def plot_axes(fig):
# create some data to use for the plot
dt = 0.001
t = arange(0.0, 10.0, dt)
r = exp(-t[:1000]/0.05) # impulse response
x = randn(len(t))
s = convolve(x,r,mode=2)[:len(x)]*dt # colored noise
# the main axes is subplot(111) by default
axes = fig.gca()
axes.plot(t, s)
axes.set_xlim((0, 1))
axes.set_ylim((1.1*min(s), 2*max(s)))
axes.set_xlabel('time (s)')
axes.set_ylabel('current (nA)')
axes.set_title('Gaussian colored noise')
# this is an inset axes over the main axes
a = fig.add_axes([.65, .6, .2, .2], axisbg='y')
n, bins, patches = a.hist(s, 400, normed=1)
a.set_title('Probability')
a.set_xticks([])
a.set_yticks([])
# this is another inset axes over the main axes
a = fig.add_axes([.2, .6, .2, .2], axisbg='y')
a.plot(t[:len(r)], r)
a.set_title('Impulse response')
a.set_xlim((0, 0.2))
a.set_xticks([])
a.set_yticks([])
def findNoisyArea(self):
"""
Argument :
- None
Return :
- None
Use to detect the noisy area (the area without atoms) by an edge
detection technique.
"""
OD = self.computeFirstOD()
yProfile = py.sum(OD, axis=1)
derivative = py.gradient(yProfile)
N = 10
# because the derivative is usually very noisy, a sliding average is
# performed in order to smooth the signal. This is done by a
# convolution with a gate function of size "N".
res = py.convolve(derivative, py.ones((N, )) / N, mode='valid')
mean = res.mean()
# index of the maximum value of the signal.
i = res.argmax()
while res[i] >= mean:
# once "i" is greater or equal to the mean of the derivative,
# we have found the upper bound of the noisy area.
i -= 1
# index of the minimum value of the signal.
upBound = i - 50
i = res.argmin()
while res[i] < mean:
# once "i" is smaller or equal to the mean of the derivative,
# we have found the lower bound of the noisy area.
i += 1
downBound = i + 50
self.setNoisyArea((upBound, downBound))
return OD
def slidingAverage(x, N):
tmp = convolve(
x,
ones((N, )) / N,
mode='valid',
)
return r_[tmp[0] * ones(N / 2), tmp, tmp[-1] * ones(N / 2 - 1 + N % 2)]
def fairness(principal_list,xlabel,ylabel,output_filename):
'''
@param {list} principal_list --- Each element is either a 0 or a
1. 0 if transaction by principal a, 1 if by principal b.
'''
# note: I have little idea how the following code works. It was
# mostly copied from the previous paper's scripts. Check there if
# confused.
float_princ_list = map(
lambda princ_num : float(princ_num), principal_list)
window = pylab.ones(10)/10.0
rate = pylab.convolve(float_princ_list, window, 'same')
_fairness_plot_set_defaults()
plt.plot(rate, color='red')
yticks = [-.1, 0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.1]
ylabels = ['', '0%', '20%', '40%', '60%', '80%', '100%', '']
plt.yticks(yticks, ylabels, fontsize=12)
# plt.xticks(xtiks, xlabels, fontsize=7)
plt.xlabel(xlabel, fontsize=16, verticalalignment='top')
plt.ylabel(ylabel, fontsize=18)
plt.savefig(output_filename)
def psp_parameter_estimate_fixmem(time, value):
smoothing_kernel = 10
smoothed_value = p.convolve(
value,
p.ones(smoothing_kernel) / float(smoothing_kernel),
"same")
mean_est_part = int(len(value) * .1)
mean_estimate = p.mean(smoothed_value[-mean_est_part:])
noise_estimate = p.std(value[-mean_est_part:])
integral = p.sum(smoothed_value - mean_estimate) * (time[1] - time[0])
f = 1.
A_estimate = (max(smoothed_value) - mean_estimate) / (1. / 4.)
min_A = noise_estimate
if A_estimate < min_A:
A_estimate = min_A
t1_est = integral / A_estimate * f
t2_est = 2 * t1_est
tmax_est = time[p.argmax(smoothed_value)] + p.log(t2_est / t1_est) * (t1_est * t2_est) / (t1_est - t2_est)
return p.array([
tmax_est,
A_estimate,
t1_est,
mean_estimate])
def _createRmat( h_list, rmat, nstim, ntime ):
'''
This function ...
Aguments
--------
Keyword arguments
-----------------
'''
nsplit = len(h_list)
npop, _ = rmat.shape
Rmat = pl.zeros((nsplit*npop, nstim*ntime))
for istim in xrange(nstim):
for isplit in xrange(nsplit):
for ipop in xrange(npop):
rvec = rmat[ipop, istim*ntime:(istim+1)*ntime]
h = h_list[isplit]
tmp_vec= pl.convolve(rvec, h)
tmp_vec=tmp_vec[:ntime]
Rmat[ipop+isplit*npop,\
istim*ntime:(istim+1)*ntime]=tmp_vec
return Rmat
def alpha_psp_parameter_estimate(time, value, smoothing_samples=10):
t1_est_min = time[1] - time[0]
mean_est_part = len(value) * .1
mean_estimate = p.mean(value[-mean_est_part:])
noise_estimate = p.std(value[-mean_est_part:])
smoothed_value = p.convolve(
value - mean_estimate,
p.ones(smoothing_samples) / float(smoothing_samples),
"same") + mean_estimate
integral = p.sum(smoothed_value - mean_estimate) * (time[1] - time[0])
f = 1.
height_estimate = (max(smoothed_value) - mean_estimate)
min_height = noise_estimate
if height_estimate < min_height:
height_estimate = min_height
t1_est = integral / height_estimate * f
if t1_est < t1_est_min:
t1_est = t1_est_min
t2_est = 2 * t1_est
tmax_est = time[p.argmax(smoothed_value)]
tstart_est = tmax_est + p.log(t2_est / t1_est) \
* (t1_est * t2_est) / (t1_est - t2_est)
return p.array(
[height_estimate, t1_est, t2_est, tstart_est, mean_estimate])
def broadgauss(x, y, sigma):
'''Gaussian function for broadening
'''
bla = True
plot = False
c = 299792458.
if bla:
print " sigma = ", round(sigma, 4), " km/s"
sigma = sigma * 1.0e3 / c * pl.mean(x) # sigma in Å
if bla:
print " sigma = ", round(sigma, 3), " Å "
xk = x - pl.mean(x)
g = make_gauss(1, 0, sigma)
yk = [g(i) for i in xk]
if bla:
print " Integral of the gaussian function: ", pl.trapz(
yk, xk).__format__('5.3')
if plot:
pl.figure(2)
pl.plot(xk, yk, '+-')
pl.show()
#if bla: print" size y:", y.size
y = pl.convolve(y, yk, mode='same')
#if bla: print" size y:", y.size
return y / max(y)
def lowpassFIR(data, freq, samp_rate=200, winlen=2048):
"""
FIR-Lowpass Filter
Filter data by passing data only below a certain frequency.
:param data: Data to filter, type numpy.ndarray.
:param freq: Data below this frequency pass.
:param samprate: Sampling rate in Hz; Default 200.
:param winlen: Window length for filter in samples, must be power of 2;
Default 2048
:return: Filtered data.
"""
# There is not currently an FIR-filter design program in SciPy. One
# should be constructed as it is not hard to implement (of course making
# it generic with all the options you might want would take some time).
#
# What kind of window are you currently using?
#
# For your purposes this is what I would do:
# SRC: Travis Oliphant
# http://aspn.activestate.com/ASPN/Mail/Message/scipy-user/2009409]
#
#winlen = 2**11 #2**10 = 1024; 2**11 = 2048; 2**12 = 4096
#give frequency bins in Hz and sample spacing
w = fft.fftfreq(winlen, 1 / float(samp_rate))
#cutoff is low-pass filter
myfilter = where((abs(w) < freq), 1., 0.)
#ideal filter
h = fft.ifft(myfilter)
beta = 11.7
#beta implies Kaiser
myh = fft.fftshift(h) * get_window(beta, winlen)
return convolve(abs(myh), data)[winlen / 2:-winlen / 2]
def plot_axes(fig):
# create some data to use for the plot
dt = 0.001
t = arange(0.0, 10.0, dt)
r = exp(-t[:1000]/0.05) # impulse response
x = randn(len(t))
s = convolve(x,r,mode=2)[:len(x)]*dt # colored noise
# the main axes is subplot(111) by default
axes = fig.gca()
axes.plot(t, s)
axes.set_xlim((0, 1))
axes.set_ylim((1.1*min(s), 2*max(s)))
axes.set_xlabel('time (s)')
axes.set_ylabel('current (nA)')
axes.set_title('Gaussian colored noise')
# this is an inset axes over the main axes
a = fig.add_axes([.65, .6, .2, .2], axisbg='y')
n, bins, patches = a.hist(s, 400, normed=1)
a.set_title('Probability')
a.set_xticks([])
a.set_yticks([])
# this is another inset axes over the main axes
a = fig.add_axes([.2, .6, .2, .2], axisbg='y')
a.plot(t[:len(r)], r)
a.set_title('Impulse response')
a.set_xlim((0, 0.2))
a.set_xticks([])
a.set_yticks([])
def _shapeStim(self,
isi=1,
variation=0,
width=0.05,
weight=10,
start=0,
finish=1,
stimshape='gaussian'):
from pylab import r_, convolve, shape, exp, zeros, hstack, array, rand
# Create event times
timeres = 0.001 # Time resolution = 1 ms = 500 Hz (DJK to CK: 500...?)
pulselength = 10 # Length of pulse in units of width
currenttime = 0
timewindow = finish - start
allpts = int(timewindow / timeres)
output = []
while currenttime < timewindow:
# Note: The timeres/2 subtraction acts as an eps to avoid later int rounding errors.
if currenttime >= 0 and currenttime < timewindow - timeres / 2:
output.append(currenttime)
currenttime = currenttime + isi + variation * (rand() - 0.5)
# Create single pulse
npts = pulselength * width / timeres
x = (r_[0:npts] - npts / 2 + 1) * timeres
if stimshape == 'gaussian':
pulse = exp(-2 * (2 * x / width - 1)**
2) # Offset by 2 standard deviations from start
pulse = pulse / max(pulse)
elif stimshape == 'square':
pulse = zeros(shape(x))
pulse[int(npts / 2):int(npts / 2) +
int(width / timeres)] = 1 # Start exactly on time
else:
raise Exception('Stimulus shape "%s" not recognized' % stimshape)
# Create full stimulus
events = zeros((allpts))
events[array(array(output) / timeres, dtype=int)] = 1
fulloutput = convolve(
events, pulse, mode='full'
) * weight # Calculate the convolved input signal, scaled by rate
fulloutput = fulloutput[
npts / 2 - 1:-npts /
2] # Slices out where the convolved pulse train extends before and after sequence of allpts.
