"""PSS_utils.py
A place to organize methods used by multiple modules
"""
from __future__ import (absolute_import, division,
print_function, unicode_literals)
import numpy as np
import scipy as sp
from astropy import units as u
from pint import models
#try:
# import pyfftw
# use_pyfftw = True
#except:
# use_pyfftw = False
[docs]def shift_t(y, shift, dt=1):
"""
Shift timeseries data in time.
Shift array, y, in time by amount, shift. For dt=1 units of samples
(including fractional samples) are used. Otherwise, shift and dt are
assumed to have the same physical units (i.e. seconds).
Parameters
----------
y : array like, shape (N,), real
Time series data.
shift : int or float
Amount to shift
dt : float
Time spacing of samples in y (aka cadence).
Returns
-------
out : ndarray
Time shifted data.
Examples
--------
>>>shift_t(y, 20)
# shift data by 20 samples
>>>shift_t(y, 0.35, dt=0.125)
# shift data sampled at 8 Hz by 0.35 sec
Uses np.roll() for integer shifts and the Fourier shift theorem with
real FFT in general. Defined so positive shift yields a "delay".
"""
if isinstance(shift, int) and dt is 1:
out = np.roll(y, shift)
else:
yfft = np.fft.rfft(y) # hermicity implicitely enforced by rfft
fs = np.fft.rfftfreq(len(y), d=dt)
phase = -1j*2*np.pi*fs*shift
yfft_sh = yfft * np.exp(phase)
out = np.fft.irfft(yfft_sh)
return out
def down_sample(ar, fact):
"""down_sample(ar, fact)
down sample array, ar, by downsampling factor, fact
"""
#TODO this is fast, but not as general as possible
downsampled = ar.reshape(-1, fact).mean(axis=1)
return downsampled
def rebin(ar, newlen):
"""rebin(ar, newlen)
down sample array, ar, to newlen number of bins
This is a general downsampling rebinner, but is slower than down_sample().
'ar' must be a 1-d array
"""
newBins = np.linspace(0, ar.size, newlen, endpoint=False)
stride = newBins[1] - newBins[0]
maxWid = int(np.ceil(stride))
ar_new = np.empty((newlen, maxWid)) # init empty array
ar_new.fill(np.nan) # fill with NaNs (no extra 0s in mean)
for ii, lbin in enumerate(newBins):
rbin = int(np.ceil(lbin + stride))
# fix for potential last bin rounding error
if rbin > ar.size: # Not sure how to force this for test...
rbin = ar.size
lbin = int(np.ceil(lbin))
ar_new[ii, 0:rbin-lbin] = ar[lbin:rbin]
return sp.nanmean(ar_new, axis=1) # ingnore NaNs in mean
def top_hat_width(subband_df, subband_f0, DM):
"""top_hat_width(subband_df, subband_f0, DM)
Returns width of a top-hat pulse to convolve with pulses for dipsersion
broadening. Following Lorimer and Kramer, 2005 (sec 4.1.1 and A2.4)
subband_df : subband bandwidth (MHz)
subband_f0 : subband center frequency (MHz)
DM : dispersion measure (pc/cm^3)
return top_hat_width (milliseconds)
"""
D = 4.148808e3 # sec*MHz^2*pc^-1*cm^3, dispersion const
width_sec = 2*D * DM * (subband_df) / (subband_f0)**3
return width_sec * 1.0e+3 # ms
def savitzky_golay(y, window_size, order, deriv=0, rate=1):
# courtesy scipy recipes
r"""Smooth (and optionally differentiate) data with a Savitzky-Golay filter.
The Savitzky-Golay filter removes high frequency noise from data.
It has the advantage of preserving the original shape and
features of the signal better than other types of filtering
approaches, such as moving averages techniques.
Parameters
----------
y : array_like, shape (N,)
the values of the time history of the signal.
window_size : int
the length of the window. Must be an odd integer number.
order : int
the order of the polynomial used in the filtering.
Must be less then `window_size` - 1.
deriv: int
the order of the derivative to compute
(default = 0 means only smoothing)
Returns
-------
ys : ndarray, shape (N)
the smoothed signal (or it's n-th derivative).
Notes
-----
The Savitzky-Golay is a type of low-pass filter, particularly
suited for smoothing noisy data. The main idea behind this
approach is to make for each point a least-square fit with a
polynomial of high order over a odd-sized window centered at
the point.
