Learning_r.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
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   },
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "from tensorflow.python.framework import ops\n",
    "from tensorflow.python.ops import gen_nn_ops\n",
    "from tensorflow.python.ops import array_ops\n",
    "from tensorflow.python.ops import control_flow_ops\n",
    "from tensorflow.python.ops import linalg_ops\n",
    "from tensorflow.python.ops import math_ops\n",
    "import networkx as nx\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (<ipython-input-3-aeaa3c06242a>, line 7)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-3-aeaa3c06242a>\"\u001b[0;36m, line \u001b[0;32m7\u001b[0m\n\u001b[0;31m    with ops.control_de pendencies([grad_e.op, grad_v.op]):\u001b[0m\n\u001b[0m                                 ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "@ops.RegisterGradient(\"gradient_no_unitary_adjustment\")\n",
    "def _test1(op, grad_e, grad_v):\n",
    "    \"\"\"Gradient for SelfAdjointEigV2 derived with Joan with no adjustment for subspace\"\"\"\n",
    "    e = op.outputs[0]\n",
    "    v = op.outputs[1]\n",
    "    #dim = v.get_shape()\n",
    "    with ops.control_de pendencies([grad_e.op, grad_v.op]):\n",
    "        if grad_v is not None:  \n",
    "            E = array_ops.diag(e)\n",
    "            #v_proj = arrary.ops.slice(v, [0,0], [])\n",
    "            grad_grassman = grad_v# - math_ops.batch_matmul(math_ops.batch_matmul(v, array_ops.transpose(grad_v)), v)\n",
    "            grad_a = math_ops.batch_matmul(grad_grassman, math_ops.batch_matmul(E, array_ops.transpose(grad_v)))+math_ops.batch_matmul(grad_v, math_ops.batch_matmul(E, array_ops.transpose(grad_grassman)))\n",
    "    return grad_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "@ops.RegisterGradient(\"grassman_with_2d\")\n",
    "def _test1(op, grad_e, grad_v):\n",
    "    \"\"\"Gradient for SelfAdjointEigV2 derived with Joan with no adjustment for subspace\"\"\"\n",
    "    e = op.outputs[0]\n",
    "    v = op.outputs[1]\n",
    "    #dim = v.get_shape()\n",
    "    with ops.control_dependencies([grad_e.op, grad_v.op]):\n",
    "        if grad_v is not None:  \n",
    "            E = array_ops.diag(e)\n",
    "            v_proj = array_ops.slice(v, [0,0], [20,2])\n",
    "            grad_grassman = grad_v - math_ops.batch_matmul(math_ops.batch_matmul(v_proj, array_ops.transpose(v_proj)), grad_v)\n",
    "            grad_a = math_ops.batch_matmul(grad_grassman, math_ops.batch_matmul(E, array_ops.transpose(grad_v)))+math_ops.batch_matmul(grad_v, math_ops.batch_matmul(E, array_ops.transpose(grad_grassman)))\n",
    "    return grad_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def balanced_stochastic_blockmodel(communities=2, groupsize=3, p_in=0.5, p_out=0.1, seed=None):\n",
    "    #gives dense adjacency matrix representaiton of randomly generated SBM with balanced community size\n",
    "\n",
    "    G = nx.planted_partition_graph(l=communities, k=groupsize, p_in=p_in, p_out =p_out, seed=seed)\n",
    "    A = nx.adjacency_matrix(G).todense()\n",
    "    \n",
    "    return A\n",
    "def target_subspace(adj, groupsize, communities, diag, dim_proj):\n",
    "    normalizer = tf.cast(2.0*groupsize*communities, dtype=tf.float64)\n",
    "    total_degree = tf.cast(tf.reduce_sum(adj), dtype=tf.float64)\n",
    "    r = tf.sqrt(total_degree/normalizer)\n",
    "    BH_op = (tf.square(r)-1)*tf.diag(tf.ones(shape=[communities*groupsize], dtype=tf.float64))-r*adj+diag \n",
    "    val, vec = tf.self_adjoint_eig(BH_op) #this is already normalized so no need to normalize\n",
    "    subspace = tf.slice(vec, [0,0], [communities*groupsize, dim_proj])\n",
    "    return r, subspace\n",
    "\n",
    "def proj_magnitude(space, vector):\n",
    "    projection_op = tf.matmul(space, tf.transpose(space))\n",
    "    projection = tf.matmul(projection_op, vector)\n",
    "    return tf.sqrt(tf.reduce_sum(tf.square(projection))) #tf.reduce_sum(tf.abs(projection))#\n",
    "\n",
    "\n",
    "def rnd_vec_normed(communities, groupsize, seed=None):\n",
    "    rnd_vec1 = tf.Variable(tf.random_normal(shape=[communities*groupsize,1], mean=0.0,stddev=1.0,\n",
    "                                                    dtype=tf.float64,\n",
    "                                                    seed=seed))\n",
    "    return normalize_vec(rnd_vec1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Let's create a dataset\n",
    "communities = 2\n",
    "group_size = 10\n",
    "\n",
    "data_easy = [np.asarray(balanced_stochastic_blockmodel(communities, group_size, p, 0.1*p)).astype(np.double) for p in np.linspace(0.2, 0.4,70)]\n",
    "data_hard = [np.asarray(balanced_stochastic_blockmodel(communities, group_size, p, 0.5*p)).astype(np.double) for q in np.linspace(0.2, 0.4,7)]\n",
    "\n",
    "data = data_easy+data_hard\n",
    "np.random.shuffle(data)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
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   "outputs": [
    {
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      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#we need to do online training for now as I cannot write eigendecomposition in batch\n",
    "\n",
    "data[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
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   "outputs": [],
   "source": [
    "def learn_average_deg_variable(communities = 2, group_size = 10, seed_v=None, name='grassman_with_2d', projection_dim=2, \n",
    "                     print_ratio=10, l_rate=0.1, mean=0.3, sd=1.0):\n",
    "    \"\"\"testing to see if the loss will decrease backproping through very simple function\"\"\"\n",
    "    \n",
    "    #now p and q will be generated from a range of \n",
    "    \n",
    "    X = tf.placeholder(dtype=tf.float64, shape=[communities*group_size, communities*group_size])\n",
    "    \n",
    "    B = tf.cast(X, dtype = tf.float64)\n",
    "    \n",
    "    Diag = tf.diag(tf.reduce_sum(B,0))\n",
    "    Diag = tf.cast(Diag, tf.float64)\n",
    "    \n",
    "    #by symmetry I should make this a bit more constrained.  so\n",
    "\n",
    "    v =  tf.Variable(tf.random_normal(shape=[communities*group_size,1], mean=mean,\n",
    "                                 stddev=sd, dtype=tf.float64,\n",
    "                                 seed=seed_v, name=None))\n",
    "    \n",
    "     \n",
    "    \n",
    "    degree = tf.cast(communities*group_size, dtype=tf.float64)\n",
    "    r_param = tf.div(tf.cast(1.0, dtype=tf.float64), degree)*tf.matmul(tf.transpose(v), tf.matmul(Diag, v))\n",
    "\n",
    "    \n",
    "    BH = (tf.square(r_param)-1)*tf.diag(tf.ones(shape=[communities*group_size], dtype=tf.float64))-tf.mul(r_param, B)+Diag \n",
    "    \n",
    "\n",
    "    with tf.Session() as sess:\n",
    "        g = tf.get_default_graph()\n",
    "        \n",
    "        with g.gradient_override_map({'SelfAdjointEigV2': name}):\n",
    "            eigenval, eigenvec = tf.self_adjoint_eig(BH)\n",
    "            #we try to do svm in this subspace \n",
    "            #or we can project it down to 1 dimensions, do the clustering there via some threshold and check if it makes sense \n",
    "            #by computing the loss, if it is too big, we change the angle we project down to...\n",
    "            \n",
    "            \n",
    "            eigenvec_proj = tf.slice(eigenvec, [0,0], [communities*group_size, projection_dim])\n",
    "            \n",
    "            \n",
    "            \n",
    "            true_assignment_a = tf.concat(0, [-1*tf.ones([group_size], dtype=tf.float64),\n",
    "                                      tf.ones([group_size], dtype=tf.float64)])\n",
    "            true_assignment_b = -1*true_assignment_a\n",
    "            true_assignment_a = tf.expand_dims(true_assignment_a, 1)\n",
    "            true_assignment_b = tf.expand_dims(true_assignment_b, 1)\n",
    "\n",
    "            \n",
    "            projected_a = tf.matmul(tf.matmul(eigenvec_proj, tf.transpose(eigenvec_proj)), true_assignment_a)#tf.transpose(true_assignment_a))\n",
    "            projected_b = tf.matmul(tf.matmul(eigenvec_proj, tf.transpose(eigenvec_proj)), true_assignment_b)#tf.transpose(true_assignment_b))\n",
    "            \n",
    "            \n",
    "            \n",
    "            loss = tf.minimum(tf.reduce_sum(tf.square(tf.sub(projected_a, true_assignment_a))),\n",
    "                              tf.reduce_sum(tf.square(tf.sub(projected_b, true_assignment_b))))\n",
    "            \n",
    "            optimizer = tf.train.GradientDescentOptimizer(l_rate)\n",
    "            \n",
    "            train = optimizer.minimize(loss, var_list=[v])\n",
    "\n",
    "            eigenvec_grad = tf.gradients(eigenvec, v)\n",
    "            loss_grad = tf.gradients(loss, v)\n",
    "            \n",
    "            \n",
    "            \n",
    "            r_op, target = target_subspace(adj=B, groupsize=group_size, communities=communities, diag=Diag, dim_proj=projection_dim)  \n",
    "            \n",
    "            r_op_projection_a = tf.matmul(tf.matmul(target, tf.transpose(target)), true_assignment_a)\n",
    "            r_op_projection_b = tf.matmul(tf.matmul(target, tf.transpose(target)), true_assignment_b)\n",
