Protein Visualization.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import math\n",
    "#the world, time emperor\n",
    "import time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''\n",
    "whole functions for 2D HP Absolute calculator\n",
    "'''\n",
    "\n",
    "def check_contact_list(current_contact, contacts, contact_threshold):\n",
    "    contact_check = False\n",
    "    for i in range(len(contacts)):\n",
    "        contact_count = 0\n",
    "        for j in range(len(contacts[i])):\n",
    "            for k in range(len(current_contact)):\n",
    "                if(np.array_equal(current_contact[k],contacts[i][j])):\n",
    "                    contact_count += 1\n",
    "        if contact_count >= contact_threshold:\n",
    "            contact_check = True\n",
    "            break\n",
    "    return contact_check\n",
    "\n",
    "def count_HP_2D_contacts_absolute(move_seq, hp_seq):\n",
    "    '''\n",
    "    count the contacts within protein (H-H, P-P, H-P) and return the contact tuples\n",
    "    abs move : clockwise, 0=N, 1=E, 2=S, 3=W, OR None if initial amino acid (which doesnt have any move)\n",
    "    hp set : 0=P, 1=H\n",
    "    move length = N-1 ; seq length = N\n",
    "    '''\n",
    "    \n",
    "    move_len = len(move_seq)\n",
    "    seq_len = len(hp_seq)\n",
    "    coords = np.zeros((seq_len,2))\n",
    "    \n",
    "    #coordinate data structure\n",
    "    list_coord_dict = []\n",
    "    \n",
    "    #movement coordinate translation\n",
    "    move_N = np.array([0,1])\n",
    "    move_E = np.array([1,0])\n",
    "    move_S = np.array([0,-1])\n",
    "    move_W = np.array([-1,0])\n",
    "    moves_coor = np.array([move_N, move_E, move_S, move_W])\n",
    "    \n",
    "    #interpret the movements to coordinate\n",
    "    \n",
    "    coord_dict = {\"type\":hp_seq[0], \"coord\":coords[0], \"move\":None}\n",
    "    list_coord_dict.append(coord_dict)\n",
    "    \n",
    "    for i in range(1, seq_len):\n",
    "        '''\n",
    "        if move_seq[i-1] == 0 :\n",
    "            coord[i] = coord[i-1] + move_N\n",
    "        elif move_seq[i-1] == 1 :\n",
    "            coord[i] = coord[i-1] + move_E\n",
    "        elif move_seq[i-1] == 2 :\n",
    "            coord[i] = coord[i-1] + move_S\n",
    "        elif move_seq[i-1] == 3 :\n",
    "            coord[i] = coord[i-1] + move_W\n",
    "        '''  \n",
    "        coords[i] = coords[i-1] + moves_coor[move_seq[i-1]]\n",
    "        coord_dict = {\"type\":hp_seq[i], \"coord\":coords[i], \"move\":move_seq[i-1]}\n",
    "        list_coord_dict.append(coord_dict)\n",
    "    #print(list_coord_dict)\n",
    "    \n",
    "    #find contacts (which is adjacent neighbour but not connected (i & k>=i+3))\n",
    "    contacts = []\n",
    "    for i in range(1, len(coords)):\n",
    "        #check each 4 directions:\n",
    "        for j in range(len(moves_coor)):\n",
    "            contact = {}\n",
    "            neighbour_coor = coords[i]+moves_coor[j]\n",
    "            current_contact = (coords[i], neighbour_coor)\n",
    "            \n",
    "            #get the type of contact\n",
    "            #if()\n",
    "            \n",
    "            #check if terminal\n",
    "            if i == len(coords)-1:\n",
    "                #check if not i-1\n",
    "                contact_rule = (not np.array_equal(neighbour_coor, coords[i-1])) and (neighbour_coor.tolist() in coords.tolist())\n",
    "                #threshold = 2 because the contact list only has at most 2 members\n",
    "                unique_contact = check_contact_list(current_contact, contacts, 2)\n",
    "                #if isnt direct neighbor and is not already evaluated\n",
    "                if contact_rule and (not unique_contact):\n",
    "                    contacts.append(current_contact)\n",
    "            else:\n",
    "                #check if not direct neighbours\n",
    "                contact_rule = ( (not np.array_equal(neighbour_coor, coords[i+1])) and (not np.array_equal(neighbour_coor, coords[i-1])) ) and (neighbour_coor.tolist() in coords.tolist())\n",
    "                #if isnt direct neighbor and is not already evaluated\n",
    "                unique_contact = check_contact_list(current_contact, contacts, 2)\n",
    "                if contact_rule and (not unique_contact):\n",
    "                    contacts.append(current_contact)\n",
    "\n",
    "    '''\n",
    "    ==>to be continued with contact type identification & set unique contacts\n",
    "    '''\n",
    "    #identify contact types\n",
    "    list_contact_dict = []\n",
    "    for i in range(len(contacts)):\n",
    "        contact_dict = {\"coord\":contacts[i]}\n",
    "        contact_type = []\n",
    "        for j in range(len(list_coord_dict)):\n",
    "            if(np.array_equal(contacts[i][0], list_coord_dict[j][\"coord\"])):\n",
    "                contact_type.append(list_coord_dict[j][\"type\"])\n",
    "            if(np.array_equal(contacts[i][1], list_coord_dict[j][\"coord\"])):\n",
    "                contact_type.append(list_coord_dict[j][\"type\"])\n",
    "        contact_dict[\"type\"] = np.array(sorted(contact_type))\n",
    "        list_contact_dict.append(contact_dict)\n",
    "        \n",
    "    #print(list_contact_dict)\n",
    "                    \n",
    "    #count each types\n",
    "    contact_count_dict = {'HH':0, 'HP':0, 'PP':0}\n",
    "    for contact_dict in list_contact_dict:\n",
    "        type_HH = np.array([1,1])\n",
    "        type_HP = np.array([0,1])\n",
    "        type_PP = np.array([0,0])\n",
    "        if np.array_equal(type_HH, contact_dict[\"type\"]):\n",
    "            contact_count_dict['HH'] += 1\n",
    "        elif np.array_equal(type_HP, contact_dict[\"type\"]):\n",
    "            contact_count_dict['HP'] += 1\n",
    "        elif np.array_equal(type_PP, contact_dict[\"type\"]):\n",
