Example-5-MC-GP-IRS-CVA.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Overview\n",
    "This example demonstrates the application of GPs to pricing a counterparty portfolio of IRS contracts with 11 currencies and 10 FX processes. In the data, the interest rates appear first and then the FX processes, so that if 0<=j<=num_rates-1, then the j-th process is the j-th interest rate and, ignoring j=0, the (num_rates+j-1)-th process is the FX process whose foreign currency is the j-th one.\n",
    "\n",
    "For example, in the case of 3 currencies (and therefore 2 FX rates) we would have a spacial arrangement like this:\n",
    "\n",
    "|rate_0|rate_1|rate_2|FX_0|FX_1|\n",
    "\n",
    "\n",
    "In the rates cube, [i,j,k] refers to the i-th coarse time step, j-th interest rate process if $j\\leq #ratesj \\leq \\#ratesj\\leq#rates$ or (j-num_rates)-th FX process otherwise, and k-th Monte-Carlo scenario.\n",
    "\n",
    "## Data Download\n",
    "\n",
    "Please download the following five npz files from google drive:\n",
    "\n",
    "- https://drive.google.com/file/d/1-0fMzY8sgoAvkT_BJN7bLUdRY_3Ozjoz/view?usp=drive_web\n",
    "\n",
    "- https://drive.google.com/file/d/1-EX-V08JVhB7ZsuzFqwXvK7JsQErWtWu/view?usp=drive_web\n",
    "\n",
    "- https://drive.google.com/file/d/1-AniapWnwDeU5IlsR1IrLdwWTKFnlqxr/view?usp=drive_web\n",
    "\n",
    "- https://drive.google.com/file/d/1-73kFXfe5OIrPDXmRqNVxOieUXnio8jt/view?usp=drive_web\n",
    "- https://drive.google.com/file/d/1-6xGJJx4FQJ6eOvsnSEH3SordmvVlrgD/view?usp=drive_web"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy import *\n",
    "from sklearn import gaussian_process\n",
    "from sklearn.gaussian_process.kernels import ConstantKernel, RBF, Matern\n",
    "\n",
    "\n",
    "%matplotlib inline\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "mtm_irs=np.load('../IRS/mtm_irs.npz')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "rates_and_fx=np.load('../IRS/rates_and_fx.npz')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "irs_params=np.load('../IRS/irs_params.npz')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "rate_params=np.load('../IRS/rate_params.npz')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Aggregate underlying data together"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The aggregation of the data is as follows:\n",
    "- Select counterparty portfolio (1 of 5)\n",
    "- Select a IRS contract i\n",
    "- Select times t={t_j}\n",
    "- Get M simulated prices from mtm_irs[t, i, M]\n",
    "\n",
    "- Get currency from irs_params['arr_0'][i]\n",
    "- Get foreign rate and FX if currency neq 0, else get domestic rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "cpty_idx=0\n",
    "port_idx=[]\n",
    "for i in range(len(irs_params['arr_0'])):\n",
    " if (irs_params['arr_0'][i][5]==cpty_idx):\n",
    "    port_idx.append(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "port_idx=np.array(port_idx)\n",
    "T = np.shape(mtm_irs['arr_0'])[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(101, 50, 32768)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.shape(mtm_irs['arr_0'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reset dates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "reset_idx=(np.arange(101)-1)//5*5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "M= 2000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# construct IRS mapping to rates\n",
    "irs_map ={}\n",
    "for i in port_idx:\n",
    "    ccy=irs_params['arr_0'][i][6]\n",
    "    if (ccy==0):\n",
    "       irs_map[i]=[0] #domestic rate\n",
    "    else:\n",
    "       irs_map[i]=[ccy, 10+ccy] # foreign rate + FX rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "mtm = []\n",
    "rates_fx = []\n",
    "prev_rates_fx = []\n",
    "for t in arange(5,T,10):     \n",
    " mtm.append(mtm_irs['arr_0'][t,port_idx,:2*M])\n",
    " prev_rates_fx.append(rates_and_fx['arr_0'][t-5,:,:2*M].T) # previous reset date\n",
    " rates_fx.append(rates_and_fx['arr_0'][t,:,:2*M].T)\n",
    "\n",
    "nt = len(arange(1,T,10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# option method for sampling the input space\n",
    "def stratified_sampling(ar, M):\n",
    "    quantiles = [0,0.25,0.5,0.75, 1]\n",
    "    num_buckets = len(quantiles)-1\n",
    "    q= np.quantile(ar, quantiles, axis=0)\n",
    "    \n",
    "    idx=np.array([], dtype=int)\n",
    "    sum_ =0\n",
    "    dim = np.shape(ar)[1]\n",
    "    #print(dim)\n",
    "    num_samples = int(M/(num_buckets**dim))\n",
    "    #print(num_samples)\n",
    "    if (dim==2): # domestic\n",
    "        for i in range(num_buckets):\n",
    "          for j in range(num_buckets):\n",
    "           idx_=np.where((ar[:,0] >= q[i,0]) & (ar[:,0] <= q[i+1,0]) & (ar[:,1] >= q[j,1]) & (ar[:,1] <= q[j+1,1]))\n",
    "           if (len(idx_[0])> num_samples):\n",
    "             idx__=idx_[0][:num_samples]\n",
    "\n",
    "           else: # oversample\n",
    "             idx__=np.random.choice(idx_[0], num_samples) # sample with replacement \n",
    "\n",
    "           sum_+=len(idx__) \n",
    "           #print(i,j,sum_)\n",
    "           idx= np.append(idx,idx__)\n",
    "    else: \n",
    "         counter =0\n",
    "         for i in range(num_buckets):\n",
    "          for j in range(num_buckets):\n",
    "            for k in range(num_buckets):\n",
    "               idx_=np.where((ar[:,0] >= q[i,0]) & (ar[:,0] <= q[i+1,0]) & (ar[:,1] >= q[j,1]) & (ar[:,1] <= q[j+1,1]) & (ar[:,2] >= q[k,2]) & (ar[:,2] <= q[k+1,2]))\n",
    "               if (len(idx_[0])> num_samples):\n",
    "                 idx__=idx_[0][:num_samples]\n",
    "                 idx= np.append(idx,idx__)\n",
    "                 sum_+=len(idx__)\n",
    "               elif(len(idx_[0])>0): # oversample\n",
    "                 idx__=np.random.choice(idx_[0], num_samples) # sample with replacement \n",
    "                 \n",
    "                 #print(i,j,sum_)\n",
    "                 idx= np.append(idx,idx__)\n",
    "                 sum_+=len(idx__)\n",
    "               else:\n",
    "                 counter+=1 \n",
    "                 print(i,j,k,0, counter)\n",
    "                  \n",
    "    \n",
    "    # ensure that minimums and maximums are in the training set\n",