    "            r_op_loss = tf.minimum(tf.reduce_sum(tf.square(tf.sub(r_op_projection_a, true_assignment_a))),\n",
    "                              tf.reduce_sum(tf.square(tf.sub(r_op_projection_b, true_assignment_b))))\n",
    "            \n",
    "            init = tf.initialize_all_variables()\n",
    "            \n",
    "            \n",
    "            sess.run(init)\n",
    "            sess.run(train, feed_dict={X:data[0]})\n",
    "            a,r, b,c,d= sess.run([v, r_param, r_op_loss, r_op, tf.transpose(r_op_projection_a)], feed_dict={X:data[0]})\n",
    "            a_lst = []\n",
    "            r_lst = []\n",
    "            b_lst = []\n",
    "            c_lst = []\n",
    "            d_lst = []\n",
    "            \n",
    "            a_lst.append(a)\n",
    "            r_lst.append(r)\n",
    "            b_lst.append(b)\n",
    "            c_lst.append(None)\n",
    "            d_lst.append(d)\n",
    "            \n",
    "            print \"initial v: {}. r_param: {}. r_op = sqrt(average degree) : {} . Loss associated with r_op: {}. r_op assignments {}.\".format(a, r, c, b, d)\n",
    "            for i in range(len(data)):   \n",
    "                try:\n",
    "                    sess.run(feed_dict={X:data[i]})\n",
    "                    sess.run(train)\n",
    "                except: \n",
    "                    pass\n",
    "                \n",
    "                if i%print_ratio==0:  \n",
    "                    #print i\n",
    "                    try:\n",
    "                        a,r, b,c,d = sess.run([v, r_param, loss, tf.gradients(loss, v), tf.transpose(projected_a)], feed_dict={X:data[i]}) \n",
    "                        a_lst.append(a)\n",
    "                        r_lst.append(r)\n",
    "                        b_lst.append(b)\n",
    "                        c_lst.append(c)\n",
    "                        d_lst.append(d)\n",
    "                    except:\n",
    "                        a,r, b,c,d = None, None, None, None, None \n",
    "                        a_lst.append(a)\n",
    "                        r_lst.append(r)\n",
    "                        b_lst.append(b)\n",
    "                        c_lst.append(c)\n",
    "                        d_lst.append(d)\n",
    "                    #print \"current r: {}, current loss: {}, gradient of loss/r is {} and current assignments (up to sign) {}.\".format(a,b,c,d)  \n",
    "\n",
    "    d = {\"v\": a_lst, \"r_param\": r_lst, \"loss\": b_lst, \"gradient_loss_v\": c_lst, \"projection\": d_lst}\n",
    "    d = pd.DataFrame(d)\n",
    "    d.to_csv(\"/Users/xiangli/Desktop/clusternet/Learning_r_matrix_data/r{}rate{}p{}q{}step{}.csv\".format(mean, l_rate, p, q, print_ratio))\n",
    "    return  d\n",
    "                \n",
    "\n",
    "                \n",
    "                "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
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   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-63-ef734265e48d>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mlearn_average_deg_variable\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprint_ratio\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'grassman_with_2d'\u001b[0m\u001b[0;34m,\u001b[0m  \u001b[0ml_rate\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.00001\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmean\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.01\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m<ipython-input-62-371a578ab198>\u001b[0m in \u001b[0;36mlearn_average_deg_variable\u001b[0;34m(communities, group_size, seed, seed_v, name, projection_dim, print_ratio, l_rate, mean, sd)\u001b[0m\n\u001b[1;32m     75\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     76\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 77\u001b[0;31m             \u001b[0msess\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minit\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     78\u001b[0m             \u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mc\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0md\u001b[0m\u001b[0;34m=\u001b[0m \u001b[0msess\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mr_param\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mr_op_loss\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mr_op\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtranspose\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mr_op_projection_a\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfeed_dict\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m{\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     79\u001b[0m             \u001b[0ma_lst\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/xiangli/anaconda/lib/python2.7/site-packages/tensorflow/python/client/session.pyc\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self, fetches, feed_dict, options, run_metadata)\u001b[0m\n\u001b[1;32m    715\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    716\u001b[0m       result = self._run(None, fetches, feed_dict, options_ptr,\n\u001b[0;32m--> 717\u001b[0;31m                          run_metadata_ptr)\n\u001b[0m\u001b[1;32m    718\u001b[0m       \u001b[0;32mif\u001b[0m \u001b[0mrun_metadata\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    719\u001b[0m         \u001b[0mproto_data\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtf_session\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mTF_GetBuffer\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrun_metadata_ptr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/xiangli/anaconda/lib/python2.7/site-packages/tensorflow/python/client/session.pyc\u001b[0m in \u001b[0;36m_run\u001b[0;34m(self, handle, fetches, feed_dict, options, run_metadata)\u001b[0m\n\u001b[1;32m    913\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mfinal_fetches\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mfinal_targets\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    914\u001b[0m       results = self._do_run(handle, final_targets, final_fetches,\n\u001b[0;32m--> 915\u001b[0;31m                              feed_dict_string, options, run_metadata)\n\u001b[0m\u001b[1;32m    916\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    917\u001b[0m       \u001b[0mresults\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/xiangli/anaconda/lib/python2.7/site-packages/tensorflow/python/client/session.pyc\u001b[0m in \u001b[0;36m_do_run\u001b[0;34m(self, handle, target_list, fetch_list, feed_dict, options, run_metadata)\u001b[0m\n\u001b[1;32m    963\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mhandle\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    964\u001b[0m       return self._do_call(_run_fn, self._session, feed_dict, fetch_list,\n\u001b[0;32m--> 965\u001b[0;31m                            target_list, options, run_metadata)\n\u001b[0m\u001b[1;32m    966\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    967\u001b[0m       return self._do_call(_prun_fn, self._session, handle, feed_dict,\n",
      "\u001b[0;32m/Users/xiangli/anaconda/lib/python2.7/site-packages/tensorflow/python/client/session.pyc\u001b[0m in \u001b[0;36m_do_call\u001b[0;34m(self, fn, *args)\u001b[0m\n\u001b[1;32m    970\u001b[0m   \u001b[0;32mdef\u001b[0m \u001b[0m_do_call\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    971\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 972\u001b[0;31m       \u001b[0;32mreturn\u001b[0m \u001b[0mfn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    973\u001b[0m     \u001b[0;32mexcept\u001b[0m \u001b[0merrors\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mOpError\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    974\u001b[0m       \u001b[0mmessage\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcompat\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mas_text\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0me\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmessage\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/xiangli/anaconda/lib/python2.7/site-packages/tensorflow/python/client/session.pyc\u001b[0m in \u001b[0;36m_run_fn\u001b[0;34m(session, feed_dict, fetch_list, target_list, options, run_metadata)\u001b[0m\n\u001b[1;32m    948\u001b[0m                 run_metadata):\n\u001b[1;32m    949\u001b[0m       \u001b[0;31m# Ensure any changes to the graph are reflected in the runtime.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 950\u001b[0;31m       \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_extend_graph\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    951\u001b[0m       \u001b[0;32mwith\u001b[0m \u001b[0merrors\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mraise_exception_on_not_ok_status\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mstatus\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    952\u001b[0m         return tf_session.TF_Run(session, options,\n",
