{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Generating haplotypes for simulated populations."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
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""
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""
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"source": [
"import scipy\n",
"import numpy as np\n",
"from sklearn.decomposition import PCA\n",
"from scipy.stats import invgamma\n",
"from scipy.stats import beta\n",
"\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import pandas as pd\n",
"\n",
"import plotly\n",
"import plotly.plotly as py\n",
"import plotly.graph_objs as go\n",
"from plotly.offline import download_plotlyjs, init_notebook_mode, plot, iplot\n",
"from plotly.graph_objs import *\n",
"\n",
"import Lab_modules.Modules_tools\n",
"\n",
"init_notebook_mode(connected=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is a very rough approach at generating haplotypes for two or more different populations.\n",
"\n",
"For each population, alternative allele frequencies will be drawn randomly from the chosen distribution. \n",
"\n",
"Each individual will then have his haplotype drawn using the allele frequency vector pertaining to his population."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"scrolled": false
},
"outputs": [
{
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"config": {
"linkText": "Export to plot.ly",
"plotlyServerURL": "https://plot.ly",
"showLink": true
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"layout": {
"bargap": 0.2,
"bargroupgap": 0.1,
"title": "frequency distribution. a= 1.8; b= 0.2",
"xaxis": {
"title": "Value"
},
"yaxis": {
"title": "Count"
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"## the distribution i chose here was the beta distribution.\n",
"# doc: https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.beta.html#scipy.stats.beta\n",
"\n",
"# This is because with the right parameters a and b, the probability density produced \n",
"# resembles that often seen in allele frequency densities.\n",
"# let's see what that looks like:\n",
"\n",
"a, b = 1.8, .2\n",
"r= beta.rvs(a, b, size=1000)\n",
"r= [1-x for x in r] \n",
"\n",
"fig= go.Histogram(\n",
" x=r,\n",
" histnorm='',\n",
" name='control',\n",
" opacity=0.75\n",
")\n",
"\n",
"layout = go.Layout(\n",
" title='frequency distribution. a= {}; b= {}'.format(a,b),\n",
" xaxis=dict(\n",
" title='Value'\n",
" ),\n",
" yaxis=dict(\n",
" title='Count'\n",
" ),\n",
" bargap=0.2,\n",
" bargroupgap=0.1\n",
")\n",
"fig= [fig]\n",
"\n",
"fig = go.Figure(data=fig, layout=layout)\n",
"iplot(fig, filename='styled histogram')"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(650, 200)\n"
]
}
],
"source": [
"# a= 1.8 and b= .1 seem appropriate, lets proceed to create our populations\n",
"\n",
"# We must first define the number of populations, the length of the haplotypes desired, and their respective population sizes:\n",
"N_pops= 3\n",
"L= 200\n",
"Sizes= [250,100,300]\n",
"labels= np.repeat(np.array([x for x in range(N_pops)]),Sizes)\n",
"\n",
"data= []\n",
"\n",
"for k in range(N_pops):\n",
" \n",
" probs= beta.rvs(a, b, size=L)\n",
" probs[(probs > 1)]= 1\n",
" \n",
" m= Sizes[k]\n",
" Haps= [[np.random.choice([1,0],p= [1-probs[x],probs[x]]) for x in range(L)] for acc in range(m)]\n",
" \n",
" data.extend(Haps)\n",
"\n",
"data= np.array(data)\n",
"print(data.shape)"
]
},
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"cell_type": "code",
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"text": [
"PC1: 0.191; PC2: 0.068; PC3: 0.016; PC4: 0.015; PC5: 0.014; PC6: 0.014; PC7: 0.013; PC8: 0.013; PC9: 0.012; PC10: 0.012; PC11: 0.012; PC12: 0.011; PC13: 0.011; PC14: 0.011; PC15: 0.011; PC16: 0.01; PC17: 0.01; PC18: 0.01; PC19: 0.01; PC20: 0.01; PC21: 0.01; PC22: 0.009; PC23: 0.009; PC24: 0.009; PC25: 0.009; PC26: 0.009; PC27: 0.009; PC28: 0.008; PC29: 0.008; PC30: 0.008; PC31: 0.008; PC32: 0.008; PC33: 0.008; PC34: 0.008; PC35: 0.007; PC36: 0.007; PC37: 0.007; PC38: 0.007; PC39: 0.007; PC40: 0.007; PC41: 0.007; PC42: 0.007; PC43: 0.007; PC44: 0.007; PC45: 0.006; PC46: 0.006; PC47: 0.006; PC48: 0.006; PC49: 0.006; PC50: 0.006; PC51: 0.006; PC52: 0.006; PC53: 0.006; PC54: 0.006; PC55: 0.005; PC56: 0.005; PC57: 0.005; PC58: 0.005; PC59: 0.005; PC60: 0.005; PC61: 0.005; PC62: 0.005; PC63: 0.005; PC64: 0.005; PC65: 0.005; PC66: 0.005; PC67: 0.005; PC68: 0.004; PC69: 0.004; PC70: 0.004; PC71: 0.004; PC72: 0.004; PC73: 0.004; PC74: 0.004; PC75: 0.004; PC76: 0.004; PC77: 0.004; PC78: 0.004; PC79: 0.004; PC80: 0.004; PC81: 0.004; PC82: 0.004; PC83: 0.004; PC84: 0.004; PC85: 0.003; PC86: 0.003; PC87: 0.003; PC88: 0.003; PC89: 0.003; PC90: 0.003; PC91: 0.003; PC92: 0.003; PC93: 0.003; PC94: 0.003; PC95: 0.003; PC96: 0.003; PC97: 0.003; PC98: 0.003; PC99: 0.003; PC100: 0.003\n",
"(650, 100)\n"
]
}
],
"source": [
"n_comp = 100\n",
"\n",
"pca = PCA(n_components=n_comp, whiten=False,svd_solver='randomized')\n",
"features = pca.fit_transform(data)\n",
"\n",
"var_comps= pca.explained_variance_ratio_\n",
"print(\"; \".join(['PC{0}: {1}'.format(x+1,round(var_comps[x],3)) for x in range(n_comp)]))\n",
"print(features.shape)"
]
},
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"cell_type": "code",
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}
],
"layout": {
"margin": {
"b": 0,
"l": 0,
"r": 0,
"t": 0
},
"xaxis": {
"title": "PC1: 0.191"
},
"yaxis": {
"title": "PC2: 0.068"
}
}
},
"text/html": [
""
],
"text/vnd.plotly.v1+html": [
""
]
},
"metadata": {},
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],
"source": [
"## lets visualize the result now:\n",
"colors_pres= ['red','black','yellow']\n",
"\n",
"fig_data= [go.Scatter(\n",
" x= features[[x for x in range(sum(Sizes)) if labels[x] == i],0],\n",
" y= features[[x for x in range(sum(Sizes)) if labels[x] == i],1],\n",
" mode= \"markers\",\n",
" marker= {\n",
" 'color': colors_pres[i],\n",
" 'line': {'width': 0},\n",
" 'size': 8,\n",
" 'symbol': 'circle',\n",
" \"opacity\": .8\n",
" },\n",
" name= str(i)\n",
" ) for i in range(N_pops)]\n",
"\n",
"\n",
"layout = go.Layout(\n",
" margin=dict(\n",
" l=0,\n",
" r=0,\n",
" b=0,\n",
" t=0\n",
" ),\n",
" yaxis=dict(\n",
" title='PC2: {}'.format(round(var_comps[1],3))),\n",
" xaxis=dict(\n",
" title= 'PC1: {}'.format(round(var_comps[0],3)))\n",
")\n",
"\n",
"fig = go.Figure(data=fig_data, layout=layout)\n",
"iplot(fig)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This looks very nice. Frequencies drawn at random from a predetermined beta distribution produce very different vectors, which translate into neatly separated populations. \n",
"\n",
"Here, the degree of differentiation between our populations will be proportional to the correlation between the vectors we created them with. However, by drawing at random from a single beta distribution, we really have no hand over the relative distances between these vectors.\n",
"\n",
"How can we simulate populations, or vectors, in a way that allows us to have at least some control over their relative differences? \n",
"\n",
"Population genetics models could provide us with an answer, by assuming mutation rates, growth rates, recombination and standard age gaps to coalesce our four populations and extract ancestral vectors and sizes at nodes of our choosing.\n",
"\n",
"\n",
"- If we don't need the information generated in that process however, a more pragmatic approach is possible.\n",
"\n",
"Since what we are looking to do is identify a degree of correlation between these vectors before we generate their associated haplotypes, it stands that a PCA should do the job. \n",
"\n",
"In the first part, we drew four vectors only for stable values of _a_ and _b_, the beta parameters. Let's make those parameters vary, and draw 10 vectors at each change."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"# Simulate frequency vectors. \n",
"# We must first define the number of populations, the length of the haplotypes desired, and their respective population sizes\n",
"L= 300\n",
"\n",
"import itertools as it\n",
"n= 200\n",
"\n",
"# Vary a (beta distribution parameter).\n",
"a_range= np.linspace(1,2,20)\n",
"a_set= [i for i in a_range for _ in range(n)]\n",
"\n",
"# vary b.\n",
"b_range= np.linspace(0.1,.4,20)\n",
"b_set= [i for i in b_range for _ in range(n)]\n",
"\n",
"## length of haplotypes to extract.\n",
"L_set= [L] * n * 20\n",
"\n",
"\n",
"background_1= np.array([a_set,b_set,L_set]).T\n",
"\n",
"vector_lib= []\n",
"for k in range(background_1.shape[0]):\n",
" \n",
" probs= beta.rvs(background_1[k,0], background_1[k,1], size=int(background_1[k,2]))\n",
" probs= 1-probs\n",
" probs[(probs > 1)]= 1\n",
" \n",
" \n",
" vector_lib.append(probs)\n",
"\n",