    "    idx_min= np.argmin(ar, axis=0)\n",
    "    idx_max= np.argmax(ar, axis=0)\n",
    "    \n",
    "    idx[0:dim]=idx_min\n",
    "    idx[dim:(2*dim)]=idx_max\n",
    "    print(sum_)\n",
    "    return(idx)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## GP kernel specification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "sk_kernel_matern = Matern(length_scale=1.0, nu=0.5, length_scale_bounds=(0.01,10000)) #(1e-05, 1000.0))  #100000.0\n",
    "sk_kernel_rbf = RBF(length_scale=1.0, length_scale_bounds=(0.01,10000)) #(1e-05, 1000.0))  #100000.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/kernels.py:1377: RuntimeWarning: invalid value encountered in true_divide\n",
      "  / np.sqrt(D.sum(2))[:, :, np.newaxis]\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00070292]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 57, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00070292]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 50, 'nit': 7, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00190499]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 53, 'nit': 7, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00214538]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 76, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00080003]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 53, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00512432]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 85, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([0.00404718]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 56, 'nit': 4, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/kernels.py:1377: RuntimeWarning: invalid value encountered in true_divide\n",
      "  / np.sqrt(D.sum(2))[:, :, np.newaxis]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 0\n",
      "1000\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00067002]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 92, 'nit': 12, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.0660011]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 50, 'nit': 3, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00172575]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 49, 'nit': 3, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([0.01139044]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 62, 'nit': 7, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.07107468]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 68, 'nit': 4, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.07009967]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 64, 'nit': 4, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([0.00100087]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 66, 'nit': 7, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([0.14399784]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 77, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([0.01198732]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 56, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00034107]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 66, 'nit': 8, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 1\n",
      "1000\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/kernels.py:1377: RuntimeWarning: invalid value encountered in true_divide\n",
      "  / np.sqrt(D.sum(2))[:, :, np.newaxis]\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-2.77354162]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 44, 'nit': 2, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-3.52652234]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 55, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-1.39766849]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 56, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-1.9350774]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 55, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/kernels.py:1377: RuntimeWarning: invalid value encountered in true_divide\n",
      "  / np.sqrt(D.sum(2))[:, :, np.newaxis]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 2\n",
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     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00018881]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 89, 'nit': 7, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00182142]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 47, 'nit': 4, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00686176]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 49, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([0.00288527]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 63, 'nit': 8, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00030311]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 48, 'nit': 4, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00018881]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 58, 'nit': 7, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00030311]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 69, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([0.00120486]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 50, 'nit': 7, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.01087859]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 48, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00018881]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 50, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00018881]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 78, 'nit': 8, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00066308]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 48, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 3\n",
      "1000\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/kernels.py:1377: RuntimeWarning: invalid value encountered in true_divide\n",