      "\u001b[0;32m/Users/xiangli/anaconda/lib/python2.7/site-packages/tensorflow/python/client/session.pyc\u001b[0m in \u001b[0;36m_extend_graph\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    992\u001b[0m         graph_def, self._current_version = self._graph._as_graph_def(\n\u001b[1;32m    993\u001b[0m             \u001b[0mfrom_version\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_current_version\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 994\u001b[0;31m             add_shapes=self._add_shapes)\n\u001b[0m\u001b[1;32m    995\u001b[0m         \u001b[0;31m# pylint: enable=protected-access\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    996\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/xiangli/anaconda/lib/python2.7/site-packages/tensorflow/python/framework/ops.pyc\u001b[0m in \u001b[0;36m_as_graph_def\u001b[0;34m(self, from_version, add_shapes)\u001b[0m\n\u001b[1;32m   2204\u001b[0m         \u001b[0mop\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_nodes_by_id\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mop_id\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2205\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mfrom_version\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0mNone\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mop_id\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0mfrom_version\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2206\u001b[0;31m           \u001b[0mgraph\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnode\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mextend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mop\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnode_def\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2207\u001b[0m           \u001b[0;32mif\u001b[0m \u001b[0mop\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0moutputs\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0madd_shapes\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2208\u001b[0m             \u001b[0;32massert\u001b[0m \u001b[0;34m\"_output_shapes\"\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mgraph\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnode\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mattr\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/xiangli/anaconda/lib/python2.7/site-packages/google/protobuf/internal/containers.pyc\u001b[0m in \u001b[0;36mextend\u001b[0;34m(self, elem_seq)\u001b[0m\n\u001b[1;32m    387\u001b[0m       \u001b[0mnew_element\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmessage_class\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    388\u001b[0m       \u001b[0mnew_element\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_SetListener\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlistener\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 389\u001b[0;31m       \u001b[0mnew_element\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mMergeFrom\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmessage\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    390\u001b[0m       \u001b[0mvalues\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnew_element\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    391\u001b[0m     \u001b[0mlistener\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mModified\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/xiangli/anaconda/lib/python2.7/site-packages/google/protobuf/internal/python_message.pyc\u001b[0m in \u001b[0;36mMergeFrom\u001b[0;34m(self, msg)\u001b[0m\n\u001b[1;32m   1249\u001b[0m           \u001b[0mfield_value\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfield\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_default_constructor\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1250\u001b[0m           \u001b[0mfields\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mfield\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfield_value\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1251\u001b[0;31m         \u001b[0mfield_value\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mMergeFrom\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvalue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1252\u001b[0m       \u001b[0;32melif\u001b[0m \u001b[0mfield\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcpp_type\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mCPPTYPE_MESSAGE\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1253\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_is_present_in_parent\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/xiangli/anaconda/lib/python2.7/site-packages/google/protobuf/internal/containers.pyc\u001b[0m in \u001b[0;36mMergeFrom\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m    595\u001b[0m   \u001b[0;32mdef\u001b[0m \u001b[0mMergeFrom\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    596\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0mkey\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 597\u001b[0;31m       \u001b[0mself\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mMergeFrom\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    598\u001b[0m     \u001b[0;31m# self._message_listener.Modified() not required here, because\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    599\u001b[0m     \u001b[0;31m# mutations to submessages already propagate.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/xiangli/anaconda/lib/python2.7/site-packages/google/protobuf/internal/containers.pyc\u001b[0m in \u001b[0;36m__getitem__\u001b[0;34m(self, key)\u001b[0m\n\u001b[1;32m    544\u001b[0m     \u001b[0;32mexcept\u001b[0m \u001b[0mKeyError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    545\u001b[0m       \u001b[0mkey\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_key_checker\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mCheckValue\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 546\u001b[0;31m       \u001b[0mnew_element\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_message_descriptor\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_concrete_class\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    547\u001b[0m       \u001b[0mnew_element\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_SetListener\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_message_listener\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    548\u001b[0m       \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_values\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnew_element\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Users/xiangli/anaconda/lib/python2.7/site-packages/google/protobuf/internal/python_message.pyc\u001b[0m in \u001b[0;36minit\u001b[0;34m(self, **kwargs)\u001b[0m\n\u001b[1;32m    484\u001b[0m     \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_unknown_fields\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    485\u001b[0m     \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_is_present_in_parent\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mFalse\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 486\u001b[0;31m     \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_listener\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmessage_listener_mod\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mNullMessageListener\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    487\u001b[0m     \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_listener_for_children\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_Listener\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    488\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0mfield_name\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfield_value\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "learn_average_deg_variable(print_ratio=1, name='grassman_with_2d',  l_rate=0.00001, mean=0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Let's create a dataset\n",
    "communities = 2\n",
    "group_size = 10\n",
    "\n",
    "data_easy = [np.asarray(balanced_stochastic_blockmodel(communities, group_size, p, 0.1*p)).astype(np.double) for p in np.linspace(0.1, 0.3,50)]\n",
    "data_hard = [np.asarray(balanced_stochastic_blockmodel(communities, group_size, p, 0.5*p)).astype(np.double) for q in np.linspace(0.1, 0.3,5)]\n",
    "\n",
    "#data = data_easy+data_hard\n",
    "np.random.shuffle(data)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def learn_average_deg_variable(communities = 2, group_size = 10, seed_v=None, projection_dim=2, print_ratio=10, l_rate=0.00000001, mean=0.3, sd=0.1):\n",
    "    \"\"\"testing to see if the loss will decrease backproping through very simple function\"\"\"\n",
    "    \n",
    "    #now p and q will be generated from a range of \n",
    "    \n",
    "    X = tf.placeholder(dtype=tf.float64, shape=[communities*group_size, communities*group_size])\n",
    "    \n",
    "    B = tf.cast(X, dtype = tf.float64)\n",
    "    \n",
    "    Diag = tf.diag(tf.reduce_sum(B,0))\n",
    "    Diag = tf.cast(Diag, tf.float64)\n",
    "    \n",
    "    #by symmetry I should make this a bit more constrained.  so\n",
    "\n",
    "    v =  tf.Variable(tf.random_normal(shape=[communities*group_size,1], mean=mean,\n",
    "                                 stddev=sd, dtype=tf.float64,\n",
    "                                 seed=seed_v, name=None))\n",
    "    v_sqr = tf.square(v)\n",
    "    \n",
    "     \n",
    "    \n",
    "    degree = tf.cast(communities*group_size, dtype=tf.float64)\n",
    "    r_param = tf.div(tf.cast(1.0, dtype=tf.float64), degree)*tf.matmul(tf.transpose(v_sqr), tf.matmul(Diag, v_sqr))\n",
