def xs_interp (inp_ene, inp_xs, inp_ene_interp, plot_cs):
inp_ene = inp_ene # energies from Talys
inp_xs = inp_xs # xs from talys
inp_ene_interps = inp_ene_interp # energies for interpolation
out_xs_A = []
out_xs = np.array([]) # iterpolated xs
plot_fig = plot_cs
x_ene = np.linspace (0,660,3301)
spl = UnivariateSpline(inp_ene, inp_xs, s = 0.25)
y_xs = spl(x_ene)
for inp_ene_interp in inp_ene_interps:
out_xs_A.append(spl.__call__(inp_ene_interp))
out_xs = np.append(out_xs, out_xs_A)
# optional_plot
if plot_fig:
plt.plot (inp_ene, inp_xs, 'ro', ms = 5)
plt.plot (x_ene, y_xs, lw = 3, c = 'g', alpha = 0.6)
plt.plot (inp_ene_interps, out_xs, 'o', ms = 3)
plt.show()
return out_xs
def thickness_finder(ezz, zz, nbins, sym=True, nbspl=30):
if sym == True: # if membrane is symmetric
zzlow = zz[:len(zz) // 2]
# Reverse array
zzupp = zz[::-1]
zzupp = zzupp[:len(zz) // 2]
ezzlow = ezz[:len(ezz) // 2]
# Reverse array
ezzupp = ezz[::-1]
ezzupp = ezzupp[:len(ezz) // 2]
ezzmeanlow = np.mean((ezzlow, ezzupp), axis=0)
ezzmeanupp = ezzmeanlow[::-1]
# Concatenate
if (nbins % 2) == 0:
ezzmean = np.hstack((ezzmeanlow, ezzmeanupp))
else:
zzcentre = zz[len(zz) // 2]
ezzcentre = ezz[len(zz) // 2]
ezz = np.hstack((ezzmeanlow, ezzcentre, ezzmeanupp))
zz = zz[2:-2]
ezz = ezz[2:-2]
knots = np.linspace(zz[0], zz[-1], nbspl - 2, endpoint=True)[1:-1]
# Build design matrix and smooth ezz by means of ridge regression
Bmat = Bmatspl(zz, knots=knots, q=3)
reg = RidgeCV(alphas=(np.logspace(-15, 15, 300001)),
store_cv_values=True,
normalize=True)
reg.fit(Bmat, ezz)
ezzsmooth = np.dot(Bmat, reg.coef_)
# Interpolate function in finer grid
dz = 1e-3
zgrid = np.arange(zz[0], zz[-1], dz)
ezzsmoothspl = UnivariateSpline(zz, ezzsmooth, k=3, s=0)
smooth = ezzsmoothspl.__call__(zgrid, nu=0)
# Calculate derivatives
dsmooth = np.gradient(smooth)
d2smooth = np.gradient(dsmooth)
# Find critical points
### First derivative
idx_min = argrelextrema(dsmooth, np.less_equal, order=len(zgrid) // 10)
idx_max = argrelextrema(dsmooth, np.greater_equal, order=len(zgrid) // 10)
idx11, val11 = findclosest(len(zgrid) // 2, idx_min[0])
idx12, val12 = findclosest(len(zgrid) // 2, idx_max[0])
### Second derivative
idx_min = argrelextrema(d2smooth, np.less_equal, order=len(zgrid) // 10)
idx_max = argrelextrema(d2smooth, np.greater_equal, order=len(zgrid) // 10)
idx21, val21 = findclosest(idx11, idx_max[0][idx_max[0] > idx11])
idx22, val22 = findclosest(idx12, idx_max[0][idx_max[0] < idx12])
#db= abs(zgrid[idx12] - zgrid[idx11])
dh = abs(zgrid[idx22] - zgrid[idx21])
return dh
def Accept_data():
# Read in data from entry for info tables
n = info['current_exp']
for row,var in enumerate(info_vars):
val = float(t0['etr'][var].get())
info[var][n] = val #accept all values as given in entry
s,e = cut(n)
for var in info_vars:
if '_start' in var:
val = max(info[var][n],data[var[0]][n][0],data[var[0]][n][s])