Examples
--------
t = np.linspace(-4, 4, 500)
y = np.exp( -t**2 ) + np.random.normal(0, 0.05, t.shape)
ysg = savitzky_golay(y, window_size=31, order=4)
import matplotlib.pyplot as plt
plt.plot(t, y, label='Noisy signal')
plt.plot(t, np.exp(-t**2), 'k', lw=1.5, label='Original signal')
plt.plot(t, ysg, 'r', label='Filtered signal')
plt.legend()
plt.show()
References
----------
.. [1] A. Savitzky, M. J. E. Golay, Smoothing and Differentiation of
Data by Simplified Least Squares Procedures. Analytical
Chemistry, 1964, 36 (8), pp 1627-1639.
.. [2] Numerical Recipes 3rd Edition: The Art of Scientific Computing
W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery
Cambridge University Press ISBN-13: 9780521880688
"""
from math import factorial
try:
window_size = np.abs(np.int(window_size))
order = np.abs(np.int(order))
except TypeError: # ValueError, msg:
raise ValueError("window_size and order have to be of type int")
if window_size % 2 != 1 or window_size < 1:
raise TypeError("window_size size must be a positive odd number")
if window_size < order + 2:
raise TypeError("window_size is too small for the polynomials order")
order_range = range(order+1)
half_window = int((window_size -1) // 2)
# precompute coefficients
b = np.mat([[k**i for i in order_range] for k in range(-half_window,
half_window+1)])
m = np.linalg.pinv(b).A[deriv] * rate**deriv * factorial(deriv)
# pad the signal at the extremes with
# values taken from the signal itself
firstvals = y[0] - np.abs(y[1:half_window+1][::-1] - y[0])
lastvals = y[-1] + np.abs(y[-half_window-1:-1][::-1] - y[-1])
y = np.concatenate((firstvals, y, lastvals))
return np.convolve(m[::-1], y, mode='valid')
def find_nearest(array, value):
"""Returns the argument of the element in an array nearest to value.
For half width at value use array[max:].
"""
diff=np.abs(array-value)
idx = diff.argmin()
if idx == 0 or array[1] < value:
idx = 1
return idx
def acf2d(array, speed='fast', mode='full', xlags=None, ylags=None):
"""Courtesy of Michael Lam's PyPulse
Calculate the autocorrelation of a 2 dimensional array.
"""
from scipy.signal import fftconvolve, correlate
if speed == 'fast' or speed == 'slow':
ones = np.ones(np.shape(array)) # very close for either speed
norm = fftconvolve(ones, ones, mode=mode)
if speed=='fast':
return fftconvolve(array, np.flipud(np.fliplr(array)),
mode=mode)/norm
else:
return correlate(array, array, mode=mode)/norm
elif speed == 'exact':
#NOTE: (r,c) convention is flipped from (x,y),
# also that increasing c is decreasing y
LENX = len(array[0])
LENY = len(array)
if xlags is None:
xlags = np.arange(-1*LENX+1, LENX)
if ylags is None:
ylags = np.arange(-1*LENY+1, LENY)
retval = np.zeros((len(ylags), len(xlags)))
for i, xlag in enumerate(xlags):
print(xlag)
for j, ylag in enumerate(ylags):
if ylag > 0 and xlag > 0:
A = array[:-1*ylag, xlag:] # the "stationary" array
B = array[ylag:, :-1*xlag]
elif ylag < 0 and xlag > 0:
A = array[-1*ylag:, xlag:]
B = array[:ylag, :-1*xlag]
elif ylag > 0 and xlag < 0: # optimize later via symmetries
A = array[:-1*ylag, :xlag]
B = array[ylag:, -1*xlag:]
elif ylag < 0 and xlag < 0:
A = array[-1*ylag:, :xlag]
B = array[:ylag, -1*xlag:]
else: # one of the lags is zero
if ylag == 0 and xlag > 0:
A = array[-1*ylag:, xlag:]
B = array[:, :-1*xlag]
elif ylag == 0 and xlag < 0:
A = array[-1*ylag:, :xlag]
B = array[:, -1*xlag:]
elif ylag > 0 and xlag == 0:
A = array[:-1*ylag, :]
B = array[ylag:, -1*xlag:]
elif ylag < 0 and xlag == 0:
A = array[-1*ylag:, :]
B = array[:ylag, -1*xlag:]
else:
A = array[:, :]
B = array[:, :]
#print xlag,ylag,A,B
C = A*B
C = C.flatten()
goodinds = np.where(np.isfinite(C))[0] # check for good values
retval[j, i] = np.mean(C[goodinds])
return retval
def text_search(search_list, header_values, filepath, header_line=0,
file_type='txt'):
""" Method for pulling value from a txt file.
search_list = list of string-type values that demarcate the line in a txt
file from which to pull values
header_values = string of column headers or array of column numbers
(in Python numbering) the values from which to pull
filepath = file path of txt file. (string)
header_line = line with headers for values.
file_type = 'txt' or 'csv'
returns: tuple of values matching header values for the search terms given.
