def entropy(y, bins): """ Return the entropy of the data in y \sum p_i log2(p_i) where p_i is the probability of observing y in the ith bin of bins. bins can be a number of bins or a range of bins; see hist Compare S with analytic calculation for a Gaussian x = mu + sigma*randn(200000) Sanalytic = 0.5 * ( 1.0 + log(2*pi*sigma**2.0) ) """ n,bins = hist(y, bins) n = n.astype(Float) n = take(n, nonzero(n)) # get the positive p = divide(n, len(y)) delta = bins[1]-bins[0] S = -1.0*asum(p*log(p)) + log(delta) #S = -1.0*asum(p*log(p)) return S
def entropy(y, bins):
"""
Return the entropy of the data in y
\sum p_i log2(p_i) where p_i is the probability of observing y in
the ith bin of bins. bins can be a number of bins or a range of
bins; see hist
Compare S with analytic calculation for a Gaussian
x = mu + sigma*randn(200000)
Sanalytic = 0.5 * ( 1.0 + log(2*pi*sigma**2.0) )
"""
n, bins = hist(y, bins)
n = n.astype(Float)
n = take(n, nonzero(n)) # get the positive
p = divide(n, len(y))
delta = bins[1] - bins[0]
S = -1.0 * asum(p * log(p)) + log(delta)
#S = -1.0*asum(p*log(p))
return S
def __call__(self, value, clip=None):
if clip is None:
clip = self.clip
if isinstance(value, (int, float)):
vtype = 'scalar'
val = ma.array([value])
else:
vtype = 'array'
val = ma.asarray(value)
self.autoscale(val)
vmin, vmax = self.vmin, self.vmax
if vmin > vmax:
raise ValueError("minvalue must be less than or equal to maxvalue")
elif vmin<=0:
raise ValueError("values must all be positive")
elif vmin==vmax:
return 0.*value
else:
if clip:
mask = ma.getmask(val)
val = ma.array(nx.clip(val.filled(vmax), vmin, vmax),
mask=mask)
result = (ma.log(val)-nx.log(vmin))/(nx.log(vmax)-nx.log(vmin))
if vtype == 'scalar':
result = result[0]
return result
def release_zoom(self, event):
'the release mouse button callback in zoom to rect mode'
if self._xypress is None: return
x, y = event.x, event.y
lastx, lasty, a, ind, lim, trans = self._xypress
# ignore singular clicks - 5 pixels is a threshold
if abs(x-lastx)<5 or abs(y-lasty)<5 or not a.in_axes(x,y):
self._xypress = None
self.release(event)
self.draw()
return
xmin, ymin, xmax, ymax = lim
# zoom to rect
lastx, lasty = a.transData.inverse_xy_tup( (lastx, lasty) )
x, y = a.transData.inverse_xy_tup( (x, y) )
if x<lastx: xmin, xmax = x, lastx
else: xmin, xmax = lastx, x
if y<lasty: ymin, ymax = y, lasty
else: ymin, ymax = lasty, y
if self._button_pressed == 1:
a.set_xlim((xmin, xmax))
a.set_ylim((ymin, ymax))
elif self._button_pressed == 3:
Xmin,Xmax=a.get_xlim()
Ymin,Ymax=a.get_ylim()
if a.get_xscale()=='log':
alpha=log(Xmax/Xmin)/log(xmax/xmin)
x1=pow(Xmin/xmin,alpha)*Xmin
x2=pow(Xmax/xmin,alpha)*Xmin
else:
alpha=(Xmax-Xmin)/(xmax-xmin)
x1=alpha*(Xmin-xmin)+Xmin
x2=alpha*(Xmax-xmin)+Xmin
if a.get_yscale()=='log':
alpha=log(Ymax/Ymin)/log(ymax/ymin)
y1=pow(Ymin/ymin,alpha)*Ymin
y2=pow(Ymax/ymin,alpha)*Ymin
else:
alpha=(Ymax-Ymin)/(ymax-ymin)
y1=alpha*(Ymin-ymin)+Ymin
y2=alpha*(Ymax-ymin)+Ymin
a.set_xlim((x1, x2))
a.set_ylim((y1, y2))
self.draw()
self._xypress = None
self._button_pressed == None
self.push_current()
self.release(event)
def release_zoom(self, event):
'the release mouse button callback in zoom to rect mode'
