ch05.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "第5章 厳密解から近似解へ\n",
    "=="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "$\\mathbf{Ax}$と$\\mathbf{b}$に少し差があっても許容するように$(P^{0})$ を考え直すことにする。ここでは許容誤差$\\epsilon > 0$を用いて，問題$(P_{0})$の誤差を許容する変形版を次のように定義する．\n",
    "\n",
    "$$ (P_{0}^{\\epsilon}): \\, \\min_{x} \\|x\\|_{0} \\text{ subject to } \\|\\mathbf{b} - \\mathbf{Ax}\\|_{2}^{2} \\leq \\epsilon$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from matplotlib.font_manager import FontProperties\n",
    "\n",
    "font_path = u'/Library/Fonts/ヒラギノ角ゴ Pro W3.otf'\n",
    "font_prop = FontProperties(fname=font_path)\n",
    "plt.rc('font',family=font_prop.get_name())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "OMPによる$(P_{0}^{\\epsilon})$の解法\n",
    "--\n",
    "停止条件を$\\epsilon_{0}=\\epsilon$とすれば，このアルゴリズムは制約条件$\\|\\mathbf{b}-\\mathbf{Ax}\\|_{2}\\leq\\epsilon$が満たされるまで解ベクトルの非ゼロ要素を積算することになる．修正はこのように軽微で済むので，OMPを実装し実行することは簡単で，広く使われている．\n",
    "\n",
    "* $(P_{0})$の場合と特にアルゴリズムの変更はない"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 貪欲アルゴリズム\n",
    "class Greedy(object):\n",
    "    def __init__(self, A, b, eps=1e-4):\n",
    "        \"\"\"\n",
    "        A m×n行列\n",
    "        b n要素の観測\n",
    "        eps 誤差の閾値\n",
    "        \"\"\"\n",
    "        self.A = A\n",
    "        self.b = b\n",
    "        self.eps = eps\n",
    "\n",
    "    def OMP(self):\n",
    "        \"\"\" 直交マッチング追跡(orthogonal matching pursuit; OMP) \"\"\"\n",
    "        # 初期化\n",
    "        x = np.zeros(self.A.shape[1])\n",
    "        S = np.zeros(self.A.shape[1], dtype=np.uint8)\n",
    "        r = self.b.copy()\n",
    "        rr = np.dot(r, r)\n",
    "        for _ in xrange(self.A.shape[1]):\n",
    "            # 誤差計算\n",
    "            err = rr - np.dot(self.A[:, S == 0].T, r) ** 2\n",
    "            \n",
    "            # サポート更新\n",
    "            ndx = np.where(S == 0)[0]\n",
    "            S[ndx[err.argmin()]] = 1\n",
    "    \n",
    "            # 解更新\n",
    "            As = self.A[:, S == 1]\n",
    "            pinv = np.linalg.pinv(np.dot(As, As.T))\n",
    "            x[S == 1] = np.dot(As.T, np.dot(pinv, self.b))\n",
    "        \n",
    "            # 残差更新\n",
    "            r = self.b - np.dot(self.A, x)\n",
    "            rr = np.dot(r, r)\n",
    "            if rr < self.eps:\n",
    "                break\n",
    "                \n",
    "        return x, S\n",
    "    \n",
    "    def MP(self):\n",
    "        \"\"\" マッチング追跡(matching pursuit; MP) \"\"\"\n",
    "        # 初期化\n",
    "        x = np.zeros(self.A.shape[1])\n",
    "        S = np.zeros(self.A.shape[1], dtype=np.uint8)\n",
    "        r = self.b.copy()\n",
    "        rr = np.dot(r, r)\n",
    "        for _ in xrange(1000):\n",
    "            # 誤差計算\n",
    "            err = rr - np.dot(self.A.T, r) ** 2\n",
    "\n",
    "            # サポート更新\n",
    "            j = err.argmin()\n",
    "            S[j] = 1\n",
    "    \n",
    "            # 解更新\n",
    "            a = self.A[:, j]\n",
    "            z = np.dot(a, r)\n",
    "            x[j] += z\n",
    "    \n",
    "            # 残差更新\n",
    "            r -= z * a\n",
    "            rr = np.dot(r, r)\n",
    "            if rr < self.eps:\n",
    "                break\n",
    "                \n",
    "        return x, S\n",
    "\n",
    "    def WMP(self, t=0.5):\n",
    "        \"\"\" \n",
    "        弱マッチング追跡(weak matching pursuit; WMP)     \n",
    "        t スカラー(0<t<1)\n",
    "        \"\"\"\n",
    "        # 初期化\n",
    "        x = np.zeros(self.A.shape[1])\n",
    "        S = np.zeros(self.A.shape[1], dtype=np.uint8)\n",
    "        r = self.b.copy()\n",
    "        rr = np.dot(r, r)\n",
    "        for _ in xrange(1000):\n",
    "            # 誤差計算\n",
    "            max_zz = 0\n",
    "            j0 = 0\n",
    "            for j in xrange(self.A.shape[1]):\n",
    "                a = self.A[:, j]\n",
    "                z = np.dot(a, r)\n",
    "                if np.abs(z) > t * np.sqrt(rr):\n",
    "                    j0 = j\n",
    "                    break\n",
    "                if z ** 2 > max_zz:\n",
    "                    max_zz = z ** 2\n",
    "                    j0 = j \n",
    "    \n",
    "            # サポート更新\n",
    "            S[j0] = 1\n",
    "    \n",
    "            # 解更新\n",
    "            a = self.A[:, j0]\n",
    "            z = np.dot(a, r)\n",
    "            x[j0] += z\n",
    "    \n",
    "            # 残差更新\n",
    "            r -= z * a\n",
    "            rr = np.dot(r, r)\n",
    "            if rr < self.eps:\n",
    "                break\n",
    "                \n",
    "        return x, S\n",
    "\n",
    "    def Threshold(self, k):\n",
    "        \"\"\" \n",
    "        閾値アルゴリズム(thresholding algorithm) \n",
    "        k 列の個数\n",
    "        \"\"\"\n",
    "        # 初期化\n",
    "        x = np.zeros(self.A.shape[1])\n",
    "        S = np.zeros(self.A.shape[1], dtype=np.uint8)\n",
    "        r = self.b.copy()\n",
    "        rr = np.dot(r, r)\n",
    "\n",
    "        # 誤差計算\n",
    "        err = rr - np.dot(self.A.T, r) ** 2\n",
    "\n",
    "        # サポートの更新\n",
    "        ndx = np.argsort(err)[:k]\n",
    "        S[ndx] = 1\n",
    "        \n",
    "        # 解更新\n",
    "        As = self.A[:, S == 1]\n",
    "        pinv = np.linalg.pinv(np.dot(As, As.T))\n",
    "        x[S == 1] = np.dot(As.T, np.dot(pinv, self.b))\n",
    "        \n",
    "        return x, S"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "基底追跡ノイズ除去（basis pursuit denoising; BPDN）\n",
    "--\n",
    "$$ (P_{1}^{\\epsilon}): \\, \\min_{x} \\|x\\|_{1} \\text{ subject to } \\|\\mathbf{b}-\\mathbf{Ax}\\|_{2}$$\n",
    "\n",
    "適切なラグランジュ乗数$\\lambda$に対して，$(P_{1}^{\\epsilon})$の解は，以下の制約なし最適化問題の解に一致する．\n",
    "\n",
    "$$ (Q_{1}^{\\lambda}): \\, \\min_{x} \\lambda \\|x\\|_1 + \\frac{1}{2} \\|\\mathbf{b} - \\mathbf{Ax}\\|^{2}_{2}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "反復重み付け最小二乗法（IRLS）\n",
    "--\n",
    "* $(Q_{1}^{\\lambda})$を解く単純な方法\n",
    "\n",
    "$\\mathbf{X} = \\rm{diag}(|\\mathbf{x}|)$とすると，$\\|\\mathbf{x}\\|_{1} = \\mathbf{x}^{T}\\mathbf{X}^{-1}\\mathbf{x}$である．つまり$\\ell_{1}$ノルムは（重み付き）2乗$\\ell_{2}$ノルムと見なすことができる．現在の近似界を$\\mathbf{x}_{k_1}$が与えられたら，$\\mathbf{X}_{k-1}=\\rm{diag}(|\\mathbf{x}_{k-1}|)$とおいて以下の問題を解く．\n",
    "\n",
    "$$ (M_{k}):\\, \\min_{x} \\lambda \\mathbf{x}^{T}\\mathbf{X}^{-1}_{k-1}\\mathbf{x} + \\frac{1}{2}\\|\\mathbf{b}-\\mathbf{Ax}\\|_{2}^{2}$$\n",
    "\n",
    "* 思いつき：$\\|\\mathbf{x}\\|_{0} = \\mathbf{x}^{T}\\mathbf{X}^{-2}\\mathbf{x}$となる？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "IRLSの具体例\n",
    "--"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 数値例生成\n",
    "class NumericalExample2(object):\n",
    "    def __init__(self, n=100, m=200, k=4, sig=0.1):\n",
    "        \"\"\" \n",
    "        n 行数\n",
