Fisher_Information.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import glob\n",
    "import seaborn as sns\n",
    "from tqdm import tqdm\n",
    "%matplotlib inline\n",
    "plt.ioff()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/fas/jiang/sk943/anaconda3/lib/python3.6/site-packages/h5py/__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
      "  from ._conv import register_converters as _register_converters\n",
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "from hamest import *\n",
    "import keras\n",
    "from keras.models import Sequential\n",
    "from keras.optimizers import Adam, Nadam\n",
    "from ringham import *\n",
    "\n",
    "n=3\n",
    "batch_size = 512\n",
    "\n",
    "nb_drives = qubitring_ndrives(n)\n",
    "hs = np.stack([_.full() for _ in qubitring_all_ops(n)])\n",
    "\n",
    "_epsilons = [0.1]*n\n",
    "_etas = [0.01]*n\n",
    "_deltas = [2.]*qubitring_ndrives(n)\n",
    "jitter = 0.05\n",
    "s = np.random.RandomState(seed=36)\n",
    "_epsilons *= s.normal(loc=1., scale=jitter, size=n)\n",
    "_etas     *= s.normal(loc=1., scale=jitter, size=n)\n",
    "_deltas   *= s.normal(loc=1., scale=jitter, size=qubitring_ndrives(n))\n",
    "\n",
    "H0 = qubitring_H0(n, _epsilons, _etas).full()\n",
    "Hdrives = np.stack([_.full() for _ in qubitring_Hdrives(n, _deltas)])\n",
    "\n",
    "val_seed = 1\n",
    "train_seed = 42\n",
    "validation_data = next(qubitring_datagen(H0, Hdrives, n=n, batch_size=batch_size, Delta=1., seed=val_seed, average_over=float('inf')))\n",
    "\n",
    "model = Sequential()\n",
    "model.add(StateProbabilitiesPaulied(nqubits=n, ndrives=nb_drives, paulies=hs,\n",
    "                                    l1_lambda=0))\n",
    "model.compile(loss='mse', optimizer=Nadam(lr=5e-4), metrics=['mse', 'mae', 'binary_crossentropy'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class FIStateProbabilitiesPaulied(Layer):\n",
    "    '''Calculate the Fisher Information matrix for a `StateProbabilitiesPaulied` estimator.\n",
    "    \n",
    "    XXX There is a lot of code duplication here.\n",
    "    XXX You have to say the batch size in advance, including when creating the input to this layer.\n",
    "    '''\n",
    "    def __init__(self, ndrives, nqubits, paulies, batch_size=512, l1_lambda=None, **kwargs):\n",
    "        self.ndrives = ndrives\n",
    "        self.nqubits = nqubits\n",
    "        self.lenpaulies = paulies.shape[0]\n",
    "        self.paulies = tf.constant(value=paulies, dtype='complex128')\n",
    "        self.regularizer_k = L1variable(l1=l1_lambda) if l1_lambda else None\n",
    "        self.regularizer_b = L1variable(l1=l1_lambda) if l1_lambda else None\n",
    "        self.batch_size = batch_size\n",
    "        super().__init__(input_shape=(self.ndrives,), **kwargs)\n",
    "\n",
    "    def build(self, input_shape):\n",
    "        w_init = 'normal'\n",
    "        b_init = 'normal'\n",
    "        self.kernel = self.add_weight(name='kernel', \n",
    "                                      shape=(self.ndrives,self.lenpaulies,),\n",
    "                                      initializer=w_init,\n",
    "                                      trainable=False,\n",
    "                                      regularizer=self.regularizer_k)\n",
    "        self.bias = self.add_weight(name='bias', \n",
    "                                    shape=(self.lenpaulies,),\n",
    "                                    initializer=b_init,\n",
    "                                    trainable=False,\n",
    "                                    regularizer=self.regularizer_b)\n",
    "        super().build(input_shape)\n",
    "        \n",
    "    def tensorflowH(self, x):\n",
    "        pauli_weights = K.bias_add(K.dot(x, self.kernel), self.bias)\n",
    "        self._tensorflowH = tf.tensordot(tf.cast(pauli_weights, 'complex128'), self.paulies, axes=[[1],[0]])\n",
    "        return self._tensorflowH\n",
    "\n",
    "    def call(self, x):\n",
    "        H = self.tensorflowH(x)\n",
    "        e, v = tf.self_adjoint_eig(H)\n",
    "        expe = tf.exp(-1j*e)\n",
    "        amp = tf.einsum('is,ijs->ij', tf.conj(v)[:,0,:]*expe, v)\n",
    "        P = tf.abs(amp)**2\n",
    "        oneoverp = 1./P\n",
    "        def jac(singlep, wrt): # this works on p of shape (2**nqubits,)\n",
    "            #print(singlep.shape)\n",
    "            p_list = tf.unstack(singlep,axis=0,)\n",
    "            jacobian_list = [tf.gradients(p_, wrt)[0] for p_ in p_list]  # list [grad(y0, x), grad(y1, x), ...]\n",
    "            stack = tf.stack(jacobian_list)\n",
    "            #print(jacobian_list[0].shape, stack.shape)\n",
    "            return stack\n",
    "        def bodywrt(allp,wrt):\n",
    "            def body(old_g, t):\n",
    "                g = jac(allp[t,:],wrt)\n",
    "                new_g = tuple(tf.cond(tf.equal(ti, t),\n",
    "                                      lambda :g,\n",
    "                                      lambda :old_g[ti])\n",
    "                              for ti in range(len(old_g)))\n",
    "                return new_g, t + 1\n",
    "            return body\n",
    "        def cond(_, t):\n",
    "            return tf.less(t, tf.shape(x)[0])\n",
    "\n",
    "        p_k = tf.while_loop(cond, bodywrt(P,self.kernel),\n",
    "                            [(tf.zeros((2**self.nqubits,*self.kernel.shape), dtype='float64'),)*self.batch_size,\n",
    "                             tf.constant(0)])\n",
    "        p_b = tf.while_loop(cond, bodywrt(P,self.bias),\n",
    "                            [(tf.zeros((2**self.nqubits,*self.bias.shape  ), dtype='float64'),)*self.batch_size,\n",
    "                             tf.constant(0)])\n",
    "        p_k = tf.stack(p_k[0],name='dpdk')\n",
    "        p_b = tf.stack(p_b[0],name='dpdb')\n",
    "        p_b = tf.Print(p_b,[p_b[0,:,0]], summarize=15)\n",
    "        #print(p_k.shape,p_b.shape,oneoverp.shape)\n",
    "        I_k = tf.einsum('ipjk,iplm,ip->ijklm', p_k, p_k, oneoverp)\n",
    "        I_b = tf.einsum('ipj,ipk,ip->ijk', p_b, p_b, oneoverp)\n",
    "        #print(I_k.shape,I_b.shape)\n",
    "        return [I_k, I_b]\n",
    "\n",
    "    def compute_output_shape(self, input_shape):\n",
    "        return [(input_shape[0], *[self.ndrives,self.lenpaulies]*2),\n",
