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# how to do the same as Michael Betancourt in
# https://betanalpha.github.io/assets/case_studies/gp_part3/part3.html

import numpy as np
from scipy.stats import invgamma
from scipy.optimize import minimize

f = lambda x, lims: \
    (np.array([invgamma(a=x[0], scale=x[1]).cdf(lims[0]) - 0.01, 
               invgamma(a=x[0], scale=x[1]).sf(lims[1]) - 0.01])**2

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# directories a and b
comm -12 <(ls a) <(ls b)

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import re
import requests
from itertools import product
import numpy as np

url = 'https://www.eso.org/observing/etc/bin/simu/espresso'


form_data = {
    'almanac_time_option': 'almanac_time_option_ut_time',

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from scipy import optimize
gauss = lambda x,p: p[0]*exp(-(x-p[1])**2/(2*p[2]**2)) + p[3]
gaussfit = lambda x,y,p0: optimize.leastsq(lambda p, x, y: gauss(x, p) - y, p0, args=(x, y))[0]

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import matplotlib.pyplot as plt
import numpy as np
from scipy.interpolate import LSQUnivariateSpline


def continuum(wave, flux, type='ratio', order=1, low_reject=2, high_reject=0,
              niter=10):
    
    m1 = np.ones_like(wave, dtype=np.bool) # use all points at first
    m1 &= flux!=0 # but remove those where flux = 0

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from re import split
from glob import glob

natsort = lambda s: [int(t) if t.isdigit() else t.lower() for t in split(r'(\d+)', s)]

files = sorted(glob(path), key=natsort)

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from numpy import sin
from scipy import optimize
sine = lambda t, p: p[0] * sin(1. / p[1] * t + p[2]) + p[3]
sinefit = lambda t, y, ye, p0, **kwargs: optimize.leastsq(lambda p, t, y, ye: (sine(t, p) - y)/ye, p0, args=(t, y, ye), **kwargs)[0]

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months = {
    'Jan': 1,
    'Feb': 2,
    'Mar': 3,
    'Apr': 4,
    'May': 5,
    'Jun': 6,
    'Jul': 7,
    'Aug': 8,
    'Sep': 9,

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import numpy as np

###############################################################################
# the following is mostly a copy of the scipy implementation of
# binned_statistic and binned_statistic_dd
# but allowing for a weights parameter
from scipy._lib.six import callable, xrange
from scipy._lib._numpy_compat import suppress_warnings

## careful here!

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from sympy import symbols, sin, nsolve

E = symbols('E')

def eccentric_anomaly(M, ecc, prec=15):
  return nsolve(E - e*sin(E) - M, M, prec=prec)


import mpmath as mp