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dmargala/wavelength_distortion.ipynb

Created December 20, 2016 01:54
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non-parametric fitting
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wavelength_distortion.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Inverse problem\n",
"\n",
"Given a series of measurements of relative offsets between transitions, can one uncover (to reasonable accuracy) the generating function of the offsets."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"%config InlineBackend.figure_format='retina'\n",
"# %load_ext autoreload\n",
"# the \"1\" means: always reload modules marked with \"%aimport\"\n",
"# %autoreload 1\n",
"\n",
"from __future__ import absolute_import, division, print_function\n",
"import matplotlib as mpl\n",
"from matplotlib import pyplot as plt\n",
"from matplotlib.pyplot import GridSpec\n",
"# import seaborn as sns\n",
"import mpld3\n",
"import numpy as np\n",
"import pandas as pd\n",
"import os, sys\n",
"import warnings"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def generate_distortion(wavelength, amplitude=300.0, omega=50.0):\n",
" return amplitude * np.sin(wavelength / omega)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x11017df90>]"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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1xq9fHzoaIBlIJjKOVZziKzeZoBkQSI/t26X5863pmkUv4iX3Z8LsBFA7JBMZ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\nJ3hiEsdtAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10c9d77d0>"
]
},
"metadata": {
"image/png": {
"height": 255,
"width": 393
}
},
"output_type": "display_data"
}
],
"source": [
"true_x = np.arange(3000, 9000, 50)\n",
"true_y = generate_distortion(true_x, omega=500)\n",
"plt.plot(true_x, true_y)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def n_components(high=10):\n",
" return np.random.randint(3, high)\n",
"\n",
"def xvals(n_components):\n",
" return 6000 * np.random.rand(n_components) + 3000.0\n",
"\n",
"def yvals(xvals):\n",
" return generate_distortion(xvals, omega=500)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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SVIlhQpIkSVIlhglJkiRJlRgmJEmSJFVimJAkSZJUiWFCmsYGBgYYGhpqu21o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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x110692750>"
]
},
"metadata": {
"image/png": {
"height": 255,
"width": 393
}
},
"output_type": "display_data"
}
],
"source": [
"ns = n_components()\n",
"xs = xvals(ns)\n",
"ys = yvals(xs)\n",
"\n",
"ysigmas = np.random.rand(ns) * 50.0 + 20 \n",
"\n",
"y_measurement = np.random.randn(ns) * ysigmas + ys\n",
"\n",
"plt.scatter(xs, ys, c='k', marker='x')\n",
"for (xplot, yplot, eplot) in zip(xs, y_measurement, ysigmas):\n",
" plt.errorbar(xplot, yplot, eplot, c='b')\n",
" plt.scatter(xplot, yplot, c='b');\n",
" \n",
"# x = np.arange(3000, 9000, 50)\n",
"# y = generate_distortion(x, omega=500)\n",
"# plt.plot(x, y)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from itertools import combinations, islice, takewhile\n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"df = pd.DataFrame(columns=['system', 'wavelength', 'vshift', 'sigma'])\n",
"n_systems = 100\n",
"names = [''.join(x) for x in islice(combinations('abcdefghijklmnopqrstuvwxyz', 2), n_systems)]\n",
"count = 0\n",
"abs_count = 0\n",
"for _ in range(n_systems):\n",
" name = names[count]\n",
" count += 1\n",
" ns = n_components()\n",
" xs = xvals(ns)\n",
" ys = yvals(xs)\n",
" ysigmas = np.random.rand(ns) * 50.0 + 20 \n",
" y_measurement = np.random.randn(ns) * ysigmas + ys\n",
" index = np.argsort(xs)\n",
" xs = xs[index]\n",
" y_measurement = y_measurement[index]\n",
" ysigmas = ysigmas[index]\n",
" for single in range(ns):\n",
" abs_count += 1\n",
" df.loc[abs_count] = [name, \n",
" xs[single], \n",
" y_measurement[single] - y_measurement[0],\n",
" ysigmas[single]]\n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"df = df.sort_index()"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>system</th>\n",
" <th>wavelength</th>\n",
" <th>vshift</th>\n",
" <th>sigma</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>ab</td>\n",
" <td>4566.521183</td>\n",
" <td>0.000000</td>\n",
" <td>45.282598</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>ab</td>\n",
" <td>5627.455054</td>\n",
" <td>-195.059145</td>\n",
" <td>68.708108</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>ab</td>\n",
" <td>7608.839528</td>\n",
" <td>120.127497</td>\n",
" <td>37.005477</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>ab</td>\n",
" <td>8351.023738</td>\n",
" <td>-233.144530</td>\n",
" <td>48.110434</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>ac</td>\n",
" <td>4599.395340</td>\n",
" <td>0.000000</td>\n",
" <td>44.885352</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>ac</td>\n",
" <td>5030.020902</td>\n",
" <td>-380.621822</td>\n",
" <td>32.452088</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>ac</td>\n",
" <td>8236.826524</td>\n",
" <td>-317.768479</td>\n",
" <td>59.041174</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>ac</td>\n",
" <td>8996.176191</td>\n",
" <td>-322.786856</td>\n",
" <td>54.580293</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>ad</td>\n",
" <td>4247.885938</td>\n",
" <td>0.000000</td>\n",
" <td>24.063224</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>ad</td>\n",
" <td>4469.167508</td>\n",
" <td>-64.446509</td>\n",
" <td>58.281801</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" system wavelength vshift sigma\n",
"1 ab 4566.521183 0.000000 45.282598\n",
"2 ab 5627.455054 -195.059145 68.708108\n",
"3 ab 7608.839528 120.127497 37.005477\n",
"4 ab 8351.023738 -233.144530 48.110434\n",
"5 ac 4599.395340 0.000000 44.885352\n",
"6 ac 5030.020902 -380.621822 32.452088\n",
"7 ac 8236.826524 -317.768479 59.041174\n",
"8 ac 8996.176191 -322.786856 54.580293\n",
"9 ad 4247.885938 0.000000 24.063224\n",
