debug.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from function import RBF_kernel,linear_kernel\n",
    "from sklearn.metrics.pairwise import laplacian_kernel\n",
    "import scipy\n",
    "from scipy.stats import multivariate_normal\n",
    "from scipy.stats._multivariate import _PSD\n",
    "from scipy.stats._multivariate import multivariate_normal_gen\n",
    "#np.random.seed(1234)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "# path = '/Users/lilingyu/E/PhD/Python/'\n",
    "# path = '/storage3/yhhuang/users/lingyu/'\n",
    "# path = '/data/users/lingyu/'\n",
    "# path = '/home/lly/Python/'\n",
    "#path = '/mnt/lingyu/nfs_share2/Python/'\n",
    "path = '/mnt/jackywang/nfs_share2/spatialde'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def _pinv_1d(v, eps=1e-5):\n",
    "    return np.array([0 if abs(x) <= eps else 1/x for x in v], dtype=float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# class new_normal(multivariate_normal_gen):\n",
    "#     def __init__(self,seed = None):\n",
    "#         super().__init__(seed)\n",
    "    \n",
    "#     def "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Gaussian:\n",
    "\n",
    "    def __init__(self,mean,cov,spatial,ss_loc,dependency=None,d=5,kernel='RBF',l=0.01):\n",
    "        \"\"\"\n",
    "        number of superspots: M\n",
    "        mean: N-length 1-d array\n",
    "        cov: full pre-determined covariance matrix\n",
    "        dependency format: M-length list of lists, the i-th element indicates the superspots that the i-th superspot is dependent on\n",
    "        ss_loc: M-length list of lists, the i-th element indicates the spots (ordinal) that the i-th superspots contain\n",
    "        l: hyperparameter for kernel\n",
    "        \"\"\"\n",
    "        super().__init__()\n",
    "        if mean.ndim == 1:\n",
    "            self.all_mean = np.array(mean)[:,np.newaxis]\n",
    "        else:\n",
    "            self.all_mean = np.array(mean)       \n",
    "        self.all_cov = cov\n",
    "        self.dependency = dependency   # temporarily assuming dependency[i] > i \n",
    "        self.M = len(dependency)\n",
    "        self.ss_loc = ss_loc\n",
    "        self.spatial = spatial\n",
    "        self.cond_mean = None\n",
    "        self.l = l\n",
    "        self.d = d\n",
    "        self._initialize()\n",
    "    \n",
    "    def _initialize(self):\n",
    "        self._init_ds_loc()\n",
    "        self._init_inv()\n",
    "        self._init_ss_cov()        \n",
    "        #self._init_cond_cov()\n",
    "\n",
    "    def _init_ds_loc(self):\n",
    "        self.ds_loc = []        \n",
    "        for i,ds in enumerate(self.dependency):\n",
    "           ind = []\n",
    "           for ss in ds:\n",
    "               ind += self.ss_loc[ss]\n",
    "           self.ds_loc.append(ind)\n",
    "    \n",
    "    def _init_inv(self):\n",
    "        self.ds_inv_sums = []\n",
    "        self.ds_inv_col_sums = []\n",
    "        for i,loc in enumerate(self.ds_loc):\n",
    "            ds_cov = self.all_cov[np.ix_(loc,loc)]\n",
    "            if len(ds_cov) == 0:\n",
    "                self.ds_inv_col_sums.append(ds_cov)\n",
    "                self.ds_inv_sums.append(ds_cov)\n",
    "            else:\n",
    "                inv = np.linalg.solve(ds_cov, np.identity(len(ds_cov)))\n",
    "                self.ds_inv_col_sums.append(np.sum(inv,axis=0))\n",
    "                self.ds_inv_sums.append(np.sum(inv))\n",
    "\n",
    "    def _init_ss_cov(self):       #M*M covariance between superspots\n",
    "        mean_loc = []\n",
    "        for i,loc in enumerate(self.ss_loc):\n",
    "            mean_loc.append(np.average(self.spatial[loc],axis=0))\n",
    "        mean_loc = np.array(mean_loc)\n",
    "        #self.ss_cov = RBF_kernel(mean_loc,self.l)\n",
    "        self.ss_cov = laplacian_kernel(mean_loc)\n",
    "        print(self.ss_cov)\n",
    "\n",
    "    \n",
    "    # def _init_cond_cov(self):\n",
    "    #     eps = 1e-5\n",
    "    #     self.cond_U = []\n",
    "    #     self.log_pdet = []\n",
    "    #     for i in range(self.M):\n",
    "    #         in_cov = self.all_cov[np.ix_(self.ss_loc[i],self.ss_loc[i])]   \n",
    "    #         if len(self.dependency[i]) == 0:\n",
    "    #             cond_cov = in_cov\n",
    "    #         else:\n",
    "    #             cond_cov = in_cov - np.ones_like(in_cov)*self.ds_inv_sums[i]*np.average(self.ss_cov[i,self.dependency[i]])**2\n",
    "    #         #treat cond_cov as positive definite \n",
    "    #         s, u = scipy.linalg.eigh(cond_cov)\n",
    "    #         #print(len(s[s<=0]))\n",
    "    #         d = s[s > eps]\n",
    "    #         s_pinv = _pinv_1d(s,eps)\n",
    "    #         print(len(s_pinv[s_pinv<eps]),len(s_pinv[s_pinv<-eps]))\n",
    "    #         print(s_pinv[s_pinv<-eps])\n",
    "    #         self.cond_U.append(np.multiply(u, np.sqrt(s_pinv)))\n",
    "    #         #print(np.isnan(self.cond_U).any())\n",
    "    #         self.log_pdet.append(np.sum(np.log(d)))\n",
    "    \n",
    "        \n",
    " \n",
    "    def get_cond_dev(self,dev, i=0, y=None, all_mean=None):    #dev:N*G\n",
    "        return dev[self.ss_loc[i]] -  np.average(self.ss_cov[i,self.dependency[i]])*self.ds_inv_col_sums[i] @ dev[self.ds_loc[i]]\n",
    "\n",
    "     \n",
    "    # def gs_nll_total(self,Y):\n",
    "    #     \"\"\"\n",
    "    #     Y: observation of dimension N*G\n",
    "    #     \"\"\"\n",
    "    #     N,G = Y.shape\n",
    "    #     ll = np.log(2 * np.pi)*N*G + np.sum(self.log_pdet)*G\n",
    "    #     dev = Y - self.all_mean    #N*G\n",
    "    #     for i in range(self.M):\n",
    "    #         U = self.cond_U[i]\n",
    "    #         if len(self.dependency[i]) == 0:\n",
    "    #             cond_dev = dev[self.ss_loc[i]]\n",
    "    #         else:\n",
    "    #             cond_dev = self.get_cond_dev(dev,i)\n",
    "    #         for g in range(G):\n",
    "    #             ll += np.sum(np.square(cond_dev[:,g].T @ U), axis=-1)\n",
    "    #     return -0.5*ll\n",
    "    \n",
    "    # def gs_nll_sep(self,Y):    \n",
    "    #     \"\"\"\n",
    "    #     Y: observation of dimension N*G\n",
    "    #     \"\"\"\n",
    "    #     N,G = Y.shape\n",
    "    #     ll = np.log(2 * np.pi)*N + np.sum(self.log_pdet)\n",
    "    #     result = [-0.5*ll]*G\n",
    "    #     print(result)\n",
    "    #     dev = Y - self.all_mean    #N*G\n",
    "    #     for i in range(self.M):\n",
    "    #         U = self.cond_U[i]\n",
    "    #         if len(self.dependency[i]) == 0:\n",
    "    #             cond_dev = dev[self.ss_loc[i]]\n",
    "    #         else:\n",
    "    #             cond_dev = self.get_cond_dev(dev,i)\n",
    "    #         for g in range(G):\n",
    "    #             result[g] += -0.5*np.sum(np.square(cond_dev[:,g].T @ U), axis=-1)\n",
    "    #     return np.array(result)\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Gaussian_psd(Gaussian):\n",
    "    def __init__(self,mean,cov,spatial,ss_loc,dependency=None,d=5,kernel='RBF',l=0.01):\n",
    "        super().__init__(mean,cov,spatial,ss_loc,dependency,d,kernel,l)\n",
    "        self._init_cond_cov()\n",
    "        \n",
    "        \n",
    "    def _init_cond_cov(self):\n",
    "        eps = 1e-5\n",
    "        self.cond_U = []\n",
    "        self.log_pdet = []\n",
    "        for i in range(self.M):\n",
    "            in_cov = self.all_cov[np.ix_(self.ss_loc[i],self.ss_loc[i])]   \n",
    "            if len(self.dependency[i]) == 0:\n",
    "                cond_cov = in_cov\n",
    "            else:\n",
    "                cond_cov = in_cov - np.ones_like(in_cov)*self.ds_inv_sums[i]*np.average(self.ss_cov[i,self.dependency[i]])**2\n",
    "            #treat cond_cov as positive definite \n",
    "            s, u = scipy.linalg.eigh(cond_cov)\n",
    "            #print(len(s[s<=0]))\n",
    "            d = s[s > eps]\n",
    "            s_pinv = _pinv_1d(s,eps)\n",
    "            print(len(s_pinv[s_pinv<eps]),len(s_pinv[s_pinv<-eps]))\n",
    "            print(s_pinv[s_pinv<-eps])\n",
    "            self.cond_U.append(np.multiply(u, np.sqrt(s_pinv)))\n",
    "            #print(np.isnan(self.cond_U).any())\n",
    "            self.log_pdet.append(np.sum(np.log(d)))\n",
    "    \n",
    "    def gs_nll_sep(self,Y):    \n",
    "        \"\"\"\n",
    "        Y: observation of dimension N*G\n",
    "        \"\"\"\n",
    "        N,G = Y.shape\n",
    "        ll = np.log(2 * np.pi)*N + np.sum(self.log_pdet)\n",
    "        result = [-0.5*ll]*G\n",
    "        #print(result)\n",
    "        dev = Y - self.all_mean    #N*G\n",
    "        for i in range(self.M):\n",
    "            U = self.cond_U[i]\n",
    "            if len(self.dependency[i]) == 0:\n",
    "                cond_dev = dev[self.ss_loc[i]]\n",
    "            else:\n",
    "                cond_dev = self.get_cond_dev(dev,i)\n",
    "            for g in range(G):\n",
    "                result[g] += -0.5*np.sum(np.square(cond_dev[:,g].T @ U), axis=-1)\n",
    "        return np.array(result)\n",
    "    \n",
    "\n",
    "    \n",
    "class Gaussian_gen(Gaussian):\n",
    "    def __init__(self,mean,cov,spatial,ss_loc,dependency=None,d=5,kernel='RBF',l=0.01):\n",
    "        super().__init__(mean,cov,spatial,ss_loc,dependency,d,kernel,l)\n",
    "        self._init_cond_cov()\n",
    "        \n",
    "        \n",
    "    def _init_cond_cov(self):\n",
    "        eps = 1e-5\n",
    "        self.cond_inv = []\n",
    "        self.log_pdet = []\n",
    "        for i in range(self.M):\n",
    "            in_cov = self.all_cov[np.ix_(self.ss_loc[i],self.ss_loc[i])]   \n",
    "            if len(self.dependency[i]) == 0:\n",
    "                cond_cov = in_cov\n",
    "            else:\n",
    "                cond_cov = in_cov - np.ones_like(in_cov)*self.ds_inv_sums[i]*np.average(self.ss_cov[i,self.dependency[i]])**2\n",
    "            #treat cond_cov as positive definite \n",
    "            self.cond_inv.append(np.linalg.inv(cond_cov))\n",
    "            #print(np.linalg.det(cond_cov))\n",
    "            #self.log_pdet.append(np.log(np.linalg.det(cond_cov)))\n",
    "            s, u = scipy.linalg.eigh(cond_cov)\n",
    "            #print(len(s[s<=0]))\n",
    "            d = s[s > eps]\n",
    "            s_pinv = _pinv_1d(s,eps)\n",
    "            # print(len(s_pinv[s_pinv<eps]),len(s_pinv[s_pinv<-eps]))\n",
    "            print(s_pinv[s_pinv<eps])\n",
    "            print(\"det:\",np.sum(np.log(d)))\n",
    "            # self.cond_U.append(np.multiply(u, np.sqrt(s_pinv)))\n",
    "            # #print(np.isnan(self.cond_U).any())\n",
    "            # self.log_pdet.append(np.sum(np.log(d)))\n",
    "    \n",
    "    def gs_nll_sep(self,Y):    \n",
    "        \"\"\"\n",
    "        Y: observation of dimension N*G\n",
    "        \"\"\"\n",
    "        N,G = Y.shape\n",
    "        ll = np.log(2 * np.pi)*N + np.sum(self.log_pdet)\n",
    "        result = [-0.5*ll]*G\n",
    "        dev = Y - self.all_mean    #N*G\n",
    "        for i in range(self.M):\n",
    "            inv = self.cond_inv[i]\n",
    "            if len(self.dependency[i]) == 0:\n",
    "                cond_dev = dev[self.ss_loc[i]]\n",
    "            else:\n",
    "                cond_dev = self.get_cond_dev(dev,i)\n",
    "            for g in range(G):\n",
    "                result[g] += -0.5* (cond_dev[:,g].T @ inv @ cond_dev[:,g])\n",
    "        return np.array(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_l_limits(X):\n",