if self._xypress is None: return
x, y = event.x, event.y
lastx, lasty, a, ind, lim, trans = self._xypress
# ignore singular clicks - 5 pixels is a threshold
if abs(x - lastx) < 5 or abs(y - lasty) < 5 or not a.in_axes(x, y):
self._xypress = None
self.release(event)
self.draw()
return
xmin, ymin, xmax, ymax = lim
# zoom to rect
lastx, lasty = a.transData.inverse_xy_tup((lastx, lasty))
x, y = a.transData.inverse_xy_tup((x, y))
if x < lastx: xmin, xmax = x, lastx
else: xmin, xmax = lastx, x
if y < lasty: ymin, ymax = y, lasty
else: ymin, ymax = lasty, y
if self._button_pressed == 1:
a.set_xlim((xmin, xmax))
a.set_ylim((ymin, ymax))
elif self._button_pressed == 3:
Xmin, Xmax = a.get_xlim()
Ymin, Ymax = a.get_ylim()
if a.get_xscale() == 'log':
alpha = log(Xmax / Xmin) / log(xmax / xmin)
x1 = pow(Xmin / xmin, alpha) * Xmin
x2 = pow(Xmax / xmin, alpha) * Xmin
else:
alpha = (Xmax - Xmin) / (xmax - xmin)
x1 = alpha * (Xmin - xmin) + Xmin
x2 = alpha * (Xmax - xmin) + Xmin
if a.get_yscale() == 'log':
alpha = log(Ymax / Ymin) / log(ymax / ymin)
y1 = pow(Ymin / ymin, alpha) * Ymin
y2 = pow(Ymax / ymin, alpha) * Ymin
else:
alpha = (Ymax - Ymin) / (ymax - ymin)
y1 = alpha * (Ymin - ymin) + Ymin
y2 = alpha * (Ymax - ymin) + Ymin
a.set_xlim((x1, x2))
a.set_ylim((y1, y2))
self.draw()
self._xypress = None
self._button_pressed == None
self.push_current()
self.release(event)
def specgram(x,
NFFT=256,
Fs=2,
detrend=detrend_none,
window=window_hanning,
noverlap=128):
"""
Compute a spectrogram of data in x. Data are split into NFFT
length segements and the PSD of each section is computed. The
windowing function window is applied to each segment, and the
amount of overlap of each segment is specified with noverlap
See pdf for more info.
The returned times are the midpoints of the intervals over which
the ffts are calculated
"""
x = asarray(x)
assert (NFFT > noverlap)
if log(NFFT) / log(2) != int(log(NFFT) / log(2)):
raise ValueError, 'NFFT must be a power of 2'
# zero pad x up to NFFT if it is shorter than NFFT
if len(x) < NFFT:
n = len(x)
x = resize(x, (NFFT, ))
x[n:] = 0
# for real x, ignore the negative frequencies
if typecode(x) == Complex: numFreqs = NFFT
else: numFreqs = NFFT // 2 + 1
windowVals = window(ones((NFFT, ), typecode(x)))
step = NFFT - noverlap
ind = arange(0, len(x) - NFFT + 1, step)
n = len(ind)
Pxx = zeros((numFreqs, n), Float)
# do the ffts of the slices
for i in range(n):
thisX = x[ind[i]:ind[i] + NFFT]
thisX = windowVals * detrend(thisX)
fx = absolute(fft(thisX))**2
# Scale the spectrum by the norm of the window to compensate for
# windowing loss; see Bendat & Piersol Sec 11.5.2
Pxx[:, i] = divide(fx[:numFreqs], norm(windowVals)**2)
t = 1 / Fs * (ind + NFFT / 2)
freqs = Fs / NFFT * arange(numFreqs)
return Pxx, freqs, t
def liaupunov(x, fprime): """ x is a very long trajectory from a map, and derivs is the analytic derivative of the map. Return lambda = 1/n\sum ln|fprime(x_i)|. See Sec 10.5 Strogatz (1994) "Nonlinear Dynamics and Chaos". """ return mean(log(fprime(x)))
def liaupunov(x, fprime):
"""
x is a very long trajectory from a map, and derivs is the analytic
derivative of the map. Return lambda = 1/n\sum ln|fprime(x_i)|.