"""
#TODO Make work for other file types.
#if file_type == 'txt':
# delimiter = ''
#elif file_type == 'csv':
# delimiter = ','
check = 0
output_values = list()
with open(filepath, 'r') as f: # read file to local memory
searchfile = f.readlines()
# Find Column Numbers from column names
if any(isinstance(elem, str) for elem in header_values):
column_num = []
parsed_header = searchfile[header_line].split()
for ii, header in enumerate(header_values):
column_num.append(parsed_header.index(header))
else:
column_num = np.array(header_values)
# Find Values using search keys and column numbers.
for line in searchfile:
if all(ii in line for ii in search_list):
info = line.split()
for jj, value in enumerate(column_num):
output_values.append(info[value])
check += 1
if check == 0:
raise ValueError('Combination {0} '.format(search_list)+' not found in \
same line of text file.')
if check > 1:
raise ValueError('Combination {0} '.format(search_list)+' returned \
multiple results in txt file.')
return tuple([float(i) for i in output_values])
[docs]def make_quant(param, default_unit):
"""
Convenience function to intialize a parameter as an astropy quantity.
Parameters
----------
param : attribute
Parameter to initialize.
default_unit : string
Name of an astropy unit, set as default for this parameter.
Returns
-------
An astropy quantity
Examples
--------
self.f0 = make_quant(f0,'MHz')
"""
default_unit = u.core.Unit(default_unit)
if hasattr(param, 'unit'):
try:
param.to(default_unit)
except u.UnitConversionError:
raise ValueError("Quantity {0} with incompatible unit {1}"
.format(param, default_unit))
quantity = param
else:
quantity = param * default_unit
return quantity
def get_pint_models(psr_name, psr_file_path):
"""Function that returns pint model given a specific pulsar"""
# will need to add section for J1713 T2 file. gls is not file wanted for this specfic pulsar.
model_name = "{0}{1}_NANOGrav_11yv1.gls.par".format(psr_file_path,psr_name)
par_model = models.get_model(model_name)
return par_model
[docs]def make_par(signal, pulsar, outpar = "simpar.par"):
"""
Function to create a par file for simulated pulsar.
Parameters
----------
signal : class
PsrSigSim Signal class object
pulsar : class
PsrSigSim Pulsar class object
outpar : string
Name of output par file.
"""
# Get parameters and other things that should go into this file
par_lines = []
par_lines.append("PSR %s\n" % (pulsar.name))
par_lines.append("LAMBDA 0.0\n" ) # Default for now
par_lines.append("BETA 0.0\n" ) # Default for now
par_lines.append("PMLAMBDA 0.0\n" ) # Default for now
par_lines.append("PMBETA 0.0\n" ) # Default for now
par_lines.append("PX 0.0\n" ) # Default for now
par_lines.append("POSEPOCH 56000.0\n" ) # Default for now
par_lines.append("F0 %s\n" % (1.0/pulsar.period))
par_lines.append("PEPOCH 56000.0\n" ) # Default for now
par_lines.append("START 50000.0\n" ) # Default for now
par_lines.append("FINISH 60000.0\n" ) # Default for now
par_lines.append("DM %s\n" % (signal.dm))
par_lines.append("EPHEM DE436\n" ) # Default for now
par_lines.append("ECL IERS2010\n" ) # Default for now
par_lines.append("CLK TT(BIPM2015) \n" ) # Default for now
par_lines.append("UNITS TDB\n" ) # Default for now
par_lines.append("TIMEEPH FB90\n" ) # Default for now
par_lines.append("T2CMETHOD TEMPO\n" ) # Default for now
par_lines.append("CORRECT_TROPOSPHERE N\n" ) # Default for now
par_lines.append("PLANET_SHAPIRO N\n" ) # Default for now
par_lines.append("DILATEFREQ N\n" ) # Default for now
par_lines.append("TZRMJD 56000.0\n" ) # Default for now
par_lines.append("TZRFRQ 1500.0\n" ) # Default for now
par_lines.append("TZRSITE @\n" ) # Default for now
par_lines.append("MODE 1\n" ) # Default for now
# Write out the file
with open(outpar, 'w') as op:
op.writelines(par_lines)
op.close()