"10 ad 4469.167508 -64.446509 58.281801"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.head(10)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Non parametric model"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Model the distortion function using an arbitrary number parameters evenly spaced by wavelength"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"wlen_start = 3000\n",
"wlen_stop = 9000\n",
"wlen_binsize = 50\n",
"wlen_num_bins = (wlen_stop - wlen_start + 2*wlen_binsize) // wlen_binsize\n",
"wlen_bins = np.linspace(wlen_start - wlen_binsize, wlen_stop + wlen_binsize, wlen_num_bins + 1)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"122"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"wlen_num_bins"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"123"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"len(wlen_bins)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# find bin corresponding to each wavelength\n",
"df['wavelength_bin_index'] = pd.cut(df['wavelength'], wlen_bins, labels=np.arange(wlen_num_bins).astype(int))"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# find each system's reference wavelength bin and add that to each of the observations in that system\n",
"new_df = df.merge(df.groupby('system').agg({'wavelength_bin_index': 'min'}).reset_index(), how='left', on='system')"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>system</th>\n",
" <th>wavelength</th>\n",
" <th>vshift</th>\n",
" <th>sigma</th>\n",
" <th>wavelength_bin_index_x</th>\n",
" <th>wavelength_bin_index_y</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>ab</td>\n",
" <td>4566.521183</td>\n",
" <td>0.000000</td>\n",
" <td>45.282598</td>\n",
" <td>32</td>\n",
" <td>32</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>ab</td>\n",
" <td>5627.455054</td>\n",
" <td>-195.059145</td>\n",
" <td>68.708108</td>\n",
" <td>53</td>\n",
" <td>32</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>ab</td>\n",
" <td>7608.839528</td>\n",
" <td>120.127497</td>\n",
" <td>37.005477</td>\n",
" <td>93</td>\n",
" <td>32</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>ab</td>\n",
" <td>8351.023738</td>\n",
" <td>-233.144530</td>\n",
" <td>48.110434</td>\n",
" <td>108</td>\n",
" <td>32</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>ac</td>\n",
" <td>4599.395340</td>\n",
" <td>0.000000</td>\n",
" <td>44.885352</td>\n",
" <td>32</td>\n",
" <td>32</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>ac</td>\n",
" <td>5030.020902</td>\n",
" <td>-380.621822</td>\n",
" <td>32.452088</td>\n",
" <td>41</td>\n",
" <td>32</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>ac</td>\n",
" <td>8236.826524</td>\n",
" <td>-317.768479</td>\n",
" <td>59.041174</td>\n",
" <td>105</td>\n",
" <td>32</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>ac</td>\n",
" <td>8996.176191</td>\n",
" <td>-322.786856</td>\n",
" <td>54.580293</td>\n",
" <td>120</td>\n",
" <td>32</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>ad</td>\n",
" <td>4247.885938</td>\n",
" <td>0.000000</td>\n",
" <td>24.063224</td>\n",
" <td>25</td>\n",
" <td>25</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>ad</td>\n",
" <td>4469.167508</td>\n",
" <td>-64.446509</td>\n",
" <td>58.281801</td>\n",
" <td>30</td>\n",
" <td>25</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" system wavelength vshift sigma wavelength_bin_index_x \\\n",
"0 ab 4566.521183 0.000000 45.282598 32 \n",
"1 ab 5627.455054 -195.059145 68.708108 53 \n",
"2 ab 7608.839528 120.127497 37.005477 93 \n",
"3 ab 8351.023738 -233.144530 48.110434 108 \n",
"4 ac 4599.395340 0.000000 44.885352 32 \n",
"5 ac 5030.020902 -380.621822 32.452088 41 \n",
"6 ac 8236.826524 -317.768479 59.041174 105 \n",
"7 ac 8996.176191 -322.786856 54.580293 120 \n",
"8 ad 4247.885938 0.000000 24.063224 25 \n",
"9 ad 4469.167508 -64.446509 58.281801 30 \n",
"\n",
" wavelength_bin_index_y \n",
"0 32 \n",
"1 32 \n",
"2 32 \n",
"3 32 \n",
"4 32 \n",
"5 32 \n",
"6 32 \n",
"7 32 \n",
"8 25 \n",
"9 25 "
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"new_df.head(10)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Build \"Model\" matrix as a sparse matrix"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import scipy.sparse"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# remove rows where the wavelength bin of the observation is the same as the reference wavelength bin for that system\n",
"filtered = new_df[new_df['wavelength_bin_index_x'] != new_df['wavelength_bin_index_y']]"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>system</th>\n",
" <th>wavelength</th>\n",
" <th>vshift</th>\n",
" <th>sigma</th>\n",
" <th>wavelength_bin_index_x</th>\n",
" <th>wavelength_bin_index_y</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>ab</td>\n",
" <td>5627.455054</td>\n",
" <td>-195.059145</td>\n",
" <td>68.708108</td>\n",
" <td>53</td>\n",
" <td>32</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>ab</td>\n",
" <td>7608.839528</td>\n",
" <td>120.127497</td>\n",
" <td>37.005477</td>\n",
" <td>93</td>\n",
" <td>32</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>ab</td>\n",
" <td>8351.023738</td>\n",
" <td>-233.144530</td>\n",
" <td>48.110434</td>\n",
" <td>108</td>\n",
" <td>32</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>ac</td>\n",
" <td>5030.020902</td>\n",
" <td>-380.621822</td>\n",
" <td>32.452088</td>\n",
" <td>41</td>\n",
" <td>32</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>ac</td>\n",
" <td>8236.826524</td>\n",
" <td>-317.768479</td>\n",
" <td>59.041174</td>\n",
" <td>105</td>\n",
" <td>32</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>ac</td>\n",
" <td>8996.176191</td>\n",
" <td>-322.786856</td>\n",
" <td>54.580293</td>\n",
" <td>120</td>\n",
" <td>32</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>ad</td>\n",
" <td>4469.167508</td>\n",
" <td>-64.446509</td>\n",
" <td>58.281801</td>\n",
" <td>30</td>\n",
" <td>25</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>ad</td>\n",