    "                (input_shape[0], *[self.lenpaulies]*2)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:Falling back to exponential-space implementation of einsum() because index \"p\" is summed over more than two inputs.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:Falling back to exponential-space implementation of einsum() because index \"p\" is summed over more than two inputs.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:Falling back to exponential-space implementation of einsum() because index \"p\" is summed over more than two inputs.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:Falling back to exponential-space implementation of einsum() because index \"p\" is summed over more than two inputs.\n"
     ]
    }
   ],
   "source": [
    "i = keras.Input(batch_shape=(batch_size,nb_drives),)\n",
    "hk,hb = FIStateProbabilitiesPaulied(nqubits=n, ndrives=nb_drives, paulies=hs, batch_size=batch_size)(i)\n",
    "fi = keras.Model(inputs=[i],outputs=[hk,hb])\n",
    "fi.compile(loss='mse', optimizer=Nadam(lr=5e-4),)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "model.load_weights('./current_test/mod_checkpoint_3_0.0_inf_64_1024')\n",
    "fi.set_weights(model.get_weights())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(512, 12)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "validation_data[0].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1min 31s, sys: 5.38 s, total: 1min 37s\n",
      "Wall time: 29 s\n"
     ]
    }
   ],
   "source": [
    "%time ks, bs = fi.predict(validation_data[0], batch_size=batch_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = np.mean(ks, axis=0)\n",
    "b = np.mean(bs, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "s = k.shape\n",
    "k_flat = np.reshape(k, (s[0]*s[1],s[2]*s[3]))\n",
    "indices = [i*s[0]+i for i in range(s[0])]\n",
    "k_onlydiag = k_flat[indices,:][:,indices]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b3afbbcc0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(b,vmin=0,vmax=2)\n",
    "ticks=['Z1','Z2','Z3','X1','X2','X3','Y1','Y2','Y3','12','23','31']\n",
    "ax = plt.gca()\n",
    "ax.set_xticks(range(12))\n",
    "ax.set_yticks(range(12))\n",
    "ax.set_xticklabels(ticks)\n",
    "ax.set_yticklabels(ticks)\n",
    "plt.colorbar()\n",
    "plt.title('Fisher Information for\\nthe parameters β')\n",
    "plt.tight_layout()\n",
    "plt.savefig('FI_b.png',dpi=400,bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b3b560f94a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(k_flat,vmin=0,vmax=2)\n",
    "ax = plt.gca()\n",
    "ax.set_xticks(range(6,12**2,12))\n",
    "ax.set_yticks(range(6,12**2,12))\n",
    "ax.set_xticklabels(['']*12)\n",
    "ax.set_yticklabels(['']*12)\n",
    "plt.title('Fisher Information for all\\ncomponents of the parameter matrix α')\n",
    "plt.tight_layout()\n",
    "plt.savefig('FI_a.png',dpi=400,bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2b3afb9cae48>]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b3a9b21f860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(k_flat.diagonal())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b3b56253668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(k_onlydiag,vmin=0,vmax=2)\n",
    "ax = plt.gca()\n",
    "ax.set_xticks(range(12))\n",
    "ax.set_yticks(range(12))\n",
    "ax.set_xticklabels(ticks)\n",
    "ax.set_yticklabels(ticks)\n",
    "plt.title('Fisher Information for the\\ndiagonal of the parameter matrix α')\n",
    "plt.tight_layout()\n",
    "plt.savefig('FI_ad.png',dpi=400,bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "class ReLURegularizer(Regularizer):\n",
    "    '''A naive soft cutoff regularizer.\n",
    "    \n",
    "    XXX For production use this need to be annealable.'''\n",
    "    def __call__(self, x):\n",
    "        regularization = K.relu(K.mean(K.abs(x)**2)-1)*20\n",
    "        return regularization\n",
    "\n",
    "    def get_config(self):\n",
    "        raise NotImplementedError\n",
    "\n",
    "class AvgFIStateProbabilitiesPaulied(Layer):\n",
    "    '''Optimize the drives for maximum Fisher Information (for a `StateProbabilitiesPaulied` estimator).\n",
    "    \n",
    "    Looks only at the diagonals of the Fisher Information matrix.\n",
    "    \n",
    "    XXX There is a lot of code duplication here (and the gradient is evaluated manually, because the while_loop op is slow and painful)\n",
    "    XXX You have to say the drive batch size in advance (it is not the input batch size)!\n",
    "    XXX This is takes input of batch size 1 only (and does not use the input for calculations - a side effect of using Keras for something it is not meant for).\n",
    "    '''\n",
    "    def __init__(self, ndrives, nqubits, paulies, batch_size=512, power_reg=None, use_tanh=False, prodloss=False, **kwargs):\n",
    "        self.ndrives = ndrives\n",
    "        self.nqubits = nqubits\n",
    "        self.lenpaulies = paulies.shape[0]\n",
    "        self.paulies = tf.constant(value=paulies, dtype='complex128')\n",
    "        self.regularizer_d = ReLURegularizer() if power_reg else None\n",
    "        self.batch_size = batch_size\n",
    "        self.use_tanh = use_tanh\n",
    "        self.prodloss = prodloss\n",
    "        super().__init__(input_shape=(self.ndrives,), **kwargs)\n",
    "\n",
    "    def build(self, input_shape):\n",
    "        w_init = 'normal'\n",
    "        b_init = 'normal'\n",
    "        d_init = 'normal'\n",
    "        self.kernel = self.add_weight(name='kernel', \n",
    "                                      shape=(self.ndrives,self.lenpaulies,),\n",
    "                                      initializer=w_init,\n",
    "                                      trainable=False)\n",
    "        self.bias = self.add_weight(name='bias', \n",
    "                                    shape=(self.lenpaulies,),\n",
    "                                    initializer=b_init,\n",
    "                                    trainable=False)\n",
    "        self.drives = self.add_weight(name='bias', \n",
    "                                      shape=(self.batch_size, self.ndrives),\n",
    "                                      initializer=d_init,\n",
    "                                      trainable=True,\n",
    "                                      regularizer=self.regularizer_d)\n",
    "        super().build(input_shape)\n",
    "        \n",
    "    def tensorflowH(self, x):\n",
    "        pauli_weights = K.bias_add(K.dot(x, self.kernel), self.bias)\n",
    "        self._tensorflowH = tf.tensordot(tf.cast(pauli_weights, 'complex128'), self.paulies, axes=[[1],[0]])\n",
    "        return self._tensorflowH # indices [batch, hilbert, hilbert]\n",
    "    \n",
    "    def call(self, x):\n",
    "        if self.use_tanh:\n",
    "            d = K.tanh(self.drives)\n",
    "        else:\n",
    "            d = self.drives\n",
    "        H = self.tensorflowH(d)\n",
    "        def HtoP(H):\n",
    "            e, v = tf.self_adjoint_eig(H)\n",
    "            cv = tf.conj(v)\n",