fulltime = (r_[0:allpts] * timeres +
start) * 1e3 # Create time vector and convert to ms
fulltime = hstack(
(0, fulltime, fulltime[-1] + timeres *
1e3)) # Create "bookends" so always starts and finishes at zero
fulloutput = hstack(
(0, fulloutput,
0)) # Set weight to zero at either end of the stimulus period
events = hstack((0, events, 0)) # Ditto
stimvecs = deepcopy([fulltime, fulloutput,
events]) # Combine vectors into a matrix
return stimvecs
def broadgauss(x, y, sigma):
'''Gaussian function for broadening
'''
bla = True
plot = False
c = 299792458.
if bla:
print " sigma = ", round(sigma, 4), " km/s"
sigma = sigma * 1.0e3/c * pl.mean(x) # sigma in Å
if bla:
print " sigma = ", round(sigma, 3), " Å "
xk = x - pl.mean(x)
g = make_gauss(1, 0, sigma)
yk = [g(i) for i in xk]
if bla:
print " Integral of the gaussian function: ", pl.trapz(yk, xk).__format__('5.3')
if plot:
pl.figure(2)
pl.plot(xk, yk, '+-')
pl.show()
#if bla: print" size y:", y.size
y = pl.convolve(y, yk, mode='same')
#if bla: print" size y:", y.size
return y/max(y)
def SVMAF(self,freq,n,l):
#Apply the SVMAF filter to the material parameters
runningMean=lambda x,N: py.hstack((x[:N-1],py.convolve(x,py.ones((N,))/N,mode='same')[N-1:-N+1],x[(-N+1):]))
#calculate the moving average of 3 points
n_smoothed=runningMean(n,3)
#evaluate H_smoothed from n_smoothed
H_smoothed=self.H_theory(freq,[n_smoothed.real,n_smoothed.imag],l)
H_r=H_smoothed.real
H_i=H_smoothed.imag
f=1
#the uncertainty margins
lb_r=self.H.getFReal()-self.H.getFRealUnc()*f
lb_i=self.H.getFImag()-self.H.getFImagUnc()*f
ub_r=self.H.getFReal()+self.H.getFRealUnc()*f
ub_i=self.H.getFImag()+self.H.getFImagUnc()*f
#ix=all indices for which after smoothening n H is still inbetwen the bounds
ix=py.all([H_r>=lb_r,H_r<ub_r,H_i>=lb_i,H_i<ub_i],axis=0)
# #dont have a goood idea at the moment, so manually:
for i in range(len(n_smoothed)):
if ix[i]==0:
n_smoothed[i]=n[i]
print("SVMAF changed the refractive index at " + str(sum(ix)) + " frequencies")
return n_smoothed
def getmovingAveragedData(self,window_size_GHz=-1):
#so far unelegant way of convolving the columns one by one
#even not nice, improvement possible?
if window_size_GHz<0.5e9:
window_size=int(self.getEtalonSpacing()/self.getfbins())
else:
window_size=int(window_size_GHz/self.getfbins())
window_size+=window_size%2+1
window=py.ones(int(window_size))/float(window_size)
dataabs=py.convolve(self.getFAbs(), window, 'valid')
dataph=py.convolve(self.getFPh(), window, 'valid')
one=py.ones((window_size-1)/2,)
dataabs=py.concatenate((dataabs[0]*one,dataabs,dataabs[-1]*one))
dataph=py.concatenate((dataph[0]*one,dataph,dataph[-1]*one))
return py.column_stack((self.fdData[:,:3],dataabs,dataph,self.fdData[:,5:]))
def smooth(x,window_len=11,window='hanning'):
"""smooth the data using a window with requested size.
This method is based on the convolution of a scaled window with the signal.
The signal is prepared by introducing reflected copies of the signal
(with the window size) in both ends so that transient parts are minimized
in the begining and end part of the output signal.
Copied and modified from http://scipy-cookbook.readthedocs.io/items/SignalSmooth.html (16/10/2017 - RProux)
input:
x: the input signal
window_len: the dimension of the smoothing window; should be an odd integer
window: the type of window from 'flat', 'hanning', 'hamming', 'bartlett', 'blackman'
flat window will produce a moving average smoothing.
output:
the smoothed signal
example:
t=linspace(-2,2,0.1)
x=sin(t)+randn(len(t))*0.1
y=smooth(x)
see also:
numpy.hanning, numpy.hamming, numpy.bartlett, numpy.blackman, numpy.convolve
scipy.signal.lfilter
TODO: the window parameter could be the window itself if an array instead of a string
NOTE: the window_len parameter should always be odd for reliable output (will shift slightly the data if even)
"""
if x.ndim != 1:
raise ValueError("smooth only accepts 1 dimension arrays.")
if x.size < window_len:
raise ValueError("Input vector needs to be bigger than window size.")
if window_len < 3:
return x
if window not in ['flat', 'hanning', 'hamming', 'bartlett', 'blackman']:
raise ValueError("Window is one of 'flat', 'hanning', 'hamming', 'bartlett', 'blackman'")
s = pl.r_[x[window_len-1:0:-1],x,x[-2:-window_len-1:-1]]
print(s)
print(len(s))
if window == 'flat': #moving average
w = pl.ones(window_len, 'd')
else:
w = eval('pl.{}(window_len)'.format(window))
y = pl.convolve(w / w.sum(), s, mode='valid')
return y[int(pl.floor(window_len/2)) : -int(pl.ceil(window_len/2) - 1)]
def smooth(x, beta):
""" kaiser window smoothing """
window_len = 11
# extending the data at beginning and at the end
# to apply the window at the borders
s = pylab.r_[x[window_len - 1:0:-1], x, x[-1:-window_len:-1]]
w = pylab.kaiser(window_len, beta)
y = pylab.convolve(w / w.sum(), s, mode='valid')
return y[5:len(y) - 5]
def smooth(x,beta):
""" kaiser window smoothing """
window_len=11
# extending the data at beginning and at the end
# to apply the window at the borders
s = pylab.r_[x[window_len-1:0:-1],x,x[-1:-window_len:-1]]
w = pylab.kaiser(window_len,beta)
y = pylab.convolve(w/w.sum(),s,mode='valid')
return y[5:len(y)-5]
def zMeasures(current, v, delay, sampr, f1, bwinsz=1):
## zero padding
current = current[int(delay * sampr - 0.5 * sampr +
1):-int(delay * sampr - 0.5 * sampr)]
current = np.hstack((np.repeat(current[0], int(delay * sampr)), current,
np.repeat(current[-1], int(delay * sampr))))
current = current - np.mean(current)
v = v[int(delay * sampr - 0.5 * sampr) +
1:-int(delay * sampr - 0.5 * sampr)]
v = np.hstack((np.repeat(v[0], int(delay * sampr)), v,
np.repeat(v[-1], int(delay * sampr))))
v = v - np.mean(v)
## input and transfer impedance
f_current = (fft(current) / len(current))[0:int(len(current) / 2)]
f_cis = (fft(v) / len(v))[0:int(len(v) / 2)]
z = f_cis / f_current
## impedance measures
Freq = np.linspace(0.0, sampr / 2.0, len(z))
zAmp = abs(z)
zPhase = np.arctan2(np.imag(z), np.real(z))
zRes = np.real(z)
zReact = np.imag(z)
## smoothing
fblur = np.array([1.0 / bwinsz for i in range(bwinsz)])
zAmp = convolve(zAmp, fblur, 'same')
zPhase = convolve(zPhase, fblur, 'same')
## trim
mask = (Freq >= 0.5) & (Freq <= f1)
Freq, zAmp, zPhase, zRes, zReact = Freq[mask], zAmp[mask], zPhase[
mask], zRes[mask], zReact[mask]
## resonance
zResAmp = np.max(zAmp)
zResFreq = Freq[np.argmax(zAmp)]
Qfactor = zResAmp / zAmp[0]
fVar = np.std(zAmp) / np.mean(zAmp)
return Freq, zAmp, zPhase, zRes, zReact, zResAmp, zResFreq, Qfactor, fVar
def makestim(isi=1,
variation=0,
width=0.05,
weight=10,
start=0,
finish=1,
stimshape='gaussian'):
from pylab import r_, convolve, shape
# Create event times
timeres = 0.005 # Time resolution = 5 ms = 200 Hz
pulselength = 10 # Length of pulse in units of width
currenttime = 0
timewindow = finish - start
allpts = int(timewindow / timeres)
output = []
while currenttime < timewindow:
if currenttime >= 0 and currenttime < timewindow:
output.append(currenttime)
currenttime = currenttime + isi + variation * (rand() - 0.5)
# Create single pulse
npts = min(pulselength * width / timeres,
allpts) # Calculate the number of points to use
x = (r_[0:npts] - npts / 2 + 1) * timeres
if stimshape == 'gaussian':
pulse = exp(-(x / width * 2 - 2)**
2) # Offset by 2 standard deviations from start
pulse = pulse / max(pulse)
elif stimshape == 'square':
pulse = zeros(shape(x))
pulse[int(npts / 2):int(npts / 2) +
int(width / timeres)] = 1 # Start exactly on time
else:
raise Exception('Stimulus shape "%s" not recognized' % stimshape)
# Create full stimulus
events = zeros((allpts))
events[array(array(output) / timeres, dtype=int)] = 1
fulloutput = convolve(
events, pulse, mode='same'
) * weight # Calculate the convolved input signal, scaled by rate
fulltime = (r_[0:allpts] * timeres +
start) * 1e3 # Create time vector and convert to ms
fulltime = hstack(
(0, fulltime, fulltime[-1] + timeres *
1e3)) # Create "bookends" so always starts and finishes at zero
fulloutput = hstack(
(0, fulloutput,
0)) # Set weight to zero at either end of the stimulus period
events = hstack((0, events, 0)) # Ditto
stimvecs = [fulltime, fulloutput, events] # Combine vectors into a matrix
return stimvecs
def mov_avg(data, tailLength):
"""
returns the moving average for a 1D array data
"""
data1 = concatenate((data[tailLength:0:-1],data,data[-tailLength:]))
#print "mov avg idat shape:", data1.shape, "tailLength:", tailLength
avgFilter = array([1./(2.*tailLength+1.),]*(2*tailLength + 1))
#print "avgFilter:", avgFilter.shape
res = convolve(data1,avgFilter)[2*tailLength:-2*tailLength]
#print "mov avg shape:", res.shape
return res
def getDR(self):
#this function should return the dynamic range
#this should be the noiselevel of the fft
noiselevel=py.sqrt(py.mean(abs(py.fft(self._tdData.getAllPrecNoise()[0]))**2))
#apply a moving average filter on log
window_size=5
window=py.ones(int(window_size))/float(window_size)
hlog=py.convolve(20*py.log10(self.getFAbs()), window, 'valid')
one=py.ones((2,))
hlog=py.concatenate((hlog[0]*one,hlog,hlog[-1]*one))
return hlog-20*py.log10(noiselevel)
def findAreaOfInterest(self):
"""
Argument :
- None
Return :
- None
Use to detect the AOI by an edge detection technique.
