{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [],
   "source": [
    "mu = 3\n",
    "tau = 2\n",
    "N = 100\n",
    "\n",
    "np.random.seed(0)\n",
    "x = np.random.normal(mu,1./np.sqrt(tau),N)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [],
   "source": [
    "a_0 = 1\n",
    "b_0 = 1\n",
    "mu_0 = 0\n",
    "lambda_0 = 0.001\n",
    "\n",
    "X=np.sum(x)\n",
    "X2=np.sum(np.square(x))\n",
    "\n",
    "Niter=30\n",
    "\n",
    "a1=np.zeros(Niter)\n",
    "b1=np.zeros(Niter)\n",
    "mu1=np.zeros(Niter)\n",
    "lambda1=np.zeros(Niter)\n",
    "\n",
    "\n",
    "\n",
    "a1[0]=a_0\n",
    "b1[0]=b_0\n",
    "mu1[0]=mu_0\n",
    "lambda1[0]=lambda_0*a_0/b_0\n",
    "\n",
    "for iter in range(1,Niter):\n",
    "    mu1[iter]=(lambda_0*mu_0 + X)/(lambda_0+N)\n",
    "    lambda1[iter]=(lambda_0+N)*a1[iter-1]/b1[iter-1]\n",
    "    a1[iter]=a_0+(N+1)/2.\n",
    "    b1[iter]=b_0+1./2*(X2-2*mu1[iter]*X+N*mu1[iter]**2+N*1./lambda1[iter]+lambda_0*mu_0**2 - \\\n",
    "                       2*lambda_0*mu1[iter]*mu_0 + lambda_0*mu1[iter]**2+lambda_0*1./lambda1[iter] )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.00000000e+00 1.00000000e+00 0.00000000e+00 1.00000000e-03]\n",
      " [5.15000000e+01 2.69002932e+01 3.04226023e+00 1.00001000e+02]\n",
      " [5.15000000e+01 2.66614611e+01 3.04226023e+00 1.91449642e+02]\n",
      " [5.15000000e+01 2.66591423e+01 3.04226023e+00 1.93164639e+02]\n",
      " [5.15000000e+01 2.66591198e+01 3.04226023e+00 1.93181440e+02]\n",
      " [5.15000000e+01 2.66591196e+01 3.04226023e+00 1.93181603e+02]\n",
      " [5.15000000e+01 2.66591196e+01 3.04226023e+00 1.93181604e+02]]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(a1)\n",
    "plt.plot(b1)\n",
    "plt.plot(mu1)\n",
    "plt.plot(lambda1)\n",
    "plt.yscale('log')\n",
    "\n",
    "pars = np.column_stack((a1,b1,mu1,lambda1))\n",
    "\n",
    "print(pars[:7,:])\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.0422602307514377 100.001 51.0 26.400293200305597\n"
     ]
    }
   ],
   "source": [
    "muc = (lambda_0*mu_0 + X)/(lambda_0+N)\n",