    "\n",
    "    \n",
    "    BH = (tf.square(r_param)-1)*tf.diag(tf.ones(shape=[communities*group_size], dtype=tf.float64))-tf.mul(r_param, B)+Diag \n",
    "    \n",
    "\n",
    "    with tf.Session() as sess:\n",
    "        g = tf.get_default_graph()\n",
    "        \n",
    "        with g.gradient_override_map({'SelfAdjointEigV2': 'grassman_with_2d'}):\n",
    "            eigenval, eigenvec = tf.self_adjoint_eig(BH)\n",
    "            #we try to do svm in this subspace \n",
    "            #or we can project it down to 1 dimensions, do the clustering there via some threshold and check if it makes sense \n",
    "            #by computing the loss, if it is too big, we change the angle we project down to...\n",
    "            \n",
    "            \n",
    "            eigenvec_proj = tf.slice(eigenvec, [0,0], [communities*group_size, projection_dim])\n",
    "            \n",
    "            \n",
    "            \n",
    "            true_assignment_a = tf.concat(0, [-1*tf.ones([group_size], dtype=tf.float64),\n",
    "                                      tf.ones([group_size], dtype=tf.float64)])\n",
    "            true_assignment_b = -1*true_assignment_a\n",
    "            true_assignment_a = tf.expand_dims(true_assignment_a, 1)\n",
    "            true_assignment_b = tf.expand_dims(true_assignment_b, 1)\n",
    "\n",
    "            \n",
    "            projected_a = tf.matmul(tf.matmul(eigenvec_proj, tf.transpose(eigenvec_proj)), true_assignment_a)#tf.transpose(true_assignment_a))\n",
    "            projected_b = tf.matmul(tf.matmul(eigenvec_proj, tf.transpose(eigenvec_proj)), true_assignment_b)#tf.transpose(true_assignment_b))\n",
    "            \n",
    "            \n",
    "            \n",
    "            loss = tf.minimum(tf.reduce_sum(tf.square(tf.sub(projected_a, true_assignment_a))),\n",
    "                              tf.reduce_sum(tf.square(tf.sub(projected_b, true_assignment_b))))\n",
    "            \n",
    "            optimizer = tf.train.AdamOptimizer(l_rate)\n",
    "            \n",
    "            train = optimizer.minimize(loss, var_list=[v])\n",
    "\n",
    "            eigenvec_grad = tf.gradients(eigenvec, v)\n",
    "            loss_grad = tf.gradients(loss, v)\n",
    "            \n",
    "            r_op, target = target_subspace(adj=B, groupsize=group_size, communities=communities, diag=Diag, dim_proj=projection_dim)\n",
    "            r_diff = (r_op-r_param) #difference between r_op and r_param is how close we are to the average degree\n",
    "            \n",
    "            \n",
    "            init = tf.initialize_all_variables()\n",
    "            \n",
    "            \n",
    "            sess.run(init)\n",
    "            a,r, b= sess.run([v, r_param, r_diff], feed_dict={X:data[0]})\n",
    "            a_lst = []\n",
    "            r_lst = []\n",
    "            r_diff_list = []\n",
    "            b_lst = []\n",
    "            c_lst = []\n",
    "            d_lst = []\n",
    "            \n",
    "            a_lst.append(a)\n",
    "            r_lst.append(r)\n",
    "            r_diff_list.append(b)\n",
    "            b_lst.append(None)\n",
    "            c_lst.append(None)\n",
    "            d_lst.append(None)\n",
    "            \n",
    "            print \"initial v: {}. r_param: {}, difference between r_param and sqrt average deg {}.\".format(a, r, b)\n",
    "            for i in range(len(data)):   \n",
    "                try:\n",
    "                    sess.run(train, feed_dict={X:data[i]})\n",
    "                    #if i%print_ratio==0:  \n",
    "                    #print i\n",
    "                        #try:\n",
    "                    a,r, k, b,c,d = sess.run([v, r_param, r_diff, loss, tf.gradients(loss, v), tf.transpose(projected_a)], feed_dict={X:data[i]}) \n",
    "                    a_lst.append(a)\n",
    "                    r_lst.append(r)\n",
    "                    r_diff_list.append(k)\n",
    "                    b_lst.append(b)\n",
    "                    c_lst.append(c)\n",
    "                    d_lst.append(d)\n",
    "                    \n",
    "                            \n",
    "                except: \n",
    "                    a,r, k, b,c,d = None, None, None, None, None, None \n",
    "                    a_lst.append(a)\n",
    "                    r_lst.append(r)\n",
    "                    r_diff_list.append(k)\n",
    "                    b_lst.append(b)\n",
    "                    c_lst.append(c)\n",
    "                    d_lst.append(d)\n",
    "                    pass\n",
    "                \n",
    "\n",
    "                    #print \"current r: {}, current loss: {}, gradient of loss/r is {} and current assignments (up to sign) {}.\".format(a,b,c,d)  \n",
    "\n",
    "    d = {\"v\": a_lst, \"r_param\": r_lst, \"r_diff\": r_diff_list, \"loss\": b_lst, \"gradient_loss_v\": c_lst, \"projection\": d_lst}\n",
    "    d = pd.DataFrame(d)\n",
    "    easy_size = len(data)\n",
    "    d.to_csv(\"/Users/xiangli/Desktop/clusternet/Learning_r_matrix_data/mean{}l_rate{}step{}data_size{}.csv\".format(mean, l_rate, print_ratio, easy_size))\n",
    "    return  d\n",
    "                "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#data = data+data+data+data\n",
    "#np.random.shuffle(data)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "initial v: [[ 0.33278568]\n",
      " [ 0.40563987]\n",
      " [ 0.48760857]\n",
      " [ 0.21069585]\n",
      " [ 0.09485482]\n",
      " [ 0.27115713]\n",
      " [ 0.46239166]\n",
      " [ 0.32648871]\n",
      " [ 0.47354541]\n",
      " [ 0.28008422]\n",
      " [ 0.17787136]\n",
      " [ 0.281964  ]\n",
      " [ 0.27863064]\n",
      " [ 0.50821174]\n",
      " [ 0.36968949]\n",
      " [ 0.21332368]\n",
      " [ 0.43487074]\n",
      " [ 0.28825561]\n",
      " [ 0.22069374]\n",
      " [ 0.15399564]]. r_param: [[ 0.03601875]], difference between r_param and sqrt average deg [[ 0.88593569]].\n"
     ]
    },
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>gradient_loss_v</th>\n",
       "      <th>loss</th>\n",
       "      <th>projection</th>\n",
       "      <th>r_diff</th>\n",
       "      <th>r_param</th>\n",
       "      <th>v</th>\n",
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       "      <td>[[0.908844763879]]</td>\n",
       "      <td>[[0.0131096818504]]</td>\n",
       "      <td>[[0.232785689119], [0.305639878578], [0.387608...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>[[[0.276727279016], [0.91040992538], [0.0], [0...</td>\n",
       "      <td>17.994715</td>\n",
       "      <td>[[1.8336051726e-15, 1.29135422539e-15, -1.0, 2...</td>\n",
       "      <td>[[1.09021450378]]</td>\n",
       "      <td>[[0.00523061122638]]</td>\n",
       "      <td>[[0.142644314213], [0.212153142486], [0.320602...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>[[[-4.71235516682e-12], [-2.21382332671e-11], ...</td>\n",
       "      <td>15.985191</td>\n",
       "      <td>[[-6.89865205893e-10, -9.17816299371e-10, -0.0...</td>\n",
       "      <td>[[1.15987636616]]</td>\n",
       "      <td>[[0.00201863769827]]</td>\n",
       "      <td>[[0.072965017458], [0.139887881018], [0.268807...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>[[[0.000793670266822], [0.0966187306958], [0.8...</td>\n",
       "      <td>17.997046</td>\n",
       "      <td>[[-2.00371086751e-10, -9.99218805376e-11, -0.0...</td>\n",
       "      <td>[[1.11729791742]]</td>\n",
       "      <td>[[0.000736071326968]]</td>\n",
       "      <td>[[0.0137247402961], [0.0748670613236], [0.2218...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>[[[1.93471720866e-15], [-4.23978983044e-16], [...</td>\n",
       "      <td>17.270838</td>\n",
       "      <td>[[2.58006073159e-18, 4.40591554232e-15, 3.3099...</td>\n",
       "      <td>[[1.18254423931]]</td>\n",
       "      <td>[[0.000671717310256]]</td>\n",
       "      <td>[[-0.0363468361048], [0.0199096050621], [0.182...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>[[[-0.0], [-0.00614487609122], [0.23322657962]...</td>\n",
       "      <td>18.456797</td>\n",
       "      <td>[[0.0, 5.09763363833e-22, -9.80267452651e-17, ...</td>\n",
       "      <td>[[0.921738214932]]</td>\n",
       "      <td>[[0.000216230797665]]</td>\n",
       "      <td>[[-0.0795020127338], [-0.0274769240511], [0.14...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>[[[1.2625584945e-07], [3.84213922233e-08], [-1...</td>\n",
       "      <td>17.998956</td>\n",
       "      <td>[[-6.00353717975e-11, -0.000391631636956, -9.4...</td>\n",
       "      <td>[[1.22396191465]]</td>\n",
       "      <td>[[0.000782956744689]]</td>\n",
       "      <td>[[-0.117189691079], [-0.0688598680645], [0.115...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>[[[1.10202365149e-05], [3.24473943292e-06], [-...</td>\n",
       "      <td>18.000083</td>\n",
       "      <td>[[0.000286206587598, 1.40425981494e-08, -8.428...</td>\n",
       "      <td>[[1.49828184585]]</td>\n",
       "      <td>[[0.00171815415115]]</td>\n",
       "      <td>[[-0.150413684148], [-0.105341439584], [0.0882...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>[[[1.81823012462e-05], [1.35959202279e-05], [-...</td>\n",
       "      <td>17.996688</td>\n",
