{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "

Data simulation and cross correlation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this notebook, we are going to start with the stellar simulation from last, where we took a template spectrum and convolved it with a smoothing kernel. Now we are going to finish it by adding noise.\n", "

\n", "After that, we'll simulate a spectrum with a radial velocity, and see if we can recover it using cross-correlation, experimenting with different S/N." ] }, { "cell_type": "code", "execution_count": 153, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Spectrum simulation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's start with our simulation of a stellar spectrum from last time." ] }, { "cell_type": "code", "execution_count": 160, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "minimum dispersion: 0.300000 maximum dispersion: 0.300000\n", "using dispersion: 0.300000\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#read in stellar model, plot and determine dispersion\n", "from astropy.io import ascii\n", "a=ascii.read('star.txt')\n", "\n", "wave=a['WAVE']\n", "plt.plot(wave,a['FLUX'])\n", "dispersion=wave[1:]-wave[0:-1]\n", "print('minimum dispersion: {:f} maximum dispersion: {:f}'.format(dispersion.min(),dispersion.max()))\n", "disp=dispersion.mean()\n", "print('using dispersion: {:f}'.format(disp))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As before, we'll simulate a low resolution spectrum with $\\delta\\lambda=2.5$ Angstrom. Create the smoothing kernel for this resolution, in the pixel units of our model spectrum." ] }, { "cell_type": "code", "execution_count": 161, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 161, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "dlambda = 2.5 # delta(lambda) in Angtroms\n", "sig = 2.5/2.354 # corresponding sigma in Angstyroms\n", "sig_pixels = sig / disp # corresponding sigma in pixels, given disp\n", "\n", "def gauss(x,mean=0,sig=1) :\n", " \"\"\" Return normalized Gaussian function here\"\"\"\n", " return 1/sig/np.sqrt(2*np.pi)*np.exp(-(x-mean)**2/2/sig**2) # add code here\n", "\n", "# create a gaussian kernel with this sigma. Let this extend from -5*sig to 5*sig. Note that we want this to be an odd \n", "# number to prevent the convolution from shifting the spectrum.\n", "x=np.arange(-5*sig_pixels,5*sig_pixels+1)\n", "kernel= gauss(x,0,sig_pixels) #use your gauss routine to fill the kernel array\n", "\n", "# plot it\n", "plt.plot(kernel)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "OK, now convolve our spectrum with the smoothing kernel using numpy.convolve()" ] }, { "cell_type": "code", "execution_count": 162, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(5000, 5050)" ] }, "execution_count": 162, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sim=np.convolve(a['FLUX'],kernel,mode='same')\n", "plt.clf()\n", "plt.plot(wave,a['FLUX'])\n", "plt.plot(wave,sim)\n", "plt.xlim(5000,5050)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "OK, let's add noise to the image. Suppose we want to generate a spectrum with some specified median S/N. For a S/N target, what do we need to scale the median flux level to, given Poisson statistics?" ] }, { "cell_type": "code", "execution_count": 163, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 163, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sntarg=100 # Choose a S/N here\n", "fluxtarg=sntarg**2 # what does the flux need to be to reach this target S/N?\n", "\n", "# scale the model spectrum to the desired target flux\n", "sim=sim/np.median(sim)*fluxtarg\n", "# plot should have a median of the desired level\n", "plt.plot(sim)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now add Poisson noise using np.random.poisson() " ] }, { "cell_type": "code", "execution_count": 165, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 165, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "noisesim = np.random.poisson(sim) # get a Poisson sampling of the spectrum\n", "\n", "#plot both the spectrum with noise and the noiseless one\n", "plt.plot(wave,noisesim)\n", "plt.plot(wave,sim)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we