"vector_lib= np.array(vector_lib)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And reduce their dimension through PCA."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"PC1: 0.015; PC2: 0.005; PC3: 0.005; PC4: 0.005; PC5: 0.005; PC6: 0.005; PC7: 0.005; PC8: 0.005; PC9: 0.005; PC10: 0.005; PC11: 0.005; PC12: 0.005; PC13: 0.005; PC14: 0.005; PC15: 0.005; PC16: 0.005; PC17: 0.005; PC18: 0.005; PC19: 0.005; PC20: 0.005; PC21: 0.005; PC22: 0.005; PC23: 0.005; PC24: 0.005; PC25: 0.005; PC26: 0.005; PC27: 0.005; PC28: 0.005; PC29: 0.005; PC30: 0.005; PC31: 0.005; PC32: 0.005; PC33: 0.005; PC34: 0.004; PC35: 0.004; PC36: 0.004; PC37: 0.004; PC38: 0.004; PC39: 0.004; PC40: 0.004; PC41: 0.004; PC42: 0.004; PC43: 0.004; PC44: 0.004; PC45: 0.004; PC46: 0.004; PC47: 0.004; PC48: 0.004; PC49: 0.004; PC50: 0.004; PC51: 0.004; PC52: 0.004; PC53: 0.004; PC54: 0.004; PC55: 0.004; PC56: 0.004; PC57: 0.004; PC58: 0.004; PC59: 0.004; PC60: 0.004; PC61: 0.004; PC62: 0.004; PC63: 0.004; PC64: 0.004; PC65: 0.004; PC66: 0.004; PC67: 0.004; PC68: 0.004; PC69: 0.004; PC70: 0.004; PC71: 0.004; PC72: 0.004; PC73: 0.004; PC74: 0.004; PC75: 0.004; PC76: 0.004; PC77: 0.004; PC78: 0.004; PC79: 0.004; PC80: 0.004; PC81: 0.004; PC82: 0.004; PC83: 0.004; PC84: 0.004; PC85: 0.004; PC86: 0.004; PC87: 0.004; PC88: 0.004; PC89: 0.004; PC90: 0.004; PC91: 0.004; PC92: 0.004; PC93: 0.004; PC94: 0.003; PC95: 0.003; PC96: 0.003; PC97: 0.003; PC98: 0.003; PC99: 0.003; PC100: 0.003\n",
"features shape: (650, 100)\n"
]
}
],
"source": [
"n_comp = 100\n",
"\n",
"pca_vectors = PCA(n_components=n_comp, whiten=False,svd_solver='randomized')\n",
"features_vectors = pca_vectors.fit_transform(vector_lib)\n",
"var_comps= pca_vectors.explained_variance_ratio_\n",
"\n",
"print(\"; \".join(['PC{0}: {1}'.format(x+1,round(pca_vectors.explained_variance_ratio_[x],3)) for x in range(n_comp)]))\n",
"print('features shape: {}'.format(features.shape))"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
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"a: 1.0; b: 0.1, L: 300.0; index = 0",
"a: 1.0; b: 0.1, L: 300.0; index = 1",
"a: 1.0; b: 0.1, L: 300.0; index = 2",
"a: 1.0; b: 0.1, L: 300.0; index = 3",
"a: 1.0; b: 0.1, L: 300.0; index = 4",
"a: 1.0; b: 0.1, L: 300.0; index = 5",
"a: 1.0; b: 0.1, L: 300.0; index = 6",
"a: 1.0; b: 0.1, L: 300.0; index = 7",
"a: 1.0; b: 0.1, L: 300.0; index = 8",
"a: 1.0; b: 0.1, L: 300.0; index = 9",
"a: 1.0; b: 0.1, L: 300.0; index = 10",
"a: 1.0; b: 0.1, L: 300.0; index = 11",
"a: 1.0; b: 0.1, L: 300.0; index = 12",
"a: 1.0; b: 0.1, L: 300.0; index = 13",
"a: 1.0; b: 0.1, L: 300.0; index = 14",
"a: 1.0; b: 0.1, L: 300.0; index = 15",
"a: 1.0; b: 0.1, L: 300.0; index = 16",
"a: 1.0; b: 0.1, L: 300.0; index = 17",
"a: 1.0; b: 0.1, L: 300.0; index = 18",
"a: 1.0; b: 0.1, L: 300.0; index = 19",
"a: 1.0; b: 0.1, L: 300.0; index = 20",
"a: 1.0; b: 0.1, L: 300.0; index = 21",
"a: 1.0; b: 0.1, L: 300.0; index = 22",
"a: 1.0; b: 0.1, L: 300.0; index = 23",
"a: 1.0; b: 0.1, L: 300.0; index = 24",
"a: 1.0; b: 0.1, L: 300.0; index = 25",
"a: 1.0; b: 0.1, L: 300.0; index = 26",
"a: 1.0; b: 0.1, L: 300.0; index = 27",
"a: 1.0; b: 0.1, L: 300.0; index = 28",
"a: 1.0; b: 0.1, L: 300.0; index = 29",
"a: 1.0; b: 0.1, L: 300.0; index = 30",
"a: 1.0; b: 0.1, L: 300.0; index = 31",
"a: 1.0; b: 0.1, L: 300.0; index = 32",
"a: 1.0; b: 0.1, L: 300.0; index = 33",
"a: 1.0; b: 0.1, L: 300.0; index = 34",
"a: 1.0; b: 0.1, L: 300.0; index = 35",
"a: 1.0; b: 0.1, L: 300.0; index = 36",
"a: 1.0; b: 0.1, L: 300.0; index = 37",
"a: 1.0; b: 0.1, L: 300.0; index = 38",
"a: 1.0; b: 0.1, L: 300.0; index = 39",
"a: 1.0; b: 0.1, L: 300.0; index = 40",
"a: 1.0; b: 0.1, L: 300.0; index = 41",
"a: 1.0; b: 0.1, L: 300.0; index = 42",
"a: 1.0; b: 0.1, L: 300.0; index = 43",
"a: 1.0; b: 0.1, L: 300.0; index = 44",
"a: 1.0; b: 0.1, L: 300.0; index = 45",
"a: 1.0; b: 0.1, L: 300.0; index = 46",
"a: 1.0; b: 0.1, L: 300.0; index = 47",
"a: 1.0; b: 0.1, L: 300.0; index = 48",
"a: 1.0; b: 0.1, L: 300.0; index = 49",
"a: 1.0; b: 0.1, L: 300.0; index = 50",
"a: 1.0; b: 0.1, L: 300.0; index = 51",
"a: 1.0; b: 0.1, L: 300.0; index = 52",
"a: 1.0; b: 0.1, L: 300.0; index = 53",
"a: 1.0; b: 0.1, L: 300.0; index = 54",
"a: 1.0; b: 0.1, L: 300.0; index = 55",
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"a: 1.0; b: 0.1, L: 300.0; index = 57",
"a: 1.0; b: 0.1, L: 300.0; index = 58",
"a: 1.0; b: 0.1, L: 300.0; index = 59",
"a: 1.0; b: 0.1, L: 300.0; index = 60",
"a: 1.0; b: 0.1, L: 300.0; index = 61",
"a: 1.0; b: 0.1, L: 300.0; index = 62",
"a: 1.0; b: 0.1, L: 300.0; index = 63",
"a: 1.0; b: 0.1, L: 300.0; index = 64",
"a: 1.0; b: 0.1, L: 300.0; index = 65",
"a: 1.0; b: 0.1, L: 300.0; index = 66",
"a: 1.0; b: 0.1, L: 300.0; index = 67",
"a: 1.0; b: 0.1, L: 300.0; index = 68",
"a: 1.0; b: 0.1, L: 300.0; index = 69",
"a: 1.0; b: 0.1, L: 300.0; index = 70",
"a: 1.0; b: 0.1, L: 300.0; index = 71",
"a: 1.0; b: 0.1, L: 300.0; index = 72",
"a: 1.0; b: 0.1, L: 300.0; index = 73",
"a: 1.0; b: 0.1, L: 300.0; index = 74",
"a: 1.0; b: 0.1, L: 300.0; index = 75",
"a: 1.0; b: 0.1, L: 300.0; index = 76",
"a: 1.0; b: 0.1, L: 300.0; index = 77",
"a: 1.0; b: 0.1, L: 300.0; index = 78",
"a: 1.0; b: 0.1, L: 300.0; index = 79",
"a: 1.0; b: 0.1, L: 300.0; index = 80",
"a: 1.0; b: 0.1, L: 300.0; index = 81",
"a: 1.0; b: 0.1, L: 300.0; index = 82",
"a: 1.0; b: 0.1, L: 300.0; index = 83",
"a: 1.0; b: 0.1, L: 300.0; index = 84",
"a: 1.0; b: 0.1, L: 300.0; index = 85",
"a: 1.0; b: 0.1, L: 300.0; index = 86",
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"a: 1.0; b: 0.1, L: 300.0; index = 88",
"a: 1.0; b: 0.1, L: 300.0; index = 89",
"a: 1.0; b: 0.1, L: 300.0; index = 90",
"a: 1.0; b: 0.1, L: 300.0; index = 91",
"a: 1.0; b: 0.1, L: 300.0; index = 92",
"a: 1.0; b: 0.1, L: 300.0; index = 93",
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"a: 1.0; b: 0.1, L: 300.0; index = 95",
"a: 1.0; b: 0.1, L: 300.0; index = 96",
"a: 1.0; b: 0.1, L: 300.0; index = 97",
"a: 1.0; b: 0.1, L: 300.0; index = 98",
"a: 1.0; b: 0.1, L: 300.0; index = 99",
"a: 1.0; b: 0.1, L: 300.0; index = 100",
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"a: 1.0; b: 0.1, L: 300.0; index = 105",
"a: 1.0; b: 0.1, L: 300.0; index = 106",
"a: 1.0; b: 0.1, L: 300.0; index = 107",
"a: 1.0; b: 0.1, L: 300.0; index = 108",
"a: 1.0; b: 0.1, L: 300.0; index = 109",
"a: 1.0; b: 0.1, L: 300.0; index = 110",
"a: 1.0; b: 0.1, L: 300.0; index = 111",
"a: 1.0; b: 0.1, L: 300.0; index = 112",
"a: 1.0; b: 0.1, L: 300.0; index = 113",
"a: 1.0; b: 0.1, L: 300.0; index = 114",
"a: 1.0; b: 0.1, L: 300.0; index = 115",
"a: 1.0; b: 0.1, L: 300.0; index = 116",
"a: 1.0; b: 0.1, L: 300.0; index = 117",
"a: 1.0; b: 0.1, L: 300.0; index = 118",
"a: 1.0; b: 0.1, L: 300.0; index = 119",
"a: 1.0; b: 0.1, L: 300.0; index = 120",
"a: 1.0; b: 0.1, L: 300.0; index = 121",
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"a: 1.0; b: 0.1, L: 300.0; index = 123",
"a: 1.0; b: 0.1, L: 300.0; index = 124",
"a: 1.0; b: 0.1, L: 300.0; index = 125",
"a: 1.0; b: 0.1, L: 300.0; index = 126",
"a: 1.0; b: 0.1, L: 300.0; index = 127",
"a: 1.0; b: 0.1, L: 300.0; index = 128",
"a: 1.0; b: 0.1, L: 300.0; index = 129",
"a: 1.0; b: 0.1, L: 300.0; index = 130",
"a: 1.0; b: 0.1, L: 300.0; index = 131",
"a: 1.0; b: 0.1, L: 300.0; index = 132",
"a: 1.0; b: 0.1, L: 300.0; index = 133",
"a: 1.0; b: 0.1, L: 300.0; index = 134",
"a: 1.0; b: 0.1, L: 300.0; index = 135",
"a: 1.0; b: 0.1, L: 300.0; index = 136",
"a: 1.0; b: 0.1, L: 300.0; index = 137",
"a: 1.0; b: 0.1, L: 300.0; index = 138",
"a: 1.0; b: 0.1, L: 300.0; index = 139",
"a: 1.0; b: 0.1, L: 300.0; index = 140",
"a: 1.0; b: 0.1, L: 300.0; index = 141",
"a: 1.0; b: 0.1, L: 300.0; index = 142",
"a: 1.0; b: 0.1, L: 300.0; index = 143",
"a: 1.0; b: 0.1, L: 300.0; index = 144",
"a: 1.0; b: 0.1, L: 300.0; index = 145",
"a: 1.0; b: 0.1, L: 300.0; index = 146",
"a: 1.0; b: 0.1, L: 300.0; index = 147",
"a: 1.0; b: 0.1, L: 300.0; index = 148",
"a: 1.0; b: 0.1, L: 300.0; index = 149",
"a: 1.0; b: 0.1, L: 300.0; index = 150",
"a: 1.0; b: 0.1, L: 300.0; index = 151",
"a: 1.0; b: 0.1, L: 300.0; index = 152",
"a: 1.0; b: 0.1, L: 300.0; index = 153",
"a: 1.0; b: 0.1, L: 300.0; index = 154",
"a: 1.0; b: 0.1, L: 300.0; index = 155",
"a: 1.0; b: 0.1, L: 300.0; index = 156",
"a: 1.0; b: 0.1, L: 300.0; index = 157",
"a: 1.0; b: 0.1, L: 300.0; index = 158",
"a: 1.0; b: 0.1, L: 300.0; index = 159",
"a: 1.0; b: 0.1, L: 300.0; index = 160",
"a: 1.0; b: 0.1, L: 300.0; index = 161",
"a: 1.0; b: 0.1, L: 300.0; index = 162",
"a: 1.0; b: 0.1, L: 300.0; index = 163",
"a: 1.0; b: 0.1, L: 300.0; index = 164",
"a: 1.0; b: 0.1, L: 300.0; index = 165",
"a: 1.0; b: 0.1, L: 300.0; index = 166",
"a: 1.0; b: 0.1, L: 300.0; index = 167",
"a: 1.0; b: 0.1, L: 300.0; index = 168",
"a: 1.0; b: 0.1, L: 300.0; index = 169",
"a: 1.0; b: 0.1, L: 300.0; index = 170",
"a: 1.0; b: 0.1, L: 300.0; index = 171",
"a: 1.0; b: 0.1, L: 300.0; index = 172",
"a: 1.0; b: 0.1, L: 300.0; index = 173",
"a: 1.0; b: 0.1, L: 300.0; index = 174",
"a: 1.0; b: 0.1, L: 300.0; index = 175",
"a: 1.0; b: 0.1, L: 300.0; index = 176",
"a: 1.0; b: 0.1, L: 300.0; index = 177",
"a: 1.0; b: 0.1, L: 300.0; index = 178",
"a: 1.0; b: 0.1, L: 300.0; index = 179",
"a: 1.0; b: 0.1, L: 300.0; index = 180",
"a: 1.0; b: 0.1, L: 300.0; index = 181",
"a: 1.0; b: 0.1, L: 300.0; index = 182",
"a: 1.0; b: 0.1, L: 300.0; index = 183",
"a: 1.0; b: 0.1, L: 300.0; index = 184",
"a: 1.0; b: 0.1, L: 300.0; index = 185",
"a: 1.0; b: 0.1, L: 300.0; index = 186",
"a: 1.0; b: 0.1, L: 300.0; index = 187",
"a: 1.0; b: 0.1, L: 300.0; index = 188",
"a: 1.0; b: 0.1, L: 300.0; index = 189",
"a: 1.0; b: 0.1, L: 300.0; index = 190",