"""
OD = self.findNoisyArea()
max = 0
bestAngle = None
for angle in range(-10, 10, 1):
# the best angle is the one for wich the maximum peak is reached
# on the yProfile (integral on the horizontal direction) ...
image = rotate(OD, angle)
yProfile = py.sum(image, axis=1)
newMax = yProfile.max()
if newMax > max:
max = newMax
bestAngle = angle
# ... once found, the resulting OD image is kept and used to find the
# the top and bottom bounds by edge detection.
bestOD = rotate(OD, bestAngle)
YProfile = py.sum(bestOD, axis=1)
derivative = py.gradient(YProfile)
N = 10
# because the derivative is usually very noisy, a sliding average is
# performed in order to smooth the signal. This is done by a
# convolution with a gate function of size "N".
res = py.convolve(derivative, py.ones((N, )) / N, mode='valid')
mean = res.mean()
# index of the maximum value of the signal.
i = res.argmax()
while res[i] > mean:
# once "i" is greater or equal to the mean of the derivative,
# we have found the upper bound of the AOI.
i -= 1
# for security we take an extra 50 pixels.
y0 = int(i - 50)
# index of the minimum value of the signal.
i = res.argmin()
while res[i] < mean:
# once "i" is smaller or equal to the mean of the derivative,
# we have found the lower bound of the AOI.
i += 1
# Again, for security, we take an extra 50 pixels.
y1 = int(i + 50)
# The horizontal bound are taken to be maximal, but for security, we
# take an extra 50 pixels.
x0 = 50
x1 = py.shape(OD)[0] - 50
self.setAreaOfInterest(area=(x0, x1, y0, y1), angle=bestAngle)
return bestOD[y0:y1, x0:x1]
def mov_avg(data, tailLength):
"""
returns the moving average for a 1D array data
"""
data1 = concatenate((data[tailLength:0:-1], data, data[-tailLength:]))
#print "mov avg idat shape:", data1.shape, "tailLength:", tailLength
avgFilter = array([
1. / (2. * tailLength + 1.),
] * (2 * tailLength + 1))
#print "avgFilter:", avgFilter.shape
res = convolve(data1, avgFilter)[2 * tailLength:-2 * tailLength]
#print "mov avg shape:", res.shape
return res
def decoder(data,code,iflip):
"""convolves each data profile with the code sequence"""
times=py.shape(data)[0]
hts=py.shape(data)[1]
codelength=py.shape(code)[0]
code_rev=code[::-1] #decoding requires using the inverse of the code
deflip=1
#pdb.set_trace()
for i in range (times):
temp=py.convolve(data[i,:],code_rev)
data[i,:]=deflip*temp[codelength-1:codelength+hts]
deflip=deflip*iflip #call with iflip=-1 if tx has flip
#pdb.set_trace()
return data
def decoder(data, code, iflip):
"""convolves each data profile with the code sequence"""
times = py.shape(data)[0]
hts = py.shape(data)[1]
codelength = py.shape(code)[0]
code_rev = code[::-1] #decoding requires using the inverse of the code
deflip = 1
#pdb.set_trace()
for i in range(times):
temp = py.convolve(data[i, :], code_rev)
data[i, :] = deflip * temp[codelength - 1:codelength + hts]
deflip = deflip * iflip #call with iflip=-1 if tx has flip
#pdb.set_trace()
return data
def smooth(x,window_len=11,window='hanning'):
if x.ndim != 1:
raise ValueError, "smooth only accepts 1 dimension arrays."
if x.size < window_len:
raise ValueError, "Input vector needs to be bigger than window size."
if window_len<3:
return x
if not window in ['flat', 'hanning', 'hamming', 'bartlett', 'blackman']:
raise ValueError, "Window is one of 'flat', 'hanning', 'hamming', 'bartlett', 'blackman'"
s=p.r_[2*x[0]-x[window_len-1::-1],x,2*x[-1]-x[-1:-window_len:-1]]
if window == 'flat': #moving average
w=p.ones(window_len,'d')
else:
w=eval('p.'+window+'(window_len)')
y=p.convolve(w/w.sum(),s,mode='same')
return y[window_len:-window_len+1]
def match(Signal=None, Window=None):
"""
.
Parameters
__________
Signal : ndarray
Input signal data.
Window :
Returns
_______
kwrvals : dict
A keyworded return values dict is returned with the following keys:
Event :
See Also
________
pl.convolve
Notes
_____
Example
_______
"""
# Check
if Signal is None:
raise TypeError, "An input signal is needed."
#
lw = len(Window)
lx = len(Signal)
if lw > lx:
raise AttributeError(
"Window length must be less or equal to the length of the input signal."
)
kwrvals = {}
#kwrvals['dt']=pl.array(map(lambda i: pl.sqrt(sum((Signal[i+lw]-Window)**2)), pl.arange(0, lx-lw))).argmin()
kwrvals['dt'] = pl.convolve(Window, Signal).argmax()
return kwrvals
def decoder_ht(data, code, iflip=1., dropheights=False):
"""convolves each data profile with the code sequence"""
times = data.shape[2]
hts = data.shape[1]
chs = data.shape[0]
numcodes = code.shape[0]
codelength = code.shape[1]
code_rev = code[:, ::-1] #decoding requires using the inverse of the code
deflip = iflip
for ch in range(chs):
for i in range(times):
if i % numcodes == 0:
deflip = deflip * iflip #call with iflip=-1 if tx has flip
code_i = i % numcodes
temp = py.convolve(data[ch, :, i], code_rev[code_i, :])
data[ch, :, i] = deflip * temp[codelength - 1:codelength + hts]
return data
def decoder_ht(data,code, iflip = 1., dropheights = False):
"""convolves each data profile with the code sequence"""
times = data.shape[2]
hts = data.shape[1]
chs = data.shape[0]
numcodes = code.shape[0]
codelength= code.shape[1]
code_rev=code[:,::-1] #decoding requires using the inverse of the code
deflip = iflip
for ch in range(chs):
for i in range (times):
if i % numcodes == 0 :
deflip=deflip*iflip #call with iflip=-1 if tx has flip
code_i = i % numcodes
temp=py.convolve(data[ch,:,i],code_rev[code_i,:])
data[ch,:,i]=deflip*temp[codelength-1:codelength+hts]
return data
def smoothed_histogram_window(ax, pdf, bins):
wsize = 20
bins = 0.5 * (bins[:-1] + bins[1:])
# for wsize in range(5, 30, 5):
# extending the data at beginning and at the end
# to apply the window at the borders
ps = plt.r_[pdf[wsize-1:0:-1], pdf, pdf[-1:-wsize:-1]]
w = plt.hanning(wsize)
pc = plt.convolve(w/w.sum(), ps, mode='valid')
pc = pc[wsize/2:len(ps)-wsize/2]
pc = pc[0:len(bins)]
# plt.plot(bins, pc)
# plt.fill_between(bins, 0, pc, alpha=0.1)
return pc, bins
def make_graphs(stats, fileout):
Gaussian = scipy.signal.gaussian(WindowSize, 2)
Gaussian = Gaussian / sum(Gaussian)
fontP = FontProperties()
fontP.set_size('small')
perRoundStats = [['Turns per round', 'Time per round'], ['Created nodes per round', 'Cumulative nodes per round'], ['Pulses per round']]
for i, subset in enumerate(perRoundStats):
plt.subplot(len(perRoundStats), 1, i + 1)
for pr in subset:
plot = stats[pr]
if i == 0 and smoothed: plot = pylab.convolve(plot, Gaussian, 'same')
plt.plot(plot, label=pr) # drawstyle = 'steps'
plt.xlabel('Round')
plt.legend(prop = fontP)
if fileout == 'show': plt.show()
else: plt.savefig(fileout)
def create_band(band, res, plt=False, high=0, conv=False):
'''
print, "create_band, band, res, /bw, /plt, high=high, /conv"
print, "This program will create a top hat band convolved with a gaussain of sigma = res with freq data spaced from 0 to 1000 (default) GHz"
print, "band = bandpass region in GHz"
print, "res = freq. spacing in GHz"
print, "/plt plot bandpass"
print, "high=high upper GHz region"
print, "r = create_band([140, 160], 2.0, /bw, high=500.0)"
return, 0
'''
npts = pl.ceil(4000.0)
if high : npts = pl.ceil(high*1.0/.25)
freq = pl.arange(npts)*.25
response = pl.zeros(len(freq))
inb = pl.where((freq < band[1]) & (freq > band[0]))[0]
if band[0] == band[1] : inb = pl.where_closest(freq, band(0))[0]
if inb[0] == -1:
print "Band not between 0-1000 GHZ"
return 0
response[inb] = 1
#let's convolve the band with our resolution.
if conv:
xx = .25*pl.arange(6*res/.25+1)-3*res
con =pl.exp(-xx**2/(2*res**2))/pl.sqrt(2*pl.pi)/res
normalization=1./sum(abs(con))
response = pl.convolve(response, con,'same')*normalization
if plt:
pl.figure()
pl.plot(freq, response,'D')
pl.xlabel('Freq(GHz)')
pl.ylabel('Reponse')
pl.xlim(band[0] - 3*res, band[1] + 3*res)
result = {'Freq': freq, 'resp': response}
return result
def Errorline_faded ( x, y, e, al, **kwargs ):
"""An Errorline that fades
Similar to an Error line but fades out according to al.
IMPORTANT: This line is going to be made up of lots of small lines and
small rectangular patches.
:Parameters:
*x*
x values of the line
*y*
y values of the line. If y.shape == 2, then se is called for
every sample of y to derive an upper and lower limit
*e*
error (in y direction) This could take either a scalar giving the
(constant) error, an array of scalar errors, or an array of
observations. In the latter case, se is applied to every sample
of e
*al*
alpha values for the different line segments
*color*,*edgecolor*,*facecolor*,*ax*
see Errorline()
"""
c = dvis.color.colorsequence ( kwargs.setdefault ( 'color', [0,0,0]))[0]
kwargs.setdefault ( 'edgecolor', dvis.color.cmix ( c, 'w', 3 ) )
kwargs.setdefault ( 'facecolor', dvis.color.cmix ( c, 'w', 1.5 ) )
ax = kwargs.setdefault ( 'ax', pl.gca() )
fade = pl.convolve ( [.5,.5], al, 'valid' )
yup = y+e
ydown = y-e
n = len(fade)
l,f = [],[]
for i in xrange ( n ):
f += ax.fill (
[x[i],x[i+1],x[i+1],x[i]],
[yup[i],yup[i+1],ydown[i+1],ydown[i]],
ec='none', fc=kwargs['facecolor'], alpha=fade[i] )
l += ax.plot ( x[i:i+2], y[i:i+2], color=c, alpha=fade[i] )
return l,f
def broaden(self, fwhm=1e-10, linetype=1, eta=[]):
output = Spectrum(self.wavelengths)
window = max(output.wavelengths) - min(output.wavelengths)
center = max(output.wavelengths) - window/2
if fwhm <= 0:
raise ValueError('The linewidth must be positive and nonzero.')