    "    Xsq = np.sum(np.square(X), 1)\n",
    "    R2 = -2. * np.dot(X, X.T) + (Xsq[:, None] + Xsq[None, :])\n",
    "    R2 = np.clip(R2, 0, np.inf)\n",
    "    R_vals = np.unique(R2.flatten())\n",
    "    R_vals = R_vals[R_vals > 1e-8]\n",
    "    \n",
    "    l_min = np.sqrt(R_vals.min()) / 2.\n",
    "    l_max = np.sqrt(R_vals.max()) * 2.\n",
    "    \n",
    "    return l_min, l_max"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1 1 []\n",
      "0 1 [0]\n",
      "1 1 [1]\n",
      "-1 0 [0]\n",
      "0 0 [1, 3]\n",
      "1 0 [2, 4]\n",
      "-1 -1 [3]\n",
      "0 -1 [4, 6]\n",
      "1 -1 [5, 7]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(9000, 2)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## 9 superspots\n",
    "N = 9000\n",
    "spatial = []\n",
    "dependency = []\n",
    "for i in range(3):\n",
    "    for j in range(3):\n",
    "        spatial.append(np.random.multivariate_normal(np.array([j-1,1-i]),np.identity(2)*0.2,1000))\n",
    "        d = []\n",
    "        if (i-1) > -1:\n",
    "            d.append((i-1)*3+j)\n",
    "        if (j-1) > -1:\n",
    "            d.append(i*3+j-1)\n",
    "        dependency.append(d)\n",
    "        print(j-1,1-i,d)\n",
    "spatial = np.vstack(spatial)\n",
    "spatial.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "l = 0.8\n",
    "#cov = RBF_kernel(spatial,0.8)\n",
    "cov = laplacian_kernel(spatial)\n",
    "mean = np.zeros(N)\n",
    "Y = np.random.multivariate_normal(mean,cov,200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "eps: 8.056818952814166e-07\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([9676.39232825, 9642.95021206, 9810.85496288, 9714.7454243 ,\n",
       "       9659.15887891, 9502.97832548, 9621.13615196, 9675.84574254,\n",
       "       9694.71323467, 9699.90048492, 9720.60993432, 9631.66666866,\n",
       "       9723.20596772, 9558.5700378 , 9662.37409481, 9636.05407331,\n",
       "       9564.66148917, 9671.29461373, 9657.14092893, 9791.69297996,\n",
       "       9674.04119967, 9739.67164113, 9787.19939283, 9691.40435195,\n",
       "       9675.14854213, 9650.02562732, 9662.97819741, 9588.23832363,\n",
       "       9497.5184583 , 9555.02738034, 9733.68603872, 9531.86828331,\n",
       "       9565.4621766 , 9604.50702129, 9648.31116133, 9580.47396614,\n",
       "       9579.39559254, 9591.73914673, 9744.67539496, 9667.37981651,\n",
       "       9555.43435876, 9641.44916775, 9660.64314063, 9731.19314037,\n",
       "       9685.26606149, 9663.80112295, 9554.10298934, 9543.69736   ,\n",
       "       9538.46223033, 9653.94254798, 9636.27820788, 9793.34774272,\n",
       "       9733.05029184, 9575.81280047, 9639.25682629, 9620.25562001,\n",
       "       9628.76392424, 9696.07039447, 9642.05565199, 9563.09861677,\n",
       "       9750.68955244, 9706.97141492, 9637.85514368, 9648.89958003,\n",
       "       9515.33288106, 9699.28420103, 9668.03035486, 9651.15818722,\n",
       "       9593.10068488, 9701.3096922 , 9624.9445785 , 9652.77340726,\n",
       "       9747.48757505, 9570.99889174, 9583.06560534, 9718.78635462,\n",
       "       9603.233163  , 9663.05923902, 9690.95457561, 9759.65635062,\n",
       "       9743.16466399, 9729.89433   , 9748.7632385 , 9644.43437188,\n",
       "       9664.98909902, 9543.95625054, 9701.67323838, 9753.35962381,\n",
       "       9733.22138004, 9729.64872922, 9640.40454737, 9599.70246159,\n",
       "       9672.84280985, 9782.97499829, 9685.86734231, 9688.27926395,\n",
       "       9878.20957491, 9689.45415942, 9800.27861664, 9764.4419238 ,\n",
       "       9690.19990883, 9746.72367275, 9761.50531418, 9617.01279807,\n",
       "       9639.79452566, 9699.99796657, 9723.70836564, 9802.76138577,\n",
       "       9640.51707759, 9596.63739928, 9580.63796602, 9647.75983467,\n",
       "       9665.24908213, 9634.62864138, 9708.35701417, 9722.74857747,\n",
       "       9650.66490935, 9702.64921964, 9670.49292339, 9593.28071143,\n",
       "       9574.52814824, 9649.11041174, 9643.69801357, 9630.23368685,\n",
       "       9653.53601429, 9725.8128103 , 9650.98043948, 9609.51333094,\n",
       "       9575.31616877, 9546.88688739, 9658.13608129, 9655.08512553,\n",
       "       9656.84216592, 9639.75420831, 9699.37564108, 9718.68100964,\n",
       "       9765.62983352, 9724.66690046, 9676.66305684, 9556.16757475,\n",
       "       9704.83119765, 9762.50442821, 9662.71011496, 9564.26240804,\n",
       "       9663.49539001, 9603.26488072, 9600.00808891, 9733.96875519,\n",
       "       9694.96156454, 9666.39167435, 9621.69598446, 9612.80381462,\n",
       "       9794.94007997, 9762.75820165, 9666.86236041, 9708.7944215 ,\n",
       "       9711.02166164, 9715.31068264, 9524.57944538, 9651.31547992,\n",
       "       9656.20482499, 9555.32626303, 9705.29683492, 9733.82267265,\n",
       "       9585.22398165, 9743.5254821 , 9594.34170462, 9631.30845756,\n",
       "       9634.42244254, 9577.0186156 , 9586.07645606, 9578.45543984,\n",
       "       9669.9137206 , 9628.8055231 , 9677.65013204, 9642.12707142,\n",
       "       9798.74805241, 9620.73895713, 9658.98947036, 9595.05909485,\n",
       "       9639.2991457 , 9527.02470235, 9633.62537406, 9681.66149817,\n",
       "       9592.21365394, 9709.85965598, 9664.38651215, 9747.86904063,\n",
       "       9588.04278989, 9602.32511321, 9711.66172132, 9609.57225953,\n",
       "       9700.68790685, 9657.6328826 , 9767.78183385, 9635.61925189,\n",
       "       9752.85706181, 9695.21476345, 9761.0750321 , 9687.71382442])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "multivariate_normal.logpdf(Y, mean, cov)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1 1 []\n",
      "0 1 [0]\n",
      "1 1 [1]\n",
      "-1 0 [0]\n",
      "0 0 [1, 3]\n",
      "1 0 [2, 4]\n",
      "-1 -1 [3]\n",
      "0 -1 [4, 6]\n",
      "1 -1 [5, 7]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(9000, 2)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## 9 superspots\n",
    "N = 9000\n",
    "spatial = []\n",
    "dependency = []\n",
    "for i in range(3):\n",
    "    for j in range(3):\n",
    "        spatial.append(np.random.multivariate_normal(np.array([j-1,1-i]),np.identity(2)*0.2,1000))\n",
    "        d = []\n",
    "        if (i-1) > -1:\n",
    "            d.append((i-1)*3+j)\n",
    "        if (j-1) > -1:\n",
    "            d.append(i*3+j-1)\n",
    "        dependency.append(d)\n",
    "        print(j-1,1-i,d)\n",
    "spatial = np.vstack(spatial)\n",
    "spatial.shape\n",
    "\n",
    "# spatial = np.random.randn(N,2)\n",
    "# dependency = [[],[0],[0,1],[1,2],[2,3],[3,4],[4,5],[5,6]]\n",
    "# mean = np.random.randn(10000)\n",
    "# cut = np.linspace(0,N,9).astype(int)\n",
    "# ss_loc = [list(range(cut[i],cut[i+1])) for i in range(8)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "cov = laplacian_kernel(spatial)\n",
    "mean = np.zeros(N)\n",
    "Y = np.random.multivariate_normal(mean,cov,200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.29727764,  1.05465461,  1.70272835, ...,  1.40716251,\n",
       "         0.66534525,  0.49891368],\n",
       "       [ 1.2276277 ,  1.08637652,  1.30093299, ..., -0.84486675,\n",
       "        -1.0382536 , -0.86213476],\n",
       "       [ 1.62990907,  0.87923236,  1.18367949, ...,  0.50586848,\n",
       "         1.21587636,  0.17273494],\n",
       "       ...,\n",
       "       [ 0.59103518, -0.83727368, -0.06494127, ..., -0.74878414,\n",
       "        -1.1899472 , -0.55435183],\n",
       "       [-1.70051099, -0.69348697, -1.77794094, ..., -0.45916863,\n",
       "         0.45698769,  0.20317698],\n",
       "       [-0.60105843, -1.63014763, -1.13555041, ...,  0.74460248,\n",
       "         1.02189369,  1.75775647]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "eps: 8.019729069114857e-07\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([9677.66288126, 9539.82151642, 9565.86453337, 9692.15329299,\n",
       "       9667.88173557, 9630.43646993, 9664.55102955, 9741.1403455 ,\n",
       "       9608.66638227, 9578.75779831, 9730.86758035, 9658.90688015,\n",
       "       9570.37493995, 9568.56465806, 9772.89946809, 9682.50435345,\n",
       "       9552.26041247, 9665.72276059, 9585.11589172, 9562.05466387,\n",
       "       9805.7429111 , 9612.87863031, 9668.57741937, 9644.99950481,\n",
       "       9609.95441297, 9702.77272293, 9760.01607336, 9604.900401  ,\n",
       "       9686.86246275, 9702.23477733, 9713.29164202, 9673.20628105,\n",
       "       9571.39202529, 9677.78626862, 9679.43406429, 9677.96717538,\n",
       "       9602.38708499, 9657.0466424 , 9704.31425334, 9634.850724  ,\n",
       "       9718.43748722, 9586.01179273, 9641.64267106, 9609.76640281,\n",
       "       9636.38540688, 9499.80021955, 9762.75113819, 9642.60293147,\n",
       "       9596.01362565, 9556.83287893, 9765.76462702, 9582.00224764,\n",
       "       9734.44155846, 9769.36513767, 9624.72591534, 9728.06430302,\n",
       "       9655.7558204 , 9645.56146925, 9592.50759143, 9618.89639657,\n",
       "       9756.84724504, 9570.74366532, 9632.2809991 , 9639.73755675,\n",
       "       9700.27133059, 9670.27656801, 9703.93047831, 9731.60468615,\n",
       "       9531.6641531 , 9797.58022112, 9604.07443616, 9770.42369407,\n",
       "       9689.65173258, 9592.20427969, 9633.71974905, 9715.68929166,\n",
       "       9651.34198043, 9497.06481554, 9843.6794669 , 9599.29776853,\n",
       "       9686.53462394, 9642.05601959, 9649.95043444, 9540.40239496,\n",
       "       9631.5282254 , 9676.60487145, 9661.64764489, 9598.74730703,\n",
       "       9611.15161776, 9579.65134059, 9700.84548535, 9696.42829296,\n",
       "       9608.26823988, 9623.89236071, 9647.89737546, 9623.04906183,\n",
       "       9705.26996216, 9652.86488665, 9599.22492371, 9701.12520009,\n",
       "       9439.71048221, 9597.86009828, 9808.08700179, 9763.48486406,\n",
       "       9554.86882722, 9559.6765943 , 9609.12689976, 9636.19035659,\n",
       "       9713.73949786, 9680.06013829, 9596.12908198, 9721.71603194,\n",
       "       9701.30658801, 9617.131154  , 9621.60461967, 9679.07177885,\n",
       "       9566.79193337, 9616.91118139, 9619.64115658, 9621.92821183,\n",
       "       9606.55670998, 9634.83429246, 9761.28126636, 9550.75234919,\n",
       "       9576.74428357, 9590.503385  , 9749.849361  , 9684.27561961,\n",
       "       9703.85483481, 9643.16095909, 9622.86888972, 9532.14618106,\n",
       "       9761.99440702, 9657.79463347, 9597.69434297, 9601.56921427,\n",
       "       9556.92386149, 9657.66062301, 9671.81515299, 9585.27631187,\n",
       "       9497.01240956, 9607.120111  , 9673.50734354, 9592.81561719,\n",
       "       9653.71810983, 9628.53112574, 9619.76799232, 9739.70738322,\n",
       "       9661.58402408, 9754.03331578, 9679.96657563, 9675.05371543,\n",
       "       9649.12380947, 9621.81007187, 9608.37387632, 9573.0850933 ,\n",
       "       9672.55101278, 9580.76573104, 9716.68823337, 9663.35993001,\n",
       "       9710.71173007, 9691.38941208, 9640.57095876, 9688.82341613,\n",
       "       9640.34033671, 9612.69171945, 9644.30321995, 9589.17272092,\n",
       "       9683.53773119, 9599.34419781, 9587.8680248 , 9692.20761279,\n",
       "       9582.65687195, 9592.1894487 , 9632.1184045 , 9676.72322484,\n",
       "       9652.64342421, 9610.276011  , 9602.49162457, 9630.50122021,\n",
       "       9787.65762383, 9635.94502915, 9586.83465988, 9566.05107291,\n",
       "       9685.33837459, 9615.34649458, 9736.97663639, 9618.44946097,\n",