"a: 1.0; b: 0.1, L: 300.0; index = 191",
"a: 1.0; b: 0.1, L: 300.0; index = 192",
"a: 1.0; b: 0.1, L: 300.0; index = 193",
"a: 1.0; b: 0.1, L: 300.0; index = 194",
"a: 1.0; b: 0.1, L: 300.0; index = 195",
"a: 1.0; b: 0.1, L: 300.0; index = 196",
"a: 1.0; b: 0.1, L: 300.0; index = 197",
"a: 1.0; b: 0.1, L: 300.0; index = 198",
"a: 1.0; b: 0.1, L: 300.0; index = 199",
"a: 1.0526315789473684; b: 0.11578947368421054, L: 300.0; index = 200",
"a: 1.0526315789473684; b: 0.11578947368421054, L: 300.0; index = 201",
"a: 1.0526315789473684; b: 0.11578947368421054, L: 300.0; index = 202",
"a: 1.0526315789473684; b: 0.11578947368421054, L: 300.0; index = 203",
"a: 1.0526315789473684; b: 0.11578947368421054, L: 300.0; index = 204",
"a: 1.0526315789473684; b: 0.11578947368421054, L: 300.0; index = 205",
"a: 1.0526315789473684; b: 0.11578947368421054, L: 300.0; index = 206",
"a: 1.0526315789473684; b: 0.11578947368421054, L: 300.0; index = 207",
"a: 1.0526315789473684; b: 0.11578947368421054, L: 300.0; index = 208",
"a: 1.0526315789473684; b: 0.11578947368421054, L: 300.0; index = 209",
"a: 1.0526315789473684; b: 0.11578947368421054, L: 300.0; index = 210",
"a: 1.0526315789473684; b: 0.11578947368421054, L: 300.0; index = 211",
"a: 1.0526315789473684; b: 0.11578947368421054, L: 300.0; index = 212",
"a: 1.0526315789473684; b: 0.11578947368421054, L: 300.0; index = 213",
"a: 1.0526315789473684; b: 0.11578947368421054, L: 300.0; index = 214",
"a: 1.0526315789473684; b: 0.11578947368421054, L: 300.0; index = 215",
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"a: 1.0526315789473684; b: 0.11578947368421054, L: 300.0; index = 217",
"a: 1.0526315789473684; b: 0.11578947368421054, L: 300.0; index = 218",
"a: 1.0526315789473684; b: 0.11578947368421054, L: 300.0; index = 219",
"a: 1.0526315789473684; b: 0.11578947368421054, L: 300.0; index = 220",
"a: 1.0526315789473684; b: 0.11578947368421054, L: 300.0; index = 221",
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"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1753",
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"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1755",
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"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1757",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1758",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1759",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1760",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1761",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1762",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1763",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1764",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1765",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1766",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1767",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1768",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1769",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1770",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1771",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1772",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1773",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1774",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1775",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1776",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1777",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1778",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1779",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1780",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1781",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1782",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1783",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1784",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1785",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1786",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1787",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1788",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1789",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1790",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1791",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1792",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1793",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1794",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1795",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1796",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1797",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1798",
"a: 1.4210526315789473; b: 0.22631578947368425, L: 300.0; index = 1799",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1800",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1801",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1802",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1803",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1804",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1805",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1806",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1807",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1808",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1809",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1810",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1811",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1812",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1813",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1814",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1815",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1816",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1817",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1818",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1819",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1820",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1821",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1822",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1823",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1824",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1825",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1826",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1827",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1828",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1829",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1830",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1831",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1832",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1833",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1834",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1835",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1836",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1837",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1838",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1839",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1840",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1841",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1842",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1843",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1844",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1845",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1846",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1847",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1848",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1849",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1850",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1851",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1852",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1853",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1854",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1855",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1856",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1857",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1858",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1859",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1860",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1861",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1862",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1863",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1864",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1865",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1866",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1867",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1868",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1869",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1870",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1871",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1872",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1873",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1874",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