{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "tefun=lambda r,rho,N:pow(1-rho**2,(N-1)/2.)*pow(1-r**2,(N-4)/2.)/pow(1-rho*r,N-1.5)*(1+(1+rho*r)/8./(N-0.5))"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "import sympy\n",
    "sr,sk,sn=[sympy.Symbol(a) for a in \"r k n\".split()]\n",
    "sympy.integrate(pow(1-sk**2,(sn-1)/2.)*pow(1-sr**2,(sn-4)/2.)/pow(1-sk*sr,sn-1.5),sr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayesovský přístup\n",
    "\n",
    "integrujeme pres $\\rho$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fb9ef836780>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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U1JC39FWy585FvL2JS0mh3XXDddm+Um1EY+5yGXGMbw1ycC2qDSvf8Svp48dT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\nExroSinlJjTQlVLKTWigK6WUm/h/OPiZ1+y70S0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb9f1a61358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as pl\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "from scipy import integrate as ig\n",
    "Ns=list(range(2,10,2))+list(range(10,50,5))\n",
    "norms=[ig.quad(lambda x:tefun(x,0.5,n),-0.99,0.99)[0] for n in Ns]#gaussova kvadratura\n",
    "ints05=[ig.quad(lambda x:tefun(x,0.5,n),-0.99,0.5)[0] for n in Ns]\n",
    "#zavislost na N sqrt(aN+b)/sqrt(a_2 N+b_2)\n",
    "pl.plot(Ns,1/np.r_[norms]**2,'+')\n",
    "zz1=np.polyfit(Ns,1/np.r_[norms]**2,1)\n",
    "pl.plot(Ns,1/np.r_[ints05]**2,'+')\n",
    "pl.plot(Ns,np.polyval(zz1,Ns))\n",
    "zz05=np.polyfit(Ns,1/np.r_[ints05]**2,1)\n",
    "pl.plot(Ns,np.polyval(zz05,Ns))\n",
    "pl.xlabel(\"velik. souboru\")\n",
    "pl.legend([\"integ.cely\",\"kvantil 0.5\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.43121001,  0.26442757,  0.21709263,  0.18458887,  0.15844065,\n",
       "        0.11076818,  0.07919624,  0.05744818,  0.04209682,  0.03108073,\n",
       "        0.02308156,  0.01722121])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYcAAAD8CAYAAACcjGjIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb9ef9b7dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "normsb=[ig.quad(lambda x:tefun(x,0.7,n),-0.99,0.99)[0] for n in Ns]#gaussova kvadratura\n",
    "ints05b=[ig.quad(lambda x:tefun(x,0.7,n),-0.99,0.5)[0] for n in Ns]\n",
    "pl.plot(Ns,1/np.r_[normsb]**2,'+')\n",
    "zz1b=np.polyfit(Ns,1/np.r_[normsb]**2,1)\n",
    "pl.plot(Ns,1/np.r_[ints05b]**2,'+')\n",
    "np.array(ints05b)/np.array(normsb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.49238729,  0.43973428,  0.45102028,  0.45945963,  0.46479238,\n",
       "        0.47233256,  0.47647905,  0.47919075,  0.48114018,  0.48262816,\n",
       "        0.48381192,  0.48478272])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array(ints05)/np.array(norms)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.54827236,  0.54827236,  0.54827236,  0.54827236,  0.54827236,\n",
       "        0.54827236,  0.54827236,  0.54827236,  0.54827236,  0.54827236,\n",
       "        0.54827236,  0.54827236])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(np.polyval(zz1[1:],Ns)/np.polyval(zz05[1:],Ns))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'np' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-1-abf0ff19d4ed>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mrsmul\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mr_\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m0.99\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m0.05\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mintsmul\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mr_\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mig\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mquad\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0mtefun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0.5\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m0.99\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mr\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrsmul\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mnorms\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;31m#integral po r1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mpl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrsmul\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;36m0.025\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mintsmul\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mintsmul\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m'x'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mpol1\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpolyfit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrsmul\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;36m0.025\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mintsmul\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mintsmul\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m6\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'np' is not defined"