" <td>6416.882732</td>\n",
" <td>-147.496402</td>\n",
" <td>53.545029</td>\n",
" <td>69</td>\n",
" <td>25</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td>ad</td>\n",
" <td>8613.355298</td>\n",
" <td>-558.910533</td>\n",
" <td>51.321055</td>\n",
" <td>113</td>\n",
" <td>25</td>\n",
" </tr>\n",
" <tr>\n",
" <th>13</th>\n",
" <td>ae</td>\n",
" <td>3687.006450</td>\n",
" <td>457.157704</td>\n",
" <td>68.575640</td>\n",
" <td>14</td>\n",
" <td>1</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" system wavelength vshift sigma wavelength_bin_index_x \\\n",
"1 ab 5627.455054 -195.059145 68.708108 53 \n",
"2 ab 7608.839528 120.127497 37.005477 93 \n",
"3 ab 8351.023738 -233.144530 48.110434 108 \n",
"5 ac 5030.020902 -380.621822 32.452088 41 \n",
"6 ac 8236.826524 -317.768479 59.041174 105 \n",
"7 ac 8996.176191 -322.786856 54.580293 120 \n",
"9 ad 4469.167508 -64.446509 58.281801 30 \n",
"10 ad 6416.882732 -147.496402 53.545029 69 \n",
"11 ad 8613.355298 -558.910533 51.321055 113 \n",
"13 ae 3687.006450 457.157704 68.575640 14 \n",
"\n",
" wavelength_bin_index_y \n",
"1 32 \n",
"2 32 \n",
"3 32 \n",
"5 32 \n",
"6 32 \n",
"7 32 \n",
"9 25 \n",
"10 25 \n",
"11 25 \n",
"13 1 "
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"filtered.head(10)"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# the column indices corresponding to the wavelength bin in the feature vector\n",
"model_cols = filtered[['wavelength_bin_index_x', 'wavelength_bin_index_y']].values.ravel()"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 53, 32, 93, 32, 108, 32, 41, 32, 105, 32, 120, 32, 30,\n",
" 25, 69, 25, 113, 25, 14, 1])"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model_cols[:20] "
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# the row indices corresponding to each \"observation\"\n",
"model_rows = np.repeat(np.arange(len(filtered)), 2)"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9])"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model_rows[:20]"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# these are the values in the model matrix\n",
"model_coefs = np.tile([1, -1], len(filtered))"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1,\n",
" -1, 1, -1])"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model_coefs[:20]"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(463, 926, 926, 926)"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"len(filtered), len(model_cols), len(model_rows), len(model_coefs)"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# create the model matrix, essentially the X matrix, or list of each observation's \"feature vector\"\n",
"model_matrix = scipy.sparse.csc_matrix((model_coefs, (model_rows, model_cols)), shape=(len(filtered), wlen_num_bins))"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<463x122 sparse matrix of type '<type 'numpy.int64'>'\n",
"\twith 926 stored elements in Compressed Sparse Column format>"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model_matrix"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Solve $X \\cdot \\vec{\\beta} = \\vec{y}$"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from sklearn import linear_model"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"model_y = filtered['vshift'].values"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"regr = linear_model.LinearRegression(fit_intercept=False)\n",
"regr.fit(model_matrix, model_y.ravel())\n",
"soln = regr.coef_"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"len(soln) == wlen_num_bins"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"wlen_bin_centers = 0.5*(wlen_bins[1:] + wlen_bins[:-1])"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"len(wlen_bin_centers) == wlen_num_bins"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## compare fit results with source distortion function\n"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x117bdc110>]"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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VVDIleSzpFM41HTsGjzzibudhqVTWNMuUSMELbZJhjPkG8C1gOZDpFLNeB34m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\nasl9y4LSoEdSzspd1DJd42LsMf75d732nOgaK1IoWrfm4x4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5w8SJcP75MG+e/3nIED+7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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x117bdc190>"
]
},
"metadata": {
"image/png": {
"height": 255,
"width": 396
}
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(wlen_bin_centers, soln, lw=0, marker='+')\n",
"plt.plot(true_x, true_y, c='r')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"note depending on the wavelength bin size and the coverage of observations, you may see no/some/a lot of points along 0. this happens if there are no observations in a given wavelength bin.\n",
"\n",
"this fitting method assumed each of the bins is independent!! can adjust model matrix coefficient so that neighboring bins influence each other."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Visualize \"Model\" matrix"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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eyhdwxwLAouhAHoEOZNjShAAA1KYDuSIdyJTw4h9gcjqQgVlwoBoAYE5K6lBF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jxL8tX1T73DpZRFb/6NsNjQ/fm89RJY0VE/07dKvpbzPGSKfK0so3ga0WwBdVTNC9Ke/l0j5Avy\nyBfkkS8mKYYs1kK+dCCv4OsO5B98+eXWS2FDNUnzkkmWmufh55/Pv+399sczIKIuuA28EQUAAPJ8\n8vZtRCzvQFZAXsHUCAtuiy/daEHN8/BU0cj4uO+GP2ibDmQAAPZKMWRTRlhAI+a+FponSwtqjseK\nwtCIGxrfAABXo2gFeTQ43Jx+6wUAAAAAANAmBWQAAAAAAEYpIG9oGIatlwCHJV+QR74gz6r5KmX+\nBgfg+HUQc1+33ryZv7GYfN2Yrpu/PTzM3xjVQr5cRG8FUxfR6/rehfUOwAzkNskX5JEvyLNqvswH\n5cY4fh3E3Ncuc1dXJV+QZ0m+XETvAO7P562XAIclX5BHvuADFhZlF+fLRW1gkuPXQcz9Qsvr1qrk\nC/K0kC8dyCuY6kDmGHQgAwC/beuuXgVkAADeuVYHshnIAAAAAACMMsICAAA+pOYsso8+mn/bjK7e\nmq5mXcUAAMygAxkAAAAAgFEKyAAAAAAAjFJA3tAwDFsvgRV13fytBaXM21olX5BHvjiEuQe6Up7G\nUszdHh7mbyPkC/LIF+SRL/iAmvedI1rIV1dargAdRNd1JSLiB19++Wz/J2/fvtjH/sxN0Oefz7/P\n+/OrlnJVc/9djdS7X5AvyCNf3Jyag/h52UFcviCPfEEe+YI8S/L1ydu3ERFRSllUvnERvRV9/PHH\nz/58fz6/2Mf+zP0O5p/9av59tvC0mPvvaqVj+n3yBXnki0OoaaL4ar2DuHxBHvmCPPIFH1DzvnOk\nyNJCvnQgr+DrDuRScwVvSFAT9/408z49rQEAAIClFhZaV1Wz1jcV/bsTY85eq+ufphcv7UA2AxkA\nAAAAgFEKyAAAAAAAjDIDGQAAAIB92NOYA3Yz6qFazXNr67VegQ5kAAAAAABGKSBvaBiGrZcAhyVf\nkEe+II98QR75gjzyBXlayFdXalrJeZWu60pERHl8fL6/71/sg0w1ce9PM++z0aewfHEIjZ6eJ1+Q\nR74gj3xBnsX5OuqYA7iCJfnq+qfe4VLKog+MOpA3dH8+b70EOCz5gjzyBXnkC/LIF+SRL8jTQr50\nIK9gqgMZ1nZLHcjQtLnHg48+mn+fuisAAAD4Bh3IAAAAAACkUkAGAAAAAGBUxeRxAGBSzZiiuaMp\njKUAAABgYzqQAQAAAAAYpYC8oWEYtl4CHJZ8QR75gjzyBXnkC/LIF+RpIV9dKWXrNRxe13UlIqK8\nd3pz1/cv9kGmmrifZg64eUw6w75mrd3ItUTli6uoeSK+qZgKtfPRFPIFVzLyGtOdTlHGXiPGDnZA\nFccvyCNfkGdJvrr+qXe4lLLozaQZyCu6XC7P/vy97373xT7IVPN10d3dvNtlPYVr1jr2KihfrG5u\naCLygrMS+YI83/vud+Py1VdbLwMOyfEL8sgX5GkhXzqQVzDVgQxru6UOZLgKHchAJgc7AAAS6UAG\nqtV89swoDNd8Tu5PFffruxmy1IRGUXhfFO7I4osnAAAOxkX0AAAAAAAYpYAMAAAAAMAoIywAgHZl\nXavB6ACyGH0DAMDB6EDe0DAMWy8BDku+II98QR75gjzyBXnkC/K0kK+uZHX28Nu6risREeXx+ZW+\nur5/sQ+ObM2L6MkX5Fk1XzqQuTGOX5BHviCPfEGeJfnq+qfe4VLKoiuDG2GxofvzeeslwGE1m6+a\nYljNadCwosX5qslBVqFXUZhGNXv8ggOQL8gjX5CnhXzpQF7BVAcy3Jo1O5CbpYAMbRSQAQAADk4H\nMsBrzC1c1RRvFcOgjouMAQAA7IaL6AEAAAAAMEoBGQAAAACAUUZYAE2qGv+bMUKi5rR5p+NTKWOS\nCgAAQHNcB+gQdCBvaBiGrZcAhzV89tnWS4DDcvyCPPIFeeQL8sgX5GkhX12p+SaAV+m6rkRE/ODL\nL5/t/+Tt2xf74MhqXm0+/3z+be/PL/dN5mvuHZ9H7hSuZG4WWv3+3fEL8sgX5JEvyCNfkGdJvj55\n+zYiIkopiz5eGmGxoo8//vjZn+/P5xf7gCeffLzs5yfzJXMkqfk+tj/NvM/H160lm+MX5JEvyCNf\n3JwVRwfI143JGCMZYeTjhBbypQN5BV93IJfHRisBACx2SwVkAAB2wOxZsigg70bXP00vXtqBbAYy\nAAAAAACjjLAAAACAa9L5SRadn7Sg5nXLc+sQdCADAAAAADBKARkAAAAAgFEKyBsahmHrJcBhyRfk\nkS+4klJebMMwjO4Hllt8/BrL5tT25s38DWp03fzt4WH+tpD3h5CnhXx1xRvSdF3XlYiI8vj4fH/f\nv9gHXId8sbaaw2l/mnmfjT6F5QuuZOSFozudoox9kDcjFRZbfPwyexYmeX8IeZbkq+ufeodLKYve\nTOpA3tD9+bz1EuCw5AvyyBfkkS/II1+QR74gTwv50oG8gqkO5Fsz96mmwQbYo5rD6WlmU9KjhiTY\nHx2KAPtT89rtAyuwI9fqQDZwaUWXy2XrJWxq7iHZ4RjYo5qvY+/u5t3uxg8bcHxzXwwivCAAALAZ\nHcgrOHIH8i3N/AQA4IbpUIR9cUYIgBnIAAAAAADkUkAGAAAAAGCUAvKGhmHYeglwWPIFeeSrYaXM\n32iSfK2sJjNv3szfaJJ83Zium789PMzfGCVfkKeFfJmBvIKpGchd3+9+LrIZyLTqCPmCVslXw8xo\n3T35WpkZqTdFviCPfEGeJfkyA/kA7s/nrZcAhyVfkEe+II98QR75gjzyBXlayJcO5BVMdSAfgQ5k\ngIPT0bo9HZIAAMAr6EAGAAAAACCVAjIAAAAAAKNcIhiA5Yw52BcjEfalJjMeAwAA4Mp0IAMAAAAA\nMEoBeUPDMGy9BDgs+YI8gwvwQhrHL8gjX5BHviBPC/nqig+B6bquKxER5fHx+f6+f7Fvb2qePv1p\n5n3u+1dyexodXXCEfG3OmAMmyBfkkS/II1+QR74gz5J8df1T73ApZVFBRgfyhu7P562XAIclX5BH\nviCPfEEe+YI88gV5WsiXDuQVTHUgH4EOZFrtQOYKdCADAADAbl2rA7niEz9wU+Z+4fHRR/PvU+Fw\nX2oK/h5bAAAAOCQjLAAAAAAAGKWADAAAAADAKCMsWMT4252pecDmjqYwugAAAAAYo3B0CArIK7pc\nLs/+/MUXX8Snn366yVqupeZ14O5u3u3e+zWxlZ0/YEfIF7RKviCPfEEe+YI88gV5WshXV2oqgLxK\n13UlIqK8d1Gyru9f7GtBzVOiP1Xcb3v/VA6s1XzBEcgX5JEvyCNfkEe+bkzNYz337OYIZzhPWJKv\nrn+aXlxKWdTebQbyhu7P562XAIclX5BHviCPfEEe+YI88gV5WsiXDuQVTHUgt0oHMgAAAACjdCDv\nxrU6kM1ABgAAAG6Xi3zBk7lZUBS+OUZYAAAAAAAwSgEZAAAAAIBRRlgAAADQPmMGqFHzfHlTURpx\nOj5HNve1Uw5ujg7kDQ3DsPUS4LDkC/LIF+SRL8gjX5BHviBPC/nqSs23crxK13UlIqK8d5XKru9f\n7GtBzVOiP1Xcb3v/VA6s1XzBEcgX5JEv+ICFHcjydWN0IK9KviDPknx1/VPvcCll0ak5Rlhs6P58\n3noJcFjyBXnkC/LI1wSjC45rxSKffN2YmtcCReHF5AvytJAvHcgrmOpAbpUOZAAAmqKAfFy6RAEg\nzbU6kM1ABgAAAABglBEWAMDt0c0IbZibRZ2nx2XMAAA0TwcyAAAAAACjFJABAAAAABilgLyhYRi2\nXkKbSpm/wQT5gjzN5qvm+PHmzfwNVtRsvrJ03bzt4WH+BhNuLl+wIvmCPC3kqyuKcOm6risREeXx\n8fn+vn+xrwU1T4n+VHG/c/+p5lJyBa3mC46g2XzVHD/MU6VRzeYLDkC+II98QZ4l+er6p97hUsqi\nApq2mg3dn89bL2Gxqvqti6SwoiPkK4PvZ7iGZvPlQkwcQLP5ggOQL8gjX0zyIXSxFvKlA3kFUx3I\nrap5Spwqar2Pv6WADFtz7AYAAGA1PoRuSgfyDl0ul62XMEvNVwp3d/Nve/kq404v828LVOXboRsA\nAADQgbyCvXUgA/sz96U8ZW45AABwO3SU4toju3GtDuT+KqsBAAAAAOBwFJABAAAAABilgLyhYRi2\nXgIclnxBHvmCPPIFeZrNVynzN8hS8zx88+bFNpxOo/s5qK6bvz08zN8Y1cLxywzkFUzNQO763lxk\nSHJr+TIDmTXdWr5gTfIFeZrNl3mytGDhTNuulChjz09FQVhsyfHLDOQDuD+ft14CHJZ8QR75gjzy\nBXnkC/Lcb70AOLAWjl86kFcw1YEMcC06kAEAGlLz2e+jj+bfVjcnABV0IAMAAAAAkEoBGQAAAACA\nUS6JCQAAwA83d2bWUS/0VjP+0VgKAA5EBzIAAAAAAKMUkDc0DMPWS4DDki/II1+QR74gj3xBHvmC\nPC3kqys1p+HwKl3XlYiI8t6VeLu+f7EPuI5by9fcl/L+VHGft/Pro9Kt5QvWJF+srubz4GnmG4lG\nn8PyBXnkC/IsyVfXP/UOl1IWzZfSgbyh+/N56yXAYckX5JEvyCNfkEe+II98QZ4W8qUDeQVTHcgA\n16IDGQAOruZzW81F7Gru983Ma7C7KBwANEEHMgAAAAAAqRSQAQAAAAAYNfMcJAAAgCubOz6hZiTD\nnmSMj4ioGyFR87s1mgIAbpIOZAAAAAAARikgb2gYhq2XAIclX5BHviCPfEEe+YI88gV5WshXV2pO\nm+JVuq4rERHl8fH5/r5/sY86WRejZv9uLV9zs3CqOPv10VmqTLi1fMGaDpGvjLEMRidwBYfIFzT6\nIVi+IM+SfHX9U+9wKWXRC4IO5A3dn89bLwEOS74gj3xBHvmCPPIFeeQL8rSQLx3IK/i6A/kHX365\n9VIOp+bZqwGZI5ubhc8/n3+f99sfowA4urkHpgY+OAEA7M0nb99GxPIOZAXkFUyNsGBczVOyP1Xc\nr18/AAB71ehp68CVzM343NE/Ecb/AEZYAAAAAACQSwEZAAAAAIBRFec+AAAANG5Pox5q1uq0dTi2\nua9H8g1sQAfyhoZh2HoJcFjyBXnkC/LIF+SRL8gjX5CnhXy5iN4Kpi6i1/W9C+uNcBE9rkG+II98\nQR75ugIdyDoUJ8gX5JEvyLMkX9e6iJ4RFhu6P5+3XgIclnxBHvmCPPI1oeZD00cfzb/t1oXWmgL2\n1ms9APmCPPIFeVrIlw7kFUx1IDNOBzIAAM8ctYAMAJBIBzLAHu3ptFoAyDb3uKgoDACwGRfRAwAA\nAABglAIyAAAAAACjjLBg15zhTxNcQZ1Kc58yXuOAw5v7QueYCACvY4wiV6ADeUPDMGy9BDgs+YI8\n8gV55AvyyBfkkS/I00K+ulLzTQSv0nVdiYj4wZdfPtv/ydu3L/YRUfOM/Pzz+be9P1cvhR1rNl81\nT9qzJ+1RzX2da/X7/2bzBQcgX5BHviCPfEGeJfn65O3biIgopSz6eGmExYo+/vjjZ3++P59f7KPO\nJx9vvQJa1Wy+WlwTV1HzfWx/mnmfj69bS7Zm8wV7M/LCcX8+x8d3dy9v65RSWMzxC/LI18qMUbwp\nLeRLB/IKvu5ALo+NVgIAWOyWCsjAlZhJCAC8hgIyM3X90/TipR3IZiADAAAAADDKCAuAhTSQUcvz\nAA5MRxAA1POhqk7N78B7CK5AAXlFl8tl6yUACWoGAXmrc1w1z4Ox8aZjHDbg4Oa+GER4QQAAYDNm\nIK/ADGQ4Nl+WE1H3PDjN/Pr2UbMA7I8OZACo50MVpDAD+QCGYdh6CXBYS/NVyvytP83fOK6um789\nPszbWuX4BR9Q82Lw8PBiG37u50b3Q5qaNz075/gFeSbzNff15c2b+RvcmBaOXzqQVzDVgdz1va5k\nSLI0XzUvjTWF4SLyHIDjF+SRL1Z3Q11/8gV5JvM19zXGWTkwacnxSwfyAdyfz1svAQ5LviCPfEEe\n+YI88gV55AvytJAvHcgrMAMZ9kcHcqUb6l4CgOaZxQ0AhA5kAAAAAACSmT4OsMx5TlcAACAASURB\nVNBhG2p1LwGNcJIDVKoJguMyALW8Obs5OpABAAAAABilA3lFl8tl6yUAM9VMh7+7m3/bw74M+CUA\niWpek/W4AADAdbmI3gqmLqI3DEMMw7DFkuDw5AvyyBfX4GKl4+QL8sgXXMnIQXz47LMY7u9f3tb4\ngn2Z+wbNCMNVLTl+XesiegrIK5gqIHd9/2IfcB3yBXnki2tQQB4nX5BHvuBKRg7i3ekUZaxQqIC8\nLwrITVpy/LpWAdkM5A3dn89bLwEOS74gj3xBHvmCPPIFeeQL8rSQLx3IK5jqQAYAuFU6kAF4lbkH\nEJ2vdWoOzLpPYTd0IAMAAAAAkEoBGQAAAACAURXnHQAAAHAoNaetGwlAlozxCUYn1KnJt98t3Bwd\nyAAAAAAAjFJA3tAwDFsvAQ5LviCPfEEe+YI88gV55AvytJCvrtScKsKrdF1XIiLK4/PLgnd9/2If\ncB3yBXnki2uoeQvanyrud+dPTfliUtbntrnjACJ2f9q6fEEe+YI8S/LV9U+9w6WURXOodCBv6P58\n3noJcFjyBXnkC/LIF+SRL8gjX5CnhXzpQF7BVAcyAMCt0oEMlXQgAwCVrtWBXPFuAdbhQtAAwDc5\n3nNYNW98swq9isIA1FK4uTkKyCu6XC5bL2EXanorvAwBwD7VHO/v7ubf1tstDksQAICN7HaERdd1\n/1JE3EXEPxURfzgivhURv1hK+e4HfuY7EfFvRcS3I+JHIuJXIuI/jIifL2X8hMeu6/5ERPzMu7/n\nFBH/fUT8e6WU/6hirUZYVPBFFgAcX83x/lTR8vComZI9aaEDGQBqKdzshhEWT4XgfzIifiMi/qeI\n+Mc/dOOu634yIv7jiPi/IuKXIuLXI+JfiIh/JyK+ExH/ysjP/LmI+CsR8fcj4q9HxG9GxE9FxBdd\n1/0TpZR/81r/mFsw9/XFnEMAOL6azxKKwhxWTRAUhQF4jYzGUV9q3px+6wUs8G9ExI+VUn40Iv61\n+MA0g67rvhUR/35E/FZE3JVS/mwp5S/GU1fx34yIn+q67l9+72d+f0T82xHxv0bEHy2l/OullD8f\nT0XrX42IP9913beX/AOGYVjy48AHyBfkkS/II1+QR74gj3xBnhbytdsRFt/Udd1dRPwgJkZYdF33\nZyLiP4iIL0opf+a9//ZJRPxyRHxVSvnkG/s/j4ifjYjPSimfv/czfzoifiEi/lop5U/PWN/oCIuu\n729qrIUOZNZ0a/mCNckX5JEvyCNfXIVT90fJ18qMQLopS/J1rREWe+5ArvFJPF2r5T8b+W//eUT8\nnxHxna7rPnrvZ2LiZ/7Td//7dsmi7s/nJT8OfIB8QR75gjzyBXnkC/LIF+RpIV+30oH8X0XEH42I\nHy+l/Lcj//2/i4g/FBF/qJTyP7zb979ExO+JiH+0lPK/jfzMP4iI3xkRv6uU8n//kPW5iF7oQAYA\nAGDndCDTAh3IzOQienV+9N3//u8T//3r/f9I5c/8zne3+2ABGQAAAHbvqMVTxTj2xkVYWdmtjLD4\nYb5OXk079mt+BgAAAABgN26lgPx1F/GPTvz3f/i929X8zP8xdxFd309uLVxREQAAAADYj2EYJuuN\n13IrM5D/ekT8qYj4U6WUX3rvv53iqVj8UUT8Q6WU//fd/v8iIr4TEd8ppfyt937m90bE/xwR/2Mp\n5ffPWN9hZyBnPH1OFWcEPToTAwAA4KWMD2vGNwDsihnIdb6MiH81Iv75iPil9/7bXTzNMr58XTz+\nxs/80+9+5m+99zN/7N3//nLNIi6Xy7M/f/HFF/Hpp5/W3EVzMr5+uLubf9v3fqXw246QL2iVfEEe\n+YI88nUFPqwxQb4gTwv5upUO5G9FxK9GxLci4p8ppfztd/t/x7uf+3ZE/HQp5fvf+Jk/EBF/NyJ+\nIyJ+vJTy997t/90R8V9HxB+Mke7kifWNdiB3fb/7rmQdyLTqCPmCVskX5JEvyHNz+dKBzIpuLl+w\noiX5uvkO5K7rfjIi/sV3f/y97/73O13X/dV3///vl1L+QkREKeUfdF33ZyPi+xFx6brub0TEr0fE\nn4yIH4uI73+zePzuZ36t67q/EBF/OSL+m67rfikifjMifioifl9E/KU5xeMPuT+fl/x4mpr3Gf2p\n4n5nPtcVhbmGVvMFRyBfkEe+IM9kvuZ+AOoWffa+jpoPa3OLvTWFXkVhJjh+QZ4W8rXbDuSu6+4j\n4kO/wV8rpfxj7/3MT0TEz0bET0TEj0TEr0TEL0TEz5eJX0TXdX88In4mIv5IPF108O+8u/0vVqx1\nVzOQty4gAwAArEYB+XVrAaB51+pA3m0BeU8UkN/d7z7++QAAwC1RQH7dWgBo3s2PsAAAAGChmoJk\nCwXUuY5aaK15DFpYLwCH0G+9AAAAAAAA2qSADAAAAADAKAXkDQ3DsPUS4LDki5tTyvxtIfmCPPLF\nVdQcE968mb/tSde92IbPPhvdHw8P8zZgkuMX5GkhXy6it4Kpi+h1fd/khfVcRI8jaDVfkGbFGZby\nBXnki6vImP8bsfsiqnxBHvmCPEvy5SJ6B3B/Pi/6+Raud7Gn62hwW5bmC5rQaAFAviCPfHEVLrQ2\nSr6uoIUPoTRJviBPC/nSgbyCqQ7kpbKO3TX3e6qoVzzezntTgOtotIAMANwoBWSAXdGBvEOXy+Wq\n91dT+q95ltTc793d/Nte+Z8PwDd5QQYAACCBDuQV1HYgz31IzB8GAABYyVG7b53xBHBY1+pA7q+y\nGgAAAAAADkcBGQAAAACAUQrIGxqGYeslwGHJF+RZnK9S5m9wYxy/IM9kvuYek968mb/tSdfN3x4e\n5m/cFMcvyNNCvsxAXsHUDOSu70fnIpuBDMtN5QtYbnG+jjpDEq7A8QvyTOZr7nHJ/F+Y5PgFeZbk\nywzkA7g/n7deAhyWfEEe+YI88gV55AvyyBfkaSFfOpBXMNWBPEUHchIdbwC5dHABAAA0QwcyAAAA\nAACpFJABAAAAABi1s8vD8k01UxYOO72h5h/mlGmAXHMPIF5jAeD/d9gPawAchQLyii6Xy6zbzX37\ncHdX8Xd/Nf+2h31LUvULu6QtAwAAAAD2wkX0VjB1Eb1hGGIYhhe3n/uQnGoaan9r/m139aW2DmQm\nTOULWE6+II98QZ5m86UDmQNoNl9wAEvyda2L6Ckgr2CqgNz1/Yt9NWoeuv5Ucb+vXxI0Y2m+gGny\nBXnki6tQkBy1ar40unBjHL8gz5J8XauA7CJ6G7o/n7deAhyWfEEe+YI88gV55AvyyBfkaSFfOpBX\nMNWBvJQOZAAAboKOWh2tAEA1HcgAAAAAAKRSQAYAAAAAYFTFuU0ABzD39M+jnv4KAC2Ze1w2kqHu\nvclRfwcAwCZ0IAMAAAAAMEoBeUPDMGy9BDgs+YI88gV55AvyyBfkkS/I00K+ulJzNV9epeu6EhFR\nHh+f7+/7F/tq1Dx0/anifmuW5IrYtGDkedidTlHGTt+cewqsUz9h0tLjFzBNviCPfEEe+YI8S/LV\n9U+9w6WURUU5Hcgbuj+ft14CHJZ8QR75gjzyBXnkC/LIF+RpIV86kFcw1YG8lA5keKfmeagDGQAA\nALgB1+pArricMa1Jq91mFOMiFOTI46rkAAAA69BIBjdHAXlFl8vlqvdX85p9dzf/tpevKhZRdceX\nijsGAAAAALZmhMUKskZY1Nzdm48q7ve3dCADAAAAI3Qgw24YYXFgc1+LTxWPXtVc4zAOAACa4UMa\nAJDNKEvgA/qtF3DLhmHYeglwWPIFeeQL8sgX5JEvyDM4ux3StHD8MsJiBVMjLLq+Hx1rMfch6U/z\n11DXgQz7N5UvYDn5WpkO5JsiX5BHvuADFnYgd6VEGXsfogMZFlty/LrWCAsdyBu6P5+3XgIclnxB\nnlXzVcr8bU9q/l1v3szf2D3HL8gjX/ABXTd/e3h4sd2fz6P7geVaOH7pQF5B7UX0dCADwDtH7b41\nZxAAAEjmInoAwD7VnH710Ufzb7un4mlNsXtP/y4AAOBwjLAAAAAAAGCUAjIAAAAAAKOMsACAKUed\nv5tl7u/rqGMpAAAADkgH8oaGYdh6CXBY8gV55AvyyBfkkS/II1+Qp4V8daWmu4pX6bquRESU9y4a\n1PX9i30R8xu4+tP8NZSK6xXBEUzlC6roQB41ma+5v683FSdA6UDmxjh+QR75gjzyBXmW5Kvrn3qH\nSymLPrAaYbGh+/N5vb9MEYQbs2q+2Jea10OFzlGT+Zp7/Lih3xXUcvyCPPIFeeQL8rSQLx3IK5jq\nQJ6S0oH8oIAMEBEKyAAAANyEa3Ugm4EMAAAAAMAoIyx2rOarg3Ka/1B3j7rogAOrOcsiq6t4bhe0\nM0IAAADYmALyii6Xy6zbzT25+u7jir877mbftpu5TgAAAADg2MxAXkHWDORTxQzkh5h/Yx3IAMl0\nIAMAAJDMDOQDGIZhdH/XzdseHuZvfTzM3uAIpvLFzpQyb2vB3LWW8nRxvjlbo+QL8sgX5JEvyCNf\nkKeFfOlAXsFUB3LX97O7ksfUPHR9Rbdyef2SoBlL80Uj9tSpW/OiPLc4nDWDeSH5gjzyBXnkC/LI\nF+RZki8dyAdwfz5vvQQ4LPmCPPIFeeQL8sgX5JEvyNNCvnQgr6B2BvJcOpBJtafOT/blhjp1AQAA\nYCs6kAEAAAAASKWADAAAAADAqHYv8Q5z1JwKb9SC0QG0oSaLnl8AAACwKR3IAAAAAACMUkDe0DAM\nq/1dXTd/21wp87c3b+Zv1D0RHh7mbY1aM19wa+RrXTWHRfZPviCPfEGeVfPlzRE3poXjV1cEKl3X\ndSUiojw+Pt/f9y/21ah56E4V9dPHrWuCGWMWIpoudnJ9S/MFTJOvdZnWdFvkC/LIF+RZNV/eHHFj\nluSr6596h0spi8KgLXNFl8vl2Z+/993vvthXo6b0f3c3/7YLlrS+w/7DWGppvoBp8rWumuO9j0j7\nJ1+QR74gj3xBnhbypQN5BVMdyADAbap5+9WfKu7XWw0AOLajdt86ExlSXKsD2QxkAAAAAABGKSAD\nAAAAADDKDGQAAADgWPY26mHueo86vqHmMdjTvwsOQgcyAAAAAACjFJA3NAzD1kuAw5IvyCNfkEe+\nII98QR75gjwt5KsrNad18Cpd15WIiPL4/NLoXd+/2Adch3xBHvlarubtV3+quF8Py+7JF02b++LV\nwjiAEfJ1ELc+6qFR8gV5luSr6596h0spiw7OOpA3dH8+b70EOCz5gjzyBXnkC/LIF+SRL8jTQr50\nIK9gqgMZALhNOpCBXdp5BzIHoQMZYLZrdSBXvKICAAD8EDXfkCg0bq/m8ZpbkFOMI9Pc1w3PQ4Cr\nMcICAAAAAIBRCsgAAAAAAIwywgIa5MxPAL7mdZ4mZIw5iHCKeQtqXmQ8XgDHZtY9ExSQV3S5XJ79\n+YsvvohPP/10k7XQtppLW3rZHidfkEe+lqt5nb+7m3/b995qsEOHyJcnLY06RL6gUfIFeVrIV1dq\nugl4la7rSkREeXx+afSu71/s47hqotafKu7XU2iUfEEe+YI88gV55AvyyFfDaooRp5nFCI/1qpbk\nq+ufpheXUhb1H5qBvKH783nrJcBhyRfkkS/II1+QR74gj3xBnhbypQN5BVMdyNwWHcgAAADAqnQg\n37RrdSCbgQwAAHBNLkIEwB45LjHBCAsAAAAAAEYpIAMAAAAAMMoICwDgGGrmuzk9D6hV8xrzZubH\nrIeH160FAOaqed/ruMQEHcgbGoZh6yXAYckX5JEvyCNfkEe+II98QZ4W8tWVmm/SeZWu60pERHnv\nKpVd37/Yx3HVRK2feeHTiIjiKTRKviBPs/nSgcwBNJsvdCAfgHxBHvmCPEvy1fVPvcOllEUfgIyw\n2ND9+bz1EuCw5AvyLM5X1pfXcws2EYo2NMvxq2FOAd49+YI88gV5WsiXDuQVTHUgc1t0IAO8o4AM\nAACQ7lodyGYgAwAAAAAwygiLG2Es5L54DIBdmnuwyeoU1lUMsD8+qABA8xSQV3S5XDb7u2tOFva2\nLEfNY3B3N/+2Gz6tAF7HixwAAMBumIG8ghZmIPtif3s1j8Gp4qudRw13QCu27kAGYH98UAGANGYg\nH8AwDIt+vpT5W3+av5Gj6+Zvjw/zN8YtzRcwbTJfc1/kHh7mb7A3NW/QRjh+cQg1OXjzZv62kHxB\nHvmCPC3kSwfyCqY6kLu+X9SVXPPQ1RSGy3aN0nA1S/MFTJMv+ICF3ZTyxSHU5GDFs1LkC/LIF+RZ\nkq9rdSCbgbyh+/N56yXAYckX5JEvVrf1Ke