1875",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1876",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1877",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1878",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1879",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1880",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1881",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1882",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1883",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1884",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1885",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1886",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1887",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1888",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1889",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1890",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1891",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1892",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1893",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1894",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1895",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1896",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1897",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1898",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1899",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1900",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1901",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1902",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1903",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1904",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1905",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1906",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1907",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1908",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1909",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1910",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1911",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1912",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1913",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1914",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1915",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1916",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1917",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1918",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1919",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1920",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1921",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1922",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1923",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1924",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1925",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1926",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1927",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1928",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1929",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1930",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1931",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1932",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1933",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1934",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1935",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1936",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1937",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1938",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1939",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1940",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1941",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1942",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1943",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1944",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1945",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1946",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1947",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1948",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1949",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1950",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1951",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1952",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1953",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1954",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1955",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1956",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1957",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1958",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1959",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1960",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1961",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1962",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1963",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1964",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1965",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1966",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1967",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1968",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1969",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1970",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1971",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1972",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1973",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1974",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1975",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1976",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1977",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1978",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1979",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1980",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1981",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1982",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1983",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1984",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1985",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1986",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1987",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1988",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1989",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1990",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1991",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1992",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1993",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1994",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1995",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1996",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1997",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1998",
"a: 1.4736842105263157; b: 0.24210526315789477, L: 300.0; index = 1999",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2000",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2001",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2002",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2003",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2004",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2005",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2006",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2007",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2008",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2009",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2010",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2011",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2012",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2013",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2014",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2015",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2016",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2017",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2018",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2019",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2020",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2021",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2022",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2023",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2024",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2025",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2026",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2027",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2028",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2029",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2030",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