    "            contact_count_dict['PP'] += 1\n",
    "    \n",
    "    #print(contact_count_dict)\n",
    "    \n",
    "    return contact_count_dict\n",
    "\n",
    "def transform_real_move(x, ranges, moveset):\n",
    "    '''\n",
    "    x : real vector : [1.35324, 0, -34., .....]\n",
    "    ranges : the range for vector transformation : [-4,-2,0,2,4], length of range = N+1, where N is moveset type \n",
    "    moveset : the type of moveset : [N, E, S, W]\n",
    "    '''\n",
    "    x_move = np.array([-1]*len(x))\n",
    "    for i in range(len(x)):\n",
    "        for j in range(len(ranges)-1):\n",
    "            if(ranges[j]<x[i] and x[i]<=ranges[j+1]):\n",
    "                x_move[i] = moveset[j]\n",
    "    return x_move\n",
    "    \n",
    "def protein_fitness(EHH, EHP, EPP, count_HH, count_HP, count_PP):\n",
    "    fitness = (EHH*count_HH) + (EHP*count_HP) + (EPP*count_PP)\n",
    "    return fitness\n",
    "\n",
    "def F_protein(x, hps, ranges, moveset, E_values, return_move_seq=True):\n",
    "    '''\n",
    "    Calculate the energy value of protein sequence\n",
    "    '''\n",
    "    x_move = transform_real_move(x, ranges, moveset)\n",
    "    contact_count = count_HP_2D_contacts_absolute(x_move, hps)\n",
    "    #print(contact_count)\n",
    "    seq_fitness = protein_fitness(E_values[\"HH\"], E_values[\"HP\"], E_values[\"PP\"], contact_count[\"HH\"], contact_count[\"HP\"], contact_count[\"PP\"])\n",
    "    #print(seq_fitness)\n",
    "    if return_move_seq:\n",
    "        return (seq_fitness, x_move)\n",
    "    else:\n",
    "        return seq_fitness\n",
    "    \n",
    "    \n",
    "'''\n",
    "Differential Evolution Functions\n",
    "'''\n",
    "def clip_boundary_psp(vec, domain):\n",
    "    '''\n",
    "    custom clipping function for protein folding, added mini padding for low boundary since alpha < moveset (not <=)\n",
    "    to make sure the vector is within domain,\n",
    "    if outside, clip them\n",
    "    '''\n",
    "    dim = len(domain)\n",
    "    for i in range(dim):\n",
    "        if(vec[i]<domain[i][0]):\n",
    "            vec[i] = domain[i][0] + 1e-1\n",
    "        elif(vec[i]>domain[i][1]):\n",
    "            vec[i] = domain[i][1]\n",
    "    return vec\n",
    "\n",
    "\n",
    "\n",
    "def diff_evo_psp(F, protein_params, domain, pop_n, mut_weight, CR, itr, stop_threshold, scheme=None, log=False, return_array_per_iter=False):\n",
    "    '''\n",
    "    specialized differential evolution for protein folding\n",
    "    params\n",
    "        protein_params : dictionary of : 'hp_seq' hp sequence array [0,1,0,1,1...], 'range' range of movement sequence [-4,-2,0,....], \n",
    "                        'move_type'moveset type [0,1,2,3], 'e_val' energy contact values {'HH', 'HP', 'PP'}\n",
    "        other params are the same as normal differential evolution\n",
    "    '''\n",
    "    \n",
    "    #unpack values first to avoid confusion\n",
    "    hp_seq = protein_params[\"hp_seq\"]\n",
    "    ranges = protein_params[\"range\"]\n",
    "    moveset = protein_params[\"move_type\"]\n",
    "    e_val = protein_params[\"e_val\"]\n",
    "    \n",
    "    dim = len(domain)\n",
    "    population = np.array([np.random.uniform(low=domain[i][0], high=domain[i][1], size=(pop_n,)) for i in range(dim)]).T\n",
    "    \n",
    "    it=0\n",
    "    \n",
    "    if return_array_per_iter:\n",
    "        fittest_vectors = np.zeros((itr, dim))\n",
    "    \n",
    "    fittest_F = math.inf\n",
    "    while((it<itr) and (fittest_F>stop_threshold)):\n",
    "        if log:\n",
    "            print(\"iter : \",it)\n",
    "            fittest_vec = None\n",
    "        for i in range(pop_n):\n",
    "            #target vector = i\n",
    "            tar_vec = population[i]\n",
    "            \n",
    "            #mutation\n",
    "            dist_vec_idx = [j for j in range(pop_n) if j!=i]\n",
    "            donor_vec = None\n",
    "            #default scheme, rand/1/bin\n",
    "            if not scheme:\n",
    "                #x/y : rand/1 mutation scheme\n",
    "                dist_vec_idx = np.random.choice(dist_vec_idx, 3, False)\n",
    "                donor_vec = population[dist_vec_idx[0]] + (mut_weight*(population[dist_vec_idx[1]]-population[dist_vec_idx[2]]))\n",
    "                # clip out of bound vectors\n",
    "                donor_vec = clip_boundary_psp(donor_vec, domain)\n",
    "            else:\n",
    "                if(scheme[0]=='best'):\n",
    "                    dist_vec = [population[j] for j in dist_vec_idx]\n",
    "                    \n",
    "                    #best_vec_idx = np.argmin(np.array([F(j) for j in dist_vec]))\n",
    "                    best_vec_idx = np.argmin(np.array([F_protein(x=j, hps=hp_seq, ranges=ranges, moveset=moveset, E_values=e_val, return_move_seq=False) for j in dist_vec]))\n",
    "                    \n",
    "                    dist_vec_idx = []\n",
    "            #crossover\n",
    "            #binomial crossover\n",
    "            jr = np.random.randint(dim, size=1)\n",
    "            crossover_idx = np.random.uniform(0, 1, dim) <= CR\n",
    "            u_vec = np.zeros(dim)\n",
    "            for j in range(dim):\n",
    "                if (crossover_idx[j] == True) or (j == jr):\n",
    "                    u_vec[j] = donor_vec[j]\n",
    "                else:\n",
    "                    u_vec[j] = tar_vec[j]\n",
    "            #print(tar_vec, donor_vec, crossover_idx, jr, u_vec)\n",
    "            \n",
    "            #selection, minimization\n",
    "            u_fit = F(u_vec, hp_seq, ranges, moveset, e_val, False)\n",
    "            tar_vec_fit = F(tar_vec, hp_seq, ranges, moveset, e_val, False)\n",
    "            if u_fit <= tar_vec_fit :\n",
    "                population[i] = u_vec\n",
    "            \n",