See Sec 10.5 Strogatz (1994) "Nonlinear Dynamics and Chaos".
"""
return mean(log(fprime(x)))
def specgram(x, NFFT=256, Fs=2, detrend=detrend_none,
window=window_hanning, noverlap=128):
"""
Compute a spectrogram of data in x. Data are split into NFFT
length segements and the PSD of each section is computed. The
windowing function window is applied to each segment, and the
amount of overlap of each segment is specified with noverlap
See pdf for more info.
The returned times are the midpoints of the intervals over which
the ffts are calculated
"""
assert(NFFT>noverlap)
if log(NFFT)/log(2) != int(log(NFFT)/log(2)):
raise ValueError, 'NFFT must be a power of 2'
# zero pad x up to NFFT if it is shorter than NFFT
if len(x)<NFFT:
n = len(x)
x = resize(x, (NFFT,))
x[n:] = 0
# for real x, ignore the negative frequencies
if x.typecode()==Complex: numFreqs = NFFT
else: numFreqs = NFFT//2+1
windowVals = window(ones((NFFT,),x.typecode()))
step = NFFT-noverlap
ind = arange(0,len(x)-NFFT+1,step)
n = len(ind)
Pxx = zeros((numFreqs,n), Float)
# do the ffts of the slices
for i in range(n):
thisX = x[ind[i]:ind[i]+NFFT]
thisX = windowVals*detrend(thisX)
fx = absolute(fft(thisX))**2
# Scale the spectrum by the norm of the window to compensate for
# windowing loss; see Bendat & Piersol Sec 11.5.2
Pxx[:,i] = divide(fx[:numFreqs], norm(windowVals)**2)
t = 1/Fs*(ind+NFFT/2)
freqs = Fs/NFFT*arange(numFreqs)
return Pxx, freqs, t
def pyxplothist(graph, x_sample, Nbins=80, bin_range=None, norm=False, bars=0,
lw=0, lt=0, color=(0,0,0), xlogscale=False, ylogscale=False,
y_given=None, title=False):
""" Plots a histogram of 'x_sample'.
Arguments:
'x_sampe' - data
'Nbins' - number of bins
'bin_range' - intervall to be divided into 'Nbins' equidistant parts
'norm' - normalization of histogram
(comparison with density function)
'bars' - style parameter: bars (bars=1) or steps (bars=0)
'lw', 'lt' - linewidth, linetype
'title' - title
'color' - color of histogram (r,g,b)
'xlogscale' - takes bins with logarithmically constant width,
makes only sense, when 'xaxistype' of 'graph'
is set to 'log'
'ylogscale' - activates necessary changes, if y-axis is logarithmic,
makes only sense, when 'yaxistype' of 'graph'
is set to 'log'
'ygiven' - if you already know the y-values
"""
steps = 1-bars
# determine max. x-value for the bins
x_max = max(x_sample)
if bin_range != None:
x_max = bin_range[1]
# changes due to logarithmic x-axis:
# take log of the data, check if data or range is <= zero
if xlogscale:
if min(x_sample) > 0:
x_sample = log(x_sample)
if bin_range != None:
if bin_range[0] > 0 and bin_range[1] > 0:
bin_range = (log(bin_range[0]),log(bin_range[1]))
else:
print "Given range includes values <= 0!"
print "Ignoring given range..."
bin_range = None
else:
print "Data is smaller than zero, no logarithmic x-axis possible!"
print "Continuing linearly..."