       "       9605.92433572, 9603.68573516, 9728.36874219, 9608.54708597,\n",
       "       9676.43354505, 9531.27334261, 9768.54061051, 9689.43278336,\n",
       "       9608.92074939, 9650.70839215, 9587.41801272, 9640.31270793])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "likelihood_1 = multivariate_normal.logpdf(Y, mean, cov)\n",
    "likelihood_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "ss_loc = [list(range(1000*i, 1000*(i+1))) for i in range(9)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.         0.59894227 0.37245344 0.58798847 0.36358244 0.21886323\n",
      "  0.35648358 0.22164918 0.13249949]\n",
      " [0.59894227 1.         0.60936088 0.37136635 0.59764641 0.36541623\n",
      "  0.21977752 0.36288944 0.22122248]\n",
      " [0.37245344 0.60936088 1.         0.22629613 0.36418234 0.58762573\n",
      "  0.13392382 0.22113063 0.3557478 ]\n",
      " [0.58798847 0.37136635 0.22629613 1.         0.61834961 0.37222367\n",
      "  0.59180784 0.37696177 0.22534369]\n",
      " [0.36358244 0.59764641 0.36418234 0.61834961 1.         0.59906662\n",
      "  0.36773837 0.60719757 0.36442765]\n",
      " [0.21886323 0.36541623 0.58762573 0.37222367 0.59906662 1.\n",
      "  0.22029979 0.3637518  0.59335703]\n",
      " [0.35648358 0.21977752 0.13392382 0.59180784 0.36773837 0.22029979\n",
      "  1.         0.60563216 0.36845616]\n",
      " [0.22164918 0.36288944 0.22113063 0.37696177 0.60719757 0.3637518\n",
      "  0.60563216 1.         0.59778924]\n",
      " [0.13249949 0.22122248 0.3557478  0.22534369 0.36442765 0.59335703\n",
      "  0.36845616 0.59778924 1.        ]]\n",
      "[]\n",
      "det: -4295.117522334454\n",
      "[-0.00314335]\n",
      "det: -4335.419685739484\n",
      "[-0.00274507]\n",
      "det: -4287.674674357132\n",
      "[-0.00327938]\n",
      "det: -4248.113624040283\n",
      "[-0.00154752]\n",
      "det: -4250.630741200524\n",
      "[-0.00166556]\n",
      "det: -4275.391887910983\n",
      "[-0.00260546]\n",
      "det: -4252.816675889392\n",
      "[-0.00150963]\n",
      "det: -4305.928529469289\n",
      "[-0.00166479]\n",
      "det: -4285.071909777465\n"
     ]
    }
   ],
   "source": [
    "model_2 = Gaussian_gen(mean,cov,spatial,ss_loc,dependency=dependency,kernel='RBF',l=0.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf,\n",
       "       inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf,\n",
       "       inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf,\n",
       "       inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf,\n",
       "       inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf,\n",
       "       inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf,\n",
       "       inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf,\n",
       "       inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf,\n",
       "       inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf,\n",
       "       inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf,\n",
       "       inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf,\n",
       "       inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf,\n",
       "       inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf,\n",
       "       inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf,\n",
       "       inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf, inf,\n",
       "       inf, inf, inf, inf, inf])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "likelihood_2 = model_2.gs_nll_sep(Y.T)\n",
    "likelihood_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan\n",
      " nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan\n",
      " nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan\n",
      " nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan\n",
      " nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan\n",
      " nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan\n",
      " nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan\n",
      " nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan\n",
      " nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan\n",
      " nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan\n",
      " nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan nan\n",
      " nan nan]\n"
     ]
    }
   ],
   "source": [
    "print(likelihood_1-likelihood_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "316\n",
      "295\n",
      "310\n",
      "289\n",
      "298\n",
      "289\n",
      "313\n",
      "297\n",
      "285\n"
     ]
    }
   ],
   "source": [
    "model_3 = Gaussian(mean,cov,spatial,ss_loc,dependency=[[]]*9,kernel='RBF',l=0.8)\n",
    "likelihood_3 = model_3.gs_nll_sep(Y.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-7598.99229431 -7629.48116858 -7619.97595529 -7550.00217159\n",
      " -7612.94454487 -7622.96862256 -7686.75506969 -7598.96112408\n",
      " -7592.23490549 -7577.14233449 -7552.11703457 -7552.65651036\n",
      " -7624.7758211  -7552.78746133 -7554.86891622 -7630.25920768\n",
      " -7643.45759    -7571.56736976 -7637.35085587 -7623.37883261\n",
      " -7649.78524757 -7571.86582808 -7649.46715962 -7600.48114096\n",
      " -7544.59362964 -7573.38093977 -7646.84343299 -7559.97716664\n",
      " -7615.87227734 -7702.34240025 -7590.53013053 -7588.74011536\n",
      " -7590.44965499 -7581.45877773 -7598.10285861 -7619.64258939\n",
      " -7545.20977793 -7551.80612553 -7643.09574327 -7640.70139836\n",
      " -7555.06736936 -7694.13270064 -7599.19838972 -7633.85576053\n",
      " -7588.99626569 -7658.52441802 -7572.04249776 -7576.98166125\n",
      " -7631.06610103 -7613.59689126 -7649.72452571 -7569.00970384\n",
      " -7580.88203611 -7700.37015828 -7635.76492145 -7606.04102779\n",
      " -7675.61270271 -7671.66711021 -7578.84875293 -7606.05404597\n",
      " -7605.26138174 -7546.66851175 -7604.60025868 -7586.03737671\n",
      " -7618.79193516 -7603.56133813 -7586.82277665 -7666.08037899\n",
      " -7635.282856   -7510.1460201  -7640.51943496 -7650.42373814\n",
      " -7568.13507475 -7626.62606505 -7584.81589402 -7613.87431105\n",
      " -7628.45845182 -7559.5251524  -7633.66178883 -7624.75782879\n",
      " -7626.16630165 -7611.96001244 -7535.02152404 -7571.71027418\n",
      " -7600.72363142 -7628.31174087 -7568.93837183 -7556.68729778\n",
      " -7554.54813567 -7661.00483525 -7621.21055454 -7620.12731243\n",
      " -7592.07917705 -7591.52675554 -7603.63466659 -7595.1965108\n",
      " -7544.72850294 -7576.89569184 -7632.85188941 -7576.31926118\n",
      " -7602.33351126 -7607.66577215 -7574.35796777 -7573.56478508\n",
      " -7537.35789538 -7603.56367992 -7654.89979177 -7612.4676285\n",
      " -7646.36163817 -7583.06177847 -7586.12948072 -7556.10612894\n",
      " -7555.85679531 -7648.17491571 -7691.81910568 -7613.13059505\n",
      " -7574.67485829 -7590.2161996  -7675.84179578 -7595.14654474\n",
      " -7588.30854045 -7594.07726995 -7608.62580804 -7621.63660121\n",
      " -7612.84473906 -7569.19252795 -7610.23440532 -7585.28996445\n",
      " -7557.71808689 -7569.92249583 -7648.83517095 -7578.98350801\n",
      " -7626.13536512 -7602.48841713 -7572.37762995 -7549.33236464\n",
      " -7632.3737695  -7617.75625338 -7636.2760821  -7602.85797325\n",
      " -7664.20543182 -7608.27208955 -7629.11007415 -7619.06019473\n",
      " -7591.42544176 -7651.61835567 -7613.1763568  -7565.26952026\n",
      " -7587.84479832 -7610.86559579 -7629.07434788 -7616.51535414\n",
      " -7589.14329018 -7629.60048962 -7609.07403459 -7648.08147596\n",
      " -7559.58849534 -7621.76937005 -7605.03102311 -7566.22240261\n",
      " -7513.93550156 -7596.43160995 -7614.2357031  -7575.87475209\n",
      " -7691.46159658 -7597.77946615 -7665.64574323 -7583.90976708\n",
      " -7599.54085807 -7597.99610342 -7610.60782416 -7573.78142489\n",
      " -7591.85171346 -7628.47194116 -7581.09454479 -7605.15584469\n",
      " -7589.7802929  -7556.63725977 -7581.09144012 -7641.23158415\n",
      " -7596.79566863 -7591.24778371 -7586.97885313 -7576.36191705\n",
      " -7611.26021409 -7623.61443303 -7574.31808954 -7617.89553158\n",
      " -7641.23979557 -7593.85995308 -7618.96229425 -7609.03984462\n",
      " -7588.4016823  -7604.6398971  -7632.49502403 -7622.23833937\n",
      " -7541.80450645 -7594.78910903 -7571.95066318 -7567.19535421]\n"
     ]
    }
   ],
   "source": [
    "print(likelihood_3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1 1 []\n",
      "0 1 [0]\n",
      "1 1 [0, 1]\n",
      "2 1 [1, 2]\n",
      "3 1 [2, 3]\n",
      "4 1 [3, 4]\n",
      "5 1 [4, 5]\n",
      "6 1 [5, 6]\n",
      "7 1 [6, 7]\n",
      "8 1 [7, 8]\n",
      "9 1 [8, 9]\n",
      "10 1 [9, 10]\n",
      "11 1 [10, 11]\n",
      "12 1 [11, 12]\n",
      "13 1 [12, 13]\n",
      "14 1 [13, 14]\n",
      "15 1 [14, 15]\n",
      "16 1 [15, 16]\n",
      "17 1 [16, 17]\n",
      "18 1 [17, 18]\n",
      "19 1 [18, 19]\n",
      "20 1 [19, 20]\n",
      "21 1 [20, 21]\n",
      "22 1 [21, 22]\n",
      "23 1 [22, 23]\n",
      "24 1 [23, 24]\n",
      "25 1 [24, 25]\n",
      "26 1 [25, 26]\n",
      "27 1 [26, 27]\n",
      "28 1 [27, 28]\n",
      "-1 0 [0]\n",
      "0 0 [0, 1, 30]\n",
      "1 0 [0, 1, 2, 30, 31]\n",
      "2 0 [1, 2, 3, 31, 32]\n",
      "3 0 [2, 3, 4, 32, 33]\n",
      "4 0 [3, 4, 5, 33, 34]\n",
      "5 0 [4, 5, 6, 34, 35]\n",
      "6 0 [5, 6, 7, 35, 36]\n",
      "7 0 [6, 7, 8, 36, 37]\n",
      "8 0 [7, 8, 9, 37, 38]\n",
      "9 0 [8, 9, 10, 38, 39]\n",
      "10 0 [9, 10, 11, 39, 40]\n",
      "11 0 [10, 11, 12, 40, 41]\n",
      "12 0 [11, 12, 13, 41, 42]\n",
      "13 0 [12, 13, 14, 42, 43]\n",
      "14 0 [13, 14, 15, 43, 44]\n",
      "15 0 [14, 15, 16, 44, 45]\n",
      "16 0 [15, 16, 17, 45, 46]\n",
      "17 0 [16, 17, 18, 46, 47]\n",
      "18 0 [17, 18, 19, 47, 48]\n",
      "19 0 [18, 19, 20, 48, 49]\n",
      "20 0 [19, 20, 21, 49, 50]\n",
      "21 0 [20, 21, 22, 50, 51]\n",
      "22 0 [21, 22, 23, 51, 52]\n",
      "23 0 [22, 23, 24, 52, 53]\n",
      "24 0 [23, 24, 25, 53, 54]\n",
      "25 0 [24, 25, 26, 54, 55]\n",
      "26 0 [25, 26, 27, 55, 56]\n",
      "27 0 [26, 27, 28, 56, 57]\n",
      "28 0 [27, 28, 29, 57, 58]\n",
      "-1 -1 [0, 30]\n",
      "0 -1 [0, 1, 30, 31, 60]\n",
      "1 -1 [0, 1, 2, 30, 31, 32, 60, 61]\n",
      "2 -1 [1, 2, 3, 31, 32, 33, 61, 62]\n",
      "3 -1 [2, 3, 4, 32, 33, 34, 62, 63]\n",
      "4 -1 [3, 4, 5, 33, 34, 35, 63, 64]\n",
      "5 -1 [4, 5, 6, 34, 35, 36, 64, 65]\n",
      "6 -1 [5, 6, 7, 35, 36, 37, 65, 66]\n",
      "7 -1 [6, 7, 8, 36, 37, 38, 66, 67]\n",
      "8 -1 [7, 8, 9, 37, 38, 39, 67, 68]\n",
      "9 -1 [8, 9, 10, 38, 39, 40, 68, 69]\n",
      "10 -1 [9, 10, 11, 39, 40, 41, 69, 70]\n",
      "11 -1 [10, 11, 12, 40, 41, 42, 70, 71]\n",
      "12 -1 [11, 12, 13, 41, 42, 43, 71, 72]\n",
      "13 -1 [12, 13, 14, 42, 43, 44, 72, 73]\n",
      "14 -1 [13, 14, 15, 43, 44, 45, 73, 74]\n",
      "15 -1 [14, 15, 16, 44, 45, 46, 74, 75]\n",
      "16 -1 [15, 16, 17, 45, 46, 47, 75, 76]\n",
      "17 -1 [16, 17, 18, 46, 47, 48, 76, 77]\n",
      "18 -1 [17, 18, 19, 47, 48, 49, 77, 78]\n",
      "19 -1 [18, 19, 20, 48, 49, 50, 78, 79]\n",
      "20 -1 [19, 20, 21, 49, 50, 51, 79, 80]\n",
      "21 -1 [20, 21, 22, 50, 51, 52, 80, 81]\n",
      "22 -1 [21, 22, 23, 51, 52, 53, 81, 82]\n",
      "23 -1 [22, 23, 24, 52, 53, 54, 82, 83]\n",
      "24 -1 [23, 24, 25, 53, 54, 55, 83, 84]\n",
      "25 -1 [24, 25, 26, 54, 55, 56, 84, 85]\n",
      "26 -1 [25, 26, 27, 55, 56, 57, 85, 86]\n",
      "27 -1 [26, 27, 28, 56, 57, 58, 86, 87]\n",
      "28 -1 [27, 28, 29, 57, 58, 59, 87, 88]\n",
      "-1 -2 [30, 60]\n",