info[var][n]=val #update with correct minimum limit
#val = data[var[0]][n][s]
elif '_end' in var:
val = val = min(info[var][n],data[var[0]][n][-1],data[var[0]][n][e])
info[var][n]=val #update with correct maximum limit
elif 'n_points' in var:
val = int(len(data['t'][n])/(max(int(len(data['t'][n])/info[var][n]),1)))-1
info[var][n]=val
normalize_mass(n)
spl = UnivariateSpline(data['t'][n],data['x_exp'][n],s=info['s.factor'][n])
data['dx_exp'][n] = spl.__call__(data['t'][n],nu=1)*(-1) # first derivative
Plot_raw_data()
create_equally_spaced_data()
write_info_text()
def thermCond_fit_UnivariateSpline_model(T, data=[]):
# This is a fitting model for creating an equation when given a list of x,y values
x = data[0]
y = data[1]
if len(x) <= 5:
order = len(x)-1
else:
order = 5
fit = UnivariateSpline(x, y, k=order)
thermCond = fit.__call__(T)
return thermCond
def thermCond_fit_UnivariateSpline_model(T, data=[]):
# This is a fitting model for creating an equation when given a list of x,y values
x = data[0]
y = data[1]
if len(x) <= 5:
order = len(x) - 1
else:
order = 5
fit = UnivariateSpline(x, y, k=order)
thermCond = fit.__call__(T)
return thermCond
def extract_info_from_data(filenames):
info['n_data'] = len(data['T'])
info['filenames']=filenames
#add derivative
data['dx_exp'] = {}
for n in range(info['n_data']):
data['T'][n] += 273.15
data['x_exp'].append(1)
info['s.factor'].append(1e-4)
info['T_start'].append(data['T'][n][0])
info['t_start'].append(data['t'][n][0])
info['T_end'].append(data['T'][n][-1])
info['t_end'].append(data['t'][n][-1])
info['mass norm. temp.'].append(100)
normalize_mass(n)
spl = UnivariateSpline(data['t'][n],data['x_exp'][n],s=info['s.factor'][n])
data['dx_exp'][n] = spl.__call__(data['t'][n],nu=1)*(-1) # first derivative
info['max'].append(max(data['dx_exp'][n]))
#info['n_points'].append(len(data['t'][n]))
info['n_points'].append(100)
def __call__(self, x):
"""Overloaded call method.
"""
return numpy.power(10.,
UnivariateSpline.__call__(self, numpy.log10(x)))
def __call__(self, x, nu=0):
return UnivariateSpline.__call__(self, x%self.period, nu)
def __call__(self, x):
outside = self.is_outside_domain(x)
return np.where(outside, self.fill_value,
UnivariateSpline.__call__(self, x))
from scipy.interpolate import UnivariateSpline import numpy #coeffs are stored in coeffs array with coeffs[i] being coeff of x^i log_ic =[-2,-1,0,1,2] curr_gain =[100,140,175,165,100] z=UnivariateSpline(log_ic,curr_gain,k=3) #print(z.__call__([0,3,4,6,7,9],nu=0,ext=None)) a=z.derivative() b=a.derivative() c=b.derivative() coeffs=[0,0,0,0] coeffs[0]=(z.__call__(0,nu=0,ext=None)) coeffs[1]=(a.__call__(0,nu=0,ext=None)) coeffs[2]=(b.__call__(0,nu=0,ext=None)/2) coeffs[3]=(c.__call__(0,nu=0,ext=None)/6) print(str(coeffs[3])+"*x^3+ "+str(coeffs[2])+"*x^2+ "+str(coeffs[1])+"*x^1+ "+str(coeffs[0]))
def __call__(self, x):
"""Overloaded call method.