    "        m 列数\n",
    "        k 非ゼロの要素数 \n",
    "        A 冗長なシステム行列 mxn\n",
    "        x スパースな解 m\n",
    "        b ノイズを含む観測 n\n",
    "        S サポート m\n",
    "        \"\"\"\n",
    "        # 冗長なシステム行列A\n",
    "        self.A = (np.random.rand(n, m) - 0.5) * 2\n",
    "        self.A = np.dot(self.A, np.diag(1. / np.sqrt(np.diag(np.dot(self.A.T, self.A)))))    \n",
    "        \n",
    "        #　スパースなx\n",
    "        self.x = np.zeros(m)\n",
    "        ndx = np.random.randint(0, m - 1, k)\n",
    "        for i in ndx:\n",
    "            self.x[i] = np.random.rand() + 1.\n",
    "            if np.random.rand() < 0.5:\n",
    "                self.x[i] *= -1.\n",
    "\n",
    "        # 雑音を含む観測n\n",
    "        self.b = np.dot(self.A, self.x) + randn(n) * sig\n",
    "        \n",
    "        # サポートS\n",
    "        self.S = np.zeros(m, dtype=np.uint8)\n",
    "        self.S[ndx] = 1\n",
    "        \n",
    "        # 雑音の標準偏差\n",
    "        self.sig = sig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy.optimize import minimize\n",
    "\n",
    "# 基底追跡ノイズ除去（basis pursuit denoising; BPDN）\n",
    "class BPDN(object):\n",
    "    def __init__(self, A, b, niter=1000):\n",
    "        \"\"\"\n",
    "        A m×n行列\n",
    "        b n要素の観測\n",
    "        sig 雑音の標準偏差\n",
    "        eps 誤差の閾値\n",
    "        iter 反復回数\n",
    "        \"\"\"\n",
    "        self.A = A\n",
    "        self.b = b\n",
    "        self.eps = 1e-3\n",
    "        self.niter = niter\n",
    "                \n",
    "    def IRLS(self, lam=0.05):    \n",
    "        \"\"\" 反復重み付け最小二乗(iterative-reweighted-least-squares; IRLS) \"\"\"\n",
    "\n",
    "        def f(x, *args):\n",
    "            \"\"\" コスト関数 \"\"\"\n",
    "            lam, w, A, b = args\n",
    "            reg = lam * np.dot(x.T, x / w) \n",
    "            err = b - np.dot(A, x)\n",
    "            err2 = np.dot(err.T, err)\n",
    "            return reg + 0.5 * err2\n",
    "\n",
    "        # 初期化\n",
    "        x = np.ones(self.A.shape[1])\n",
    "        w = np.ones(self.A.shape[1])\n",
    "        xs = []\n",
    "        for i in xrange(self.niter):\n",
    "            x_prev = x.copy()\n",
    "            res = minimize(f, x, args=(lam, w, self.A, self.b))\n",
    "            x = res.x\n",
    "            xs.append(x)\n",
    "            w = np.abs(x) + self.eps\n",
    "            update = np.sum(np.abs(x - x_prev))\n",
    "            if update < 1e-6:\n",
    "                break\n",
    "        \n",
    "        # サポート\n",
    "        S = np.zeros(self.A.shape[1], dtype=np.uint8)\n",
    "        S[np.abs(x) > 0] = 1\n",
    "\n",
    "        return x, S, xs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 指標\n",
    "def l2_err(x, x2):\n",
    "    \"\"\" 正規化L2誤差 \"\"\"\n",
    "    return np.dot(x - x2, x - x2) / np.dot(x, x)\n",
    "\n",
    "def dist_S(S, S2):\n",
    "    \"\"\" サポート間距離 \"\"\"\n",
    "    val = max(np.sum(S), np.sum(S2))\n",
    "    return float(val - np.sum(S * S2)) / val\n",
    "\n",
    "def residual(A, x, b, sig):\n",
    "    \"\"\" 残差とノイズパワーの比 \"\"\"\n",
    "    r = np.dot(A, x) - b \n",
    "    power = len(b) * (sig ** 2)\n",
    "    return np.abs(np.log(np.dot(r, r) / power))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\lambda$の値の決め方\n",
    "--\n",
    "* $(P_{0}^{\\epsilon})$，$(P_{1}^{\\epsilon})$では$\\epsilon=\\sqrt{n}\\sigma$とすれば良い\n",
    "* $(Q^{1}_{\\lambda})$では$\\lambda$の値が直感的に求まらない．\n",
    "* 経験的には、$\\sigma$と非ゼロ要素の標準偏差の比に近い値を$\\lambda$とする．ここでは非ゼロ要素の標準偏差はおおよそ2なので，$\\sigma/2=0.05$付近の値を$\\lambda$とする．"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\lambda$に対する正規化$\\ell_{2}$誤差\n",
    "--"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 0.0001 0.155651702041 11.64517735\n",
      "1 0.000111033631817 0.155510116674 11.4360273207\n",
      "2 0.000123284673944 0.155398168673 11.2212351385\n",
      "3 0.000136887450954 0.154923245527 11.0171652167\n",
      "4 0.000151991108295 0.154820420521 10.8126854896\n",
      "5 0.000168761247579 0.154500307322 10.6041496149\n",
      "6 0.000187381742286 0.154273618626 10.3949626399\n",
      "7 0.000208056753822 0.154067757176 10.1886478285\n",
      "8 0.000231012970008 0.153765268098 9.98372745626\n",
      "9 0.000256502090568 0.153502929372 9.77297257562\n",
      "10 0.000284803586844 0.153215966973 9.56792397412\n",
      "11 0.000316227766017 0.152900619973 9.3599734787\n",
      "12 0.000351119173422 0.152543467346 9.15259929784\n",
      "13 0.000389860370255 0.152157496273 8.94391124754\n",
      "14 0.000432876128108 0.151764460567 8.74046701986\n",
      "15 0.000480638086306 0.151262495585 8.53262140726\n",
      "16 0.000533669923121 0.150766261295 8.32613285135\n",
      "17 0.000592553097555 0.150204861788 8.12168637525\n",
      "18 0.000657933224658 0.149603993848 7.91634092167\n",
      "19 0.000730527154266 0.148916504857 7.71095002974\n",
      "20 0.00081113083079 0.148182578644 7.5075251295\n",
      "21 0.000900628020211 0.147378177202 7.30454423906\n",
      "22 0.001 0.14641781588 7.10164453521\n",
      "23 0.00111033631817 0.145443861533 6.90042082815\n",
      "24 0.00123284673944 0.1443500542 6.70044362852\n",
      "25 0.00136887450954 0.143151146623 6.50170607611\n",
      "26 0.00151991108295 0.141839960592 6.30426793908\n",
      "27 0.00168761247579 0.140414846475 6.10839745357\n",
      "28 0.00187381742286 0.138888346638 5.91395950791\n",
      "29 0.00208056753822 0.137173648397 5.72114538043\n",
      "30 0.00231012970008 0.135292106955 5.52963541466\n",
      "31 0.00256502090568 0.133162618995 5.33941707973\n",
      "32 0.00284803586844 0.130740618299 5.15037467145\n",
      "33 0.00316227766017 0.128031143677 4.96205068332\n",
      "34 0.00351119173422 0.124974714134 4.77425348215\n",
      "35 0.00389860370255 0.121566278211 4.58683020868\n",
      "36 0.00432876128108 0.117791750783 4.39983112753\n",
      "37 0.00480638086306 0.113661545628 4.21304108694\n",
      "38 0.00533669923121 0.109251966897 4.02661467417\n",
      "39 0.00592553097555 0.104606940305 3.84083357755\n",
      "40 0.00657933224658 0.0997951904163 3.6564418809\n",
      "41 0.00730527154266 0.0948732736159 3.47450632456\n",
      "42 0.0081113083079 0.0898977534154 3.29563276178\n",
      "43 0.00900628020211 0.0849172097492 3.11989921178\n",
      "44 0.01 0.0799998821448 2.94728217783\n",
      "45 0.0111033631817 0.0751788767489 2.77785798093\n",
      "46 0.0123284673944 0.0704693700212 2.6108739074\n",
      "47 0.0136887450954 0.0658884301464 2.44474894889\n",
      "48 0.0151991108295 0.0615302467074 2.280300485\n",
      "49 0.0168761247579 0.0574199094916 2.1208933095\n",
      "50 0.0187381742286 0.0534934384718 1.96969773739\n",
      "51 0.0208056753822 0.0496894009626 1.8261803403\n",
      "52 0.0231012970008 0.0460545571063 1.68821299195\n",
      "53 0.0256502090568 0.0426663118449 1.55502188773\n",