     ]
    }
   ],
   "source": [
    "rsmul=np.r_[0:0.99:0.05]\n",
    "intsmul=np.r_[[ig.quad(lambda x:tefun(x,0.5,10),-0.99,r)[0] for r in rsmul],norms[4]] #integral po r1\n",
    "\n",
    "pl.plot(rsmul+0.025,intsmul[1:]-intsmul[:-1],'x')\n",
    "pol1=np.polyfit(rsmul+0.025,intsmul[1:]-intsmul[:-1],6)\n",
    "pl.plot(rsmul,np.polyval(pol1,rsmul))\n",
    "pl.xlabel(\"horni mez kvantilu\")\n",
    "#pl.plot(rsmul+0.025,intsmul[1:]-intsmul[:-1],'+')\n",
    "pl.title(\"hustota prsti pro N=10,rho=0.5\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7fb9ef66a240>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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pX5bxsdF0u6SOv8sSCRkKdylxSQeP8+i0lSzenMJ1zevwz1sup0Ylrb8uUpQU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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb9ef91b898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pl.plot(rsmul+0.025,np.polyval(np.polyint(pol1),rsmul+0.025)/0.05+intsmul[0])\n",
    "pl.plot(rsmul,intsmul[:-1],'x')\n",
    "levs=[0.8,0.9,0.95,0.98]\n",
    "pl.title(\"kumulat. distrib.fce pro N=10\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "levs=[0.01,0.05,0.1,0.9,0.95,0.99]\n",
    "def polygon(rho=0.25,n=10,step=0.05,infit=False):\n",
    "    #nafituje hustotu prsti polynomem 6.radu\n",
    "    #spocte kumulativ. distrib. fci\n",
    "    #najde polohu kvantilu\n",
    "    rsmul=np.r_[0:1.001:step]\n",
    "    intsmul=np.r_[[ig.quad(lambda x:tefun(x,rho,n),-0.99,r)[0] for r in rsmul]]\n",
    "    rsmul=rsmul[:-1]\n",
    "    pol1=np.polyfit(rsmul+step/2.,intsmul[1:]-intsmul[:-1],6)\n",
    "    resid=np.polyval(pol1,rsmul+step/2.)-intsmul[1:]+intsmul[:-1]\n",
    "    ipol1=np.polyint(pol1)/step #kumulativ. fce\n",
    "    ipol1[-1]=intsmul[0]\n",
    "    ipol1/=intsmul[-1]\n",
    "    if infit:\n",
    "        lop1=np.polyfit(np.polyval(ipol1,rsmul),rsmul,7)\n",
    "        return np.polyval(lop1,levs)\n",
    "    arot=[np.roots(np.polyadd(ipol1,[-l])) for l in levs] # kdy polynom ipol1 dosahne hodnoty l\n",
    "    arot=[a[a.imag==0] for a in arot]\n",
    "    brot=[]\n",
    "    for a in arot:\n",
    "        sel=(a.real>0)*(a.real<1)\n",
    "        if sum(sel)==0:brot.append(0)\n",
    "        else:brot.append(a[sel][0].real)\n",
    "    #pos=[a[sel][0].real for a in arot]\n",
    "    #if len(pos)<len(levs): pos+=[0]*(len(levs)-len(pos))\n",
    "    return np.array(brot)#jen smysluplna reseni"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fb9ef5c6cc0>]"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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CsBSDTzSW8BRNY4HoGk80jqW9cy6+Jt/oW9GHipmlOedS/c4RCBpLeIqmsUB0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\nnIpeRCTKqehFRKLc/wEEb90dWlJ8CwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb9efa3c278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rlev=np.r_[0:0.95:0.05]\n",
    "komplet=np.array([polygon(rho,20,infit=False) for rho in rlev])\n",
    "pl.plot(komplet[:,4],rlev)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "x and y arrays must be equal in length along interpolation axis.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-51-d808b687a2d1>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mscipy\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0minterpolate\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mip\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mfu1\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mip\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minterp1d\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkomplet\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mzval\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mscipy\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0moptimize\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mop\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mop\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfsolve\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0mfu1\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m0.5\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0.2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/lib64/python3.6/site-packages/scipy/interpolate/interpolate.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, x, y, kind, axis, copy, bounds_error, fill_value, assume_sorted)\u001b[0m\n\u001b[1;32m    429\u001b[0m                  assume_sorted=False):\n\u001b[1;32m    430\u001b[0m         \u001b[0;34m\"\"\" Initialize a 1D linear interpolation class.\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 431\u001b[0;31m         \u001b[0m_Interpolator1D\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0maxis\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    432\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    433\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbounds_error\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbounds_error\u001b[0m  \u001b[0;31m# used by fill_value setter\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/lib64/python3.6/site-packages/scipy/interpolate/polyint.