# Trapezoidal
elif linetype is 0:
pass
# Gaussian
elif linetype is 1:
sigma = fwhm / (2 * log(2)**0.5)
slit = exp(-(output.wavelengths - center)**2/(2 * sigma**2))
# Lorentzian
elif linetype is 2:
gamma = fwhm
slit = 0.5 * (gamma / ((output.wavelengths - center)**2 \
+ 0.25 * gamma**2)) / pi
# Pseudo-Voigt
elif linetype is 3:
if not eta:
print "Eta required for pseudo-Voigt profile, quitting"
sys.exit(0)
sigma = fwhm
sigma_g = fwhm / (2 * log(2)**0.5)
g = exp(-(output.wavelengths - center)**2/(2 * sigma_g**2)) \
/ (sigma_g * (2*pi)**0.5)
l = (0.5 * sigma / pi) \
/ ((output.wavelengths - center)**2 + .25 * sigma**2)
slit = eta * l + (1 - eta) * g
output.intensities = pylab.convolve(self.intensities, slit, 'same')
return output
# step 2 : calculate psp. Its maximum is used below as a fudge-factor for the psp amplitude
psp = ( Cm * pF ) / ( tau_s * ms ) * (1/( Cm * pF )) * (e/( tau_s * ms ) ) * \
( ((-t_psp * exp(-t_psp/(tau_s * ms) )) / (1/( tau_s * ms )-1 / ( tau_m * ms ) )) +\
(exp(-t_psp/( tau_m * ms )) - exp(-t_psp/( tau_s * ms ))) / ((1/( tau_s * ms ) - 1/( tau_m * ms ))**2) )
# step 3: normalize to amplitude 1, thereby obtaining the maximum
fudge = 1 / numpy.max(psp) # fudge is also used below
psp *= fudge
# step 4: pad with zeros on the left side. Avoids offsets when using convolution
tmp = numpy.zeros(2 * len(psp))
tmp[len(psp) - 1:-1] += psp
psp = tmp
del tmp
P = a * weight * pylab.convolve(gauss, psp)
l = len(P)
t_P = convolution_resolution * numpy.linspace(
-l / 2., l / 2., l) + pulsetime + 1. # one ms delay
#########################################################################
# simulation section
nest.ResetKernel()
nest.SetStatus([0], [{'resolution': simulation_resolution}])
J = Cm * weight / tau_s * fudge
nest.SetDefaults('static_synapse', {'weight': J})
n = nest.Create(
# step 2 : calculate psp. Its maximum is used below as a fudge-factor for the psp amplitude
psp = ( Cm * pF ) / ( tau_s * ms ) * (1/( Cm * pF )) * (e/( tau_s * ms ) ) * \
( ((-t_psp * exp(-t_psp/(tau_s * ms) )) / (1/( tau_s * ms )-1 / ( tau_m * ms ) )) +\
(exp(-t_psp/( tau_m * ms )) - exp(-t_psp/( tau_s * ms ))) / ((1/( tau_s * ms ) - 1/( tau_m * ms ))**2) )
# step 3: normalize to amplitude 1, thereby obtaining the maximum
fudge = 1/numpy.max(psp) # fudge is also used below
psp *= fudge
# step 4: pad with zeros on the left side. Avoids offsets when using convolution
tmp = numpy.zeros(2*len(psp))
tmp[len(psp)-1:-1] += psp
psp = tmp
del tmp
P = a * weight * pylab.convolve(gauss, psp)
l = len(P)
t_P = convolution_resolution * numpy.linspace( -l/2., l/2., l) + pulsetime + 1. # one ms delay
#########################################################################
# simulation section
nest.ResetKernel()
nest.SetStatus([0],[{'resolution':simulation_resolution}])
J = Cm*weight/tau_s*fudge
nest.SetDefaults('static_synapse', {'weight':J} )
def main():
import optparse
from numpy import sum
# Parse command line
parser = optparse.OptionParser(usage=USAGE)
parser.add_option("-p",
"--plot",
action="store_true",
help="Generate pdf with IR-spectrum")
parser.add_option("-i",
"--info",
action="store_true",
help="Set up/ Calculate vibrations & quit")
parser.add_option("-s",
"--suffix",
action="store",
help="Call suffix for binary e.g. 'mpirun -n 4 '",
default='')
parser.add_option("-r",
"--run",
action="store",
help="path to FHI-aims binary",
default='')
parser.add_option("-x",
"--relax",
action="store_true",
help="Relax initial geometry")
parser.add_option("-m",
"--molden",
action="store_true",
help="Output in molden format")
parser.add_option("-w",
"--distort",
action="store_true",
help="Output geometry distorted along imaginary modes")
parser.add_option("-t",
"--submit",
action="store",
help="""\
Path to submission script, string <jobname>
will be replaced by name + counter, string
<outfile> will be replaced by filename""")
parser.add_option("-d",
"--delta",
action="store",
type="float",
help="Displacement",
default=0.0025)
options, args = parser.parse_args()
if options.info:
print __doc__
sys.exit(0)
if len(args) != 2:
parser.error("Need exactly two arguments")
AIMS_CALL = options.suffix + ' ' + options.run
hessian_thresh = -1
name = args[0]
mode = args[1]
delta = options.delta
run_aims = False
if options.run != '': run_aims = True
submit_script = options.submit is not None
if options.plot:
import matplotlib as mpl
mpl.use('Agg')
from pylab import figure
if options.plot or mode == '1':
from pylab import savetxt, transpose, eig, argsort, sort,\
sign, pi, dot, sum, linspace, argmin, r_, convolve
# Constant from scipy.constants
bohr = constants.value('Bohr radius') * 1.e10
hartree = constants.value('Hartree energy in eV')
at_u = constants.value('atomic mass unit-kilogram relationship')
eV = constants.value('electron volt-joule relationship')
c = constants.value('speed of light in vacuum')
Ang = 1.0e-10
hbar = constants.value('Planck constant over 2 pi')
Avo = constants.value('Avogadro constant')
kb = constants.value('Boltzmann constant in eV/K')
hessian_factor = eV / (at_u * Ang * Ang)
grad_dipole_factor = (eV / (1. / (10 * c))) / Ang #(eV/Ang -> D/Ang)
ir_factor = 1
# Asign all filenames
inputgeomerty = 'geometry.in.' + name
inputcontrol = 'control.in.' + name
atomicmasses = 'masses.' + name + '.dat'
xyzfile = name + '.xyz'
moldenname = name + '.molden'
hessianname = 'hessian.' + name + '.dat'
graddipolename = 'grad_dipole.' + name + '.dat'
irname = 'ir.' + name + '.dat'
deltas = array([-delta, delta])
coeff = array([-1, 1])
c_zero = -1. / (2. * delta)
f = open('control.in', 'r') # read control.in template
template_control = f.read()
f.close
if submit_script:
f = open(options.submit, 'r') # read submission script template
template_job = f.read()
f.close
folder = '' # Dummy
########### Central Point ##################################################
if options.relax and mode == '0':
# First relax input geometry
filename = name + '.out'
folder = name + '_relaxation'
if not os.path.exists(folder): os.mkdir(folder) # Create folder
shutil.copy('geometry.in', folder + '/geometry.in') # Copy geometry
new_control = open(folder + '/control.in', 'w')
new_control.write(template_control +
'relax_geometry trm 1E-3\n') # Relax!
new_control.close()
os.chdir(folder) # Change directoy
print 'Central Point'
if run_aims:
os.system(AIMS_CALL + ' > ' +
filename) # Run aims and pipe the output
# into a file named 'filename'
if submit_script: replace_submission(template_job, name, 0, filename)
os.chdir('..')
############################################################################
# Check for relaxed geometry
if os.path.exists(folder + '/geometry.in.next_step'):
geometry = open(folder + '/geometry.in.next_step', 'r')
else:
geometry = open('geometry.in', 'r')
# Read input geometry
n_line = 0
struc = structure()
lines = geometry.readlines()
for line in lines:
n_line = n_line + 1
if line.rfind('set_vacuum_level') != -1: # Vacuum Level
struc.vacuum_level = float(split_line(line)[-1])
if line.rfind('lattice_vector') != -1: # Lattice vectors and periodic
lat = split_line(line)[1:]
struc.lattic_vector = append(struc.lattic_vector,
float64(array(lat))[newaxis, :],
axis=0)
struc.periodic = True
if line.rfind('atom') != -1: # Set atoms
line_vals = split_line(line)
at = Atom(line_vals[-1], line_vals[1:-1])
if n_line < len(lines):
nextline = lines[n_line]
if nextline.rfind(
'constrain_relaxation') != -1: # constrained?