       "      <td>[[-1.49240444399e-09, -0.000824537460295, -1.7...</td>\n",
       "      <td>[[1.22144945049]]</td>\n",
       "      <td>[[0.00329542089926]]</td>\n",
       "      <td>[[-0.179907855374], [-0.13772743612], [0.06400...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>[[[-0.36900616545], [-0.399266720399], [0.0101...</td>\n",
       "      <td>16.992304</td>\n",
       "      <td>[[-1.93195920567e-15, 2.8718044269e-17, 6.7739...</td>\n",
       "      <td>[[0.998074108798]]</td>\n",
       "      <td>[[0.00192589120196]]</td>\n",
       "      <td>[[-0.202129515694], [-0.164700999041], [0.0422...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>[[[-0.0251305824806], [-0.00620438493764], [1....</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>[[-2.37788745356e-17, 2.11444222816e-16, -7.60...</td>\n",
       "      <td>[[0.997740685947]]</td>\n",
       "      <td>[[0.00225931405277]]</td>\n",
       "      <td>[[-0.221801022215], [-0.188846499722], [0.0227...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>[[[-2.9865061304], [-3.34717031751], [2.037753...</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>[[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,...</td>\n",
       "      <td>[[1.04756014398]]</td>\n",
       "      <td>[[0.00124870418852]]</td>\n",
       "      <td>[[-0.19199711509], [-0.18119794082], [0.005252...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>[[[2.60049749422], [2.62256525634], [0.0004514...</td>\n",
       "      <td>17.988225</td>\n",
       "      <td>[[5.32235620988e-09, 6.67475459286e-09, 2.6888...</td>\n",
       "      <td>[[1.30132623916]]</td>\n",
       "      <td>[[0.00251424188514]]</td>\n",
       "      <td>[[-0.189044220702], [-0.189577456832], [-0.010...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>[[[1.29059250441e-05], [2.29129895142e-05], [3...</td>\n",
       "      <td>17.993141</td>\n",
       "      <td>[[-5.25122956564e-09, -2.49652887663e-06, 1.13...</td>\n",
       "      <td>[[1.28136733797]]</td>\n",
       "      <td>[[0.00315591989999]]</td>\n",
       "      <td>[[-0.186376589205], [-0.197147744394], [-0.024...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>[[[-6.05184833639e-06], [-2.47573184696e-05], ...</td>\n",
       "      <td>16.984871</td>\n",
       "      <td>[[-1.00300927815, -3.48526681192e-09, -1.00300...</td>\n",
       "      <td>[[1.11500626639]]</td>\n",
       "      <td>[[0.00302772235809]]</td>\n",
       "      <td>[[-0.183962408714], [-0.203998602205], [-0.037...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>[[[-0.346420571758], [-1.01978246694], [-0.029...</td>\n",
       "      <td>18.003148</td>\n",
       "      <td>[[0.00314671042677, 1.04464112646e-17, 5.53037...</td>\n",
       "      <td>[[1.09229345119]]</td>\n",
       "      <td>[[0.00315166381678]]</td>\n",
       "      <td>[[-0.178801560005], [-0.20338984279], [-0.0494...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>[[[-0.227751294072], [-0.692559110748], [-0.02...</td>\n",
       "      <td>16.992467</td>\n",
       "      <td>[[-3.99468631194e-15, 4.4358734792e-18, 5.4481...</td>\n",
       "      <td>[[0.998114983804]]</td>\n",
       "      <td>[[0.00188501619608]]</td>\n",
       "      <td>[[-0.172093368933], [-0.197888004516], [-0.059...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>[[[-0.0], [-3.62800394736], [-0.0], [0.0], [0....</td>\n",
       "      <td>17.305732</td>\n",
       "      <td>[[-1.0, -3.90948375763e-20, -0.487275783999, -...</td>\n",
       "      <td>[[1.04676882987]]</td>\n",
       "      <td>[[0.00204001830174]]</td>\n",
       "      <td>[[-0.166001339602], [-0.168563883834], [-0.069...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>[[[-0.734928891933], [-0.0], [-0.240993357531]...</td>\n",
       "      <td>17.996365</td>\n",
       "      <td>[[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,...</td>\n",
       "      <td>[[0.893991566455]]</td>\n",
       "      <td>[[0.000435624545014]]</td>\n",
       "      <td>[[-0.153031179364], [-0.141912821732], [-0.077...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>[[[-0.164884130329], [-0.188026677426], [-0.14...</td>\n",
       "      <td>18.000642</td>\n",
       "      <td>[[0.000641587319812, -2.4156677636e-17, 9.5765...</td>\n",
       "      <td>[[1.0948033217]]</td>\n",
       "      <td>[[0.000641793309284]]</td>\n",
       "      <td>[[-0.139482772734], [-0.115662021389], [-0.084...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>[[[0.532916736445], [0.408017682959], [0.17825...</td>\n",
       "      <td>16.998722</td>\n",
       "      <td>[[-1.00023906473, -0.000320395908978, -1.00007...</td>\n",
       "      <td>[[1.18257542077]]</td>\n",
       "      <td>[[0.000640535853812]]</td>\n",
       "      <td>[[-0.132296900185], [-0.0960608027947], [-0.09...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>[[[0.137711162062], [0.0325857317742], [0.1065...</td>\n",
       "      <td>17.997634</td>\n",
       "      <td>[[7.91684554067e-11, 2.36784169188e-10, 1.4074...</td>\n",
       "      <td>[[1.3030189418]]</td>\n",
       "      <td>[[0.00082153923723]]</td>\n",
       "      <td>[[-0.127037489272], [-0.0785750525861], [-0.09...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>[[[-0.168336338574], [-0.0], [-0.319495745188]...</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>[[2.82541051002e-22, -1.0, 4.39844828051e-19, ...</td>\n",
       "      <td>[[0.921382057232]]</td>\n",
       "      <td>[[0.000572388497371]]</td>\n",
       "      <td>[[-0.120615113606], [-0.0626540562527], [-0.10...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>[[[-0.293811196719], [-0.0155023489135], [-0.2...</td>\n",
       "      <td>17.999011</td>\n",
       "      <td>[[6.00638694098e-14, 9.70040207513e-11, 8.6789...</td>\n",
       "      <td>[[1.20316979076]]</td>\n",
       "      <td>[[0.000989667119754]]</td>\n",
       "      <td>[[-0.111665425859], [-0.047943036256], [-0.107...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>[[[-0.000143241493009], [-7.98478884579e-06], ...</td>\n",
       "      <td>15.998045</td>\n",
       "      <td>[[3.61059767148e-08, -0.00072228659385, -1.000...</td>\n",
       "      <td>[[1.02397314254]]</td>\n",
       "      <td>[[0.000721934059458]]</td>\n",
       "      <td>[[-0.103511521137], [-0.0345427150487], [-0.11...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>[[[1.07851977503e-07], [1.35468280316e-09], [4...</td>\n",
       "      <td>17.998545</td>\n",
       "      <td>[[5.16011535396e-15, 1.92430625286e-11, 6.4076...</td>\n",
       "      <td>[[1.26418466553]]</td>\n",
       "      <td>[[0.00072639853587]]</td>\n",
       "      <td>[[-0.0960832454104], [-0.0223349078817], [-0.1...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>[[[-0.0987374353011], [-0.000269453901918], [-...</td>\n",
       "      <td>15.997506</td>\n",
       "      <td>[[-3.88983101624e-07, -2.75904537643e-13, -1.2...</td>\n",
       "      <td>[[1.0481853702]]</td>\n",
       "      <td>[[0.000623477967001]]</td>\n",
       "      <td>[[-0.0882050698451], [-0.0111990585248], [-0.1...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>[[[-0.0235830104221], [-1.0431314024e-07], [-0...</td>\n",
       "      <td>16.998602</td>\n",
       "      <td>[[-6.00765103638e-16, 1.02636981398e-17, 2.472...</td>\n",
       "      <td>[[0.999650490688]]</td>\n",
       "      <td>[[0.000349509312048]]</td>\n",
       "      <td>[[-0.0807561724201], [-0.00105215321591], [-0....</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>[[[1.44569669447e-15], [-4.91123325929e-18], [...</td>\n",
       "      <td>17.998380</td>\n",
       "      <td>[[-4.35697094445e-17, -2.71351510175e-15, -1.0...</td>\n",
       "      <td>[[1.11762916663]]</td>\n",
       "      <td>[[0.000404822115875]]</td>\n",
       "      <td>[[-0.0739692634888], [0.00819298983526], [-0.1...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>191</th>\n",
       "      <td>[[[4.15983579603e-05], [3.0193422125e-05], [-4...</td>\n",
       "      <td>17.000000</td>\n",
       "      <td>[[4.16312693138e-17, -2.6302272772e-14, 1.9082...</td>\n",
       "      <td>[[0.974679354849]]</td>\n",
       "      <td>[[7.96321967064e-08]]</td>\n",
       "      <td>[[0.00774323994016], [0.00876754692996], [-0.0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>192</th>\n",
       "      <td>[[[4.45019555392e-05], [0.0], [-0.000297985928...</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>[[1.69001936728e-24, -1.0, -4.86409097057e-23,...</td>\n",
       "      <td>[[0.921954358519]]</td>\n",
       "      <td>[[8.7210125764e-08]]</td>\n",
       "      <td>[[0.00773931700679], [0.00876280514868], [-0.0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>193</th>\n",
       "      <td>[[[0.000324956978155], [0.000283343661952], [-...</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>[[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,...</td>\n",
       "      <td>[[1.04880871572]]</td>\n",
       "      <td>[[1.32446211657e-07]]</td>\n",
       "      <td>[[0.0077283079389], [0.00875379852244], [-0.01...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>194</th>\n",
       "      <td>[[[0.0], [0.0], [-4.34600818428e-05], [-9.4044...</td>\n",
       "      <td>17.364424</td>\n",