      "  / np.sqrt(D.sum(2))[:, :, np.newaxis]\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00697322]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 57, 'nit': 7, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([0.03923705]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 88, 'nit': 8, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.01634854]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 47, 'nit': 4, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.0014117]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 53, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00081136]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 73, 'nit': 8, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([0.00315644]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 131, 'nit': 13, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00672197]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 48, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00081136]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 64, 'nit': 8, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00289595]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 49, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/kernels.py:1377: RuntimeWarning: invalid value encountered in true_divide\n",
      "  / np.sqrt(D.sum(2))[:, :, np.newaxis]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 4\n",
      "1000\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00374552]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 74, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00175592]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 84, 'nit': 7, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00374552]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 65, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([0.11201584]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 78, 'nit': 9, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00013614]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 63, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00168436]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 67, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00204409]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 69, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 5\n",
      "1000\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/kernels.py:1377: RuntimeWarning: invalid value encountered in true_divide\n",
      "  / np.sqrt(D.sum(2))[:, :, np.newaxis]\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.0063325]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 51, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.04671999]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 53, 'nit': 4, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([0.00710928]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 88, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([0.07538365]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 85, 'nit': 8, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00132875]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 51, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.07474192]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 49, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.08594092]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 50, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/kernels.py:1377: RuntimeWarning: invalid value encountered in true_divide\n",
      "  / np.sqrt(D.sum(2))[:, :, np.newaxis]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 6\n",
      "1000\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00017965]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 67, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([0.01402303]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 55, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([0.00388539]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 64, 'nit': 7, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00118028]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 51, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00118028]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 70, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00118028]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 62, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00118028]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 78, 'nit': 7, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([0.01148725]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 63, 'nit': 7, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/kernels.py:1377: RuntimeWarning: invalid value encountered in true_divide\n",
      "  / np.sqrt(D.sum(2))[:, :, np.newaxis]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 7\n",
      "1000\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00036779]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 70, 'nit': 10, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00033841]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 47, 'nit': 4, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([0.13889766]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 48, 'nit': 3, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([0.00068239]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 70, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.06312991]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 59, 'nit': 7, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.06179003]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 48, 'nit': 3, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00033841]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 68, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00334186]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 60, 'nit': 8, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.09670907]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 60, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([0.00122169]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 83, 'nit': 8, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([0.00440169]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 46, 'nit': 3, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 8\n",
      "1000\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/kernels.py:1377: RuntimeWarning: invalid value encountered in true_divide\n",