2031",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2032",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2033",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2034",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2035",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2036",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2037",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2038",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2039",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2040",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2041",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2042",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2043",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2044",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2045",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2046",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2047",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2048",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2049",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2050",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2051",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2052",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2053",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2054",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2055",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2056",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2057",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2058",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2059",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2060",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2061",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2062",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2063",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2064",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2065",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2066",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2067",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2068",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2069",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2070",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2071",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2072",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2073",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2074",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2075",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2076",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2077",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2078",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2079",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2080",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2081",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2082",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2083",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2084",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2085",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2086",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2087",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2088",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2089",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2090",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2091",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2092",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2093",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2094",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2095",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2096",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2097",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2098",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2099",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2100",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2101",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2102",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2103",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2104",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2105",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2106",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2107",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2108",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2109",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2110",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2111",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2112",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2113",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2114",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2115",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2116",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2117",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2118",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2119",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2120",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2121",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2122",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2123",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2124",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2125",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2126",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2127",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2128",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2129",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2130",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2131",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2132",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2133",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2134",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2135",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2136",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2137",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2138",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2139",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2140",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2141",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2142",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2143",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2144",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2145",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2146",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2147",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2148",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2149",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2150",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2151",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2152",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2153",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2154",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2155",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2156",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2157",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2158",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2159",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2160",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2161",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2162",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2163",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2164",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2165",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2166",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2167",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2168",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2169",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2170",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2171",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2172",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2173",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2174",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2175",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2176",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2177",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2178",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2179",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2180",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2181",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2182",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2183",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2184",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2185",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2186",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2187",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2188",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2189",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2190",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2191",