    "            expe = tf.exp(-1j*e)\n",
    "            amp = tf.einsum('is,ijs->ij', cv[:,0,:]*expe, v)\n",
    "            return tf.abs(amp)**2\n",
    "        P = HtoP(H)\n",
    "        oneoverP = 1/P\n",
    "        delta = tf.constant(1e-6,dtype=tf.complex128) # XXX No, I do not want to talk about this. It haunts my dreams already.\n",
    "        deltar = tf.cast(delta,tf.float64)\n",
    "        P_dbias = HtoP(tf.reshape(tf.expand_dims(H,1)+tf.expand_dims(self.paulies,0)*delta,[-1,2**self.nqubits,2**self.nqubits]))\n",
    "        P_dbias = tf.reshape(P_dbias, [self.batch_size,self.lenpaulies,2**self.nqubits])\n",
    "        P_dbias = (P_dbias - tf.expand_dims(P,1))/deltar\n",
    "        P_dkernel = HtoP(tf.reshape(\n",
    "            tf.expand_dims(tf.expand_dims(H,1),1)+tf.einsum('bp,qij->bpqij',tf.cast(d,tf.complex128),self.paulies)*delta,\n",
    "            [-1,2**self.nqubits,2**self.nqubits]))\n",
    "        P_dkernel = tf.reshape(P_dkernel, [self.batch_size,self.ndrives,self.lenpaulies,2**self.nqubits])\n",
    "        P_dkernel = (P_dkernel - tf.expand_dims(tf.expand_dims(P,1),1))/deltar\n",
    "        \n",
    "        I_k = tf.reshape(tf.einsum('bdei,bdei,bi->de', P_dkernel, P_dkernel, oneoverP), [-1])\n",
    "        I_b = tf.einsum('bdi,bdi,bi->d', P_dbias, P_dbias, oneoverP)\n",
    "        I = tf.reshape(tf.concat([I_k,I_b],0), [1,-1])/self.batch_size\n",
    "        if self.prodloss:\n",
    "            return tf.log(I)\n",
    "        return I\n",
    "\n",
    "    def compute_output_shape(self, input_shape):\n",
    "        return (1, (self.ndrives+1)*self.lenpaulies)\n",
    "    \n",
    "def negmean(y_true, y_pred):\n",
    "    return -tf.reduce_mean(y_pred)\n",
    "def negmeanexp(y_true, y_pred):\n",
    "    return -tf.exp(tf.reduce_mean(y_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:Falling back to exponential-space implementation of einsum() because index \"i\" is summed over more than two inputs.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:Falling back to exponential-space implementation of einsum() because index \"i\" is summed over more than two inputs.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:Falling back to exponential-space implementation of einsum() because index \"i\" is summed over more than two inputs.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:Falling back to exponential-space implementation of einsum() because index \"i\" is summed over more than two inputs.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 2.53 s, sys: 87.7 ms, total: 2.62 s\n",
      "Wall time: 964 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.45772857566786884"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i = keras.Input(batch_shape=(1,1))\n",
    "o = AvgFIStateProbabilitiesPaulied(nqubits=n, ndrives=nb_drives, paulies=hs, batch_size=batch_size, power_reg=False, use_tanh=False)(i)\n",
    "fii = keras.Model(inputs=[i],outputs=[o])\n",
    "fii.compile(loss=negmean, optimizer=Nadam(lr=0.1))\n",
    "fii.set_weights([validation_data[0]]+model.get_weights())\n",
    "%time np.mean(fii.predict(np.array([1]),batch_size=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:Falling back to exponential-space implementation of einsum() because index \"i\" is summed over more than two inputs.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:Falling back to exponential-space implementation of einsum() because index \"i\" is summed over more than two inputs.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:Falling back to exponential-space implementation of einsum() because index \"i\" is summed over more than two inputs.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:Falling back to exponential-space implementation of einsum() because index \"i\" is summed over more than two inputs.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 2.54 s, sys: 80.5 ms, total: 2.63 s\n",
      "Wall time: 977 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.252073658185657"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i = keras.Input(batch_shape=(1,1))\n",
    "o = AvgFIStateProbabilitiesPaulied(nqubits=n, ndrives=nb_drives, paulies=hs, batch_size=batch_size, power_reg=False, use_tanh=True)(i)\n",
    "fio1 = keras.Model(inputs=[i],outputs=[o])\n",
    "fio1.compile(loss=negmean, optimizer=Nadam(lr=0.1))\n",
    "fio1.set_weights([validation_data[0]]+model.get_weights())\n",
    "%time np.mean(fio1.predict(np.array([1]),batch_size=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1min 26s, sys: 6.41 s, total: 1min 32s\n",
      "Wall time: 25 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "fake_data = np.ones((1,))\n",
    "h1 = fio1.fit(x=fake_data,y=fake_data,batch_size=1,epochs=20,verbose=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5578511074226239"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(fio1.predict(np.array([1]),batch_size=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "#fio1.save_weights('optimized_drives1')\n",
    "fio1.load_weights('optimized_drives1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:Falling back to exponential-space implementation of einsum() because index \"b\" is summed over more than two inputs.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:Falling back to exponential-space implementation of einsum() because index \"b\" is summed over more than two inputs.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:Falling back to exponential-space implementation of einsum() because index \"b\" is summed over more than two inputs.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:Falling back to exponential-space implementation of einsum() because index \"b\" is summed over more than two inputs.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 2.37 s, sys: 61.9 ms, total: 2.43 s\n",
      "Wall time: 2.2 s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1.0060460678539516"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i = keras.Input(batch_shape=(1,1))\n",
    "o = AvgFIStateProbabilitiesPaulied(nqubits=n, ndrives=nb_drives, paulies=hs, batch_size=batch_size, power_reg=True, use_tanh=False)(i)\n",
    "fio2 = keras.Model(inputs=[i],outputs=[o])\n",
    "fio2.compile(loss=negmean, optimizer=Nadam(lr=0.05), metrics=[negmean])\n",
    "fio2.set_weights([validation_data[0]]+model.get_weights())\n",
    "%time np.mean(fio2.predict(np.array([1]),batch_size=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "#K.set_value(fio2.optimizer.lr, 0.001)\n",
    "#K.get_value(fio2.optimizer.lr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 44.4 s, sys: 3.5 s, total: 47.9 s\n",
      "Wall time: 13.9 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "fake_data = np.ones((1,))\n",