at = Atom(line_vals[-1], line_vals[1:-1], True)
else:
at = Atom(line_vals[-1], line_vals[1:-1])
struc.join(at)
geometry.close()
n_atoms = struc.n()
n_constrained = n_atoms - sum(struc.constrained)
# Atomic mass file
mass_file = open(atomicmasses, 'w')
mass_vector = zeros([0])
for at_unconstrained in struc.atoms[struc.constrained == False]:
mass_vector = append(mass_vector,
ones(3) * 1. / sqrt(at_unconstrained.mass()))
line = '{0:10.5f}'.format(at_unconstrained.mass())
for i in range(3):
line = line + '{0:11.4f}'.format(at_unconstrained.coord[i])
line = line + '{0:}\n'.format(at_unconstrained.kind)
mass_file.writelines(line)
mass_file.close()
# Init
dip = zeros([n_constrained * 3, 3])
hessian = zeros([n_constrained * 3, n_constrained * 3])
index = 0
counter = 1
# Set up / Read folders for displaced atoms
for atom in arange(n_atoms)[struc.constrained == False]:
for coord in arange(3):
for delta in deltas:
filename=name+'.i_atom_'+str(atom)+'.i_coord_'+str(coord)+'.displ_'+\
str(delta)+'.out'
folder=name+'.i_atom_'+str(atom)+'.i_coord_'+str(coord)+'.displ_'+\
str(delta)
if mode == '0': # Put new geometry and control.in into folder
struc_new = copy.deepcopy(struc)
struc_new.atoms[atom].coord[coord]=\
struc_new.atoms[atom].coord[coord]+delta
geoname='geometry.i_atom_'+str(atom)+'.i_coord_'+str(coord)+\
'.displ_'+str(delta)+'.in'
if not os.path.exists(folder): os.mkdir(folder)
new_geo = open(folder + '/geometry.in', 'w')
newline='#\n# temporary structure-file for finite-difference '+\
'calculation of forces\n'
newline=newline+'# displacement {0:8.4f} of \# atom '.format(delta)+\
'{0:5} direction {1:5}\n#\n'.format(atom,coord)
new_geo.writelines(newline + struc_new.to_str())
new_geo.close()
new_control = open(folder + '/control.in', 'w')
template_control = template_control.replace(
'relax_geometry', '#relax_geometry')
new_control.write(template_control+'compute_forces .true. \n'+\
'final_forces_cleaned '+\
'.true. \noutput dipole \n')
new_control.close()
os.chdir(folder) # Change directoy
print 'Processing atom: '+str(atom+1)+'/'+str(n_atoms)+', coord.: '+\
str(coord+1)+'/'+str(3)+', delta: '+str(delta)
if run_aims:
os.system(AIMS_CALL + ' > ' +
filename) # Run aims and pipe the output
# into a file named 'filename'
if submit_script:
replace_submission(template_job, name, counter,
filename)
# os.system('qsub job.sh') # Mind the environment variables
os.chdir('..')
if mode == '1': # Read output
forces_reached = False
atom_count = 0
data = open(folder + '/' + filename)
for line in data.readlines():
if line.rfind(
'Dipole correction potential jump') != -1:
dip_jump = float(split_line(line)[-2]) # Periodic
if line.rfind('| Total dipole moment [eAng]') != -1:
dip_jump = float64(
split_line(line)[-3:]) # Cluster
if forces_reached and atom_count < n_atoms: # Read Forces
struc.atoms[atom_count].force = float64(
split_line(line)[2:])
atom_count = atom_count + 1
if atom_count == n_atoms:
forces_reached = False
if line.rfind('Total atomic forces') != -1:
forces_reached = True
data.close()
if struc.periodic:
dip[index, 2] = dip[
index,
2] + dip_jump * coeff[deltas == delta] * c_zero
else:
dip[index, :] = dip[index, :] + dip_jump * coeff[
deltas == delta] * c_zero
forces = array([])
for at_unconstrained in struc.atoms[struc.constrained ==
False]:
forces = append(
forces,
coeff[deltas == delta] * at_unconstrained.force)
hessian[index, :] = hessian[index, :] + forces * c_zero
counter = counter + 1
index = index + 1
if mode == '1': # Calculate vibrations
print 'Entering hessian diagonalization'
print 'Number of atoms = ' + str(n_atoms)
print 'Name of Hessian input file = ' + hessianname
print 'Name of grad dipole input file = ' + graddipolename
print 'Name of Masses input file = ' + atomicmasses
print 'Name of XYZ output file = ' + xyzfile
print 'Threshold for Matrix elements = ' + str(hessian_thresh)
if (hessian_thresh < 0.0): print ' All matrix elements are taken'+\
' into account by default\n'
savetxt(hessianname, hessian)
savetxt(graddipolename, dip)
mass_mat = mass_vector[:, newaxis] * mass_vector[newaxis, :]
hessian[abs(hessian) < hessian_thresh] = 0.0
hessian = hessian * mass_mat * hessian_factor
hessian = (hessian + transpose(hessian)) / 2.
# Diagonalize hessian (scipy)
print 'Solving eigenvalue system for Hessian Matrix'
freq, eig_vec = eig(hessian)
print 'Done ... '
eig_vec = eig_vec[:, argsort(freq)]
freq = sort(sign(freq) * sqrt(abs(freq)))
ZPE = hbar * (freq) / (2.0 * eV)
freq = (freq) / (200. * pi * c)
grad_dipole = dip * grad_dipole_factor
eig_vec = eig_vec * mass_vector[:, newaxis] * ones(
len(mass_vector))[newaxis, :]
infrared_intensity = sum(dot(transpose(grad_dipole),eig_vec)**2,axis=0)*\
ir_factor
reduced_mass = sum(eig_vec**2, axis=0)
norm = sqrt(reduced_mass)
eig_vec = eig_vec / norm
# The rest is output, xyz, IR,...
print 'Results\n'
print 'List of all frequencies found:'
print 'Mode number Frequency [cm^(-1)] Zero point energy [eV] '+\
'IR-intensity [D^2/Ang^2]'
for i in range(len(freq)):
print '{0:11}{1:25.8f}{2:25.8f}{3:25.8f}'.format(
i + 1, freq[i], ZPE[i], infrared_intensity[i])
print '\n'
print 'Summary of zero point energy for entire system:'
print '| Cumulative ZPE = {0:15.8f} eV'.format(sum(ZPE))
print '| without first six eigenmodes = {0:15.8f} eV\n'.format(
sum(ZPE) - sum(ZPE[:6]))
print 'Stability checking - eigenvalues should all be positive for a '+\
'stable structure. '
print 'The six smallest frequencies should be (almost) zero:'
string = ''
for zz in ZPE[:6]:
string = string + '{0:25.8f}'.format(zz)
print string
print 'Compare this with the largest eigenvalue, '
print '{0:25.8f}'.format(freq[-1])
nums = arange(n_atoms)[struc.constrained == False]
nums2 = arange(n_atoms)[struc.constrained]
newline = ''
newline_ir = '[INT]\n'
if options.molden:
newline_molden = '[Molden Format]\n[GEOMETRIES] XYZ\n'
newline_molden = newline_molden + '{0:6}\n'.format(n_atoms) + '\n'
for i_atoms in range(n_constrained):
newline_molden = newline_molden + '{0:6}'.format(
struc.atoms[nums[i_atoms]].kind)
for i_coord in range(3):
newline_molden = newline_molden + '{0:10.4f}'.format(
struc.atoms[nums[i_atoms]].coord[i_coord])
newline_molden = newline_molden + '\n'
newline_molden = newline_molden + '[FREQ]\n'
for i in range(len(freq)):
newline_molden = newline_molden + '{0:10.3f}\n'.format(freq[i])
newline_molden = newline_molden + '[INT]\n'
for i in range(len(freq)):
newline_molden = newline_molden + '{0:17.6e}\n'.format(
infrared_intensity[i])
newline_molden = newline_molden + '[FR-COORD]\n'
newline_molden = newline_molden + '{0:6}\n'.format(n_atoms) + '\n'
for i_atoms in range(n_constrained):
newline_molden = newline_molden + '{0:6}'.format(
struc.atoms[nums[i_atoms]].kind)
for i_coord in range(3):
newline_molden = newline_molden + '{0:10.4f}'.format(
struc.atoms[nums[i_atoms]].coord[i_coord] / bohr)
newline_molden = newline_molden + '\n'
newline_molden = newline_molden + '[FR-NORM-COORD]\n'
for i in range(len(freq)):
newline = newline + '{0:6}\n'.format(n_atoms)
if freq[i] > 0:
newline = newline + 'stable frequency at '
elif freq[i] < 0:
newline = newline + 'unstable frequency at '
if options.distort and freq[i] < -50:
struc_new = copy.deepcopy(struc)
for i_atoms in range(n_constrained):
for i_coord in range(3):
struc_new.atoms[i_atoms].coord[i_coord]=\
struc_new.atoms[i_atoms].coord[i_coord]+\
eig_vec[(i_atoms)*3+i_coord,i]
geoname = name + '.distorted.vibration_' + str(
i + 1) + '.geometry.in'
new_geo = open(geoname, 'w')
newline_geo = '#\n# distorted structure-file for based on eigenmodes\n'
newline_geo=newline_geo+\
'# vibration {0:5} :{1:10.3f} 1/cm\n#\n'.format(i+1,freq[i])
new_geo.writelines(newline_geo + struc_new.to_str())
new_geo.close()
elif freq[i] == 0:
newline = newline + 'translation or rotation '
newline = newline + '{0:10.3f} 1/cm IR int. is '.format(freq[i])
newline = newline + '{0:10.4e} D^2/Ang^2; red. mass is '.format(
infrared_intensity[i])
newline = newline + '{0:5.3f} a.m.u.; force const. is '.format(
1.0 / reduced_mass[i])
newline = newline + '{0:5.3f} mDyne/Ang.\n'.format(
((freq[i] *
(200 * pi * c))**2) * (1.0 / reduced_mass[i]) * at_u * 1.e-2)
if options.molden: newline_molden=newline_molden+\
'vibration {0:6}\n'.format(i+1)
for i_atoms in range(n_constrained):
newline = newline + '{0:6}'.format(
struc.atoms[nums[i_atoms]].kind)
for i_coord in range(3):
newline = newline + '{0:10.4f}'.format(
struc.atoms[nums[i_atoms]].coord[i_coord])
for i_coord in range(3):
newline = newline + '{0:10.4f}'.format(
eig_vec[(i_atoms) * 3 + i_coord, i])
if options.molden:
newline_molden = newline_molden + '{0:10.4f}'.format(
eig_vec[(i_atoms) * 3 + i_coord, i] / bohr)
newline = newline + '\n'
if options.molden: newline_molden = newline_molden + '\n'
for i_atoms in range(n_atoms - n_constrained):
newline = newline + '{0:6}'.format(
struc.atoms[nums2[i_atoms]].kind)
for i_coord in range(3):
newline = newline + '{0:10.4f}'.format(
struc.atoms[nums2[i_atoms]].coord[i_coord])
for i_coord in range(3):
newline = newline + '{0:10.4f}'.format(0.0)
newline = newline + '\n'
newline_ir = newline_ir + '{0:10.4e}\n'.format(
infrared_intensity[i])
xyz = open(xyzfile, 'w')
xyz.writelines(newline)
xyz.close()
ir = open(irname, 'w')
ir.writelines(newline_ir)
ir.close()
if options.molden:
molden = open(moldenname, 'w')
molden.writelines(newline_molden)
molden.close()
if mode == '1' and options.plot:
x = linspace(freq.min() - 500, freq.max() + 500, 1000)
z = zeros(len(x))
for i in range(len(freq)):
z[argmin(abs(x - freq[i]))] = infrared_intensity[i]
window_len = 150
gauss = signal.gaussian(window_len, 10)
s = r_[z[window_len - 1:0:-1], z, z[-1:-window_len:-1]]
z_convolve = convolve(gauss / gauss.sum(), s,
mode='same')[window_len - 1:-window_len + 1]
fig = figure(0)
ax = fig.add_subplot(111)
ax.plot(x, z_convolve, 'r', lw=2)
ax.set_xlim([freq.min() - 500, freq.max() + 500])
ax.set_ylim([-0.01, ax.get_ylim()[1]])
ax.set_yticks([])
ax.set_xlabel('Frequency [1/cm]', size=20)
ax.set_ylabel('Intensity [a.u.]', size=20)
fig.savefig(name + '_IR_spectrum.pdf')
print '\n Done. '
BO2 = zeros((tmax / avgOn, N2))
Hrv = HRF()
'##################################################### MAIN ###########################################################'
'#################### TC_998'
t0 = time()
for i in range(nTC):
TC1[i * step:(i + 1) * step, :] = np_load(dir_TC1 + dir_sub +
'TC_%i.npy' % i)
print 'TC 998 loaded : %.2fs' % (time() - t0)
'#################### BO_998'
t0 = time()
for k in range(N1):
Bk = convolve(TC1[:, k], Hrv)[:tmax]
for o in range(avgOn):
BO1[:, k] += Bk[o::avgOn]
BO1 /= avgOn
np_save(dir_BO1 + 'BO_%i_' % N1 + name + '.npy', BO1)
print 'BO 998 generated : %.2fs' % (time() - t0)
'#################### BO_66, FC_B66, FC_B998'
t0 = time()
for n in range(N1):
BO2[:, D998_D66[n]] += BO1[:, n]
for t in range(BO1.shape[0]):
BO2[t, :] /= AvgN_D66
np_save(dir_BO2 + 'BO_%i_' % N2 + name + '.npy', BO2)
FC2 = fastPearsonCorrelation(BO2)
del BO2
def exercise1():
""" this function gives a visualization of the whole data set
scatter plots for the different neurons and directions, as well as the mean spikes druing the timeline and the estimated fring rate (by a kernel convolution, window of width 100)"""
