def crossSpectra(data, frequency=10, notation=None, anti_aliasing=True):
"""
Calculates the spectrum for a set of data
Parameters
----------
data: pandas.DataFrame or pandas.Series
dataframe with one (will return the spectrum) or two (will return to cross-spectrum) columns
frequency: float
frequency of measurement of signal to pass to numpy.fft.rfftfreq
anti_aliasing: bool
whether or not to apply anti-aliasing according to Gobbi, Chamecki & Dias, 2006 (doi:10.1029/2005WR004374)
notation: notation object
notation to be used
Returns
--------
spectrum: pandas.DataFrame
whose column is the spectrum or coespectrum of the input dataframe
"""
from . import notation
from . import algs
import numpy as np
import pandas as pd
from itertools import combinations
notation=algs.get_notation(notation)
N = len(data)
combs = list(combinations(data.columns, 2))
names = [ notation.cross_spectrum % (a, b) for a, b in combs ]
specs = pd.DataFrame(columns = names)
#---------
# Calculate spectra here
for (a, b) in combs:
spec_name = notation.cross_spectrum % (a, b)
spec = np.fft.rfft(data.loc[:,a])
specs.loc[:, spec_name ] = np.conj(spec) * np.fft.rfft(data.loc[:,b])
#---------
#---------
# Anti-aliasing is done here
if anti_aliasing:
RA = np.array([ 1. + np.cos(np.pi*k/N) for k in range(N/2+1) ])/2.
specs = specs.multiply(RA**2., axis='rows')
#---------
#---------
# Now we normalize the spectrum and calculate their frequency
specs *= 2./(frequency*N)
freq = np.fft.rfftfreq(len(data), d=1./frequency)
specs.index = freq
specs.index.name='Frequency'
#---------
return specs
def rotate2D(data, notation=None):
"""Rotates the coordinates of wind data
Parameters
----------
data: pandas DataFrame
the dataFrame to be rotated
notation: notation object
a notation object to know which are the wind variables
Returns
-------
pandas.DataFrame
the complete data input with the wind components rotated
"""
from math import atan2, sqrt
import numpy as np
import algs
#-------
# Getting the names for u, v, w
defs = algs.get_notation(notation)
wind_vars = [ defs.u, defs.v, defs.w ]
#-------
#-------
# Definition of the coefficients used to created the rotation matrix
wind_vec = data[wind_vars].mean().values
m_u, m_v, m_w = wind_vec
alpha = atan2(m_v,m_u)
beta =-atan2(m_w, sqrt((m_u**2.)+(m_v**2.)))
#-------
#-------
# Definition of rotation matrix
DC= np.zeros((3,3))
DC[0,0],DC[0,1],DC[0,2] = np.cos(alpha)*np.cos(beta), np.cos(beta)*np.sin(alpha),-np.sin(beta)
DC[1,0],DC[1,1],DC[1,2] =-np.sin(alpha) , np.cos(alpha) , 0.
DC[2,0],DC[2,1],DC[2,2] = np.cos(alpha)*np.sin(beta), np.sin(alpha)*np.sin(beta), np.cos(beta)
#-------
#-------
# Application of rotation as a matrix product
data[wind_vars] = np.dot(DC, data[wind_vars].values.T).T
#-------
return data
def spectra(data, frequency=10, notation=None, anti_aliasing=True):
"""
Calculates the cross-spectra for a set of data
Parameters
----------
data: pandas.DataFrame or pandas.Series
dataframe with more than one columns
frequency: float
frequency of measurement of signal to pass to numpy.fft.rfftfreq
anti_aliasing: bool
whether or not to apply anti-aliasing according to Gobbi, Chamecki & Dias, 2006 (doi:10.1029/2005WR004374)
Returns
-------
spectra: pandas.DataFrame
whose column is the spectrum or coespectrum of the input dataframe
"""
from . import notation
from . import algs
import numpy as np
import pandas as pd
if len(data.columns) < 2:
raise TypeError('DataFrame has to has more than 1 column.')
notation = algs.get_notation(notation)
N = len(data)
names = [ notation.spectrum % a for a in data.columns ]
specs = pd.DataFrame(columns = names)
#---------
# Calculate cross-spectra here
for name, col in zip(names, data.columns):
spec = np.fft.rfft(data.loc[:, col ])
specs.loc[:, name ] = np.conj(spec) * spec
#---------
#---------
# Since it's the spectra, we can ignore the imaginary part
specs = specs.apply(np.real)
#---------
#---------
# Anti-aliasing is done here
if anti_aliasing:
RA = np.array([ 1. + np.cos(np.pi*k/N) for k in range(N/2+1) ])/2.
specs = specs.multiply(RA**2., axis='rows')
#---------
#---------
# Now we normalize the spectrum and calculate their frequency
specs *= 2./(frequency*N)
freq = np.fft.rfftfreq(len(data), d=1./frequency)
specs.index = freq
specs.index.name='Frequency'
#---------
return specs
def detrend(data, how='linear', rule=None, notation=None, suffix=None, units=None, inplace=True, ignore=[], **kwargs):
"""
Returns the detrended fluctuations of a given dataset
Parameters
----------
data: pandas.DataFrame, pandas.Series
dataset to be detrended
how: string
how of average to apply. Currently {'movingmean', 'movingmedian', 'block', 'linear', 'poly'}.
rule: pandas offset string
the blocks for which the trends should be calculated in the block and linear type
window: pandas date offset string or int
if moving mean/median is chosen, this tells us the window size to pass to pandas. If int,
this is the number of points used in the window. If string we will to guess the number of
points from the index.
Small windows (equivalent to 1min approx) work better when using rollingmedian.
block_func: str, function
how to resample in block type. Default is mean but it can be any numpy function
that returns a float. E.g, median.
degree: int
degree of polynomial fit (only if how=='linear' or how=='polynomial')
Returns
-------
pandas.DataFrame or pandas.Series
fluctuations of the input data
"""
from scipy import signal
from . import algs
import pandas as pd
how=algs.stripDown(how.lower(), args='-_')
df=data.copy()
if ignore:
df = df.drop(ignore, axis=1)
defs = algs.get_notation(notation)
#-----------
# We can only use scipy's detrend function safely if index in not datetime
if isinstance(df.index, pd.DatetimeIndex):
df = df - trend(df, how=how, rule=rule, **kwargs)
else:
#-----------
# If possible, try to use scipy's optimized functions
if how=='linear' and rule==None:
try:
df = df.apply(signal.detrend, axis=0, type=how)
except:
df = df - trend(df, how=how, rule=rule, **kwargs)
elif (any(w==how for w in ['block', 'blockaverage', 'blockmean'])) and (rule==None):
try:
df = df.apply(signal.detrend, axis=0, type='constant')
except:
df=df-trend(df, how=how, rule=rule, **kwargs)
#-----------
#-----------
# If not, use our trending function
else:
df = df - trend(df, how=how, rule=rule, **kwargs)
#-----------
#-----------
#-----------
# We rename the columns names to indicate that they are fluctuations
if units:
newunits = { defs.fluctuations % el : units[el] if el in units.keys() else None for el in df.columns }
#-----------
#-----------
# Rename the columns
if suffix != '':
df = df.rename(columns = lambda x: defs.fluctuations % x)
#-----------
#-----------
# If units are not be changed in place, we copy them
if units:
if not inplace:
units = units.copy()
units.update(newunits)
#-----------
if inplace:
return df
else:
return df, units