"a: 1.526315789473684; b: 0.2578947368421053, L: 300.0; index = 2192",
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"a: 1.5789473684210527; b: 0.27368421052631586, L: 300.0; index = 2394",
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"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2400",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2401",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2402",
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"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2404",
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"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2460",
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"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2478",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2479",
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"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2486",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2487",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2488",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2489",
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"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2500",
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"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2510",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2511",
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"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2513",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2514",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2515",
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"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2518",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2519",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2520",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2521",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2522",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2523",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2524",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2525",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2526",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2527",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2528",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2529",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2530",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2531",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2532",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2533",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2534",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2535",
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"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2537",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2538",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2539",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2540",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2541",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2542",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2543",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2544",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2545",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2546",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2547",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2548",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2549",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2550",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2551",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2552",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2553",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2554",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2555",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2556",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2557",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2558",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2559",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2560",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2561",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2562",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2563",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2564",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2565",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2566",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2567",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2568",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2569",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2570",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2571",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2572",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2573",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2574",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2575",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2576",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2577",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2578",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2579",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2580",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2581",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2582",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2583",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2584",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2585",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2586",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2587",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2588",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2589",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2590",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2591",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2592",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2593",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2594",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2595",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2596",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2597",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2598",
"a: 1.631578947368421; b: 0.2894736842105263, L: 300.0; index = 2599",
"a: 1.6842105263157894; b: 0.3052631578947369, L: 300.0; index = 2600",
"a: 1.6842105263157894; b: 0.3052631578947369, L: 300.0; index = 2601",
"a: 1.6842105263157894; b: 0.3052631578947369, L: 300.0; index = 2602",
"a: 1.6842105263157894; b: 0.3052631578947369, L: 300.0; index = 2603",
"a: 1.6842105263157894; b: 0.3052631578947369, L: 300.0; index = 2604",
"a: 1.6842105263157894; b: 0.3052631578947369, L: 300.0; index = 2605",
"a: 1.6842105263157894; b: 0.3052631578947369, L: 300.0; index = 2606",
"a: 1.6842105263157894; b: 0.3052631578947369, L: 300.0; index = 2607",
"a: 1.6842105263157894; b: 0.3052631578947369, L: 300.0; index = 2608",
"a: 1.6842105263157894; b: 0.3052631578947369, L: 300.0; index = 2609",
"a: 1.6842105263157894; b: 0.3052631578947369, L: 300.0; index = 2610",
"a: 1.6842105263157894; b: 0.3052631578947369, L: 300.0; index = 2611",
"a: 1.6842105263157894; b: 0.3052631578947369, L: 300.0; index = 2612",
"a: 1.6842105263157894; b: 0.3052631578947369, L: 300.0; index = 2613",
"a: 1.6842105263157894; b: 0.3052631578947369, L: 300.0; index = 2614",
"a: 1.6842105263157894; b: 0.3052631578947369, L: 300.0; index = 2615",
"a: 1.6842105263157894; b: 0.3052631578947369, L: 300.0; index = 2616",
"a: 1.6842105263157894; b: 0.3052631578947369, L: 300.0; index = 2617",
"a: 1.6842105263157894; b: 0.3052631578947369, L: 300.0; index = 2618",
"a: 1.6842105263157894; b: 0.3052631578947369, L: 300.0; index = 2619",
"a: 1.6842105263157894; b: 0.3052631578947369, L: 300.0; index = 2620",
"a: 1.6842105263157894; b: 0.3052631578947369, L: 300.0; index = 2621",
"a: 1.6842105263157894; b: 0.3052631578947369, L: 300.0; index = 2622",
"a: 1.6842105263157894; b: 0.3052631578947369, L: 300.0; index = 2623",
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"Principal component analysis of the vectors produced. Their index along the vector_lib array can be examined by hovering above the points,\n",
"\n",
"Their distances in this space are our indicators of correlation among these vectors. Chose them according to the scenarios intended and generate the haplotypes. Below i chose four, and plotted the result of a PCA on the resulting data set. I won't comment on them, the process is random, and so will be the relationships betweem the populations.\n",
"\n",
"We'll also calculate the pairwise Fsts between these populations based on their frequency vectors. These can then be compared to their distances in feature space."