      "54 0.0284803586844 0.0395834947462 1.4266669131\n",
      "55 0.0316227766017 0.0368544700642 1.30491917966\n",
      "56 0.0351119173422 0.0344310800957 1.19284209448\n",
      "57 0.0389860370255 0.0321702501017 1.08922633275\n",
      "58 0.0432876128108 0.0300023522922 0.99110730113\n",
      "59 0.0480638086306 0.0279223089893 0.894764117069\n",
      "60 0.0533669923121 0.026008945517 0.797808616427\n",
      "61 0.0592553097555 0.0243914000345 0.700261295636\n",
      "62 0.0657933224658 0.0232045832223 0.604066987171\n",
      "63 0.0730527154266 0.0225323365978 0.511970327552\n",
      "64 0.081113083079 0.0224197140395 0.425625827282\n",
      "65 0.0900628020211 0.0229271380187 0.344824349049\n",
      "66 0.1 0.0241211370088 0.267983046286\n",
      "67 0.111033631817 0.0261120189929 0.192632478588\n",
      "68 0.123284673944 0.0291020937195 0.117663598196\n",
      "69 0.136887450954 0.0333651378755 0.04360763684\n",
      "70 0.151991108295 0.0391734528537 0.0310871603311\n",
      "71 0.168761247579 0.0468519331964 0.10812699036\n",
      "72 0.187381742286 0.0566811138548 0.189951824849\n",
      "73 0.208056753822 0.0689470763398 0.279669856887\n",
      "74 0.231012970008 0.0841160231809 0.378907371144\n",
      "75 0.256502090568 0.102823336654 0.488335842448\n",
      "76 0.284803586844 0.125866779584 0.608107931462\n",
      "77 0.316227766017 0.15424029759 0.738057509919\n",
      "78 0.351119173422 0.189166027653 0.87774949128\n",
      "79 0.389860370255 0.232138705219 1.02653082162\n",
      "80 0.432876128108 0.28496853009 1.18355613841\n",
      "81 0.480638086306 0.349802920729 1.34777761586\n",
      "82 0.533669923121 0.428834234956 1.51743090446\n",
      "83 0.592553097555 0.521123281738 1.68571298284\n",
      "84 0.657933224658 0.613930095381 1.83360365984\n",
      "85 0.730527154266 0.692740770276 1.95089252911\n",
      "86 0.81113083079 0.774576411469 2.06251239279\n",
      "87 0.900628020211 0.843922853901 2.15422327842\n",
      "88 1.0 0.911673652069 2.23871240281\n",
      "89 1.11033631817 0.980111150659 2.31510069038\n",
      "90 1.23284673944 0.994817406957 2.33066554179\n",
      "91 1.36887450954 0.996969500324 2.33308169046\n",
      "92 1.51991108295 0.997863814002 2.33418131616\n",
      "93 1.68761247579 0.998373305684 2.33486530071\n",
      "94 1.87381742286 0.998707390757 2.33535055783\n",
      "95 2.08056753822 0.998944636894 2.3357197616\n",
      "96 2.31012970008 0.999122183591 2.33601300756\n",
      "97 2.56502090568 0.999259652268 2.33625224429\n",
      "98 2.84803586844 0.999368919937 2.33645126537\n",
      "99 3.16227766017 0.999457653836 2.33661934159\n"
     ]
    }
   ],
   "source": [
    "ne2 = NumericalExample2()\n",
    "\n",
    "bpdn = BPDN(ne2.A, ne2.b, niter=100)\n",
    "lams = np.logspace(-4, 0.5, 100)\n",
    "errs = []\n",
    "ress = []\n",
    "x_lams = []\n",
    "for i, lam in enumerate(lams):\n",
    "    x_IRLS, S_IRLS, xs = bpdn.IRLS(lam=lam)\n",
    "    err = l2_err(ne2.x, x_IRLS)\n",
    "    res = residual(ne2.A, x_IRLS, ne2.b, ne2.sig)\n",
    "    print i, lam, err, res\n",
    "    errs.append(err)\n",
    "    ress.append(res)\n",
    "    x_lams.append(x_IRLS)\n",
    "x_lams = np.array(x_lams)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "破線は$\\left|\\log(\\|\\mathbf{A\\hat{x}_{\\lambda}}-\\mathbf{b}\\|)/(n\\sigma^{2})\\right|$の値を示しており，$\\lambda$がどの値のときに残差$\\|\\mathbf{A\\hat{x}_{\\lambda}}-\\mathbf{b}\\|$がノイズパワー$n\\sigma^{2}$と同程度になるのかを表している．これは$\\lambda$の値を決める別の経験則であり，図からわかるように，このようにして$\\lambda$を決めると最適解にかなり近づく．"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 270,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PqquhefPE5UxDMAzDyDJt27bN2pLXAFVVcPTRWesuEExDMAzDSMDmzdC7N2zdCk3y/M9o\n0xAMwziAHTt2sGHDhqDNyBuqq90Kp/keDBJR4JeXGvk23huZlovjvcnWMQ3B33tq2rRp/PSnP41Z\nNh80hGTqpKshNArKyd5j+eYnCwiGUYQU0mzlbFAMbxhBChqCiHQF2qjq2rC004AKVW3wUH8kMA5o\nBdQAV6nq1rD8jsCjwGFAA/BLVZ0dpR3TEAwjRerq6ujSpQs7duygpKQkaHNynrIyeP55OOaYoC1J\nn7Q1BBEZLSLfFZEfAUcAg0TkVyLSWP92j8GgLTAeuEBVTwb+DNwfUex+4DeqOgo4F+jixUbDMLzT\nunVrunXrxtq1a4M2JSVUlWuuuYa9e/f63tcXX7j9DwYM8L2rwEkYEEJ/se8G6oHvAPuAvcDIsCBQ\n77G/McCLqroDQFVnAF9NMRSRdkBT4DsiUgk8CVR7bDtj5Np4b7Jp+T7em6icaQjeyiTyU/iwUb5p\nCFu3bmXSpEmUlJT4riEsXQr9+kGzZqYhAIzADfE0hI6vEEfTJGwqBZZHpNWJSJvQ5yNxQWNR6Anh\nTlxQMAwjw5xyyinU13v9Wy63WLduHb169cpKX0uWQBa3bA4UTxqCiHwDFxjOBx4GNgI3AWsBAU5T\n1YT/OyJyDbBBVaeGpb0MXKSq20RkOPAHVR0Zlv8icJmqbo9oyzQEwyhSpkyZwsSJE5k6dWriwmny\ni19Amzb5vQdCOPE0BK9q0l6gE9AcOAQXEPap6uWhDl712M4yYDgQ/r/YXVW3hT6vwQ1JhdMMF3QO\nYuzYsZSWlgLQsWNHysvLGTVqFLD/8cjO7dzOC+/81VdfPUAM97O/JUtg2LBKKitz5/qTOa+srGTi\nxIkAX/1exkRV4x7AicDrwHmhf48B7gP+j/1PGK8maidUriMwF+gUOj8HeDSizEzghNDn/sBrMdpS\nv6ioqPClTrwysfKipSdKi8xP5Xq84JefEpVLx1fxzv3yU6ptB3lPJXueKby2e+211+oDDzzguU6i\nMvF80rev6pIlictFOw/aT9HqhH47o/5Ge3lCWI3TELrgBF+AbUBr4EkR+TXwkYg0VdXIv+4jg882\nEbkZmC4iXwC1wFUichNQraozgWuAR0WkGU6s/qEHGw3DKCIuvvhiunbt6ns/u3bBRx9B376+d5UT\neNUQRuGGitoAi4HDVPWfItIJmAg8o6rP+WhnNJvUi+2GYRipsmgRXHIJfPBB0JZkjrQ1BFWtDGvs\nEGBTKH2riFwAXOHlCcEwjNxi9erV7Nq1i8GDBwdtSk5STG8YQQpLV6jqZ6q6XkSuCyX1BpYXUjBo\nFGQyXSdemVh50dITpUXmp3I9XvDLT4nKpeOreOd++SnVtrNxT82cOZPx48cn5SevtqVCEH6KlV9Z\nWcnSpQcGhGTvsXzzk5eJaYeLSLWITBCRShE5QkTGAieJSGdgMm5+gWEYecbAgQNZsmRJ0GbkLMX2\nhJBQQxCRbsB9qvofIfH3aeA/gMHAPGCeqv7Ld0sPtss0BMNIk02bNtGvXz+2bNmCSNRh5aJm4ECY\nPLkw1jBqJN21jJoAQ0TkZ8ApofMVuOUsHgkiGBiGkRm6du1KSUkJNTU1QZvimcmTJ/PMM8/43k99\nPaxZ45atKBa8BIRNuBnKzwBXA5vZP1HsdhEZl+TyFTlPro73ek3L9/HeROVMQ/BWxqufBg4ceNAP\nbC5rCHPmzGHz5s1J1UlFQ3jmmUp69YKWLeOXKyoNQVX34jSCm4Hrgd8C64EOqvpLoCfwWNLWGYaR\nE1x88cW0aNEiaDM88+GHHyaecZsB1q0rLv0AvGkIzXCTxWqBBcA3gHeBk3B7FrQCmqnqVf6aepBd\npiEYRhEycOBAnnvuOYYMGeJrP3fe6Sam3X23r91knbQ0BFXdg1tiol2o/AVAGXA28HNgEG4oyTAM\nw1dUlbVr12blCaHY3jACb6+dNg2VE9zSFY1HCW556t7APT7amHVyebzXS1oujfemWsc0hGDvqVzV\nED799FNat25Nu3btkrIlFQ1h/vzKgzbFKXQNwctM5QbgMtxOaZ/hBOY63PyDBuAO3CqohmEYvtKu\nXTumTJniez9797o1jMrKfO8qp0h6T+WvKoq0UdUvRKQEaFAPW2hmEtMQDMPwi5UrYcwY+PDDoC3J\nPGnvqRylwZ8B40TkfqAD8Gga9hmGETBz5szhrbfeCtqMnKEY9QNIMSAA7wC3ATfitrxMtZ2cJN/G\neyPTcmW8N506piFk95567rnnePbZZ2OWyfd7KlkNYckSaNv24DqFriGk+kP+BTBWVRtU9VlgTort\nGIaRA5SWltqaRmEsXQpZeJEp50hZQwga0xAMI3Ns3LiRoUOHUltbG7QpOcHw4fDII/C1rwVtSeZJ\nW0MQkR+KyKkicpaI9A1L7yIiRabDG0bh0aNHD+rr69m0aVPQpsSkoaGBk046ib179/rcDyxbxkGv\nnBYDXoeMNgKjca+ZdhCRfwdQ1c24PZYLilwf7zUNIXqeaQje8qKlv/HGGwwZMoT3338/aplcuKdq\nampYtWoVJSUHvi2faQ1h/Xro1Amqqg6uU+gagtcd06aKyKvAxcBVQBcR+QFu+etPk7bMMIyc4/rr\nr6dHjx5BmxETm6HsP2nNQwDGqKr/s0Si928agmEUEZMmTeKll15i8uTJvvZz333w8cfwwAO+dhMY\nGZmHICItQ5PQAFDVL4A6ERkpIvmzVKJhGHmJPSH4TzKvnY7h4AlonwMjgOkZsygHyPXxXtMQoueZ\nhuAtL10/ebUtFeK1u3r1avr06ZNUHa9lwvMbA0Iq373I83z77nnSEABU9cXQfsoXqerkUNpcYK6I\nnJm0dYZhGElwxx130Lp1a1/7UHUBYcAAeO89X7vKSZLWEETkYeBeVV0fljZDVbMaFExDMAwj03z0\nEYwYAZ98ErQl/hFPQ/D0hCAidwG7AMXtpfx3EWkUk5sCnTJhqGEYwTJt2jS2b9/OpZdeGrQpgVDM\n+gF41xBeAKaGjv8Dxoad/wM41w/jgiLfxnsj03JhvDfdOqYhBHNPbd++nalTp+akhpBOHa8aQnhA\nKEYNwcsGOS1wcw9aq+oHMY7cnd5oGIZnwienFSPF/oTgSUMQkd7ApcAZwFZgO24HNXBBpZOqftMv\nI2PYZBqCYWSY+vp6OnTowNatW2nZsmXQ5mSdE090eyifckrQlvhH2vMQVHWNqt6J20f5U2Cmql4S\nOi7KdjAwDMMfmjdvTp8+fVi2bFnQphzAjTfeyKRJk3zto/ENo2J+Qkhq+WtV3aaqlwN7RaS5TzYF\nTr6M98ZKy/fx3kTlTEPwViZVPw0ZMoTnn38+bp1s31PvvfcenTt3TqpOMmUqKyupqYGSEujaNXad\notcQoqGqk1S1XkSai8jdIjI6lXYMw8g9brnlFo477rigzTiAVatWRZ2UlkmK/ekAvGsIM4FtwA6g\nG/AR0EVVvysirYF5qprVVU9NQzCM4mDPnj20bduWHTt20Ly5fwMTDz3kgsKECb51kROkPQ8BaAYs\nBP4OTFDVq0XkAxH5I05c/iIzphqGYRzIunXr6NGjh6/BAOwJAdLbC3k7cJuqXq2qX8+UQblAPo33\nRksLerw3E3VMQ7C1jBqJtYZRMrZ40RAiA0IxaghenxA6AkfhFrLrJCIn42Yn/1pEOgNXqOr2pC00\nDMNIwDe+8Q1OOOEEX/tQhfffh8GDfe0m5/GqIYwFjgYWA51xgWQ9sAK3i9qdqnqBf2ZGtck0BMMw\nMsLatTBypNsHodDJxDyEicAJqvossBK37HUn4ExgNTBdRNp5NGakiLwiIrNF5HkRiboOkoj0EpEt\nXts1DCNzTJs2jRtvvDFoM7JGdTXk2ItVgeApIIjIJKCfiDwCXAPcgdsf4W1gj6r+n6ru8NBOW2A8\ncIGqngz8Gbg/SrlmwCPAh8CXHq8lY+TbeG9kmmkIsdNMQ/Dmp/Xr1/P666/HzM+3eypRmSlTKg8K\nCMWoIXh9QrgUWAVci/uhvgW4DugPPCsiAzzaNAZ4sTF4qOoMINomrvcCf8K96rrPY9uGYWSIo446\niqVLl7Jnz56gTckKK1faEwJ41xDaAKXAEqAn0EpVl4fyLgR2qeo0D+38D7BBVZ8PS/sHcFloS05E\n5HvAEFW9VUQqgNNUtSFKW6YhGIaPlJWV8de//pUhQ4YEZsO+ffsQEZo0SeeFyMQccQTMng29e/va\nTU6QloYQGr6ZFlrVVIHLcE8LjfwA+KdHW3aHjnBa4+Y5ICJDgIuB28NN8Ni2YRgZpLy8nIULFwZq\nw5w5cxg92t+FEDZtgp074aijfO0mL0j42qmq7hGR8B/xkaoaPoxTn8Sf6suA4bh9FBrpoarbQp+/\njxtCmiUiApQDc0TkT6r6ZGRjY8eO/WrT7Y4dO1JeXs6oUaOA/eNlqZyHj7V5rf/ggw8m7H/hwoX8\n5Cc/Sap+pE2x7AuvH6tuqv5I5XpinUe7nmT8Ee96otkTq06081SuJ5P3h5frScafseonun8az9u3\nb091dTWXXXZZ1PxMfd/iXc/q1aspLS1N+/saz97qajjkkAd5440D873cT4nurWjl0/FPKv6vrKxk\n4sSJ1NTUJH59V1UTHsD0sM8vxsrz0E5HYC5uuWyAc4BH45SvBJrEyFO/qKio8KVOvDKx8qKlJ0qL\nzE/lerzgl58SlUvHV/HO/fJTqm0HeU9VVFTo559/rrt27YqZ7weR7f785z/XO+64I6k6yZa55x7V\n888/OD+V717keS5+90K/nVF/c71qCBuAmbjhm9OBVxuzgNGqemTCRva3dSpwN265i1rc5jvXANWq\nOjOi7HychnDQG0ymIRhG4fPd736Xb33rW1xyySW+9XHRRXD22XDZZb51kVNkYi2jZcBPo7UN/C0Z\nY1S1Aohc6uK3McqOSKZtwzAKi1WrVtG3b19f+6iuhltv9bWLvMGrdF+vqtujHNuAej8NDILIMcBM\n1YlXJlZetPREaZH5qVyPF/zyU6Jy6fgq3rlffkq17SDvqWTPM0Vku5s2bUoYENLx044dsGED1NYe\nnJ/Kdy/yPN++e16fEARARM7EzT/YGZae1WWvDcMoHtavX497v8QfFi2CQYOgaVPfusgrEmoIoZ3R\nZqrqqBj5r+PG+bM6oG8agmFkh7q6Olq3bh20Gb7w0EOweDH86U9BW5I90pqHoKr1sYJBiAcBi6+G\nUYCsXLky0IlpfmNrGB1I2tP/VPVFVd2bCWNyhXwb741MMw0hdpppCMn5qXfv3tTW1jJt2rS45TNF\ntv3UGBBS1QuipeWzhuDvfHDDMPKapk2bMmTIENasWRO0KRmnvh6WL4cCfgBKGk/zEHIR0xAMIztc\nffXVDBw4kOuuuy6r/a5du5ZevXr5to5RVZWbe/DBB740n7OkvR+CYRjFS3l5OdXV1Vntc/fu3ZSV\nlbF3r3+j0XPnwtcLavPf9LGAEIV8G++NTDMNIXaaaQjJ+2no0KGsWLEiadtSobHd1atXc+SRR9K8\neXPPdZIt8+abcNJJsfNNQzAMw4jg+OOP56677spqn8uWLaN///6+ta8Kc+bAiSf61kVeYhqCYRg5\nx29+8xu2bNnCfffd50v769bBiBFQUwM+znvLSUxDMAwjr1i+fLmvTwhvveWGi4otGCTCAkIU8m28\nNzLNNITYaaYh5MdaRs2bN/c8IS4VP4XrB7HaKEYNwetaRoZhGFnjscce87X9N9+E73/f1y7yEtMQ\nDMPwxFtvvcWIESNo1qxZ0Kakxdat0KsXbNkCeX4pKWEagmEYaXPllVfyQQHM4po71wnKxRgMEmEB\nIQr5Nt4bmWYaQuw00xBS99PQoUNZsGCBZ9tSIRt+ahSUE7VRjBqCBQTDMDwxbNgwqqqqgjYjbSIF\nZWM/piEYhuGJ2bNnc9NNNzF37lxf+5k/fz5lZWW0b98+423v3g1dusAnn0C7dhlvPi8wDcEwjLQ5\n7rjjeO+993xdXwjgsssu46OPPvKl7aoq6NeveINBIiwgRCHfxnsj00xDiJ1mGkLqfmrXrh1jx45l\n+/btvvlq1qxZrFu3LuE+ypG2eS0TTT+I1YZpCIZhGHF45JFH6NKli2/tf/zxxxx++OG0aNHCl/Zf\nfx1OPtlUbVUGAAAVNElEQVSXpgsC0xAMw8gZpk6dyp/+9CemT5+e8bZ37YJu3eCjj6BDh4w3nzeY\nhmAYRl7wwQcfMGjQIF/arqx022UWczBIhAWEKOTbeG9kmmkIsdNMQ8jttYy2bt3K6NGjk6rj1U/T\np8OZZ3pvoxg1BFvLyDCMnOHss89m1KhRGW9XFaZPhylTMt50QWEagmEYSTFr1izatGnD1/No/8kV\nK2D0aKcfFPuS1/E0BHtCMAwjKaqrq9mwYUNeBYQZM+CMMywYJMI0hCjk23hvZJppCLHTTENI30/D\nhw/n9ddfT2hbKvjlp0mTKjnrrOTaKEYNwQKCYRhJMXToUFatWsW+ffuCNsUTdXXw/vtw+ulBW5L7\nmIZgGEbS9OvXjylTpmT0FdF//OMfHH/88fTs2TNjbQL8859w333utVPD5iEYhpFhhg0bxrvvvpvR\nNm+//XY+++yzjLYJ7u2ieMNFxn4sIEQh38Z7I9NMQ4idZhpCZuYhjBw5kmOPPTahfV7Zs2cPq1ev\n5tNPP026bjwfqDpB+ZBDYpeJ1YZpCIZhGB4YMmQI5eXlGWtv5cqV9OzZM+NrGFVVuTeLjjoqo80W\nLKYhGIYROH/961955plnmJLhmWPXXw+tW8Odd2a02bzG5iEYhpHTLF68OONrGO3bB5Mnw6xZGW22\noMn6kJGIjBSRV0Rktog8LyKdIvK/LiJviMhboSNzz6Ueybfx3sg00xBip5mGkJtrGY0YMYJzzz03\no36aPdutbjpgQGJ7TUNwZPUJQUTaAuOB0aq6Q0TOBO4HLg8r9gDwHVX9WESOAP4CJLfalWEYecXZ\nZ58NZPYHdNIkuOSSjDVXFGRVQxCR7wCDVPXOsLSXVfWM0OdWwGmqOi103gmYoqqjorRlGoJhBMia\nNWu49957efTRR4M25SB274bu3eG99+CII4K2JrfIpXkIpcDyiLQ6EWkDoKq7woJBN+A54PasWmgY\nhie6du3KU0895fsey6kwYwYce6wFg2TJtqi8O3SE0xpoFp4gIqcCtwJXq+qKWI2NHTuW0tJSADp2\n7Eh5eflXS+c2Pnqmch7+2Oq1/oMPPpiw/4ULF/KTn/wkqfqRNsWyL7x+rLqp+iOV64l1Hu16kvFH\nvOuJZk+sOtHOU7meTN4fXq4nGX/Gqp/o/knmvGfPnixZsoQtW7ZkxF/xrifWebTreeCBSo4/HiC6\n/V7+f7zcT4nurVSux8t5MvdTZWUlEydOpKamhhNOOIG4qGrWDuA04KaItEUR52cAM4EOCdpSv6io\nqPClTrwysfKipSdKi8xP5Xq84JefEpVLx1fxzv3yU6ptB3lPeT2/9NJL9YknnohvZBJkwk/bt6u2\nb6+6ebP3dlP5nsVKy8Y9lY6fQr+dUX9Xs60hdARmAGep6lYROQc4R1V/EMovAaqAE1V1R4K2NJu2\nG4ZxMA888ACrVq3ikUceSbmN+++/n3POOYf+/ftnxKYnnoCXXoIXXshIcwVHzmgIqroNuBmYLiKz\ngIuBG0TkJhEZAxwDdAemisjrIlIpInOzaaNhGN4ZPnx42msaPfTQQzRpkpmfIlX4wx/g6qsz0lzR\nkfV5CKpaoapfV9XTVfVSVd2pqr9V1ZlANXCoqo4OHaOAU7JtY+QYYKbqxCsTKy9aeqK0yPxUrscL\nfvkpUbl0fBXv3C8/pdp2kPeU1/Pjjz+ep556Kr6Rcdi2bRubN2+mT58+MW1LRHidN96A+noYMyZ2\nmURtpJuWjXvKr/spp2YqRxsDUtX6IGwxDCMxLVu2pF+/finXf++99xg8eHDGnhDGj4cf/ch2RksV\nW8vIMIzAeOihh1iyZAkTJkxIu60PP4Tjj4d166BNmwwYV6DkjIZgGIYRzsKFCzO2jPbDD8P3v2/B\nIB0sIEQh38Z7I9NMQ4idZhpCZjWEdLnqqqs499xz02q3srKSnTth4kS49trYZRK1kak00xACYvx4\naNIEmjZ1/zZp4sYOmzWDli3d0aKFyxdx+SUlLr95c/dvScn+o2lT9+/mzbBpk8sPP2xc0jCi0zh8\nK0l+SUaMGJGR/p98EkaNgiOPzEhzRUteawg/+pGyb59b5lYVGhrcsWePW8vkyy/d0Zje0ODK1te7\nMvX17nzvXnfe2Na+fe688Wgs1xgwGoNK+NEYYJo3d0eLFgd/Dv+3ZUto1erAfxs/Nx6tW+8/2rRx\n/7Zt68pZcDJyiX/7t3/jwQcfZNiwYVnvu74eysrgL3+Bk07Kevd5R8HuhzB+fPb6Ut0fKBoDSORR\nX7//2L37wM+R543Batcu2LLlwPPGo65u/791dbBzJ3zxhWujTRsXHNq12/9v+/b7/+3YETp1cv+G\nf+7UCbp0gQ4d3BOTYWSCvn378u677wYSEB57DPr3t2CQEWJNYc71gyJeumLWrArdulV1wwbVpUtV\n589X/f3vK/SFF1Sfekr1Rz+q0F//WvXGG1X/+79VTz65Qk8/XXXYMNWjjlLt2FG1aVPVzp1V+/dX\nPfFE1fPOU73iCtVbblEdP1518mTVykrVZctUt21TbWhI7ZpTrWNLV+TH0hWNPPzww3rFFVfEtMUr\nyfppxw7VTp0qtKoqvXZt6Qp35PUTQrHStOn+v/wb+eILN4YKboXHxs8AlZUHnoN7ytm6FT77zB2b\nNrnj009h5UqYMwdqa6GmBj75xD0d9ejhjsMPh5493RPNtm1u3La01NljQ1nFyfDhw3niiSey3u8D\nD8Bxx7nDSJ+81hDy1fZ8ZOdOFxg2bnTHRx+5Y/1699732rUuGPTuDX37uuPoo91uVQMGHBi8jMJj\n165ddOnShS1bttCyZUtPdU499VSmTJlCxxRvjk2b3L31zjsQmuhseCCehmABwcgIqu6JY80aWLXK\nHcuXw9KlsGyZ0zaGDIFjjnFHeTkMHOgEeqMwOOGEE3j88ccZPHhwwrI1NTUMGjSIzz77LOk3kxr5\n6U+ddvfwwylVL1psYlqS5Ns745FpQcxDEIHOnWH4cLjoIrj1VnjqKXj3Xfj8c5g3D378Y9i+vZIZ\nM+C733VPDSNHuqUGnn3WPWk0xnibh5B/8xDmzp3rKRjA/glpkcHAq59WrXJvFd12W/p+ipVv8xAM\nwweaNHE6w5FHurejGvWMzz+H6mqYPx/++lf3F1+TJnDyyU6rOOww9/aI6RL5QTJ/6S9atIjy8vKU\n+mlogP/+b7jlFujWzT2FGpnBhoyMnEHVrUcze7YTwisq9q9cOWYMnH66+wEw8p+LL76YM844g//8\nz/9Muu4f/+ieDt56y71gYSSHaQhG3rJ6Nbz6Ksyc6QJE375w1llw9tlueMrmUuQnAwcO5Nlnn016\nHaO1a93/++zZToMyksc0hCTJt/HeyLQgNIRM12ks16cP/OAH8I9/uFdif/c7WL68ku9/3w0rXXGF\n2x2rrs40BK95fmkIyTBr1iwGDRrkybZGVOHKK+H66w8MBqYhZK6OBQQjb2jWDE45xQWIDz5wQwYD\nB8Lvfw/du8Ptt8PTT7u5EUYwbNmyhXXr1iUs16NHD0qSfMXsf//XrTN2ww2pWmckwoaMjIJg82b3\npDBlitMfvv51OP98+Na3oGvXoK0rHp544gkqKyvT2kUtGvPmwb//u9sRbcCAjDZddJiGYBQVO3fC\njBnwt7/BK6/A0KFwwQXwne+4N5cM/1i0aBEXXXQRSzP46s/HH8OIETBhAoStlG2kiGkISZJv472R\naYWkISST15jeti1ceCE89xw891wlP/4xvP22+8vy2GMreeghN9s6si3TEFI/b2TQoEGsX7+ezz//\nPKZd8Yhsd/du96T3gx/EDgamIWSujgUEo6Bp0QLOO89pCzU