4rFsPki0OoyeGKZ5vIF+SRL8jTQr50IK8gawayDmQA\n4CbcUAEZAACuxQxkAAAAAABSGWEBAMD6as7M+uij+bfN6Opt9HR8AABYgw5kAAAAAABGKSADAAAA\nADBKAXlDwzBsvQQ4LPmCPM3mq5T5GzlqHoOPPpq/PTzM33au2XzBAcgX5JEvyNNCvrriQ1S6rutK\nRER5b9Zf1/cv9tWoeej6U8X9vn5J0Iyl+QKmNZuvmgNjzUxb5qt5DN5UXIrjAIXhuZrNFxyAfEEe\n+YI8S/LV9U+9w6WURR+AdCBv6P583noJcFjyBXnkC/LIF+SRL8gjX5CnhXzpQF7BVAfyUjqQiQgd\nd8Cx6WgFAAB4FR3IAAAAAACkUkAGAAAAAGBUxbmecEO2HgvhlG2AJzWvsV7jAAAArk4HMgAAAAAA\noxSQNzQMw9ZLgMOSL8gjX5BHviCPfEEe+YI8LeSrKzWnyvMqXdeViIjy+Ph8f9+/2BdRN71grlPF\nlIPHo54BbCzETZnKF7CcfEEe+YI88gV55AuuZKR21Z1OUcZqTzPG/XV9/+5uy6L5q2Ygr+hyuTz7\n8/e++90X+yIiMkr6d3fzbzuypNvjF7Z7U/kClpMvyCNfkEe+II98QZ7vffe7cfnqq03XoAN5BV93\nID8+zPs2rj/Nu9/iyz0AAPZs7meRjIsWAwCsYcMz4q/VgWwGMgAAAAAAoxSQAQAAAAAYZQYyAABw\nPTUXUfroo3m3c9FiAGCvakZxNfqeRwcyAAAAAACjFJA3NHw2bL0EOKxhGLZeAhyWfEEe+YI88gV5\n5AvytJCvrtRcCZBX6bquREQ8Pjw/na8/9S/2Pe2fd7+l4uxAuDVd30epOYUWmE2+Glbzvq7mVDpW\n02y+Nrx6OFxLs/mCA5AvyLMkX13/1DtcSln05l8H8obO5/PWS4DDupcvSCNfkEe+II98QR75gjwt\n5EsH8gqmOpCn6EAGAF5FBzJZdCADAOzOtTqQK97dsRaf547JZ3oAXkXhjhYc4OrhAAAfpHAzSQF5\nRZevLrNud3c38/7m3R2NqOn1v62XIQCuZu6biAhvJAAAgFmMsFhB7QiL08yy/qPmjl3xRRYAr6ID\nGQAA8h2wcGOExQ7NfW4pDO/L3NeXubOtI8y3BuAb9jQ64IBvugEA2Lm571E1Y0zqt17ALRuGYesl\nwGHJF+SRL8gjX5BHviCPfEGeFvJlhMUKvh5hUR6ft5V2ff9iH/ujA7lN8gV55ItJOpAXky/II1+Q\nR75o2s47kJfkywiLA7g/n7deAhyWfHEVimGj5OvGmMG8KvmCPPIFeeSLps39rNbo+9MW8qUDeQVT\nHcgcgw5kODAFZFBABgCAnbpWB7IZyAAAAAAAjDLCAlaiObENcxvpPF4HppsS6tS8IMoBtMEZNADA\nFSkgr+hyuWy9BBLMfXt+dzf/Pj1V8sx9vHyUIiIEFwAAgJtnBvIKzECGXDUvY3NnUZtDDfCOTkZo\ngzNoAIBKZiAfwDAMWy8BDmv4bNh6CXBYjl+QR74gj3xBHvmCPC3kSwfyCqY6kLu+15UMVzD2Mtaf\n+nh8eJkvHciwnOPXjdGBvCr5YpIO5MXkC/LIF+RZkq9rdSCbgbyh+/N56yXAYZ3lC9I0e/xS6Kwz\n9/elELWqZvPF9lzQcjH5gjzyBXlayJcO5BWYgQy5zEAGIkIBuZYCMgAAHJoZyAAAAAAApDLCAgBu\nzZ46dc38zDP3sfW7AgCAm6YDGQAAAACAUQrIAAAAAACMUkDe0DAMWy8BDmv4bNh6CRxBKfO3rdWs\n9c2b+duIVY9fXTd/e3iYv0GjvD+EPPIFeeQL8rSQr6608KH34LquKxER5fHx+f6+f7EPqDf2Mtaf\n+nh8eJmv/jTzPkWTCLOCI0aLrY5fkEe+II98QR75gjxL8tX1T73DpZRFH1h1IG/o/nzeeglwWGf5\ngjSOX5BHviCPfEEe+YI8LeRLB/IKpjqQgeuoeRnbVQfynrpf92TFTl0AAADYig5kAAAAAABSKSAD\nAAAAADCq4txcYO9MRGjg32V8wvZqngR+rwCQyxtUAGieAvKKLpfL1kvgxtVMPN/T2/Oaf9fd3bzb\nNRHXuYuNaGTBAAAAwNG4iN4Kpi6iNwxDDMOwxZI4kIwLyEU0chG5BeQL8sgX5JGvG3PU7ttGz7iS\nL8gjX5BnSb6udRE9BeQVTBWQu75/sQ9qKSCPky/II1+QR75ujALyqgVk+YI88gV5luTrWgVkF9Hb\n0P35vPUS4LDkC/LIF+SRL8gjX5BHviBPC/nSgbyCqQ5kuAYdyACwU0ftPmX+Y+uCuQBAIh3IAAAA\nAACkUkAGAAAAAGBUxTlTAHBjnF4O1Gr04mGsbO4xweMKAOyADmQAAAAAAEYpIG9oGIatlwCHJV+Q\nR74gz+AC15DG8QvyyBfkaSFfXfEmNV3XdSUiojw+Pt/f9y/2Qa2aCPenivvd+VNzcb6MLjgup5cv\n5vgFeeQL8sgX5JEvyLMkX13/1DtcSllUuNCBvKH783nrJcBhyRfkkS/II1+QR74gj3xBnhbypQN5\nBVMdyHANOpCT6EA+Lh3IAAAA3IBrdSBXfDIG9k6dM+YXDxUOj6smCB5bGuD7LACAG+BNHw1TQF7R\n5XLZegkcUM05BHd38297809XvyygETWv8z5KAAAA12aExQqMsCBTTYRPFV8ZPR618VIHMrAzmlEA\nAG6AN30kMMICiIi648Zhi8I15v7CFIWBRObXA0BDFO7I4vorHES/9QJu2TAMWy8BDku+II98QR75\ngjzyBXnkC/K0kC8jLFYwNcKi63tjLSCJfEEe+VpOBzJTJvM190mjMw4mOX7dGJ2fq5IvyLMkX9ca\nYaEDeUP35/PWS4DDki/II1+QR74gj3xBHvmCPC3kSwfyClxEDwD4Jh3IVNOBDFBHBzKAi+gBAMCu\n1RQ3TjO/SdCwAPCk5gs1RWGADzLCAgAAAACAUQrIAAAAAACMMsICAG5MzVnzxqluz2NARHgiAAC8\nlmtJLKYDeUPDMGy9BDgs+YI88gV5hs8+23oJcFiOX5BHviBPC/nqSk0bEq/SdV2JiPjBl18+2//J\n27cv9gHXIV8wrebIP/YdvHwtV/MYfP75/Nven6uXQmMm8zX3iXD2JIApjl+QR74gz5J8ffL2bURE\nlFIWtVcbYbGijz/++Nmf78/nF/uA65Avbk3N98H9qeJ+H1/uk691ffLx1itgTZP5kjlYzPEL8sgX\nV5HV5PpmZvnz4SHn71+ohXzpQF7B1x3I5XHkUzgAXMGaBWQAAICrU0C+uq5/ml68tAPZDGQAAAAA\nAEYZYQEAAABwNDXdnN2i5kSYVvM8nNspHFHXLXzAzuK16UAGAAAAAGCUAjIAAAAAAKMUkDc0DMPW\nS4DDki/II1+QR74gz+J8lTJ/gyw1z8M3b+ZvCzl+Manr5m8PD/O3G9JCvrri4Jau67oSEVEen1/K\nvuv7F/uA65Avbk3N4bw/VdzvSIzkC/LIF+RZnC/zZGlBC/NkRzh+QZ4l+er6p97hUsqiA5OL6G3o\n/nzeeglwWPIFeeQL8sgXfMDCAu5kvube74rFOJhU8+XEis9Dxy/I00K+dCCvYKoDGQCuZc0OZADY\nRFYHsAIyAAd1rQ5kM5ABAAAAABhlhAUAAMCt2nqubwvzXOf+u3QVA3CjdCADAAAAADBKARkAAAAA\ngFEKyBsahmHrJcBhyRfkkS/II18HUcq8beu/v5SnsRBztwxdN397eJi/jZAvyCNfkKeFfHUl840L\nERHRdV2JiCiPzy9l3/X9i33AdcgXt6bmcN6fKu53JEbyBXnk6yDmvihnzBSu+fsj8uYKN0i+II98\nQZ4l+er6p97hUsqiNx06kDd0fz5vvQQ4LPmCPPIFeeQL8sgX5JEvyNNCvnQgr2CqAxkArmXNDmTg\nBtW8yGR11W4to6t35x29AEDbdCADAAAAAJBKARkAAAAAgFFJl9IFWI+zaqGOHAAR4UJrtWpePI/6\nOwDgydYXS4WVKSCv6HK5bL0EOKSaSe4O3xxVTQ7u7ubf1qELiAgvHAAAN8xF9FYwdRG9YRhiGIYt\nlgSHMvYyNnw2xHA/vNjvC2COquZwfqr4+vhxpInO8QvyrJovHcjcGMcvyHNz+dKBzIqW5OtaF9FT\nQF7BVAG56/sX+4AnNS9N/Wl0b0S8zFcROVjM8QvyyBfkkS/IszhfLcwlzPhi1ZeqXMGSfF2rgOwi\nehu6P5+3XgIcmHxBFscvyCNfkEe+II98QZ4W8qUDeQVTHcjAtOUdyBP3K4bA/9fenYdLUlcHH/+e\nO6gRMBhxJ6gsLiTGRIyE5dVZwBWXLLigEYlLNgnEuL1RM3MZTWIWl6hv1MQgGDcUlcjrAsLMBYKi\nSSQxSkAElSUIQgREFnXm5I9fNfT0rb63+/atXr+f5+mnZqqqq391b59b1adPnZIkSdJ4sQJZasRq\nVSB7Ez1JE8+2Upo0tkyTJEnSTOj1xHcceu33c/I964nhcUj4a6hMIA/RgneklnrWz7UR3hhek6bX\n97enWpIkSZoJfqiTxpotLIbAFhaSNP2aaLtiyxVJklbI6jhJ6t8kVYyrJ95ET5IkSZIkSZLUKBPI\nIzQ/Pz/qIUhTy/iSmmN8Sc0xvqTmzB9//KiHIE0tj19Sc8YhvmxhMQTdXh/QOAAAIABJREFUWljE\n3JxtLaSGGF8atllqYWF8SUsY8LJ540taQj/xVXN5dWSSde0qvLxaGpjHL6k5g8SXLSymwKaNG0c9\nBGlqGV9Sc4wvqTnGl9ScTaMegDTFPH5JzRmH+LICeQi8iZ4kTb9ZqkCWtARv3CU1Z8AK5K6sQJYk\nTanVqkDu46gqSdJsaeo7VnNG0oQxaSWNh34OoMaXmuIXhZJmkAnkIVpYWBj1ECRJfWjqGp21a3tb\nz8OGNIF6DXAwyCVJkjQRbGExBLawkKTJ1NQhck2PX99ut3hKGg9WIEuSWqxAljRBbGEhSdIKNNGr\nGPrrV2xiWJowTV02bxJCksaDXxRK0pLmRj2AWTY/Pz/qIUhTy/iSmmN8Sc2ZP/74UQ9Bmloev6Tm\nGF9Sc8YhvmxhMQTdWljE3JxtLaSGGF/qZhwqkCed8SWtkpo/SLFmDVlXsWYFsjQwj1/qygrkgRlf\nUnMGiS9bWEyBTRs3jnoI0tQyvrQazNfUM77Glx0RxsCASYhNXebPUhJCaorHL3Vlq6KBGV9Sc8Yh\nvqxAHoJWBfLWLVtGPRRJmnn9HPU2b+593U2jP6ZLfb2/J/tj6pTo54/MGHxwkCRJ0mRZv2EDMHgF\nsgnkIejWwkKSNHz9HPbW9HGdjjfG0ziYoUKn8eVl0JKkFg/MkkbMFhaSJK1AP+fmJoU1DuzbPWGa\nugxakibNtCZP/aJQ0gyaG/UAJEmSJEmSJEnjyQpkSZIkSVrOtFZTSv2w+tYrTSTNJCuQR2h+fn7U\nQ5CmlvElNcf4kppjfEnNMb6k5hhfUnPGIb68id4QdLuJXszNeWM9qSHGl9Qc42u47IE8W4yvMWYF\n8sQzvlaBFcjqwviSmjNIfHkTvSmwaePGUQ9BmlrGl9Qc40tqjvHVRVPJW5NhM8X4WgW2b1AXxpfU\nnHGILyuQh6BbBbIkSdJyrECWMIEsSZK0AqtVgWwPZEmSJEmSJElSLVtYjKFeCyFsrSZJktp5bqCJ\n0+uJb1PVv16OL0mSxsmY3nPBBPIQLSws9LRer28VPyNKkjT9+mk2tnZt7+v2eFoijQff3JIkSSNj\nD+Qh6LcHshXIkiSppZ9TtTV9lAZst5hS42DUFciSJEnjZJUrkO2BPIEyd3xsmp9fNC+z3ACnl4ek\n7ubn50c9BGlqGV