]
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" pops fst\n",
"0 (0, 1) 0.093189\n",
"1 (0, 2) 0.108052\n",
"2 (0, 3) 0.101388\n",
"3 (0, 4) 0.109989\n",
"4 (1, 2) 0.096115\n",
"5 (1, 3) 0.090412\n",
"6 (1, 4) 0.089475\n",
"7 (2, 3) 0.109192\n",
"8 (2, 4) 0.093444\n",
"9 (3, 4) 0.105544\n"
]
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"text": [
"D:\\GitHub\\Genetic-data-analysis\\Notebooks\\Lab_modules\\StructE_tools.py:419: RuntimeWarning:\n",
"\n",
"invalid value encountered in double_scalars\n",
"\n"
]
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"source": [
"Pops= [3,15,1,30,75]\n",
"N_pops= len(Pops)\n",
"L= 200\n",
"Sizes= [50,50,50,50,50]\n",
"labels= np.repeat(np.array([x for x in range(N_pops)]),Sizes)\n",
"\n",
"data= []\n",
"\n",
"for k in range(N_pops):\n",
" \n",
" probs= vector_lib[Pops[k],:]\n",
" \n",
" m= Sizes[k]\n",
" Haps= [[np.random.choice([1,0],p= [1-probs[x],probs[x]]) for x in range(L)] for acc in range(m)]\n",
" \n",
" data.extend(Haps)\n",
"\n",
"data= np.array(data)\n",
"\n",
"### Calculate pairwise Fst based on frequency vectors selected.\n",
"from Lab_modules.StructE_tools import return_fsts, return_fsts2\n",
"freqs_selected= vector_lib[Pops,:]\n",
"Pairwise= return_fsts2(freqs_selected)\n",
"\n",
"print(Pairwise)"
]
},
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"cell_type": "code",
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"name": "stdout",
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"text": [
"PC1: 0.159; PC2: 0.122; PC3: 0.101; PC4: 0.089\n",
"(250, 4)\n"
]
}
],
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"n_comp = 4\n",
"\n",
"pca = PCA(n_components=n_comp, whiten=False,svd_solver='randomized')\n",
"\n",
"features= pca.fit_transform(data)\n",
"\n",
"\n",
"print(\"; \".join(['PC{0}: {1}'.format(x+1,round(pca.explained_variance_ratio_[x],3)) for x in range(n_comp)]))\n",
"print(features.shape)"
]
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"## lets visualize the result now:\n",
"\n",
"fig_data= [go.Scatter3d(\n",
" x = features[[x for x in range(sum(Sizes)) if labels[x] == i],0],\n",
" y = features[[x for x in range(sum(Sizes)) if labels[x] == i],1],\n",
" z = features[[x for x in range(sum(Sizes)) if labels[x] == i],2],\n",
" mode= \"markers\",\n",
" marker= {\n",
" 'line': {'width': 1},\n",
" 'size': 5,\n",
" 'symbol': 'circle',\n",
" \"opacity\": 1\n",
" },\n",
" name= 'pop: {}'.format(Pops[i])\n",
" ) for i in range(N_pops)]\n",
"\n",
"\n",
"layout = go.Layout(\n",
" margin=dict(\n",
" l=0,\n",
" r=0,\n",
" b=0,\n",
" t=0\n",
" )\n",
")\n",
"\n",
"fig = go.Figure(data=fig_data, layout=layout)\n",
"iplot(fig)\n"
]
},
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"source": [
"## Expanding range of genetic distances.\n",
"\n",
"\n",
"So far we saw how to generate proxy populations along and explored a manner to select them based on correlation.\n",
"\n",
"One questioon remains: how differentiated are the pops we generated? If we select randomly from the vector_lib data set, what differentiation can we expect between the selected populations?\n",
"\n",
"To answer this question, we will sample randomly from the vector_lib data set, calculate pairwise Fsts, and look at their distribution."
]
},
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"cell_type": "code",
"execution_count": null,
"metadata": {},
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"source": [
"### distribution of genetic distances generated on first layer:\n",
"\n",
"N_sample= 500\n",
"\n",
"Pops_test= np.random.choice(vector_lib.shape[0],N_sample)\n",
"\n",
"Fsts_test, Total_fst= return_fsts(vector_lib,Pops_test)\n"
]
},
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"title": "Distribution of genetic distances generated in layer I."
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"source": [
"### Distribution of feature space distances between control populations for even and biased scenarios\n",
"from sklearn.neighbors import KernelDensity\n",
"Fsts_den= Fsts_test.fst\n",
"\n",
"Fsts_den= np.nan_to_num(Fsts_den)\n",
"\n",
"X_plot = np.linspace(0, .5, 1000)\n",
"\n",
"kde = KernelDensity(kernel='gaussian', bandwidth=0.005).fit(np.array(Fsts_den).reshape(-1,1))\n",
"\n",
"log_dens = kde.score_samples(X_plot.reshape(-1,1))\n",
"\n",
"fig_roost_dens= [go.Scatter(x=X_plot, y=np.exp(log_dens), \n",
" mode='lines', fill='tozeroy', name= 'Biased senarios',\n",
" line=dict(color='blue', width=2))]\n",
"\n",
"##\n",
"\n",
"layout= go.Layout(\n",
" title= 'Distribution of genetic distances generated in layer I.'\n",
")\n",
"\n",
"fig = go.Figure(data=fig_roost_dens, layout= layout)\n",
"iplot(fig)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Distribution of pairwise Fsts between frequency vectors randomly selected from the vector_lib data set.\n",
"\n",
"The result is not optimal. We learn that our approach generates populations along a limited range of genetic distances, roughly 0.09 to 0.15.\n",
"\n",
"We will try to expand that range, resorting to the PCA transformation of these vectors.\n",
"\n",
"We will extract the inverse transformation of new coordinates, drawn at small distance intervals between one another.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### MRCA - Most Recent Common Ancestor.\n",
"\n",
"The following block serves to tie all the populations in the vector data set together.\n",
"\n",
"The random generation of frequency vectors creates vectors distinct along, assymptotically, all possible directions.\n",
"\n",
"Here, we limit the number of possible directions, by creating a data set made entirely of vectors generated as described for the manipulation of genetic distances, i.e. from equally distant coordinates between two initial projections. We continue to rely on pairs of initial projections. However, here, only one projection is made to vary, while the other is chosen beforehand and remains the same. \n",
"\n",
"The result is the starshaped distribution observed in the next graph.\n"
]
},
{
"cell_type": "code",