       "      <td>[[0.0, 0.0, -1.72858731204e-56, -1.20294431517...</td>\n",
       "      <td>[[0.806225731619]]</td>\n",
       "      <td>[[4.32109700902e-08]]</td>\n",
       "      <td>[[0.00771837157738], [0.00874566948779], [-0.0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>195</th>\n",
       "      <td>[[[2.25311904729e-05], [3.28111392295e-05], [-...</td>\n",
       "      <td>18.975090</td>\n",
       "      <td>[[-1.1969035698e-23, -2.47150714836e-16, -9.36...</td>\n",
       "      <td>[[0.974679349174]]</td>\n",
       "      <td>[[8.5306634148e-08]]</td>\n",
       "      <td>[[0.00770819058782], [0.00873705026879], [-0.0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>196</th>\n",
       "      <td>[[[-7.17520409792e-19], [-1.04583923156e-18], ...</td>\n",
       "      <td>18.534813</td>\n",
       "      <td>[[-2.34423983355e-17, -3.07987251227e-16, -3.4...</td>\n",
       "      <td>[[1.26491096918]]</td>\n",
       "      <td>[[9.48907861638e-08]]</td>\n",
       "      <td>[[0.00769900186065], [0.00872927109846], [-0.0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>197</th>\n",
       "      <td>[[[3.78332387075e-05], [5.51912038846e-05], [-...</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>[[-9.3594149779e-58, -2.38299102249e-26, 6.916...</td>\n",
       "      <td>[[0.921954400182]]</td>\n",
       "      <td>[[4.55477884536e-08]]</td>\n",
       "      <td>[[0.00768983002928], [0.00872131935188], [-0.0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>198</th>\n",
       "      <td>[[[-7.87981013266e-19], [-3.45115165954e-18], ...</td>\n",
       "      <td>17.743194</td>\n",
       "      <td>[[9.11242893629e-23, 6.9983831061e-18, 3.50981...</td>\n",
       "      <td>[[1.44913746346]]</td>\n",
       "      <td>[[2.11161328675e-07]]</td>\n",
       "      <td>[[0.00768155231834], [0.00871414278515], [-0.0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>199</th>\n",
       "      <td>[[[0.0], [4.64686506364e-05], [-3.58152042316e...</td>\n",
       "      <td>17.000000</td>\n",
       "      <td>[[-1.0, 1.4848358026e-17, -1.00000000143, -0.9...</td>\n",
       "      <td>[[0.94868316487]]</td>\n",
       "      <td>[[1.33180988177e-07]]</td>\n",
       "      <td>[[0.00767408165929], [0.00870687798995], [-0.0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>200</th>\n",
       "      <td>[[[-4.71933267706e-20], [-2.29842946199e-20], ...</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>[[-1.18901680233e-22, -1.0000000902, -2.310717...</td>\n",
       "      <td>[[1.14017533547]]</td>\n",
       "      <td>[[8.96296807181e-08]]</td>\n",
       "      <td>[[0.00766733945213], [0.00870032157318], [-0.0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>201</th>\n",
       "      <td>[[[0.0], [9.24880791954e-05], [-0.000142647078...</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>[[-1.0, -3.39484876493e-26, 5.55111512314e-17,...</td>\n",
       "      <td>[[0.92195433363]]</td>\n",
       "      <td>[[1.12099413805e-07]]</td>\n",
       "      <td>[[0.00766125474175], [0.00869282750087], [-0.0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>202</th>\n",
       "      <td>[[[-1.6871467053e-17], [-2.11207657742e-17], [...</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>[[3.09861982296e-08, 2.27739112113e-16, -7.977...</td>\n",
       "      <td>[[1.49999981408]]</td>\n",
       "      <td>[[1.85917200076e-07]]</td>\n",
       "      <td>[[0.00765576347736], [0.00868606433059], [-0.0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>203</th>\n",
       "      <td>[[[9.16396680916e-05], [0.0], [-0.000206592893...</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>[[4.92180377241e-23, -1.0, -1.31555286067e-16,...</td>\n",
       "      <td>[[0.948683220774]]</td>\n",
       "      <td>[[7.72769381801e-08]]</td>\n",
       "      <td>[[0.00764864547054], [0.00867996085177], [-0.0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>204</th>\n",
       "      <td>[[[-6.95571609586e-19], [-1.01720664395e-18], ...</td>\n",
       "      <td>18.933379</td>\n",
       "      <td>[[4.09246765119e-15, 6.47624499527e-08, -0.114...</td>\n",
       "      <td>[[1.14017529872]]</td>\n",
       "      <td>[[1.26383960614e-07]]</td>\n",
       "      <td>[[0.00764222184453], [0.00867445278381], [-0.0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>205</th>\n",
       "      <td>[[[9.11236595016e-05], [0.0], [-0.000205669270...</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>[[-2.49033336556e-23, -1.0, 1.34144021912e-17,...</td>\n",
       "      <td>[[0.948683223281]]</td>\n",
       "      <td>[[7.47697634586e-08]]</td>\n",
       "      <td>[[0.00763426232564], [0.00866948210174], [-0.0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>206</th>\n",
       "      <td>[[[-3.26358500205e-18], [-1.1166114248e-17], [...</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>[[4.08684605825e-22, 2.76125570103e-18, 1.6623...</td>\n",
       "      <td>[[1.41421335576]]</td>\n",
       "      <td>[[2.06608951645e-07]]</td>\n",
       "      <td>[[0.00762707945008], [0.00866499642977], [-0.0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>207</th>\n",
       "      <td>[[[4.24683168095e-05], [0.0], [-0.000287831030...</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>[[5.35204209023e-17, -1.0, -2.65637411854e-20,...</td>\n",
       "      <td>[[0.921954382433]]</td>\n",
       "      <td>[[6.32959576783e-08]]</td>\n",
       "      <td>[[0.00761958437959], [0.00866094849119], [-0.0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>208</th>\n",
       "      <td>[[[-3.58330518212e-20], [-3.95234623759e-20], ...</td>\n",
       "      <td>18.962468</td>\n",
       "      <td>[[-6.69455671528e-18, 1.83082284382e-16, 0.131...</td>\n",
       "      <td>[[1.20415934922]]</td>\n",
       "      <td>[[1.08660527797e-07]]</td>\n",
       "      <td>[[0.00761282079199], [0.00865729561198], [-0.0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>209</th>\n",
       "      <td>[[[1.5472563364e-20], [7.59450964762e-21], [-2...</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>[[-5.67721009662e-23, -1.00000007446, -1.58359...</td>\n",
       "      <td>[[1.14017534939]]</td>\n",
       "      <td>[[7.57129944438e-08]]</td>\n",
       "      <td>[[0.00760671736868], [0.00865399927438], [-0.0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>210</th>\n",
       "      <td>[[[5.33779313117e-05], [7.86917839893e-05], [-...</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>[[0.0, 7.47475920019e-24, 2.27730369509e-16, 0...</td>\n",
       "      <td>[[0.974679404429]]</td>\n",
       "      <td>[[3.00520987006e-08]]</td>\n",
       "      <td>[[0.00759992649638], [0.00864965149415], [-0.0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>211</th>\n",
       "      <td>[[[-7.06442753413e-19], [-1.73761369973e-18], ...</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>[[-2.84684900251e-17, -2.04197839766e-08, -2.5...</td>\n",
       "      <td>[[1.22474478971]]</td>\n",
       "      <td>[[8.16791343694e-08]]</td>\n",
       "      <td>[[0.00759379859041], [0.00864572817072], [-0.0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>212</th>\n",
       "      <td>[[[4.19300496839e-05], [9.28940315349e-05], [-...</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>[[-2.2247455249e-26, -4.32362946952e-18, 6.554...</td>\n",
       "      <td>[[0.999999944473]]</td>\n",
       "      <td>[[5.55273520492e-08]]</td>\n",
       "      <td>[[0.00758725574553], [0.00864055783798], [-0.0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>213</th>\n",
       "      <td>[[[-7.61810571274e-19], [-1.87662484002e-18], ...</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>[[-7.70624408047e-17, -1.98696547387e-08, -1.7...</td>\n",
       "      <td>[[1.22474479191]]</td>\n",
       "      <td>[[7.94786172956e-08]]</td>\n",
       "      <td>[[0.00758135178436], [0.0086358923684], [-0.00...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>214</th>\n",
       "      <td>[[[5.00688224803e-05], [0.000221956766203], [-...</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>[[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,...</td>\n",
       "      <td>[[0.948683271114]]</td>\n",
       "      <td>[[2.69365362557e-08]]</td>\n",
       "      <td>[[0.0075748081329], [0.00862776330695], [-0.00...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>215</th>\n",
       "      <td>[[[4.16097991491e-05], [6.14742420094e-05], [-...</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>[[-3.22472564908e-16, -1.62764587446e-16, -1.0...</td>\n",
       "      <td>[[1.09544502248]]</td>\n",
       "      <td>[[9.25309552086e-08]]</td>\n",
       "      <td>[[0.00756789003411], [0.00861933976702], [-0.0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>216</th>\n",
       "      <td>[[[4.03791358435e-11], [2.38583429132e-11], [-...</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>[[-2.98822380086e-17, -5.49611379219e-17, 2.60...</td>\n",
       "      <td>[[0.999999908797]]</td>\n",
       "      <td>[[9.12027282827e-08]]</td>\n",
       "      <td>[[0.00756164766415], [0.00861173900145], [-0.0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>217</th>\n",
       "      <td>[[[-9.94901830581e-05], [-0.000294128736056], ...</td>\n",
       "      <td>17.000000</td>\n",