      "0 -2 [30, 31, 60, 61, 90]\n",
      "1 -2 [30, 31, 32, 60, 61, 62, 90, 91]\n",
      "2 -2 [31, 32, 33, 61, 62, 63, 91, 92]\n",
      "3 -2 [32, 33, 34, 62, 63, 64, 92, 93]\n",
      "4 -2 [33, 34, 35, 63, 64, 65, 93, 94]\n",
      "5 -2 [34, 35, 36, 64, 65, 66, 94, 95]\n",
      "6 -2 [35, 36, 37, 65, 66, 67, 95, 96]\n",
      "7 -2 [36, 37, 38, 66, 67, 68, 96, 97]\n",
      "8 -2 [37, 38, 39, 67, 68, 69, 97, 98]\n",
      "9 -2 [38, 39, 40, 68, 69, 70, 98, 99]\n",
      "10 -2 [39, 40, 41, 69, 70, 71, 99, 100]\n",
      "11 -2 [40, 41, 42, 70, 71, 72, 100, 101]\n",
      "12 -2 [41, 42, 43, 71, 72, 73, 101, 102]\n",
      "13 -2 [42, 43, 44, 72, 73, 74, 102, 103]\n",
      "14 -2 [43, 44, 45, 73, 74, 75, 103, 104]\n",
      "15 -2 [44, 45, 46, 74, 75, 76, 104, 105]\n",
      "16 -2 [45, 46, 47, 75, 76, 77, 105, 106]\n",
      "17 -2 [46, 47, 48, 76, 77, 78, 106, 107]\n",
      "18 -2 [47, 48, 49, 77, 78, 79, 107, 108]\n",
      "19 -2 [48, 49, 50, 78, 79, 80, 108, 109]\n",
      "20 -2 [49, 50, 51, 79, 80, 81, 109, 110]\n",
      "21 -2 [50, 51, 52, 80, 81, 82, 110, 111]\n",
      "22 -2 [51, 52, 53, 81, 82, 83, 111, 112]\n",
      "23 -2 [52, 53, 54, 82, 83, 84, 112, 113]\n",
      "24 -2 [53, 54, 55, 83, 84, 85, 113, 114]\n",
      "25 -2 [54, 55, 56, 84, 85, 86, 114, 115]\n",
      "26 -2 [55, 56, 57, 85, 86, 87, 115, 116]\n",
      "27 -2 [56, 57, 58, 86, 87, 88, 116, 117]\n",
      "28 -2 [57, 58, 59, 87, 88, 89, 117, 118]\n",
      "-1 -3 [60, 90]\n",
      "0 -3 [60, 61, 90, 91, 120]\n",
      "1 -3 [60, 61, 62, 90, 91, 92, 120, 121]\n",
      "2 -3 [61, 62, 63, 91, 92, 93, 121, 122]\n",
      "3 -3 [62, 63, 64, 92, 93, 94, 122, 123]\n",
      "4 -3 [63, 64, 65, 93, 94, 95, 123, 124]\n",
      "5 -3 [64, 65, 66, 94, 95, 96, 124, 125]\n",
      "6 -3 [65, 66, 67, 95, 96, 97, 125, 126]\n",
      "7 -3 [66, 67, 68, 96, 97, 98, 126, 127]\n",
      "8 -3 [67, 68, 69, 97, 98, 99, 127, 128]\n",
      "9 -3 [68, 69, 70, 98, 99, 100, 128, 129]\n",
      "10 -3 [69, 70, 71, 99, 100, 101, 129, 130]\n",
      "11 -3 [70, 71, 72, 100, 101, 102, 130, 131]\n",
      "12 -3 [71, 72, 73, 101, 102, 103, 131, 132]\n",
      "13 -3 [72, 73, 74, 102, 103, 104, 132, 133]\n",
      "14 -3 [73, 74, 75, 103, 104, 105, 133, 134]\n",
      "15 -3 [74, 75, 76, 104, 105, 106, 134, 135]\n",
      "16 -3 [75, 76, 77, 105, 106, 107, 135, 136]\n",
      "17 -3 [76, 77, 78, 106, 107, 108, 136, 137]\n",
      "18 -3 [77, 78, 79, 107, 108, 109, 137, 138]\n",
      "19 -3 [78, 79, 80, 108, 109, 110, 138, 139]\n",
      "20 -3 [79, 80, 81, 109, 110, 111, 139, 140]\n",
      "21 -3 [80, 81, 82, 110, 111, 112, 140, 141]\n",
      "22 -3 [81, 82, 83, 111, 112, 113, 141, 142]\n",
      "23 -3 [82, 83, 84, 112, 113, 114, 142, 143]\n",
      "24 -3 [83, 84, 85, 113, 114, 115, 143, 144]\n",
      "25 -3 [84, 85, 86, 114, 115, 116, 144, 145]\n",
      "26 -3 [85, 86, 87, 115, 116, 117, 145, 146]\n",
      "27 -3 [86, 87, 88, 116, 117, 118, 146, 147]\n",
      "28 -3 [87, 88, 89, 117, 118, 119, 147, 148]\n",
      "-1 -4 [90, 120]\n",
      "0 -4 [90, 91, 120, 121, 150]\n",
      "1 -4 [90, 91, 92, 120, 121, 122, 150, 151]\n",
      "2 -4 [91, 92, 93, 121, 122, 123, 151, 152]\n",
      "3 -4 [92, 93, 94, 122, 123, 124, 152, 153]\n",
      "4 -4 [93, 94, 95, 123, 124, 125, 153, 154]\n",
      "5 -4 [94, 95, 96, 124, 125, 126, 154, 155]\n",
      "6 -4 [95, 96, 97, 125, 126, 127, 155, 156]\n",
      "7 -4 [96, 97, 98, 126, 127, 128, 156, 157]\n",
      "8 -4 [97, 98, 99, 127, 128, 129, 157, 158]\n",
      "9 -4 [98, 99, 100, 128, 129, 130, 158, 159]\n",
      "10 -4 [99, 100, 101, 129, 130, 131, 159, 160]\n",
      "11 -4 [100, 101, 102, 130, 131, 132, 160, 161]\n",
      "12 -4 [101, 102, 103, 131, 132, 133, 161, 162]\n",
      "13 -4 [102, 103, 104, 132, 133, 134, 162, 163]\n",
      "14 -4 [103, 104, 105, 133, 134, 135, 163, 164]\n",
      "15 -4 [104, 105, 106, 134, 135, 136, 164, 165]\n",
      "16 -4 [105, 106, 107, 135, 136, 137, 165, 166]\n",
      "17 -4 [106, 107, 108, 136, 137, 138, 166, 167]\n",
      "18 -4 [107, 108, 109, 137, 138, 139, 167, 168]\n",
      "19 -4 [108, 109, 110, 138, 139, 140, 168, 169]\n",
      "20 -4 [109, 110, 111, 139, 140, 141, 169, 170]\n",
      "21 -4 [110, 111, 112, 140, 141, 142, 170, 171]\n",
      "22 -4 [111, 112, 113, 141, 142, 143, 171, 172]\n",
      "23 -4 [112, 113, 114, 142, 143, 144, 172, 173]\n",
      "24 -4 [113, 114, 115, 143, 144, 145, 173, 174]\n",
      "25 -4 [114, 115, 116, 144, 145, 146, 174, 175]\n",
      "26 -4 [115, 116, 117, 145, 146, 147, 175, 176]\n",
      "27 -4 [116, 117, 118, 146, 147, 148, 176, 177]\n",
      "28 -4 [117, 118, 119, 147, 148, 149, 177, 178]\n",
      "-1 -5 [120, 150]\n",
      "0 -5 [120, 121, 150, 151, 180]\n",
      "1 -5 [120, 121, 122, 150, 151, 152, 180, 181]\n",
      "2 -5 [121, 122, 123, 151, 152, 153, 181, 182]\n",
      "3 -5 [122, 123, 124, 152, 153, 154, 182, 183]\n",
      "4 -5 [123, 124, 125, 153, 154, 155, 183, 184]\n",
      "5 -5 [124, 125, 126, 154, 155, 156, 184, 185]\n",
      "6 -5 [125, 126, 127, 155, 156, 157, 185, 186]\n",
      "7 -5 [126, 127, 128, 156, 157, 158, 186, 187]\n",
      "8 -5 [127, 128, 129, 157, 158, 159, 187, 188]\n",
      "9 -5 [128, 129, 130, 158, 159, 160, 188, 189]\n",
      "10 -5 [129, 130, 131, 159, 160, 161, 189, 190]\n",
      "11 -5 [130, 131, 132, 160, 161, 162, 190, 191]\n",
      "12 -5 [131, 132, 133, 161, 162, 163, 191, 192]\n",
      "13 -5 [132, 133, 134, 162, 163, 164, 192, 193]\n",
      "14 -5 [133, 134, 135, 163, 164, 165, 193, 194]\n",
      "15 -5 [134, 135, 136, 164, 165, 166, 194, 195]\n",
      "16 -5 [135, 136, 137, 165, 166, 167, 195, 196]\n",
      "17 -5 [136, 137, 138, 166, 167, 168, 196, 197]\n",
      "18 -5 [137, 138, 139, 167, 168, 169, 197, 198]\n",
      "19 -5 [138, 139, 140, 168, 169, 170, 198, 199]\n",
      "20 -5 [139, 140, 141, 169, 170, 171, 199, 200]\n",
      "21 -5 [140, 141, 142, 170, 171, 172, 200, 201]\n",
      "22 -5 [141, 142, 143, 171, 172, 173, 201, 202]\n",
      "23 -5 [142, 143, 144, 172, 173, 174, 202, 203]\n",
      "24 -5 [143, 144, 145, 173, 174, 175, 203, 204]\n",
      "25 -5 [144, 145, 146, 174, 175, 176, 204, 205]\n",
      "26 -5 [145, 146, 147, 175, 176, 177, 205, 206]\n",
      "27 -5 [146, 147, 148, 176, 177, 178, 206, 207]\n",
      "28 -5 [147, 148, 149, 177, 178, 179, 207, 208]\n",
      "-1 -6 [150, 180]\n",
      "0 -6 [150, 151, 180, 181, 210]\n",
      "1 -6 [150, 151, 152, 180, 181, 182, 210, 211]\n",
      "2 -6 [151, 152, 153, 181, 182, 183, 211, 212]\n",
      "3 -6 [152, 153, 154, 182, 183, 184, 212, 213]\n",
      "4 -6 [153, 154, 155, 183, 184, 185, 213, 214]\n",
      "5 -6 [154, 155, 156, 184, 185, 186, 214, 215]\n",
      "6 -6 [155, 156, 157, 185, 186, 187, 215, 216]\n",
      "7 -6 [156, 157, 158, 186, 187, 188, 216, 217]\n",
      "8 -6 [157, 158, 159, 187, 188, 189, 217, 218]\n",
      "9 -6 [158, 159, 160, 188, 189, 190, 218, 219]\n",
      "10 -6 [159, 160, 161, 189, 190, 191, 219, 220]\n",
      "11 -6 [160, 161, 162, 190, 191, 192, 220, 221]\n",
      "12 -6 [161, 162, 163, 191, 192, 193, 221, 222]\n",
      "13 -6 [162, 163, 164, 192, 193, 194, 222, 223]\n",
      "14 -6 [163, 164, 165, 193, 194, 195, 223, 224]\n",
      "15 -6 [164, 165, 166, 194, 195, 196, 224, 225]\n",
      "16 -6 [165, 166, 167, 195, 196, 197, 225, 226]\n",
      "17 -6 [166, 167, 168, 196, 197, 198, 226, 227]\n",
      "18 -6 [167, 168, 169, 197, 198, 199, 227, 228]\n",
      "19 -6 [168, 169, 170, 198, 199, 200, 228, 229]\n",
      "20 -6 [169, 170, 171, 199, 200, 201, 229, 230]\n",
      "21 -6 [170, 171, 172, 200, 201, 202, 230, 231]\n",
      "22 -6 [171, 172, 173, 201, 202, 203, 231, 232]\n",
      "23 -6 [172, 173, 174, 202, 203, 204, 232, 233]\n",
      "24 -6 [173, 174, 175, 203, 204, 205, 233, 234]\n",
      "25 -6 [174, 175, 176, 204, 205, 206, 234, 235]\n",
      "26 -6 [175, 176, 177, 205, 206, 207, 235, 236]\n",
      "27 -6 [176, 177, 178, 206, 207, 208, 236, 237]\n",
      "28 -6 [177, 178, 179, 207, 208, 209, 237, 238]\n",
      "-1 -7 [180, 210]\n",
      "0 -7 [180, 181, 210, 211, 240]\n",
      "1 -7 [180, 181, 182, 210, 211, 212, 240, 241]\n",
      "2 -7 [181, 182, 183, 211, 212, 213, 241, 242]\n",
      "3 -7 [182, 183, 184, 212, 213, 214, 242, 243]\n",
      "4 -7 [183, 184, 185, 213, 214, 215, 243, 244]\n",
      "5 -7 [184, 185, 186, 214, 215, 216, 244, 245]\n",
      "6 -7 [185, 186, 187, 215, 216, 217, 245, 246]\n",
      "7 -7 [186, 187, 188, 216, 217, 218, 246, 247]\n",
      "8 -7 [187, 188, 189, 217, 218, 219, 247, 248]\n",
      "9 -7 [188, 189, 190, 218, 219, 220, 248, 249]\n",
      "10 -7 [189, 190, 191, 219, 220, 221, 249, 250]\n",
      "11 -7 [190, 191, 192, 220, 221, 222, 250, 251]\n",
      "12 -7 [191, 192, 193, 221, 222, 223, 251, 252]\n",
      "13 -7 [192, 193, 194, 222, 223, 224, 252, 253]\n",
      "14 -7 [193, 194, 195, 223, 224, 225, 253, 254]\n",
      "15 -7 [194, 195, 196, 224, 225, 226, 254, 255]\n",
      "16 -7 [195, 196, 197, 225, 226, 227, 255, 256]\n",
      "17 -7 [196, 197, 198, 226, 227, 228, 256, 257]\n",
      "18 -7 [197, 198, 199, 227, 228, 229, 257, 258]\n",
      "19 -7 [198, 199, 200, 228, 229, 230, 258, 259]\n",
      "20 -7 [199, 200, 201, 229, 230, 231, 259, 260]\n",
      "21 -7 [200, 201, 202, 230, 231, 232, 260, 261]\n",
      "22 -7 [201, 202, 203, 231, 232, 233, 261, 262]\n",
      "23 -7 [202, 203, 204, 232, 233, 234, 262, 263]\n",
      "24 -7 [203, 204, 205, 233, 234, 235, 263, 264]\n",
      "25 -7 [204, 205, 206, 234, 235, 236, 264, 265]\n",
      "26 -7 [205, 206, 207, 235, 236, 237, 265, 266]\n",
      "27 -7 [206, 207, 208, 236, 237, 238, 266, 267]\n",
      "28 -7 [207, 208, 209, 237, 238, 239, 267, 268]\n",
      "-1 -8 [210, 240]\n",
      "0 -8 [210, 211, 240, 241, 270]\n",
      "1 -8 [210, 211, 212, 240, 241, 242, 270, 271]\n",
      "2 -8 [211, 212, 213, 241, 242, 243, 271, 272]\n",
      "3 -8 [212, 213, 214, 242, 243, 244, 272, 273]\n",
      "4 -8 [213, 214, 215, 243, 244, 245, 273, 274]\n",
      "5 -8 [214, 215, 216, 244, 245, 246, 274, 275]\n",
      "6 -8 [215, 216, 217, 245, 246, 247, 275, 276]\n",
      "7 -8 [216, 217, 218, 246, 247, 248, 276, 277]\n",
      "8 -8 [217, 218, 219, 247, 248, 249, 277, 278]\n",
      "9 -8 [218, 219, 220, 248, 249, 250, 278, 279]\n",
      "10 -8 [219, 220, 221, 249, 250, 251, 279, 280]\n",
      "11 -8 [220, 221, 222, 250, 251, 252, 280, 281]\n",
      "12 -8 [221, 222, 223, 251, 252, 253, 281, 282]\n",
      "13 -8 [222, 223, 224, 252, 253, 254, 282, 283]\n",
      "14 -8 [223, 224, 225, 253, 254, 255, 283, 284]\n",
      "15 -8 [224, 225, 226, 254, 255, 256, 284, 285]\n",
      "16 -8 [225, 226, 227, 255, 256, 257, 285, 286]\n",
      "17 -8 [226, 227, 228, 256, 257, 258, 286, 287]\n",
      "18 -8 [227, 228, 229, 257, 258, 259, 287, 288]\n",
      "19 -8 [228, 229, 230, 258, 259, 260, 288, 289]\n",
      "20 -8 [229, 230, 231, 259, 260, 261, 289, 290]\n",
      "21 -8 [230, 231, 232, 260, 261, 262, 290, 291]\n",
      "22 -8 [231, 232, 233, 261, 262, 263, 291, 292]\n",
      "23 -8 [232, 233, 234, 262, 263, 264, 292, 293]\n",
      "24 -8 [233, 234, 235, 263, 264, 265, 293, 294]\n",
      "25 -8 [234, 235, 236, 264, 265, 266, 294, 295]\n",
      "26 -8 [235, 236, 237, 265, 266, 267, 295, 296]\n",
      "27 -8 [236, 237, 238, 266, 267, 268, 296, 297]\n",
      "28 -8 [237, 238, 239, 267, 268, 269, 297, 298]\n",
      "-1 -9 [240, 270]\n",
      "0 -9 [240, 241, 270, 271, 300]\n",
      "1 -9 [240, 241, 242, 270, 271, 272, 300, 301]\n",
      "2 -9 [241, 242, 243, 271, 272, 273, 301, 302]\n",
      "3 -9 [242, 243, 244, 272, 273, 274, 302, 303]\n",
      "4 -9 [243, 244, 245, 273, 274, 275, 303, 304]\n",