18L3vwYIFbtb0iSfC88+7CXFGZigp\nKeHYY4+lqqoqav6+ffvYs2ePp7ZUXSA4/HA358DwHxsyMoqS+np47TX4+99h6lQ3ae78892wUv/+\nQVuX3/z4xz+mZ8+e3BBF/V2wYAFXXnklCxYsiNuGqpvBPn+++39q29Yva4sPGzIyjAiaN4czz4TH\nH3eL9t17L2zYAKNHuzeXbrkF/vWv/UtpGN75xje+QevWraPmVVVVMWTIkLj1w4PBzJkWDLKJBYQo\n5Nt4b2RasWsI8dKinZeUuEBw4YWVfPQR/PnPbrnvyy5zy3xfc40Tp3fv9mR6UjanWyfXNASAc845\nhx/+8IdR8xYsWMDQoUNj1q2oqDwgGHToELOoJ1u8ljENwWEBwTDCaNIEvvY1uOcet0rrrFkuKNxx\nBxx6qHtb6ckn3V4RRvJUVVXF3FWtrg7uuss9mXkNBkZmMQ3BMDzy6acwfbqb7/Daa26/hzPPhG9+\n070W2axZ0BbmNnv27KFjx47U1tbSNmIcaP16N2dk0CC3JWarVgEZWQTYPATDyDB79rhXWadPd2st\nrVnjVnE9/XQ3/DRggK3SGsnq1au57LLLePvttw9Ir6iASy5xM5D/53/Mb35jonKS5Nt4b2SaaQix\n0zI13tu4jMZvfwtVVbBihdvjobraLb7XowdceqlbbmHVKjc2niz5qiHEok+fPgcEgx07nD7z//6f\nG4a7/np4443k2zUNIXN1LCAYRgY49FD3V+4TT7gVOd9+G0491S21cMopLlhceik8+igsWVL4by/V\n19fzyCOPxMyfMQMGD3b7ci9e7JY3N4LHhowMw2dU3VPC7NkwZ477d/t2t95S4zF8OLRvH7SlmUNV\n6dKlCwsXLqRXr15fpb/1Fowb54Lmo4+6ITYju5iGYBg5xiefwNy57kli3jxYuNDNyB0+3K291Lj3\ndD5vCPTLX/6SSZMmMXXqS3zySRn33uv22b7tNviP/zARPihMQ0gS0xC8UcwaQrJEtt29u5sV/bvf\nwZtvuiW7//Y3OO0098bN3XdD376VdOvmxOqrr4bx4918iA8/dPMkEtkctIYwduwvGTToFwwZcjJX\nXPEy55/vtJb/+q/YwSCI716s/GLUEGxPZcPIAUpK3PpK4ZN4KyqgXz+3Z3Dj8dJL7kd10ybo3Rs6\ndnRDTkcf7TYT6tPHzZtIcquBjPD55+5p55VX4OWX3Wu63/ve5Tz2WD/GjbuIoUNfoHnz4dk3zPCM\nDRkZRh5SV+d0iVWrYOVKd6xe7Y7aWjjiCDjqKHcceaQbjjriCPfvoYdCp06p7Ue8bx989pnTANas\nccf777s3rTZuhOOOc/MyzjjDDX019vHxxx9TX19PaWlpJt1gpIBpCIZRRHz5pRt2WrvWDS+tW+d+\nrDdscP9u2uRE7Q4d3BNGmzZuvaDWrd0PeJMm7qivh127XHs7drhAsH27CyalpS7Y9O7t5lwMGwZl\nZcE8mRjJES8goKpZPYCRwCvAbOB5oFNEfj/gn0AlMB04MkY76hcVFRW+1IlXJlZetPREaZH5qVyP\nF/zyU6Jy6fgq3rlffkq1bT/vqT17VGtrVVesUK2uVv3DHyp05kzVl19WnT5d9e67K/SVV1Rnz1ad\nP1914sQK3bRJde/e1K/HC0H4KVZ+qmnZuKfS8VPotzPq73NW47mItAXGA6NVdYeInAncD1weyhfg\nKeDbqvqxiBwHTADOyqadhcbChQsZNWpU0GbkPMXkp5ISN3R06KHufNs2J1430qrVgedffAGHHLL/\nvJh8lQ5556dYkcKPA/gOcFtE2sthn4cCT0Tkvwg0i9JW0hGyWBk3blzQJuQF5ifvmK+8kYt+Is4T\nQrZfOy0Flkek1YlImzj5a4Cj/TXrQArttVO/KLTXTv0k3+6pYvJTrPxMvHbqF375KdsBYXfoCKc1\n0CxOfkuguc92HcDEiRN9qROvTKy8aOmJ0iLz165dm9C2VPDLT4nKpeOreOd++Slav5mqE4SfIP/u\nqURlUvmexUrLxj3ll5+y+paRiJwGDFfV34alLVLVY0Of+wA3qOrVYfkVwPmquiWiLXvFyDAMIwU0\nxltG2X5JbAFwl4g8pqpbReQcYG5Y/odAuYgcqarrQqLyzshgALEvyDAMw0iNrM9DEJFTgbuBL4Ba\n4CrgGqBaVWeKSDnuTaR9wOfAD1S1JqtGGoZhFCF5OzHNMAzDyCy2uJ1hGIYBWEAwDMMwQuRkQBCR\nEnFk9XXTfMR85Q3zk3fS8ZWINBWRFJbNy08K7b7KyYAAnAe8AbwTnigiI0XkFRGZLSLPi0inaJVF\n5AYR+VE2DM0BUvKViPQWkcdF5FYRuT6bBgdEqn7qLiKPiMjNInJnNg0OkHS+f9cAj2fDyBwhKV+J\nSJfQ/XSniNwWhMFxiTWFORcO4K2wz22BfwHtQudnAv8Xpc75wJXAD4O2P5d9BRwGtA59nhC0/Tns\np2FAt9DnXwdtfy77KqzsvUHbnqu+Av4LOCL0+abGz7ly5OoTQiP7wj6PAV5U1R0AqjoD6AEgIv8j\nIveIyAlAF9xqqsU2TyEpXwGHAseIyGTg/WwbGyDJ+mkPsFNEfoJbV6uYSPb7d0wANuYKnnwF9FfV\nDaHPHwB9s2diYvJp9fJSYqyDpKq/BxCRh4FNwE+A/iKyQFXnZdfMnKCUxL4qBd5X1YtE5H4R6aCq\n27NrZuCUkthPrYFfAPep6udZti+XKCWBr8Iotj/GIikl9pptH4vI0aq6ErfU/9RsGxePfAoIidZB\nQlWvBRCRvsDZRRoMwIOvgP7Az0XkE2B3EQYD8OanH+P+uvuFiDTBDRsVY2Dw4qtGWvpvTk4Tz1dP\nA3eIyDbgc1VdnW3j4pFPAWEZMJwDI2p3Vd0WWVBVV+FmOxcrCX2lqq/ghtaKGS/31G9VtQHcfh0a\nGvwtQpL5/l2XNatyk0S++mH2TfJGrmsI4fYtAL4VptZHroNU7JivvJGUnxqDQehzsQUDu6e8UxC+\nytknBBFphXvMAkBVt4nIzcB0EQlfB6noMV95w/zkHfOVdwrJV7aWkWEYhgHk/pCRYRiGkSUsIBiG\nYRiABQTDMAwjhAUEwzAMA7CAYBiGYYSwgGAYhmEAFhAMwzCMEBYQDMMwDMACgmFkFBHpKCLPxNq8\nyTByGQsIhpFBQguYvQZcGLQthpEsFhAMI/NMw22taBh5hQUEw8gwqloLtBGRdkHbYhjJYAHBMDKM\niLQAdgBnB22LYSSDBQTDyCChXdV+BdwGfDtgcwwjKSwgGEZm+T3wlKouBHqKSLQtJg0jJ7GAYBgZ\nQkQuABao6gehpGnAWQGaZBhJYRvkGIZhGIA9IRiGYRghLCAYhmEYgAUEwzAMI4QFBMMwDAOwgGAY\nhmGEsIBgGIZhABYQDMMwjBAWEAzDMAwA/j8xw0Hn9zssVQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b438850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogx(lams, errs)\n",
    "plt.semilogx(lams, ress, '--k')\n",
    "plt.xlim(lams[0], lams[-1])\n",
    "plt.ylim(0, 1)\n",
    "plt.grid(True, which=\"both\")\n",
    "plt.ylabel(u'正規化'+'$\\ell_{2}$'+u'誤差')\n",
    "plt.xlabel('$\\lambda$')\n",
    "plt.savefig('lambda.png', dpi=220)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "最も良い$\\lambda$の値を用いた場合と，それよりも大きい値と小さい値を用いた場合の，三つの解\n",
    "--"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 272,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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7mIGHwwBO4eTk2K2XzMCJ3CslWj6dzJsZeF1t2vAWMqqLGTiR+6VEAHcyb2bg\ndbVpw1vIqC4GcCL3S4kqdGbg9Wvblr+RTnXl5FgAZxU6kXsxA09xrEKncJiBE7lfSmTgDOD169KF\nWRbV5QRw7htE7pUSGTir0MP7atMmHF53LXa/fCGmXXstvtq0KdFFIpfIzrZH7DIDJ3KvlMrAGcD9\nvtq0CXMGDcK0jRuRDaAMwNTlyzFh0SKclJ+f6OJRgjnHCjNwIvdKmQy8dWsgPT3RJXGP4oKC2uAN\nANkApm3ciOKCgkQWi1zCybyZgRO5V0oE8Nxctn+H8pWUIPTcnA3At21bIopDLuMEbmbgRO6VEgE8\nLw+48MJEl8Jd0vLyUBYyrAxAWufOiSgOuYxThc4MnMi9UiKAd+gAzJuX6FK4y9iiIkzt3r02iJcB\nmNq9O8YWFSWyWOQSrEIncr+U6MRGdZ2Un48JixbhoYIC+LZtQ1rnzphQVMQObASAVehEXiCqGt8F\niGi8l9GQrzZtQnFBAXwlJUjLy8NYBimiRv31r8DIkfab4AziRPEhIlBVifTzSZ2B81Yposg4GTh/\nqY7IvZK6DZy3ShFFJjvbMu+0pD5DEHlbUh+evFWKqPm+2rQJ8//nWgyo4BP6iNwsqavQnVulAoM4\nb5Uiqp/T7DTDaXZ6js1ORG6V1Bk4b5Uiah42OxF5R1Jn4LxViqh52OxE5B1JHcABC+JTn3020cUg\n8gQ2OxF5R1JXoRNR87DZicg7kv5BLkTUPLUPP6ppduLDj4jiI9oHuTCAExERJUC0AZxV6ERERB7E\nAE5ERORBDOBEREQeFHEAF5EcEXlGRN4RkbUiclssC0ZERET1iyYD/wWAVar6AwB9AVwoIj1iUyxy\nm6VLlya6CBQD3I7JgduRgOgC+McAngQAVfUBOBzl/MjFeMJIDtyOyYHbkYAonsSmqgsBQEQEQAGA\nHar6eawKRkRERPWLKmMWkQ4AXgSwXVUnxqZIRERE1JhGH+QiItcCuAmAM6HU/P8TAPMBTFHVpQ18\nnk9xISIiCiMhT2ITkfsBrFdV/lIIERHRURZNAP8YwH4AlbCsPAPATFX9e+yKR0REROFEE8DTVbU6\n4H0aUNsjnTxMRFqq6pGa/zMAZKrqoQQXi5qgZntVw7ZZRaLLQ5EJtx1FJB12zq6qeZ+rqgcTWExK\nsIg7sQUG75r3vsDgLSLniMjCmge9zBeR9tEUlI6q10VkiYi8DWAxrL8DRGSqiPxTRJaLyK8SW0Sq\nx3AA/wLJeERDAAAgAElEQVSwwhkgIuki8tuAbXdlwLjvisg/RGSpiLwuIiclotBUR53tCOBcABtE\n5G0RWQLgTWcEt6P7iMhQEfmg5rVIRE6K+bGoqjF/AcgBsBJAbs37ywA8FY9l8RWX7bcozLCfAngg\n4P1fAJyf6LLyVe82fD/g/wIA42r+bwlgEYDusKavFQA614zrC+D1RJedr3q343AAt4aZhtvRZS8A\nrWpiYJua9/0BPBfrYzFeD165BMBrWlO9o6pvAOgcp2VR7GWLyBM1V4JzRCQbwBgAjwdM8xiAQYkp\nHjVBYA3ZcABzAUCtaWQuAOcJip+o6raacR8BqBKRzKNcVqpf4HbMA/B9EXlTRN4SkR/WDOd2dJ8c\nAHeq6oGa92UA0gEMQwyPxXgF8G4AQh/qUl4TCMjFRCQHwMkAHlLVgQA+BTAdQEdV3RIw6ecAvnf0\nS0hNFHhrSrUGN3l9AaAnwh+nXwLgI5HdKR9AKaxG8yoA94vI8eB2dB1V3a01t1fXPGL8Cdh51BfL\nYzHiJ7E14kjNK1AWAF4RupyqlopIF1WtrBn0ewDvw04cgVqB29PNAnunHggZ52y7w6h7nLYC0CKO\n5aLI3Q1A1epYd4vI87B28XDnW25HFxCRHwMYC+AqVd0hIjE9FuOVgX8G4NSQYSeo6r44LY9iqzZ7\nqzlZHAGwXUSOC5jmVACbj3K5KDJHano1O5xt9znqHqenAPj6KJWLmifc+boC4c+33I4JJiI3AvgR\ngOGquqNmcEyPxXgF8A8BjHB6novIFQCWxWlZFEMi0hHA+yLStub9dbBttwjAnTXD0gGMA/BCospJ\njQo8tlcAuAWwWwRhGcGLADYB6OP0dhWRvgBKVfXbo1tUakDgdrwf9lRMiEgugJGwY5Pb0WVqHjN+\nK4CrA2ozgRgfi3GpQlfVfSJyL+x2pDIA3ziFJndT1V0iMgPAQhEph10dTgBQDuABEVlW8/+LqsqL\nMhcSkdawJivHgwAeF5H3YbUps1R1a8204wA8LSLVsKr2nx3t8lJ4YbZjEYA/iMj1AHwAZqjqnppp\nuR3d5QIAHQEstt/7QhqAvQCuBPC7WB2LET/IhYiIiOoSEdGQ4CoimSHZePTLYQAnIiLynni1gRMR\nEVEcMYATERF5EAM4ERGRBzGAExEReRADOBERkQcxgBMREXkQAzgREZEHMYATERF5EAM4ERGRBzGA\nExEReVBUAVxEhorIBzWvRc4vqRAREVF8RfwsdBFpBeBdABer6gER6Q/gdlW9JpYFJCIiorqiycBz\nANypqgdq3pdHOT8iIiJqopj8GpmI9AAwF8B4Vf006hkSERFRgzKinYGI/BjAWABXqeqOMOP5e6VE\nRERhqKpE+tmoAriI3AjgEgDDG/qhcv7muPcVFhaisLAw0cWgKHE7Jgdux+QgEnHsBhBFABeRDgBu\nBdBPGaGJiIiOqmgy8AsAdASwuOYqIg3AXlUdGYuCERERUf2iCeCvqOrLgQNEJDPK8pBLDRw4MNFF\noBjgdkwO3I4ExKgXeoMLEGENOxERUQgRiaoTG+/bJiIi8iAGcCIiIg9iACciIvIgBnAiIiIPYgAn\nIiLyIAZwIiIiD2IAJyIi8iAGcCIiIg9iACciIvIgBnAiIiIPYgAnIiLyIAZwIiIiD2IAJyIi8iAG\ncCIiIg9iACciIvIgBnAiIiIPYgAnIiLyIAZwIiIiD2IAJyIi8iAGcCIiIg9iACciIvIgBnAiIiIP\nYgAnIiLyIAZwIiIiD8pIdAGIiCh2vtq0CcUFBfCVlCAtLw9ji4pwUn5+ootFcSCqGt8FiGi8l0FE\nRBa85wwahGkbNyIbQBmAqd27Y8KiRQziLiQiUFWJ9POsQiciShLFBQW1wRsAsgFM27gRxQUFiSwW\nxQkDOBFRkvCVlNQGb0c2AN+2bYkoDsUZAzgRUZJIy8tDWciwMgBpnTsnojgUZwzgRERJYmxREaZ2\n714bxJ028LFFRYksFsUJO7ERESWR2l7o27YhrXNn9kJ3sWg7sTGAExERJQB7oRMREaUgBnAiIiIP\nYgAnIkoyf/wj8MwziS4FxRsDOBFRklm5Eli9OtGloHjjs9CJiJLMrl1AVlaiS0HxxgBORJRkGMBT\nA6vQiSguKioqgv42dVxTxkez7FSwa5e9KLkxgBOlCJ/Ph8mTJ+O8885Dr169cNttt+Hw4cMRTVtS\nUoJRo0ahf//+6NevH0aOHIktW7bUji8vL0ffvn2Rn5+P8ePHB827oXFNGf/pp59i8ODBOOuss9C3\nb19MmDABlZWVTf58Kti9mwE8FTCAE6WIyZMno3Xr1njvvffw8ccfIysrC3fffXdE095yyy0YOnQo\nVq1ahQ8//BBDhw7FuHHjasdnZWVh/fr1KCwsRHZ28M9rNDSusfHV1dUYNWoU7rrrLqxYsQKrV69G\nZWUlZs2a1eT5J7vqamDvXgvgfIZWcmMAJ3Kx2bNn49577416PuXl5XjllVdQWFgIwJ4AVVRUhBde\neAHl5eXNnnb9+vUYM2ZM7WfGjBmD//znP2GX3aJFi3rL1dC4cONFBC+99BIuuuii2veXX345vvji\ni4jmn4z27AHatwcyMoDS0kSXhuKJAZzIxSZMmID58+dj586dUc1nzZo16Nq1K9LT02uHpaenY8CA\nAVgdcr9RU6YdMWIEHnvsMagqfD4f5syZg5EjR4Zdtkj9T4psaFy48WlpaejZs2ft+z179uCJJ57A\nqFGjIpp/Mtq1C+jY0V6sRk9u7IVO5GIigmuuuQZPP/00Jk+eHDTuyy+/xNy5c53nKddOr6oQEQwY\nMADDhg0DAGzfvh09evSoM/8TTjgBO3bsCBrWlGkLCwsxfPhwzJ49Gz6fD3369MGrr74ak+/cFAsW\nLMC0adOwefNmTJo0CYMHDz5qy3Y7J4AfPmz/n3xyoktE8cIATuRy119/PYYNG1YngJ988sm4//77\nmzSPli1bhq1OPnz4cFCm3ZRpKysrMXz4cEycOBEjR46EqqK4uBiXXXYZlixZclSy3jFjxmDMmDE4\ndOgQ7rjjDkyZMgXTp0+P+3K9IDSAU/JiFTqRy+3evRuHDh3CypUrI57HKaecgpKSkjrDN2zYgLy8\nvGZNu2zZMnTq1Km2ylxEcMMNNyA9PR3r16+PuIyRaN26NR555BEUFxcf1eW6GavQUwczcCIXW7hw\nITZs2ID77rsPTz31FM4444zacYFV6IHCVaHn5+dj1apV8Pl8SEuz6/aKigqUlJTgtNNOC/p8Y9Mu\nXrwYWWGeEpKbm4uDBw/G9PuHWrt2LT777DNceeWVtcNEBNXV1XFdrpcwA08dDOBELvX8889jzZo1\nmDlzJkpLSzFlyhTMmjULLVu2BNC8KvSMjAyMHj0a9913H2bMmFHbs3zEiBF1brVqbNqzzz4bEydO\nxJo1a9CnTx8AwOLFi7Fu3Tr07t07aF4+nw8+ny9smRoaV9/4tm3b4vbbb0fPnj3Rq1cv+Hw+TJ8+\nHUOGDGn2/JPVrl3Ad79rATzKvo/kcqxCJ3Kh5cuX46233sLMmTMBADk5ORgxYgTmzZsX8TwfeOAB\nlJaWolevXjjnnHNQXl6Ohx9+GIB1XDvzzDNrO6k1NG3Hjh0xb948TJo0CWeeeSZ69+6NBx98EC+/\n/HKdzLy0tBQHDhwIW56GxtU3vlu3bliwYAHGjx+Ps846C2eccQZKS0vx6KOPNnv+yYpV6KlDNM53\n+ouIxnsZRERkLroIuPdey8B/9zvg9dcTXSKqT81dIxH3+mQVOhFREmEbeOpgACciSiIM4KmDAZyI\nKEn4fPYo1WOPBY4cYQBPduzERkSUJPbtA7KzgRYtgJwc+2GTkEfdUxJhACciShJO9TkAiLAnerJj\nACciShKBARxgAE92DOBEREmCATy1MIATESWJ3bsZwFNJVAFcRM4RkYUi8o6IzBeR9rEqWKSqq4HB\ng4Hnnkt0SYiIji5m4Kkl4gAuIjkAHgMwWlV/AOBPAB6OVcEi9dhjwNatwKRJ1iOTKNX99a/At98m\nuhQUa2vXAi+8EDyMATy1RJOBXwLgNVU9CACq+gaAzjEpVYQ+/xy4/37gtdeA4cOBqVMTWRqixHvo\nIeD664FLLuEFbTL59FPg0kuB224DAn9JlQE8tUTzIJduAD4PGVYuItmqWhY48L//BdLSgDZtgLZt\n7QlB335r9yf6fEBGBnDCCTa+osLacQ4fbnpB9u2zq9E5cyxon3wyMGMG0LMncNNNwP/7f/5p9+wB\ntm8HSktt2S1aAJmZ/r+q/hcQ/n3g33DDmjNN6P9paUB6et2/IvYC6v4NN8z5m5Fh3w2wBztUVNj8\nWrUCjjsuuAwlJTYuMxM4dAgoK7MmifpIA0/wDR3X0PusLKB9e6B1ayuj86qosG3UVLHaDk35G/h/\naSmwf79tq2OOAaqqgFWr7CT7ne8A/fvbgzUCv3dT/h44APzjH/bKzwdGjgTOOw84/njbRgcP2q9N\nVVXZ9Glp/v1ExDLv3/0O+OQTC+SDB9vJPiPD/x18Pv93adnS7iE+9ljbDxx/+5st66ST/PcWOy/A\ntt2xx9p8fT4b3tDfwGMqsAz1DT982I7v1auBDh2AAQOACy6wde3YtcvWV+i2DP2/OePCvXfWbVqa\nf32H/u9819D11JR9TgQ49VRbl4B99pNPbLwz/wMHgCuvtG3avz9w4YU2/cCBwLZtdQP4l18C69bZ\neaBDB1tv1dX+c3Bmph177dvb/KurrRbz229t3VdX2zHaqpXta5WV/r/OKy3NzicdO1pZKyr8x3F1\ndfD5LNz/IrbeSkuBt98G/vlPm9+llwJ9+9qyMzLqrtfm/MxGWpp9z6ws288zM618O3fa/h24fUNf\noZoyLPT9ccfZ8RNLEf+YiYj8EsBWVX01YNibAK5S1X0Bw7Rdu6lQdTboQGRlDcQxx9iKTE+3jb1t\nm23AqirbycL83HC9srOB3r2Bs88GfvEL21AA8JvfWFB6/HH/tKeeastp186mc3bAigr7G27DhXsf\n+DfcsOZM4/zvnLTCnfScQNbcwFNdbd9N1Q6CzEyb144dFmSci5v337cfQWjf3tZD69a2XjPqucRr\naLdpzklR1S4U9u61k0XLlv5XixbBgaQpYrEdmvs3J8cuTH0++x4A0K+fXUD+97+2nvfvb94FAmDr\nYNAgYOhQOwm/9BLw0Ud2gZuRYfvv8ccHB+TAwHfsscCLLwLdutn7yZOBV16p/wR15IidtG++GXjk\nEf866dYNOO00u/gtL7dt4rwA+8zu3bavhbv4DD1hBy439H244ZmZQK9ewOmnWxmWLQNWrABuvBEY\nNgz4/e/tIqdDh/D7Quj/jb1vaFzg+nWOy8D/fT7/9w18NXWfO3zY5nH33Xa8/uY39j4rK3g5t99u\n2wmwfeK662w7VFUB775rPycKABs2AFdf7Q+mu3dbsFJF7Tm4stK2a1mZDdu71/9rZq1aWbkOHbJX\nRoZtj9CXz2eBcOdO+/7O8duypX3/wPUTeE4L/D893T5z/vl2sblzJ/DGG8B//uM/T4euV+dc3xTV\n1fYdysv9yaNz4dGmjX/7hr5CNXZ+q28aVeCRR5bi44+X1g6fNm1aVD9mEk0AvxhAf1WdGTBsrar2\nDpku6NfInCvJUKq2Ulu3bt5Gachzz9mB/Ze/+Id17AisXx+cfaaiiy8G7rkH+OEP7f1f/wr86U/A\nq682/DlKvOpqO9FnZTVcCxKJp58GFi0CnnnGP+y44ywLdNMxs2UL8OCDlqnddBMwbpz/JOx1771n\nTYFHjtivil14YWy3sxMIQ8+zToDv0MECd7KrrLQLklgfQ/WZNs0uSJYssTgHJPbXyD4E8D8i8n+q\nuldErgCwrLEP1beyRCzji6U2bYKr1QC7+szNje1yvKhtW8sKHfv2Wa0EuV96euyPFUd2tmVigcrK\nmlcjdjR06WJNZsnovPMs8YiXzMzww1u2BPLy4rdct6lvPcTLlCnWT+uGG4Dnn4/NhUPEuW5NNfm9\nAF4XkbcAXA1gcvRFip3cXH/bBmBVyVVVqXF12Zh27YID+P79FtQptWVlBT87W9WqHd0WwIm8RgR4\n6inro3XkSGzmGdWvkanqEgBnx6YosRcawJ3s+2hVmbhZ27bBvZIZwAmom4EfOmSZWayatYhSmdOv\nIVaS+rAMF8CTpZ0sWqFV6AzgBFgAD8zAy8vjV11PRNFJ+gAe2AbO9m8/BnAKJysrOAN3Y/s3EZmk\nDuBt2gRn4AcOMIA7GMApnHAZOAM4kTsldQDPyrLOAlVV9p5V6H7shU7hhMvAWYVO5E5JHcCdh2yU\nltp7VqH7tWvHTmxUV2gnNmbgRO6V1AEcCG4HZwD3YxU6hdOqld1u6Tz+kxk4kXslfQAPbAdnG7gf\nAziFIxJ8LzgzcCL3SvoAHngrGdvA/RjAqT6BHdmYgRO5V8oFcGbgxgngzi8HVVX5n89LqS2wIxsz\ncCL3SokAzjbwupxfCTp0yAJ5u3Z8Qh0ZZuBE3hDVo1S9gG3g9XOy8NJSVp+THzNwIm9IiQycbeDh\nOQGc7d8UiBk4kTekXABnBu7HAE7hMAMn8oakr0JnG3j9WIVO4QQ+zIUZOJF7JX0Gzjbw+jk/Kep0\nYiMCeB84kVekRAbONvDw2rWz4F1Wxgyc/JiBE3lDygVwZuB+rEKncAI7sTEDJ3KvpK9Cd9rAq6vt\nnmdmE37sxEbhBHZiYwZO5F5JH8CdNvDSUjsxpSX9N266wDZwBnByMAMn8oaUqUJn+3ddTgbONnAK\nxAycyBtSKoCz/TtYYCc29kInBzNwIm9gAE9hzMApHGbgRN6QEgG8tNQCFQN4MPZCp3CYgRN5Q9IH\n8PR0oFUr4Jtv2AYeyunExgycAjn3gVdU2PsWLRJbHiIKL+kDOGCZ97ZtzMBDsQqdwnGq0Jl9E7lb\nStxUlZsLlJQwgIdyMnDAaimIAH8VOtu/idwtJQJ4mzYM4OFkZgKtW7MHOgVjBk7kDSkRwJ0qdLaB\n19W2LavPKRgzcCJvSKkAzgy8LgZwCsUMnMgb2IktxbVtC+TkJLoU5CZZWfa7AaWlzMCJ3CwlAnib\nNkBlJQN4OAzgFCotzTo17tnDDJzIzVIigDuBm23gdbVrxwBOdWVlAbt2MQMncrOUCuDMwOtiBk7h\nZGdbAGcGTuReDOAprn17ZllUFzNwIvdLiQDuVJ0zgNc1aRJ/I53qcjLwHj0SXRIiqk9KnLrZBl6/\n444Djj020aUgt2EGTuR+KRXAmYETNQ3bwIncLyWq0HNz7baYjJT4tk331aZNKC4ogK+kBGl5eRhb\nVIST8vMTXSxyAWbgRO6XEiGtTRtWn4f6atMmzBk0CNM2bkQ2gDIAU5cvx4RFixjECdnZwLffMgMn\ncrOUqEI/8UTgsssSXQp3KS4oqA3eAJANYNrGjSguKEhkscglsrMBVWbgRG6WEgH8mGOA4uJEl8Jd\nfCUlCD03ZwPwbduWiOKQyziZNzNwIvdKiQBOdaXl5aEsZFgZgLTOnRNRHHIZJ/NmACdyLwbwFDW2\nqAhTu3evDeJlAKZ2746xRUWJLBa5hBO4WYVO5F4p0YmN6jopPx8TFi3CQwUF8G3bhrTOnTGBvdCp\nBjNwIvdjAE9hJ+XnY+qzzya6GORCzMCJ3C/pAzjvdSZqPmbgRO6X1AGc9zoTRcYJ4MzAidwrqTux\n8V5noub7atMmvD7rWpyHC/Hgz67FV5s2JbpIRBRGUmfgvNeZqHmcWquHnFqrvwBTV7DWisiNkjoD\n573ORM3DWisi70jqAM57nYmah7VWRN6R1FXovNeZqHmcWqvAIM5aKyJ3ElWN7wJENN7LIKLYCHvn\nRvfubAMnigMRgapKxJ9nACeiQLXPTqipteKzE4jigwGciIjIg6IN4EndiY2IiChZMYATERF5EAM4\nERGRBzGAExEReVDEAVxEckTkGRF5R0TWishtsSwYucvSpUsTXQSKAW7H5MDtSEB0GfgvAKxS1R8A\n6AvgQhHpEZtikdvwhJEcuB2TA7cjAdE9ie1jAO8DgKr6ROQwWCVPRER0VEQcwFV1IQCIiAAoALBD\nVT+PVcGIiIioflE9yEVEOgD4PwBvqurceqbhU1yIiIjCiOuT2ETkWgA3AXAmlJr/fwJgPoApqro0\n0gIQERFR80WcgYvI/QDWq+qzsS0SERERNSaaAP4xgP0AKmFZeQaAmar699gVj4iIiMKJJoCnq2p1\nwPs0wHqkx6hslCAi0lJVj9T8nwEgU1UPJbhY1AQ126sats0qEl0eiky47Sgi6bBzdlXN+1xVPZjA\nYlKCRXzbV2DwrnnvCwzeInKOiCysedDLfBFpH01B6ah6XUSWiMjbABbD+jtARKaKyD9FZLmI/Cqx\nRaR6DAfwLwArnAEiki4ivw3YdlcGjPuuiPxDRJaKyOsiclIiCk111NmOAM4FsEFE3haRJQDedEZw\nO7qPiAwVkQ9qXotE5KSYH4uqGvMXgBwAKwHk1ry/DMBT8VgWX3HZfovCDPspgAcC3v8FwPmJLitf\n9W7D9wP+LwAwrub/lgAWAegOa/paAaBzzbi+AF5PdNn5qnc7Dgdwa5hpuB1d9gLQqiYGtql53x/A\nc7E+FuP14JVLALymNdU7qvoGgM5xWhbFXraIPFFzJThHRLIBjAHweMA0jwEYlJjiURME1pANBzAX\nANSaRuYCcJ6g+ImqbqsZ9xGAKhHJPMplpfoFbsc8AN8XkTdF5C0R+WHNcG5H98kBcKeqHqh5XwYg\nHcAwxPBYjFcA7wYg9KEu5TWBgFxMRHIAnAzgIVUdCOBTANMBdFTVLQGTfg7ge0e/hNREgfeWVmtw\nk9cXAHoi/HH6JQA+Etmd8gGUwmo0rwJwv4gcD25H11HV3Vpze3XNI8afgJ1HfbE8FqN5lGpDjtS8\nAmUB4BWhy6lqqYh0UdXKmkG/hz0ytzRk0lbg9nSzwN6pB0LGOdvuMOoep60AtIhjuShydwNQtTrW\n3SLyPKxdPNz5ltvRBUTkxwDGArhKVXeISEyPxXhl4J8BODVk2Amqui9Oy6PYqs3eak4WRwBsF5Hj\nAqY5FcDmo1wuisyRml7NDmfbfY66x+kpAL4+SuWi5gl3vq5A+PMtt2OCiciNAH4EYLiq7qgZHNNj\nMV4B/EMAI5ye5yJyBYBlcVoWxZCIdATwvoi0rXl/HWzbLQJwZ82wdADjALyQqHJSowKP7RUAbgHs\nFkFYRvAigE0A+ji9XUWkL4BSVf326BaVGhC4He+HPRUTIpILYCTs2OR2dJmax4zfCuDqgNpMIMbH\nYlyq0FV1n4jcC7sdqQzAN06hyd1UdZeIzACwUETKYVeHEwCUA3hARJbV/P+iqvKizIVEpDWsycrx\nIIDHReR9WG3KLFXdWjPtOABPi0g1rKr9Z0e7vBRemO1YBOAPInI9AB+AGaq6p2Zabkd3uQBARwCL\n7fe+kAZgL4ArAfwuVsdiVD9mQkRERMFERDQkuIpIZkg2Hv1yGMCJiIi8J15t4ERERBRHDOBEREQe\nxABORETkQQzgREREHsQATkRE5EEM4ERERB7EAE5ERORBDOBEREQexABORETkQVEFcBEZKiIf1LwW\nOQ9iJyIioviK+FGqItIKwLsALlbVAyLSH8DtqnpNLAtIREREdUWTgecAuFNVnR8oL49yfkRERNRE\nMfkxExHpAWAugPGq+mnUMyQiIqIGRf174CLyY9iPkl+lqjuiLhERERE1KqoALiI3ArgEwPD6fudU\nRPh7pURERGGoqkT62Wg6sXUAsAhAv9AfLg+ZrqHR5BGFhYUoLCxMdDEoStyOyYHbMTmISFQBPJoM\n/AIAHQEsFhHAOrDtVdWRUcyTiIiImiCaAP6Kqr4cOEBEMqMsDxERETVBxLd9hasXr68dnLxv4MCB\niS4CxQC3Y3LgdiQgRreRNbgAtoETERHVEW0bOB+8QkRE5EEM4ERERB7EAE5ERORBDOBEREQexABO\nRETkQQzgREREHsQATkRE5EEM4ERERB7EAE5ERORBDOBEREQexABORETkQQzgREREHsQATkRE5EEM\n4ERERB7EAE5ERORBDOBEREQexABORETkQQzgREREHsQATkRE5EEM4ERERB7EAE5ERORBDOBEREQe\nxABORETkQQzgREREHpSR6AIQEVHsfLVpE4oLCuArKUFaXh7GFhXhpPz8RBeL4kBUNb4LENF4L4OI\niCx4zxk0CNM2bkQ2gDIAU7t3x4RFixjEXUhEoKoS6edZhU5ElCSKCwpqgzcAZAOYtnEjigsKElks\nihMGcCKiJOErKakN3o5sAL5t2xJRHIozBnAioiSRlpeHspBhZQDSOndORHEozhjAiYiSxNiiIkzt\n3r02iDtt4GOLihJZLIoTdmIjIkoitb3Qt21DWufO7IXuYtF2YmMAJyIiSgD2QiciIkpBDOBEREQe\nxABORETkQQzgREREHsQATkRE5EEM4EQUkYqKiqC/zRnf2GeJqHEM4EQpwufzYfLkyTjvvPPQq1cv\n3HbbbTh8+HDYaUtKSjBq1Cj0798f/fr1w8iRI7Fly5ba8eXl5ejbty/y8/Mxfvz4Op9vaHxjn/30\n008xePBgnHXWWejbty8mTJiAysrKJn+PxspOlCwYwIlSxOTJk9G6dWu89957+Pjjj5GVlYW77747\n7LS33HILhg4dilWrVuHDDz/E0KFDMW7cuNrxWVlZWL9+PQoLC5GdHfr07YbHNzSuuroao0aNwl13\n3YUVK1Zg9erVqKysxKxZs5r8PRorO1GyYAAncrHZs2fj3nvvjXo+5eXleOWVV1BYWAjAHiBRVFSE\nF154AeXl5XWmX79+PcaMGVP7fsyYMfjPf/4Tdt4tWrRocNkNjQ8dJyJ46aWXcNFFF9W+v/zyy/HF\nF180+Xs0p+xEXsYATuRiEyZMwPz587Fz586o5rNmzRp07doV6enptcPS09MxYMAArF69us70I0aM\nwAeWRjcAAA1SSURBVGOPPQZVhc/nw5w5czBy5Miw8xZp+EFSDY0PHZeWloaePXvWvt+zZw+eeOIJ\njB49usnfozllJ/KyjEQXgIjqJyK45ppr8PTTT2Py5MlB47788kvMnTvXeRxj7fSqChHBgAEDMGzY\nMADA9u3b0aNHjzrzP+GEE7Bjx446wwsLCzF8+HDMnj0bPp8Pffr0wauvvhqHbxjeggULMG3aNGze\nvBmTJk3CpZdeCqBp3yPRZSc6WhjAiVzu+uuvx7Bhw+oE8JNPPhn3339/k+bRsmXLsFXZhw8fDspm\nAaCyshLDhw/HxIkTMXLkSKgqiouLcdlll2HJkiWNZtyxMGbMGIwZMwaHDh3CHXfcgSlTpmD69OmN\nfg83lJ3oaGEVOpHL7d69G4cOHcLKlSsjnscpp5yCkpKSOsM3bNiAvLy8oGHLli1Dp06daqudRQQ3\n3HAD0tPTsX79+ojLEInWrVvjkUceQXFxMYDGv4ebyk4Ub8zAiVxs4cKF2LBhA+677z489dRTOOOM\nM2rHBVahBwpXhZ6fn49Vq1bB5/MhLc2u2ysqKlBSUoLTTjst6PP79u1DVlZWnbLk5ubi4MGDsf6K\nQdauXYvPPvsMV155Ze0wEUF1dTWAxr/H4sWLE1Z2oqONAZzIpZ5//nmsWbMGM2fORGlpKaZMmYJZ\ns2ahZcuWAJpXhZ6RkYHRo0fjvvvuw4wZM2p7b48YMaLOrVxnn302Jk6ciDVr1qBPnz4AgMWLF2Pd\nunXo3bt30LQ+nw8+n6/e5TY0Pty4tm3b4vbbb0fPnj3Rq1cv+Hw+TJ8+HUOGDGnS92hO2Ym8jgGc\nyIWWL1+Ot956C08++SQAICcnByNGjMC8efNw/fXXRzTPBx54AHfffTd69eqFNm3a4Oyzz8bDDz8M\nwDqHDR8+HK+99ho6deqEefPmYdKkSTh48CCOHDmCTp064eWXX66T3ZaWluLAgQP1LrOh8eHGdevW\nDQsWLMD48eNRUVGBqqoqnHvuuXj00Ueb9D06duzY5LITeZ04vVfjtgARjfcyiIiIvKbmrpGIe1ay\nExsREZEHMYATERF5EAM4ERGRBzGAExEReRADOBERkQcxgBMREXkQAzgREZEHMYATERF5UFQBXETO\nEZGFIvKOiMwXkfaxKhgRERHVL+InsYlIDoAlAC5S1YMichmAMap6Y8h0fBIbERFRiEQ+ie0SAK+p\n6kEAUNU3AHSOYn5ERETURNEE8G4APg8ZVi4i2WGmJSIiohiK5tfIjtS8AmUByAyd8KKL7G9oTXpD\n75tS6y5hKh5Ch110EVBQYMP37wfGjwdKShqfN9UVbn0ns4b2wXi3CkW7rqP5/HXXATfc4H8/fjyw\nbl3iyhOLzydiuYn4rCpQVgbs2wdUVwMtW/pfLVoAaR7vthzNOo1HfAk3rLFp0tOBhQsbX35TRBPA\nPwPQH8CrAcNOUNV9oRN26VJY+3+fPgPRp8/A2vcNffmGNla4DRA6zOcD7rkH2L4dmD4dGDIE6NcP\nKCys+1lqWLJ2Y1BteD+LdFw0olnX0W6n994D/va34AD+7LPAggVApL/GGW2ZErXvJWo7RPt9s7OB\ntm2BjAzgyBH/q6LC28dxLMoey/gSblhj06xduxRr1y6NWQyKphNbOwBvABiiqntF5AoAV6jquJDp\nEtqJ7cAB4IorgLVrgVtuAWbOTL1Mkqip/v1vy7hXrbL3+/cDJ55oxxGPG6LYirYTW8QZuKruE5F7\nAbwuImUAvgFwS6Tzi5c2bYA33wQWL7ZAzpMQUf26dAG2bPG///proGtXHjdEbhRNFTpUdQmAs2NU\nlrjJygKGDk10KYjc7/jjrf308GGgVSsL5l26JLpURBSOx7s0EFEspaUBeXnA1q323snAich9GMCJ\nKEjXrha4AWbgRG7GAE5EQQLbwZmBE7kXAzgRBWEGTuQNDOBEFIQZOJE3MIATURAnA/f57KmFJ56Y\n6BIRUTgM4EQUxMnAv/kGaNfObicjIvdhACeiIE4G/vXXbP8mcjMGcCIK0ratPXlt3Tq2fxO5GQM4\nEdXRtSvw/vvMwIncjAGciOro0oUBnMjtGMCJqI6uXYENG1iFTuRmDOBEVIeTeTMDJ3IvBnAiqsPJ\nvJmBE7kXAzgR1dGlC5CRAXTqlOiSEFF9GMCJqI7vfhfo0wdIT090SYioPqKq8V2AiMZ7GURERF4j\nIlBVifTzzMCJiIg8iAGciIjIgxjAiYiIPIgBnIiIyIMYwImIiDyIAZyIiMiDGMCJiIg8iAGciIjI\ngxjAiYiIPIgBnIiIyIMYwImIiDyIAZyIiMiDGMCJiIg8iAGciIjIgxjAiYiIPIgBnIiIyIMYwImI\niDyIAZyIiMiDGMCJiIg8iAGciIjIgxjAiYiIPCgj0QWgxPlq0yYUFxTAV1KCtLw8jC0qwkn5+Yku\nFhERNYGoanwXIKLxXgY131ebNmHOoEGYtnEjsgGUAZjavTsmLFrEIE5EdBSICFRVIv08q9BTVHFB\nQW3wBoBsANM2bkRxQUEii0VERE3EAJ6ifCUltcHbkQ3At21bIopDRETNxACeotLy8lAWMqwMQFrn\nzokoDhERNRMDeIoaW1SEqd271wZxpw18bFFRIotFRERNxE5sKay2F/q2bUjr3Jm90ImIjqJoO7El\nfQDnrVJERORGDOAN4K1SRETkVryNrAG8VYqIiJJVUj+JjbdKETUfm52IvCGpA7hzq1RgEOetUkT1\nC9vstHw5m52IXCipq9B5qxRR87DZicg7kjoDPyk/HxMWLcJDAbdKTWB1IFG92OxE5B1JHcABC+JT\nn3020cUg8gQ2OxF5R1JXoRNR87DZicg7kvo+cCJqPj6hj+jo4INciIiIPIgPciEiIkpBDOBEREQe\nxABORETkQREHcBHJEZFnROQdEVkrIrfFsmBERERUv2gy8F8AWKWqPwDQF8CFItIjNsUit1m6dGmi\ni0AxwO2YHLgdCYgugH8M4EkAUFUfgMNRzo9cjCeM5MDtmBy4HQmI4klsqroQAEREABQA2KGqn8eq\nYERERFS/qDJmEekA4EUA21V1YmyKRERERI1p9EEuInItgJsAOBNKzf8/ATAfwBRVXdrA5/kUFyL6\n/+3dTWgdVRjG8f/TNDbaRHERxYrUD9AqLiy4UkQXKghqVNDWhR8IYhbVXREEEZSSKi4UrVUKLgQV\npSvR2Brb6iLWICKIFqugoqIVq9aaRtM2eV3MuWW8ubHxZubOXHh+MHDPzMC88HLmnTkzc66ZtVDJ\nTGySRoDPI8L/FGJmZtZhiyngnwJ/AEfI7sqXAo9HxJvFhWdmZmatLKaA90TETK69BI69kW5dTNKy\niJhOv5cCvRHxV8Vh2QKkfM2Q5exw1fFYe1rlUVIP2Tn7aGoPRMSfFYZpFWv7JbZ88U7t2XzxlnSZ\npO1popfXJZ26mECto0Yl7ZK0E9hB9r4Dkh6R9I6kDyU9UG2INo8h4H1gorFCUo+kZ3O5W5Pbdr6k\ntyS9J2lU0soqgrY55uQRuBz4StJOSbuAbY0NzmP9SLpB0gdpGZO0svC+GBGFL0A/8BEwkNrXAS+W\ncSwvpeRvrMW6O4CNufYrwBVVx+pl3hyO534/DAyn38uAMeA8skdfE8CKtG01MFp17F7mzeMQsK7F\nPs5jzRagL9XAk1P7UuDlovtiWROvXAu8EWl4JyLeBlaUdCwr3nJJm9OV4DOSlgO3Apty+zwNXFNN\neLYA+RGyIWALQGSPRrYAjRkUP4uIH9O2T4Cjkno7HKvNL5/HM4GLJW2T9K6kq9N657F++oH1EXEw\ntQ8BPcCNFNgXyyrgZwPNk7pMpUJgNSapHzgXeDIirgL2AI8CgxHxfW7XvcCFnY/QFij/acpM/PuR\n15fARbTup18DnhK5ns4BJslGNNcCI5JOx3msnYjYH+nz6jTF+Gay8+hskX2x7ZnYjmM6LXknAb4i\nrLmImJR0VkQcSaueB8bJThx5fTifdZZ/O/Vg07ZG7v5mbj/tA04oMS5r34NARDbGul/Sq2TPxVud\nb53HGpB0G3A3sDYi9kkqtC+WdQf+BbCqad0ZEXGgpONZsY7dvaWTxTTwk6TTcvusAr7tcFzWnun0\nVnNDI3d7mdtPLwC+61Bc9v+0Ol8fpvX51nmsmKR7gFuAoYjYl1YX2hfLKuAfAzc13jyXdD2wu6Rj\nWYEkDQLjkk5J7TvJcjcGrE/reoBh4LWq4rTjyvftCeA+yD4RJLsj2Ap8A1zSeNtV0mpgMiJ+62yo\n9h/yeRwhmxUTSQPAzWR903msmTTN+Drg9txoJhTcF0sZQo+IA5IeIvsc6RDwcyNoq7eI+EXSBmC7\npCmyq8P7gSlgo6Td6ffWiPBFWQ1JOpHskVXDE8AmSeNkoylPRcQPad9h4CVJM2RD7fd2Ol5rrUUe\nHwNekHQXMAtsiIhf077OY71cCQwCO7L/+2IJ8DuwBniuqL7Y9kQuZmZmNpckRVNxldTbdDe++OO4\ngJuZmXWfsp6Bm5mZWYlcwM3MzLqQC7iZmVkXcgE3MzPrQi7gZmZmXcgF3MzMrAu5gJuZmXWhfwBm\nnzXsTAAVZgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b1bd150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(3, 1, figsize=(7, 7))\n",