    "lambdac = lambda_0 + N\n",
    "ac = a_0 + N/2.\n",
    "bc = b_0 + 0.5*(X2-1./N*X**2)+N*lambda_0/(lambda_0+N)*(X-N*mu_0)**2/(2*N**2)\n",
    "\n",
    "print(muc,lambdac,ac,bc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYAAAAEQCAYAAAC5oaP8AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAAsTAAALEwEAmpwYAAAYpUlEQVR4nO3dfXBV1b3/8fcXEjQgIkpAHi9PIk8jECKKEUiFFv0JNIKMt1basVTGYsHbqPTKtaU6OqVTBZz6q4CCV0VpUXBM1REcBAHLU9AgmAAV5CEVJQpIACFIvvePHKJikIBh75D1ec2cSc7JPmd912SyP1lr7722uTsiIhKeWnEXICIi8VAAiIgESgEgIhIoBYCISKAUACIigVIAiIgEKvIAMLMLzOxFM9tgZgVm1jvqGkREBJJiaPNR4HV3v9HM6gB1Y6hBRCR4FuWFYGbWAMgD2rquQBMRiVXUI4A2QBHwlJl1A9YAd7r7ga9vZGajgFEA9erV69mxY8eIyxQROXutWbPmU3dPPdl2UY8A0oEVQIa7rzSzR4F97v67E70nPT3dc3NzI6tRRORsZ2Zr3D39ZNtFfRC4ECh095WJ5y8CaRHXICIiRBwA7v4xsMPMLk281B/Ij7IGEREpE8dZQGOA5xJnAG0Bbo2hBhGR4EUeAO6eB5x0bkpERM4sXQksIhIoBYCISKAUACIigVIAiIgESgEgIhIoBYCISKAUACIigVIAiIgESgEgIhIoBYCISKAUACIigVIAiIgESgEgIhIoBYCISKAUACIigVIAiIgESgEgIhIoBYCISKAUACIigVIAiIgESgEgIhIoBYCISKAUACIigVIAiIgESgEgIhIoBYCISKAUACIigUqKukEz2woUA0eBL909PeoaREQkhgBI+IG7fxpT2yIigqaARESCFUcAOLDAzNaY2agY2hcREeKZArra3f9tZo2BN8xsg7sv+foGiWAYBdCqVasYShQRqfkiHwG4+78TX3cBLwG9Kthmurunu3t6ampq1CWKiAQh0gAws3pmVv/Y98CPgPVR1iAiImWingJqArxkZsfaft7dX4+4BhERIeIAcPctQLco2xQRkYrpNFARkUApAEREAqUAEBEJlAJARCRQCgARkUApAEREAqUAEBEJlAJARCRQCgARkUApAEREAqUAEBEJlAJARCRQCgARkUApAEREAqUAEBEJlAJARCRQCgARkUApAEREAqUAEBEJlAJARCRQCgARkUApAEREAqUAEBEJlAJARCRQCgARkUApAEREAqUAEBEJlAJARCRQsQSAmdU2s3fN7JU42hcRkfhGAHcCBTG1LSIixBAAZtYCuB54Muq2RUTkK3GMAKYA44DSE21gZqPMLNfMcouKiiIrTEQkJJEGgJkNAna5+5rv2s7dp7t7urunp6amRlSdiEhYoh4BZABDzGwr8DfgGjObFXENIiJCxAHg7ve6ewt3bw38J/Cmu98SZQ0iIlJG1wGIiAQqKa6G3X0xsDiu9kVEQqcRgIhIoBQAIiKBUgCIiARKASAiEigFgIhIoBQAIiKBUgCIiARKASAiEigFgIhIoBQAIiKBUgCIiARKASAiEigFgIhIoBQAIiKBUgCIiARKASAiEigFgIhIoBQAIiKBUgCIiARKASAiEigFgIhIoBQAIiKBUgCIiARKASAiEigFgIhIoBQAIiKBUgCIiASqUgFgZo+ZWePv25iZnWtmq8xsrZm9b2b3f9/PFBGR01PZEcCvgNZV0N5h4Bp37wZ0B641syur4HNFROQUJVVyO6uKxtzdgf2Jp8mJh1fFZ4uIyKk5lWMA51T0opldYWabKvshZlbbzPKAXcAb7r6ygm1GmVmumeUWFRWdQokiIlJZlR0BACw2s63Ae8DaxNetQBZwYWU/xN2PAt3N7ALgJTPr6u7rj9tmOjAdID09XSMEEZEz4FQCYApQF7gM+A1Q/2s/e/xUG3b3vWa2CLgWWH+y7UVEpGqdSgD83d1XHXtiZv8BNAMOuPt7lfkAM0sFjiR2/inAD4E/nUrBIiJSNU4lAL7B3bcB207xbU2Bp82sNmXHH+a4+yunW4OIiJy+ygbA/1B20PZ7SYwUenzfzxERke+vUgHg7n8804WIiEi0tBSEiEigFAAiIoFSAIiIBEoBICISKAWAiEigFAAiIoFSAIiIBEoBICISKAWAiEigFAAiIoFSAIiIBEoBICISKAWAyPdQdptrkbOTAkDkNGzatIlf/epX1KtXj1atWpGVlcWECRNYvXp13KWJVJoCQOQUfPDBB2RlZdGxY0dmzpxJVlYWGRkZbNy4kQcffJDevXvz+OOnfIdUkVic9h3BRELz4Ycf0q9fPw4ePMh9993HHXfcQZMmTcp/vnfvXm655RZGjx7Nhg0bmDJlCmYWY8Ui300BIFIJBw4cICsri4MHD7J06VK6du36rW0uuOACXn75Ze655x4mT55MrVq1mDRpkkJAqi0FgMhJuDu33XYb69at47XXXivf+e/bt49nnnmGJk2acPXVV9O0aVNq167NI488QmlpKVOmTKFLly788pe/jLkHIifg7tX60bNnTxeJ07x58xzwBx980N3djx496jNmzPDGjRs7UP5o27at33///V5aWupHjx71/v37+3nnnecfffRRzD2Q0AC5Xon9qw4Ci3yHgwcPkp2dTdeuXfntb3/Lhg0b6NWrFyNHjqR9+/b885//ZOXKlTzyyCO0b9+eCRMmMHbsWMyMqVOnUlJSwrhx4+LuhkiFFAAi3+HRRx9l69atPPbYYxw+fJghQ4awbds2nnvuOZYuXUqdOnVo1aoV2dnZvP7662RnZ/PYY48xadIk2rdvz913382sWbNYt25d3F0R+bbKDBPifGgKSOKyf/9+b9SokV933XXu7n777be7mfnixYv9448/9htuuKF8+ueKK67whx56yLds2eLDhg3zpKQkX7lypRcVFXmdOnV8zJgxMfdGQkIlp4DMq/mVjOnp6Z6bmxt3GRKgxx9/nNGjR7Ns2TKOHj1Kv379uPvuuxkyZAjDhg1j3759/O53vwMgJyeHVatWcdFFF7Fo0SIGDx5MUlIS69ev59Zbb2X+/Pl88sknJCcnx9wrCYGZrXH39JNtpykgkROYM2cOnTt3JiMjg4ceeogmTZpw5ZVXcs0119CwYUNWrVpF27Zt6d+/PytWrGDt2rUcPnyY0aNHM3XqVDZv3swTTzzBjTfeyJ49e1i1alXcXRL5BgWASAU+/fRTlixZwrBhw1i7di0LFixg9OjRjBkzhi5duvDmm2+SnZ3NzTffTO/evenYsSMLFy5k8uTJLFu2jFWrVtGvXz/++Mc/kpGRgZkxf/78uLsl8g0KAJEKvP3225SWljJw4EBmz55NUlISycnJ7Ny5k4cffphbbrmFRYsWMW3aNGbOnElqairZ2dlMnjyZG264gYcffpjbb7+dnTt3smrVKvr06cO8efPi7pbIN0QaAGbW0swWmVm+mb1vZndG2b5IZa1cuZKkpCR69OjBCy+8QGZmJlOnTuWqq65i4sSJLFmyhJkzZ/Lhhx/SqlUrli1bxty5c8nPz6d58+YUFxezbt06GjVqxPPPP8/w4cN5//33yc/Pj7trIuWiHgF8Cdzl7p2BK4E7zKxzxDWInNT69evp2LEjmzdvZsuWLXTv3p3t27fToUMHFi5cyIwZM1ixYgUTJ05kwIABDB06lB49evDjH/+Y559/noEDB/LMM88wePBgFixYwODBgwFYuHBhzD0T+UqkAeDuO939ncT3xUAB0DzKGkQqY/PmzbRv354FCxYAZcs+JCcns3z5cnr37o27M3XqVO68804eeugh5s+fT6dOnWjdujW7d++mZcuWFBYW0qxZM/bs2cPBgwdp1qwZK1eujLlnIl+J7RiAmbUGegDf+osws1FmlmtmuUVFRZHXJrJ9+3Zat27N22+/Tfv27cnNzSUtLY2NGzdy0003cdddd9GvXz8efvhhxo8fz8aNG7n88st54oknuOSSS9i8eTNQFhwA77zzDj179mTt2rVxdkvkG2IJADM7