      "  / np.sqrt(D.sum(2))[:, :, np.newaxis]\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00256619]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 48, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00063531]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 105, 'nit': 9, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00063531]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 69, 'nit': 8, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00063531]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 89, 'nit': 7, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.25141017]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 53, 'nit': 4, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00063531]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 67, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00063531]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 48, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00377276]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 55, 'nit': 7, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.39596003]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 48, 'nit': 2, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00560628]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 45, 'nit': 2, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00063531]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 68, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.14125347]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 59, 'nit': 4, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.0001034]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 64, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
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     "text": [
      "0 9\n",
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     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/kernels.py:1377: RuntimeWarning: invalid value encountered in true_divide\n",
      "  / np.sqrt(D.sum(2))[:, :, np.newaxis]\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([0.53690675]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 56, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
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      "0 10\n",
      "1000\n"
     ]
    },
    {
     "name": "stderr",
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     "text": [
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/kernels.py:1377: RuntimeWarning: invalid value encountered in true_divide\n",
      "  / np.sqrt(D.sum(2))[:, :, np.newaxis]\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.01539106]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 88, 'nit': 4, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00082807]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 66, 'nit': 8, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([0.00148695]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 57, 'nit': 8, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.0007965]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 50, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.01348244]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 50, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00238021]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 49, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.08486529]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 57, 'nit': 4, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00148429]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 68, 'nit': 7, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00082807]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 54, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([0.00576695]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 80, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
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     "text": [
      "0 11\n",
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     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/kernels.py:1377: RuntimeWarning: invalid value encountered in true_divide\n",
      "  / np.sqrt(D.sum(2))[:, :, np.newaxis]\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-33.90419808]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 48, 'nit': 3, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-1.0477902]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 73, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([22.20313885]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 48, 'nit': 3, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-10.13372708]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 48, 'nit': 4, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/kernels.py:1377: RuntimeWarning: invalid value encountered in true_divide\n",
      "  / np.sqrt(D.sum(2))[:, :, np.newaxis]\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00027958]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 67, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00013609]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 56, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.0068127]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 61, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00174044]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 56, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.03273413]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 88, 'nit': 8, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([0.00030302]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 60, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.03051902]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 100, 'nit': 10, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/kernels.py:1377: RuntimeWarning: invalid value encountered in true_divide\n",
      "  / np.sqrt(D.sum(2))[:, :, np.newaxis]\n"
     ]
    },
    {
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     "output_type": "stream",
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    },
    {
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     "text": [
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-1.20085051]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 77, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.08533236]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 56, 'nit': 8, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-14.54094668]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 59, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