      "5 -9 [244, 245, 246, 274, 275, 276, 304, 305]\n",
      "6 -9 [245, 246, 247, 275, 276, 277, 305, 306]\n",
      "7 -9 [246, 247, 248, 276, 277, 278, 306, 307]\n",
      "8 -9 [247, 248, 249, 277, 278, 279, 307, 308]\n",
      "9 -9 [248, 249, 250, 278, 279, 280, 308, 309]\n",
      "10 -9 [249, 250, 251, 279, 280, 281, 309, 310]\n",
      "11 -9 [250, 251, 252, 280, 281, 282, 310, 311]\n",
      "12 -9 [251, 252, 253, 281, 282, 283, 311, 312]\n",
      "13 -9 [252, 253, 254, 282, 283, 284, 312, 313]\n",
      "14 -9 [253, 254, 255, 283, 284, 285, 313, 314]\n",
      "15 -9 [254, 255, 256, 284, 285, 286, 314, 315]\n",
      "16 -9 [255, 256, 257, 285, 286, 287, 315, 316]\n",
      "17 -9 [256, 257, 258, 286, 287, 288, 316, 317]\n",
      "18 -9 [257, 258, 259, 287, 288, 289, 317, 318]\n",
      "19 -9 [258, 259, 260, 288, 289, 290, 318, 319]\n",
      "20 -9 [259, 260, 261, 289, 290, 291, 319, 320]\n",
      "21 -9 [260, 261, 262, 290, 291, 292, 320, 321]\n",
      "22 -9 [261, 262, 263, 291, 292, 293, 321, 322]\n",
      "23 -9 [262, 263, 264, 292, 293, 294, 322, 323]\n",
      "24 -9 [263, 264, 265, 293, 294, 295, 323, 324]\n",
      "25 -9 [264, 265, 266, 294, 295, 296, 324, 325]\n",
      "26 -9 [265, 266, 267, 295, 296, 297, 325, 326]\n",
      "27 -9 [266, 267, 268, 296, 297, 298, 326, 327]\n",
      "28 -9 [267, 268, 269, 297, 298, 299, 327, 328]\n",
      "-1 -10 [270, 300]\n",
      "0 -10 [270, 271, 300, 301, 330]\n",
      "1 -10 [270, 271, 272, 300, 301, 302, 330, 331]\n",
      "2 -10 [271, 272, 273, 301, 302, 303, 331, 332]\n",
      "3 -10 [272, 273, 274, 302, 303, 304, 332, 333]\n",
      "4 -10 [273, 274, 275, 303, 304, 305, 333, 334]\n",
      "5 -10 [274, 275, 276, 304, 305, 306, 334, 335]\n",
      "6 -10 [275, 276, 277, 305, 306, 307, 335, 336]\n",
      "7 -10 [276, 277, 278, 306, 307, 308, 336, 337]\n",
      "8 -10 [277, 278, 279, 307, 308, 309, 337, 338]\n",
      "9 -10 [278, 279, 280, 308, 309, 310, 338, 339]\n",
      "10 -10 [279, 280, 281, 309, 310, 311, 339, 340]\n",
      "11 -10 [280, 281, 282, 310, 311, 312, 340, 341]\n",
      "12 -10 [281, 282, 283, 311, 312, 313, 341, 342]\n",
      "13 -10 [282, 283, 284, 312, 313, 314, 342, 343]\n",
      "14 -10 [283, 284, 285, 313, 314, 315, 343, 344]\n",
      "15 -10 [284, 285, 286, 314, 315, 316, 344, 345]\n",
      "16 -10 [285, 286, 287, 315, 316, 317, 345, 346]\n",
      "17 -10 [286, 287, 288, 316, 317, 318, 346, 347]\n",
      "18 -10 [287, 288, 289, 317, 318, 319, 347, 348]\n",
      "19 -10 [288, 289, 290, 318, 319, 320, 348, 349]\n",
      "20 -10 [289, 290, 291, 319, 320, 321, 349, 350]\n",
      "21 -10 [290, 291, 292, 320, 321, 322, 350, 351]\n",
      "22 -10 [291, 292, 293, 321, 322, 323, 351, 352]\n",
      "23 -10 [292, 293, 294, 322, 323, 324, 352, 353]\n",
      "24 -10 [293, 294, 295, 323, 324, 325, 353, 354]\n",
      "25 -10 [294, 295, 296, 324, 325, 326, 354, 355]\n",
      "26 -10 [295, 296, 297, 325, 326, 327, 355, 356]\n",
      "27 -10 [296, 297, 298, 326, 327, 328, 356, 357]\n",
      "28 -10 [297, 298, 299, 327, 328, 329, 357, 358]\n",
      "-1 -11 [300, 330]\n",
      "0 -11 [300, 301, 330, 331, 360]\n",
      "1 -11 [300, 301, 302, 330, 331, 332, 360, 361]\n",
      "2 -11 [301, 302, 303, 331, 332, 333, 361, 362]\n",
      "3 -11 [302, 303, 304, 332, 333, 334, 362, 363]\n",
      "4 -11 [303, 304, 305, 333, 334, 335, 363, 364]\n",
      "5 -11 [304, 305, 306, 334, 335, 336, 364, 365]\n",
      "6 -11 [305, 306, 307, 335, 336, 337, 365, 366]\n",
      "7 -11 [306, 307, 308, 336, 337, 338, 366, 367]\n",
      "8 -11 [307, 308, 309, 337, 338, 339, 367, 368]\n",
      "9 -11 [308, 309, 310, 338, 339, 340, 368, 369]\n",
      "10 -11 [309, 310, 311, 339, 340, 341, 369, 370]\n",
      "11 -11 [310, 311, 312, 340, 341, 342, 370, 371]\n",
      "12 -11 [311, 312, 313, 341, 342, 343, 371, 372]\n",
      "13 -11 [312, 313, 314, 342, 343, 344, 372, 373]\n",
      "14 -11 [313, 314, 315, 343, 344, 345, 373, 374]\n",
      "15 -11 [314, 315, 316, 344, 345, 346, 374, 375]\n",
      "16 -11 [315, 316, 317, 345, 346, 347, 375, 376]\n",
      "17 -11 [316, 317, 318, 346, 347, 348, 376, 377]\n",
      "18 -11 [317, 318, 319, 347, 348, 349, 377, 378]\n",
      "19 -11 [318, 319, 320, 348, 349, 350, 378, 379]\n",
      "20 -11 [319, 320, 321, 349, 350, 351, 379, 380]\n",
      "21 -11 [320, 321, 322, 350, 351, 352, 380, 381]\n",
      "22 -11 [321, 322, 323, 351, 352, 353, 381, 382]\n",
      "23 -11 [322, 323, 324, 352, 353, 354, 382, 383]\n",
      "24 -11 [323, 324, 325, 353, 354, 355, 383, 384]\n",
      "25 -11 [324, 325, 326, 354, 355, 356, 384, 385]\n",
      "26 -11 [325, 326, 327, 355, 356, 357, 385, 386]\n",
      "27 -11 [326, 327, 328, 356, 357, 358, 386, 387]\n",
      "28 -11 [327, 328, 329, 357, 358, 359, 387, 388]\n",
      "-1 -12 [330, 360]\n",
      "0 -12 [330, 331, 360, 361, 390]\n",
      "1 -12 [330, 331, 332, 360, 361, 362, 390, 391]\n",
      "2 -12 [331, 332, 333, 361, 362, 363, 391, 392]\n",
      "3 -12 [332, 333, 334, 362, 363, 364, 392, 393]\n",
      "4 -12 [333, 334, 335, 363, 364, 365, 393, 394]\n",
      "5 -12 [334, 335, 336, 364, 365, 366, 394, 395]\n",
      "6 -12 [335, 336, 337, 365, 366, 367, 395, 396]\n",
      "7 -12 [336, 337, 338, 366, 367, 368, 396, 397]\n",
      "8 -12 [337, 338, 339, 367, 368, 369, 397, 398]\n",
      "9 -12 [338, 339, 340, 368, 369, 370, 398, 399]\n",
      "10 -12 [339, 340, 341, 369, 370, 371, 399, 400]\n",
      "11 -12 [340, 341, 342, 370, 371, 372, 400, 401]\n",
      "12 -12 [341, 342, 343, 371, 372, 373, 401, 402]\n",
      "13 -12 [342, 343, 344, 372, 373, 374, 402, 403]\n",
      "14 -12 [343, 344, 345, 373, 374, 375, 403, 404]\n",
      "15 -12 [344, 345, 346, 374, 375, 376, 404, 405]\n",
      "16 -12 [345, 346, 347, 375, 376, 377, 405, 406]\n",
      "17 -12 [346, 347, 348, 376, 377, 378, 406, 407]\n",
      "18 -12 [347, 348, 349, 377, 378, 379, 407, 408]\n",
      "19 -12 [348, 349, 350, 378, 379, 380, 408, 409]\n",
      "20 -12 [349, 350, 351, 379, 380, 381, 409, 410]\n",
      "21 -12 [350, 351, 352, 380, 381, 382, 410, 411]\n",
      "22 -12 [351, 352, 353, 381, 382, 383, 411, 412]\n",
      "23 -12 [352, 353, 354, 382, 383, 384, 412, 413]\n",
      "24 -12 [353, 354, 355, 383, 384, 385, 413, 414]\n",
      "25 -12 [354, 355, 356, 384, 385, 386, 414, 415]\n",
      "26 -12 [355, 356, 357, 385, 386, 387, 415, 416]\n",
      "27 -12 [356, 357, 358, 386, 387, 388, 416, 417]\n",
      "28 -12 [357, 358, 359, 387, 388, 389, 417, 418]\n",
      "-1 -13 [360, 390]\n",
      "0 -13 [360, 361, 390, 391, 420]\n",
      "1 -13 [360, 361, 362, 390, 391, 392, 420, 421]\n",
      "2 -13 [361, 362, 363, 391, 392, 393, 421, 422]\n",
      "3 -13 [362, 363, 364, 392, 393, 394, 422, 423]\n",
      "4 -13 [363, 364, 365, 393, 394, 395, 423, 424]\n",
      "5 -13 [364, 365, 366, 394, 395, 396, 424, 425]\n",
      "6 -13 [365, 366, 367, 395, 396, 397, 425, 426]\n",
      "7 -13 [366, 367, 368, 396, 397, 398, 426, 427]\n",
      "8 -13 [367, 368, 369, 397, 398, 399, 427, 428]\n",
      "9 -13 [368, 369, 370, 398, 399, 400, 428, 429]\n",
      "10 -13 [369, 370, 371, 399, 400, 401, 429, 430]\n",
      "11 -13 [370, 371, 372, 400, 401, 402, 430, 431]\n",
      "12 -13 [371, 372, 373, 401, 402, 403, 431, 432]\n",
      "13 -13 [372, 373, 374, 402, 403, 404, 432, 433]\n",
      "14 -13 [373, 374, 375, 403, 404, 405, 433, 434]\n",
      "15 -13 [374, 375, 376, 404, 405, 406, 434, 435]\n",
      "16 -13 [375, 376, 377, 405, 406, 407, 435, 436]\n",
      "17 -13 [376, 377, 378, 406, 407, 408, 436, 437]\n",
      "18 -13 [377, 378, 379, 407, 408, 409, 437, 438]\n",
      "19 -13 [378, 379, 380, 408, 409, 410, 438, 439]\n",
      "20 -13 [379, 380, 381, 409, 410, 411, 439, 440]\n",
      "21 -13 [380, 381, 382, 410, 411, 412, 440, 441]\n",
      "22 -13 [381, 382, 383, 411, 412, 413, 441, 442]\n",
      "23 -13 [382, 383, 384, 412, 413, 414, 442, 443]\n",
      "24 -13 [383, 384, 385, 413, 414, 415, 443, 444]\n",
      "25 -13 [384, 385, 386, 414, 415, 416, 444, 445]\n",
      "26 -13 [385, 386, 387, 415, 416, 417, 445, 446]\n",
      "27 -13 [386, 387, 388, 416, 417, 418, 446, 447]\n",
      "28 -13 [387, 388, 389, 417, 418, 419, 447, 448]\n",
      "-1 -14 [390, 420]\n",
      "0 -14 [390, 391, 420, 421, 450]\n",
      "1 -14 [390, 391, 392, 420, 421, 422, 450, 451]\n",
      "2 -14 [391, 392, 393, 421, 422, 423, 451, 452]\n",
      "3 -14 [392, 393, 394, 422, 423, 424, 452, 453]\n",
      "4 -14 [393, 394, 395, 423, 424, 425, 453, 454]\n",
      "5 -14 [394, 395, 396, 424, 425, 426, 454, 455]\n",
      "6 -14 [395, 396, 397, 425, 426, 427, 455, 456]\n",
      "7 -14 [396, 397, 398, 426, 427, 428, 456, 457]\n",
      "8 -14 [397, 398, 399, 427, 428, 429, 457, 458]\n",
      "9 -14 [398, 399, 400, 428, 429, 430, 458, 459]\n",
      "10 -14 [399, 400, 401, 429, 430, 431, 459, 460]\n",
      "11 -14 [400, 401, 402, 430, 431, 432, 460, 461]\n",
      "12 -14 [401, 402, 403, 431, 432, 433, 461, 462]\n",
      "13 -14 [402, 403, 404, 432, 433, 434, 462, 463]\n",
      "14 -14 [403, 404, 405, 433, 434, 435, 463, 464]\n",
      "15 -14 [404, 405, 406, 434, 435, 436, 464, 465]\n",
      "16 -14 [405, 406, 407, 435, 436, 437, 465, 466]\n",
      "17 -14 [406, 407, 408, 436, 437, 438, 466, 467]\n",
      "18 -14 [407, 408, 409, 437, 438, 439, 467, 468]\n",
      "19 -14 [408, 409, 410, 438, 439, 440, 468, 469]\n",
      "20 -14 [409, 410, 411, 439, 440, 441, 469, 470]\n",
      "21 -14 [410, 411, 412, 440, 441, 442, 470, 471]\n",
      "22 -14 [411, 412, 413, 441, 442, 443, 471, 472]\n",
      "23 -14 [412, 413, 414, 442, 443, 444, 472, 473]\n",
      "24 -14 [413, 414, 415, 443, 444, 445, 473, 474]\n",
      "25 -14 [414, 415, 416, 444, 445, 446, 474, 475]\n",
      "26 -14 [415, 416, 417, 445, 446, 447, 475, 476]\n",
      "27 -14 [416, 417, 418, 446, 447, 448, 476, 477]\n",
      "28 -14 [417, 418, 419, 447, 448, 449, 477, 478]\n",
      "-1 -15 [420, 450]\n",
      "0 -15 [420, 421, 450, 451, 480]\n",
      "1 -15 [420, 421, 422, 450, 451, 452, 480, 481]\n",
      "2 -15 [421, 422, 423, 451, 452, 453, 481, 482]\n",
      "3 -15 [422, 423, 424, 452, 453, 454, 482, 483]\n",
      "4 -15 [423, 424, 425, 453, 454, 455, 483, 484]\n",
      "5 -15 [424, 425, 426, 454, 455, 456, 484, 485]\n",
      "6 -15 [425, 426, 427, 455, 456, 457, 485, 486]\n",
      "7 -15 [426, 427, 428, 456, 457, 458, 486, 487]\n",
      "8 -15 [427, 428, 429, 457, 458, 459, 487, 488]\n",
      "9 -15 [428, 429, 430, 458, 459, 460, 488, 489]\n",
      "10 -15 [429, 430, 431, 459, 460, 461, 489, 490]\n",
      "11 -15 [430, 431, 432, 460, 461, 462, 490, 491]\n",
      "12 -15 [431, 432, 433, 461, 462, 463, 491, 492]\n",
      "13 -15 [432, 433, 434, 462, 463, 464, 492, 493]\n",
      "14 -15 [433, 434, 435, 463, 464, 465, 493, 494]\n",
      "15 -15 [434, 435, 436, 464, 465, 466, 494, 495]\n",
      "16 -15 [435, 436, 437, 465, 466, 467, 495, 496]\n",
      "17 -15 [436, 437, 438, 466, 467, 468, 496, 497]\n",
      "18 -15 [437, 438, 439, 467, 468, 469, 497, 498]\n",
      "19 -15 [438, 439, 440, 468, 469, 470, 498, 499]\n",
      "20 -15 [439, 440, 441, 469, 470, 471, 499, 500]\n",
      "21 -15 [440, 441, 442, 470, 471, 472, 500, 501]\n",
      "22 -15 [441, 442, 443, 471, 472, 473, 501, 502]\n",
      "23 -15 [442, 443, 444, 472, 473, 474, 502, 503]\n",
      "24 -15 [443, 444, 445, 473, 474, 475, 503, 504]\n",
      "25 -15 [444, 445, 446, 474, 475, 476, 504, 505]\n",
      "26 -15 [445, 446, 447, 475, 476, 477, 505, 506]\n",
      "27 -15 [446, 447, 448, 476, 477, 478, 506, 507]\n",
      "28 -15 [447, 448, 449, 477, 478, 479, 507, 508]\n",
      "-1 -16 [450, 480]\n",