xlogscale = False
if y_given != None:
x_l = x_sample
x_hist = y_given
Nbins = len(x_l)
else:
## histogram of 'x_sample': gives number 'x_hist' of sample points within
## 'Nbins' different of bins within 'bin_range', where the bins are
## specified by their left edge coordinate 'x_l'
x_hist, x_l = histogram(x_sample, bins=Nbins, range=bin_range, normed=norm)
# if logarithmic x-axis: exponentiate bin positions and data
if xlogscale:
x_l = exp(x_l)
x_sample = exp(x_sample)
y_min = 0
# offset for logarithmic y-axis
if ylogscale:
x_hist = x_hist+1e-16
y_min = 1e-16
# plot histogram manually
for i in xrange(Nbins):
# horzontal lines
if i < Nbins-1:
graph.pyxplot(([x_l[i],x_l[i+1]],[x_hist[i],x_hist[i]]),
style="l", color=color, lt=lt, lw=lw, title=False)
else:
graph.pyxplot(([x_l[i],x_max],[x_hist[i],x_hist[i]]),
style="l", color=color, lt=lt, lw=lw, title=False)
# vertical lines
if i != Nbins-1:
graph.pyxplot(([x_l[i+1],x_l[i+1]],[x_hist[i],x_hist[i+1]]),
style="l", color=color, lt=lt, lw=lw, title=False)
if i == 0:
graph.pyxplot(([x_l[i],x_l[i]],[x_hist[i],y_min]),
style="l", color=color, lt=lt, lw=lw, title=title)
if i == Nbins-1:
graph.pyxplot(([x_max,x_max],[x_hist[i],y_min]),
style="l", color=color, lt=lt, lw=lw, title=False)
def convertxy_loglog(position):
"""Convert from [0.0, 1.0] coordinates to canvas coordinates
on a logarithmic scale in x- and y-direction"""
return ( (log(position[0])-log(xmin))/(log(xmax)-log(xmin)),
(log(position[1])-log(ymin))/(log(ymax)-log(ymin)) )
def release_zoom(self, event):
'the release mouse button callback in zoom to rect mode'
if self._xypress is None: return
x, y = event.x, event.y
lastx, lasty, a, ind, lim, trans = self._xypress
# ignore singular clicks - 5 pixels is a threshold
if abs(x-lastx)<5 or abs(y-lasty)<5:
self._xypress = None
self.release(event)
self.draw()
return
xmin, ymin, xmax, ymax = lim
# zoom to rect
lastx, lasty = a.transData.inverse_xy_tup( (lastx, lasty) )
x, y = a.transData.inverse_xy_tup( (x, y) )
Xmin,Xmax=a.get_xlim()
Ymin,Ymax=a.get_ylim()
if Xmin < Xmax:
if x<lastx: xmin, xmax = x, lastx
else: xmin, xmax = lastx, x
if xmin < Xmin: xmin=Xmin
if xmax > Xmax: xmax=Xmax
else:
if x>lastx: xmin, xmax = x, lastx
else: xmin, xmax = lastx, x
if xmin > Xmin: xmin=Xmin
if xmax < Xmax: xmax=Xmax
if Ymin < Ymax:
if y<lasty: ymin, ymax = y, lasty
else: ymin, ymax = lasty, y
if ymin < Ymin: ymin=Ymin
if ymax > Ymax: ymax=Ymax
else:
if y>lasty: ymin, ymax = y, lasty
else: ymin, ymax = lasty, y
if ymin > Ymin: ymin=Ymin
if ymax < Ymax: ymax=Ymax
if self._button_pressed == 1:
a.set_xlim((xmin, xmax))
a.set_ylim((ymin, ymax))
elif self._button_pressed == 3:
if a.get_xscale()=='log':
alpha=log(Xmax/Xmin)/log(xmax/xmin)
x1=pow(Xmin/xmin,alpha)*Xmin
x2=pow(Xmax/xmin,alpha)*Xmin
else:
alpha=(Xmax-Xmin)/(xmax-xmin)
x1=alpha*(Xmin-xmin)+Xmin
x2=alpha*(Xmax-xmin)+Xmin
