zero padding
tmp = pad(tmp,
pad_width=((0, 0), (coeffs[i][1].shape[1] / 2,
coeffs[i][1].shape[1] / 2)),
mode='constant') # or 'constant' for zero padding
tmp = _windowing_lr(tmp, siz[1])
tmp = _windowing_lr(tmp.T, siz[0]).T
# FFT:
fcV = fftshift(fft(tmp, axis=0, threads=2))
my, mx = fcV.shape
# Damping of vertical stripes:
damp = 1 - npexp(-(arange(-floor(my / 2.), -floor(my / 2.) + my)**2) /
(2 * (sigma**2)))
dampprime = kron(ones((1, mx)), damp.reshape((damp.shape[0], 1)))
fcV = fcV * dampprime
# Inverse FFT:
fcV = ifftshift(fcV)
n_byte_align(fcV, simd_alignment)
fcVflt = ifft(fcV, axis=0, threads=2)
## Crop image:
tmp = fcVflt[fcVflt.shape[0] / 4:(fcVflt.shape[0] / 4 + siz[0]),
fcVflt.shape[1] / 4:(fcVflt.shape[1] / 4 + siz[1])]
# Dump back coefficients:
cVHDtup = (coeffs[i][0], tmp, coeffs[i][2])
coeffsFlt.append(cVHDtup)
# Get wavelet reconstruction:
im_f = real(waverec2(coeffsFlt, wname))
# Return filtered image (an additional row and/or column might be present):
return im_f[0:im.shape[0], 0:im.shape[1]].astype(float32)
def exp(x):
r"""Exponential (e-base)
"""
return npexp(x)
def sigmoid(x):
""" Sigmoid function with input vector x """
sig = 1 / (1 + npexp(-x))
return sig