      "0 -16 [450, 451, 480, 481, 510]\n",
      "1 -16 [450, 451, 452, 480, 481, 482, 510, 511]\n",
      "2 -16 [451, 452, 453, 481, 482, 483, 511, 512]\n",
      "3 -16 [452, 453, 454, 482, 483, 484, 512, 513]\n",
      "4 -16 [453, 454, 455, 483, 484, 485, 513, 514]\n",
      "5 -16 [454, 455, 456, 484, 485, 486, 514, 515]\n",
      "6 -16 [455, 456, 457, 485, 486, 487, 515, 516]\n",
      "7 -16 [456, 457, 458, 486, 487, 488, 516, 517]\n",
      "8 -16 [457, 458, 459, 487, 488, 489, 517, 518]\n",
      "9 -16 [458, 459, 460, 488, 489, 490, 518, 519]\n",
      "10 -16 [459, 460, 461, 489, 490, 491, 519, 520]\n",
      "11 -16 [460, 461, 462, 490, 491, 492, 520, 521]\n",
      "12 -16 [461, 462, 463, 491, 492, 493, 521, 522]\n",
      "13 -16 [462, 463, 464, 492, 493, 494, 522, 523]\n",
      "14 -16 [463, 464, 465, 493, 494, 495, 523, 524]\n",
      "15 -16 [464, 465, 466, 494, 495, 496, 524, 525]\n",
      "16 -16 [465, 466, 467, 495, 496, 497, 525, 526]\n",
      "17 -16 [466, 467, 468, 496, 497, 498, 526, 527]\n",
      "18 -16 [467, 468, 469, 497, 498, 499, 527, 528]\n",
      "19 -16 [468, 469, 470, 498, 499, 500, 528, 529]\n",
      "20 -16 [469, 470, 471, 499, 500, 501, 529, 530]\n",
      "21 -16 [470, 471, 472, 500, 501, 502, 530, 531]\n",
      "22 -16 [471, 472, 473, 501, 502, 503, 531, 532]\n",
      "23 -16 [472, 473, 474, 502, 503, 504, 532, 533]\n",
      "24 -16 [473, 474, 475, 503, 504, 505, 533, 534]\n",
      "25 -16 [474, 475, 476, 504, 505, 506, 534, 535]\n",
      "26 -16 [475, 476, 477, 505, 506, 507, 535, 536]\n",
      "27 -16 [476, 477, 478, 506, 507, 508, 536, 537]\n",
      "28 -16 [477, 478, 479, 507, 508, 509, 537, 538]\n",
      "-1 -17 [480, 510]\n",
      "0 -17 [480, 481, 510, 511, 540]\n",
      "1 -17 [480, 481, 482, 510, 511, 512, 540, 541]\n",
      "2 -17 [481, 482, 483, 511, 512, 513, 541, 542]\n",
      "3 -17 [482, 483, 484, 512, 513, 514, 542, 543]\n",
      "4 -17 [483, 484, 485, 513, 514, 515, 543, 544]\n",
      "5 -17 [484, 485, 486, 514, 515, 516, 544, 545]\n",
      "6 -17 [485, 486, 487, 515, 516, 517, 545, 546]\n",
      "7 -17 [486, 487, 488, 516, 517, 518, 546, 547]\n",
      "8 -17 [487, 488, 489, 517, 518, 519, 547, 548]\n",
      "9 -17 [488, 489, 490, 518, 519, 520, 548, 549]\n",
      "10 -17 [489, 490, 491, 519, 520, 521, 549, 550]\n",
      "11 -17 [490, 491, 492, 520, 521, 522, 550, 551]\n",
      "12 -17 [491, 492, 493, 521, 522, 523, 551, 552]\n",
      "13 -17 [492, 493, 494, 522, 523, 524, 552, 553]\n",
      "14 -17 [493, 494, 495, 523, 524, 525, 553, 554]\n",
      "15 -17 [494, 495, 496, 524, 525, 526, 554, 555]\n",
      "16 -17 [495, 496, 497, 525, 526, 527, 555, 556]\n",
      "17 -17 [496, 497, 498, 526, 527, 528, 556, 557]\n",
      "18 -17 [497, 498, 499, 527, 528, 529, 557, 558]\n",
      "19 -17 [498, 499, 500, 528, 529, 530, 558, 559]\n",
      "20 -17 [499, 500, 501, 529, 530, 531, 559, 560]\n",
      "21 -17 [500, 501, 502, 530, 531, 532, 560, 561]\n",
      "22 -17 [501, 502, 503, 531, 532, 533, 561, 562]\n",
      "23 -17 [502, 503, 504, 532, 533, 534, 562, 563]\n",
      "24 -17 [503, 504, 505, 533, 534, 535, 563, 564]\n",
      "25 -17 [504, 505, 506, 534, 535, 536, 564, 565]\n",
      "26 -17 [505, 506, 507, 535, 536, 537, 565, 566]\n",
      "27 -17 [506, 507, 508, 536, 537, 538, 566, 567]\n",
      "28 -17 [507, 508, 509, 537, 538, 539, 567, 568]\n",
      "-1 -18 [510, 540]\n",
      "0 -18 [510, 511, 540, 541, 570]\n",
      "1 -18 [510, 511, 512, 540, 541, 542, 570, 571]\n",
      "2 -18 [511, 512, 513, 541, 542, 543, 571, 572]\n",
      "3 -18 [512, 513, 514, 542, 543, 544, 572, 573]\n",
      "4 -18 [513, 514, 515, 543, 544, 545, 573, 574]\n",
      "5 -18 [514, 515, 516, 544, 545, 546, 574, 575]\n",
      "6 -18 [515, 516, 517, 545, 546, 547, 575, 576]\n",
      "7 -18 [516, 517, 518, 546, 547, 548, 576, 577]\n",
      "8 -18 [517, 518, 519, 547, 548, 549, 577, 578]\n",
      "9 -18 [518, 519, 520, 548, 549, 550, 578, 579]\n",
      "10 -18 [519, 520, 521, 549, 550, 551, 579, 580]\n",
      "11 -18 [520, 521, 522, 550, 551, 552, 580, 581]\n",
      "12 -18 [521, 522, 523, 551, 552, 553, 581, 582]\n",
      "13 -18 [522, 523, 524, 552, 553, 554, 582, 583]\n",
      "14 -18 [523, 524, 525, 553, 554, 555, 583, 584]\n",
      "15 -18 [524, 525, 526, 554, 555, 556, 584, 585]\n",
      "16 -18 [525, 526, 527, 555, 556, 557, 585, 586]\n",
      "17 -18 [526, 527, 528, 556, 557, 558, 586, 587]\n",
      "18 -18 [527, 528, 529, 557, 558, 559, 587, 588]\n",
      "19 -18 [528, 529, 530, 558, 559, 560, 588, 589]\n",
      "20 -18 [529, 530, 531, 559, 560, 561, 589, 590]\n",
      "21 -18 [530, 531, 532, 560, 561, 562, 590, 591]\n",
      "22 -18 [531, 532, 533, 561, 562, 563, 591, 592]\n",
      "23 -18 [532, 533, 534, 562, 563, 564, 592, 593]\n",
      "24 -18 [533, 534, 535, 563, 564, 565, 593, 594]\n",
      "25 -18 [534, 535, 536, 564, 565, 566, 594, 595]\n",
      "26 -18 [535, 536, 537, 565, 566, 567, 595, 596]\n",
      "27 -18 [536, 537, 538, 566, 567, 568, 596, 597]\n",
      "28 -18 [537, 538, 539, 567, 568, 569, 597, 598]\n",
      "-1 -19 [540, 570]\n",
      "0 -19 [540, 541, 570, 571, 600]\n",
      "1 -19 [540, 541, 542, 570, 571, 572, 600, 601]\n",
      "2 -19 [541, 542, 543, 571, 572, 573, 601, 602]\n",
      "3 -19 [542, 543, 544, 572, 573, 574, 602, 603]\n",
      "4 -19 [543, 544, 545, 573, 574, 575, 603, 604]\n",
      "5 -19 [544, 545, 546, 574, 575, 576, 604, 605]\n",
      "6 -19 [545, 546, 547, 575, 576, 577, 605, 606]\n",
      "7 -19 [546, 547, 548, 576, 577, 578, 606, 607]\n",
      "8 -19 [547, 548, 549, 577, 578, 579, 607, 608]\n",
      "9 -19 [548, 549, 550, 578, 579, 580, 608, 609]\n",
      "10 -19 [549, 550, 551, 579, 580, 581, 609, 610]\n",
      "11 -19 [550, 551, 552, 580, 581, 582, 610, 611]\n",
      "12 -19 [551, 552, 553, 581, 582, 583, 611, 612]\n",
      "13 -19 [552, 553, 554, 582, 583, 584, 612, 613]\n",
      "14 -19 [553, 554, 555, 583, 584, 585, 613, 614]\n",
      "15 -19 [554, 555, 556, 584, 585, 586, 614, 615]\n",
      "16 -19 [555, 556, 557, 585, 586, 587, 615, 616]\n",
      "17 -19 [556, 557, 558, 586, 587, 588, 616, 617]\n",
      "18 -19 [557, 558, 559, 587, 588, 589, 617, 618]\n",
      "19 -19 [558, 559, 560, 588, 589, 590, 618, 619]\n",
      "20 -19 [559, 560, 561, 589, 590, 591, 619, 620]\n",
      "21 -19 [560, 561, 562, 590, 591, 592, 620, 621]\n",
      "22 -19 [561, 562, 563, 591, 592, 593, 621, 622]\n",
      "23 -19 [562, 563, 564, 592, 593, 594, 622, 623]\n",
      "24 -19 [563, 564, 565, 593, 594, 595, 623, 624]\n",
      "25 -19 [564, 565, 566, 594, 595, 596, 624, 625]\n",
      "26 -19 [565, 566, 567, 595, 596, 597, 625, 626]\n",
      "27 -19 [566, 567, 568, 596, 597, 598, 626, 627]\n",
      "28 -19 [567, 568, 569, 597, 598, 599, 627, 628]\n",
      "-1 -20 [570, 600]\n",
      "0 -20 [570, 571, 600, 601, 630]\n",
      "1 -20 [570, 571, 572, 600, 601, 602, 630, 631]\n",
      "2 -20 [571, 572, 573, 601, 602, 603, 631, 632]\n",
      "3 -20 [572, 573, 574, 602, 603, 604, 632, 633]\n",
      "4 -20 [573, 574, 575, 603, 604, 605, 633, 634]\n",
      "5 -20 [574, 575, 576, 604, 605, 606, 634, 635]\n",
      "6 -20 [575, 576, 577, 605, 606, 607, 635, 636]\n",
      "7 -20 [576, 577, 578, 606, 607, 608, 636, 637]\n",
      "8 -20 [577, 578, 579, 607, 608, 609, 637, 638]\n",
      "9 -20 [578, 579, 580, 608, 609, 610, 638, 639]\n",
      "10 -20 [579, 580, 581, 609, 610, 611, 639, 640]\n",
      "11 -20 [580, 581, 582, 610, 611, 612, 640, 641]\n",
      "12 -20 [581, 582, 583, 611, 612, 613, 641, 642]\n",
      "13 -20 [582, 583, 584, 612, 613, 614, 642, 643]\n",
      "14 -20 [583, 584, 585, 613, 614, 615, 643, 644]\n",
      "15 -20 [584, 585, 586, 614, 615, 616, 644, 645]\n",
      "16 -20 [585, 586, 587, 615, 616, 617, 645, 646]\n",
      "17 -20 [586, 587, 588, 616, 617, 618, 646, 647]\n",
      "18 -20 [587, 588, 589, 617, 618, 619, 647, 648]\n",
      "19 -20 [588, 589, 590, 618, 619, 620, 648, 649]\n",
      "20 -20 [589, 590, 591, 619, 620, 621, 649, 650]\n",
      "21 -20 [590, 591, 592, 620, 621, 622, 650, 651]\n",
      "22 -20 [591, 592, 593, 621, 622, 623, 651, 652]\n",
      "23 -20 [592, 593, 594, 622, 623, 624, 652, 653]\n",
      "24 -20 [593, 594, 595, 623, 624, 625, 653, 654]\n",
      "25 -20 [594, 595, 596, 624, 625, 626, 654, 655]\n",
      "26 -20 [595, 596, 597, 625, 626, 627, 655, 656]\n",
      "27 -20 [596, 597, 598, 626, 627, 628, 656, 657]\n",
      "28 -20 [597, 598, 599, 627, 628, 629, 657, 658]\n",
      "-1 -21 [600, 630]\n",
      "0 -21 [600, 601, 630, 631, 660]\n",
      "1 -21 [600, 601, 602, 630, 631, 632, 660, 661]\n",
      "2 -21 [601, 602, 603, 631, 632, 633, 661, 662]\n",
      "3 -21 [602, 603, 604, 632, 633, 634, 662, 663]\n",
      "4 -21 [603, 604, 605, 633, 634, 635, 663, 664]\n",
      "5 -21 [604, 605, 606, 634, 635, 636, 664, 665]\n",
      "6 -21 [605, 606, 607, 635, 636, 637, 665, 666]\n",
      "7 -21 [606, 607, 608, 636, 637, 638, 666, 667]\n",
      "8 -21 [607, 608, 609, 637, 638, 639, 667, 668]\n",
      "9 -21 [608, 609, 610, 638, 639, 640, 668, 669]\n",
      "10 -21 [609, 610, 611, 639, 640, 641, 669, 670]\n",
      "11 -21 [610, 611, 612, 640, 641, 642, 670, 671]\n",
      "12 -21 [611, 612, 613, 641, 642, 643, 671, 672]\n",
      "13 -21 [612, 613, 614, 642, 643, 644, 672, 673]\n",
      "14 -21 [613, 614, 615, 643, 644, 645, 673, 674]\n",
      "15 -21 [614, 615, 616, 644, 645, 646, 674, 675]\n",
      "16 -21 [615, 616, 617, 645, 646, 647, 675, 676]\n",
      "17 -21 [616, 617, 618, 646, 647, 648, 676, 677]\n",
      "18 -21 [617, 618, 619, 647, 648, 649, 677, 678]\n",
      "19 -21 [618, 619, 620, 648, 649, 650, 678, 679]\n",
      "20 -21 [619, 620, 621, 649, 650, 651, 679, 680]\n",
      "21 -21 [620, 621, 622, 650, 651, 652, 680, 681]\n",
      "22 -21 [621, 622, 623, 651, 652, 653, 681, 682]\n",
      "23 -21 [622, 623, 624, 652, 653, 654, 682, 683]\n",
      "24 -21 [623, 624, 625, 653, 654, 655, 683, 684]\n",
      "25 -21 [624, 625, 626, 654, 655, 656, 684, 685]\n",
      "26 -21 [625, 626, 627, 655, 656, 657, 685, 686]\n",
      "27 -21 [626, 627, 628, 656, 657, 658, 686, 687]\n",
      "28 -21 [627, 628, 629, 657, 658, 659, 687, 688]\n",
      "-1 -22 [630, 660]\n",
      "0 -22 [630, 631, 660, 661, 690]\n",
      "1 -22 [630, 631, 632, 660, 661, 662, 690, 691]\n",
      "2 -22 [631, 632, 633, 661, 662, 663, 691, 692]\n",
      "3 -22 [632, 633, 634, 662, 663, 664, 692, 693]\n",
      "4 -22 [633, 634, 635, 663, 664, 665, 693, 694]\n",
      "5 -22 [634, 635, 636, 664, 665, 666, 694, 695]\n",
      "6 -22 [635, 636, 637, 665, 666, 667, 695, 696]\n",
      "7 -22 [636, 637, 638, 666, 667, 668, 696, 697]\n",
      "8 -22 [637, 638, 639, 667, 668, 669, 697, 698]\n",
      "9 -22 [638, 639, 640, 668, 669, 670, 698, 699]\n",
      "10 -22 [639, 640, 641, 669, 670, 671, 699, 700]\n",
      "11 -22 [640, 641, 642, 670, 671, 672, 700, 701]\n",
      "12 -22 [641, 642, 643, 671, 672, 673, 701, 702]\n",
      "13 -22 [642, 643, 644, 672, 673, 674, 702, 703]\n",
      "14 -22 [643, 644, 645, 673, 674, 675, 703, 704]\n",
      "15 -22 [644, 645, 646, 674, 675, 676, 704, 705]\n",
      "16 -22 [645, 646, 647, 675, 676, 677, 705, 706]\n",
      "17 -22 [646, 647, 648, 676, 677, 678, 706, 707]\n",
      "18 -22 [647, 648, 649, 677, 678, 679, 707, 708]\n",
      "19 -22 [648, 649, 650, 678, 679, 680, 708, 709]\n",
      "20 -22 [649, 650, 651, 679, 680, 681, 709, 710]\n",
      "21 -22 [650, 651, 652, 680, 681, 682, 710, 711]\n",
      "22 -22 [651, 652, 653, 681, 682, 683, 711, 712]\n",
      "23 -22 [652, 653, 654, 682, 683, 684, 712, 713]\n",
      "24 -22 [653, 654, 655, 683, 684, 685, 713, 714]\n",