    "ax = ax.flatten()\n",
    "ndx = np.where(ne2.x != 0)[0]\n",
    "for i, j in enumerate([42, 64, 86]):\n",
    "    ax[i].plot(x_lams[j])\n",
    "    ax[i].plot(ndx, ne2.x[ndx], 'ro')\n",
    "    ax[i].set_yticks([-2, 0, 2])\n",
    "    ax[i].text(90, 0.4, '$\\lambda=${:.7f}'.format(lams[j]), fontsize=12)\n",
    "plt.tight_layout()\n",
    "plt.savefig('IRLS.png', dpi=220)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "全ての$\\lambda$に対するすべてのIRLSの解\n",
    "--\n",
    "各曲線は，$\\lambda$の変化に伴って各要素の値が変化する経路を表している．破線は各$\\mathbf{x}_{0}$の要素を表している．"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 273,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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myAiijCDIsMaCkXyYLWAUK4KVgJSAbNAjCMgISTUk0ZCM0KXZPI9GZDYkywLI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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ad2a110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for pix in x_lams.T:\n",
    "    plt.semilogx(lams, pix)\n",
    "plt.xlim(lams[0], lams[-1])\n",
    "plt.ylim(-2, 2)\n",
    "ndx = np.where(ne2.x != 0)[0]\n",
    "for col in ndx:\n",
    "    plt.axhline(ne2.x[col], ls='--', c='k')\n",
    "plt.ylabel(u'解の要素')\n",
    "plt.xlabel('$\\lambda$')\n",
    "plt.savefig('path.png', dpi=220)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "最適な$\\lambda$を用いた場合の，IRLSの反復回数に対する関数値$\\left(\\lambda\\|\\mathbf{x}\\|_{1}+\\frac{1}{2}\\|\\mathbf{b}-\\mathbf{Ax}\\|_{2}^{2}\\right)$\n",
    "--\n",
    "* IRLSで最小化する重み付きL2正則化項ではなくL1正則化項である点に注意"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x_IRLS, S_IRLS, xs = bpdn.IRLS(lam=lams[64])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 274,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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/pfD8GWD35JooLaza/VMkaVXtm+6+EHjbzM4B5vS00ix2EqWGUHnup1fMbGhh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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a4f0ad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(A, b, x, lam):\n",
    "    r = b - np.dot(A, x)\n",
    "    return 0.5 * np.dot(r, r) + lam * np.sum(np.abs(x))\n",
    "\n",
    "fs = []\n",
    "for x in xs:\n",
    "    fs.append(f(ne2.A, ne2.b, x, 0.09))\n",
    "fs = np.array(fs)\n",
    "\n",
    "plt.semilogx(np.arange(1, len(fs)+1), fs)\n",
    "plt.grid(True, which='Both')\n",
    "plt.ylabel(u'間数値')\n",
    "plt.xlabel(u'反復回数')\n",
    "plt.savefig('iteration.png', dpi=220)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 266,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.051167351768 0.00551949196749 0.120416666667 0.0025\n",
      "0.0640001565445 0.00476345995878 0.2185 0.005\n",
      "0.0671305236641 0.00474889757365 0.232886904762 0.00375\n",
      "0.0793078671837 0.00536864537412 0.270148809524 0.00733333333333\n",
      "0.0983675519039 0.0263103933289 0.302224563835 0.0446994949495\n",
      "0.119715835107 0.0515097824601 0.31378019203 0.0825683760684\n",
      "0.165366985408 0.123296570579 0.373638950918 0.144441058941\n",
      "0.188284626782 0.197493867314 0.379683128554 0.188640144578\n",
      "0.236495649375 0.333787973061 0.407877910424 0.291407793595\n",
      "0.258104524942 0.368091867576 0.405970786459 0.305488766136\n",
      "0.310660508455 0.491574651977 0.415806464455 0.376231997578\n",
      "0.364278067416 0.578191067902 0.434394076791 0.403269120865\n",
      "0.394584244196 0.715296426831 0.422475719477 0.447155022931\n",
      "0.397576167411 0.777512809881 0.417872442723 0.471048224587\n",
      "0.454476780249 0.822825541537 0.435594178105 0.474792155299\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LassoLars\n",
    "\n",
    "eps = np.sqrt(len(ne.b)) * 0.1\n",
    "\n",
    "err_lars, err_omp, dist_lars, dist_omp = [], [], [], []\n",
    "for k in xrange(1, 16):\n",
    "    err, err2, dist, dist2 = 0, 0, 0, 0\n",
    "    for _ in xrange(200):\n",
    "        ne = NumericalExample2(n=30, m=50, k=k)\n",
    "        \n",
    "        lars = LassoLars(alpha=0.01)\n",
    "        lars.fit(ne.A, ne.b)\n",
    "        x_lars, S_lars = lars.coef_, np.where(lars.coef_ == 0, 0, 1)\n",
    "\n",
    "        greedy = Greedy(ne.A, ne.b, eps=eps)\n",
    "        x_OMP, S_OMP = greedy.OMP()\n",
    "        \n",
    "        err += l2_err(ne.x, x_lars)\n",
    "        err2 += l2_err(ne.x, x_OMP)        \n",
    "        dist += dist_S(ne.S, S_lars)\n",
    "        dist2 += dist_S(ne.S, S_OMP)\n",
    "    \n",
    "    err /= 200\n",
    "    err2 /= 200\n",
    "    dist /= 200\n",
    "    dist2 /= 200\n",
    "    print err, err2, dist, dist2\n",
    "\n",
    "    err_lars.append(err)\n",
    "    err_omp.append(err2)\n",
    "    dist_lars.append(dist)\n",
    "    dist_omp.append(dist2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 267,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4Xlzd8mqa1m7qd3i+KPYCOZ6sq29fVR0vItFZ/QoisqP4YRpj/JKeDl9+CW+/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\nnMdaCBFme/J2krYkkbQ5iaQ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EFV2LA+K9z1pXRLJaROBaEHfjWg2Cax0tzfp74FpHbwFv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\n/h8rwBYGW9+xjQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b54f790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(1, 16), err_omp, label='OMP')\n",
    "plt.plot(range(1, 16), err_lars, label='LARS')\n",
    "plt.ylabel(u'平均相対$\\ell_2$誤差')\n",
    "plt.xlabel(u'真値の非ゼロ要素の個数')\n",
    "plt.legend(loc='best')\n",
    "plt.xlim(1, 15)\n",
    "plt.savefig('l2_err_OMP_LARS.png', dpi=220)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 268,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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hqafguecs8ZvAOd5QzxQRiVbVNBG513eX7+3p60VkPlChMII0eTdn0xzunXEv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\n/+Jp3/ZihraIAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b1e2b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(1, 16), dist_omp, label='OMP')\n",
    "plt.plot(range(1, 16), dist_lars, label='LARS')\n",
    "plt.ylabel(u'サポート間距離')\n",
    "plt.xlabel(u'真値の非ゼロ要素の個数')\n",
    "plt.legend(loc='best')\n",
    "plt.xlim(1, 15)\n",
    "plt.savefig('dist_S_OMP_LARS.png', dpi=220)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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