if a.get_yscale()=='log':
alpha=log(Ymax/Ymin)/log(ymax/ymin)
y1=pow(Ymin/ymin,alpha)*Ymin
y2=pow(Ymax/ymin,alpha)*Ymin
else:
alpha=(Ymax-Ymin)/(ymax-ymin)
y1=alpha*(Ymin-ymin)+Ymin
y2=alpha*(Ymax-ymin)+Ymin
a.set_xlim((x1, x2))
a.set_ylim((y1, y2))
# Zoom with fixed aspect; modified for shared x-axes
aspect = a.get_aspect()
if aspect == 'equal' or aspect == 'scaled':
self.fix_aspect_after_zoom(a)
else:
aspect_shared = ''
if a._sharex != None: aspect_shared = a._sharex.get_aspect()
if aspect_shared == 'equal' or aspect_shared == 'scaled':
self.fix_aspect_after_zoom(a._sharex)
self.draw()
self._xypress = None
self._button_pressed == None
self.push_current()
self.release(event)
def release_zoom(self, event):
'the release mouse button callback in zoom to rect mode'
if self._xypress is None: return
x, y = event.x, event.y
lastx, lasty, a, ind, lim, trans = self._xypress
# ignore singular clicks - 5 pixels is a threshold
if abs(x - lastx) < 5 or abs(y - lasty) < 5:
self._xypress = None
self.release(event)
self.draw()
return
xmin, ymin, xmax, ymax = lim
# zoom to rect
lastx, lasty = a.transData.inverse_xy_tup((lastx, lasty))
x, y = a.transData.inverse_xy_tup((x, y))
Xmin, Xmax = a.get_xlim()
Ymin, Ymax = a.get_ylim()
if Xmin < Xmax:
if x < lastx: xmin, xmax = x, lastx
else: xmin, xmax = lastx, x
if xmin < Xmin: xmin = Xmin
if xmax > Xmax: xmax = Xmax
else:
if x > lastx: xmin, xmax = x, lastx
else: xmin, xmax = lastx, x
if xmin > Xmin: xmin = Xmin
if xmax < Xmax: xmax = Xmax
if Ymin < Ymax:
if y < lasty: ymin, ymax = y, lasty
else: ymin, ymax = lasty, y
if ymin < Ymin: ymin = Ymin
if ymax > Ymax: ymax = Ymax
else:
if y > lasty: ymin, ymax = y, lasty
else: ymin, ymax = lasty, y
if ymin > Ymin: ymin = Ymin
if ymax < Ymax: ymax = Ymax
if self._button_pressed == 1:
a.set_xlim((xmin, xmax))
a.set_ylim((ymin, ymax))
elif self._button_pressed == 3:
if a.get_xscale() == 'log':
alpha = log(Xmax / Xmin) / log(xmax / xmin)
x1 = pow(Xmin / xmin, alpha) * Xmin
x2 = pow(Xmax / xmin, alpha) * Xmin
else:
alpha = (Xmax - Xmin) / (xmax - xmin)
x1 = alpha * (Xmin - xmin) + Xmin
x2 = alpha * (Xmax - xmin) + Xmin
if a.get_yscale() == 'log':
alpha = log(Ymax / Ymin) / log(ymax / ymin)
y1 = pow(Ymin / ymin, alpha) * Ymin
y2 = pow(Ymax / ymin, alpha) * Ymin
else:
alpha = (Ymax - Ymin) / (ymax - ymin)
y1 = alpha * (Ymin - ymin) + Ymin
y2 = alpha * (Ymax - ymin) + Ymin
a.set_xlim((x1, x2))
a.set_ylim((y1, y2))
# Zoom with fixed aspect; modified for shared x-axes
aspect = a.get_aspect()
if aspect == 'equal' or aspect == 'scaled':
self.fix_aspect_after_zoom(a)
else:
aspect_shared = ''
if a._sharex != None: aspect_shared = a._sharex.get_aspect()
if aspect_shared == 'equal' or aspect_shared == 'scaled':
self.fix_aspect_after_zoom(a._sharex)
self.draw()
self._xypress = None
self._button_pressed == None
self.push_current()
self.release(event)