      "25 -22 [654, 655, 656, 684, 685, 686, 714, 715]\n",
      "26 -22 [655, 656, 657, 685, 686, 687, 715, 716]\n",
      "27 -22 [656, 657, 658, 686, 687, 688, 716, 717]\n",
      "28 -22 [657, 658, 659, 687, 688, 689, 717, 718]\n",
      "-1 -23 [660, 690]\n",
      "0 -23 [660, 661, 690, 691, 720]\n",
      "1 -23 [660, 661, 662, 690, 691, 692, 720, 721]\n",
      "2 -23 [661, 662, 663, 691, 692, 693, 721, 722]\n",
      "3 -23 [662, 663, 664, 692, 693, 694, 722, 723]\n",
      "4 -23 [663, 664, 665, 693, 694, 695, 723, 724]\n",
      "5 -23 [664, 665, 666, 694, 695, 696, 724, 725]\n",
      "6 -23 [665, 666, 667, 695, 696, 697, 725, 726]\n",
      "7 -23 [666, 667, 668, 696, 697, 698, 726, 727]\n",
      "8 -23 [667, 668, 669, 697, 698, 699, 727, 728]\n",
      "9 -23 [668, 669, 670, 698, 699, 700, 728, 729]\n",
      "10 -23 [669, 670, 671, 699, 700, 701, 729, 730]\n",
      "11 -23 [670, 671, 672, 700, 701, 702, 730, 731]\n",
      "12 -23 [671, 672, 673, 701, 702, 703, 731, 732]\n",
      "13 -23 [672, 673, 674, 702, 703, 704, 732, 733]\n",
      "14 -23 [673, 674, 675, 703, 704, 705, 733, 734]\n",
      "15 -23 [674, 675, 676, 704, 705, 706, 734, 735]\n",
      "16 -23 [675, 676, 677, 705, 706, 707, 735, 736]\n",
      "17 -23 [676, 677, 678, 706, 707, 708, 736, 737]\n",
      "18 -23 [677, 678, 679, 707, 708, 709, 737, 738]\n",
      "19 -23 [678, 679, 680, 708, 709, 710, 738, 739]\n",
      "20 -23 [679, 680, 681, 709, 710, 711, 739, 740]\n",
      "21 -23 [680, 681, 682, 710, 711, 712, 740, 741]\n",
      "22 -23 [681, 682, 683, 711, 712, 713, 741, 742]\n",
      "23 -23 [682, 683, 684, 712, 713, 714, 742, 743]\n",
      "24 -23 [683, 684, 685, 713, 714, 715, 743, 744]\n",
      "25 -23 [684, 685, 686, 714, 715, 716, 744, 745]\n",
      "26 -23 [685, 686, 687, 715, 716, 717, 745, 746]\n",
      "27 -23 [686, 687, 688, 716, 717, 718, 746, 747]\n",
      "28 -23 [687, 688, 689, 717, 718, 719, 747, 748]\n",
      "-1 -24 [690, 720]\n",
      "0 -24 [690, 691, 720, 721, 750]\n",
      "1 -24 [690, 691, 692, 720, 721, 722, 750, 751]\n",
      "2 -24 [691, 692, 693, 721, 722, 723, 751, 752]\n",
      "3 -24 [692, 693, 694, 722, 723, 724, 752, 753]\n",
      "4 -24 [693, 694, 695, 723, 724, 725, 753, 754]\n",
      "5 -24 [694, 695, 696, 724, 725, 726, 754, 755]\n",
      "6 -24 [695, 696, 697, 725, 726, 727, 755, 756]\n",
      "7 -24 [696, 697, 698, 726, 727, 728, 756, 757]\n",
      "8 -24 [697, 698, 699, 727, 728, 729, 757, 758]\n",
      "9 -24 [698, 699, 700, 728, 729, 730, 758, 759]\n",
      "10 -24 [699, 700, 701, 729, 730, 731, 759, 760]\n",
      "11 -24 [700, 701, 702, 730, 731, 732, 760, 761]\n",
      "12 -24 [701, 702, 703, 731, 732, 733, 761, 762]\n",
      "13 -24 [702, 703, 704, 732, 733, 734, 762, 763]\n",
      "14 -24 [703, 704, 705, 733, 734, 735, 763, 764]\n",
      "15 -24 [704, 705, 706, 734, 735, 736, 764, 765]\n",
      "16 -24 [705, 706, 707, 735, 736, 737, 765, 766]\n",
      "17 -24 [706, 707, 708, 736, 737, 738, 766, 767]\n",
      "18 -24 [707, 708, 709, 737, 738, 739, 767, 768]\n",
      "19 -24 [708, 709, 710, 738, 739, 740, 768, 769]\n",
      "20 -24 [709, 710, 711, 739, 740, 741, 769, 770]\n",
      "21 -24 [710, 711, 712, 740, 741, 742, 770, 771]\n",
      "22 -24 [711, 712, 713, 741, 742, 743, 771, 772]\n",
      "23 -24 [712, 713, 714, 742, 743, 744, 772, 773]\n",
      "24 -24 [713, 714, 715, 743, 744, 745, 773, 774]\n",
      "25 -24 [714, 715, 716, 744, 745, 746, 774, 775]\n",
      "26 -24 [715, 716, 717, 745, 746, 747, 775, 776]\n",
      "27 -24 [716, 717, 718, 746, 747, 748, 776, 777]\n",
      "28 -24 [717, 718, 719, 747, 748, 749, 777, 778]\n",
      "-1 -25 [720, 750]\n",
      "0 -25 [720, 721, 750, 751, 780]\n",
      "1 -25 [720, 721, 722, 750, 751, 752, 780, 781]\n",
      "2 -25 [721, 722, 723, 751, 752, 753, 781, 782]\n",
      "3 -25 [722, 723, 724, 752, 753, 754, 782, 783]\n",
      "4 -25 [723, 724, 725, 753, 754, 755, 783, 784]\n",
      "5 -25 [724, 725, 726, 754, 755, 756, 784, 785]\n",
      "6 -25 [725, 726, 727, 755, 756, 757, 785, 786]\n",
      "7 -25 [726, 727, 728, 756, 757, 758, 786, 787]\n",
      "8 -25 [727, 728, 729, 757, 758, 759, 787, 788]\n",
      "9 -25 [728, 729, 730, 758, 759, 760, 788, 789]\n",
      "10 -25 [729, 730, 731, 759, 760, 761, 789, 790]\n",
      "11 -25 [730, 731, 732, 760, 761, 762, 790, 791]\n",
      "12 -25 [731, 732, 733, 761, 762, 763, 791, 792]\n",
      "13 -25 [732, 733, 734, 762, 763, 764, 792, 793]\n",
      "14 -25 [733, 734, 735, 763, 764, 765, 793, 794]\n",
      "15 -25 [734, 735, 736, 764, 765, 766, 794, 795]\n",
      "16 -25 [735, 736, 737, 765, 766, 767, 795, 796]\n",
      "17 -25 [736, 737, 738, 766, 767, 768, 796, 797]\n",
      "18 -25 [737, 738, 739, 767, 768, 769, 797, 798]\n",
      "19 -25 [738, 739, 740, 768, 769, 770, 798, 799]\n",
      "20 -25 [739, 740, 741, 769, 770, 771, 799, 800]\n",
      "21 -25 [740, 741, 742, 770, 771, 772, 800, 801]\n",
      "22 -25 [741, 742, 743, 771, 772, 773, 801, 802]\n",
      "23 -25 [742, 743, 744, 772, 773, 774, 802, 803]\n",
      "24 -25 [743, 744, 745, 773, 774, 775, 803, 804]\n",
      "25 -25 [744, 745, 746, 774, 775, 776, 804, 805]\n",
      "26 -25 [745, 746, 747, 775, 776, 777, 805, 806]\n",
      "27 -25 [746, 747, 748, 776, 777, 778, 806, 807]\n",
      "28 -25 [747, 748, 749, 777, 778, 779, 807, 808]\n",
      "-1 -26 [750, 780]\n",
      "0 -26 [750, 751, 780, 781, 810]\n",
      "1 -26 [750, 751, 752, 780, 781, 782, 810, 811]\n",
      "2 -26 [751, 752, 753, 781, 782, 783, 811, 812]\n",
      "3 -26 [752, 753, 754, 782, 783, 784, 812, 813]\n",
      "4 -26 [753, 754, 755, 783, 784, 785, 813, 814]\n",
      "5 -26 [754, 755, 756, 784, 785, 786, 814, 815]\n",
      "6 -26 [755, 756, 757, 785, 786, 787, 815, 816]\n",
      "7 -26 [756, 757, 758, 786, 787, 788, 816, 817]\n",
      "8 -26 [757, 758, 759, 787, 788, 789, 817, 818]\n",
      "9 -26 [758, 759, 760, 788, 789, 790, 818, 819]\n",
      "10 -26 [759, 760, 761, 789, 790, 791, 819, 820]\n",
      "11 -26 [760, 761, 762, 790, 791, 792, 820, 821]\n",
      "12 -26 [761, 762, 763, 791, 792, 793, 821, 822]\n",
      "13 -26 [762, 763, 764, 792, 793, 794, 822, 823]\n",
      "14 -26 [763, 764, 765, 793, 794, 795, 823, 824]\n",
      "15 -26 [764, 765, 766, 794, 795, 796, 824, 825]\n",
      "16 -26 [765, 766, 767, 795, 796, 797, 825, 826]\n",
      "17 -26 [766, 767, 768, 796, 797, 798, 826, 827]\n",
      "18 -26 [767, 768, 769, 797, 798, 799, 827, 828]\n",
      "19 -26 [768, 769, 770, 798, 799, 800, 828, 829]\n",
      "20 -26 [769, 770, 771, 799, 800, 801, 829, 830]\n",
      "21 -26 [770, 771, 772, 800, 801, 802, 830, 831]\n",
      "22 -26 [771, 772, 773, 801, 802, 803, 831, 832]\n",
      "23 -26 [772, 773, 774, 802, 803, 804, 832, 833]\n",
      "24 -26 [773, 774, 775, 803, 804, 805, 833, 834]\n",
      "25 -26 [774, 775, 776, 804, 805, 806, 834, 835]\n",
      "26 -26 [775, 776, 777, 805, 806, 807, 835, 836]\n",
      "27 -26 [776, 777, 778, 806, 807, 808, 836, 837]\n",
      "28 -26 [777, 778, 779, 807, 808, 809, 837, 838]\n",
      "-1 -27 [780, 810]\n",
      "0 -27 [780, 781, 810, 811, 840]\n",
      "1 -27 [780, 781, 782, 810, 811, 812, 840, 841]\n",
      "2 -27 [781, 782, 783, 811, 812, 813, 841, 842]\n",
      "3 -27 [782, 783, 784, 812, 813, 814, 842, 843]\n",
      "4 -27 [783, 784, 785, 813, 814, 815, 843, 844]\n",
      "5 -27 [784, 785, 786, 814, 815, 816, 844, 845]\n",
      "6 -27 [785, 786, 787, 815, 816, 817, 845, 846]\n",
      "7 -27 [786, 787, 788, 816, 817, 818, 846, 847]\n",
      "8 -27 [787, 788, 789, 817, 818, 819, 847, 848]\n",
      "9 -27 [788, 789, 790, 818, 819, 820, 848, 849]\n",
      "10 -27 [789, 790, 791, 819, 820, 821, 849, 850]\n",
      "11 -27 [790, 791, 792, 820, 821, 822, 850, 851]\n",
      "12 -27 [791, 792, 793, 821, 822, 823, 851, 852]\n",
      "13 -27 [792, 793, 794, 822, 823, 824, 852, 853]\n",
      "14 -27 [793, 794, 795, 823, 824, 825, 853, 854]\n",
      "15 -27 [794, 795, 796, 824, 825, 826, 854, 855]\n",
      "16 -27 [795, 796, 797, 825, 826, 827, 855, 856]\n",
      "17 -27 [796, 797, 798, 826, 827, 828, 856, 857]\n",
      "18 -27 [797, 798, 799, 827, 828, 829, 857, 858]\n",
      "19 -27 [798, 799, 800, 828, 829, 830, 858, 859]\n",
      "20 -27 [799, 800, 801, 829, 830, 831, 859, 860]\n",
      "21 -27 [800, 801, 802, 830, 831, 832, 860, 861]\n",
      "22 -27 [801, 802, 803, 831, 832, 833, 861, 862]\n",
      "23 -27 [802, 803, 804, 832, 833, 834, 862, 863]\n",
      "24 -27 [803, 804, 805, 833, 834, 835, 863, 864]\n",
      "25 -27 [804, 805, 806, 834, 835, 836, 864, 865]\n",
      "26 -27 [805, 806, 807, 835, 836, 837, 865, 866]\n",
      "27 -27 [806, 807, 808, 836, 837, 838, 866, 867]\n",
      "28 -27 [807, 808, 809, 837, 838, 839, 867, 868]\n",
      "-1 -28 [810, 840]\n",
      "0 -28 [810, 811, 840, 841, 870]\n",
      "1 -28 [810, 811, 812, 840, 841, 842, 870, 871]\n",
      "2 -28 [811, 812, 813, 841, 842, 843, 871, 872]\n",
      "3 -28 [812, 813, 814, 842, 843, 844, 872, 873]\n",
      "4 -28 [813, 814, 815, 843, 844, 845, 873, 874]\n",
      "5 -28 [814, 815, 816, 844, 845, 846, 874, 875]\n",
      "6 -28 [815, 816, 817, 845, 846, 847, 875, 876]\n",
      "7 -28 [816, 817, 818, 846, 847, 848, 876, 877]\n",
      "8 -28 [817, 818, 819, 847, 848, 849, 877, 878]\n",
      "9 -28 [818, 819, 820, 848, 849, 850, 878, 879]\n",
      "10 -28 [819, 820, 821, 849, 850, 851, 879, 880]\n",
      "11 -28 [820, 821, 822, 850, 851, 852, 880, 881]\n",
      "12 -28 [821, 822, 823, 851, 852, 853, 881, 882]\n",
      "13 -28 [822, 823, 824, 852, 853, 854, 882, 883]\n",
      "14 -28 [823, 824, 825, 853, 854, 855, 883, 884]\n",
      "15 -28 [824, 825, 826, 854, 855, 856, 884, 885]\n",
      "16 -28 [825, 826, 827, 855, 856, 857, 885, 886]\n",
      "17 -28 [826, 827, 828, 856, 857, 858, 886, 887]\n",
      "18 -28 [827, 828, 829, 857, 858, 859, 887, 888]\n",
      "19 -28 [828, 829, 830, 858, 859, 860, 888, 889]\n",
      "20 -28 [829, 830, 831, 859, 860, 861, 889, 890]\n",
      "21 -28 [830, 831, 832, 860, 861, 862, 890, 891]\n",
      "22 -28 [831, 832, 833, 861, 862, 863, 891, 892]\n",
      "23 -28 [832, 833, 834, 862, 863, 864, 892, 893]\n",
      "24 -28 [833, 834, 835, 863, 864, 865, 893, 894]\n",
      "25 -28 [834, 835, 836, 864, 865, 866, 894, 895]\n",
      "26 -28 [835, 836, 837, 865, 866, 867, 895, 896]\n",
      "27 -28 [836, 837, 838, 866, 867, 868, 896, 897]\n",
      "28 -28 [837, 838, 839, 867, 868, 869, 897, 898]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(9000, 2)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## 900 superspots\n",
    "N = 9000\n",
    "spatial = []\n",
    "dependency = []\n",
    "for i in range(30):\n",
    "    for j in range(30):\n",
    "        spatial.append(np.random.multivariate_normal(np.array([j-1,1-i]),np.identity(2)*0.8,10))\n",
    "        d = []\n",
    "        for i_i in range(i-2,i+1):\n",
    "            for j_j in range(j-2,j+1):\n",
    "                if i_i > -1 and j_j > -1:\n",
    "                    d.append(i_i*30+j_j)\n",
    "        d.pop()\n",
    "        print(j-1,1-i,d)\n",
    "        dependency.append(d)\n",
    "spatial = np.vstack(spatial)\n",
    "spatial.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0.05358027,   0.35096415],\n",
       "       [ -2.00468461,   0.41092008],\n",
       "       [ -0.99038848,   0.66499494],\n",
       "       ...,\n",
       "       [ 27.50198769, -28.64120342],\n",
       "       [ 27.62668085, -28.28952938],\n",
       "       [ 28.84877734, -28.56193106]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spatial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1407.38437333, 1641.75474133, 1915.15458163, 2234.08343474,\n",