# load data1.
a1 = scipy.io.loadmat("bootstrap_joe093-3-C3-MO.mat")
a2 = scipy.io.loadmat("bootstrap_joe108-7-C3-MO.mat")
a3 = scipy.io.loadmat("bootstrap_joe112-5-C3-MO.mat")
a4 = scipy.io.loadmat("bootstrap_joe112-6-C3-MO.mat")
a5 = scipy.io.loadmat("bootstrap_joe145-4-C3-MO.mat")
data1 = a1["GDFcell"][0]
data2 = a2["GDFcell"][0]
data3 = a3["GDFcell"][0]
data4 = a4["GDFcell"][0]
data5 = a5["GDFcell"][0]
# here the binary spike trains of the neurons are stored, for every neuron and every direction
binary = plt.zeros((5, 6, 2000))
# and here the spike times, for every neuron, every direction and every trial
spike_times = [[[[] * 1] * 35] * 6] * 5
for i in plt.arange(5): # neuron
exec "%s=%s" % ("data", "data" + str(i + 1))
fig = plt.figure()
ax = plt.axes([0, 0, 1, 1])
circ = plt.Circle((0.5, 0.48), radius=0.051, edgecolor="k", LineStyle="solid", facecolor="w")
ax.add_patch(circ)
plt.text(0.453, 0.465, "Neuron " + str(i + 1))
ax.set_yticks([])
ax.set_xticks([])
for j in plt.arange(6): # direction
if j == 0:
ax = plt.axes([0.3, 0.8, 0.3, 0.1])
elif j == 1:
ax = plt.axes([0.6, 0.55, 0.3, 0.1])
elif j == 2:
ax = plt.axes([0.6, 0.3, 0.3, 0.1])
elif j == 3:
ax = plt.axes([0.3, 0.1, 0.3, 0.1])
elif j == 4:
ax = plt.axes([0.1, 0.3, 0.3, 0.1])
elif j == 5:
ax = plt.axes([0.1, 0.55, 0.3, 0.1])
data[j] = data[j].astype(int)
data[j][:, 1] = data[j][:, 1] - 1000
for k in plt.arange(35) + 1: # trials
indi = plt.find(data[j][:, 0] == k)
spike_times[i][j][k - 1] = data[j][indi, 1]
for l in spike_times[i][j][k - 1] + 999:
if l < 2000:
binary[i][j][l] += 1
# plots the scatter plots
plt.plot(data[j][indi, 1], plt.ones(data[j][indi, 1].shape[0]) * k, "b|")
plt.title("direction" + str(j + 1))
plt.xlabel("time [ms]")
plt.ylabel("trial_id")
plt.xlim([-1000, 1000])
for tick in ax.yaxis.get_major_ticks():
tick.label1.set_fontsize(8)
for tick in ax.xaxis.get_major_ticks():
tick.label1.set_fontsize(8)
fig.savefig("neuron" + str(i + 1) + "spikes", format="png")
# this is the definition of the kernel
w = 100
h = 1.0 / w
k = plt.ones((w,)) * h
# normalization by the number of trials
binary = binary / 35.0
for i in plt.arange(5):
fig = plt.figure()
ax = plt.axes([0, 0, 1, 1])
circ = plt.Circle((0.5, 0.48), radius=0.051, edgecolor="k", LineStyle="solid", facecolor="w")
ax.add_patch(circ)
plt.text(0.453, 0.465, "Neuron " + str(i + 1))
ax.set_yticks([])
ax.set_xticks([])
for j in plt.arange(6):
if j == 0:
ax = plt.axes([0.3, 0.8, 0.3, 0.1])
elif j == 1:
ax = plt.axes([0.6, 0.55, 0.3, 0.1])
elif j == 2:
ax = plt.axes([0.6, 0.3, 0.3, 0.1])
elif j == 3:
ax = plt.axes([0.3, 0.1, 0.3, 0.1])
elif j == 4:
ax = plt.axes([0.1, 0.3, 0.3, 0.1])
elif j == 5:
ax = plt.axes([0.1, 0.55, 0.3, 0.1])
# plots the mean spikes along the timeline of the experiment
plt.plot(plt.arange(-1000, 1000), binary[i][j])
plt.ylabel("mean spikes")
plt.hold(True)
ax2 = ax.twinx()
# plots the estimated firing rate on a different y axis
plt.plot(plt.arange(-1000, 1000), plt.convolve(binary[i][j], k, mode="same"), "g")
plt.title("direction" + str(j + 1))
plt.xlabel("time [ms]")
plt.ylabel("estimated r")
for tick in ax.yaxis.get_major_ticks():
tick.label1.set_fontsize(8)
for tick in ax2.yaxis.get_major_ticks():
tick.label2.set_fontsize(8)
for tick in ax.xaxis.get_major_ticks():
tick.label1.set_fontsize(8)
fig.savefig("neuron" + str(i + 1) + "rates", format="png")
out = []
inp = []
with open('../../../measurements/20140610/10Hz_random/scope_5.csv', newline='') as csvfile:
spamreader = csv.reader(csvfile, delimiter=',', quotechar='|')
ii = 0
for row in spamreader:
ii = ii+1
if ii > 3:
out.append(float(row[1]))
inp.append(float(row[2]))
# Filter
filtered_out = pylab.convolve([-1,1], out)
# Sort
high = False
digital_out = []
for o in out:
if o > 0.05:
high = False
elif o < -0.12:
high = True
if high:
digital_out.append(1)
else:
digital_out.append(0)
def build_fft(input_signal,
filter_coefficients,
threshold_windows=6,
boundary=0):
"""generate fast transform fourier by windows
Params :
input_signal : the audio signal
filter_coefficients : coefficients of the chirplet bank
threshold_windows : calcul the size of the windows
boundary : manage the bounds of the signal
Returns :
fast Fourier transform applied by windows to the audio signal
"""
num_coeffs = filter_coefficients.size
#print(n,boundary,M)
half_size = num_coeffs // 2
signal_size = input_signal.size
#power of 2 to apply fast fourier transform
windows_size = 2**ceil(log2(num_coeffs * (threshold_windows + 1)))
number_of_windows = floor(signal_size // windows_size)
if number_of_windows == 0:
return fft_based(input_signal, filter_coefficients, boundary)
windowed_fft = empty_like(input_signal)
#pad with 0 to have a size in a power of 2
windows_size = int(windows_size)
zeropadding = np.lib.pad(filter_coefficients,
(0, windows_size - num_coeffs),
'constant',
constant_values=0)
h_fft = fft(zeropadding)
#to browse the whole signal
current_pos = 0
#apply fft to a part of the signal. This part has a size which is a power
#of 2
if boundary == 0: #ZERO PADDING
#window is half padded with since it's focused on the first half
window = input_signal[current_pos:current_pos + windows_size -
half_size]
zeropaddedwindow = np.lib.pad(window, (len(h_fft) - len(window), 0),
'constant',
constant_values=0)
x_fft = fft(zeropaddedwindow)
elif boundary == 1: #SYMMETRIC
window = concatenate([
flipud(input_signal[:half_size]),
input_signal[current_pos:current_pos + windows_size - half_size]
])
x_fft = fft(window)
else:
x_fft = fft(input_signal[:windows_size])
windowed_fft[:windows_size - num_coeffs] = (ifft(
x_fft * h_fft)[num_coeffs - 1:-1]).real
current_pos += windows_size - num_coeffs - half_size
#apply fast fourier transofm to each windows
while current_pos + windows_size - half_size <= signal_size:
x_fft = fft(input_signal[current_pos - half_size:current_pos +
windows_size - half_size])
#Suppress the warning, work on the real/imagina
windowed_fft[current_pos:current_pos + windows_size -
num_coeffs] = (ifft(x_fft * h_fft)[num_coeffs -
1:-1]).real
current_pos += windows_size - num_coeffs
# print(countloop)
#apply fast fourier transform to the rest of the signal
if windows_size - (signal_size - current_pos + half_size) < half_size:
window = input_signal[current_pos - half_size:]
zeropaddedwindow = np.lib.pad(
window,
(0, int(windows_size - (signal_size - current_pos + half_size))),
'constant',
constant_values=0)
x_fft = fft(zeropaddedwindow)
windowed_fft[current_pos:] = roll(ifft(
x_fft * h_fft), half_size)[half_size:half_size +
windowed_fft.size - current_pos].real
windowed_fft[-half_size:] = convolve(input_signal[-num_coeffs:],
filter_coefficients,
'same')[-half_size:]
else:
window = input_signal[current_pos - half_size:]
zeropaddedwindow = np.lib.pad(
window,
(0, int(windows_size - (signal_size - current_pos + half_size))),
'constant',
constant_values=0)
x_fft = fft(zeropaddedwindow)
windowed_fft[current_pos:] = ifft(
x_fft * h_fft)[num_coeffs - 1:num_coeffs + windowed_fft.size -
current_pos - 1].real
return windowed_fft
def main():
import optparse
from numpy import sum
# Parse command line
parser = optparse.OptionParser(usage=USAGE)
parser.add_option("-p", "--plot", action="store_true",
help="Generate pdf with IR-spectrum, broadened with Lorentzian")
parser.add_option("-i", "--info", action="store_true",
help="Set up/ Calculate vibrations & quit")
parser.add_option("-s", "--suffix", action="store",
help="Call suffix for binary e.g. 'mpirun -n 4 '",
default='')
parser.add_option("-r", "--run", action="store",
help="path to FHI-aims binary",default='')
parser.add_option("-x", "--relax", action="store_true",
help="Relax initial geometry")
parser.add_option("-m", "--molden", action="store_true",
help="Output in molden format")
parser.add_option("-w", "--distort", action="store_true",
help="Output geometry distorted along imaginary modes")