       "      <td>[[-1.00000008293, -4.55937314159e-08, -1.00000...</td>\n",
       "      <td>[[1.18321586543]]</td>\n",
       "      <td>[[9.11874524782e-08]]</td>\n",
       "      <td>[[0.00755844741006], [0.00861010285274], [-0.0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>218</th>\n",
       "      <td>[[[4.45702182038e-19], [3.29622179136e-19], [-...</td>\n",
       "      <td>16.004242</td>\n",
       "      <td>[[0.0, -1.26881520853e-17, 7.85288128124e-08, ...</td>\n",
       "      <td>[[1.04880876963]]</td>\n",
       "      <td>[[7.8536923019e-08]]</td>\n",
       "      <td>[[0.00755555980422], [0.00860862654728], [-0.0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>219</th>\n",
       "      <td>[[[0.0], [0.0], [-2.70184251893e-05], [-4.5112...</td>\n",
       "      <td>18.267929</td>\n",
       "      <td>[[0.0, 0.0, 2.61029191456e-25, -5.14780116147e...</td>\n",
       "      <td>[[0.806225746926]]</td>\n",
       "      <td>[[2.79034893494e-08]]</td>\n",
       "      <td>[[0.00755295433004], [0.00860729448329], [-0.0...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>220</th>\n",
       "      <td>[[[0.000246018627885], [0.000182350673127], [-...</td>\n",
       "      <td>17.762709</td>\n",
       "      <td>[[-4.1120337857e-30, -5.06076032587e-17, 2.201...</td>\n",
       "      <td>[[1.18321588622]]</td>\n",
       "      <td>[[7.04038466089e-08]]</td>\n",
       "      <td>[[0.00754516071307], [0.00860316567219], [-0.0...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>221 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                                       gradient_loss_v       loss  \\\n",
       "0                                                 None        NaN   \n",
       "1    [[[1.03029556996], [2.33197051184], [9.5126845...  18.000000   \n",
       "2    [[[0.276727279016], [0.91040992538], [0.0], [0...  17.994715   \n",
       "3    [[[-4.71235516682e-12], [-2.21382332671e-11], ...  15.985191   \n",
       "4    [[[0.000793670266822], [0.0966187306958], [0.8...  17.997046   \n",
       "5    [[[1.93471720866e-15], [-4.23978983044e-16], [...  17.270838   \n",
       "6    [[[-0.0], [-0.00614487609122], [0.23322657962]...  18.456797   \n",
       "7    [[[1.2625584945e-07], [3.84213922233e-08], [-1...  17.998956   \n",
       "8    [[[1.10202365149e-05], [3.24473943292e-06], [-...  18.000083   \n",
       "9    [[[1.81823012462e-05], [1.35959202279e-05], [-...  17.996688   \n",
       "10   [[[-0.36900616545], [-0.399266720399], [0.0101...  16.992304   \n",
       "11   [[[-0.0251305824806], [-0.00620438493764], [1....  16.000000   \n",
       "12   [[[-2.9865061304], [-3.34717031751], [2.037753...  18.000000   \n",
       "13   [[[2.60049749422], [2.62256525634], [0.0004514...  17.988225   \n",
       "14   [[[1.29059250441e-05], [2.29129895142e-05], [3...  17.993141   \n",
       "15   [[[-6.05184833639e-06], [-2.47573184696e-05], ...  16.984871   \n",
       "16   [[[-0.346420571758], [-1.01978246694], [-0.029...  18.003148   \n",
       "17   [[[-0.227751294072], [-0.692559110748], [-0.02...  16.992467   \n",
       "18   [[[-0.0], [-3.62800394736], [-0.0], [0.0], [0....  17.305732   \n",
       "19   [[[-0.734928891933], [-0.0], [-0.240993357531]...  17.996365   \n",
       "20   [[[-0.164884130329], [-0.188026677426], [-0.14...  18.000642   \n",
       "21   [[[0.532916736445], [0.408017682959], [0.17825...  16.998722   \n",
       "22   [[[0.137711162062], [0.0325857317742], [0.1065...  17.997634   \n",
       "23   [[[-0.168336338574], [-0.0], [-0.319495745188]...  18.000000   \n",
       "24   [[[-0.293811196719], [-0.0155023489135], [-0.2...  17.999011   \n",
       "25   [[[-0.000143241493009], [-7.98478884579e-06], ...  15.998045   \n",
       "26   [[[1.07851977503e-07], [1.35468280316e-09], [4...  17.998545   \n",
       "27   [[[-0.0987374353011], [-0.000269453901918], [-...  15.997506   \n",
       "28   [[[-0.0235830104221], [-1.0431314024e-07], [-0...  16.998602   \n",
       "29   [[[1.44569669447e-15], [-4.91123325929e-18], [...  17.998380   \n",
       "..                                                 ...        ...   \n",
       "191  [[[4.15983579603e-05], [3.0193422125e-05], [-4...  17.000000   \n",
       "192  [[[4.45019555392e-05], [0.0], [-0.000297985928...  18.000000   \n",
       "193  [[[0.000324956978155], [0.000283343661952], [-...  18.000000   \n",
       "194  [[[0.0], [0.0], [-4.34600818428e-05], [-9.4044...  17.364424   \n",
       "195  [[[2.25311904729e-05], [3.28111392295e-05], [-...  18.975090   \n",
       "196  [[[-7.17520409792e-19], [-1.04583923156e-18], ...  18.534813   \n",
       "197  [[[3.78332387075e-05], [5.51912038846e-05], [-...  18.000000   \n",
       "198  [[[-7.87981013266e-19], [-3.45115165954e-18], ...  17.743194   \n",
       "199  [[[0.0], [4.64686506364e-05], [-3.58152042316e...  17.000000   \n",
       "200  [[[-4.71933267706e-20], [-2.29842946199e-20], ...  18.000000   \n",
       "201  [[[0.0], [9.24880791954e-05], [-0.000142647078...  18.000000   \n",
       "202  [[[-1.6871467053e-17], [-2.11207657742e-17], [...  18.000000   \n",
       "203  [[[9.16396680916e-05], [0.0], [-0.000206592893...  18.000000   \n",
       "204  [[[-6.95571609586e-19], [-1.01720664395e-18], ...  18.933379   \n",
       "205  [[[9.11236595016e-05], [0.0], [-0.000205669270...  18.000000   \n",
       "206  [[[-3.26358500205e-18], [-1.1166114248e-17], [...  18.000000   \n",
       "207  [[[4.24683168095e-05], [0.0], [-0.000287831030...  18.000000   \n",
       "208  [[[-3.58330518212e-20], [-3.95234623759e-20], ...  18.962468   \n",
       "209  [[[1.5472563364e-20], [7.59450964762e-21], [-2...  18.000000   \n",
       "210  [[[5.33779313117e-05], [7.86917839893e-05], [-...  18.000000   \n",
       "211  [[[-7.06442753413e-19], [-1.73761369973e-18], ...  18.000000   \n",
       "212  [[[4.19300496839e-05], [9.28940315349e-05], [-...  18.000000   \n",
       "213  [[[-7.61810571274e-19], [-1.87662484002e-18], ...  18.000000   \n",
       "214  [[[5.00688224803e-05], [0.000221956766203], [-...  18.000000   \n",
       "215  [[[4.16097991491e-05], [6.14742420094e-05], [-...  18.000000   \n",
       "216  [[[4.03791358435e-11], [2.38583429132e-11], [-...  16.000000   \n",
       "217  [[[-9.94901830581e-05], [-0.000294128736056], ...  17.000000   \n",
       "218  [[[4.45702182038e-19], [3.29622179136e-19], [-...  16.004242   \n",
       "219  [[[0.0], [0.0], [-2.70184251893e-05], [-4.5112...  18.267929   \n",
       "220  [[[0.000246018627885], [0.000182350673127], [-...  17.762709   \n",
       "\n",
       "                                            projection              r_diff  \\\n",
       "0                                                 None   [[0.88593569454]]   \n",
       "1    [[2.87375661629e-45, -2.60368022498e-23, -5.96...  [[0.908844763879]]   \n",
       "2    [[1.8336051726e-15, 1.29135422539e-15, -1.0, 2...   [[1.09021450378]]   \n",
       "3    [[-6.89865205893e-10, -9.17816299371e-10, -0.0...   [[1.15987636616]]   \n",
       "4    [[-2.00371086751e-10, -9.99218805376e-11, -0.0...   [[1.11729791742]]   \n",
       "5    [[2.58006073159e-18, 4.40591554232e-15, 3.3099...   [[1.18254423931]]   \n",
       "6    [[0.0, 5.09763363833e-22, -9.80267452651e-17, ...  [[0.921738214932]]   \n",
       "7    [[-6.00353717975e-11, -0.000391631636956, -9.4...   [[1.22396191465]]   \n",
       "8    [[0.000286206587598, 1.40425981494e-08, -8.428...   [[1.49828184585]]   \n",
       "9    [[-1.49240444399e-09, -0.000824537460295, -1.7...   [[1.22144945049]]   \n",
       "10   [[-1.93195920567e-15, 2.8718044269e-17, 6.7739...  [[0.998074108798]]   \n",
       "11   [[-2.37788745356e-17, 2.11444222816e-16, -7.60...  [[0.997740685947]]   \n",
       "12   [[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,...   [[1.04756014398]]   \n",
       "13   [[5.32235620988e-09, 6.67475459286e-09, 2.6888...   [[1.30132623916]]   \n",
       "14   [[-5.25122956564e-09, -2.49652887663e-06, 1.13...   [[1.28136733797]]   \n",
       "15   [[-1.00300927815, -3.48526681192e-09, -1.00300...   [[1.11500626639]]   \n",
       "16   [[0.00314671042677, 1.04464112646e-17, 5.53037...   [[1.09229345119]]   \n",
       "17   [[-3.99468631194e-15, 4.4358734792e-18, 5.4481...  [[0.998114983804]]   \n",
       "18   [[-1.0, -3.90948375763e-20, -0.487275783999, -...   [[1.04676882987]]   \n",
       "19   [[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,...  [[0.893991566455]]   \n",
       "20   [[0.000641587319812, -2.4156677636e-17, 9.5765...    [[1.0948033217]]   \n",
       "21   [[-1.00023906473, -0.000320395908978, -1.00007...   [[1.18257542077]]   \n",
       "22   [[7.91684554067e-11, 2.36784169188e-10, 1.4074...    [[1.3030189418]]   \n",
       "23   [[2.82541051002e-22, -1.0, 4.39844828051e-19, ...  [[0.921382057232]]   \n",
       "24   [[6.00638694098e-14, 9.70040207513e-11, 8.6789...   [[1.20316979076]]   \n",
       "25   [[3.61059767148e-08, -0.00072228659385, -1.000...   [[1.02397314254]]   \n",
       "26   [[5.16011535396e-15, 1.92430625286e-11, 6.4076...   [[1.26418466553]]   \n",
       "27   [[-3.88983101624e-07, -2.75904537643e-13, -1.2...    [[1.0481853702]]   \n",
       "28   [[-6.00765103638e-16, 1.02636981398e-17, 2.472...  [[0.999650490688]]   \n",
       "29   [[-4.35697094445e-17, -2.71351510175e-15, -1.0...   [[1.11762916663]]   \n",