    "            #fitness_array = np.array([F(population[j]) for j in range(pop_n)])\n",
    "            fitness_array = np.array([F_protein(x=population[j], hps=hp_seq, ranges=ranges, moveset=moveset, E_values=e_val, return_move_seq=False) for j in range(pop_n)])\n",
    "\n",
    "            fittest_vec = population[np.argmin(fitness_array)]\n",
    "            fittest_F = np.amin(fitness_array)\n",
    "            \n",
    "        if log:\n",
    "            print(fittest_F, fittest_vec)\n",
    "        \n",
    "        if return_array_per_iter:\n",
    "            fittest_vectors[it] = fittest_vec\n",
    "        \n",
    "        it+=1\n",
    "        \n",
    "    if return_array_per_iter:\n",
    "        return fittest_vectors, it\n",
    "    else:\n",
    "        return fittest_vec, it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''\n",
    "Visualization Functions\n",
    "'''\n",
    "def move_seq_2_coord(move_seq):\n",
    "    coords = np.zeros((len(move_seq)+1,2))\n",
    "    move_coords = np.array([[0,1],[1,0],[0,-1],[-1,0]])\n",
    "    for i in range(1, len(coords)):\n",
    "        coords[i] = coords[i-1] + move_coords[move_seq[i-1]]\n",
    "    return coords\n",
    "\n",
    "def initial_seq_2_coord(hp_seq):\n",
    "    coords = np.zeros((len(hp_seq), 2))\n",
    "    for i in range(1, len(coords)):\n",
    "        coords[i] = coords[i-1] + np.array([1,0])\n",
    "    return coords"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fittest vector :  [-0.82518389 -3.54127089  4.          4.          0.87998183] at iteration =  100\n",
      "Protein Fitness =  -2 , movement sequence =  [1 0 3 3 2] , runtime =  20.413153648376465\n"
     ]
    }
   ],
   "source": [
    "#test example using HPPHPH\n",
    "hp_seq = np.array([1,0,0,1,0,1])\n",
    "ranges = np.array([-4,-2,0,2,4])\n",
    "moveset = moveset = np.array([0,1,2,3])\n",
    "e_val = {'HH':-1, 'HP':0, 'PP':0}\n",
    "protein_params = {'hp_seq':hp_seq, 'range':ranges, 'move_type':moveset,\n",
    "                  'e_val':e_val}\n",
    "domain = [[ranges[0], ranges[-1]]]*(len(hp_seq)-1)\n",
    "\n",
    "\n",
    "start = time.time()\n",
    "fittest_vec, it = diff_evo_psp(F=F_protein, protein_params=protein_params, domain=domain, pop_n=20, mut_weight=0.8, CR=0.5, itr=100, stop_threshold=-1000, scheme=None)\n",
    "end = time.time()\n",
    "\n",
    "\n",
    "print(\"fittest vector : \",fittest_vec, \"at iteration = \", it)\n",
    "protein_fitness, move_seq= F_protein(fittest_vec, hp_seq, ranges, moveset, e_val, True)\n",
    "print(\"Protein Fitness = \",protein_fitness, \", movement sequence = \",move_seq,\", runtime = \",end - start)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.3026308   2.11051584 -2.81055972 -3.88135341  3.27412576]\n",
      " [ 0.3026308   2.11051584 -2.81055972 -3.88135341  3.27412576]\n",
      " [ 0.3026308   2.11051584 -2.81055972 -3.88135341  3.27412576]\n",
      " [ 0.3026308   2.11051584 -2.81055972 -3.88135341  3.27412576]\n",
      " [ 0.3026308   2.11051584 -3.9        -3.88135341  3.27412576]\n",
      " [ 0.3026308   2.11051584 -3.9        -3.88135341  3.27412576]\n",
      " [ 0.3026308   2.11051584 -3.9        -3.88135341  3.27412576]\n",
      " [ 0.3026308   2.11051584 -3.9        -3.88135341  3.27412576]\n",
      " [ 0.3026308   2.11051584 -3.9        -3.88135341  3.27412576]\n",
      " [ 0.3026308   2.11051584 -3.04272836  4.          2.57760337]\n",
      " [ 0.3026308   2.11051584 -3.04272836  4.          2.57760337]\n",
      " [ 0.3026308   2.11051584 -3.04272836  4.          2.57760337]\n",
      " [ 0.3026308   2.11051584 -3.04272836  4.          2.57760337]\n",
      " [ 0.3026308   2.11051584 -3.04272836  4.          2.57760337]\n",
      " [-3.9         2.11051584  1.90108808  2.02395952  1.08408691]\n",
      " [-3.48678359 -0.60351747  0.16280572  1.20503064  4.        ]\n",
      " [-3.48678359 -0.60351747  0.16280572  1.20503064  4.        ]\n",
      " [-2.91467869  4.          0.92663038  1.53827375 -1.21266484]\n",
      " [-2.91467869  4.          0.92663038  1.53827375 -1.21266484]\n",
      " [-2.91467869  4.          0.92663038  1.53827375 -1.21266484]\n",
      " [-2.91467869  4.          0.92663038  1.53827375 -1.21266484]\n",
      " [-2.91467869  4.          0.92663038  1.53827375 -1.21266484]\n",
      " [-2.91467869  4.          0.92663038  1.53827375 -1.21266484]\n",
      " [-2.91467869  4.          0.92663038  1.53827375 -1.21266484]\n",
      " [-2.91467869  4.          0.92663038  1.53827375 -1.21266484]\n",
      " [-2.91467869  4.          0.92663038  1.53827375 -1.21266484]\n",
      " [-2.91467869  4.          0.92663038  1.53827375 -1.21266484]\n",
      " [-2.91467869  4.          0.92663038  1.53827375 -1.21266484]\n",
      " [-2.91467869  4.          0.92663038  1.53827375 -1.21266484]\n",
      " [-2.91467869  4.          0.92663038  1.53827375 -1.21266484]\n",
      " [-2.91467869  4.          0.92663038  1.53827375 -1.21266484]\n",
      " [-2.91467869  4.          0.92663038  1.53827375 -1.21266484]\n",
      " [-2.91467869  4.          0.92663038  1.53827375 -1.21266484]\n",
      " [-2.91467869  4.          0.92663038  1.53827375 -1.21266484]\n",
      " [-2.91467869  4.          0.92663038  1.53827375 -1.21266484]\n",
      " [-2.67843879  4.          1.2062659   1.6872666  -1.56633099]\n",
      " [-2.67843879  4.          1.2062659   1.6872666  -1.56633099]\n",
      " [-2.67843879  4.          1.2062659   1.6872666  -1.56633099]\n",
      " [-2.67843879  4.          1.2062659   1.6872666  -1.56633099]\n",
      " [-2.67843879  4.          1.2062659   1.6872666  -1.56633099]\n",
      " [-2.67843879  4.          1.2062659   1.6872666  -1.56633099]\n",
      " [-2.67843879  4.          1.2062659   1.6872666  -1.56633099]\n",
      " [-2.67843879  4.          1.2062659   1.6872666  -1.56633099]\n",
      " [-2.67843879  4.          1.2062659   1.6872666  -1.56633099]\n",