parser.add_option("-t", "--submit", action="store",
help="""\
Path to submission script, string <jobname>
will be replaced by name + counter, string
<outfile> will be replaced by filename""")
parser.add_option("-d", "--delta", action="store", type="float",
help="Displacement", default=0.0025)
parser.add_option("-b", "--broadening", action="store", type="float",
help="Broadening for IR-spectrum in cm^{-1}", default=5)
options, args = parser.parse_args()
if options.info:
print __doc__
sys.exit(0)
if len(args) != 2:
parser.error("Need exactly two arguments")
AIMS_CALL=options.suffix+' '+options.run
hessian_thresh = -1
name=args[0]
mode=args[1]
delta=options.delta
broadening=options.broadening
run_aims=False
if options.run!='': run_aims=True
submit_script = options.submit is not None
if options.plot:
import matplotlib as mpl
mpl.use('Agg')
from pylab import figure
if options.plot or mode=='1' or mode=='2':
from pylab import savetxt, transpose, eig, argsort, sort,\
sign, pi, dot, sum, linspace, argmin, r_, convolve
# Constant from scipy.constants
bohr=constants.value('Bohr radius')*1.e10
hartree=constants.value('Hartree energy in eV')
at_u=constants.value('atomic mass unit-kilogram relationship')
eV=constants.value('electron volt-joule relationship')
c=constants.value('speed of light in vacuum')
Ang=1.0e-10
hbar=constants.value('Planck constant over 2 pi')
Avo=constants.value('Avogadro constant')
kb=constants.value('Boltzmann constant in eV/K')
pi=constants.pi
hessian_factor = eV/(at_u*Ang*Ang)
grad_dipole_factor=(eV/(1./(10*c)))/Ang #(eV/Ang -> D/Ang)
ir_factor = 1
# Asign all filenames
inputgeomerty = 'geometry.in.'+name
inputcontrol = 'control.in.'+name
atomicmasses = 'masses.'+name+'.dat';
xyzfile = name+'.xyz';
moldenname =name+'.molden';
hessianname = 'hessian.'+name+'.dat';
graddipolename = 'grad_dipole.'+name+'.dat';
irname = 'ir.'+name+'.dat';
deltas=array([-delta,delta])
coeff=array([-1,1])
c_zero = - 1. / (2. * delta)
f=open('control.in','r') # read control.in template
template_control=f.read()
f.close
if submit_script:
f=open(options.submit,'r') # read submission script template
template_job=f.read()
f.close
folder='' # Dummy
########### Central Point ##################################################
if options.relax and (mode=='0' or mode=='2'):
# First relax input geometry
filename=name+'.out'
folder=name+'_relaxation'
if not os.path.exists(folder): os.mkdir(folder) # Create folder
shutil.copy('geometry.in', folder+'/geometry.in') # Copy geometry
new_control=open(folder+'/control.in','w')
new_control.write(template_control+'relax_geometry trm 1E-3\n') # Relax!
new_control.close()
os.chdir(folder) # Change directoy
print 'Central Point'
if run_aims:
os.system(AIMS_CALL+' > '+filename) # Run aims and pipe the output
# into a file named 'filename'
if submit_script: replace_submission(template_job, name, 0, filename)
os.chdir('..')
############################################################################
# Check for relaxed geometry
if os.path.exists(folder+'/geometry.in.next_step'):
geometry=open(folder+'/geometry.in.next_step','r')
else:
geometry=open('geometry.in','r')
# Read input geometry
n_line=0
struc=structure()
lines=geometry.readlines()
for line in lines:
n_line= n_line+1
if line.rfind('set_vacuum_level')!=-1: # Vacuum Level
struc.vacuum_level=float(split_line(line)[-1])
if line.rfind('lattice_vector')!=-1: # Lattice vectors and periodic
lat=split_line(line)[1:]
struc.lattice_vector=append(struc.lattice_vector,float64(array(lat))
[newaxis,:],axis=0)
struc.periodic=True
if line.rfind('atom')!=-1: # Set atoms
line_vals=split_line(line)
at=Atom(line_vals[-1],line_vals[1:-1])
if n_line<len(lines):
nextline=lines[n_line]
if nextline.rfind('constrain_relaxation')!=-1: # constrained?
at=Atom(line_vals[-1],line_vals[1:-1],True)
else:
at=Atom(line_vals[-1],line_vals[1:-1])
struc.join(at)
geometry.close()
n_atoms= struc.n()
n_constrained=n_atoms-sum(struc.constrained)
# Atomic mass file
mass_file=open(atomicmasses,'w')
mass_vector=zeros([0])
for at_unconstrained in struc.atoms[struc.constrained==False]:
mass_vector=append(mass_vector,ones(3)*1./sqrt(at_unconstrained.mass()))
line='{0:10.5f}'.format(at_unconstrained.mass())
for i in range(3):
line=line+'{0:11.4f}'.format(at_unconstrained.coord[i])
line=line+'{0:}\n'.format(at_unconstrained.kind)
mass_file.writelines(line)
mass_file.close()
# Init
dip = zeros([n_constrained*3,3])
hessian = zeros([n_constrained*3,n_constrained*3])
index=0
counter=1
# Set up / Read folders for displaced atoms
for atom in arange(n_atoms)[struc.constrained==False]:
for coord in arange(3):
for delta in deltas:
filename=name+'.i_atom_'+str(atom)+'.i_coord_'+str(coord)+'.displ_'+\
str(delta)+'.out'
folder=name+'.i_atom_'+str(atom)+'.i_coord_'+str(coord)+'.displ_'+\
str(delta)
if mode=='0' or mode=='2': # Put new geometry and control.in into folder
struc_new=copy.deepcopy(struc)
struc_new.atoms[atom].coord[coord]=\
struc_new.atoms[atom].coord[coord]+delta
geoname='geometry.i_atom_'+str(atom)+'.i_coord_'+str(coord)+\
'.displ_'+str(delta)+'.in'
if not os.path.exists(folder): os.mkdir(folder)
new_geo=open(folder+'/geometry.in','w')
newline='#\n# temporary structure-file for finite-difference '+\
'calculation of forces\n'
newline=newline+'# displacement {0:8.4f} of \# atom '.format(delta)+\
'{0:5} direction {1:5}\n#\n'.format(atom,coord)
new_geo.writelines(newline+struc_new.to_str())
new_geo.close()
new_control=open(folder+'/control.in','w')
template_control=template_control.replace('relax_geometry',
'#relax_geometry')
new_control.write(template_control+'compute_forces .true. \n'+\
'final_forces_cleaned '+\
'.true. \n')
new_control.close()
os.chdir(folder) # Change directoy
print 'Processing atom: '+str(atom+1)+'/'+str(n_atoms)+', coord.: '+\
str(coord+1)+'/'+str(3)+', delta: '+str(delta)
if run_aims:
os.system(AIMS_CALL+' > '+filename)# Run aims and pipe the output
# into a file named 'filename'
if submit_script: replace_submission(template_job, name, counter,
filename)
# os.system('qsub job.sh') # Mind the environment variables
os.chdir('..')
if mode=='1' or mode=='2': # Read output
forces_reached=False
atom_count=0
data=open(folder+'/'+filename)
for line in data.readlines():
if line.rfind('Dipole correction potential jump')!=-1:
dip_jump = float(split_line(line)[-2]) # Periodic
if line.rfind('| Total dipole moment [eAng]')!=-1:
dip_jump = float64(split_line(line)[-3:]) # Cluster
if forces_reached and atom_count<n_atoms: # Read Forces
struc.atoms[atom_count].force=float64(split_line(line)[2:])
atom_count=atom_count+1
if atom_count==n_atoms:
forces_reached=False
if line.rfind('Total atomic forces')!=-1:
forces_reached=True
data.close()
if struc.periodic:
pass
#dip[index,2]=dip[index,2]+dip_jump*coeff[deltas==delta]*c_zero
else:
dip[index,:]=dip[index,:]+dip_jump*coeff[deltas==delta]*c_zero
forces=array([])
for at_unconstrained in struc.atoms[struc.constrained==False]:
forces=append(forces,coeff[deltas==delta]*at_unconstrained.force)
hessian[index,:]=hessian[index,:]+forces*c_zero
counter=counter+1
index=index+1
if mode=='1' or mode=='2': # Calculate vibrations
print 'Entering hessian diagonalization'
print 'Number of atoms = '+str(n_atoms)
print 'Name of Hessian input file = '+hessianname
print 'Name of grad dipole input file = '+graddipolename
print 'Name of Masses input file = '+atomicmasses
print 'Name of XYZ output file = '+xyzfile
print 'Threshold for Matrix elements = '+str(hessian_thresh)
if (hessian_thresh < 0.0): print ' All matrix elements are taken'+\
' into account by default\n'
savetxt(hessianname,hessian)
savetxt(graddipolename,dip)
mass_mat=mass_vector[:,newaxis]*mass_vector[newaxis,:]
hessian[abs(hessian)<hessian_thresh]=0.0
hessian=hessian*mass_mat*hessian_factor
hessian=(hessian+transpose(hessian))/2.