will add in some readout noise, which is represented by a Gaussian distribution with zero mean and a $\\sigma$ corresponding to the readout noise level of the detector, let's say 10 units here." ] }, { "cell_type": "code", "execution_count": 166, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 166, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rn=10 # desired readout noise\n", "\n", "noisesim2=noisesim+np.random.normal(0.,rn,size=len(noisesim)) # add in Gaussian noise\n", "plt.plot(wave,noisesim2,label='spectrum+Poisson+readout')\n", "plt.plot(wave,noisesim,label='spectrum+Poisson')\n", "plt.plot(wave,sim,label='spectrum')\n", "plt.legend()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For later use, let's write a routine that scale an input spectrum and adds the noise" ] }, { "cell_type": "code", "execution_count": 176, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 176, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def addnoise(spec,sn=100,rn=10) :\n", " fluxtarg=sn**2 # what does the flux need to be to reach this target S/N?\n", " # scale the model spectrum to the desired target flux\n", " sim=spec/np.median(spec)*fluxtarg\n", " \n", " return np.random.poisson(sim)+np.random.normal(0,rn,len(sim))\n", "\n", "plt.plot(wave,addnoise(sim,sn=100,rn=10),label='spectrum+Poisson+readout')\n", "plt.plot(wave,addnoise(sim,sn=100,rn=0),label='spectrum+Poisson')\n", "plt.plot(wave,sim,label='spectrum')\n", "plt.legend()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's simulate a spectrum with a radial velocity of 200 km/s. To do this, you can just shift the wavelengths by the Doppler shift:\n", "$$\\lambda_{shifted} - \\lambda_{rest} = \\lambda_{rest} \\frac{v}{c}$$\n", "To do this, we will initialize an interpolator with these shifted wavelengths using scipy.interpolate() , which we can then use to get a simulated spectrum at any desired wavelengths. We are also going to want to interpolate the rest spectrum to resampled wavelengths as well, so we can cross correlate them, so initialize an interpolator for that as well." ] }, { "cell_type": "code", "execution_count": 175, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(5000, 5050)" ] }, "execution_count": 175, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rv=200 # set desired radial velocity here (in km/s)\n", "\n", "#instantiate an interpolation for the rest spectrum\n", "interp=scipy.interpolate.CubicSpline(wave,sim)\n", "\n", "#instatiate a interpolator given the input (shifted) wavelengths and the spectrum\n", "rvinterp=scipy.interpolate.CubicSpline(wave+wave*rv/3.e5,sim)\n", "\n", "# plot the rest spectrum (here the interpolator is doing nothing!)\n", "plt.plot(wave,interp(wave),color='g',label='rest')\n", "\n", "# plot the shifted spectrum\n", "plt.plot(wave,rvinterp(wave),color='r',label='shifted')\n", "plt.legend()\n", "\n", "#plot a small segment of both\n", "plt.figure()\n", "plt.plot(wave,interp(wave),color='g',label='rest')\n", "plt.plot(wave,rvinterp(wave),color='r',label='shifted')\n", "plt.legend()\n", "plt.xlim(5000,5050)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "OK, to get the radial velocity by cross correlation, we need to resample the spectra to a $\\log\\lambda$ scale, so that the shift is independent of the wavelengths. Let's choose a $\\log\\lambda$ array with the same number of pixels and the same wavelength range as the original wavelengths." ] }, { "cell_type": "code", "execution_count": 178, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(5000, 6000)" ] }, "execution_count": 178, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import scipy\n", "wave=a['WAVE']\n", "# set up a log(wavelength) array with the same number of pixels as the original\n", "#numpy.linspace returns a uniformly spaced array between a starting and ending values with the \n", "# specified number of pixels\n", "logwave=np.linspace(np.log(wave[0]),np.log(wave[-1]),len(wave))\n", "#dlog_lambda is the spacing in log(lambda)\n", "dlog_lambda=logwave[1]-logwave[0]\n", "\n", "# interpolate to the new wavelength scale. Remember that we need to give the interpolator the wavelengths\n", "# not the log(wavelengths)\n", "sim_logwave = interp(np.exp(logwave))\n", "\n", "# plot the old and new, demonstrate they are similar, i.e. interpolator works well here\n", "plt.plot(wave,sim)\n", "plt.plot(np.exp(logwave),sim_logwave)\n", "plt.xlim(5000,6000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we'll be a little unrealistic (cheat!) and interpolate the rv shifted spectrum first, then add noise" ] }, { "cell_type": "code", "execution_count": 184, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(5000, 5050)" ] }, "execution_count": 184, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# need to be careful around edges that cubic spline interpolation doesn't give negative values,\n", "# because they will cause the Poisson routine to fail (why?). Set negatives to 0.\n", "rvsim_logwave = rvinterp(np.exp(logwave))\n", "\n", "rvsim_logwave[rvsim_logwave<0]= 0.\n", "\n", "# now add noise using the addnoise routine from above\n", "out=addnoise(rvsim_logwave,sn=100,rn=10)\n", "plt.clf()\n", "plt.plot(np.exp(logwave),sim_logwave,label='noiseless rest')\n", "plt.plot(np.exp(logwave),out,label='RV shifted with noise')\n", "plt.plot(np.exp(logwave),rvsim_logwave,label='RV shifted, no noise')\n", "plt.legend()\n", "plt.xlim(5000,5050)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "OK, now we will see if we can recover the radial velocity using cross correlation.\n", "

\n", "Apart from sampling on a $\\log\\lambda$ grid, another thing we need to be careful of in cross correlation is the continuum level. If the signal has a mean value greater than 0, the cross correlation will be \"diluted\" by the continuum contribution, and edge effects will be very significant; imagine that the signal drops to zero off the edges, which will lead to a big change in cross-correlation as the edges slide relative to each other. As a result, the mean level is typically removed before cross-correlation. Here, the continuum level is clearly a function of wavelength. We'll remove an approximate continuum by subtracting a \"median-filtered\" version of the spectrum: imagine running a window across the spectrum and taking the median value in the window around each pixel. We will use scipy.signal.medfilt() to do this, although the principle is simple.\n", "\n", "We will build this continuum subtraction into a short cross-correlation function, using numpy.correlate to do the actual cross-correlation of the continuum-removed spectra. numpy.correlate() will cross-correlate two spectra across a large range of shifts, depending on the mode keyword, but even the smallest of these is likely overkill for the RV problem, if we expect that the shift is small (pixels or tens of pixels). Here, we use it with the mode='same' option, which will produce a cross-correlation function of the same size as the first array, which means it is computing shifts from the second array being shifted one half of its length to the left up through one half of its length to the right: zero lag will be in the middle of cross-correlation array.\n", "\n", "It would be very straightforward, and possibly simpler to understand, to write your own (perhaps one-line!) cross correlation routine that returned the cross-correlation function as a function of shift (lag)." ] }, { "cell_type": "code", "execution_count": 186, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-20, 20)" ] }, "execution_count": 186, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "

" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import scipy.signal\n", "def xcorr(a,b,filter=401) :\n", " \"\"\" Cross correlate two spectra, but remove the median levels first\n", " \n", " filter gives the width for the median filtering\n", " \n", " returns the lag array and the cross correlation function\n", " \"\"\"\n", " xc=np.correlate(a-scipy.signal.medfilt(a,filter),b-scipy.signal.medfilt(b,filter),mode='same')\n", " # with mode='same', the zero shift cross-correlation is in the middle of the output array\n", " if len(xc)%2 == 0 :\n", " lag=np.arange(len(xc))-len(xc)/2\n", " else :\n", " lag=np.arange(len(xc))-(len(xc)-1)/2\n", "\n", " return lag, xc \n", "\n", "# cross correlate template with itself as a check\n", "lag,xc=xcorr(sim_logwave,sim_logwave)\n", "\n", "# cross