    "h2 = fio2.fit(x=fake_data,y=fake_data,batch_size=1,epochs=10,verbose=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.861749725126653"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(fio2.predict(np.array([1]),batch_size=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "#fio2.save_weights('optimized_drives2')\n",
    "fio2.load_weights('optimized_drives2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:Falling back to exponential-space implementation of einsum() because index \"b\" is summed over more than two inputs.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:Falling back to exponential-space implementation of einsum() because index \"b\" is summed over more than two inputs.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:Falling back to exponential-space implementation of einsum() because index \"b\" is summed over more than two inputs.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:Falling back to exponential-space implementation of einsum() because index \"b\" is summed over more than two inputs.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 2.36 s, sys: 69.7 ms, total: 2.43 s\n",
      "Wall time: 2.19 s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.19081894076010306"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i = keras.Input(batch_shape=(1,1))\n",
    "o = AvgFIStateProbabilitiesPaulied(nqubits=n, ndrives=nb_drives, paulies=hs, batch_size=batch_size, power_reg=True, use_tanh=False, prodloss=True)(i)\n",
    "fio3 = keras.Model(inputs=[i],outputs=[o])\n",
    "fio3.compile(loss=negmeanexp, optimizer=Nadam(lr=0.05), metrics=[negmeanexp])\n",
    "fio3.set_weights([validation_data[0]]+model.get_weights())\n",
    "%time np.exp(np.mean(fio3.predict(np.array([1]),batch_size=1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.001"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K.set_value(fio3.optimizer.lr, 0.001)\n",
    "K.get_value(fio3.optimizer.lr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/300\n",
      " - 1s - loss: -7.1344e-01 - negmeanexp: -7.1344e-01\n",
      "Epoch 2/300\n",
      " - 1s - loss: -7.1540e-01 - negmeanexp: -7.1540e-01\n",
      "Epoch 3/300\n",
      " - 1s - loss: -7.1639e-01 - negmeanexp: -7.1639e-01\n",
      "Epoch 4/300\n",
      " - 1s - loss: -7.1723e-01 - negmeanexp: -7.1723e-01\n",
      "Epoch 5/300\n",
      " - 1s - loss: -7.1799e-01 - negmeanexp: -7.1799e-01\n",
      "Epoch 6/300\n",
      " - 1s - loss: -7.1868e-01 - negmeanexp: -7.1868e-01\n",
      "Epoch 7/300\n",
      " - 1s - loss: -7.1932e-01 - negmeanexp: -7.1932e-01\n",
      "Epoch 8/300\n",
      " - 1s - loss: -7.1992e-01 - negmeanexp: -7.1992e-01\n",
      "Epoch 9/300\n",
      " - 1s - loss: -7.2049e-01 - negmeanexp: -7.2049e-01\n",
      "Epoch 10/300\n",
      " - 1s - loss: -7.2103e-01 - negmeanexp: -7.2103e-01\n",
      "Epoch 11/300\n",
      " - 1s - loss: -7.2155e-01 - negmeanexp: -7.2155e-01\n",
      "Epoch 12/300\n",
      " - 1s - loss: -7.2206e-01 - negmeanexp: -7.2206e-01\n",
      "Epoch 13/300\n",
      " - 1s - loss: -7.2254e-01 - negmeanexp: -7.2254e-01\n",
      "Epoch 14/300\n",
      " - 1s - loss: -7.2296e-01 - negmeanexp: -7.2296e-01\n",
      "Epoch 15/300\n",
      " - 1s - loss: -7.2346e-01 - negmeanexp: -7.2346e-01\n",
      "Epoch 16/300\n",
      " - 1s - loss: -7.2391e-01 - negmeanexp: -7.2391e-01\n",
      "Epoch 17/300\n",
      " - 1s - loss: -7.2434e-01 - negmeanexp: -7.2434e-01\n",
      "Epoch 18/300\n",
      " - 1s - loss: -7.2476e-01 - negmeanexp: -7.2476e-01\n",
      "Epoch 19/300\n",
      " - 1s - loss: -7.2518e-01 - negmeanexp: -7.2518e-01\n",
      "Epoch 20/300\n",
      " - 1s - loss: -7.2557e-01 - negmeanexp: -7.2557e-01\n",
      "Epoch 21/300\n",
      " - 1s - loss: -7.2596e-01 - negmeanexp: -7.2596e-01\n",
      "Epoch 22/300\n",
      " - 1s - loss: -7.2634e-01 - negmeanexp: -7.2634e-01\n",
      "Epoch 23/300\n",
      " - 1s - loss: -7.2671e-01 - negmeanexp: -7.2671e-01\n",
      "Epoch 24/300\n",
      " - 1s - loss: -7.2708e-01 - negmeanexp: -7.2708e-01\n",
      "Epoch 25/300\n",
      " - 1s - loss: -7.2743e-01 - negmeanexp: -7.2743e-01\n",
      "Epoch 26/300\n",
      " - 1s - loss: -7.2773e-01 - negmeanexp: -7.2773e-01\n",
      "Epoch 27/300\n",
      " - 1s - loss: -7.2812e-01 - negmeanexp: -7.2812e-01\n",
      "Epoch 28/300\n",
      " - 1s - loss: -7.2842e-01 - negmeanexp: -7.2842e-01\n",
      "Epoch 29/300\n",
      " - 1s - loss: -7.2874e-01 - negmeanexp: -7.2874e-01\n",
      "Epoch 30/300\n",
      " - 1s - loss: -7.2907e-01 - negmeanexp: -7.2907e-01\n",
      "Epoch 31/300\n",
      " - 1s - loss: -7.2938e-01 - negmeanexp: -7.2938e-01\n",
      "Epoch 32/300\n",
      " - 1s - loss: -7.2967e-01 - negmeanexp: -7.2967e-01\n",
      "Epoch 33/300\n",
      " - 1s - loss: -7.2995e-01 - negmeanexp: -7.2995e-01\n",
      "Epoch 34/300\n",
      " - 1s - loss: -7.3028e-01 - negmeanexp: -7.3028e-01\n",
      "Epoch 35/300\n",
      " - 1s - loss: -7.3058e-01 - negmeanexp: -7.3058e-01\n",
      "Epoch 36/300\n",
      " - 1s - loss: -7.3088e-01 - negmeanexp: -7.3088e-01\n",
      "Epoch 37/300\n",
      " - 1s - loss: -7.3118e-01 - negmeanexp: -7.3118e-01\n",
      "Epoch 38/300\n",
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      " - 1s - loss: -7.5917e-01 - negmeanexp: -7.5917e-01\n",
      "Epoch 216/300\n",
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      "Epoch 217/300\n",
      " - 1s - loss: -7.5943e-01 - negmeanexp: -7.5943e-01\n",
      "Epoch 218/300\n",
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      "Epoch 219/300\n",
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      "Epoch 220/300\n",
      " - 1s - loss: -7.5991e-01 - negmeanexp: -7.5991e-01\n",
      "Epoch 221/300\n",
      " - 1s - loss: -7.5997e-01 - negmeanexp: -7.5997e-01\n",
      "Epoch 222/300\n",
      " - 1s - loss: -7.6008e-01 - negmeanexp: -7.6008e-01\n",
      "Epoch 223/300\n",
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      "Epoch 224/300\n",
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      "Epoch 225/300\n",
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      "Epoch 226/300\n",
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      "Epoch 227/300\n",
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      "Epoch 228/300\n",
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      "Epoch 229/300\n",
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      "Epoch 230/300\n",
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      "Epoch 231/300\n",
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      "Epoch 232/300\n",
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      "Epoch 233/300\n",
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      "Epoch 234/300\n",
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      "Epoch 235/300\n",
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      "Epoch 236/300\n",
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      "Epoch 237/300\n",
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      "Epoch 238/300\n",
      " - 1s - loss: -7.5917e-01 - negmeanexp: -7.5917e-01\n",
      "Epoch 239/300\n",
      " - 1s - loss: -7.5918e-01 - negmeanexp: -7.5918e-01\n",
      "Epoch 240/300\n",
      " - 1s - loss: -7.5917e-01 - negmeanexp: -7.5917e-01\n",
      "Epoch 241/300\n",
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      "Epoch 242/300\n",
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      "Epoch 243/300\n",
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      "Epoch 244/300\n",
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      "Epoch 245/300\n",
      " - 1s - loss: -7.5951e-01 - negmeanexp: -7.5951e-01\n",
      "Epoch 246/300\n",
      " - 1s - loss: -7.5959e-01 - negmeanexp: -7.5959e-01\n",
      "Epoch 247/300\n",
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      "Epoch 248/300\n",
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      "Epoch 249/300\n",
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      "Epoch 250/300\n",
      " - 1s - loss: -7.5999e-01 - negmeanexp: -7.5999e-01\n",
      "Epoch 251/300\n",
      " - 1s - loss: -7.6014e-01 - negmeanexp: -7.6014e-01\n",
      "Epoch 252/300\n",
      " - 1s - loss: -7.6019e-01 - negmeanexp: -7.6019e-01\n",
      "Epoch 253/300\n",
      " - 1s - loss: -7.6033e-01 - negmeanexp: -7.6033e-01\n",
      "Epoch 254/300\n",
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      "Epoch 255/300\n",
      " - 1s - loss: -7.6064e-01 - negmeanexp: -7.6064e-01\n",
      "Epoch 256/300\n",
      " - 1s - loss: -7.6077e-01 - negmeanexp: -7.6077e-01\n",
      "Epoch 257/300\n",
      " - 1s - loss: -7.6088e-01 - negmeanexp: -7.6088e-01\n",
      "Epoch 258/300\n",
      " - 1s - loss: -7.6101e-01 - negmeanexp: -7.6101e-01\n",
      "Epoch 259/300\n",
      " - 1s - loss: -7.6105e-01 - negmeanexp: -7.6105e-01\n",
      "Epoch 260/300\n",
      " - 1s - loss: -7.6121e-01 - negmeanexp: -7.6121e-01\n",
      "Epoch 261/300\n",
      " - 1s - loss: -7.6141e-01 - negmeanexp: -7.6141e-01\n",
      "Epoch 262/300\n",
      " - 1s - loss: -7.6145e-01 - negmeanexp: -7.6145e-01\n",
      "Epoch 263/300\n",
      " - 1s - loss: -7.6147e-01 - negmeanexp: -7.6147e-01\n",
      "Epoch 264/300\n",
      " - 1s - loss: -7.6166e-01 - negmeanexp: -7.6166e-01\n",
      "Epoch 265/300\n",
      " - 1s - loss: -7.6180e-01 - negmeanexp: -7.6180e-01\n",
      "Epoch 266/300\n",
      " - 1s - loss: -7.6192e-01 - negmeanexp: -7.6192e-01\n",
      "Epoch 267/300\n",
      " - 1s - loss: -7.6211e-01 - negmeanexp: -7.6211e-01\n",
      "Epoch 268/300\n",
      " - 1s - loss: -7.6221e-01 - negmeanexp: -7.6221e-01\n",
      "Epoch 269/300\n",
      " - 1s - loss: -7.6235e-01 - negmeanexp: -7.6235e-01\n",
      "Epoch 270/300\n",
      " - 1s - loss: -7.6248e-01 - negmeanexp: -7.6248e-01\n",
      "Epoch 271/300\n",
      " - 1s - loss: -7.6271e-01 - negmeanexp: -7.6271e-01\n",
      "Epoch 272/300\n",
      " - 1s - loss: -7.6283e-01 - negmeanexp: -7.6283e-01\n",
      "Epoch 273/300\n",
      " - 1s - loss: -7.6292e-01 - negmeanexp: -7.6292e-01\n",
      "Epoch 274/300\n",
      " - 1s - loss: -7.6308e-01 - negmeanexp: -7.6308e-01\n",
      "Epoch 275/300\n",
      " - 1s - loss: -7.6316e-01 - negmeanexp: -7.6316e-01\n",
      "Epoch 276/300\n",
      " - 1s - loss: -7.6337e-01 - negmeanexp: -7.6337e-01\n",
      "Epoch 277/300\n",
      " - 1s - loss: -7.6171e-01 - negmeanexp: -7.6344e-01\n",
      "Epoch 278/300\n",
      " - 1s - loss: -7.6006e-01 - negmeanexp: -7.6006e-01\n",
      "Epoch 279/300\n",
      " - 1s - loss: -7.6063e-01 - negmeanexp: -7.6063e-01\n",
      "Epoch 280/300\n",
      " - 1s - loss: -7.6075e-01 - negmeanexp: -7.6075e-01\n",
      "Epoch 281/300\n",
      " - 1s - loss: -7.6081e-01 - negmeanexp: -7.6081e-01\n",
      "Epoch 282/300\n",
      " - 1s - loss: -7.6085e-01 - negmeanexp: -7.6085e-01\n",
      "Epoch 283/300\n",
      " - 1s - loss: -7.6088e-01 - negmeanexp: -7.6088e-01\n",
      "Epoch 284/300\n",
      " - 1s - loss: -7.6093e-01 - negmeanexp: -7.6093e-01\n",
      "Epoch 285/300\n",
      " - 1s - loss: -7.6098e-01 - negmeanexp: -7.6098e-01\n",
      "Epoch 286/300\n",
      " - 1s - loss: -7.6105e-01 - negmeanexp: -7.6105e-01\n",
      "Epoch 287/300\n",
      " - 1s - loss: -7.6113e-01 - negmeanexp: -7.6113e-01\n",
      "Epoch 288/300\n",
      " - 1s - loss: -7.6121e-01 - negmeanexp: -7.6121e-01\n",
      "Epoch 289/300\n",
      " - 1s - loss: -7.6131e-01 - negmeanexp: -7.6131e-01\n",
      "Epoch 290/300\n",
      " - 1s - loss: -7.6142e-01 - negmeanexp: -7.6142e-01\n",
      "Epoch 291/300\n",
      " - 1s - loss: -7.6151e-01 - negmeanexp: -7.6151e-01\n",
      "Epoch 292/300\n",
      " - 1s - loss: -7.6155e-01 - negmeanexp: -7.6155e-01\n",
      "Epoch 293/300\n",
      " - 1s - loss: -7.6169e-01 - negmeanexp: -7.6169e-01\n",
      "Epoch 294/300\n",
      " - 1s - loss: -7.6182e-01 - negmeanexp: -7.6182e-01\n",
      "Epoch 295/300\n",
      " - 1s - loss: -7.6191e-01 - negmeanexp: -7.6191e-01\n",
      "Epoch 296/300\n",
      " - 1s - loss: -7.6208e-01 - negmeanexp: -7.6208e-01\n",
      "Epoch 297/300\n",
      " - 1s - loss: -7.6218e-01 - negmeanexp: -7.6218e-01\n",
      "Epoch 298/300\n",
      " - 1s - loss: -7.6239e-01 - negmeanexp: -7.6239e-01\n",
      "Epoch 299/300\n",
      " - 1s - loss: -7.6249e-01 - negmeanexp: -7.6249e-01\n",
      "Epoch 300/300\n",
      " - 1s - loss: -7.6259e-01 - negmeanexp: -7.6259e-01\n",
      "CPU times: user 21min 7s, sys: 1min 41s, total: 22min 49s\n",
      "Wall time: 5min 50s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "fake_data = np.ones((1,))\n",
    "h3 = fio3.fit(x=fake_data,y=fake_data,batch_size=1,epochs=300,verbose=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#fio3.save_weights('optimized_drives2')\n",
    "fio3.load_weights('optimized_drives2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "#opt_drives = np.tanh(fio1.get_weights()[0])\n",
    "#opt_drives = fio2.get_weights()[0]\n",
    "opt_drives = fio3.get_weights()[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1min 26s, sys: 5.45 s, total: 1min 32s\n",
      "Wall time: 24.3 s\n"
     ]
    }
   ],
   "source": [
    "%time ks, bs = fi.predict(opt_drives, batch_size=batch_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "kn = np.mean(ks, axis=0)\n",
    "bn = np.mean(bs, axis=0)\n",
    "s = k.shape\n",
    "kn_flat = np.reshape(kn, (s[0]*s[1],s[2]*s[3]))\n",