D5gL/Je77zv+5+4+3d3T3T09NTU1+gIlaIcOHWL//v2kpqayYcMGOnfuTH5+Pg0aNADgs88+Y8+ePfz+979nzJgxvPnmm7Ro0YLx48dz8OBBOnTowOrVq2nXrh07duwAYOvWrbRp04Zt27bpLmJSbUQeAGaWTNnO/zl312kRUu3s2bMHgIYNG7JlyxaaNGnCoUOHKCkpoX79+syfP5+0tDSKioqYOnUq/fv3p7i4mMzMTOrUqYO7s3//ftq0aUNBQQGpqans2LGDFi1aUFxcTHFxccw9FCkT9VlABswACtx9UpRti1TWF198AUBSUhKHDx/mnHPOAeDw4cM0bdqUgoICMjIyyMvLK3/PnDlzSElJoUWLFhw6dAiAlJQUPvvsM84//3yKi4s5//zzgbJ7C4hUB1GPADKAEcA1ZpaXePy/iGsQ+U4lJSUAlJaWAlC7dm2gbGqofv36FBcX07ZtWwoKCujUqRNt27blxRdfBODiiy9m//79ANSqVYvPP/+cunXrcvDgQVJSUoCyFUZFqoNIbwjj7ssA3R5JqrVjO/xatb75/1FycjKHDh3CzNi7dy+NGjXitddew8zKT/M8cOAA9evXL3/Pueeey5EjR0hOTubLL78s/xyR6kBXAosc59iUzzFHjhwBynbmu3fvplWrVhQUFNClSxeOHDlCSUkJI0aMwN356KOPqFu3bvn7GjRowIEDB8pHAUD5SEAkbgoAkeMcm6svLi7m4osv5vPPPwegTp06FBYW0qdPH3JycujVqxfp6ekMHjyYtLQ08vPzKSoqok6dOpgZu3btok2bNnzyySc0adKEnTt3Urt2bRo2bBhn90TKKQBEjtOgQQOSkpIoKiqiS5cubNq0iXbt2pWPBK666ipKSkqYN28eq1evJicnB3dn2rRpAOzevZvLLruM9evXc+mll1JSUkK7du3Kl41IStKtuKV6UACIHMfMaN68Odu2bSM9PZ28vDzS0tJYt24dF154IQsXLuTWW29l0qRJzJo1i3/84x+kpaXxl7/8hR/84AcsX76cLl26cOjQIS688EIAunTpwrvvvkunTp1i7p3IVxQAIhXo2LEjBQUFZGVlceTIEVq2bMnu3bsZMGAA8+bNY9CgQWRmZjJixAiGDBnCgQMHePbZZ7n44otJSUnhwIEDXHTRRezdu5fzzjuPVq1asWHDBjIzM+Pumkg5BYBIBS677DLy8/Pp2rUrLVu2ZO3atTRu3Jjt27fTrVs3brzxRgYOHMj8+fOZMWMGeXl5lJSUMHv2bIYPH84rr7zCT3/6U15++WX69+/Pq6++CsCAAQNi7pnIVxQAIhUYMGAAJSUlLF26lNtuu42FCxfym9/8hhUrVjBq1CgGDRrEvffey9ixY3njjTdo1qwZI0eOLF/vJzU1lbZt2/LJJ58wduxYpk2bRo8ePejevXvcXRMppwAQqUCfPn2oW7cuL7zwAiNHjiQpKYn33nuP3r17M27cOPr3788DDzxAUVERr7/+OsOGDePVV1+lW7du5OXl8ec//5nJkyeTlpZG8+bNycvLY8SIEZRdDC9SPSgARCqQkpLCL37xC2bNmkVpaSn33Xcfs2fPZsSIEVxxxRWMHTuWefPm8fe//52XXnqJSy65hD/96U/MnDmT8ePH88orr7Bjxw4effRRnnrqKWrXrs1NN90Ud7dEvsGq+8qE6enpnpubG3cZEqCtW7fSvn17fv7znzN16lR69+7Nli1bWLx4MRs3biQ7O5vCwsLy7Tt37szPfvYztm/fzl//+lcmTpzIbbfdRseOHbnyyivJycmJsTcSEjNb4+7pJ9tOJySLnEDr1q255557mDhxItdddx1z5syhb9++9O3bl7Fjx/LWW2+xbds29u7dS58+fTAzbr75ZhYsWMBdd93FuHHjGDFiBHv27OEPf/hD3N0R+TZ3r9aPnj17ukhcSkpKvFevXt6gQQNfs2aNf/DBB56VleVm5uecc45ffvnlPnz4cG/Xrp0DnpSU5E8++aS7uz/77LMO+IQJE+LthAQHyPVK7F81BSRyEtu2baNv377s2bOHnJwcMjMz2bRpE1OmTGH58uXs27ev/Ayf66+/nu7duzNt2jTGjBlDRkYGb7zxhhaAk0hVdgpIASBSCYWFhQwcOJDNmzfzyCOPMGrUqAp36h9//DG//vWvmTt3LgMHDmTOnDnlawuJREUBIFLFPvvsM4YOHcqyZcto2LAhQ4cOZejQoZSWlrJ582b+9a9/8fTTT3Po0CEeeOAB7rnnnm8tKS0SBQWAyBng7rz66qvMnj2bnJyc8pu/ANSrV4/MzEwmTZpEhw4dYqxSQqcAEDnDvvjiC5YsWUL9+vVp164djRs31oVeUi3oNFCRMywlJYWBAwfGXYbIadMEpYhIoBQAIiKBUgCIiARKASAiEigFgIhIoBQAIiKBUgCIiARKASAiEigFgIhIoCINADObaWa7zGx9lO2KiMi3RT0C+F/g2ojbFBGRCkQaAO6+BNgdZZsiIlIxHQMQEQlUtQwAMxtlZrlmlltUVBR3OSIiNVK1DAB3n+7u6e6enpqaGnc5IiI1UrUMABEROfOiPg10NrAcuNTMCs1sZJTti4jIVyK9I5i7/yTK9kRE5MQ0BSQiEigFgIhIoBQAIiKBUgCIiARKASAiEigFgIhIoBQAIiKBUgCIiARKASAiEigFgIhIoBQAIiKBUgCIiARKASAiEigFgIhIoBQAIiKBUgCIiARKASAiEigFgIhIoBQAIiKBUgCIiARKASAiEigFgIhIoBQAIiKBUgCIiARKASAiEigFgIhIoBQAIiKBUgCIiAQq8gAws2vNbKOZfWBm/x11+yIiUibSADCz2sD/B64DOgM/MbPOUdYgIiJlkiJurxfwgbtvATCzvwE/BvJP9IaNGzeSmZkZTXUiIgGJOgCaAzu+9rwQuOL4jcxsFDAq8fTwW2+9tT6C2uLQCPg07iLOIPXv7Kb+nb0urcxGUQdApbj7dGA6gJnlunt6zCWdETW5b6D+ne3Uv7OXmeVWZruoDwL/G2j5tectEq+JiEjEog6A1cAlZtbGzOoA/wnkRFyDiIgQ8RSQu39pZr8G5gO1gZnu/v5J3jb9zFcWm5rcN1D/znbq39mrUn0zdz/ThYiISDWkK4FFRAKlABARCVS1DYCavGSEmc00s11mViOvbzCzlma2yMzyzex9M7sz7pqqkpmda2arzGxton/3x11TVTOz2mb2rpm9EnctVc3MtprZOjPLq+zpkmcTM7vAzF40sw1mVmBmvU+4bXU8BpBYMmIT8EPKLhZbDfzE3U94xfDZxMz6AvuBZ9y9a9z1VDUzawo0dfd3zKw+sAbIqkG/PwPquft+M0sGlgF3uvuKmEurMmaWDaQD57v7oLjrqUpmthVId/caeRGYmT0NLHX3JxNnW9Z1970VbVtdRwDlS0a4ewlwbMmIGsHdlwC7467jTHH3ne7+TuL7YqCAsqvAawQvsz/xNDnxqH7/SZ0mM2sBXA88GXctcmrMrAHQF5gB4O4lJ9r5Q/UNgIqWjKgxO5CQmFlroAewMuZSqlRiiiQP2AW84e41qX9TgHFAacx1nCkOLDCzNYllZ2qSNkAR8FRiCu9JM6t3oo2rawBIDWBm5wFzgf9y931x11OV3P2ou3en7Gr2XmZWI6byzGwQsMvd18Rdyxl0tbunUbYq8R2JKdmaIglIAx539x7AAeCEx1CrawBoyYizXGJufC7wnLvPi7ueMyUxvF4EXBtzKVUlAxiSmCf/G3CNmc2Kt6Sq5e7/TnzdBbxE2ZRzTVEIFH5tRPoiZYFQoeoaAFoy4iyWOEg6Ayhw90lx11PVzCzVzC5IfJ9C2ckKG2Itqoq4+73u3sLdW1P2d/emu98Sc1lVxszqJU5MIDE18iOgxpyN5+4fAzvM7NhqoP35juX2q+tqoKezZMRZw8xmA5lAIzMrBCa4+4x4q6pSGcAIYF1inhxgvLu/Fl9JVaop8HTibLVawBx3r3GnS9ZQTYCXyv5HIQl43t1fj7ekKjcGeC7xz/MW4NYTbVgtTwMVEZEzr7pOAYmIyBmmABARCZQCQEQkUAoAEZFAKQBERAKlABARCZQCQEQkUAoAkUoys1pmVmxmE457vaGZuZn9PK7aRE6HAkCk8joA5wHvHPd6j8TXd6MtR+T7UQCIVN6xRbUqCoDDfMeaKyLVkQJApPLSKFsq+fiVadOA9