      " [-2.67843879  4.          1.2062659   1.6872666  -1.56633099]\n",
      " [-2.67843879  4.          1.2062659   1.6872666  -1.56633099]\n",
      " [-2.67843879  4.          1.2062659   1.6872666  -1.56633099]\n",
      " [-2.67843879  4.          1.2062659   1.6872666  -1.56633099]\n",
      " [-2.67843879  4.          1.2062659   1.6872666  -1.56633099]\n",
      " [-2.67843879  4.          1.2062659   1.6872666  -1.56633099]\n",
      " [-2.67843879  4.          1.2062659   1.6872666  -1.56633099]\n",
      " [-2.67843879  4.          1.2062659   1.6872666  -1.56633099]\n",
      " [-3.9         3.22507363  1.2062659   0.17091282 -0.1361223 ]\n",
      " [-3.9         3.22507363  1.2062659   0.17091282 -0.1361223 ]\n",
      " [-3.9         3.22507363  1.2062659   0.17091282 -0.1361223 ]\n",
      " [-3.63833578  3.62289865  1.54864561  0.17091282 -0.92051524]\n",
      " [-3.63833578  2.12153374  1.54864561  0.17091282 -0.92051524]\n",
      " [-3.63833578  2.12153374  1.54864561  0.17091282 -0.92051524]\n",
      " [-3.63833578  2.12153374  1.54864561  0.17091282 -0.92051524]\n",
      " [-3.63833578  2.12153374  1.54864561  0.17091282 -0.92051524]\n",
      " [-3.63833578  2.12153374  1.54864561  0.17091282 -0.92051524]\n",
      " [-3.63833578  2.12153374  1.54864561  0.17091282 -0.92051524]\n",
      " [-3.63833578  2.12153374  1.54864561  0.17091282 -0.92051524]\n",
      " [-3.63833578  2.12153374  1.54864561  0.17091282 -0.92051524]\n",
      " [-3.63833578  2.12153374  1.54864561  0.17091282 -0.92051524]\n",
      " [-3.63833578  2.12153374  1.54864561  0.17091282 -0.92051524]\n",
      " [-3.63833578  2.12153374  1.54864561  0.17091282 -0.92051524]\n",
      " [-3.63833578  2.12153374  1.54864561  0.17091282 -0.92051524]\n",
      " [-3.63833578  2.12153374  1.54864561  0.17091282 -0.92051524]\n",
      " [-3.63833578  2.12153374  1.54864561  0.17091282 -0.92051524]\n",
      " [-3.63833578  2.12153374  1.54864561  0.17091282 -0.92051524]\n",
      " [-3.63833578  2.12153374  1.54864561  0.17091282 -0.92051524]\n",
      " [-3.63833578  2.12153374  1.54864561  0.17091282 -0.92051524]\n",
      " [-3.63833578  2.12153374  1.54864561  0.17091282 -0.92051524]\n",
      " [-3.63833578  2.12153374  1.54864561  0.17091282 -0.92051524]\n",
      " [-3.63833578  2.12153374  1.54864561  0.17091282 -0.92051524]\n",
      " [-3.63833578  2.12153374  1.54864561  0.17091282 -0.92051524]\n",
      " [-3.63833578  2.12153374  1.54864561  0.17091282 -0.92051524]\n",
      " [-3.63833578  2.12153374  1.54864561  0.17091282 -0.92051524]\n",
      " [-3.63833578  2.12153374  1.54864561  0.17091282 -0.92051524]\n",
      " [-2.15207197 -1.87214226  0.37580501  0.06017848  3.84998279]\n",
      " [-2.15207197 -1.87214226  0.37580501  0.06017848  3.84998279]\n",
      " [-2.15207197 -1.87214226  0.37580501  0.06017848  3.84998279]\n",
      " [-2.15207197 -1.87214226  0.37580501  0.06017848  3.84998279]\n",
      " [-2.15207197 -1.87214226  0.37580501  0.06017848  3.84998279]\n",
      " [-2.15207197 -1.87214226  0.37580501  0.06017848  3.84998279]\n",
      " [-2.15207197 -1.87214226  0.37580501  0.06017848  3.84998279]\n",
      " [-2.15207197 -1.87214226  0.37580501  0.06017848  3.84998279]\n",
      " [-2.7833372  -0.7895875   0.37580501  0.06017848  2.74463697]\n",
      " [-2.7833372  -0.7895875   0.37580501  0.06017848  2.74463697]\n",
      " [-2.7833372  -0.7895875   0.37580501  0.06017848  2.74463697]\n",
      " [-2.7833372  -0.7895875   0.37580501  0.06017848  2.74463697]\n",
      " [-2.7833372  -0.7895875   0.37580501  0.06017848  2.74463697]\n",
      " [-2.7833372  -0.7895875   0.37580501  0.06017848  2.74463697]\n",
      " [-2.7833372  -0.7895875   0.37580501  0.06017848  2.74463697]\n",
      " [-2.7833372  -0.7895875   0.37580501  0.06017848  2.74463697]\n",
      " [-2.69241254 -0.92771044  0.93360062  1.45428689  2.74463697]\n",
      " [-2.69241254  3.07473758  0.93360062  0.75739304 -0.65569128]\n",
      " [-3.05648759  3.07473758  1.68759229  0.75739304 -0.35202681]\n",
      " [-3.05648759 -0.88131545  1.68759229  0.49225747  3.15979753]]\n",
      "runtime =  21.309634923934937\n"
     ]
    }
   ],
   "source": [
    "#test example using HPPHPH, multiple arrays per iteration return\n",
    "hp_seq = np.array([1,0,0,1,0,1])\n",
    "ranges = np.array([-4,-2,0,2,4])\n",
    "moveset = moveset = np.array([0,1,2,3])\n",
    "e_val = {'HH':-1, 'HP':0, 'PP':0}\n",
    "protein_params = {'hp_seq':hp_seq, 'range':ranges, 'move_type':moveset,\n",
    "                  'e_val':e_val}\n",
    "domain = [[ranges[0], ranges[-1]]]*(len(hp_seq)-1)\n",
    "\n",
    "\n",
    "start = time.time()\n",
    "fittest_vecs, it = diff_evo_psp(F=F_protein, protein_params=protein_params, domain=domain, pop_n=20, mut_weight=0.8, CR=0.5, itr=100, stop_threshold=-1000, return_array_per_iter=True)\n",
    "end = time.time()\n",
    "\n",
    "print(fittest_vecs)\n",
    "#print(\"fittest vector : \",fittest_vec, \"at iteration = \", it)\n",
    "#protein_fitness, move_seq= F_protein(fittest_vec, hp_seq, ranges, moveset, e_val, True)\n",
    "print(\"runtime = \",end - start)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#visualization\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "coords = move_seq_2_coord(move_seq)\n",
    "coords = coords.T\n",
    "x = coords[0]\n",
    "y = coords[1]\n",
    "\n",
    "#plt.plot(x,y, 'ro')\n",
    "\n",
    "f = plt.figure()\n",
    "ax = f.add_subplot(111)\n",
    "ax.yaxis.set_label_position(\"right\")\n",
    "plt.ylabel(\"ITER 0\", fontsize=20)\n",
    "\n",
    "def connectpoints(x,y,p1,p2):\n",
    "    x1, x2 = x[p1], x[p2]\n",
    "    y1, y2 = y[p1], y[p2]\n",
    "    plt.plot([x1,x2],[y1,y2],'k-')\n",
    "    \n",
    "for i in range(len(x)):\n",
    "    if hp_seq[i] == 0:\n",
    "        plt.scatter(x[i], y[i], marker='o', label='first', s=100., c='r')\n",
    "    else:\n",