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    {
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     "output_type": "stream",
     "text": [
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/kernels.py:1377: RuntimeWarning: invalid value encountered in true_divide\n",
      "  / np.sqrt(D.sum(2))[:, :, np.newaxis]\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00090797]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 50, 'nit': 7, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00506976]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 54, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([0.05103556]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 54, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00189003]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 54, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00986381]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 44, 'nit': 1, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00745212]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 48, 'nit': 3, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/kernels.py:1377: RuntimeWarning: invalid value encountered in true_divide\n",
      "  / np.sqrt(D.sum(2))[:, :, np.newaxis]\n"
     ]
    },
    {
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    {
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     "text": [
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00366862]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 47, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00028368]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 48, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00578175]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 49, 'nit': 4, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([0.00212764]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 50, 'nit': 7, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00028368]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 48, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00738124]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 87, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00087095]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 86, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
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    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/kernels.py:1377: RuntimeWarning: invalid value encountered in true_divide\n",
      "  / np.sqrt(D.sum(2))[:, :, np.newaxis]\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.0923355]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 66, 'nit': 4, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00154169]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 80, 'nit': 8, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00154169]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 127, 'nit': 12, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00318583]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 47, 'nit': 4, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00331742]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 74, 'nit': 7, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00154169]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 64, 'nit': 7, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00279752]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 47, 'nit': 4, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00392475]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 47, 'nit': 4, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.01500522]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 61, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00154169]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 47, 'nit': 4, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/kernels.py:1377: RuntimeWarning: invalid value encountered in true_divide\n",
      "  / np.sqrt(D.sum(2))[:, :, np.newaxis]\n"
     ]
    },
    {
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    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.01271602]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 47, 'nit': 4, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.001697]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 77, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.03758782]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 130, 'nit': 9, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00056914]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 67, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00056914]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 99, 'nit': 7, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00146125]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 77, 'nit': 7, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([0.00028381]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 52, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([0.11374952]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 72, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.0010502]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 52, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00151929]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 51, 'nit': 7, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([0.11278613]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 48, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00146125]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 48, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n"
     ]
    },
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      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/kernels.py:1377: RuntimeWarning: invalid value encountered in true_divide\n",