939yxhqEjltCgCRyuvJt//7h7IRgKZ/5KyjABCpvO4ct6M3s8bApce/LnI2UACIVIKZtQMuAI4e96MxlP0d5UVcksj3Vi3vByBSDfVMfP2lme2g7F7APwKOnfqZbmbvuPsXsVQncho0AhCpnDRgN2X3V70feBaoDwwH9gE3aecvZxvdEEakEsxsAWV/Lz+MuxaRqqIRgEjlpAFr4i5CpCopAEROwsz+A7gIBYDUMJoCEhEJlEYAIiKBUgCIiARKASAiEigFgIhIoBQAIiKBUgCIiARKASAiEqj/A4i1FAySOyFuAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.special import gamma\n",
    "\n",
    "def f(x,y,mu1,lambda1,a1,b1):\n",
    "    return (2*np.pi/lambda1)*np.exp(-0.5*(x-mu1)**2*lambda1)*y**(a1-1)*b1**(a1)*np.exp(-b1*y)*1./gamma(a1)\n",
    "\n",
    "def f2(x,y,mu1,lambda1,a1,b1):\n",
    "    return (2*np.pi/lambda1)*np.exp(-0.5*(x-mu1)**2*lambda1*y)*y**(a1-0.5)*b1**(a1)*np.exp(-b1*y)*1./gamma(a1)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "x = np.linspace(0, 6, 100)\n",
    "y = np.linspace(0, 6, 100)\n",
    "\n",
    "X, Y = np.meshgrid(x, y)\n",
    "\n",
    "plt.figure()\n",
    "Z = f(X, Y,mu1[0],lambda1[0],a1[0],b1[0])\n",
    "plt.xlabel(r'$\\mu$',size=16)\n",
    "plt.ylabel(r'$\\tau$',size=16)\n",
    "\n",
    "plt.contour(X, Y, Z, colors='black');\n",
    "\n",
    "plt.figure()\n",
    "Z = f(X, Y,mu1[1],lambda1[1],a1[0],b1[0])\n",
    "plt.xlabel(r'$\\mu$',size=16)\n",
    "plt.ylabel(r'$\\tau$',size=16)\n",
    "\n",
    "plt.contour(X, Y, Z, colors='black');\n",
    "\n",
    "plt.figure()\n",
    "Z = f(X, Y,mu1[1],lambda1[1],a1[1],b1[1])\n",
    "plt.xlabel(r'$\\mu$',size=16)\n",
    "plt.ylabel(r'$\\tau$',size=16)\n",
    "\n",
    "plt.contour(X, Y, Z, colors='black');\n",
    "\n",
    "plt.figure()\n",
    "Z = f(X, Y,mu1[3],lambda1[3],a1[3],b1[3])\n",
    "plt.xlabel(r'$\\mu$',size=16)\n",
    "plt.ylabel(r'$\\tau$',size=16)\n",
    "plt.xlim(2,4)\n",
    "plt.ylim(1,3)\n",
    "\n",
    "plt.contour(X, Y, Z, colors='black');\n",
    "\n",
    "\n",
    "plt.figure()\n",
    "Z = f2(X, Y,muc,lambdac,ac,bc)\n",
    "plt.xlabel(r'$\\mu$',size=16)\n",
    "plt.ylabel(r'$\\tau$',size=16)\n",
    "plt.xlim(2,4)\n",
    "plt.ylim(1,3)\n",
    "\n",
    "plt.contour(X, Y, Z, colors='black');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}