"""
return numpy.power(10., UnivariateSpline.__call__(self, numpy.log10(x)))
def __call__(self, x):
outside = self.is_outside_domain(x)
return np.where(outside, self.fill_value,
UnivariateSpline.__call__(self, x))
def extract_raw_features(df_subset_dict,
index_col,
analysis_column,
date_col,
le_time_periods=10,
trans_parameter=0.5,
max_time_lag=20,
smoothing_factor=1222,
min_adjustment_val=0.001):
# Takes in a df_subset_dict created by the "create_df_subset_dict" method above and extracts raw features
# Assumes exactly ONE feature is being inputted for analysis
# Could probably refactor to do as multiple, but for now it will be one variable at a time
# This for loop already takes some time to complete, so multiple variables may be unwieldy
# Begin analysis
analysis_time_series_features_raw_dct = {}
for index, df_subset in df_subset_dict.items():
# Extract unique category name for each set of data
index = df_subset[index_col].unique().item()
# Set the activity date as the index and convert the activity date into a datetime index
# So that the seasonal decomposition function to transform the data later works
df_subset[date_col] = pd.to_datetime(df_subset[date_col])
analysis_df = df_subset[[date_col,
analysis_column]].set_index(date_col)
# Convert analysis data to numeric data in case data is "object" datatype
analysis_df[analysis_column] = pd.to_numeric(
analysis_df[analysis_column], errors='coerce')
##### RAW FEATURE PRE-PROCESSING ######
# Process raw data for feature calculation later (we will perform the transformation needed for the TSA features below)
# Skew & Kurtosis Calculations (These are direct calculations, so these are simpler)
analysis_skew_raw = skew(analysis_df[analysis_column])
analysis_kurtosis_raw = kurtosis(analysis_df[analysis_column])
### Autocorrelation Pre-processing ###
# Because this involves comparing the original data with various time-lagged versions of the data
# We need to iteratively calculate many different autocorrelation series (Qh = n∑hk=1 rk^2)
# Where n is the length of the time series, k is the current lag considered and h is the maximum time lag being considered (~20)
# We will store the results of this in dictionaries to be saved into the final dictionary
h = max_time_lag
analysis_autocorrelation_raw_dct = {
'LENGTH': len(analysis_df),
'VALUES': {}
}
for k in range(1, h + 1):
analysis_autocorrelation_raw = pd.concat(
[analysis_df, analysis_df.shift(k)],
axis=1).corr().iloc[0, 1] # Could be [1,0] too
analysis_autocorrelation_raw_dct['VALUES'].update(
{k: analysis_autocorrelation_raw})
### The "chaos" metric (Lyapunov Exponent) Pre-processing ###
# The paper says that for this metric, for all i = 1,2,...,n Xj should be the "nearest" point to Xi
# I am taking that definition to mean that Xj is the next consecutive point to Xi (i.e. j = i + 1)
# It also says that |Xj - Xi| should be small; for the most part this appears to be true with how I've defined it
# So we will take the difference of each consecutive point (|X2 - X1|, |X3 - X2|, etc.) as a new dataframe
# And then take the quotient of each point at varying points in the future to the current point
# I.e. |Xj+n - Xi+n| / |Xj - Xi| with n the number of time points looking ahead (the le_time_periods variable above)
# The final formula for each individual point is (1/n) * log(|Yj+n − Yi+n|/|Yj − Yi|)
analysis_diff = analysis_df.diff(periods=1)
analysis_lyapunov_exponents_dct = {}
for n in range(1, le_time_periods + 1):
analysis_lyapunov_exponents = abs(analysis_diff) / abs(
analysis_diff.shift(n))
analysis_lyapunov_exponent = analysis_lyapunov_exponents[
analysis_column].apply(lambda x: (1 / n) * log(x) if x > 0 and
x < float('Inf') else np.nan)
analysis_lyapunov_exponents_dct[n] = analysis_lyapunov_exponent