       "       2606.12320346, 3040.11839755, 3546.3863945 , 4136.96271474,\n",
       "       4825.88714239, 5629.53749331])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l_min,l_max = get_l_limits(spatial.T)\n",
    "space = np.logspace(np.log10(l_min), np.log10(l_max), 10)\n",
    "space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "l = 0.01\n",
    "cov = RBF_kernel(spatial,2000)\n",
    "mean = np.zeros(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.99999983, 0.99999943, ..., 0.99981073, 0.99979691,\n",
       "        0.99980849],\n",
       "       [0.99999983, 1.        , 0.99999939, ..., 0.99981156, 0.99979714,\n",
       "        0.99980906],\n",
       "       [0.99999943, 0.99999939, 1.        , ..., 0.99979029, 0.99977543,\n",
       "        0.99978779],\n",
       "       ...,\n",
       "       [0.99981073, 0.99981156, 0.99979029, ..., 1.        , 0.99999918,\n",
       "        0.99999989],\n",
       "       [0.99979691, 0.99979714, 0.99977543, ..., 0.99999918, 1.        ,\n",
       "        0.99999964],\n",
       "       [0.99980849, 0.99980906, 0.99978779, ..., 0.99999989, 0.99999964,\n",
       "        1.        ]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cov"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-12730.39775729, -12629.86353084, -12856.94944374, -12826.45465341,\n",
       "       -12701.95580482, -12838.06670866, -12786.02161908, -12767.25596832,\n",
       "       -12686.00826903, -12800.77888523, -12706.92688168, -12654.58972984,\n",
       "       -12817.53509089, -12766.76758385, -12658.4973617 , -12697.72514758,\n",
       "       -12788.19559384, -12756.75196618, -12761.02696204, -12705.15462501,\n",
       "       -12790.66038136, -12835.94011022, -12796.8221687 , -12748.01474654,\n",
       "       -12785.9504986 , -12661.90766572, -12715.4158938 , -12779.27043072,\n",
       "       -12753.82783245, -12679.17024229, -12701.53241931, -12720.9413291 ,\n",
       "       -12776.15650683, -12831.16407091, -12842.87821073, -12778.87288523,\n",
       "       -12770.67473708, -12797.60493389, -12793.48784439, -12709.70602491,\n",
       "       -12744.74952638, -12853.00459517, -12755.45577009, -12714.50965405,\n",
       "       -12866.24223763, -12560.96265729, -12698.18686624, -12729.76406729,\n",
       "       -12827.71006524, -12787.83551144, -12776.3650922 , -12688.51255542,\n",
       "       -12720.30418177, -12717.11331438, -12801.91138031, -12711.80765601,\n",
       "       -12728.84123791, -12816.70903245, -12801.57896389, -12890.32309802,\n",
       "       -12841.66985111, -12732.09113584, -12698.27692437, -12871.26860467,\n",
       "       -12812.12762362, -12874.72730022, -12710.56899668, -12749.51645666,\n",
       "       -12802.81334831, -12860.39120941, -12829.81207234, -12670.55015962,\n",
       "       -12775.30941169, -12756.73339597, -12846.52862334, -12861.75545997,\n",
       "       -12736.40507811, -12733.00228068, -12777.56426362, -12802.54424362,\n",
       "       -12833.12350684, -12849.35486648, -12854.60086111, -12833.90988215,\n",
       "       -12749.67798068, -12848.54211345, -12853.16569566, -12762.92697276,\n",
       "       -12822.01355348, -12786.39243069, -12790.2957058 , -12753.32315498,\n",
       "       -12787.34748884, -12802.57090663, -12736.53602896, -12691.95003022,\n",
       "       -12844.75807947, -12779.60819795, -12729.01520753, -12670.93411249,\n",
       "       -12681.52793264, -12849.79805632, -12720.46634898, -12784.92575871,\n",
       "       -12778.95302297, -12750.83584894, -12909.56617827, -12611.62416852,\n",
       "       -12739.38915388, -12715.54163847, -12756.54146937, -12727.29018769,\n",
       "       -12823.48784597, -12768.37547579, -12735.96037872, -12810.36882845,\n",
       "       -12702.32359315, -12702.69371558, -12787.82553023, -12704.21365047,\n",
       "       -12718.72068957, -12710.15289827, -12886.55440608, -12759.0405618 ,\n",
       "       -12732.97103215, -12777.30261843, -12640.44170247, -12813.82005706,\n",
       "       -12733.86945577, -12877.43548243, -12896.71288672, -12866.36354056,\n",
       "       -12716.04317124, -12677.47911515, -12716.0310914 , -12858.79625563,\n",
       "       -12854.10546676, -12822.95181992, -12848.73146485, -12803.83521208,\n",
       "       -12698.06684795, -12749.77484246, -12755.99183319, -12860.92143345,\n",
       "       -12714.06851566, -12738.4999718 , -12791.16208355, -12779.51181893,\n",
       "       -12722.31460702, -12684.44893873, -12735.91501201, -12692.14633894,\n",
       "       -12669.38664775, -12780.39514222, -12724.40748798, -12797.93750436,\n",
       "       -12705.81653254, -12664.72446741, -12755.33942004, -12796.29560681,\n",
       "       -12782.99620224, -12688.46666189, -12805.59364543, -12807.0299767 ,\n",
       "       -12587.75052678, -12724.96227223, -12788.12813858, -12664.72106712,\n",
       "       -12690.46644791, -12799.87366443, -12689.22486192, -12883.04272012,\n",
       "       -12778.48051193, -12746.11230426, -12856.38113812, -12813.85318208,\n",
       "       -12690.04885356, -12788.52248035, -12687.10505654, -12824.86871536,\n",
       "       -12879.59676078, -12780.59561393, -12746.38221296, -12880.6935665 ,\n",
       "       -12905.08882988, -12738.31088615, -12790.52828616, -12746.82828421,\n",
       "       -12827.09007758, -12748.88024345, -12770.7114492 , -12774.64612561,\n",
       "       -12759.53091269, -12705.08012179, -12820.73643926, -12820.5135204 ,\n",
       "       -12794.13484289, -12744.98382727, -12695.0442644 , -12815.89349969])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y = np.random.multivariate_normal(mean,cov,200)\n",
    "likelihood_4 = multivariate_normal.logpdf(Y, mean, cov, allow_singular = True)\n",
    "likelihood_4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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    }
   ],
   "source": [
    "ss_loc = [list(range(10*i, 10*(i+1))) for i in range(900)]\n",
    "model_5 = Gaussian(mean,cov,spatial,ss_loc,dependency=dependency,kernel='RBF',l=0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 8.34112953  7.04775877 13.95386109 15.91672855 14.76929411 19.40152929\n",
      " 17.46886248  9.08099774  7.87386012 14.48274956 16.80378302 14.22803228\n",
      "  6.2711115  18.44721041 10.62187273 15.7061917  15.28882018 14.29443844\n",
      "  9.26870808 15.26397126 12.00109952 17.7104031  11.48411331  8.62344162\n",
      " 13.18235915 14.81156338 14.92842213 15.81408369 15.21933596 17.5119041\n",
      " 12.22077894 10.81701356 18.0490416  16.3475818  23.06263016  7.62072149\n",
      " 16.14318027 12.05292038 13.94508413 16.67194628 18.08007399 10.73867536\n",
      " 15.82101245 16.49958953 22.92288573 21.06495912  7.96816741 11.61896329\n",
      " 18.40309176 19.43827296 18.29795761 11.32626461 20.08704117 10.42537331\n",
      " 20.60176909 25.76587513 12.14030826 17.25218817 10.4451668  11.30782237\n",
      " 20.85838621 13.81863378 13.73304435 14.34766715  9.57808525 17.34432456\n",
      " 16.90516101 12.0483742  23.78313767 13.08598304  9.71961807 16.71212237\n",
      " 14.01515707 13.10806254 11.95995474 18.96374162 19.11641895 13.57358539\n",
      " 19.65238289 20.29889617  6.71910725 24.10889504 20.10498618 15.76811874\n",
      " 15.45405263 14.85601368  3.06567038 19.34170177 12.24351928 12.72326351\n",
      " 14.34125753 12.24477543 14.04003671 16.32540008 20.78499333 10.17342029\n",
      " 12.65239935 13.17804059 22.01939047 13.12544237 13.91124551 13.1390234\n",
      " 22.83189016 10.79037459 11.49127925 13.81483726 19.07863027  6.20049123\n",
      " 18.68026082  9.64984808 19.05193802 11.2040789  21.27872287 21.95182399\n",
      " 19.18291724 13.07834548 10.63792572 10.59830309  8.10568171 16.11524835\n",
      "  7.76366439 18.48167189 22.47953369 16.19486694 13.79734773  8.30759796\n",
      " 11.76696193 27.62688262  9.42715294 16.50007754 23.60854068 22.64716018\n",
      " 13.59884828 16.26638837  7.87293706 13.39414889 14.69056299 12.23208806\n",
      " 19.05561811 17.64497521 14.46740058 23.05336272 14.83676751 18.36193655\n",
      " 15.31733638 11.01016519 15.84801485 14.97059367 15.88682438 10.24449699\n",
      " 14.8090334  17.04758535 18.04736707 10.28557879 15.06120833 15.65632997\n",
      " 11.36034429 13.48945409 15.57295614 14.02969622 19.61864141 15.99656587\n",
      " 27.39705437 10.38663221 12.51999366 12.55827507 18.4926313  16.39292432\n",
      " 14.8253203  11.35013807 15.51805156  7.8313975  12.12966918 13.18298908\n",
      " 14.45334595 11.78021313 14.71675864 10.08583202 16.85791925 10.13559069\n",
      " 12.718876   18.23493213 13.11624042 10.62373328 19.33847332 12.97540796\n",
      " 12.28025787 14.93315027 25.64360829 13.52425801 14.7752431  15.89174275\n",
      "  2.43942098 11.98543156 23.84069958 13.40531772 14.19988799 13.4258821\n",
      " 14.78287794 23.98480703]\n"
     ]
    }
   ],
   "source": [
    "likelihood_5 = model_5.gs_nll_sep(Y.T)\n",
    "print(likelihood_4-likelihood_5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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      " -6.47895571e-04  6.21791987e-05 -6.39909995e-05  6.03059016e-06\n",
      " -1.62436343e-04  1.05593799e-04  2.42003080e-06  3.17729136e-05\n",
      " -2.79537529e-04  1.33792373e-04  1.23762884e-04 -3.03807306e-04\n",
      " -8.23974569e-05 -1.03367463e-04  3.66941780e-04  1.36187737e-07\n",
      "  1.70419818e-04  5.79614552e-05  4.64193614e-04  5.99252216e-05\n",
      "  1.51820368e-05 -1.09944474e-04 -6.26042856e-05 -9.18081259e-05\n",
      "  1.39299576e-04 -6.32238589e-05 -2.78962580e-06 -7.78931280e-07\n",
      " -7.61822230e-06  1.24962025e-06 -9.91165325e-05  3.83348088e-05\n",
      " -9.04020271e-05 -1.16456911e-04 -8.78331357e-05  1.84765689e-04\n",
      " -3.42237981e-05 -3.50070426e-04 -1.71377102e-04 -4.37541639e-05\n",
      " -3.12884731e-06 -5.35858235e-05  2.00326031e-05 -2.41221314e-05\n",
      "  4.69539251e-04 -1.52020890e-04 -3.78577442e-05 -3.20655454e-05\n",
      " -7.38599301e-05 -3.07913251e-05 -4.86193421e-05 -1.91874751e-05\n",
      " -6.39995415e-06  2.39028101e-04  3.12974626e-05  2.86293143e-05\n",
      "  7.71745799e-05 -8.62326488e-07 -5.14660915e-05  3.51806648e-05]\n"
     ]
    }
   ],
   "source": [
    "model_6 = Gaussian(mean,cov,spatial,ss_loc,dependency=[[]]*900,kernel='RBF',l=0.01)\n",
    "likelihood_6 = model_6.gs_nll_sep(Y.T)\n",
    "print(likelihood_5-likelihood_6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.74951767, 0.73792676, ..., 0.        , 0.        ,\n",
       "        0.        ],\n",
       "       [0.74951767, 1.        , 0.9094827 , ..., 0.        , 0.        ,\n",
       "        0.        ],\n",
       "       [0.73792676, 0.9094827 , 1.        , ..., 0.        , 0.        ,\n",
       "        0.        ],\n",
       "       ...,\n",
       "       [0.        , 0.        , 0.        , ..., 1.        , 0.4159953 ,\n",
       "        0.18284992],\n",
       "       [0.        , 0.        , 0.        , ..., 0.4159953 , 1.        ,\n",
       "        0.08334105],\n",
       "       [0.        , 0.        , 0.        , ..., 0.18284992, 0.08334105,\n",
       "        1.        ]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cov"
   ]
  }
 ],
 "metadata": {
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   "display_name": "biotransfer",
   "language": "python",
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   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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