correlate template with object\n", "lag,xc2=xcorr(out,sim_logwave)\n", "\n", "# plot cross correlation as a function of lag\n", "plt.plot(lag,xc/xc.max())\n", "plt.plot(lag,xc/xc.max(),'bo', label='autocorrelation')\n", "plt.plot(lag,xc2/xc2.max(),'ro',label='cross correlation of shifted and rest')\n", "plt.legend()\n", "plt.xlim(-20,20)\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can look for the peak of the cross correlation, which will give us the pixel shift in the $\\log\\lambda$ data arrays. To turn that into a velocity, we need to determine the velocity shift per pixel, which is just $d\\log\\lambda \\times c$" ] }, { "cell_type": "code", "execution_count": 195, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "dloglambda: 0.000064 velocity per pixel: 19.068622\n", "peak pixel: 6671 corresponding lag: 10.000000\n", "corresponding RV: 190.686222\n" ] } ], "source": [ "print('dloglambda: {:f} velocity per pixel: {:f}'.format(dlog_lambda,dlog_lambda*3.e5))\n", "# get the peak pixel, the lag corresponding to this pixel, and the corresping RV\n", "imax=xc2.argmax()\n", "print('peak pixel: {:d} corresponding lag: {:f}'.format(imax,lag[imax]))\n", "print('corresponding RV: {:f}'.format(lag[imax]*dlog_lambda*3.e5))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How well does this match the input radial velocity? Note that we can do (much) better by fitting for the peak: if you look carefully you can see that the cross-correlation is not symmetric around the peak pixel. Write this as a function so we can use it later (always good to write things as function!)" ] }, { "cell_type": "code", "execution_count": 200, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "10.0\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# plot around peak\n", "plt.plot(lag,xc2/xc2.max(),'ro',label='cross correlation of shifted and rest')\n", "plt.xlim(lag[imax-5],lag[imax+5])\n", "plt.ylim(0.8,1.05)\n", "print(lag[imax])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can see by eye that the maximum is probably closer to a lag of 10.5. Getting a little ahead of ourselves, let's do a quick quadratic fit to the peak." ] }, { "cell_type": "code", "execution_count": 227, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "peak lag: 10.470327 corresponding RV: 199.654714\n" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAD4CAYAAADiry33AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAgAElEQVR4nO3dd3xUVfrH8c+TRkjoJNSQBOmhQ0QFFbuACioWMLpYsaH7sxfcVVHWuqIIlugqKqyKiIKiIiKCCiihl1AChBBCCS0QQvrz+2PGZQiBDBByJ5Pn/Xrxysy9Z2aeGZJvTs699xxRVYwxxvivAKcLMMYYc2pZ0BtjjJ+zoDfGGD9nQW+MMX7Ogt4YY/xckNMFlBQREaGxsbFOl2GMMZXKwoULd6pqZGn7fC7oY2NjSUpKcroMY4ypVERk09H22dCNMcb4OQt6Y4zxcxb0xhjj5yzojTHGz1nQG2OMnysz6EXkAxHZISIrjrJfRGS0iKSIyDIR6eaxb4iIrHP/G1KehRtToSZMgNhYCAhwfZ0woWrWYColb06vHAeMAT4+yv6+QCv3vzOAt4EzRKQe8DQQDyiwUESmquqeky3amAo1YQIMHQo5Oa77mza57gMkJFSdGkylVWaPXlXnALuP0WQA8LG6zAfqiEhj4FJghqrudof7DKBPeRRtTIUaPvxQwP4lJ8e1vSrVYCqt8rhgqimw2eN+unvb0bYfQUSGAkMBoqOjy6EkY8pRWlqpm4vTNpOxJ4eMvbls25fL9qxcMrPzyMopIOtgAftyC8gtKCK/qJiCQqVYlcAAITBACAoMIDwkkBrVgqhRLYi64SFE1qxGRI1qNKxVjeh6YTSpU53gwIBj1nDU7cZ4KI+gl1K26TG2H7lRNRFIBIiPj7eVUIxP0ehoNu/NZVWD01jVsDlrImLZWK8pm+o2Ju+lWYe1DQkKoE71YGpXD6ZW9WDCQoKoExRAcKAQIEJRsSvwC4qUnPxC0nbnsD+3kN0H8jlYUHTYcwUGCI1rh9KqQQ3aXH4fbdYvI27HRlru2kygFrsaWcfIeKE8gj4daOZxPwrIcG8/r8T2X8rh9Yw5pfIKi1ictpek1N0sStvLooQ32Vvk6lmLFtN8dwanZW3lvHYNiT2nI1F1q9OodigNa4VSKzQIkdL6OGU7kFdI5v48tmblsnlPDpt355C6K4d12/fzW/uLKYi7BIDwvBw6bkuhy84NnDHwIk7PK6RGNZ+bzcT4EPFmKUERiQW+VdUOpey7DBgG9MN1MHa0qvZwH4xdCPx1Fs4ioLuqHmu8n/j4eLW5bkxFUlVSdmQza80OfkvZxZ8bd5Fb4Ooxt2xQg27RdeicsZb248bQZsWfVG/SEEaOrNCDoAVFxWwc9zkrPvmKJSH1WRrTgVURMRSoayioY9PanNsqgvPbNqBzVB0CAk7sl42pvERkoarGl7qvrKAXkU9x9cwjgO24zqQJBlDVd8TVfRmD60BrDnCLqia5H3sr8KT7qUaq6odlFWtBbypCcbGyIHU3P67azk/J29m0y3Wgs1WDGvRqGUGvlhGcHluXOmEhDld6dDn5hSzatJd5G3Yyd/0ulm7eS7FC/fAQzm/bgH4dG3F2y0hCguxymargpIK+olnQm1NFVVmWnsXUpRlMW7aVbftyCQkMoGfL+lzUriEXtmtA49rVnS7zhO05kM+cdZn8vHoHP6/ewf7cQmqGBnFxXEOu6tqUni0iCLSevt+yoDdV2s7sPL5evIXPF2xm3Y5sggOF3q0bcEXnxlzYrqFfjm/nFRYxN2UX05Zv5ceV29iXW0jj2qFc2bUp18U3o3lEuNMlmnJmQW+qHFVlQeoePpqXyvQV2ygsVrpG1+Ha7s24rFNjalcPdrrECpNbUMTM5B18uSid2WszKSpWzm4ZwY1nRnNRu4YEBdrQjj+woDdVRl5hEVMWZ/Dh3FSSt+6jVmgQ18Y3Y9DpzWjVsKbT5Tlux75cJiZt5r9/pJGRlUujWqHc3CuWwT2iq9QvP39kQW/83r7cAibMT+OD3zeSuT+Pto1qMqRnLFd2aUr1kECny/M5hUXFzFqTyYe/b2Tu+l2EhwRy/enR3H5Oc5rUqbzHKaoyC3rjt7JyCnj/tw2M+z2V/XmFnN0ygrt6t6BXy/onfD57VbNiSxb/+W0j3yzNQASujW/G3b1b0KxemNOlmeNgQW/8TtbBAv7z6wY+dAd83w6NuPf8lnRoWtvp0iqt9D05vDN7PRMXpFOsyjXdo7j/wlbWw68kjhX0dhTG+LYSU/PmfjKB9+Zs4NyXZzH65xR6tYzg+7+fw9s3dreQP0lRdcN4/sqOzHn0fG48M4bJi7Zw3qu/MHLaKvYcyD/U0KZLrnSsR298l8fUvMUIU+J682rvIWypFcm5rSN59NI2Fu6nUPqeHN74aR1fLkonPCSIYRe05Oa0+VS7a+jhM2mGhUFiok2X7DAbujGVU2wsbNrEksateeaioSxp0pYO21J4Ivk7ev0x3enqqox12/fz4vermbl6B9HZmTw5I5FL1847fNbCmBhITXWoQgMW9KaSyqxRj5d6/41JHS8mMns3j80ex9UrZhEgQHGx0+VVOb+uy+S5F79gbWQMPVOXMmLG27Tcne7aKWL/Jw6zoDeVSnGx8umCNF76/E8OBgZz64Ip3Dfvc2rkH3Q1sN6jYwqbn8Z/68bxyrk3kRtcjaF/TGbYvIlUb9rI/k8cdqyg979rv02ltnrbPp6cvJxFaXs5s24wI995mBYZ6w81CAtzzRxpHBH0/HP8behQ+q75nRfOu4WxPa9nSvvzeaFzGOc4XZw5KjvrxviE/MJiXv9pLVe8+Rupu3L497Wd+fSpAbR4+VlXD17E9dUO+jkrIQESE4mMrM1r37/OZzNHERJZn5tSa/DIF0vJyilwukJTChu6MY5bmZHFw18sI3nrPgZ0acLTV7SnXrjvTg9sDpdbUMTomet4d84G6oWH8OLVHbmwXUOny6py7Dx645MKi4oZ8/M6Boz5nZ3ZeSTe1J03BnW1kK9kQoMDebRPW6bc24v64SHc9lESj3+5jOy8QqdLM25eBb2I9BGRNSKSIiKPl7I/RkRmisgyEflFRKI89r0sIitFJFlERotdl26AtF05XJ84n1d/XEvfjo2Z8cC5XNK+kdNlmZPQoWltpgzrxd3ntWBi0mb6vjGHBanHXFDOVJAyg15EAoGxQF8gDhgsInElmr0KfKyqnYARwAvux/YEegGdgA7A6UDvcqveVEqTF6XT9405rN2+nzcGdeHNwV19eiUn471qQYE81qctE+88C0G4/t15vPHTOoqKfWuIuKrxpkffA0hR1Q2qmg98Bgwo0SYOmOm+PctjvwKhQAhQDdcShNtPtmhTOR3IK+ShiUt5cOJS2jetzQ//dy4DujR1uixzCsTH1uO7v5/DgC5NGfXTWga/N5+MvQedLqvK8ibomwKbPe6nu7d5WgoMdN++CqgpIvVVdR6u4N/q/jddVZNPrmRTGSVv3Uf/Mb8xeXE6f7+wFZ/ecSZNbbIsv1ajWhCjru/Ca9d1ZuWWLPq+8SuzVu9wuqwqyZugL21MveTfYQ8DvUVkMa6hmS1AoYi0BNoBUbh+OVwgIuce8QIiQ0UkSUSSMjMzj+sNGN/35cJ0rhz7O/tzC5lw+xk8cHFrW7u0Crm6WxTf3n8OTepU55ZxC/j3j2tsKKeCeRP06UAzj/tRQIZnA1XNUNWrVbUrMNy9LQtX736+qmarajbwPXBmyRdQ1URVjVfV+MjIyBN8K8bX5BUW8dTXy3noi6V0i67LtPvPoWeLCKfLMg5oHhHOV/f05Lr4KN78OYUhH/zJruw8p8uqMrwJ+gVAKxFpLiIhwCBgqmcDEYkQkb+e6wngA/ftNFw9/SARCcbV27ehmypgW1Yu1787n/Hz07iz92l8clsPImtWc7os46DQ4EBevqYzLw/sxILU3fQf8zsrtmQ5XVaVUGbQq2ohMAyYjiukJ6rqShEZISL93c3OA9aIyFqgIfDXNeqTgPXAclzj+EtV9ZvyfQvG1yxO28MVY35j3fb9vJ3QjSf6trMFqM3/XHd6Mybd1RNV5Zp35jJlyRanS/J7dmWsKVdfLkznia+W06hWKO8Piae1LchtjmJndh73jF/En6m7ubP3aTx6aVs7dnMS7MpYc8oVFysvfJfMQ18sJT6mLlPu7WUhb44pokY1xt9+BglnRPPu7A3cNX4hOfl2Ne2pYEFvTtrB/CLumbCId+ds4KYzY/jo1h7UtWkMjBdCggIYeVVHnrkijpnJ27n2nXlsy8p1uiy/Y0FvTsqO/bkMSpzH9FXb+MflcYwY0J5gG483x+nmXs15f0g8qTsPMGDsb6zMsIO05cl+Is0JS9mRzVVj57J2ezbv3tid285ujk1lZE7UBW0bMunungSIcP278/lt3U6nS/IbFvTmhCxK28M178wlr7CIz+880yYkM+WiXeNaTL6nJ03rVOfmD//kq8XpTpfkFyzozXGbmbydG96bT+3qwXx5d086RdVxuiTjRxrXrs7Eu84iPrYuD3y+lHdnry/7QeaYLOjNcZm0MJ2hnyykVYOafHl3T2LqhztdkvFDtasH89GtPbi8U2Ne+H41L36/Gl87FbwysTVjjdfG/b6RZ75ZxdktI3jnpu7UqGbfPubUqRYUyBuDulK7ejDvzF5P1sF8nr+yo51rfwLsJ9WUSVUZ83MK/56xlkvbN2T04K5UCwp0uixTBQQGCM9f2YG6YSGMmZXCvoOFjLq+CyFBNhhxPCzozTGpKi9+v5p352zg6m5NeXlgJ5vOwFQoEeHhS9tQu3owI79LJq+wiDE3dCM02Dob3rKfWHNUOn4Czw58lHfnbOBva2fzav5KC3njmDvOPY3nruzAT8k7uOPjJA7mFzldUqVhP7WmVMXjJ/DUp38yrvV53P7nVzz71SsE3DkUJkxwujRThd10ZgwvX9OJ39ZlcsudozlQLQxiY+37sgwW9OYIxcXKk1NWMqHjJdw1/wuGz/qPa/WZnBwYPtzp8kwVd92aObz+w2gWRLbglmue5kDGdhhqnZBjsaA3hykuVp6YvJzPWvTivrmf8djsjw5fYiwtzanSjHEZPpwBS2fw+jevsrBpO2655mlyCoqsE3IMFvTmf1SVf0xZwedJm7lv5fc8+Ov4I9eRjI52ojRjDnF3Nq5Y/Sujvv03SVFx3DrwaXK2bne4MN9lQW8AV8g/+80qJvyRxl29W/Dg9WchYWGHNwoLg5EjS38CYyqKR2ejf/IcRn37Gn82a8/tN4wkt8AO0JbGq6AXkT4iskZEUkTk8VL2x4jITBFZJiK/iEiUx75oEflRRJJFZJWIxJZf+aY8qCovfL+acXNTuf3s5jzWpw1yYwIkJkJMDIi4viYmQkKC0+Waqm7kSFenw21A8mz+/dNbzGvYmrvHLyS/sNjB4nxTmUEvIoHAWKAvEAcMFpG4Es1eBT5W1U7ACOAFj30fA6+oajugB7CjPAo35efNn1NInLOBIWfFMPyydodmoExIgNRUKC52fbWQN74g4chOyFUP3cTIqzoxa00mf/9sMYVFFvaevLlgqgeQoqobAETkM2AAsMqjTRzwgPv2LOBrd9s4IEhVZwCoanY51W3KyX9+28hrM9ZyTfconr6ivU0zbCqHhIQjOh43ADn5hTw/LZlHJy3j1Ws7E2DTJQDeDd00BTZ73E93b/O0FBjovn0VUFNE6gOtgb0iMllEFovIK+6/EA4jIkNFJElEkjIzM4//XZgTMnHBZp77dhV9OzTixas72g+FqfRuP+c0Hrq4NZMXb2HEt6tsIjQ3b4K+tJ/+kp/ew0BvEVkM9Aa2AIW4/mI4x73/dOA04OYjnkw1UVXjVTU+MjLS++rNCfthxVYen7yMc1tH8vqgLnbFq/Ebwy5oye1nN2fc3FTe/DnF6XJ8gjdDN+lAM4/7UUCGZwNVzQCuBhCRGsBAVc0SkXRgscewz9fAmcB/yqF2c4Lmb9jF/Z8toXOzOrx7Y3eboMz4FRHhyX7t2JNTwGsz1lI3PISbzoxxuixHedONWwC0EpHmIhICDAKmejYQkQgR+eu5ngA+8HhsXRH5q5t+