### Periodicity (frequency) Pre-processing ###
# First need detrended data (original data minus a fitted regression spline with 3 knots)
# Then need all autocorrelation values on detrended data for all lags up to 1/3 the series length
# Then from the autocorrelation function above, we examine it for peaks and troughs (in the next code block)
# Frequency is the first peak provided with following conditions:
# (a) there is also a trough before it
# (b) the difference between peak and trough is at least 0.1
# (c) the peak corresponds to positive correlation
# If no such peak is found, frequency is set to 1 (equivalent to non-seasonal)
analysis_x, analysis_y = analysis_df.reset_index(
).index.values, analysis_df.values
analysis_reg_spline = UnivariateSpline(x=analysis_x,
y=analysis_y,
s=smoothing_factor)
analysis_reg_spline_values = analysis_reg_spline.__call__(analysis_x)
analysis_detrended = analysis_y.transpose(
) - analysis_reg_spline_values
# Autocorrelation values on detrended data
max_lag = int(ceil((1 / 3) * analysis_detrended.shape[1]))
analysis_detrended_autocorrelation_values = []
analysis_detrended = pd.DataFrame(analysis_detrended.transpose())
for k in range(0, max_lag):
analysis_detrended_autocorrelation = pd.concat(
[analysis_detrended,
analysis_detrended.shift(k)],
axis=1).corr().iloc[0, 1] # Could be [1,0] too
analysis_detrended_autocorrelation_values.append(
analysis_detrended_autocorrelation)
##### TRANSFORMED FEATURE PRE-PROCESSING ######
# In order to get the TSA (trend & seasonality adjusted) features, we need to assess whether the minimum values are non-negative
# We only consider a transformation if theminimum of{Yt}is non-negative. If the minimum ofYtis zero, we add a small posi-tive constant (equal to 0.001 of the maximum ofYt) to all values to avoid undefinedresults
min_analysis = min(analysis_df[analysis_column])
if min_analysis == 0:
max_analysis = max(analysis_df[analysis_column])
analysis_df[analysis_column] = analysis_df[analysis_column] + (
min_adjustment_val * max_analysis)
# Perform transformation Yt* = (Yt^λ − 1)/λ where λ != 0 and λ ∈ (−1,1)
analysis_transformed = (pow(analysis_df[analysis_column],
trans_parameter) - 1) / trans_parameter
# Decompose the transformed data to get TSA data for processing
analysis_decomposition = sm.tsa.seasonal_decompose(
analysis_transformed, model='additive', extrapolate_trend='freq')
# Calculate features based on tsa data
# Trend & Seasonality Calculations
### Skew & Kurtosis Pre-processing ###
analysis_skew_tsa = skew(analysis_decomposition.resid)
analysis_kurtosis_tsa = kurtosis(analysis_decomposition.resid)
### Autocorrelation Pre-processing ###
# Because this involves comparing the original data with various time-lagged versions of the data
# We need to iteratively calculate many different autocorrelation series (rk=Corr(Yt,Yt−k) with many k values)
# Later for actual feature calcuation, we will be using the Box-Pierce statistic (Qh = n∑hk=1 rk^2)
# Where n is the time series length, k is the current lag considered and h is the maximum time lag being considered (~20)
# We will store the results of this in dictionaries to be processed later and stored in the final dictionary
h = max_time_lag
analysis_autocorrelation_tsa_dct = {
'LENGTH': len(analysis_df),
'VALUES': {}
}
for k in range(1, h + 1):
analysis_autocorrelation_tsa = pd.concat([
analysis_decomposition.resid,
analysis_decomposition.resid.shift(k)
],
axis=1).corr().iloc[0, 1]
analysis_autocorrelation_tsa_dct['VALUES'].update(
{k: analysis_autocorrelation_tsa})
analysis_time_series_features_raw_dct[index] = {
'ANALYSIS_DECOMPOSITION':
analysis_decomposition,
'ANALYSIS_SKEW_RAW':
analysis_skew_raw,
'ANALYSIS_KURTOSIS_RAW':
analysis_kurtosis_raw,
'ANALYSIS_SKEW_TSA':
analysis_skew_tsa,
'ANALYSIS_KURTOSIS_TSA':
analysis_kurtosis_tsa,
'ANALYSIS_AUTOCORRELATION_TSA':
analysis_autocorrelation_tsa_dct,
'ANALYSIS_AUTOCORRELATION_RAW':
analysis_autocorrelation_raw_dct,
'ANALYSIS_DIFF':
analysis_diff,
'ANALYSIS_LE_VALUES_DCT':
analysis_lyapunov_exponents_dct,
'ANALYSIS_DETRENDED_AUTOCORRELATION':
analysis_detrended_autocorrelation_values,
}
return analysis_time_series_features_raw_dct