/DFdH7Y/u23h8aTzMXX72+ubdt6/0hdTFz8SUNkfGlmVOX0FuNx047LXrMr1lT\nO3+YrEAeglYF8vZtO1Ygz62ZWzSvzO9tu949Xeou5uZ6rvqX1B/jS2qO8SU1x/iSmmN8aeY0lU+t\nSQxHJllXbdzDF+dWIE+BjRs3jnoI0tTaZHxJjTG+pOYYX1JzjC+pOcaX1JxNox4AViAPRbcK5G6s\nQJYkSXcY0zsxS5IkSVOln/PuCbk/gxXIkiRJkiRJkqRGmUCWJEmSJEmSJNUa7i37JEmSbMkwlZfH\nSZIkSROtn88eM3bebQWyJEmSJEmSJKmWCeQRmj9+ftRD0DTI7P0xQ+bn50c9BGlqdY2vXv8W7bRT\n749pFdH7Y9u23h+aeB6/pOYYX1JzjC+pOeMQX5EzllQahYhIgO3btu8wf27N3KJ5ZX5v283FT9Us\n8lLwWjE3R243SKQmdI2vXv8e2ZJB6srjl9Qc40tqjvElNWeQ+Iq5UjucmQMlhKxAHqGNGzeOegjS\n1NpkfEmNMb6k5hhfUnOML6k5xpfUnHGILyuQh6BbBXI3ViDLmytJkiRJA/AqPUmSrECWJEmSJEmS\nJDVriu9OM34Wzl7oab1163rcXm+b07Rbu7b3dX3TSJIkSZIkqQ+2sBgCW1hIY6TXv3leyihJkjRe\nbPMmSVJfbGEhSZIkSZIkSWqUCeQRmj9+ftRDkKbW/Pz8qIcgTS3jS2qO8SU1Z96rb6XGePySmjMO\n8WULiyHo1sJibs1cbVsLW1hoLExSq4eascaaNWTd5Yi9Xs7opYxSVzE3R273ICQ1wfiSmmN8Sc0x\nvqTmDBJftrCYAhs3bhz1EKSptcn4khpjfEnNMb6k5hhfUnOML6k54xBfViAPgTfR00Sa8ArkrqxA\nliRJkiRJM2C1KpD7uDWtpLHU1JdAk5Ro7SeJPQ7jlSRJkiRJmhC2sJAkSZIkSZIk1TKBLEmSJEmS\nJEmqZQuLMTQOLWU1Yk309IX+2jfY6mHk+nkb+HdDkiRJkjR2/GA7FUwgD9HC2Qs7/P/EE0/k6KOP\nXrTe2rU9bm9h2VU0C3p9w8BMvWm6xdck6ae7tYdZDdM0xJc0rowvqTnGl9Qc40tqzjjEV2RTN+DS\nHSIiAXL79h3nz80tmidpdYxrfPXzJ3duTR/bHb9d1RQb1/iSpoHxNWRWRc0U40tqjvE1Y8bhqukZ\nMkh8xVzpXpyZA53I2AN5hDZt3DjqIUhTy/iSmmN8Sc0xvqTmGF9Sc4wvqTnjEF9WIA9BtwpkSbPH\nCmRJksaIFciSJPXPCuSJsVoVyPZAliQNlx/WJUlN8kOtJEnN6udzmsfPqWALC0mSJEmSJElSLRPI\nkiRJkiRJkqRatrCQpDE1Ud0bRny5sF0xJEl38LJaSZI0qcb0w60VyCM0Pz8/6iFIU8v4kppjfEnN\nMb6k5hhfUnOML6k588cfP+ohENlPZlsrEhEJsHXLlh3mr9+wYdE8SatjXOOrn7+4mzf3vu6mjX0P\nZXT62bGNve1YPz9XC5AHN67xJU0D40tqjvElNcf4kpozSHyt37ABgMwc6KOwLSyGaN26dTv8f9PG\njYvmSVod0xBf69eNegQN6eP30ut3nHNren/53N77uqo3DfEljSvjS2qO8SU1Zyria0xbB2gKDNjy\ncROw7tBDF687xFZcViAPQasCObebtZCkfphAliRJkjQUJpDVlBHeMyjm5qohDFaBbA9kSZIkSZIk\nSVItW1hIkqTV0es361ZsSJIkaRhGWPkp3aGfzz9j+t6yAlmSJEmSJEmSVMsEsiRJkiRJkiSplgnk\nEZqfnx/1EKSpZXxJqyRz0WN+fr52Pjvt1NtDUlcev6TmGF9Sc8Y2viJ6f2zb1vujCXXn190eminj\nEF+RvvEaFxEJsHXLlh3mr9+wYdE8SavD+JoOvR6hNm/ufZubNq5oKGrTNb56/UVs9JcgdePxS2qO\n8SU1x/iSmjNIfK3fsAGAzBzoRjQmkJcREXsAbwCeBOwOXA2cChyfmTf0uI0EyO3bd5i/bt06FhYW\nVnO4kirG13To9RA1t6aPbW5ffh21qfklrFu/noWtWxev22t18ZjeGEIaBx6/pOYYX1JzjK9V0E9+\nzptSz5RB4ivmSvMJE8gNioi9gS8C96YkjS8GDgA2ABcBh2Tm93vYTm0COebmFs2TtDqMr+lgAnk8\nGV9Sc4wvqTnGl7oycTcw46uLft5b/bR6syBjpgwSX6uVQLYH8tLeRUke/0Fm/kZmvjYzDwPeCjwC\n+NORjk6SJEmSJEmSGmQFchcRsRdwKfCtzNynY9mulFYWAPfNzFuX2ZYVyNKQGV/TwQrk8WR8qSsr\nuAZmfEnNMb5mjJWfQ2V8Sc2xAnm8baimZ3QuyMybgfOAnYEDhzkoSZIkSZIkSRoWE8jdPRxI4Btd\nll9STR82nOFIkiRJkiRJ0nD1cZ3GzNmtmt7YZXlr/j2HMBZJkqTR6OcS4DV99JPxMldJUpP6aZVk\nWwpJWpIJ5JVrHY16/lTV6juy3DxJq8P4Up3wbbEqjC8NzPdQV8aX1BzjS2qO8SU1Z9TxZXR316ow\n3q3L8p/uWE+SJEmSJEmSpooVyN1dTKky7tbj+KHVtFuP5DsMeqdDSZIkSZIkSRqFyH762s2QiNgb\n+Cbwrczcp2PZrsDVlATzfTLz1hEMUZIkSZIkSZIaZQuLLjLzMuAM4CERcUzH4s3ALsBJJo8lSZIk\nSZIkTSsrkJdQVSGfB9wX+BTwX8CBwDrgIuCQzPz+yAYoSZIkSZIkSQ0ygbyMiNiDUnH8ZGB3SuuK\nTwKbM/OGUY5NkiRJkiRJkppkAlmSJEmSJEmSVMseyJIkSZIkSZKkWiaQJUmSJEmSJEm1TCAPWUTs\nEREnRMRVEXFbRHwrIt4aEfcc9dikcRcR94qIl0TEJyLikoi4JSJuiIhzI+JFERFdnndwRHwmIq6P\niB9GxH9ExHER4d9AaQkR8YKI2F49XtRlnadFxEIViz+IiPMj4qhhj1WaFBFxaER8MiKurs4Fr4qI\nz0XEk2vW9fgl9SgiDo+IMyLiiuoc8dKI+GhEHNhlfeNLqkTEb0TE2yPinIi4sTr3e/8yz+k7hjxv\n1CzqJ74iYt+IeE1EnBURl0fE7RHx3Yg4NSLWLfM6L4yIL1WxdUNEbI2Iw1dtP+yBPDwRsTfwReDe\nwKnAxcABwAbgIuCQzPz+6EYojbeI+B3gXcB/A1uBy4H7Ab8O3BM4JTOf3fGcZwKnALcCJwP/Azwd\neATwscx8ztB2QJogEbEn8FXKl827Ai/NzBM61jkGeDtwHSW+fgQcAewJ/HVmvnqog5bGXET8JfBK\n4Args5TYuQ+wP3BWZv7ftnU9fkk9ioi/AF5FialTq+m+wDOAuwAvyMwPta1vfEltIuIC4FHAzcCV\nlFj4YGbWJndXEkOeN2pW9RNfEfFh4NnAhcA/U2Lr4ZTj2U7AsZn5zprn/TXwR5RzzFOAuwLPBXYH\njsnMvx14P0wgD09EnA4cBvxB+y8vIt4MvBx4d2b+/qjGJ4276hu3XTLz0x3z7wv8C/CzwBGZ+clq\n/j2AS4F7AAdn5gXV/LtSEtAHAkdm5keHthPShIiIM4EHA5+gJLx2SCBHxIMpX37eDOyfmVdU83cD\n/hXYmxJ3Xxr22KVxFBEvBd4DvA/4ncz8ScfyNZm5rfq3xy+pRxFxP+Aq4FrgFzLz+rZlaykxc1lm\n7lvNM76kDlWsXJmZl7bFzQe6JLj6jiHPGzXL+oyvo4D/yMz/6Jj/OOBMYDvwkMy8pm3ZQcB5wCXA\nYzPzpmr+g4CvADsDj8jMywfZDy/PGZKI2At4AvDtmsz/JuCHwAsi4u5DH5w0ITJzoTN5XM2/Fng3\nEMC6tkXPolT8f7h1YlOt/yPg9dX6v9fkmKVJFBHHUWLpt4Bbuqz2Yso32+9ofQgAyMwbgT+jxNfv\nNjtSaTJUH6rfCHyHmuQxQCt5XPH4JfXuwZTPtV9qTx4DZObZwA8olf4txpfUITPPzsxLe1x9JTHk\neaNmVj/xlZnv70weV/PPBRYocXRwx+LfAxL401byuHrO5cD/A+5G+Vw3EBPIw7Ohmp7RuSAzb6Z8\nW7Az5ds6Sf37cTVt/1C+nvKH9PSa9c+hJMYOjoi7NDw2aWJExH7AnwNvy8x/XmLV9dW0Lr4+W003\n1CyTZtETKAmsjwNZ9Wp9dUQc26U/q8cvqXeXUC6FPyAidm9fEBGPp1RJfr5ttvElDWYlMeR5ozS4\nupwHLB9fwSrElwnk4Xk45Y/sN7osv6SaPmw4w5GmR0SsAV5IibHPtS16eDVdFHdVpde3KH2E9m56\njNIkqGLpH4FvA69bZvWl4uu7lCtrfjYifmo1xyhNqMdSjlE/Ai4ATqN8UfNW4AvVDYXu3ba+xy+p\nR9U9ZF5NuS/GhRHxnoj4s4j4KOXD9OnsWNlofEmDWUkMed4oDaBqA3Mo5Quac9rm7wzsAdzc3tai\nzarlGk0gD89u1fTGLstb8+85hLFI0+YvgJ8HPp2Z7RUmxp3Un03ALwJHZ+bty6zba3zt1mW5NEvu\nS6n+eBWld90hlKrIR1GSW48H2vutevyS+pCZbwd+g5K0egnwmur/lwMnZeZ1basbX9JgVhJDnjdK\nK1S1QvsgpX3Fpqr1S8vQjmkmkMdHVFPvaij1ISKOpdxt9EKg9i7BSz29mhp3mnkRcQDwx5S7YH95\nNTZZTY0vCdZU0x8DT8/ML2bmLZn5deDXKHfkXhsRv9Lj9owvqU1EvJpy1/kTgH2AXYDHUCohPxQR\nb+pnc9XU+JJWZiUxZNxJNSJiDvgAcBDwkcx8ywo3NXBsmUAenuW+UfvpjvUkLSMiXga8DfgasCEz\nb+hYxbiTetDWuuJiYGPn4i5P6zW+buqyXJol36+mF7TfPAggM2/jzp51B1RTj19Sj6o72r8JODUz\nX5WZ387M2zLz3ylf0FwFvCIiHlI9xfiSBrOSGPK8UepTlTz+IHAEcDLwgprVlout5SqUe2YCeXgu\npnwI79Z35KHVtFuPZEltIuIPgXcAX6Ukj6+tWe3iaroo7qqE2V6UBvSXNTVOaULsSjkO7QfcHhHb\nWw/uTCi/t5rX+tZ7qfi6P6X668oqOSbNula8dH7R2dJKMN+9Y32PX9LynkaprFroXJCZtwJfpnzu\nfXQ12/iSBrOSGPK8UepDFUsfAZ5DqUB+fmZu71wvM2+hfFG6a0Tcr2ZTq5ZrNIE8PFur6RM7F0TE\nrpReeLcC5w9zUNIkiojXAG8BvgKs7+hr124L5YubJ9csWwvsDJyXmT+uWS7NktuB9wL/UE3bH1+p\n1jm3+v8Xq/8vFV9PraZnNTReadKcRUlw/VyX5Y+spt+qph6/pN7drZrep8vy1vwfVVPjSxrMSmLI\n80apRxFxF+DjlF7+J2bmUZm5VAuKLdW00fgygTwkmXkZcAbwkIg4pmPxZso3bidV35JL6iIi/oRy\n5/p/AQ6r7rzdzSnAdcBzI+Ixbdu4G/BGyof5dzU4XGkiVJf6/nbdAzitWu2kat7Hqv+/j5J4Pqa6\nKzAAEfEzwGsp8fWeYe6HNK4y83JKLD2ouoLmDhHxROBJlCrkz1WzPX5JvTuXkpj67Yh4YPuCiHgK\npVDnNuAL1WzjSxrMSmLI80apB9UN804Fng68NzNf1MPT3k05Dr4uIu64WV7VuulllGPgiQOPbekk\ntlZTROwNnEe5E/engP8CDgTWARcBhyyTDJNmWkS8kHLy8RPgndT38fl2Zp7U9pxnAh+jnLB8BPgf\n4BmUy6c+lpnPbXrc0iSLiE3AJuAlmXlCx7JjgL+hxNXJlOquI4A9KDfje82QhyuNrYjYg3IeuCel\nUuQCYG/gmcB24DmZeWrb+h6/pB5ERFC+fDkMuBn4JPBdSsX/4dVqx2XmO9ueY3xJbaqY+NXqv/en\nfLF5GeULGoDrMvNVHev3FUOeN2pW9RNfEfE+4IXA9yhfxNQlbRcy8+yO1/hr4OWUdhanAHeltL+4\nF3BMZg78xagJ5CGrPjxsppSW7w5cTTnJ2VxzAzBJbapEVucNvjqdnZkbOp53EPA6yp1Lfwr4JuVS\n/XcscymINPPa4u6lnQnkavnhwCuB/SlXNl1Iia0PDHWg0gSIiN0p8fQM4AGUmwWdA7wpM/+1Zn2P\nX1IPql6RLwOeS0kc70xJUn0JeHtmLrp01/iS7tTD56xvZ+Y+Hc/pO4Y8b9Qs6ie+ImIr8PhlNnl8\nZm6ueZ0XAMdQjoPbgX8D/iozP7uigXdu32OjJEmSJEmSJKmOPZAlSZIkSZIkSbVMIEuSJEmSJEmS\naplAliRJkiRJkiTVMoEsSZIkSZIkSaplAlmSJEmSJEmSVMsEsiRJkiRJkiSplglkSZIkSZIkSVIt\nE8iSJEmSJEmSpFomkCVJkiRJkiRJtUwgS5IkSZIkSZJqmUCWJEmSJEmSJNUygSxJkiRJkiRJqmUC\nWZIkSZIkSZJUywSyJEmSpk5E/HNE/HjU41gNEfHGiNgeEQevwrZeXG3reX085wPVcx446Ot32f6a\navtnNLH9ttdZtZ+jJEnSLDGBLEmSNEMiYv8qifaFLsuPrJZvi4gH1yz/qYi4LSJujoi7ND/iFcvq\nMfZ6SOqu9r70u60Etq/i63d7jaZ/XxPznpAkSRonJpAlSZJmywXA94Ffjohda5Zv4M4k24aa5YcA\ndwXOzcypqPAdE+Oc2Hwl8HPAd5vYeGZuA/YDXtTE9iVJkjQYE8iSJEkzJDMTWADWAGtrVtkAbAWu\npz6B3Eowb2loiLMoRj2ApWTmNZn5jcxsrAq52v5VTW1fkiRJK2cCWZIkafacRUla7pAgrlpW7FUt\nPwdYX/Pc1nPOanvebhHx6ojYEhFXRsTtEXFNRHwyIh7b8Rp7Vu0azu82uIg4s1rnYR3zD4qIj0fE\n1dVrXB4R74qI+/ez8xHxlIj4bERcV7Xj+GZE/EVE3KNm3Ssj4hsRsXNEvDkivlM95xsR8You24+I\neHlEXFite2VE/E1E7NraXtu65wJ/V/231Wu41UJkUc/hiHhORHw5In5Yjf+D/e5/27aeERFfqNqR\nXB8RJ0fE3jXrLeqBHBH7VPP+LiL2ioiPVuO5pRrfU/oYR20P5Paexf3sd0Q8NiJOj4ibIuKGiDgj\nIg5YZgz7RcT7I+KK6r11dbXf+3asd1BE/CgiLo6IXTqWPTAivhcRN0bEPr3uvyRJ0rjbadQDkCRJ\n0tC1qocP7Zh/GHdWF98E/FpEPCIzLwKoEqy/DNyQmV9pe94jgc3A2cCngBuABwPPAJ4aEU/JzC0A\nmXlFRGwB1rdvuyUi9gDWAV/MzPZE60uBdwG3VK9xJfAw4KXA0yLigMy8erkdj4jNwOuB66rtfA/4\nReBVwJMj4uDM/GHbU5LSsuNM4D7Ap4FtwK8BfxURd83MP+94mfcALwGuqMb8k+pn8VhK5Xe7f6BU\nez8d+ATw1bbXvalj3eOAp1Xj3gocBBwJPCoiHp2ZP1lu/1s/BuDZwFOBUyi/70cDzwLWVT+DSzt+\nBt1abOwNfBn4BnASsDvwHOBTEbEuM8/rcUx1Wq/b835HxOOA0ymfc04BLqv27WxK5f0iEXE48DFK\ncc1pwKXAnsCvA4dHxOMz8z8BMvOLEfF64E2U3/NvVtuYAz4M3At4fsfPT5IkaaKZQJYkSZoxmXlR\nRPw38MiI2D0zr68WbQBuBv4F+AF3Vim3krxrKQnQrR2b/E/gAZn5/faZEbEnJbn4VkqStuXEartH\nAa/t2NZR1eue1LadRwDvpCQp12XmtW3LDgM+B7yNkrjsKiKeQEkenwM8LTNvblv2IuC9wEbgNR1P\n3RP4d2B9Zt5erf/GajyviIg3Va1BiIh1lOTx14EDW8noiHgt5ed2P8rPFoDMPDEi1lAlkDPzQ92G\nDzwReEx70j0iTgaOoCRYT11q/zs8HXhyZn6+bVsvB95M+Vn3WkG8HnhdZr6pbTsfBf4/JSk/SAIZ\n+tjviAjgBOBuwOGZ+bm29Vv7tkMiPCLuBXyQkqx/XGZe0rbskcD5lPfFr7TmZ+ZfRsR64MiIOCsz\n3wccDzwOeG9mfmTAfZYkSRortrCQJEmaTVspybn2NhXrKDfH256ZFwLXsmObi1b/47Pa5pGZN3Um\nj6v5V1Cqah/Z0W7g45Qk6m/WjOso4Hbg5LZ5L6MUPhzXnjyuXuNM4DPAr0bE3bvubXFsNf6XtieP\nq+2cAHwNeH6X5/5BK3lcrX8NpVr1Z4CHtq13dPUab2yvZK5uONiZLO9HAm/prNgG/p7ye1yyRUON\n09uTx5W3A98GnhgRD+hxO5e1J48BMvMzwH+vYEx1+tnvxwH7AGe1J48rrX3r9FvAPYA/aU8eA2Tm\n1ygJ6V/ubGUBvIByU8G3R8TvA39Mef8c2+N+SZIkTQwrkCVJkmbTWZRk6QbglIjYD3gA8Ja2dRYo\nbS1aWsnkMzs3VrUOOJZSqXlfStuHlgT2oCTcyMxbI+IU4OiIOKxKAlP1qX04cHJm3tj2/ANbrx8R\nB9fsy70p57X7UqqhuzmQkpx+XilW3XEXqm08ICLukZk/aFt2fZUM79Sa9zNt836pmtZV3n4BGORG\ndP/W4xh6cU7njMzcFhHnUdqPPBpYtiUIcEGX+Vdw589iUL3u9/7VdLl9a9d6b+0fEZtqXqeVON4P\n+Gbb9q6LiOdTYuGdlNYqz8nM25baEUmSpElkAlmSJGk2taqID22btvoftywAz4qIRwOXA78AXNVZ\nqRkRz6L0f70F+Dyl7+wPKcnSQ4H/Q2kr0O5ESvXnC7kzIX10NYaTOtbdvZq+eon9SWDXJZZD6U8L\npU3FcttpTyDf0GXdVu/d9r7Gu1XTaxZtOPMnEbGoUrsPdeOoG8NykprxVb5bTXfrsryXMUEZVz9j\n6vc1uv3se9m3drtTvjz47WXGUPfe+hIlkf0g4MzM/K9ltiFJkjSRTCBLkiTNoOpmdpcC+1Y3rttA\nuTlee0Vpq83FBkoCOehoX1F5A3ArsH9mfrN9QUQ8iJJA7nz9cyPiMsqN+nYFfkS5sds1wBkdq7eq\nkXdubyOxAjcBt2fm/Zddc7DXgNLr+Mr2BRGxE6VidpAk8moIyvjqtH42N3ZZPs5upLd963xOAj+X\nmRf3+XrvpFQ0fw94ekQ8KzM/1uc2JEmSxp49kCVJkmZXKxn8BODxwNntC6uE2tWUBHJt/+PK3sDX\napLHc9Qkj9u8H7g78CzKTd3uBXwgMzvbPJxfTR+/zP4s53zgPhHx0GXXXLlWAr5uvw+h/vx7WzVd\nrYrdXqztnFHdzO+Q6r/dWlOMs69U0+X2rd35lKRzX++tiDiSUkF/JvAY4H+Av4uIvfrZjiRJ0iQw\ngSxJkjS7tlCSZy+nVMZurVlngZJce2L1/7oE8neAh0dEZ+XnG4CHLfH6rVYVR1WPuvYVAO+gJFn/\nJiL26VwYEXeJiLrkYKe3UPb3vR039WttZ5eqD/Mg3l+9xusj4h5t274b8GddnnN99ZwHDfja/Xhi\nRDypY94fAg8BzsjMXvofj5tzKX2KN0TEUzuWtfat0z9QqsY3R8RjOhdGxFxErO2Yty/wbkq1/G9m\n5pWU9iu7AR+pKs0lSZKmhic3kiRJs2sLJWn7Cyzuf9yyFTgS2Au4qEti8a2UJO+/R8THKf1pHwc8\nFDgNeFrdi2fmdyLiHEqCehtwQWZ+vWa9CyPixcDfAxdGxGeBSyh9lR9UvdZVwKOW2tnM/HxEvI6S\n2L6k2s63KP1tH0KpXN0CPGOp7SzzGlsi4gRKderX234ez6S0OrgI31/fAAAChklEQVSGxTfS+wJw\nG/CKiLgvcG01/22Z+cOVjmUZpwGnVeO7jHIDuidVYzymoddsVGZm9T45Hfin6kaNl1FuCLgO+Bxl\nH9ufc13Vw/sU4MsRcSZwISUe9qRULe8K/DSULyuAk4FdgGdn5rXVdj4dEW+jJKr/EvijZvdWkiRp\neKxAliRJmlGZeR3wVUqy7Ht1yVtKAjmrx5k1y8nMvwVeTLlJ2dHA8yiJu1+ptr+UE6vpXNu/617j\nH4HHAh8CfpGS5HwepX3Gh6lPembNdv6ckkz8LHAwcBxwBKU/7t9Sf4O9RdtZSma+BHgl5UaCvws8\nF/gM8GRKIvKmjvWvB34duIiSeN5cPXq9kV3r99PzEIGPVq/5YOBY4IBq3kGZeWmX5/T7uv2Oqa+f\nc91zMvNcyhcKZwGHAy+jvLfWAv9Wu5HMz1PeU++ifFHyO5Tfw89TktFHtq3+V8AvAW/JzNM7NvWa\n6jWOi4jD+9wXSZKksRWZ/Z6nSZIkSepXROwHfB34x8x84ajHI0mSJPXCCmRJkiRpFdX0giYidqG0\n+kjgE0MflCRJkrRC9kCWJEmSVtcrI+II4Gzgakp7jMOABwKnZeY/jXJwkiRJUj9MIEuSJEmr6wxK\n/9wnAPei3ETvYuDNlJsNSpIkSRPDHsiSJEmSJEmSpFr2QJYkSZIkSZIk1TKBLEmSJEmSJEmqZQJZ\nkiRJkiRJklTLBLIkSZIkSZIkqZYJZEmSJEmSJElSLRPIkiRJkiRJkqRaJpAlSZIkSZIkSbVMIEuS\nJEmSJEmSaplAliRJkiRJkiTVMoEsSZIkSZIkSaplAlmSJEmSJEmSVMsEsiRJkiRJkiSplglkSZIk\nSZIkSVKt/wU18iuKT1ULFQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x117cd4550>"
]
},
"metadata": {
"image/png": {
"height": 714,
"width": 712
}
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(10, 10))\n",
"ax.imshow(model_matrix.toarray(), interpolation='none', cmap='bwr', aspect='auto')\n",
"ax.set_ylabel('Observation index')\n",
"ax.set_xlabel('Wavelength bin index')\n",
"ax.set_title('Model Matrix')\n",
"\n",
"# draw some \"grid\" lines to help distinguish between rows belonging to different systems\n",
"for system_count in np.cumsum(filtered.groupby('system').size().values):\n",
" ax.axhline(system_count, color='gray', lw=0.5, alpha=0.5)\n",
"ax.grid(axis='x')\n",
"\n",
"ax.set_ylim(0, len(filtered))\n",
"plt.tight_layout()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I told you it was sparse!"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"anaconda-cloud": {},
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.12"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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