       "..                                                 ...                 ...   \n",
       "191  [[4.16312693138e-17, -2.6302272772e-14, 1.9082...  [[0.974679354849]]   \n",
       "192  [[1.69001936728e-24, -1.0, -4.86409097057e-23,...  [[0.921954358519]]   \n",
       "193  [[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,...   [[1.04880871572]]   \n",
       "194  [[0.0, 0.0, -1.72858731204e-56, -1.20294431517...  [[0.806225731619]]   \n",
       "195  [[-1.1969035698e-23, -2.47150714836e-16, -9.36...  [[0.974679349174]]   \n",
       "196  [[-2.34423983355e-17, -3.07987251227e-16, -3.4...   [[1.26491096918]]   \n",
       "197  [[-9.3594149779e-58, -2.38299102249e-26, 6.916...  [[0.921954400182]]   \n",
       "198  [[9.11242893629e-23, 6.9983831061e-18, 3.50981...   [[1.44913746346]]   \n",
       "199  [[-1.0, 1.4848358026e-17, -1.00000000143, -0.9...   [[0.94868316487]]   \n",
       "200  [[-1.18901680233e-22, -1.0000000902, -2.310717...   [[1.14017533547]]   \n",
       "201  [[-1.0, -3.39484876493e-26, 5.55111512314e-17,...   [[0.92195433363]]   \n",
       "202  [[3.09861982296e-08, 2.27739112113e-16, -7.977...   [[1.49999981408]]   \n",
       "203  [[4.92180377241e-23, -1.0, -1.31555286067e-16,...  [[0.948683220774]]   \n",
       "204  [[4.09246765119e-15, 6.47624499527e-08, -0.114...   [[1.14017529872]]   \n",
       "205  [[-2.49033336556e-23, -1.0, 1.34144021912e-17,...  [[0.948683223281]]   \n",
       "206  [[4.08684605825e-22, 2.76125570103e-18, 1.6623...   [[1.41421335576]]   \n",
       "207  [[5.35204209023e-17, -1.0, -2.65637411854e-20,...  [[0.921954382433]]   \n",
       "208  [[-6.69455671528e-18, 1.83082284382e-16, 0.131...   [[1.20415934922]]   \n",
       "209  [[-5.67721009662e-23, -1.00000007446, -1.58359...   [[1.14017534939]]   \n",
       "210  [[0.0, 7.47475920019e-24, 2.27730369509e-16, 0...  [[0.974679404429]]   \n",
       "211  [[-2.84684900251e-17, -2.04197839766e-08, -2.5...   [[1.22474478971]]   \n",
       "212  [[-2.2247455249e-26, -4.32362946952e-18, 6.554...  [[0.999999944473]]   \n",
       "213  [[-7.70624408047e-17, -1.98696547387e-08, -1.7...   [[1.22474479191]]   \n",
       "214  [[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,...  [[0.948683271114]]   \n",
       "215  [[-3.22472564908e-16, -1.62764587446e-16, -1.0...   [[1.09544502248]]   \n",
       "216  [[-2.98822380086e-17, -5.49611379219e-17, 2.60...  [[0.999999908797]]   \n",
       "217  [[-1.00000008293, -4.55937314159e-08, -1.00000...   [[1.18321586543]]   \n",
       "218  [[0.0, -1.26881520853e-17, 7.85288128124e-08, ...   [[1.04880876963]]   \n",
       "219  [[0.0, 0.0, 2.61029191456e-25, -5.14780116147e...  [[0.806225746926]]   \n",
       "220  [[-4.1120337857e-30, -5.06076032587e-17, 2.201...   [[1.18321588622]]   \n",
       "\n",
       "                   r_param                                                  v  \n",
       "0      [[0.0360187511891]]  [[0.332785679741], [0.405639874067], [0.487608...  \n",
       "1      [[0.0131096818504]]  [[0.232785689119], [0.305639878578], [0.387608...  \n",
       "2     [[0.00523061122638]]  [[0.142644314213], [0.212153142486], [0.320602...  \n",
       "3     [[0.00201863769827]]  [[0.072965017458], [0.139887881018], [0.268807...  \n",
       "4    [[0.000736071326968]]  [[0.0137247402961], [0.0748670613236], [0.2218...  \n",
       "5    [[0.000671717310256]]  [[-0.0363468361048], [0.0199096050621], [0.182...  \n",
       "6    [[0.000216230797665]]  [[-0.0795020127338], [-0.0274769240511], [0.14...  \n",
       "7    [[0.000782956744689]]  [[-0.117189691079], [-0.0688598680645], [0.115...  \n",
       "8     [[0.00171815415115]]  [[-0.150413684148], [-0.105341439584], [0.0882...  \n",
       "9     [[0.00329542089926]]  [[-0.179907855374], [-0.13772743612], [0.06400...  \n",
       "10    [[0.00192589120196]]  [[-0.202129515694], [-0.164700999041], [0.0422...  \n",
       "11    [[0.00225931405277]]  [[-0.221801022215], [-0.188846499722], [0.0227...  \n",
       "12    [[0.00124870418852]]  [[-0.19199711509], [-0.18119794082], [0.005252...  \n",
       "13    [[0.00251424188514]]  [[-0.189044220702], [-0.189577456832], [-0.010...  \n",
       "14    [[0.00315591989999]]  [[-0.186376589205], [-0.197147744394], [-0.024...  \n",
       "15    [[0.00302772235809]]  [[-0.183962408714], [-0.203998602205], [-0.037...  \n",
       "16    [[0.00315166381678]]  [[-0.178801560005], [-0.20338984279], [-0.0494...  \n",
       "17    [[0.00188501619608]]  [[-0.172093368933], [-0.197888004516], [-0.059...  \n",
       "18    [[0.00204001830174]]  [[-0.166001339602], [-0.168563883834], [-0.069...  \n",
       "19   [[0.000435624545014]]  [[-0.153031179364], [-0.141912821732], [-0.077...  \n",
       "20   [[0.000641793309284]]  [[-0.139482772734], [-0.115662021389], [-0.084...  \n",
       "21   [[0.000640535853812]]  [[-0.132296900185], [-0.0960608027947], [-0.09...  \n",
       "22    [[0.00082153923723]]  [[-0.127037489272], [-0.0785750525861], [-0.09...  \n",
       "23   [[0.000572388497371]]  [[-0.120615113606], [-0.0626540562527], [-0.10...  \n",
       "24   [[0.000989667119754]]  [[-0.111665425859], [-0.047943036256], [-0.107...  \n",
       "25   [[0.000721934059458]]  [[-0.103511521137], [-0.0345427150487], [-0.11...  \n",
       "26    [[0.00072639853587]]  [[-0.0960832454104], [-0.0223349078817], [-0.1...  \n",
       "27   [[0.000623477967001]]  [[-0.0882050698451], [-0.0111990585248], [-0.1...  \n",
       "28   [[0.000349509312048]]  [[-0.0807561724201], [-0.00105215321591], [-0....  \n",
       "29   [[0.000404822115875]]  [[-0.0739692634888], [0.00819298983526], [-0.1...  \n",
       "..                     ...                                                ...  \n",
       "191  [[7.96321967064e-08]]  [[0.00774323994016], [0.00876754692996], [-0.0...  \n",
       "192   [[8.7210125764e-08]]  [[0.00773931700679], [0.00876280514868], [-0.0...  \n",
       "193  [[1.32446211657e-07]]  [[0.0077283079389], [0.00875379852244], [-0.01...  \n",
       "194  [[4.32109700902e-08]]  [[0.00771837157738], [0.00874566948779], [-0.0...  \n",
       "195   [[8.5306634148e-08]]  [[0.00770819058782], [0.00873705026879], [-0.0...  \n",
       "196  [[9.48907861638e-08]]  [[0.00769900186065], [0.00872927109846], [-0.0...  \n",
       "197  [[4.55477884536e-08]]  [[0.00768983002928], [0.00872131935188], [-0.0...  \n",
       "198  [[2.11161328675e-07]]  [[0.00768155231834], [0.00871414278515], [-0.0...  \n",
       "199  [[1.33180988177e-07]]  [[0.00767408165929], [0.00870687798995], [-0.0...  \n",
       "200  [[8.96296807181e-08]]  [[0.00766733945213], [0.00870032157318], [-0.0...  \n",
       "201  [[1.12099413805e-07]]  [[0.00766125474175], [0.00869282750087], [-0.0...  \n",
       "202  [[1.85917200076e-07]]  [[0.00765576347736], [0.00868606433059], [-0.0...  \n",
       "203  [[7.72769381801e-08]]  [[0.00764864547054], [0.00867996085177], [-0.0...  \n",
       "204  [[1.26383960614e-07]]  [[0.00764222184453], [0.00867445278381], [-0.0...  \n",
       "205  [[7.47697634586e-08]]  [[0.00763426232564], [0.00866948210174], [-0.0...  \n",
       "206  [[2.06608951645e-07]]  [[0.00762707945008], [0.00866499642977], [-0.0...  \n",
       "207  [[6.32959576783e-08]]  [[0.00761958437959], [0.00866094849119], [-0.0...  \n",
       "208  [[1.08660527797e-07]]  [[0.00761282079199], [0.00865729561198], [-0.0...  \n",
       "209  [[7.57129944438e-08]]  [[0.00760671736868], [0.00865399927438], [-0.0...  \n",
       "210  [[3.00520987006e-08]]  [[0.00759992649638], [0.00864965149415], [-0.0...  \n",
       "211  [[8.16791343694e-08]]  [[0.00759379859041], [0.00864572817072], [-0.0...  \n",
       "212  [[5.55273520492e-08]]  [[0.00758725574553], [0.00864055783798], [-0.0...  \n",
       "213  [[7.94786172956e-08]]  [[0.00758135178436], [0.0086358923684], [-0.00...  \n",
       "214  [[2.69365362557e-08]]  [[0.0075748081329], [0.00862776330695], [-0.00...  \n",
       "215  [[9.25309552086e-08]]  [[0.00756789003411], [0.00861933976702], [-0.0...  \n",
       "216  [[9.12027282827e-08]]  [[0.00756164766415], [0.00861173900145], [-0.0...  \n",
       "217  [[9.11874524782e-08]]  [[0.00755844741006], [0.00861010285274], [-0.0...  \n",
       "218   [[7.8536923019e-08]]  [[0.00755555980422], [0.00860862654728], [-0.0...  \n",
       "219  [[2.79034893494e-08]]  [[0.00755295433004], [0.00860729448329], [-0.0...  \n",
       "220  [[7.04038466089e-08]]  [[0.00754516071307], [0.00860316567219], [-0.0...  \n",
       "\n",
       "[221 rows x 6 columns]"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "learn_average_deg_variable(print_ratio=1, l_rate = 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "                \n",
    "mean_list = [i for i in np.linspace(-0.5, 0.5, 10)]\n",
    "l_rate_lst = [10**(-i)/3 for i in range(4, 10, 1)]\n",
    "\n",
    "\n",
    "\n",
    "for l in range(len(l_rate_lst)):\n",
    "    for k in range(len(mean_list)):\n",
    "            learn_average_deg_variable(communities = 2, group_size = 10, projection_dim=2, print_ratio=1, l_rate=l_rate_lst[l], mean=mean_list[k], sd=0.2)\n",
    "              "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[3.3333333333333335e-05, 3.3333333333333337e-06]"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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