      "  / np.sqrt(D.sum(2))[:, :, np.newaxis]\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.04337033]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 49, 'nit': 4, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00077067]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 57, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00150398]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 68, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00150398]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 54, 'nit': 7, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.08630765]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 50, 'nit': 3, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.08513978]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 60, 'nit': 4, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00150398]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 67, 'nit': 8, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.10150157]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 71, 'nit': 2, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00418724]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 77, 'nit': 7, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00150398]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 70, 'nit': 8, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.08400771]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 50, 'nit': 3, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00056782]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 51, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n"
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    },
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      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00025265]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 50, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n"
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      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00087172]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 50, 'nit': 5, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
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      "  ConvergenceWarning)\n"
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      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00100922]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 50, 'nit': 6, 'warnflag': 2}\n",
      "  ConvergenceWarning)\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:480: ConvergenceWarning: fmin_l_bfgs_b terminated abnormally with the  state: {'grad': array([-0.00075584]), 'task': b'ABNORMAL_TERMINATION_IN_LNSRCH', 'funcalls': 52, 'nit': 5, 'warnflag': 2}\n",
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      "  ConvergenceWarning)\n",
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   ],
   "source": [
    "portfolio ={}\n",
    "for idx in port_idx:\n",
    "    portfolio[idx]={'GPs':np.array([0]*nt, dtype=object), 'weight':1, \n",
    "                    'min':np.array([0]*nt, dtype=object), \n",
    "                    'max':np.array([0]*nt, dtype=object), \n",
    "                    'min_sc_x':np.array([0]*nt, dtype=object),\n",
    "                    'max_sc_x':np.array([0]*nt, dtype=object),\n",
    "                    'min_sc_y':np.array([0]*nt, dtype=object), \n",
    "                    'max_sc_y':np.array([0]*nt, dtype=object)\n",
    "                }\n",
    "\n",
    "gps =[]\n",
    "for i in range(nt): # len(mtm)\n",
    "    for j in range(20): #len(port_idx)):\n",
    "      n_rates=len(irs_map[port_idx[j]])\n",
    "      if i>0:\n",
    "          rates_ = np.zeros([2*M,n_rates+1])  \n",
    "          rates_[:,0]=prev_rates_fx[i][:,irs_map[port_idx[j]][0]]\n",
    "          rates_[:,1:]=rates_fx[i][:,irs_map[port_idx[j]]] \n",
    "      else:\n",
    "          rates_ = np.zeros([2*M,n_rates])  \n",
    "          rates_=rates_fx[i][:,irs_map[port_idx[j]]] \n",
    "      idx=range(int(M/2)) # stratified_sampling(rates_,M)\n",
    "      print(len(idx))  \n",
    "      gp = gaussian_process.GaussianProcessRegressor(kernel=sk_kernel_matern, n_restarts_optimizer=20)\n",
    "      # rescale x and y to the unit interval\n",
    "      rates_sc_=(rates_ - np.min(rates_, axis=0))/(np.max(rates_, axis=0) -np.min(rates_, axis=0) + 1e-16)\n",
    "      irs_prices=mtm[i][j,:]\n",
    "        \n",
    "      if ((np.max(irs_prices) -np.min(irs_prices))!=0):  \n",
    "          irs_prices_sc_=(irs_prices - np.min(irs_prices))/(np.max(irs_prices) -np.min(irs_prices))\n",
    "      else:\n",
    "          irs_prices_sc_=irs_prices - np.min(irs_prices)\n",
    "      #portfolio[port_idx[j]]['GPs'][i]=gp\n",
    "      portfolio[port_idx[j]]['GPs'][i]=gp.fit(rates_sc_[idx,:],irs_prices_sc_[idx]) \n",
    "      portfolio[port_idx[j]]['min'][i]=np.min(rates_[idx,:], axis=0)\n",
    "      portfolio[port_idx[j]]['max'][i]=np.max(rates_[idx,:], axis=0)\n",
    "      portfolio[port_idx[j]]['min_sc_x'][i]=np.min(rates_, axis=0)\n",
    "      portfolio[port_idx[j]]['max_sc_x'][i]=np.max(rates_, axis=0)\n",
    "      portfolio[port_idx[j]]['min_sc_y'][i]=np.min(irs_prices)\n",
    "      portfolio[port_idx[j]]['max_sc_y'][i]=np.max(irs_prices)\n",
    "        \n",
    "      print(i,j)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def CVA_simulation(sim_params, model_params, def_model):\n",
    "    \n",
    "    M        = sim_params['M']        # number of paths\n",
    "    nt       = sim_params['nt']       # number of exposure dates \n",
    "    r        = model_params['r']\n",
    "    T        = model_params['T'] \n",
    "    t0       = model_params['t0'] \n",
    "    haz_rate = model_params['lambda']\n",
    "    n_instruments = model_params['size']\n",
    "    \n",
    "    pi = {}\n",
    "    pi['tilde'] = np.array([0.0]*nt*M, dtype='float32').reshape(nt, M)     # GP portfolio value\n",
    "    pi['exact'] = np.array([0.0]*nt*M, dtype='float32').reshape(nt, M)     # BS portfolio value\n",
    "    pi['tilde_var'] = np.array([0.0]*nt*M, dtype='float32').reshape(nt, M) # GP portfolio variance\n",
    "    dPD = np.array([0.0]*nt*M, dtype='float32').reshape(nt, M)             # default probabilities\n",
    "    dt = T/nt \n",
    "    \n",
    "    for i in range(nt): # len(mtm) \n",
    "      \n",
    "        pred_= 0\n",
    "        var_ = 0\n",
    "        obs_ = 0 \n",
    "\n",
    "        for j in range(n_instruments): # loop over instruments\n",
    "            idx=np.random.choice(range(2*M),M)\n",
    "            irs_prices=mtm[i][j,idx] # test samples\n",
    "            rates=rates_fx[i][:,irs_map[port_idx[j]]]  # test samples\n",
    "            prev_rates=prev_rates_fx[i][:,irs_map[port_idx[j]][0]]  # test samples\n",
    "               \n",
    "            n_rates=np.shape(rates)[1]\n",