# Diagonalize hessian (scipy)
print 'Solving eigenvalue system for Hessian Matrix'
freq, eig_vec = eig(hessian)
print 'Done ... '
eig_vec=eig_vec[:,argsort(freq)]
freq=sort(sign(freq)*sqrt(abs(freq)))
ZPE=hbar*(freq)/(2.0*eV)
freq = (freq)/(200.*pi*c)
grad_dipole = dip * grad_dipole_factor
eig_vec = eig_vec*mass_vector[:,newaxis]*ones(len(mass_vector))[newaxis,:]
infrared_intensity = sum(dot(transpose(grad_dipole),eig_vec)**2,axis=0)*\
ir_factor
reduced_mass=sum(eig_vec**2,axis=0)
norm = sqrt(reduced_mass)
eig_vec = eig_vec/norm
# The rest is output, xyz, IR,...
print 'Results\n'
print 'List of all frequencies found:'
print 'Mode number Frequency [cm^(-1)] Zero point energy [eV] '+\
'IR-intensity [D^2/Ang^2]'
for i in range(len(freq)):
print '{0:11}{1:25.8f}{2:25.8f}{3:25.8f}'.format(i+1,freq[i],ZPE[i],
infrared_intensity[i])
print '\n'
print 'Summary of zero point energy for entire system:'
print '| Cumulative ZPE = {0:15.8f} eV'.format(sum(ZPE))
print '| without first six eigenmodes = {0:15.8f} eV\n'.format(sum(ZPE)-
sum(ZPE[:6]))
print 'Stability checking - eigenvalues should all be positive for a '+\
'stable structure. '
print 'The six smallest frequencies should be (almost) zero:'
string=''
for zz in ZPE[:6]: string=string+'{0:25.8f}'.format(zz)
print string
print 'Compare this with the largest eigenvalue, '
print '{0:25.8f}'.format(freq[-1])
nums=arange(n_atoms)[struc.constrained==False]
nums2=arange(n_atoms)[struc.constrained]
newline=''
newline_ir='[INT]\n'
if options.molden:
newline_molden='[Molden Format]\n[GEOMETRIES] XYZ\n'
newline_molden=newline_molden+'{0:6}\n'.format(n_atoms)+'\n'
for i_atoms in range(n_constrained):
newline_molden=newline_molden+'{0:6}'.format(
struc.atoms[nums[i_atoms]].kind)
for i_coord in range(3):
newline_molden=newline_molden+'{0:10.4f}'.format(
struc.atoms[nums[i_atoms]].coord[i_coord])
newline_molden=newline_molden+'\n'
newline_molden=newline_molden+'[FREQ]\n'
for i in range(len(freq)):
newline_molden=newline_molden+'{0:10.3f}\n'.format(freq[i])
newline_molden=newline_molden+'[INT]\n'
for i in range(len(freq)):
newline_molden=newline_molden+'{0:17.6e}\n'.format(
infrared_intensity[i])
newline_molden=newline_molden+'[FR-COORD]\n'
newline_molden=newline_molden+'{0:6}\n'.format(n_atoms)+'\n'
for i_atoms in range(n_constrained):
newline_molden=newline_molden+'{0:6}'.format(
struc.atoms[nums[i_atoms]].kind)
for i_coord in range(3):
newline_molden=newline_molden+'{0:10.4f}'.format(
struc.atoms[nums[i_atoms]].coord[i_coord]/bohr)
newline_molden=newline_molden+'\n'
newline_molden=newline_molden+'[FR-NORM-COORD]\n'
for i in range(len(freq)):
newline=newline+'{0:6}\n'.format(n_atoms)
if freq[i]>0:
newline=newline+'stable frequency at '
elif freq[i]<0:
newline=newline+'unstable frequency at '
if options.distort and freq[i]<-50:
struc_new=copy.deepcopy(struc)
for i_atoms in range(n_constrained):
for i_coord in range(3):
struc_new.atoms[i_atoms].coord[i_coord]=\
struc_new.atoms[i_atoms].coord[i_coord]+\
eig_vec[(i_atoms)*3+i_coord,i]
geoname=name+'.distorted.vibration_'+str(i+1)+'.geometry.in'
new_geo=open(geoname,'w')
newline_geo='#\n# distorted structure-file for based on eigenmodes\n'
newline_geo=newline_geo+\
'# vibration {0:5} :{1:10.3f} 1/cm\n#\n'.format(i+1,freq[i])
new_geo.writelines(newline_geo+struc_new.to_str())
new_geo.close()
elif freq[i]==0:
newline=newline+'translation or rotation '
newline=newline+'{0:10.3f} 1/cm IR int. is '.format(freq[i])
newline=newline+'{0:10.4e} D^2/Ang^2; red. mass is '.format(
infrared_intensity[i])
newline=newline+'{0:5.3f} a.m.u.; force const. is '.format(
1.0/reduced_mass[i])
newline=newline+'{0:5.3f} mDyne/Ang.\n'.format(((freq[i]*(200*pi*c))**2)*
(1.0/reduced_mass[i])*at_u*1.e-2)
if options.molden: newline_molden=newline_molden+\
'vibration {0:6}\n'.format(i+1)
for i_atoms in range(n_constrained):
newline=newline+'{0:6}'.format(struc.atoms[nums[i_atoms]].kind)
for i_coord in range(3):
newline=newline+'{0:10.4f}'.format(
struc.atoms[nums[i_atoms]].coord[i_coord])
for i_coord in range(3):
newline=newline+'{0:10.4f}'.format(eig_vec[(i_atoms)*3+i_coord,i])
if options.molden: newline_molden=newline_molden+'{0:10.4f}'.format(
eig_vec[(i_atoms)*3+i_coord,i]/bohr)
newline=newline+'\n'
if options.molden: newline_molden=newline_molden+'\n'
for i_atoms in range(n_atoms-n_constrained):
newline=newline+'{0:6}'.format(struc.atoms[nums2[i_atoms]].kind)
for i_coord in range(3):
newline=newline+'{0:10.4f}'.format(
struc.atoms[nums2[i_atoms]].coord[i_coord])
for i_coord in range(3):
newline=newline+'{0:10.4f}'.format(0.0)
newline=newline+'\n'
newline_ir=newline_ir+'{0:10.4e}\n'.format(infrared_intensity[i])
xyz=open(xyzfile,'w')
xyz.writelines(newline)
xyz.close()
ir=open(irname,'w')
ir.writelines(newline_ir)
ir.close()
if options.molden:
molden=open(moldenname,'w')
molden.writelines(newline_molden)
molden.close()
if (mode=='1' or mode=='2') and options.plot:
x=linspace(freq.min()-500,freq.max()+500,1000)
z=zeros(len(x))
for i in range(len(freq)):
z[argmin(abs(x-freq[i]))]=infrared_intensity[i]
window_len=150
lorentzian=lorentz(pi,broadening,arange(250))#signal.gaussian(window_len,broadening)
s=r_[z[window_len-1:0:-1],z,z[-1:-window_len:-1]]
z_convolve=convolve(lorentzian/lorentzian.sum(),s,mode='same')[
window_len-1:-window_len+1]
fig=figure(0)
ax=fig.add_subplot(111)
ax.plot(x,z_convolve,'r',lw=2)
ax.set_xlim([freq.min()-500,freq.max()+500])
ax.set_ylim([-0.01,ax.get_ylim()[1]])
ax.set_yticks([])
ax.set_xlabel('Frequency [1/cm]',size=20)
ax.set_ylabel('Intensity [a.u.]',size=20)
fig.savefig(name+'_IR_spectrum.pdf')
print '\n Done. '
'''
1d) Now we have all ingredients to compute the membrane potential excursion
(``U``) This calculation implies a convolution of the Gaussian with the
normalized PSP (see Diesmann 2002, eq. 6.9). In order to avoid an offset in
the convolution we need to add a pad of zeros on the left side of the
normalized PSP. Later on we want to compare our analytical results with the
simulation outcome. Therefore we need a time vector (``t_U``) with the correct
temporal resolution, that places the excursion of the potential at the correct
time.
'''
tmp = numpy.zeros(2 * len(psp_norm))
tmp[len(psp_norm) - 1:-1] += psp_norm
psp_norm = tmp
del tmp
U = a * psp_amp * pylab.convolve(gauss, psp_norm)
l = len(U)
t_U = (convolution_resolution * numpy.linspace(-l / 2., l / 2., l) +
pulsetime + 1.)
'''
2. Simulation. In this section we simulate a network of multiple neurons.
All these neurons receive an individual pulse packet that is drawn from a
Gaussian distribution.
'''
'''
2.1 We reset the Kernel, define the simulation resolution and set the
verbosity using `set_verbosity()` to suppress info messages.
'''
nest.ResetKernel()
def initial_fit_values(self, time, value, smoothing_samples=10,
integral_factor=.25, tau_fraction=2):
"""
Estimate the initial fit values for the given sample data in
(time, value).
time : numpy.ndarray
array of times at which the values are measured
value : numpy.ndarray
array of voltage values
smoothing_samples : int
width of the box filter used for the convolution
integral_factor : float
The time constants are estimated using the integral and
the height of the given psp. integral_factor is the
quotient of the maximum of a psp and the integral under
it, which is 0.25 for tau_fraction = 2 for an ideal psp.
tau_fraction : float
The ratio tau_2 / tau_1, which is constant for this
estimate.
"""
mean_est_part = int(len(value) * .1)
mean_estimate = p.mean(value[-mean_est_part:])
noise_estimate = p.std(value[-mean_est_part:])
smoothed_value = p.convolve(
value - mean_estimate,
p.ones(smoothing_samples) / float(smoothing_samples),
"same") + mean_estimate
integral = p.sum(smoothed_value - mean_estimate) * (time[1] - time[0])
height_estimate = (max(smoothed_value) - mean_estimate)
min_height = noise_estimate
if height_estimate < min_height:
height_estimate = min_height
t1_est = integral / height_estimate * integral_factor
# prevent t1 from being smaller than a time step
t1_est_min = time[1] - time[0]
if t1_est < t1_est_min:
t1_est = t1_est_min
t2_est = tau_fraction * t1_est
tmax_est = time[p.argmax(smoothed_value)]
tstart_est = tmax_est + p.log(t2_est / t1_est) \
* (t1_est * t2_est) / (t1_est - t2_est)
return dict(
height=height_estimate,
tau_1=t1_est,
tau_2=t2_est,
start=tstart_est,
offset=mean_estimate)
def hammfilt(x, winsz):
from pylab import convolve
from numpy import hamming
win = hamming(winsz)
win /= sum(win)
return convolve(x, win, 'same')
insert_params()
mean = p.mean(psp_voltage, axis=0)
std = p.std(psp_voltage, axis=0)
p.figure()
p.title("mean and standard deviation, ideal trigger")
p.plot(time, mean, 'r-')
p.fill_between(time, mean - std, mean + std, alpha=.3)
p.xlabel("time / AU")
p.ylabel("voltage / AU")
insert_params()
kernel = p.ones(sliding_average_len) / float(sliding_average_len)
mean_max_index = p.argmax(mean)
for i in range(len(psp_voltage)):
smoothed = p.convolve(psp_voltage[i], kernel, "same")
shift = mean_max_index - p.argmax(smoothed)
psp_voltage[i] = p.roll(smoothed, shift)
p.figure()
p.title("mean and standard deviation, max trigger")
mean_shifted = p.mean(psp_voltage, axis=0)
std = p.std(psp_voltage, axis=0)
p.plot(time, mean_shifted, 'r-')
p.plot(time, mean, 'k--', alpha=.7)
p.ylim(offset - height * .2, None)
p.fill_between(time, mean - std, mean + std, alpha=.3)
p.xlabel("time / AU")
p.ylabel("voltage / AU")
insert_params()