    "indices = [i*s[0]+i for i in range(s[0])]\n",
    "kn_onlydiag = kn_flat[indices,:][:,indices]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8617514310694224"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(np.hstack([bn.diagonal(),kn_flat.diagonal()]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b3b1fffb128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(bn,vmin=0,vmax=2.5)\n",
    "ticks=['Z1','Z2','Z3','X1','X2','X3','Y1','Y2','Y3','12','23','31']\n",
    "ax = plt.gca()\n",
    "ax.set_xticks(range(12))\n",
    "ax.set_yticks(range(12))\n",
    "ax.set_xticklabels(ticks)\n",
    "ax.set_yticklabels(ticks)\n",
    "plt.title('Optimized Fisher Information for\\nthe parameters β')\n",
    "plt.tight_layout()\n",
    "plt.savefig('FI_b_opt.png',dpi=400,bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b3b569fe828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(kn_flat,vmin=0,vmax=2.5)\n",
    "ax = plt.gca()\n",
    "ax.set_xticks(range(6,12**2,12))\n",
    "ax.set_yticks(range(6,12**2,12))\n",
    "ax.set_xticklabels(['']*12)\n",
    "ax.set_yticklabels(['']*12)\n",
    "plt.title('Optimized Fisher Information for all\\ncomponents of the parameter matrix α')\n",
    "plt.tight_layout()\n",
    "plt.savefig('FI_k_opt.png',dpi=400,bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b3b56937c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(kn_onlydiag,vmin=0,vmax=2.5)\n",
    "ax = plt.gca()\n",
    "ax.set_xticks(range(12))\n",
    "ax.set_yticks(range(12))\n",
    "ax.set_xticklabels(ticks)\n",
    "ax.set_yticklabels(ticks)\n",
    "plt.title('Optimized Fisher Information for the\\ndiagonal of the parameter matrix α')\n",
    "plt.tight_layout()\n",
    "plt.savefig('FI_kd_opt.png',dpi=400,bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b3b56ad3978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.bar(np.arange(12)-0.2,b.diagonal(),width=0.4)\n",
    "plt.bar(np.arange(12)+0.2,bn.diagonal(),width=0.4)\n",
    "ax = plt.gca()\n",
    "ax.set_xticks(range(12))\n",
    "ax.set_xticklabels(ticks)\n",
    "plt.legend(['random','optimized'])\n",
    "plt.ylabel('Fisher Information')\n",
    "plt.title('Comparing the parameters β')\n",
    "plt.tight_layout()\n",
    "plt.savefig('FI_b_compare.png',dpi=400,bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b3b568cc908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.bar(np.arange(12)-0.2,k_onlydiag.diagonal(),width=0.4)\n",
    "plt.bar(np.arange(12)+0.2,kn_onlydiag.diagonal(),width=0.4)\n",
    "ax = plt.gca()\n",
    "ax.set_xticks(range(12))\n",
    "ax.set_xticklabels(ticks)\n",
    "plt.legend(['random','optimized'])\n",
    "plt.ylabel('Fisher Information')\n",
    "plt.title('Comparing the diagonal of the parameter matrix α')\n",
    "plt.tight_layout()\n",
    "plt.savefig('FI_kd_compare.png',dpi=400,bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sklearn.decomposition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "PCA = sklearn.decomposition.PCA(n_components=2)\n",
    "pca = PCA.fit_transform(opt_drives)\n",
    "pca_orig = PCA.transform(validation_data[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b3b574ab0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(pca[:,0],pca[:,1],alpha=0.4)\n",
    "plt.xlim(-5,+5)\n",
    "plt.ylim(-5,+5)\n",
    "ax = plt.gca()\n",
    "ax.set_aspect(1)\n",
    "plt.title('Pulse strength PCA - optimized')\n",
    "plt.tight_layout()\n",
    "plt.savefig('FI_drive_PCA_opt.png',dpi=400,bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b3b572af128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(pca_orig[:,0],pca_orig[:,1],alpha=0.4)\n",
    "plt.xlim(-5,+5)\n",
    "plt.ylim(-5,+5)\n",
    "ax = plt.gca()\n",
    "ax.set_aspect(1)\n",
    "plt.title('Pulse strength PCA')\n",
    "plt.tight_layout()\n",
    "plt.savefig('FI_drive_PCA.png',dpi=400,bbox_inches='tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "pca_all      = sklearn.decomposition.PCA(n_components=12).fit(opt_drives)\n",
    "pca_all_orig = sklearn.decomposition.PCA(n_components=12).fit(validation_data[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b3b56af25f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(pca_all_orig.singular_values_)\n",
    "plt.plot(pca_all.singular_values_)\n",
    "plt.xlabel('Dimension')\n",
    "plt.ylabel('Value')\n",
    "plt.title('Singular Values from PCA')\n",
    "plt.legend(['random','optimized'])\n",
    "plt.tight_layout()\n",
    "plt.savefig('FI_singvalues.png',dpi=400,bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b3b56eabbe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(opt_drives,normed=True)\n",
    "plt.hist(validation_data[0].flatten(),color='black',histtype='step',normed=True)\n",
    "plt.hist(opt_drives.flatten(),color='red',histtype='step',normed=True)\n",
    "plt.title('Pulse strength histogram - random vs optimized')\n",
    "plt.legend(['random','optimized']+ticks,fontsize=9)\n",
    "plt.tight_layout()\n",
    "plt.savefig('FI_drive_hist.png',dpi=400,bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0012263614503136"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(np.abs(validation_data[0])**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9964510588579097"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(np.abs(opt_drives)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "noise = 0.1\n",
    "_epsilons_false = np.random.normal(loc=1., scale=noise, size=n)*_epsilons\n",
    "_etas_false     = np.random.normal(loc=1., scale=noise, size=n)*_etas\n",
    "_deltas_false   = np.random.normal(loc=1., scale=noise, size=qubitring_ndrives(n))*_deltas\n",
    "starting_w = qubitring_perfect_pauli_weights(n, _epsilons_false, _etas_false, _deltas_false, noise=0)\n",
    "validation_data = next(qubitring_datagen(H0, Hdrives, n=n, batch_size=512, Delta=1., seed=17, average_over=float('inf')))\n",
    "model = Sequential()\n",
    "model.add(StateProbabilitiesPaulied(nqubits=n, ndrives=nb_drives, paulies=hs,\n",
    "                                    l1_lambda=2e-4))\n",
    "model.compile(loss='mse', optimizer=Nadam(lr=5e-4), metrics=['mse', 'mae', 'binary_crossentropy'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      ".....xxxxx\n",
      "2\n",
      ".....xxxxx\n",
      "4\n",
      ".....xxxxx\n",
      "8\n",
      ".....xxxxx\n",
      "16\n",
      ".....xxxxx\n",
      "32\n",
      ".....xxxxx\n",
      "64\n",
      ".....xxxxx\n",
      "128\n",
      ".....xxxxx\n"
     ]
    }
   ],
   "source": [
    "hists = []\n",
    "hists_opt = []\n",
    "avgs = [1,2,4,8,16,32,64,128] # a bit too expensive to go to bigger numbers\n",
    "weights = []\n",
    "reps = 20\n",
    "for j,a in enumerate(avgs):\n",