    "            \n",
    "            key = port_idx[j]\n",
    "            # avoid simulated rates/FX breaching boundaries of training set\n",
    "            \n",
    "            if i>0:\n",
    "              dim = n_rates+1\n",
    "              test_rates = np.zeros([M,dim])  \n",
    "              test_rates[:,0]=prev_rates[idx]\n",
    "              test_rates[:,1:]=rates[idx,:] \n",
    "            else:\n",
    "              dim = n_rates  \n",
    "              test_rates= np.zeros([M,dim])  \n",
    "              test_rates=rates[idx,:] \n",
    "              # rescale x and y to the unit interval\n",
    "            \n",
    "            for k in range(dim):\n",
    "                idx_min=np.where(test_rates[:,k]<portfolio[key]['min'][i][k])\n",
    "                idx_max=np.where(test_rates[:,k]>portfolio[key]['max'][i][k])\n",
    "                if len(idx_min[0])>0:\n",
    "                    #print(\"min\",idx_min)\n",
    "                    test_rates[idx_min,k]=portfolio[key]['min'][i][k]\n",
    "                if len(idx_max[0])>0:\n",
    "                    #print(\"max\", idx_max)\n",
    "                    test_rates[idx_max,k]=portfolio[key]['max'][i][k]\n",
    "            \n",
    "            min_=portfolio[port_idx[j]]['min_sc_x'][i]\n",
    "            max_=portfolio[port_idx[j]]['max_sc_x'][i]\n",
    "            \n",
    "            test_rates_sc=(test_rates - min_)/(max_-min_)\n",
    "            \n",
    "            pred_sc, std = portfolio[key]['GPs'][i].predict(test_rates_sc,return_std=True) \n",
    "            #print(j, np.mean(pred), np.mean(irs_prices))\n",
    "            min_y_=portfolio[port_idx[j]]['min_sc_y'][i]\n",
    "            max_y_=portfolio[port_idx[j]]['max_sc_y'][i]\n",
    "            \n",
    "            pred= min_y_ + pred_sc*(max_y_-min_y_)\n",
    "            std*=(max_y_-min_y_)\n",
    "            pred_ += portfolio[key]['weight']*pred\n",
    "            var_ += (portfolio[key]['weight']*std)**2 \n",
    "            obs_ += portfolio[key]['weight']*irs_prices\n",
    "\n",
    "        pi['tilde'][i,:] = pred_\n",
    "        pi['exact'][i,:] = obs_\n",
    "        pi['tilde_var'][i,:] = var_ \n",
    "\n",
    "\n",
    "        # compute default probabilities  \n",
    "        dPD[i,:]= haz_rate *np.exp(-haz_rate*dt)#gamma[i-1,m]*exp_factor\n",
    "\n",
    "    CVA ={}\n",
    "    CVA['tilde'] = 0\n",
    "    CVA['exact'] = 0\n",
    "    CVA['exact_up'] = 0\n",
    "    CVA['exact_down'] = 0\n",
    "    CVA['tilde_up'] = 0\n",
    "    CVA['tilde_down'] = 0\n",
    "    \n",
    "      \n",
    "    for i in range(nt):  # timesteps\n",
    "        time = i*dt\n",
    "        mu_tilde = np.mean(dPD[i,:]*pi['tilde'][i,:])*np.exp(-r*(time-t0))*dt\n",
    "        CVA['tilde'] += mu_tilde\n",
    "        std_tilde_err = np.std(dPD[i,:]*pi['tilde'][i,:])*np.exp(-r*(time-t0))*dt/sqrt(M)\n",
    "        \n",
    "        CVA['tilde_up'] += mu_tilde + 2*std_tilde_err\n",
    "        CVA['tilde_down'] += mu_tilde - 2*std_tilde_err\n",
    "        mu_exact = np.mean(dPD[i,:]*pi['exact'][i,:])*np.exp(-r*(time-t0))*dt\n",
    "        CVA['exact'] += mu_exact\n",
    "        std_exact_err = np.std(dPD[i,:]*pi['exact'][i,:])*np.exp(-r*(time-t0))*dt/sqrt(M)\n",
    "        CVA['exact_up'] += mu_exact + 2*std_exact_err\n",
    "        CVA['exact_down'] += mu_exact - 2*std_exact_err\n",
    "        \n",
    "        \n",
    "    CVA['tilde'] *= (1-def_model['recovery'])\n",
    "    CVA['tilde_up'] *= (1-def_model['recovery'])\n",
    "    CVA['tilde_down'] *= (1-def_model['recovery'])\n",
    "    CVA['exact'] *= (1-def_model['recovery'])\n",
    "    CVA['exact_up'] *= (1-def_model['recovery'])\n",
    "    CVA['exact_down'] *= (1-def_model['recovery'])\n",
    "     \n",
    "        \n",
    "    return(CVA, pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n",
      "/Users/matthewdixon/anaconda3/lib/python3.6/site-packages/sklearn/gaussian_process/gpr.py:357: UserWarning: Predicted variances smaller than 0. Setting those variances to 0.\n",
      "  warnings.warn(\"Predicted variances smaller than 0. \"\n"
     ]
    }
   ],
   "source": [
    "def_model ={}\n",
    "def_model['recovery'] = 0.4 # recovery rate\n",
    "\n",
    "sim_params ={}\n",
    "sim_params['M']   = 1000   # Number of simulations  \n",
    "sim_params['nt']  = 10     # Number of exposure dates\n",
    "    \n",
    "model_params= {}   \n",
    "model_params['r'] = 0.02\n",
    "model_params['T'] = 10.0 # Longest dated cash flow maturity in the portfolio \n",
    "model_params['t0'] = 0\n",
    "model_params['lambda']=0.05 # constant hazard rate\n",
    "model_params['size']=20 # number of instruments in portfolio\n",
    "\n",
    "\n",
    "CVA_0, pi_0= CVA_simulation(sim_params, model_params, def_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.24597032331362795"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "100*(CVA_0['exact']-CVA_0['tilde'])/CVA_0['exact'] # % error in CVA_0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'tilde': 3349.5871693198574,\n",
       " 'exact': 3357.846475151162,\n",
       " 'exact_up': 3535.9784394574003,\n",
       " 'exact_down': 3179.714510844924,\n",
       " 'tilde_up': 3522.0718258715874,\n",
       " 'tilde_down': 3177.102512768127}"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CVA_0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "epe_gp=np.mean(pi_0['tilde'], axis=1)\n",
    "epe_obs=np.mean(pi_0['exact'], axis=1)\n",
    "epe_var=np.mean(pi_0['tilde_var'], axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'EPE (Euro)')"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (10, 6), facecolor='white', edgecolor='black')\n",
    "plt.plot(0.1+np.arange(10), epe_gp, color = 'red', label = 'GP Prediction')\n",
    "plt.plot(0.1+np.arange(10), epe_obs, color = 'black', label = 'Analytical Model')\n",
    "plt.fill_between(0.1+np.arange(10), (epe_gp-2.0*np.sqrt(epe_var)), (epe_gp+2.0*np.sqrt(epe_var)), color = 'grey', alpha=0.3)\n",
    "plt.legend(loc = 'best', prop={'size':10})\n",
    "#plt.xlim([KC/2.0,2.0*KC])\n",
    "#plt.ylim([0,150])\n",
    "plt.xlabel('time (years)')\n",
    "plt.ylabel('EPE (Euro)')"
   ]
  }
 ],
 "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}