AYeP7ZsKtjIjizs+SiK6XhgfDDmd6iEW8sb/BAQILw3syEXtGvDPKSv4dllG2Q/yY2UGvaoWAsOA6UAyMFFVV4rICBHp7252HrBGRNYCDYGR7scW4Rq2mSkiy3ENA71X7u/CeCVtVw5DPlhAjdAgPr61B3XDQ5wuyZhTJigwgDE3dOP0mHo8+PlS5q3f5XRJjhFfO1gRHx+vSUlJTpfhd/YcyGfg23PZdSCfL+8+i5YNajpdkjEVYm9OPte8M4/t+3KZdFdP2jTyz+99EVmoqvGl7bMjcFVAbkERt3+cRPreg7w/JN5C3lQpdcJC+OjWHlQPDmTIB3+yNeug0yVVOAt6P1dcrDw4cQmL0vYw6rounB5bz+mSjKlwTetUZ9wtPcjOK+TmDxawL7fA6ZIqlAW9n/vXd8l8t3wbw/u147JOjZ0uxxjHxDWpxds3dmN9Zjb3TlhEQRW6etaC3o+Nn7+J93/byM09Y7nt7OZOl2OM485pFcnzV3bg13U7eXrqyipzQZWtGeun5qzN5OmpK7mgbQP+cXmcTW1gjNugHtFs2p3D27+sp3n9cO449zSnSzrlLOj90Lrt+7l3wiJaNajB6MFdCbSpDYw5zCOXtCFtVw7/+j6Z6PphXNq+kdMlnVI2dONndmXncetHCwgNCeQ/N59OjWr2u9yYkgIChH9f15lOTWvzwOdLSN66z+mSTikLej+SX1jM3RMWsWNfHu//LZ6mdao7XZIxPis0OJDEv8VTKzSY2z9KYmd2ntMlnTIW9H5CVXl66kr+3Libl6/pROdmdZwuyRif17BWKO/9LZ5dB/K4e/xC8gr9c4UqC3o/MX7+Jj79M427z2vBgC4lZ5E2xhxNx6javHptZxak7uEfX6/wyzNxLOj9wNz1O3nmm1Vc2LYBD1/SxulyjKl0Lu/UhPsuaMnEpHTGz9/kdDnlzoK+kkvfk8Ow/y6meUQ4rw/qYmfYGHOCHrioNRe2bcCz36zijw3+NQGaBX0llltQxF3jF1JQWEziTd2pGRrsdEnGVFoBAcKoQV2Irh/GPRMWkbHXf+bEsaCvpFSVJ79azoot+xh1fRdOi6zhdEnGVHq1QoNJvCmevMJi7vxkIbkF/nFw1oK+kvp43iYmL9rC/13UioviGjpdjjF+o2WDGoy6vgvLt2TxzNSVTpdTLrwKehHpIyJrRCRFRB4vZX+MiMwUkWUi8ouIRJXYX0tEtojImPIqvCpbuGk3z327iovaNeD+C1o5XY4xfufiuIYMO78lny3YzMQFm50u56SVGfQiEgiMBfoCccBgEYkr0exV4GNV7QSMAF4osf85YPbJl2t2Zudx74TFNKlTnX9f14UAO/hqzCnxwMWtOadVBE9NWcGKLVlOl3NSvOnR9wBSVHWDquYDnwEDSrSJA2a6b8/y3C8i3XEtL/jjyZdbtRUVK3//bDF7cvJ5+8Zu1K5uB1+NOVUCA4Q3BnUlIjyEu8YvZG9OvtMlnTBvgr4p4Pm3S7p7m6elwED37auAmiJS371g+L+BR471AiIyVESSRCQpMzPTu8qroFEz1vJ7yi6eG9CB9k1qO12OMX6vXngIb93YnR378nho4lKKiyvnxVTeBH1pYwMl3+3DQG8RWQz0BrYAhcA9wHeqesxBLlVNVNV4VY2PjIz0oqSqZ9aaHYyZlcL18c247vRmTpdjTJXRpVkdnrq8HTNX7yDx1w1Ol3NCvJnaMB3wTJYoIMOzgapmAFcDiEgNYKCqZonIWcA5InIPUAMIEZFsVT3igK45uq1ZB3nw8yW0bVSTZwe0d7ocY6qcm86M4Y8Nu3ll+hq6x9StdEtyetOjXwC0EpHmIhICDAKmejYQkQj3MA3AE8AHAKqaoKrRqhqLq9f/sYX88SksKub+TxeTX1jM2IRuhAYHOl2SMVWOiPDiwI40q1ud+/67mF2VbKbLMoNeVQuBYcB0IBmYqKorRWSEiPR3NzsPWCMia3EdeB15iuqtcl6bsZYFqXv419UdaWEXRRnjmJqhwYxN6MbunHweqGTj9eJrM7XFx8drUlKS02X4hNlrMxnywZ8MOr0ZLw7s5HQ5xhhcM8U+9fUKnujbljt7t3C6nP8RkYWqGl/aPrsy1kft2J/Lg58voU3Dmjx9hY3LG+MrEs6Ipm+HRrwyfQ1LNu91uhyvWND7oOJi5aGJSzmQX8iYG7pSPcTG5Y3xFSLCi1d3omGtUO77dBH7cgucLqlMFvQ+6L3RX/Lrup3889vRtDqjI0yY4HRJxhgPtcOCGT24Kxl7c3ly8nKfX6zEgt7HLH3vM17ZEky/1b8xeMkPsGkTDB1qYW+Mj+keU5cHI3P4dtlWvuh8CcTG+uzPqQW9D8nOK+T+Jbk0zN7NCz+8eehKtZwcGD7cydKMMSVNmMBd/7iZMzct45mL7iQ1K99nO2UW9D7k2akr2Rxej9e/eZXaeQcO35mW5kxRxpjSDR9O4IEDvDbtNYKLCvn7FQ9TkJvnk50yC3of8f3yrXyxMJ17k3/k9C2rjmwQHV3xRRljjs7d+Wqyfyf/mj6GpU3aMLrXYJ/slFnQ+4BtWbk8Pnk5naNqc//1Z0FY2OENwsJgpF2DZoxP8eh8Xbbmd65dNoOxZ17Ln93Pd7Co0lnQO6y4WHnoiyXkFxYz6vouBN+YAImJEBMDIq6viYmQkOB0qcYYTyNHHtYpe+and2m2L5MH+/yd/T52yqUFvcM+nJvK7ym7+OcVcYfWfU1IgNRUKC52fbWQN8b3JBzeKQtv0pDXuoWTURjIiG9KGX51kAW9g1J27OelH1ZzUbsGDLKph42pfEp0yroPHcQ957Xki4XpTF+5zenq/seC3iEFRcU8OHEpNaoF8cLVnRCxJQGN8Qf3X9iKDk1r8cTk5WTu941ZLi3oHTJ2VgrL0rMYeWUHImtWc7ocY0w5CQkKYNR1XcjOK+TxL5f5xFWzFvQOWJa+lzd/TuGqrk3p27Gx0+UYY8pZq4Y1eaxPW2au3sGkhelOl2NBX9FyC4p4cOJSImtU45n+NiulMf7qlp6x9GhejxHfrCJj70FHa7Ggr2CjflpLyo5sXrqmE7WrBztdjjHmFAkIEF69pjNFqjzm8BCOV0EvIn1EZI2IpIjIEUsBikiMiMwUkWUi8ouIRLm3dxGReSKy0r3v+vJ+A5XJorQ9vDdnA4N7NKN3a1sE3Rh/F10/jCf6tuXXdTv59M/NjtVRZtCLSCAwFugLxAGDRSSuRLNXca0H2wkYAbzg3p4D/E1V2wN9gNdFpE55FV+Z5BYU8cgXS2lcuzpP9mvndDnGmAqScEYMvVrWZ+S0VWzeneNIDd706HsAKaq6QVXzgc+AASXaxAEz3bdn/bVfVdeq6jr37QxgB1Alu7KjZqxlfeYBXhzYkZqhNmRjTFURECC85F4K9AmH5q73JuibAp5/c6S7t3laCgx0374KqCki9T0biEgPIARYX/IFRGSoiCSJSFJmZqa3tVcai9P28N6vGxjcI5pzWlXJ33PGVGlRdcN4vF87fkvZycSkih/C8SboS7uSp+SvpIeB3iKyGOgNbAEK//cEIo2BT4BbVLX4iCdTTVTVeFWNj4z0ryDMKyzi0UnLaFQrlCf7tXW6HGOMQxJ6RHNG83o8/20y27JyK/S1vQn6dMDz+vwoIMOzgapmqOrVqtoVGO7elgUgIrWAacBTqjq/XKquRMb+nMK6HdmMvNqGbIypyv4awikoLmb4VxU7hONN0C8AWolIcxEJAQYBUz0biEiEiPz1XE8AH7i3hwBf4TpQ+0X5lV05rMrYx1u/rOfqrk05v00Dp8sxxjgsNiKchy9pw8zVO/h6yZYKe90yg15VC4FhwHQgGZioqitFZISI9Hc3Ow9YIyJrgYbAX5OnXwecC9wsIkvc/7qU95vwRYVFxTz25TLqhAXzj8tLnqRkjKmqbunVnK7RdXj2m1XszK6YuXDEF+Zh8BQfH69JSUlOl3HS3p29nhe+X83YG7pxWSeb5sAYc8ja7fu5bPSv9OvYmDcGdS2X5xSRhaoaX9o+uzL2FNi06wCjflrLJXEN6dexkdPlGGN8TOuGNbnnvJZMWZLBrDU7TvnrWdCXM1Vl+FcrCAoIYMSADjb9sDGmVPec34KWDWrw1FcrOJBXWPYDToIFfTn7avEWfkvZyWN92tCodqjT5RhjfFS1oEBeGtiRjKyDvPrjmlP6Whb05WhXdh7PfbuK7jF1STgjxulyjDE+rntMPW48I4Zxc1NZsnnvKXsdC/pyNHJaMtl5hbxwdUcCAmzIxhhTtkf6tKFBzWo8OXk5hUVHXE9aLizoy8nvKTuZvHgLd/VuQeuGNZ0uxxhTSdQKDeaZK9qzaus+xs1NPSWvYUFfDnILinjq6xXE1A/j3vNbOl2OMaaS6dOhERe2bcBrM9ay5RQsUmJBXw7emb2ejTsP8PyVHQgNDnS6HGNMJSMiPDugParwzNSV5f78FvQnaUNmNm/NWk//zk1sZkpjzAmLqhvGAxe3Ysaq7Uxfua1cn9uC/iSoKv+YsoJqwQE8dbktJmKMOTm39GpO20Y1eXbqSnLyy+/cegv6kzB1aQa/p+zi0T5taVDTzpk3xpyc4MAAnr+yAxlZuYyemVJuz2tBf4L25Rbw/LRkOkXV5oYe0U6XY4zxE/Gx9bguPor3f93Auu37y+U5LehP0KgZa9mZncfzV3Yg0M6ZN8aUo8f7tqNGaBBPfb2iXOatt6A/Aasy9vHR3FRu6BFNp6gquda5MeYUqhcewqOXtuWPjbvLZd56C/rjVFys/HPKCuqEhfDIpW2cLscY46cGnd6MLs3qMHJaMvtyC07qubwKehHpIyJrRCRFRB4vZX+MiMwUkWUi8ouIRHnsGyIi69z/hpxUtT7gy0XpJG3aw+N92lInLMTpcowxfiogQHhuQAd2Hcjn9RnrTu65ymogIoHAWKAvEAcMFpGSSya9imu5wE7ACOAF92PrAU8DZwA9gKdFpO5JVeygrMZH3CEAABBPSURBVIMFvPj9arpF1+Ga7lFlP8AYY05Cx6jaDO4RzUfzUlmz7cQPzHrTo+8BpKjqBlXNBz4DBpRoEwfMdN+e5bH/UmCGqu5W1T3ADKDPCVfrsNd/WsvunHxGDOhgk5YZYyrEI5e0oWZoEE9PPfEDs94EfVNgs8f9dPc2T0uBge7bVwE1RaS+l49FRIaKSJKIJGVmZnpbe4Vas20/H8/bxOAe0XRoWtvpcowxVUTd8BAevqQN8zfs5ttlW0/oObwJ+tK6riV/rTwM9BaRxUBvYAtQ6OVjUdVEVY1X1fjISN+bRkBVefabldSoFsQjl9gBWGNMxXJ1MGsxclryCa1G5U3QpwPNPO5HARmeDVQ1Q1WvVtWuwHD3tixvHlsZfL9iG3PX7+LhS1pTN9wOwBpjKlZggPBs/w5s25fL2FnHf8WsN0G/AGglIs1FJAQYBEz1bCAiESLy13M9AXzgvj0duERE6roPwl7i3lZpHMwvYuS0ZNo1rsUNtmqUMcYh3WPqclXXprz/60bSduUc12PLDHpVLQSG4QroZGCiqq4UkREi0t/d7DxgjYisBRoCI92P3Q08h+uXxQJghHtbpfHunPVs2XuQZ/u3tytgjTGOerxvW4ICheenrTquxwV500hVvwO+K7Htnx63JwGTjvLYDzjUw69UMvYe5J3Z67m8U2N6NK/ndDnGmCquYa1Q7j2/Ja9MX8Nv63ZydqsIrx5nV8Yew4vfr0YVnuhnUxAbY3zDbWc3J7peGM9+s9LrNWYt6I9iQepupi7N4M7eLWhap7rT5RhjDAChwYEMv6wd63ZkM37+Jq8eY0FfiuJi1+mUjWuHclfv05wuxxhjDnNJXEPObhnBqJ/WsTcnv8z2FvSlmLQonRVb9vF437aEhXh1GMMYYyqMiPDU5e3Yn1vAGzPLngfHgr6EAx9P4JVPfqXblmT6X9kLJkxwuiRjjDlC20a1uP70aD6Zt4n1mdnHbGtB72nCBN4d9xOZ1Wvz1M/vI5s2wdChFvbGGJ/00CWtCaWYfz04hu7Q/WjtLOg9ZIx8hcSul9N/1S90y1jj2piTA8OHO1uYMcaUImLKJIb9OoGZTTses50FvYdXWlxEsQTw6OyPDt+RluZMQcYYcyzDh3PLvEk027vtmM0s6N2WbN7LV+3P5/YFXxO1r8QMmtG2+LcxxgelpVGtqJAnZx37mlQLelyzU46ctoqIoGLuXjrt8J1hYTBypDOFGWPMsbg7oX3Wzj1mMwt6YPrK7SxI3cMDV3Si5tg3ICYGRFxfExMhIcHpEo0x5kgjR0JYWKnzwXuq8ieJFxQV89IPq2nZoAbXxzeDMxIs2I0xlcNfWTV8OGw6+lWyVb5H/+mfaWzceYAn+rYlKLDKfxzGmMomIQFSU1kIC4/WpEon2/7cAt74aR1nnlaPC9o2cLocY4w5Jar00M07s9ez60A+4/rFIWJzzRtj/JNXPXoR6SMia0QkRUQeL2V/tIjMEpHFIrJMRPq5tweLyEcislxEkkXkifJ+Aydqa9ZB3v91IwO6NKFjlC32bYzxX2UGvYgEAmOBvkAcMFhE4ko0ewrXylNdcS01+JZ7+7VANVXtiOvy3DtFJLZ8Sj85o2asRRUetsW+jTF+zpsefQ8gRVU3qGo+8BkwoEQbBWq5b9fm0ALgCoSLSBBQHcgH9p101Sdp7fb9TFqYzk1nxdCsXpjT5RhjzCnlTdA3BTZ73E93b/P0DHCjiKTjWnLwPvf2ScABYCuQBrxa2pqxIjJURJJEJCkzM7Pk7nL38g9rCA8JYtj5LU/5axljjNO8CfrSjlJqifuDgXGqGgX0Az4RkQBcfw0UAU2A5sBDInLESh6qmqiq8aoaHxkZeVxv4HgtSN3NT8nbueu8FtQNDzmlr2WMMb7Am6BPB5p53I/i0NDMX24DJgKo6jwgFIgAbgB+UNUCVd0B/A7En2zRJ0pVeeG7ZBrUrMatvZo7VYYxxlQob4J+AdBKRJqLSAiug61TS7RJAy4EEJF2uII+0739AnEJB84EVpdX8cfrx1XbWZS2lwcubk31kECnyjDGmApVZtCraiEwDJgOJOM6u2aliIwQkf7uZg8Bd4jIUuBT4GZVVVxn69QAVuD6hfGhqi47Be+jTEXFyivT13BaZDjXdo9yogRjjHGEVxdMqep3uA6yem77p8ftVUCvUh6XjesUS8dNXpROyo5s3kroZlMdGGOqlCqReHmFRbz+0zo6Nq1N3w6NnC7HGGMqVJUI+v/+kcaWvQd5tE8bm+rAGFPl+H3QH8grZMzPKZx1Wn3ObhnhdDnGGFPh/D7oP/htI7sO5POI9eaNMVWUXwf93px8Euds4OK4hnSLrut0OcYY4wi/Dvp352wgO7/QJi4zxlRpfhv0O/bnMu73VPp3bkKbRjWdLscYYxzjt0H/9i/ryS8q5v8uau10KcYY4yi/DPqMvQeZMD+Na7pF0Twi3OlyjDHGUX4Z9G/+nIKi3HehTUNsjDF+F/Sbdh3gi6TN3NAjmqi6tqiIMcb4XdC/MXMdgQHCvbaoiDHGAH4W9Bsys/l68RZuOjOGBrVCnS7HGGN8gl8F/eiZ66gWFMidvVs4XYoxxvgMvwn6lB37mbI0g7/1jCGyZjWnyzHGGJ/hN0H/xswUwoIDufNc680bY4wnr4JeRPqIyBoRSRGRx0vZHy0is0RksYgsE5F+Hvs6icg8EVkpIstFpNwHz9ds28+3yzIY0jOWerbgtzHGHKbMFaZEJBDXkoAX41oofIGITHWvKvWXp3AtMfi2iMThWo0qVkSCgPHATaq6VETqAwXl/SZGz1xHeEgQd5xzWnk/tTHGVHre9Oh7ACmqukFV84HPgAEl2ihQy327NpDhvn0JsExVlwKo6i5VLTr5sg9Zs20/05Zv5ZZesdS13rwxxhzBm6BvCmz2uJ/u3ubpGeBGEUnH1Zu/z729NaAiMl1EFonIo6W9gIgMFZEkEUnKzMw8rjcweuY6alQL4razmx/X44wxpqrwJuhLW61DS9wfDIxT1SigH/CJiATgGho6G0hwf71KRC484slUE1U1XlXjIyMjvS5+7fb9fLdiK0N6xlAnzHrzxhhTGm+CPh1o5nE/ikNDM3+5DZgIoKrzgFAgwv3Y2aq6U1VzcPX2u51s0X8ZPXMdYcGB3H62jc0bY8zReBP0C4BWItJcREKAQcDUEm3SgAsBRKQdrqDPBKYDnUQkzH1gtjewinKwbrtrbH5ITxubN8aYYynzrBtVLRSRYbhCOxD4QFVXisgIIElVpwIPAe+JyAO4hnVuVlUF9ojIa7h+WSjwnapOK4/CR/+cQvXgQG63M22MMeaYygx6AFX9Dtewi+e2f3rcXgX0Ospjx+M6xbLcpOzI5ttlGdx5bgs7b94YY8pQKa+MHTsrhdCgQO44x860McaYslS6oN+06wBTlmwh4Yxo6tewOW2MMaYslS7o35q1nqDAAIaea2PzxhjjjUoV9Ol7cvhyUTqDTm9m880bY4yXKlXQvzt7AyJwl803b4wxXqs0Qb99Xy6fJ23mmu5RNKlT3elyjDGm0qg0QZ84ZwNFxcrdvW0tWGOMOR6VIuh3H8jnv3+kMaBzE6LrhzldjjHGVCqVIug//H0juYVF3HO+jc0bY8zx8vmg35dbwLi5qVwa14iWDWo6XY4xxlQ6Ph/04+dvYn9uIfeeb2PzxhhzInw66A/mF/GfXzdybutIOkbVdrocY4yplHw66D9fkMauA/kMs968McacMJ8N+vzCYhLnbKBHbD16NK/ndDnGGFNp+V7QL1wIsbFMfWcSGVm53H2enWljjDEnw6ugF5E+IrJGRFJE5PFS9keLyCwRWSwiy0SkXyn7s0XkYW9er3hTGu8s20Pb0CLOa+P9GrLGGGOOVGbQi0ggMBboC8QBg0UkrkSzp4CJqtoV11KDb5XYPwr43tuifmrZg5R6Udz980eIlLY2uTHGGG9506PvAaSo6gZVzQc+AwaUaKNALfft2ngsHi4iVwIbgJXeFvXWWdcSvWcrl/0+xduHGGOMOQpvgr4psNnjfrp7m6dngBtFJB3XkoP3AYhIOPAY8OyxXkBEhopIkogkHQgOZUmTtgz9czJBzaK8fBvGGGOOxpugL23sREvcHwyMU9UooB/wiYgE4Ar4UaqafawXUNVEVY1X1fjMGnWJyN7DNevnwsiR3rwHY4wxx+DN4uDpQDOP+1F4DM243Qb0AVDVeSISCkQAZwDXiMjLQB2gWERyVXXM0V5sf7Vwbl0/m9C3x0JCwnG8FWOMMaXxJugXAK1EpDmwBdfB1htKtEkDLgTGiUg7IBTIVNVz/mogIs8A2ccKeYAa1YK48au3IDTY+3dhjDHmqMoculHVQmAYMB1IxnV2zUoRGSEi/d3NHgLuEJGlwKfAzapacnjHK80jwqllIW+MMeVGTjCPT5n4+HhNSkpyugxjjKlURGShqsaXts/3row1xhhTrizojTHGz1nQG2OMn7OgN8YYP2dBb4wxfs6C3hhj/JwFvTHG+DmfO49eRDKBTU7XgWsKh51OF+Ej7LM4xD6LQ+yzOMQXPosYVS11AQ+fC3pfISJJR7v4oKqxz+IQ+ywOsc/iEF//LGzoxhhj/JwFvTHG+DkL+qNLdLoAH2KfxSH2WRxin8UhPv1Z2Bi9Mcb4OevRG2OMn7OgN8YYP2dBX4KI1BGRSSKyWkSSReQsp2tyiog8ICIrRWSFiHzqXiKyyhCRD0Rkh4is8NhWT0RmiMg699e6TtZYUY7yWbzi/jlZJiJfiUgdJ2usKKV9Fh77HhYRFZEIJ2o7Ggv6I70B/KCqbYHOuFbVqnJEpClwPxCvqh2AQFzLSFYl43CvhezhcWCmqrYCZrrvVwXjOPKzmAF0UNVOwFrgiYouyiHjOPKzQESaARfjWlrVp1jQexCRWsC5wH8AVDVfVfc6W5WjgoDqIhIEhHHkovB+TVXnALtLbB4AfOS+/RFwZYUW5ZDSPgtV/dG91CjAfCCqwgtzwFG+LwBGAY8CPneGiwX94U4DMoEPRWSxiLwvIuFOF+UEVd0CvIqrd7IVyFLVH52tyic0VNWtAO6vDRyux1fcCnzvdBFOca+fvUVVlzpdS2ks6A8XBHQD3lbVrsABqs6f5odxjz0PAJoDTYBwEbnR2aqMLxKR4UAhMMHpWpwgImHAcOCfTtdyNBb0h0sH0lX1D/f9SbiCvyq6CNioqpmqWgBMBno6XJMv2C4ijQHcX3c4XI+jRGQIcDmQoFX3opwWuDpES0UkFdcQ1iIRaeRoVR4s6D2o6jZgs4i0cW+6EFjlYElOSgPOFJEwERFcn0WVPDBdwlRgiPv2EGCKg7U4SkT6AI8B/VU1x+l6nKKqy1W1garGqmosrg5jN3ee+AQL+iPdB0wQkWVAF+BfDtfjCPdfNZOARcByXN8rPn2Zd3kTkU+BeUAbEUkXkduAF4GLRWQdrjMsXnSyxopylM9iDFATmCEiS0TkHUeLrCBH+Sx8mk2BYIwxfs569MYY4+cs6I0xxs9Z0BtjjJ+zoDfGGD9nQW+MMX7Ogt4YY/ycBb0xxvi5/wdS139wxfEz4gAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def fitpeak(lag,xcorr,plot=True) :\n", " imax=xcorr.argmax()\n", " x=lag[imax-5:imax+6]\n", " y=xcorr[imax-5:imax+6]/xcorr.max()\n", " fit=np.polyfit(x,y,2)\n", " if plot :\n", " plt.plot(x,y,'ro',label='cross correlation of shifted and rest')\n", " plt.xlim(lag[imax-5],lag[imax+5])\n", " xx=np.linspace(x[0],x[-1],100)\n", " plt.plot(xx,fit[0]*xx**2+fit[1]*xx+fit[2])\n", "\n", " #for a quadratic fit y = ax**2 + bx + c, the peak is where the derivative, 2ax +b, equals 0, so xpeak=-b/2a\n", " return -fit[1]/2/fit[0]\n", "\n", "peak=fitpeak(lag,xc2)\n", "\n", "#convert this to a velocity as above\n", "print('peak lag: {:f} corresponding RV: {:f}'.format(peak,peak*dlog_lambda*3.e5))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Better? Try doing this at different S/N for the input spectrum, and report your results. See how compact it is if we use functions for the different steps!" ] }, { "cell_type": "code", "execution_count": 231, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "S/N: 5.000000 peak lag: 10.004497 corresponding RV: 190.771965\n", "S/N: 10.000000 peak lag: 10.428714 corresponding RV: 198.861203\n", "S/N: 50.000000 peak lag: 10.449020 corresponding RV: 199.248410\n", "S/N: 100.000000 peak lag: 10.469787 corresponding RV: 199.644413\n", "S/N: 1000.000000 peak lag: 10.466854 corresponding RV: 199.588477\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for sn in [5,10,50,100,1000] :\n", " # get the simulated spectrum for this S/N\n", " out=addnoise(rvsim_logwave,sn=sn,rn=10)\n", " plt.figure()\n", " plt.plot(out)\n", " \n", " # do the cross correlation including continuum removal\n", " lag,xc2=xcorr(out,sim_logwave)\n", " \n", " # fit the cross correlation peak and report results\n", " peak=fitpeak(lag,xc2,plot=False)\n", "\n", " #convert this to a velocity as above\n", " print('S/N: {:f} peak lag: {:f} corresponding RV: {:f}'.format(sn,peak,peak*dlog_lambda*3.e5))\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 2 }