    "        plt.scatter(x[i], y[i], marker='o', label='first', s=100., c='g')\n",
    "\n",
    "    \n",
    "for i in range(len(x)-1):\n",
    "    connectpoints(x,y,i,i+1)\n",
    "    \n",
    "\n",
    "\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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3cWCCLfduYfDmQVb82xUM3jzIlnu3MHHAuVdrFIVJRFwZEc9GxNGIGJ6n3yUR8XxE7I6IG0vGVI/asQOGhmDbNpicrNoOHqyWh4aq9VoSO17YwdDtQ2x7YhsHjxwkSQ4eOci2J7YxdPsQO15w7lWudM/kGeD9wMNzdYiIlcCngI3A+cAHI+L8wnHVSyYmYNMmOHwYGo3j1zUaVfumTe6hLIGJAxNsunsThxuHaRw9fu4bRxscbhxm092b3ENRsaIwycznMvP5BbpdCOzOzD2ZeQT4AnB5ybjqMbfcMjNEpms04NZb21PPMnLLo7fQmJx/7huTDW7d5dyrzEltGONs4KUpy3uBn2/DuOoWd911XJjsBg4BF0/t02jA7bfDM8+0t7Y+98h3H2Hy6OTxjWdSHSeoNY42uHP8Tm679La21qb+smCYRMTXqH79prspM7+8iDFilracY6wRYARg7dq1i9i0esKhQ8ctrpmr3+TkXGt0gmYEyRwOHTm0cCdpHguGSWa+t3CMvcCbpiyfA+ybY6ytwFaA4eHhWQNHPWj16upke+2v5+o3OAg7d7ajomVj8OZBDh45uGC/1SevbkM16mftuDT4MWBDRJwbEScDHwC2t2FcdYurroKBgfn7DAzA1Ve3p55l5KqhqxhYMf/cD6wY4Ooh515lSi8N/vWI2Au8E7g3Iu6v298YEfcBZOarwHXA/cBzwJ9n5rNlZaun3HDD4sLk+uvbU88ycsM7b2Bg5QJhsnKA6y9y7lWm9GquezLznMw8JTPfkJn/uG7fl5mXTul3X2a+JTPXZ+YflhatHrN+PYyOwqpVM0NlYKBqHx2t+qml1p++ntErR1k1sGrGHsrAigFWDaxi9MpR1p/u3KuMn4BXe2zcCOPjMDJSnRtZsaJ6Hhmp2jduXHgbOiEbN2xkfPM4IxeMMHjKICtiBYOnDDJywQjjm8fZuMG5V7nI7M7z3MPDwzk2NtbpMiSpp0TE45k55zeSLBX3TCRJxQwTSVIxw0SSVMwwkSQVM0wkScUME0lSMcNEklTMMJEkFevaDy1GxH7gO0s8zBnA95d4jKXUy/X3cu3Q2/X3cu1g/Qv5ycyc804PS6Vrw6QdImKsE58UbZVerr+Xa4ferr+Xawfr71Ye5pIkFTNMJEnFlnuYbO10AYV6uf5erh16u/5erh2svyst63MmkqTWWO57JpKkFlhWYRIRfxwR346I8Yi4JyJOnaPfJRHxfETsjogb213nXCLiyoh4NiKORsScV4NExIsR8XREPBkRXXFTmCZq79a5Pz0ivhoRL9TPp83Rb7Ke9ycjYnu765xWy7xzGRGnRMQX6/XfjIh17a9ybouo/9qI2D9lvj/SiTpnExGfiYhXIuKZOdZHRHyy/reNR8Q72l1jy2XmsnkAvwKcVL/+BPCJWfqsBCaA84CTgaeA8ztde13bTwNvBXYCw/P0exE4o9P1Nlt7l8/9fwBurF/fONvvTr3uUKdrXexcAluA2+vXHwC+2Om6m6z/WuC2Ttc6R/2/CLwDeGaO9ZcCO4AALgK+2emaSx/Las8kM/8yM1+tF3cB58zS7UJgd2buycwjwBeAy9tV43wy87nMfL7TdZyIRdbetXNPVccd9es7gCs6WMtiLGYup/6bRoH3RES0scb5dPPvwoIy82HgwDxdLgc+l5VdwKkRcVZ7qlsayypMpvltqncG050NvDRleW/d1ksS+MuIeDwiRjpdTBO6ee7fkJkvA9TPr5+j32siYiwidkVEJwNnMXP54z71m6wfAq9rS3ULW+zvwm/Uh4lGI+JN7SmtJbr5d/2EnNTpAlotIr4GnDnLqpsy88t1n5uAV4H/PtsmZmlr2yVvi6l/Ed6dmfsi4vXAVyPi2/U7pSXVgtq7du6b2Mzaeu7PAx6MiKczc6I1FTZlMXPZ0flewGJq+wrw+cz8UURsptrL+uUlr6w1unnuT0jfhUlmvne+9RFxDfCrwHuyPng5zV5g6jucc4B9ratwfgvVv8ht7KufX4mIe6gOGSx5mLSg9q6d+4j4XkSclZkv14cjXpljG8fmfk9E7ATeTnXsv90WM5fH+uyNiJOA1zL/oZl2WrD+zPzBlMVPU50H7RUd/V1fCsvqMFdEXAL8HnBZZh6eo9tjwIaIODciTqY6MdnRq3KaERH/MCJ+4thrqosOZr2ipAt189xvB66pX18DzNjTiojTIuKU+vUZwLuBb7WtwuMtZi6n/ps2AQ/O8QarExasf9o5hsuA59pYX6ntwIfqq7ouAn547DBqz+r0FQDtfAC7qY5TPlk/jl3J8kbgvin9LgX+F9U7yps6XfeUun6d6h3Nj4DvAfdPr5/q6pen6sez3VL/Ymrv8rl/HfAA8EL9fHrdPgxsq1+/C3i6nvungQ93uOYZcwl8nOrNFMBrgLvr/y/+Cjiv0/PcZP0317/jTwFfB36q0zVPqf3zwMtAo/69/zCwGdhcrw/gU/W/7WnmuTqzVx5+Al6SVGxZHeaSJC0Nw0SSVMwwkSQVM0wkScUME0lSMcNEklTMMJEkFTNMJEnF/j8csnkY66hYWAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#multiple iteration visualization\n",
    "def connectpoints(x,y,p1,p2):\n",
    "    x1, x2 = x[p1], x[p2]\n",
    "    y1, y2 = y[p1], y[p2]\n",
    "    plt.plot([x1,x2],[y1,y2],'k-')\n",
    "\n",
    "#initial sequence\n",
    "coords = initial_seq_2_coord(hp_seq)\n",
    "coords = coords.T\n",
    "x = coords[0]\n",
    "y = coords[1]\n",
    "\n",
    "f = plt.figure()\n",
    "ax = f.add_subplot(111)\n",
    "ax.yaxis.set_label_position(\"right\")\n",
    "plt.ylabel(\"initial-seq\", fontsize=20)\n",
    "\n",
    "for i in range(len(x)):\n",
    "    if hp_seq[i] == 0:\n",
    "        plt.scatter(x[i], y[i], marker='o', label='first', s=100., c='r')\n",
    "    else:\n",
    "        plt.scatter(x[i], y[i], marker='o', label='first', s=100., c='g')\n",
    "\n",
    "for i in range(len(x)-1):\n",
    "    connectpoints(x,y,i,i+1)\n",
    "\n",
    "plt.axis('equal')\n",
    "plt.show()\n",
    "\n",
    "\n",
    "#next sequences\n",
    "prev_move_seq= transform_real_move(x=fittest_vecs[0], moveset=moveset, ranges=ranges)\n",
    "\n",
    "coords = move_seq_2_coord(prev_move_seq)\n",
    "coords = coords.T\n",
    "x = coords[0]\n",
    "y = coords[1]\n",
    "\n",
    "f = plt.figure()\n",
    "ax = f.add_subplot(111)\n",
    "ax.yaxis.set_label_position(\"right\")\n",
    "plt.ylabel(\"ITER 0\", fontsize=20)\n",
    "\n",
    "for i in range(len(x)):\n",
    "    if hp_seq[i] == 0:\n",
    "        plt.scatter(x[i], y[i], marker='o', label='first', s=100., c='r')\n",
    "    else:\n",
    "        plt.scatter(x[i], y[i], marker='o', label='first', s=100., c='g')\n",
    "\n",
    "for i in range(len(x)-1):\n",
    "    connectpoints(x,y,i,i+1)\n",
    "\n",
    "plt.axis('equal')\n",
    "plt.show()\n",
    "\n",
    "\n",
    "for itr in range(len(fittest_vecs)) :\n",
    "    move_seq= transform_real_move(x=fittest_vecs[itr], moveset=moveset, ranges=ranges)\n",
    "    if(np.array_equal(prev_move_seq, move_seq)):\n",
    "        #skip index\n",
    "        continue\n",
    "    else:\n",
    "        coords = move_seq_2_coord(move_seq)\n",
    "        coords = coords.T\n",
    "        x = coords[0]\n",
    "        y = coords[1]\n",
    "        \n",
    "        f = plt.figure()\n",
    "        ax = f.add_subplot(111)\n",
    "        ax.yaxis.set_label_position(\"right\")\n",
    "        plt.ylabel(\"ITER 0\", fontsize=20)\n",
    "        \n",
    "        for i in range(len(x)):\n",
    "            if hp_seq[i] == 0:\n",
    "                plt.scatter(x[i], y[i], marker='o', label='first', s=100., c='r')\n",
    "            else:\n",
    "                plt.scatter(x[i], y[i], marker='o', label='first', s=100., c='g')\n",
    "\n",
    "        for i in range(len(x)-1):\n",
    "            connectpoints(x,y,i,i+1)\n",
    "            \n",
    "        plt.ylabel(\"ITER \"+str(itr))\n",
    "        plt.axis('equal')\n",
    "        plt.show()\n",
    "        \n",