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, xi, yi, axis)\u001b[0m\n\u001b[1;32m     58\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdtype\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     59\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0myi\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 60\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_set_yi\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0myi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxi\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mxi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0maxis\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     61\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     62\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m__call__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/lib64/python3.6/site-packages/scipy/interpolate/polyint.py\u001b[0m in \u001b[0;36m_set_yi\u001b[0;34m(self, yi, xi, axis)\u001b[0m\n\u001b[1;32m    123\u001b[0m             \u001b[0mshape\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    124\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mxi\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0maxis\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mxi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 125\u001b[0;31m             raise ValueError(\"x and y arrays must be equal in length along \"\n\u001b[0m\u001b[1;32m    126\u001b[0m                              \"interpolation axis.\")\n\u001b[1;32m    127\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: x and y arrays must be equal in length along interpolation axis."
     ]
    }
   ],
   "source": [
    "from scipy import interpolate as ip\n",
    "fu1=ip.interp1d(komplet[:,4],zval)\n",
    "from scipy import optimize as op\n",
    "op.fsolve(lambda x:fu1(x)-0.5,0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.81747944,  0.81557469,  0.82099054])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z1=polygon(n=10)\n",
    "z2=polygon(n=20)\n",
    "z2/z1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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5/ggzm2tmy83sPTM7N4o6pekymUzcJaSOMo9e0jP//ns48US47TYYORJuvz3+JdKTnnla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\nuRAREZGsUnMhIiIiWfX/Af2m7hp3gSabAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa07e710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy import optimize as op\n",
    "step=0.05\n",
    "ipol1=np.polyint(pol1)/step\n",
    "ipol1[-1]=intsmul[0]\n",
    "ipol1/=intsmul[-1]\n",
    "zk=op.root(lambda x:np.polyval(np.polyadd(ipol1,[-levs[2]]),x),0.8)\n",
    "#op.root?\n",
    "zx=np.r_[:1:20j]\n",
    "pl.plot(zx,np.polyval(np.polyadd(ipol1,[-0.8]),zx))\n",
    "pl.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "alquant=np.array([polygon(rho,n=10) for rho in np.arange(0.05,1,0.05)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x9f87400>]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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C3Llw+unwk5/AUksVXZlU/wwLkrq8v/4Vjjwy799wwAF5gaXPfa7oqqTuw24ISV3W5Mnw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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xaeaaf98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rhos=np.arange(0.05,1,0.05)\n",
    "pl.plot(rhos,alquant[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.7164207 ,  0.77270202,  0.83002147,  0.89754835])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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CzC4FRgJPAA2A1kA1fKciREQkAB+v/phrx13LRaVrUXz8Mg5trcXcuXDBBV5XJvlRVpdO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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb09a438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lop1=np.polyfit(np.polyval(ipol1,zx),zx,7)\n",
    "iy=np.r_[0.1:.9:0.05,.9:.99:0.02]\n",
    "pl.plot(np.polyval(lop1,iy),iy)\n",
    "pl.plot(zx,np.polyval(np.polyadd(ipol1,[-0]),zx))\n",
    "np.polyval(lop1,levs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Admin\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:2: RuntimeWarning: divide by zero encountered in log\n",
      "  from ipykernel import kernelapp as app\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0xa058160>]"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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//fLcCBtuWHSFUv2ZOnUqU6dOXWzbnDlzav4+kVKq7ICI+4D7U0pHlH4P4Dng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\nx7aQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x9f9bf60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "alquant[9]\n",
    "pl.plot(np.log(zx),np.polyval(ipol1,zx))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}