"execution_count": 84,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[340 99]\n",
"[502 99]\n",
"[3847 99]\n",
"[1517 99]\n"
]
}
],
"source": [
"Iter= 50\n",
"target= [0,1]\n",
"stairs= 4\n",
"\n",
"MRCA= np.random.choice(range(vector_lib.shape[0]),1)\n",
"calypso= []\n",
"feat= []\n",
"\n",
"background= []\n",
"\n",
"for inter in range(stairs):\n",
" Pair= np.random.choice(range(vector_lib.shape[0]),2,replace= False)\n",
" Pair[1]= MRCA\n",
" print(Pair)\n",
" \n",
" coords= features_vectors[Pair,:]\n",
" \n",
" vector2= coords[target[1]] - coords[target[0]]\n",
" \n",
" for angle in np.linspace(-20,20,Iter):\n",
" \n",
" new_guy = coords[target[0]] + [angle / 10 * x for x in vector2]\n",
" \n",
" feat.append(new_guy)\n",
" \n",
" new_guy= pca_vectors.inverse_transform(new_guy)\n",
" \n",
" \n",
" new_guy[new_guy < 0]= 0\n",
" new_guy[new_guy > 1]= 1\n",
" \n",
" background.append([inter, angle])\n",
" calypso.append(new_guy)\n",
"\n",
"features= np.array(feat)\n",
"vector_lib_2= np.array(calypso)\n",
"background= np.array(background)\n"
]
},
{
"cell_type": "code",
"execution_count": 85,
"metadata": {},
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"source": [
"\n",
"## Plot vector PCA\n",
"fig_data= [go.Scatter(\n",
" x = features[:,0],\n",
" y = features[:,1],\n",
" mode= \"markers\",\n",
" text= ['a: {}; b: {}; index = {}'.format(background[k,0],background[k,1], k) for k in range(background.shape[0])],\n",
" marker= {\n",
" 'line': {'width': 0},\n",
" 'size': 6,\n",
" 'symbol': 'circle',\n",
" \"opacity\": .6\n",
" }\n",
" )]\n",
"\n",
"\n",
"layout = go.Layout(\n",
" margin=dict(\n",
" l=0,\n",
" r=0,\n",
" b=0,\n",
" t=0\n",
" )\n",
")\n",
"\n",
"fig = go.Figure(data=fig_data)\n",
"iplot(fig)\n"
]
},
{
"cell_type": "code",
"execution_count": 86,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"C:\\Users\\jgarcia\\Desktop\\Jupyter_stuff\\Genetic-data-analysis\\Notebooks\\Lab_modules\\StructE_tools.py:419: RuntimeWarning:\n",
"\n",
"invalid value encountered in double_scalars\n",
"\n"
]
}
],
"source": [
"N_sample= 100\n",
"\n",
"Pops_test= np.random.choice(vector_lib_2.shape[0],N_sample)\n",
"\n",
"freqs_selected= vector_lib_2[Pops_test,:]\n",
"Pairwise= return_fsts2(freqs_selected)\n",
"\n",
"Fsts_test_2 = Pairwise.fst\n"
]
},
{
"cell_type": "code",
"execution_count": 87,
"metadata": {},
"outputs": [
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],
"layout": {
"title": "Distribution of genetic distances generated in layer II."
}
},
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""
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""
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"source": [
"\n",
"### Distribution of feature space distances between control populations for even and biased scenarios\n",
"from sklearn.neighbors import KernelDensity\n",
"\n",
"\n",
"Fsts_den= np.nan_to_num(Fsts_test_2)\n",
"\n",
"X_plot = np.linspace(0, .5, 1000)\n",
"\n",
"kde = KernelDensity(kernel='gaussian', bandwidth=0.005).fit(np.array(Fsts_den).reshape(-1,1))\n",
"\n",
"log_dens = kde.score_samples(X_plot.reshape(-1,1))\n",
"\n",
"fig_roost_dens= [go.Scatter(x=X_plot, y=np.exp(log_dens), \n",
" mode='lines', fill='tozeroy', name= 'Biased senarios',\n",
" line=dict(color='blue', width=2))]\n",
"\n",
"##\n",
"\n",
"layout= go.Layout(\n",
" title= 'Distribution of genetic distances generated in layer II.'\n",
")\n",
"\n",
"fig = go.Figure(data=fig_roost_dens, layout= layout)\n",
"iplot(fig)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Distribution of pairwise Fsts between frequency vectors randomly selected from MRCA data set.\n",
"\n",
"\n",
"It is definitely not pretty, but the range of genetic distances produced is succesfully expanded."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Inverse transformation impact on allele frequencty distribution\n",
"\n",
"What do inverse transformed allele frequency vectors present in the `vector_lib_2` data set look like?\n",
"\n",
"We analyse the average likelihood of frequency values across vectors and look at its variance along this range."
]
},
{
"cell_type": "code",
"execution_count": 113,
"metadata": {},
"outputs": [
{
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"\n",
"def check_densities(vector_lib_2,N):\n",
" \n",
" who= np.random.choice(list(range(vector_lib_2.shape[0])),N,replace= False)\n",
" \n",
" freqs= []\n",
" \n",
" for pop in who:\n",
" \n",
" freq_vector= vector_lib_2[pop,:]\n",
"\n",
" X_plot = np.linspace(0, 1, 100)\n",
"\n",
" kde = KernelDensity(kernel='gaussian', bandwidth=0.01).fit(np.array(freq_vector).reshape(-1,1))\n",
"\n",
" log_dens= kde.score_samples(X_plot.reshape(-1,1))\n",
" \n",
" freqs.append(np.exp(log_dens))\n",
" \n",
" freqs= np.array(freqs)\n",
" \n",
" return freqs\n",
"\n",
"\n",
"dist_freq= check_densities(vector_lib_2,200)\n",
"\n",
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" x= np.linspace(0, 1, dist_freq.shape[1]),\n",
" y= np.mean(dist_freq,axis= 0),\n",
" mode= 'markers+lines',\n",
" name= 'mean'\n",
") \n",
"]\n",
"\n",
"fig_dist.append(go.Scatter(\n",
" x= np.linspace(0, 1, dist_freq.shape[1]),\n",
" y= np.std(dist_freq,axis= 0),\n",
" mode= 'markers+lines',\n",
" name= 'sd'\n",
"))\n",
"\n",
"layout= go.Layout(\n",
" title= 'Branch vectors dist',\n",
" yaxis= dict(\n",
" title= 'Likelihood'\n",
" ),\n",
" xaxis= dict(\n",
" title= 'frequency'\n",
" )\n",
")\n",
"\n",
"fig = go.Figure(data=fig_dist, layout= layout)\n",
"iplot(fig)"
]
},
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"source": [
"### Individual vector example."
]
},
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"Rand_select=115\n",
"\n",
"fig_roost_dens= [go.Scatter(x=np.linspace(0, 1, dist_freq.shape[1]), y=dist_freq[Rand_select,:], \n",
" mode='lines', fill='tozeroy', name= 'Biased senarios',\n",
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"##\n",
"\n",
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" title= 'Distribution of genetic distances generated in layer II.'\n",
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