    "    prev_move_seq = move_seq\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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tTgp5O0+4S0xsXhj60yt6xMU4uGZBBjtPNjK0BqUKNe+eaaepo5dbloZvMxJoYvALh0O4eclMXj/ZRE+/c+wNlG1eP9XIgpnTmJMSWrWRxrJ5QRYXLvVy/FyH3aGoK3j52HliHRJWBx4j0cTgJ7cunUV3n5PdVc12h6JG0dk7wL6aVq4Pwy/tdQvdk1O9fkqbK0OVMYaXj15gfUE6yVNC82r68dLE4Cfr89OZnhDL9iM6bDVU7a5spt9pBn9kw8nMGYksyZ7B6ye02mqoqmzspKa5i1uWhudFbd40MfhJfKyDzYuyePX4BZw6JWNI2nmyiWkJsRTnptkdyqRcvyiT8tNtOvotRL1s1bS6OYSvph8vvyQGEblNRE6KSKWIPDLC8x8XkSYROWDdHvJ67gERqbBuD/gjHrvcunQmLV19/O3vjugVqiHGGMMbJxvZWJhOfGx4Hg9tXpiF02V4q0KbK0PRb9+pJzs5kbPt4T96zOdviIjEAI8CtwNLgHtFZMkIqz5rjFlp3R63tk0DvgWsA9YC3xKR8BhDOAJPu+Iz+05r+YIQc+pCJw0Xe8Kyf8Hj6rkpzEiM1WHRIejlo+epauri/MWeiPju++PQaS1QaYypNsb0Ac8AW8a57a3AK8aYVmNMG/AKcJsfYrLFofqLgJYvCEWeH9Nw7F/wiI1xcM2CTF4/1YRLmytDym/fcc/PHSnffX8khjnAGa/H9day4T4kIodE5HkRmTvBbcNCSX46sVb5glgtXxBSXj/ZxKJZ00NuCs+Jun5hFk0dvRw7F9rF/6JNR697MqWYMJvbeTT+SAwjVYkafjjze2C+MWY58Crw5AS2da8o8rCIlIlIWVNTaI7MWJ2byj/86TIA/vLa/LC5sjbSdfT0s7+2NezHlgNct8AatqrNSSHD5TKcOHeJaxdk8OUwm9t5NP5IDPXAXK/HOcCQmUWMMS3GmF7r4U+B1ePd1us1HjPGFBtjijMzQ7c54EOrckibGk99W/h3QEWKtytbGHAZrg/jZiSPzOkJLJuTzOsnQ/PgKBodP3+Jlq4+tqyYE3ZzO4/GH4lhP1AkInkiEg/cA2z1XkFEvCfVvQs4bt3fDtwiIqlWp/Mt1rKw5XAIGwrSeauyWcsXhIjXTzYyPSGWVRHwhQXYvDCTd0630d7dZ3coCgZHiW0sDN+iecP5nBiMMQPA53H/oB8HfmOMOSoi3xGRu6zVvigiR0XkIPBF4OPWtq3Ad3Enl/3Ad6xlYe2aogwaO3o5dUHngrabMYbXTzZxzYIM4mLCc5jqcJsXZuEy8KYOWw0Jb1U2U5Q1jVnJiXaH4jex/ngRY8w2YNuwZd/0uv914OujbPtz4Of+iCNUbCpyN1m8VdnMwlnhNxF4JDlxvoPzl3rYvCD8+xc8Vs5NISUpjp0nG7lzRejOWR0Nevqd7Ktp5b518+wOxa8i4xAqxMxJmUJ+xlTeqtB2YLt52uLDeZjqcDEO4dqiTHbpsFXblde10Tvg4pqiyGlGAk0MAbOxMIO9Na30WdNIKnvsPNnIkuwZzJwROaf54O5naO7s40jDRbtDiWpvVTYT6xDW5oX38NThNDEEyKaiDLr7nLxzOryvgAxnb1Y0sb+2lcXZkdecd601bPWf/ngy7K+yDWdvVTSzal4q0xL80iofMjQxBMj6gnRiHMLbldpBaIfyujY+8cR+jIHfHzwXcT+edS3diLiPWCOhBEM4autyn7FtirBmJNDEEDAzEuNYkZOsI0dsUlrdQr/T3f7udIV/iYLhSqtbBi8FjYQSDOHo7apmjEETg5qYTYUZHKpv52K3lkkOtpL89MHL6iOhRMFwJfnpg8NvHQ6JuH9fOHi7spnpibEsn5Nsdyh+p4khgDYVZeIysKdazxqCbXZKIga4flFWRJQoGG51bipPfmINMQ7h1iWzIu7fF+qMMbxZ0cz6/HRiI+T6GG+R9y8KIVfPS2FqfAxvaT9D0O2pcjetfO2WhRH7o7m+IIN1eWlUNXfZHUrUqWvppr7tcsQNU/XQxBBAcVaFVZ1YJfh2V7WQmhTHogi/wHBDQTrHz12itUvLYwST52DPczFrpNHEEGAbCzOobenmTGu33aFEDWMMe6paKMlPx+EYqYBv5Fhf4O5b2Kudz0H1VkUzc1KmMD89ye5QAkITQ4B5TjW1OSl4zrRe5mz7ZTYURH6H7PKcFJLiY9hdpYkhWJwuw+6qZjYVZiASmQcemhgCrDBrGjNnJGhiCCJPZ//6KEgMcTEO1sxPY4+eMQTN4bMXudQzEJHDVD00MQSYiLCpMJPdlc1a1yZIdle1kDk9gYLMaXaHEhQbCtKpbOyk8VKP3aFEBU8NtEgqsz2cJoYg2FSUTlt3P0cbdDrGQDPGsLuqhfX56RF7mj+c58xIzxqC482KZpbOnkHa1Hi7QwkYTQxB4Dmy+MH2E1q6IMCqmrpo6uiNiv4Fj6Wzk5meGDs4RFcFztuVzeyvbaUwK7LPRjUxBMGZ1ssIsKtC69oE2p6q6Olf8IhxCOvy0rUDOsDK69p48Bf7cBl46fD5iP4e+yUxiMhtInJSRCpF5JERnv+yiBwTkUMiskNEcr2ec4rIAeu2dfi2kcC7jo3WtQmsPdUtzEmZwry0yBxGOJoNBemcbu2mvk2HRQdKpNff8uZzYhCRGOBR4HZgCXCviCwZttq7QLExZjnwPPBPXs9dNsastG53EYFK8tOJjXG3d8c4Iq9uT6hwudzXL6wviJ7+BY8NhVY/g541BExJfjqeAlyRWH/Lmz/OGNYClcaYamNMH/AMsMV7BWPMTmOM51CmFMjxw/uGjdW5qTz+F8UA/OmqORFbosFuJy900Nbdz/oI/sKOZkHWdNKmxmsHdAAtmDkNDKzPT4vI+lve/JEY5gBnvB7XW8tG80ngJa/HiSJSJiKlInL3aBuJyMPWemVNTeE3ZeZ1C7NYnD2DM3qqHzCeNvZo6l/wcDiE9fnp7KlqwRgdFh0IZXVtGOALNxRFdFIA/ySGkc7ZR/xkisjHgGLgB16L5xljioH7gB+JSMFI2xpjHjPGFBtjijMzw7M+SUl+mjVHrNPuUCLSnqoW5qcnMTtlit2h2KKkIJ1zF3uoa9GDj0AorW4hPsbB1fMiOymAfxJDPTDX63EO0DB8JRG5CfgGcJcxptez3BjTYP2tBl4HrvZDTCGpJD+dnn4Xh+p1nl5/G3C62FvdwvqCyL3oaCyeIbo6OikwSqtbWTE3mSnxMXaHEnD+SAz7gSIRyROReOAeYMjoIhG5GvhP3Emh0Wt5qogkWPczgI3AMT/EFJLWzk8DtOBZIBxtuERH70BUNiN55GdMJWt6ArurtPyKv3X2DnDk7MWI7nD25nNiMMYMAJ8HtgPHgd8YY46KyHdExDPK6AfANOC5YcNSFwNlInIQ2Al83xgTsYkhdWo8i2ZNp7S61e5QIo6n0zUaO549RIQNBemUVms/g7+V1bbidJmoSQyx/ngRY8w2YNuwZd/0un/TKNvtBpb5I4ZwUZKfzrP7z9A34CI+Vq8v9JfdVS0UZU0jc3qC3aHYan1BOr870EBFYycLZkb2XBTBVFrdSlyMsCoK+hdAr3wOupL8NC73Ozl8tt3uUCJG34CLstrWqCqDMZoNVh+LXs/gX3trWliRkxIV/QugiSHo1ua5f7y0Ocl/nis7Q3efk5kzovtsAWBuWhIZ0+L5VWldRJdsCKau3gEO1UdP/wJoYgi6tMF+Bj2i84fyuja+tfUoAP+6ozLqfwzL69po6+qnorFT63L5SVldG06XYV1+mt2hBI0mBhusy0ujrLaNfqfL7lDCXml1CwPWPBcDzsiuXzMepdUtuKyO5z6ty+UXe6tbiHVIxF/U5k0Tgw1K8tO53O/U6xn8oNj6sgqRX79mPEry0wcHNThEon5/+ENpdQvLc5JJivfLWJ2woInBBmvzrOsZavRozlcxDveF91tWzo74+jXjsTo3lV9/qoQZibGszk2J+v3hq+6+6OtfAE0MtkiflsCCmdO0A9oP9ta49+E371yqP4KW1bmp3LxkFqcudOp0sj4qr2tjIIquX/DQxGCTkvx0ympbtZ/BR6XVLSycOT2ip1mcjHX5abR1uzuh1eSVVrcQE2X9C6CJwTYl+el09zk5clb7GSar3+mivK4tqkaLjFeJNSxamyt9U1rdyvKcZKYmRE//AmhisI2nn0GbkybvyNmLdPc5WZcXXaf54zE3bQrZyYns1c/XpHX3DXDwTHvUNSOBJgbbZExLoChrmh7R+cDTv+BJsuo9IsK6vDT21rRq3aRJeqeunQGXYV0Ufr40MdioJD+d/TWtDGg/w6TsrW4hP3Nq1NdHGs3avHSaO3upbu6yO5Sw5OlfKJ6viUEF0br8NLr6nBxpuGR3KGHH6TKU1bZpM9IVePpetDlpckqrW7hqTjLToqx/ATQx2Mrzo6bzM0zc8XPu+RdKtON5VPkZU8mYlqDNlZNwuc/Jwfr2qP18aWKwUeb0BOakTuHZ/We0ps0EeUo96BnD6ESEdflp7K3WfoaJenb/afqdhoxp0dlMqYnBRuV1bZy/2EN1c5cWPJugvTWt5KYnMSs50e5QQlpJXhrnL/VwulXngR6v8ro2/v7F4wD8y/aTUfm99EtiEJHbROSkiFSKyCMjPJ8gIs9az+8Vkflez33dWn5SRG71RzzhorS6ZfDKVC14Nn4ul2F/bWtUjhaZqHX5nuZK7WcYL+/CjP1RWpjR58QgIjHAo8DtwBLgXhFZMmy1TwJtxphC4IfAP1rbLsE9R/RS4Dbgx9brRQUteDY5Jy900N7dr81I41CUNY20qfGDQ3vV2FbNSwGiuzCjP84Y1gKVxphqY0wf8AywZdg6W4AnrfvPAzeKiFjLnzHG9BpjaoBK6/WigqfgWWpSHCvnasGz8fJ01uv1C2MTEdbMT9UO6AlxF2b84Ko5UVuY0R+JYQ5wxutxvbVsxHWMMQPARSB9nNsCICIPi0iZiJQ1NTX5IezQsDo3lduumsXJCx04teDZuOytaWVOyhTmpiXZHUpYWJeXTn3bZc62X7Y7lLBQWt2CCHwrigsz+iMxyAjLhv/CjbbOeLZ1LzTmMWNMsTGmODMzc4IhhrZ1eel09Axw/JxezzAWYwz7arR/YSLeu55BzxrGY29NC0uyZ5A8Jc7uUGzjj8RQD8z1epwDNIy2jojEAslA6zi3jXiDX1xtBx5TZWMnLV19WjhvAhbNmsGMxFjtgB6H3gEn755uj/r+K38khv1AkYjkiUg87s7krcPW2Qo8YN3/MPCacQ+s3grcY41aygOKgH1+iCmsZCdPYV5akh7RjUOplTyj/Ys7ETEOYW1emvYzjMPBMxfpHXBF7YVtHj4nBqvP4PPAduA48BtjzFER+Y6I3GWt9jMgXUQqgS8Dj1jbHgV+AxwD/gh8zhjj9DWmcLQuL419ta06scoY9tW0MnNGArnp2r8wEevy0qlt6ebCpR67Qwlpe63+hWgf2OCXIiDGmG3AtmHLvul1vwf4yCjbfg/4nj/iCGfr8tN5rryeU40dLJo1w+5wQpIxhr3VLZTkp+Me1KbGy7u58q4Vs22OJnTtrWll4czppCRF98RPeuVziPB0pmo78OhqW7pp7OjV/oVJWJI9g2kJsdpceQV9A+6Jn6LxuoXhNDGEiLlpScxJmRKVV1mO197B+kiaGCYqNsbB6txUHeBwBYfPtnO536mfLzQxhJR1+Wns04lVRrXtyDmS4mO42N1vdyhhaV1+GpWNnfxg+4morP8zFs9sitHevwCaGEJKSV46LV19VOoE7u9TXtvKrlPNdPc5uf9ne/WHbRJSprjbzX+8s0qLNo5gb00rRVnTSI/SiqreNDGEEE/beame7r/P9qMXBu/3a8HBSWnp6gXcV5DqPhxqwOmivLZV+xcsmhhCyLy0JGbNSNQOwhHEWqUVHRK9hc18taEgA4c1mEv34VBHGi7R1efUgQ0WTQwhZHBiFe1neJ9zF3tJnhLLV25ZELWFzXy1OjeVe9fOA+DH96/SfehFCzMOpYkhxKzLS6epo5cancB9kDGG0uoWNhVl8rnri/QHzQcfXp0DwOU+l82RhJa9Na3kZ04la7pO/ASaGEKO51L8Ur3gfOHsAAAd/UlEQVSeYVBdSzfnLvZo04cfXDUnmanxMeypbrY7lJDhdBn217RqmRUvmhhCTF7GVDKn6wTu3jydpOs1MfgsLsbBmrw0PfDwcqzhEh29A1FfH8mbJoYQIyKsy9MJ3L3tqW4hc3oCBZlT7Q4lIpTkp1PZ2Eljh9ZNAgYPwvSM4T2aGELQuvx0ncDd4ulf0PpI/rNe54EeorS6lfnpScxK1v4FD00MIahE6yYNqmnu4sKlXj3N96Ols911k/bosGhcLsP+Wu1fGE4TQwgqzJpG+tR4SrWfYbAtXPsX/Cc2xsHavDS9wA04cb6Di5f79fqFYTQxhCAR98Qqu0418ejOyqguXbCnuoWs6QnkZWj/gj+V5KdR3dQV9fMzPF/unnJ+aoJfZiCIGD4lBhFJE5FXRKTC+vu+AeYislJE9ojIURE5JCIf9XruCRGpEZED1m2lL/FEktnJiTR39vEvL5+M2ro22r8QOJ6hv9F81lBe18YTu2sB+Ktn3o3K79hofD1jeATYYYwpAnZYj4frBv7CGLMUuA34kYikeD3/NWPMSut2wMd4IobTGpDkMtFb16a6uYumjl7WF2gzkr8tnZ3M9ITYqB62uqeqGc+EidH6HRuNr4lhC/Ckdf9J4O7hKxhjThljKqz7DUAjkOnj+0a8O5dnD96P1ro2e6rcX9Ro/LcHmmce6Gj+MZw5wz0KSetvvZ+viWGmMeYcgPU360ori8haIB6o8lr8PauJ6YciovVuLavnp7GxMIOp8TE89cl1UVkGorS6hVkzEpmv8zsHxPqCdGqauzh/MTr7GVq7+gD4y+sKtP7WMGMmBhF5VUSOjHDbMpE3EpFs4L+AB40xnkItXwcWAWuANOBvrrD9wyJSJiJlTU1NE3nrsHXn8my6+pzMmBJndyhB5+5faKUkP037FwIk2vsZ3q5qoTBrGn9z2yJNCsOMmRiMMTcZY64a4fYCcMH6wff88DeO9BoiMgN4EfhbY0yp12ufM269wC+AtVeI4zFjTLExpjgzMzpaojYWZgDwdmX01bWpauqkuVP7FwJpcfYMZiTGRmVi6Btwsb+mlY36+RqRr01JW4EHrPsPAC8MX0FE4oH/AX5pjHlu2HOepCK4+yeO+BhPRJmblsTctCnsroq+L672LwSeu58hPSovdDtwxj2/8wbr4EsN5Wti+D5ws4hUADdbjxGRYhF53Frnz4BrgY+PMCz1KRE5DBwGMoC/9zGeiLOxIIPS6hacruiqm1Ra3crs5ETmpWn/QiCtL0inrqWbhvbLdocSVG9XNuMQPfAYjU9XdRhjWoAbR1heBjxk3f8V8KtRtr/Bl/ePBusL0nlm/xmOnL3IirkpY28QATzXL1y3IFP7FwLMU2pkb00LH7w6x+Zogmd3VTNXzUkmOQr778ZDr3wOcRsKrH6GqujpZ6ho7KSlq48Sbf8NuMWzZpA8JW6w6S4adPUO8O7p9sHvlno/TQwhLnN6AgtnTmd3ZfR8cXX+heBxONxl3qPpQrd9ta0MuAwbC/XzNRpNDGFgQ2E6+2tb6el32h1KUGw7fI4ZibE0dvTaHUpUWF+QzunWbv7hpeNRURZid2Uz8TEOinO1cN5oNDGEgY0FGfQOuHjndOR/actqWymtbuVSz0DU1ogKNk87+2NvVEfFPn+7soVVuSlMiY+xO5SQpYkhDKzLTyPGIVHRnPT7g+cG72v9muDwjEgyRP4+b+3q49i5S2zU/oUr0sQQBqYnxrE8JzkqOqBd1nSmMVq/JmjWF2TgsAZ/Rfo+93Sy6/ULV6aJIUxsLMjgUP1FOnr67Q4loKqaOslNS+LLtyzU+jVBsjo3lc9sLgDge3cvi+h9/nZVM9MSYlmRk2x3KCFNE0OY2FCYjtNlInq6z+6+Acpq27j1qll87vrCiP6BCjV/sX4+AE2dkd3hv7uymXV5acTG6E/flejeCROr5qWSEOuI6Oak0uoW+pwuri2KjlpYoWTmjEQWzZrOrlORW6DybPtlalu6tRlpHDQxhInEuBjWzE+L6A7oXaeaSYxzUDxfzxTscE1RBmW1bXT3DdgdSkB4ilHq9Qtj08QQRjYUpnPyQgdNETq+f1dFE+vy0kmM02GEdrh2QSZ9zsgdlbS7spmMafEsnDnd7lBCniaGMOIZYrc7ApuT6tu6qW7q4toF2oxklzXz00iMc7DrVOR9vowxvF3VwvqCDK2/NQ6aGMLIVXOSmZEYG5HNSZ4fo+sWaPuvXRLjYliXl86uisjrZ6hs7KSpo1fnXxgnTQxhJMYhlOSnR2QH9K5TTcxOTqQgc5rdoUS1axdkUt3URX1bt92h+NV7/Qt64DEemhjCzMbCDOrbLvO/X4ycujYDThdvVzVzrZbZtp3njC3SmpNePHyO5Claf2u8NDGEmdQkd12bn74ZOXVtDpxpp6NnQPsXQkBB5jRmJydG1LDVfTUt7K9t4+Jlrb81Xj4lBhFJE5FXRKTC+jviOEMRcXrN3rbVa3meiOy1tn/WmgZUXcEZ6xQ/kura7Kpwz6al9WvsJyJcuyCTt6uaGXC67A7HL/7n3YbB+5HynQk0X88YHgF2GGOKgB3W45FcNsastG53eS3/R+CH1vZtwCd9jCfileRnEGMVtomLiYy6NrtONbFibgrJSTqbVii4piiTjp4BDpxptzsUv/Bcl6H1t8bP18SwBXjSuv8kcPd4NxR3Y/INwPOT2T5arc5N5ZHbFgHw1VsXhn3ZiPbuPg7Vt+vVziFkU6G7qF6kNCcdbbjEsjkztP7WBPiaGGYaY84BWH+zRlkvUUTKRKRURDw//ulAuzHGc5llPTDHx3iiwp+vz2VKXAx1LeE/cuStymZcBu1fCCHJSXGsmJvCGxXh3wFd19JFZWMnH7w6R+tvTcCYiUFEXhWRIyPctkzgfeYZY4qB+4AfiUgBMNLwE3OFOB62kktZU1NkHMlMVmJcDJuKMnjtRCPGjLrLwsKuU03MSNRql6Hm2qJMDtW309bVZ3coPtlxvBGAGxePdsyqRjJmYjDG3GSMuWqE2wvABRHJBrD+No7yGg3W32rgdeBqoBlIEZFYa7UcoGGk7a1tHzPGFBtjijMz9ejyxkVZnG2/zInzHXaHMmnGGHadamZTUYZWuwwx1y7IxBj3GV0423HiAoVZ08hNn2p3KGHF12/jVuAB6/4DwAvDVxCRVBFJsO5nABuBY8Z9qLsT+PCVtlcju2GR+whox/ELNkcyeRWNnZy/1KP9CyFoRY77Kvtw7me41NPP3upWPVuYBF8Tw/eBm0WkArjZeoyIFIvI49Y6i4EyETmIOxF83xhzzHrub4Avi0gl7j6Hn/kYT9TImpHIipxkdpwY8SQtLHh+dLR/IfTExjjYVJTBmxXNYdtc+eapZgZchpsWz7Q7lLATO/YqozPGtAA3jrC8DHjIur8bWDbK9tXAWl9iiGY3LJrJj3acormzl4xpCXaHM2G7KpopzJrG7JQpdoeiRnBtUSbbDp+norGTBWFYkXTH8QukJMVx9dwUu0MJO9qwG8ZuXJyFMbAzDM8a9lQ183ZlMwtnam2kUHWNdSb3D9vCr/yK02XYebKR6xdmaf/VJOgeC2NLZ89g1ozEwZEX4aK8ro0Hfr4fp8vwyrELYfejEy3OX+xBgJ0nm8KulMS7p9to6+4f7ItTE6OJIYyJCDcszuLNiiZ6B5x2hzNunik8wX1kpyUKQpP3/0u4lZJ49XgjsQ7huoXafzUZmhjC3E2Ls+jqc7K3utXuUMZtjdfUnVqiIHSV5KcTF+v+iXBYJd/DxWsnLrA2L40ZiVpmZTI0MYS5DQUZJMY5wmrYat+Ae5TL3Stna4mCELY6N5WnH1rHjMRYls5ODpv/pzOt3Zy60KnNSD7QxBDmEuNi2FSYwY4wugr6xcPnmBofw/c/tDxsfmyi1er5ady7dh5Hzl6kvTs8roL2HCTpMNXJ08QQAW5cPJP6tsucutBpdyhjGnC62H70PDcsnkliXIzd4ahxuGNZNgMuw8vHwuOsdMeJRgoypzI/Q692nixNDBHAc8r8ahg0J+2taaW1q48PLJtldyhqnJbnJJOTOoWXDp+zO5QxdfT0U1rdwo16tuATTQwRYOaMRJbNSea1MLie4cXD50iKj2HzQm3/DRciwh3LsnmrspmLl/vtDueK3qpopt9puFH7F3yiiSFC3LAoi3dOt9HSGbpz2g44XWw/cp4bFmVpM1KYuWNZNv1O93UnoezV440kT4nTvisfaWKIEDctnokx8He/OxKyFyLtq22lpauPO5Zl2x2KmqAVOcnMSZnCthBuTnJfMHme2SmJHKy/aHc4YU0TQ4Tosy5w23bkfMhepbrt8DmmxMVwvTYjhR0R4farZvFmRVPINic9ve80l3oGOHGuI2S/A+FCE0OEKK1pHZz5KBSvUnW6DH88coEbFmUxJV6bkcLRHcvdzUmvhmhz0m/2nwHcs32F4ncgnGhiiBAl+enEW1epioTeVar7alpp7uzVZqQwdvXcFGYnJ4Zkc1J33wAVjZ3EiBAjekW9r3wqu61Cx+rcVH79qRI++1Q5U+JiQq7zbdvhcyTGObh+kdauCVciwu3LsvmvPXVc6ukPqXITfzxynsv9Tr6zZSkdPQOU5KeH3HcgnOgZQwRZnZvKZzcXUtvSzdGG0Ol8c7oML1mjkZLi9VgknN2xLJs+pyvkSrA8V1bPvLQk/rwkl89dX6hJwUc+JQYRSRORV0Skwvr7vv8NEbleRA543XpE5G7ruSdEpMbruZW+xKNgy8rZxMc4eK6s3u5QBu2v1WakSHH13BSykxN58dB5u0MZdKa1mz3VLXx4dQ4iMvYGaky+njE8AuwwxhQBO6zHQxhjdhpjVhpjVgI3AN3Ay16rfM3zvDHmgI/xRL2UpHhuXjKTFw6cpW/AZXc4wHvNSFrULPw5HMLtV2Wzq6KJjp7QGJ30fHk9IvCh1Tl2hxIxfE0MW4AnrftPAnePsf6HgZeMMd0+vq+6gg8X59DW3R8Sp/ueZqTrF2ozUqT4wPJZ9A24QmKCKJfL8Hx5PRsLMpijU8T6ja+JYaYx5hyA9XesQ8J7gKeHLfueiBwSkR+KyKgTF4vIwyJSJiJlTU1NvkUd4a4tymTmjASeK7e/OenXe+to6uhlcfYMu0NRfnL13FTSkuL5952Vtl8rUFrdwtn2y3ykWM8W/GnMxCAir4rIkRFuWybyRiKSDSwDtnst/jqwCFgDpAF/M9r2xpjHjDHFxpjizEwd2XIlMQ7hT1fl8PrJRhov9dgWR3ldG9/eegyAH4fAj4jyj3fPtHOxp5/Kxk7u+6m9F5I9V17P9MRYbl2qRRn9aczEYIy5yRhz1Qi3F4AL1g++54f/SueWfwb8jzFmsGHSGHPOuPUCvwDW+vbPUR4fWZ2Dy8Bv3z1rWwyvnbiA05ojot+pFxxFitLqlsG5P/psvJDsUk8/Lx05x50rZmvtLT/ztSlpK/CAdf8B4IUrrHsvw5qRvJKK4O6fOOJjPMqSnzmN1bmpPFd2xrYJfBo73AX9HHrBUUTxvpjSAKvmpdgSx4uHztHT7+Ij2unsd74mhu8DN4tIBXCz9RgRKRaRxz0rich8YC7wxrDtnxKRw8BhIAP4ex/jUV4+sjqHqqYu3j3THvT37ul3suN4I8W5qXzlloU6hWcEWZ2bylMPlfDRNXMBqGm2ZyzJc2VnKMyaxsq59iSmSObTMBFjTAtw4wjLy4CHvB7XAnNGWO8GX95fXdkHlmfz7d8f5bmyelbNC+6P8n+/U09rVx8/vn+VnilEoNW5qayal8LRhos8/lY196yZi8MRvGsIKhs7eed0O1+/fZFeuxAAeuVzBJueGMcdV2Xzh4MNXO5zBu19XS7Dz96sYXlOMuvy0oL2viq4RIRPXZNPdVMXO08Gd+jq8+X1xDiED6563/Gm8gNNDBHuw8U5dPQO8NXnDgZt9MhrJxqpbu7ioWvy9Wguwt2xLJvZyYn89M3qoL3nvpoW/mtPLVfPTSFremLQ3jeaaGKIcPExDgT3lJrBqlH/2JvVzEmZwh1X6RDCSBcX4+DBjXmUVrdyOAiT45TXtXH/43vp6nNysL5dh0AHiCaGCLe3pnXwfjCGFh6qb2dfTSsPbpxPbIx+vKLBR9fOZVpCbFDOGvZUued0BneTpQ6BDgz95ka4kvx0EjxDCw2sDXCb/0/frGF6QuzgiBUV+WYkxnHPmrm8ePgcZ9svB/S9eq36X6JDoANKE0OEW52bylOfKuFPlmdjgJrmroC9V31bN9sOn+PedfOYHkK1+lXgPbgpD4An3q4J2Ht09w3wm7IzFGRO5Ss3L9Ah0AGkVc2igGdoYX3bZX6w/SQfWJbN1AT//9f/4u1aBPj4hvl+f20V2uakTOEDy7J5et8ZvnBjUUAm8fnPN6q5cKmXf//0KtbM19FugaRnDFFCRPi7P1lCU0cv//lGld9f/82KJv5rTx3rC9KZrVUuo9Knrsmns3eAL/76Xb93Cp+/2MN/7qriA8uyNSkEgSaGKLI6N5U7V8zmsTerafBjW3B5XRsP/mI/fU4Xe2tadaRIlOpzunAIvH6qye8j4P5p+wlcLnjk9kV+e001Ok0MUeZvbluIMfBPfzzht9d86fA5BlzukSJOLZYXtUqrW/BU5ert99/n4FB9O7995ywPbprP3LQkv7ymujJNDFEmJzWJh67J43cHGjjghxpK3X0DbD/qnuZRi+VFN88IOMFdXE/wvXijMYbv/uEY6VPj+fz1hT6/nhofTQxR6DObC8mcnsB3/3DMp8qrxhge+e/D1Ldf5pt/sliL5UU5T3G9v765iMKsafz49Wqqmjp9es2Xjpxnf20bX75lgY50CyJNDFFoWkIsX71lAeV1bXzx6cl3FD65u5atBxv46i0L+cSmfD53faEmhSi3OjeVL964gF9+Yi3xsQ4+86tyunoHJvVae6qa+fpvDzEvNYmPFut1McGkiSFK5WdOQ4DfHzo3qVm4ympb+fsXj3PT4iw+c11BYIJUYWt2yhT+7Z6rqWzs5JHfHp7wmWl5bSt//rN9XLw8wPlLPRwMQrkN9R5NDFFqX00rnvp2vQMu/nsC80M3dvTwuV+/w5zUKfzLn60MarllFT42FWXwlVsW8vuDDTyxu3bc23X3DfC3vzvy3oAGlw5oCDafEoOIfEREjoqIS0SKr7DebSJyUkQqReQRr+V5IrJXRCpE5FkRifclHjV+nlm4HAICPLv/ND9/q2bMI7t9NS386Y9309bVx3/cv5rkKdruq0b3mesKuGnxTL734nGeKq3j0THm/q5u6uSDj+7m+PkOYh1CjA5osIX40vkoIosBF/CfwFetCXqGrxMDnMI9w1s9sB+41xhzTER+A/zWGPOMiPwEOGiM+Y+x3re4uNiUlb3vrdQElde1UVrdwvKcZH65p45Xjl3gT5Zn848fWv6+K6ONMfzhUANfeuYgTmOIixGeeXi99imoMV283M+tP3yD85d6cYi74u9Tn3r/IIU/HjnP1547SGyM8K/3XM3UhFhKq1soyU/Xz5mfiEi5MWbUg3gPX2dwO2692ZVWWwtUGmOqrXWfAbaIyHHgBuA+a70ngW8DYyYG5R+rc1MHv3AbCzL4ya4q/nn7SU6e7+ALNxZy/FwHcQ7hbHsPu6uaOXexZ3BbT2VL/cKqsSRPieO2q7J5YnctLgM9Ay7++pkD/NmaHDYUZtA34OT/vFLBvppWluck8+P7V5GT6r5eQT9f9ghGraQ5wBmvx/XAOiAdaDfGDHgt1+mYbOJwCJ/dXMiKnBQ+86tyvvj0gcHnpifEcM2CTO5MTeLJ3bUMOF16eq8m5M4Vs3lm32n6nC5EBHHAP798Cl4+NbhOjEP4X3csGkwKyj5jJgYReRUYacaVbxhjXhjHe4x0OmGusHy0OB4GHgaYN2/eON5WTcbGwgzuWzePn7zhrq3vEPjL6wr4/A1FANy6dJae3qsJ81T59f7stHb18e2tR9l6sMG9kjGU17VTkp9hb7Bq7MRgjLnJx/eoB7wHIecADUAzkCIisdZZg2f5aHE8BjwG7j4GH2NSV3Dzklk8sbuW/gH3mcH6gve+qN7NT0pNxPDPTtrUeB7YMJ+Xj50f/KzpWWhoCEZT0n6gSETygLPAPcB9xhgjIjuBDwPPAA8A4zkDUQHmuYJVzwxUoOlnLTT5Oirpg8D/BTKBduCAMeZWEZkNPG6MucNa7w7gR0AM8HNjzPes5fm4k0Ia8C7wMWNM71jvq6OSlFJq4sY7KsmnxGAXTQxKKTVx400MeuWzUkqpITQxKKWUGkITg1JKqSE0MSillBpCE4NSSqkhwnJUkog0AXWT3DwD98V1oUbjmhiNa2I0romJ1LhyjTGZY60UlonBFyJSNp7hWsGmcU2MxjUxGtfERHtc2pSklFJqCE0MSimlhojGxPCY3QGMQuOaGI1rYjSuiYnquKKuj0EppdSVReMZg1JKqSuIqMQgIreJyEkRqRSRR0Z4PkFEnrWe3ysi872e+7q1/KSI3BrkuL4sIsdE5JCI7BCRXK/nnCJywLptDXJcHxeRJq/3f8jruQdEpMK6PRDkuH7oFdMpEWn3ei4g+0tEfi4ijSJyZJTnRUT+zYr5kIis8noukPtqrLjut+I5JCK7RWSF13O1InLY2ld+rUo5jrg2i8hFr/+rb3o9d8X//wDH9TWvmI5Yn6c067lA7q+5IrJTRI6LyFER+asR1gneZ8wYExE33CW9q4B8IB44CCwZts5ngZ9Y9+8BnrXuL7HWTwDyrNeJCWJc1wNJ1v3PeOKyHnfauL8+Dvz7CNumAdXW31Trfmqw4hq2/hdwl3IP9P66FlgFHBnl+TuAl3DPTFgC7A30vhpnXBs87wfc7onLelwLZNi0vzYDf/D1/9/fcQ1b907gtSDtr2xglXV/OnBqhO9j0D5jkXTGsBaoNMZUG2P6cM/zsGXYOluAJ637zwM3iohYy58xxvQaY2qASuv1ghKXMWanMabbeliKeza7QBvP/hrNrcArxphWY0wb8Apwm01x3Qs87af3HpUxZhfQeoVVtgC/NG6luGcnzCaw+2rMuIwxu633heB9tsazv0bjy+fS33EF5bMFYIw5Z4x5x7rfARwH5gxbLWifsUhKDHOAM16P63n/jh1cx7inE70IpI9z20DG5e2TuI8KPBJFpExESkXkbj/FNJG4PmSdtj4vIp4pWkNif1lNbnnAa16LA7W/xjJa3IHcVxM1/LNlgJdFpFzcc6oH23oROSgiL4nIUmtZSOwvEUnC/eP6316Lg7K/xN3EfTWwd9hTQfuMBWNqz2CREZYNH3I12jrj2Xayxv3aIvIxoBi4zmvxPGNMg7hnu3tNRA4bY6qCFNfvgaeNMb0i8mncZ1s3jHPbQMblcQ/wvDHG6bUsUPtrLHZ8tsZNRK7HnRg2eS3eaO2rLOAVETlhHVEHwzu4yzN0inuGx98BRYTI/sLdjPS2Mcb77CLg+0tEpuFORl8yxlwa/vQImwTkMxZJZwz1wFyvxzlAw2jriEgskIz7tHI82wYyLkTkJuAbwF3Ga3pTY0yD9bcaeB33kURQ4jLGtHjF8lNg9Xi3DWRcXu5h2Kl+APfXWEaLO5D7alxEZDnwOLDFGNPiWe61rxqB/8F/zadjMsZcMsZ0Wve3AXEikkEI7C/LlT5bAdlfIhKHOyk8ZYz57QirBO8zFoiOFDtuuM9+qnE3LXg6rZYOW+dzDO18/o11fylDO5+r8V/n83jiuhp3h1vRsOWpQIJ1PwOowE8dceOMK9vr/geBUvNeZ1eNFV+qdT8tWHFZ6y3E3Rkowdhf1mvOZ/TO1A8wtGNwX6D31Tjjmoe7z2zDsOVTgele93cDtwUxrlme/zvcP7CnrX03rv//QMVlPe85YJwarP1l/dt/CfzoCusE7TPmt50dCjfcvfancP/IfsNa9h3cR+EAicBz1hdlH5Dvte03rO1OArcHOa5XgQvAAeu21Vq+AThsfTkOA58Mclz/ABy13n8nsMhr209Y+7ESeDCYcVmPvw18f9h2AdtfuI8ezwH9uI/QPgl8Gvi09bwAj1oxHwaKg7SvxorrcaDN67NVZi3Pt/bTQev/+BtBjuvzXp+tUrwS10j//8GKy1rn47gHo3hvF+j9tQl3888hr/+rO+z6jOmVz0oppYaIpD4GpZRSfqCJQSml1BCaGJRSSg2hiUEppdQQmhiUUkoNoYlBKaXUEJoYlFJKDaGJQSml1BD/D37p9fmYNBpFAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "x1 = np.linspace(0.0, 5.0)\n",
    "x2 = np.linspace(0.0, 2.0)\n",
    "\n",
    "y1 = np.cos(2 * np.pi * x1) * np.exp(-x1)\n",
    "y2 = np.cos(2 * np.pi * x2)\n",
    "\n",
    "'''\n",
    "plt.subplot(3, 1, 1)\n",
    "plt.plot(x1, y1, 'o-')\n",
    "plt.title('A tale of 2 subplots')\n",
    "plt.ylabel('Damped oscillation')\n",
    "\n",
    "plt.subplot(3, 1, 2)\n",
    "plt.plot(x2, y2, '.-')\n",
    "plt.xlabel('time (s)')\n",
    "plt.ylabel('Undamped')\n",
    "\n",
    "plt.subplot(3, 1, 3)\n",
    "plt.plot(x2, y2, '.-')\n",
    "plt.xlabel('time (s)')\n",
    "plt.ylabel('Undamped')\n",
    "'''\n",
    "\n",
    "\n",
    "n=3\n",
    "for i in range(1, n+1):\n",
    "    #plt.subplot(n, 1, i)\n",
    "    plt.plot(x2, y2, '.-')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "\n",
    "f = plt.figure()\n",
    "ax = f.add_subplot(111)\n",
    "ax.yaxis.set_label_position(\"right\")\n",
    "#ax.yaxis.tick_right()\n",
    "plt.plot([2,3,4,5])\n",
    "plt.ylabel(\"iter 0\", fontsize=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 0 0 1 0 1]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[0., 0.],\n",
       "       [1., 0.],\n",
       "       [2., 0.],\n",
       "       [3., 0.],\n",
       "       [4., 0.],\n",
       "       [5., 0.]])"
      ]
     },
     "execution_count": 180,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(hp_seq)\n",
    "init_seq = initial_seq_2_coord(hp_seq)\n",
    "init_seq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}