    "    print(a)\n",
    "    gen_train = qubitring_datagen(H0, Hdrives, n=n, batch_size=batch_size, Delta=1.,\n",
    "                                  seed=7, average_over=a, step_reset=1,\n",
    "                                  spam=0)\n",
    "    gen_train_opt = qubitring_datagen(H0, Hdrives, n=n, batch_size=batch_size, Delta=1.,\n",
    "                                  seed=7, average_over=a, step_reset=1,\n",
    "                                  spam=0, specify_drives=opt_drives)\n",
    "    model.set_weights(starting_w)\n",
    "    _hists = []\n",
    "    for i in range(0,reps):\n",
    "        print('.',end='')\n",
    "        #K.set_value(model.optimizer.lr, 5e-4/3**i)\n",
    "        K.set_value(model.layers[0].regularizer_k.l1,2e-4/(1+(j+1)/len(avgs))**i if i<reps-1 else 0)\n",
    "        K.set_value(model.layers[0].regularizer_b.l1,2e-4/(1+(j+1)/len(avgs))**i if i<reps-1 else 0)\n",
    "        #model.set_weights(weights[j][0])\n",
    "        _hists.append(model.fit_generator(gen_train, verbose=0, steps_per_epoch=100, epochs=1 if i<reps-1 else 4,\n",
    "                                    validation_data=validation_data,\n",
    "                                    max_queue_size=500, workers=1).history)\n",
    "    w1 = model.get_weights()\n",
    "    model.set_weights(starting_w)\n",
    "    _hists_opt = []\n",
    "    for i in range(0,reps):\n",
    "        print('x',end='')\n",
    "        #K.set_value(model.optimizer.lr, 5e-4/2**i)\n",
    "        K.set_value(model.layers[0].regularizer_k.l1,2e-4/(1+(j+1)/len(avgs))**i if i<reps-1 else 0)\n",
    "        K.set_value(model.layers[0].regularizer_b.l1,2e-4/(1+(j+1)/len(avgs))**i if i<reps-1 else 0)\n",
    "        #model.set_weights(weights[j][1])\n",
    "        _hists_opt.append(model.fit_generator(gen_train_opt, verbose=0, steps_per_epoch=100, epochs=1 if i<reps-1 else 4,\n",
    "                                    validation_data=validation_data,\n",
    "                                    max_queue_size=500, workers=1).history)\n",
    "    w2 = model.get_weights()\n",
    "    print('')\n",
    "    hists.append(_hists)\n",
    "    hists_opt.append(_hists_opt)\n",
    "    weights.append((w1,w2))\n",
    "    #hists[j] += (_hists)\n",
    "    #hists_opt[j] += (_hists_opt)\n",
    "    #weights[j] = ((weights[j][0],w2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle\n",
    "#with open('opt_est_hist','wb') as f:\n",
    "#    pickle.dump([hists,hists_opt],f)\n",
    "#with open('opt_est_hist_redo','wb') as f:\n",
    "#    pickle.dump([hists,hists_opt],f)\n",
    "#with open('opt_est_hist_redo2','wb') as f:\n",
    "#    pickle.dump([hists,hists_opt],f)\n",
    "#with open('opt_est_hist_redo2_weights', 'wb') as f:\n",
    "#    pickle.dump(weights, f)\n",
    "with open('opt_est_hist_redo','rb') as f:\n",
    "    hists,hists_opt = pickle.load(f)\n",
    "#with open('opt_est_hist_redo2_weights', 'rb') as f:\n",
    "#    weights = pickle.load(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b6a049b0f98>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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fa4LjJ/0UhlwEJdtgbjuvnSl3QP8z4eBaeO/24Pipv4OsKbB3GXz0m+D4WQ9A6hiz5f35n4Lj5z8KiYNh80fmaL+2pj9j/o3WvQ2L/xkcv+xl82+86lXzw1xbV84xB598+wKsmR0cn/m++dr75glzmHp7de9iPTIBSCnnAfPy8/PbGazf4bm8/PLLSCmZMGECQ4YMwWLpkU/TfBNxRrd8f/Xcwx/f1FJoj8UONy0w79dXQOkOKN1utgLA/DnntfMiT298049IgnPbuXyVOrYxnggn32W+iXhqwNdgPu6KaSk/c3Lw+Y4o82tYbDtxab6JgtnSiM40Wyqt6Vbzqy0MIlOCyxeNk/Rs4W3i0kyQTXGLo+VntcfqDI43/eyguGypUxOLI/B7MJPlYePOVnFnm7hsTLJNxzoCjwfQbYFlBcXtgfG2b/Btz+8o3pbW+PsRov243tm4dojy9Q7ilg7ija1VobcfF1rLz2k3Llp+zmHj1vbjTfSjiB+nD6+97hKQYRisXLmSRYsWUVxcTHh4OOPGjWPMmDGEhYV1XICiKMoJ7EguAfW6BNDEMAy2bdvGokWL2L59OwAWiwWHw9F8s1gs6LrefNM0DSEEQgg0TcNmszFp0iSioqJC+bQURVG6zAnfBxAKmqaRl5dHXl4eBQUFbN68mbq6Ourr65tvPp8Pr9eLYRj4/X78fj9SyuZbdXU1mzZt4qqrriI+Pr67n5KiKEpI9doWQCgcPHiwuT/hqquuIjk5udvqoiiK0hlH0gJQY/oOIykpieuuuw6r1cqsWbPYtWtXxycpiqKcIFQLoBMqKip46aWXqKioYOLEiVit5uiFpmGmnRlu2voYTdMYOHCg6ltQFCXkVCdwF6iurua1115j3759ISlP13VGjx7NlClTiIyM7PgERVGUTlAJoItIKZs7ipu+b++YjtTU1LBw4UJWrlyJpmnk5+czbNgwtDazbI90IpsQgtjY2J4770FRlC6nEsAJorS0lC+//JI1a9Z0KnF0hsViISMjg5ycHHJyckhISOi5M6IVRQk5lQBOMKWlpRQWFgKda0E0aXus3+9nz549bN++neLi4kOcdeQtC4Dw8HBiYmKab+Hh4UdcRntsNhtOp7P5ZrfbOz6pE3Rdx2KxBLWqFKW3U/MATjBNb6qhMGzYMMDsuN6+fTtlZe0s8HaEpJRUVlZSWlrKli1bqK6u7vikHqIpEYTqspgQonnSYNMtVOW2vYVK28EKoW4RdnULs6+2YK+++mp0vWv3I1cJoJdyu92MGjWqS8puaGigtra24wM7wePxUFdXR11dHbW1tXg8npCU6/f7myf6+Xw+fD5fSMqVUjZPHDQMA6NpldQQld1Ufihb5ofrswpFuV1Rdlc70erbVXpkAjjW1UCVrmW320N2qUZRlO7TIy+QSinnSSlvdLsPs3qjoiiKckx6ZAJQFEVRup5KAIqiKH2USgCKoih9lEoAiqIofVSvTQAL9i7AZ4Rm6J+iKEpv1CsTwJqiNdz82c2c//b5vLbxNep99d1dJUVRlB6nVy4FYUiDBXsX8Px3z7O6aDUxjhguyr2IW0fdiq7pbCnbQml9KTbdhi50dKFj0SwMiBkAwMGag1R7qgm3hZMUlhTqp6UoitJl+vxSEJrQOCXtFE5OPZnlBct5Ye0LvLTuJX4++ucAvLz+Zd7e+nbAOeHWcBbNWATAX7/9Kx/v+hiB4KGpD3F21tnH/TkoiqJ0tV7ZAmiPx+/BptsA2FO1h4M1B/H6vfilH7/0owmNqalTAVhVuIqDtQd5bs1zVHuqmTd9XvO5iqIoPVmfbwG0p/UbeFpEGmkRaYc8dmTCSAAibZHc9MlNvL7xda4ecnWX11FRFOV46pWdwKEysd9ELul/yWGThaIoyomqz7QAjta9E+7t7iooiqJ0CdUC6IRaby3PrnmWgpqC7q6KoihKyPTKBNDQUISU/pCVV9ZQxtOrn+afq/8ZsjIVRVG6W69LAIbhZdXqmaxYcSV1dXtCUmZKeAqXD7ict7e+zdayrWozCUVReoVeNwxUSsnBg2+zafN9gKR/3u9ITr7kmLeVK6sv49y3zqXaa26HuObqNQgh+PPiP/POtncAEJg/I9wazmeXfQbAb7/+LZ/u/jSgLJfFxZzvzSHGEZptIBVFUZr06WGgQgiSky8mKmo86zf8ig0b76Ko+FMGDfwzNlvcUZcb7Yjm2TOeZeH+hUgpmxNKflI+dt2OpHHbPSQ2rWXI6bjkcUTaIwPKGhQzqPnNv2nGsaIoyvHW61oArUlpsGfPv9i2/W+AwG5PwmaLa77pugtNWNE0G0KzoQkLCM38JC80LJZIEhPORdO6ZhLY57s/595v7uW+ifdxavqpXfIzFEXpW/p0C6A1ITTS068nJmYK+w/8F09DIR5PMbW12ykvX4rfX4dheIBDb+xdU72J3Nxfd0n9st3ZJIclc9v82xgePxy7bic9Ip3fT/w9AH9e/Gd2Vu5seT4I8qLz+NXYXwFwz8J7OFhzsDmuCY2Tkk9i5tCZXVJfRVF6lx6ZAEK9KXx4eH/65/3fIeNS+jEMD1L6Gjt4DaQ02Lr1AXbveZGkpIsIDx8Qkrq0lunO5JVzX+Hp1U+zonAFfsOPIVuSUYO/oXkl06ZLTK1XNq3z1VHrq23+3uP3sLtqd+Nzktw6/1binfFooqWvf1K/SUxLn0aNt4ZHlj8SVKdT005lYspESutLeWrVU82PR9oiiXHEcFLySeRG51LrrQ1ITk1SwlNw293UeGvYXbk7KJ4akUqELYIqTxV7q/Zi0SzYdBt23Y5VsxJpj8SqWfH6vdT564LOd1lcWDQLHr+Hen/wKq9hljB0Tcfj9+AzfAgh0ISGhgYCLMKCEML8XbeT+DuKWzUrQMDfqanvB2i+NHiolnVn44pyPPTIBCClnAfMy8/Pv+F4/DwhdHTdGfR4bu7dFJfMZ+Om3zJm9GyECP2gKZtu49bRt7Yb+8OkPxz23L+e/Negx5reWCoaKiiuLWZN0ZqAeFJYEtOYRoO/gY93fhx0fpY7i4kpE6n11jbHDQyqPdX4pZ97J9xLbnQuOyp2cMV7VwSd/+CUBzk3+1zWFa/j+o+vD4o/ceoTnJx2MssOLuPW+cHP+8WzXmRs0lg+2vURd391d1B89vmzGRw7mLlb5/LHxX8Mir87/V0yIjP4z4b/8Pflfw+Kz79sPnHOOJ5e8zRPr346KL5kxhJcVhcPL3+Yl9e/HBATCNZcY/4+71t0H29teSsgHmYNY/GMxQDcueBOPtz5YUA8wZnQPDjgls9vYcHeBQHxzMhM5k2fB8DMD2eyvGB5QHxw7GBmnz8bgMvmXcaG0g0B8bFJY3nxrBcBOO+t85o/DDQ5JfUU/nHaP8z7s0+hpL4kIH5u1rk8OPVBAMb9Zxx1vsAEfGn/S7lnwj1IKRn+0nDaumbwNdwx9g6qPdVMeG1CUPynI37KT0b+hIKaAk6fc3pQ/I78O7hmyDVsr9jOhXMvDIrfO+FeLul/CeuK17X72nto6kOck3UOSw8sPexrb/7u+Yd97b27/d3Dvvbe2PTGYV97s9bO4uHlDwfFm157T6568rCvvYe+fYjJ/SYzMWVi0DGh1iMTQE9hs8WQm3sXGzb8mv0H/ktKv8u7u0odavoEGeWI4rXzXzvkcTGOGBZcseCQ8dSI1IC4IQ0qGiqa11RKi0zj8WmPB503KHYQALnRuTw27bGg+JC4IQAMjRvKo9MexW/4afA34DW8NPgbmpfdGBw7mDvH3hl0fqIrEYAR8SPajUfZowDzzfCXY36JgYEhjeZP7C6LC4DxSeObP8231vTY5JTJzWW1Z1raNHOp8FYf5K16S3lnZJxBtjs74ByX1dV8/9yscxkaOzQg7ra7m+9fmHMh45LGBcTjXfHN9y/pfwnFdcUB8X7h/Zrvzxg0g4qGioB4RmRG8/1rhlwT0HoEyIvKa77/o2E/wmt4A+JDYoc03//xiB/T1sh4cw0tq25tN56fZF6WDrOGtRsfET8CMP+G7cWbXltxzrh24zlROYD5e2gvnh6ZDkCGO6PdeNPvLy8qr914nNMcRDI4dnC7cbfN/PuNSBjRbtxpMT9k5ifmtxu3aObb8cR+E0mNSA2Kd4Ve3QkcClJKVqy8kurqjUw46RNstthurY+iKMrhHEkncK+bCBZqQggGDvgDfn8tW7Y+0N3VURRFCRl1CagTwsJyyUi/gZ27nsLtHo3TkQqIVn0Cnei4a9W5p2k23JEjEULvkvoqiqJ0hkoAnZSZeTMFhe+zadPvQlJeXNzpDB3yOLpuD0l5iqIoR0olgE7SdQfjxr5DTc0WQCIbOxWlPPQcghaB/SwVlavYtu0hVq++juHDn8FiUTOBFUU5/lQCOAIWSzhu96hjLic6ejwOexLrN/yKFSt/yMgRL2KzqXWBFEU5vlQC6CZJSRdisUTw3dpbWL7iBwwZ/Fd0PbzNRKAjmxQkhI7DkaomEymK0ikqAXSjuLhTGTliFqvX3MC3y6aHpMzw8MFkZ91KXNzpKhEoinJYvTIBSI+Hgr88SPRVP8SeldXd1Tms6OhxjB83j4qKVY2PtKwqeqR83gr27P03a777MRERQ8jKuo242FNVIlAUpV29ciJY3erV7Lr2OmRDA1Hf/z5xN/8Ua2JiF9Sw5zEMHwcL5rJzx5PU1e/GYolEiGPN84Lw8P7ERE8kOnoiERFD0bRe+dlBUU54RzIRrFcmAABfcTHFTz9D2ezZCE0jesYMEn9tLh1Qu3Ilsq4OYbcjLBbQLWhhrubWgvfAAaTXi3A4sCYkhOz5HE+G4eVgwTtUVn7XJnLkf29peKmsWkN19UYALJYIwsL6I9rOIzyKlobNFofTkYbTmY7TmYbNFh+SNZc0zYnVGtlOv4qi9G4qAbTi2buXoscfp37denLeexeAXTOvpXbx4oDj7AMGkP3OXAB2XHY59WvMRb/Snn+e8MmTjqkOvYXHU0xZ2WJKy76hrnZXQOxoLlmBxOMpoq5uL1J6Oz78KAihY7G40fWwgFU7j7o8TUfTHGiaA12zm3tFhCTBaAihI4QFTVgaJwmGoFyBmaiF1vhVhKZcGldBbS5PhOT32+YHtL0T0oJDXt8Qy829+6ha2ioBtKP1Ll6eXbvwFRVhNDSAz4f0+dBcLsImmCsYVi9YgL+sjIN/vp+IadPo9+BfQlIHpX1S+mloKKC2bhdeT0nHJ3RUHhLDX4fXV4HPW4HXV4G/zcJnR1uyIX0YRgOGvx6/UY80PCEoFyQGUvoblyT3IQ1/iMptWd4caSAPs/fFEZcsJS0tytC+j7S8L4X6/amryg29KZOXHtVmVGpDmHa0vgxgy8jAlpFxyGPDp04FoGbRYqo++wzp8SBsXbMrmNI0fLUfDke/jg9WFCVk+kwCOBqR552Lv7ISX3n5CdsXoCiKcii9MgG8sr+EDIeNKTERx1RO+JQphE+ZEqJaKYqi9Cy9bjloj2Hwwt4irv5uB4vLq0NSZtOoIEVRlN6k1yUAm6bxxsgcUh1WrlyznWUVNcdUXs3iJWyddio1S5eGqIaKoig9Q69LAADxNiv/HZlLgs3CD1ZvY1Xl0Y8AcY4cgXC5qPr4kxDWUFEUpfv1ygQAkGS3MmdkLtFWC1es3sbaqqNLAprDQcQpJ1P1ySdIf2iG5imKovQEvbITuEmKw8ackTlMX7mV81ZsId1hI8VuI8VhpZ/dRrhFwyoEdk3DqgmswpwaojV+deoa02IiiDjzLCrf/4DaZcsJGz+uox+rKIpyQujVCQAg3WnnrVG5vLi3mD31HvY1eFhXUkeRx9ep8x8dmMZlU6cgHA6qPvpIJQBFUXqNXp8AADKcdu7LSwl4zGMY1BuSBsPAa0g8UuI1mudNIiX8aO1OXj9QyhXJeaT+4x84Bg3sniegKIrSBfpEAmiPTdOwaQCH3pj98uQY7t9+gJ11DWROmXzc6qYoinI89NkE0BmXJkXzl+0HmH2glF9nJ1P+1tuUzX4de2YWwmYFiwXd7Sbh5z8HoOy//8WzdSutF6/So6OJ+/FNAJS++ireXbsRDgcxV/0QS1xcdzwtRVEUQCWAw0q22zg5JoI3Dpbyq6wkPDt2YJRXULtyo4AHAAAgAElEQVRsGdLrRXq9AQmgdtEiqr9cEFCGNS2tOQFUf/kldcuWY9TVUbtkCRkv/VutMaQoSrfpM6uBHq25BWX8eP0u5ozMYXL0sS0t0aTygw/Y94vbib7qKpL+7zchKVNRFAWObDXQXjsPIFTOinMTadF4/UBpyMqMPOccYq65mvoN6zE8oVlOWFEU5Uj1ygQgpWTfprKQlOXUNS5KiOa9onKqfKGbCJZwxx1k/OtfaOoSkKIo3eS4JQAhxEVCiOeEEO8IIc7syp+1fWURcx9ZyYLZmzH8x74BxuVJMdQZknmF5SGonUlYrQirFV9pKQfuuRd/9bGtWaQoinKkOtUJLIR4ETgfKJRSDm31+NnAY5hjKZ+XUh5y6ywp5VxgrhAiGvgb8PGxVPxwjH5O+k1J4rv5eyk/WMOZPxqKI8x61OWNjnSR57Iz+2ApM/rFhrCm0LB1K+Vz5lA1/3P0sHDQNDSHg6y33gSg8OG/U/3ll+bBjZva6FFRZPx7FgAH77+f2m/NfhKhaYSfOo2YK69Ej4oKaT0VRel9OtsCmAWc3foBYW5a+iRwDjAY+IEQYrAQYpgQ4t02t9a7qfy28bwu4fEZXPOvpbxQWsLEGf3Zt7mcNx9aTnnB0S8IJ4TgsqQYllTUsKO2IYS1hbBx40h5+G+EjRuPY/Bg7AP6Y8vJaY5b4mKxZaRjTU/DmpZq3pKTW+IxMViTk7EmJ6M5nRT/4wn2/PgnIa2joii9U6dHAQkhMoF3m1oAQogJwO+llGc1fn83gJTygUOcL4C/AJ9IKT89zM+5EbgRID09fcyuXbsOdeghfbahgOv/vYzvj07l9lHpfPTcOk794UAyh8excfEB1i3YhyPMim7V0XSBrgumXN4fm9PCjtVF7FlfCprAatMZfXYGdqeFAw0exnyznnHuMAaGO9Fo3ApbBG9Z3dFm005d44bUeOJsoR+FW79pM0Z1Fa4xY/BXV7Pv9ttbVcysV9wNN+DKz6d+wwaKHn0sqIy4W27BOWwotStXUvLMsyAE1uQkbDk52HNycA4bhhYWFvK6K4py7I7XnsApwJ5W3+8Fxh/m+J8BpwNuIUSulPLp9g6SUj4LPAvmMNCjqdhpgxK57bQ8HvtsCyPTo/jhH07C5jCfqm7RsNh0qssb8HsNDL/E7zeaN6Eu2VfN5mUFSAM8dT7cCU4GT+pHst3Glf1iea+onM219UgJBk2bbreuf8f1q/EbbK2t54WhWUfz9A7LMaB/8/26Vavxl5UHVkxKjAazFSM9HnzFxUFlSK85Mkk2ePAVFiINg9plyzCqqgDI/O8bOIcNo/TVVyl8IPiqX/YHH2BLTaHk+ecpeuzxoHjugi+xREdT+NhjlL3yH7SIcPSwcLTwcDSng7Rnn0VYLJS+/ArV8+cHnmy1kP7MMwCUvPACNQu/CQhrERGkPvYoAMXPPkf9d2vAYkFoOgiBHhNN0m/MobfFzzxLw5YtgcUnJ5Hwy18CUPT4P/Ds3h0Qt2VmEn/LzQAUPvoovoLC5sQKYM/LI/bamQAUPPgQ/oqKgPMdQ4cQM2MGAAf/+CeMurqAuGvMGKK+fzEAB+79PbTZHN41/iTc55+H9Ho5+Ic/BP1uw6ZOJfKMM/BX11D4YPDfJuKMMwifOhVfaSlFjzwaFI887zzCThqP9+BBip98Kijuvng6rlGj8OzaRcnzLwTFo664HOeQIdRv3kzZy68ExWOuuRp7bi51362l/I03guKxN96ALS2N2hUrqHh7blA87pZbsCYmULNoEZXvfxAUj7/9F1iio6n+8kuqPv0sKJ54911oLheVH39MzVdfB8WT7r0HYbFQMe9datvuAWLRSb73XgDK33yTulWrA8Kay0Xi3XcBUPbaa9Sv3xAQ16OjSbj9FwCUzJqFZ9v2wOITE5tfW0Z9PZrDEVS/UDuWBNDex9xDvv1JKR8Hgt8Nushtp+WxZm85f5i3jsHJkYzJiAYgLz+RvPzEQ56Xf24W+edmIQ3JC3d8RcHOSgZPMjcr/+uANP46IO2Y6/bYzgIe2HGAz0oqOS028pjLO5TwyZMInzzpkHHniBFkvTnnkPGwk8Y390VIKfEVFuHZthV7Xh4AjoGDiJk5M+g8PSLcjA8b3m5cs9sBcI0ejVFdg1FVhVFTjb+6GqO25Q1RejwYtYGX7oS1pS/HaGgIimNpWdrDX1KMZ+cupN+P9JuL/1mTWi6feXbsoO67NQGnNyU5MPtn6jdtDIg3lQNQt3o1np2BLVTpa9k5rnbFcnyFRYH1t7XUv3bpUvzVrXatkxI9suX1UP3VAmgz8kxvnD0uDSNo0iGANT3djHs97cbtA8z1rGRdHdVffBEUd44cCYBRXd1uPGzSRAD8FRXtxiNOP82Ml5a1G3d/7wIAfEVF7cajLr8c0sC7/0C78ZhrrwXAu29fu/G4xjdQz65d7cYT7jCTu2f79nbj3PM7ABq2bAmKt560Wb9hY1Bcj3I3369bu5aaBV8FxC39Wl57datXU7dseUC89aVfGcIRh4dz3C4BHY1jnQhWUevlgie+psHnZ97PJpMQcWQZddHb2wiPtjPslNSjrkN7GgyD077dhNeQfDFuIE69V47GVRSlGxyviWDfAnlCiCwhhA24AvjfMZQXcm6XlWeuGkNFnZfrZy3jha938MWmQvaU1mIYHSe+CdNzQv7mD2DXNB7IS2VXvYcndheEvHxFUZTO6Oww0NeAU4A4IcRe4F4p5QtCiFuAjzCHgb4opVzXZTU9SoOSI/n7ZSP57dy1/PHd9c2P2y0a0S4bTpuO06rjsunYrRq6pqEL0DUNl03nztP7kxBux+YMbYftlJgILkqI4ondhVySGEOWyx7S8hVFUTrSI9cCEkJcAFyQm5t7w5Y2nXRHS0pJaY2HbUU1bCuqZntRNRV1Xmo9fuo8fuq8fhp8Bn5D4jckPkOy4UAl0+os3HbBIEaenh6SerR2sMHL5CUbGOsO49Xh2Qhx+NFDiqIoHTleo4C6jJRyHjAvPz//hlCVKYQgNtxObLidcVkxnTrn1Ie/YE9RAwU7K0NVjQBJdit3ZiVxz9b9PLG7kAFhjoAtKTuTDlrnDIsQjHOHYdNUn4KiKB3rkQmgp5iSG8erxbvZv6Oi44OP0nUp8cw5WMaftx8ISXmTosL597Aswi2H3uhGURQFenECKNm7h9jUYxuyOTkvnn8v2sXGilrqqjw4I0K/cJtFE7wzOo9NNfVIzHkFUh5mPG0rbY/5rqqW323dx6WrtvHqiGyirb32z6soSgj0yneIdZ+9zxcvPsE5v7yP7NFjj7qck7Jj0AXstBgU7Kwkc1jX7ODl1DVGRrqOuZyx7jD62W3cuG4n01duZfaIHBLtR78GkqIovVvvSwB+L4M2/B5nto95j/yFS3/3J/r1H3RURUU4rIxKi6akvJ6YfifG0gdnx7v5z/Bsrlm7g++t2MIzQzKJsuoB/QlH2tWsCUE/uxVNdVIrSq/SIxNAq1FAR36ybkUbfCHZxQ+Rl5DK23+5jyv+8BCxqUc3imdK/3ge/WwzfseJc019SkwEc0bkMGPNds5evjkkZQ4Oc/DLrCTOiXOrRKAovUSPHAba5KhnAnvr4KkJ+A3J8xsGI6wOrv37P7Haj3xtjeW7yvj+P7/hdxNyuO57A06ooZq76xpYUlHT3Fdg9i0c+d+72m/wr73FbKtrYGi4kzsykzgrLvKE+l0oSl9xwg8DPWZWJ5z3N/RXvs+V553DnrhzsNodFO3eyeqP38flduOMdGO12dF0ncwRo3G5o6gsLqRgxzZzNU8hsNrsDBs0hDCLxjtf7OSSiem444/9Wv3xku60k+4MzQSzmf3ieLuwjId3HmTm2h3EWHWsbRJAR6ugQuCwVYA8l50p0RFMjo5geIQTXSUVRTluemcCAMg9HYZcTPiaFxn0U3M6QVVxEZsXf01ddVXAsp1X3PcQLncUe9Z9x4dPPRJQzEV33sPY9GhWbC3l4I6KEyoBhJJFE1yaFMP0hGjeLCjj24rAHcw607Joe4RPStZU1TUOgT2A26IzJNyJHoIcEGu1kOG0k+G0keGwkWS3oh1x70cwhy6IsljU+k1Kr9A7LwE1qToIT4yFlDFw1dvNHz8Nv5+6qkr8Xi9+v4/wmFisNjt11VVUFhWClPi8Xl6/51dMmTGTDXFjuHfeev46OINLrx7awQ9VjlSRx8vXZdUsKKtiWwg23DGkpMjjY2+DB38XvbztmsBt0YnQ9aBWzdHQhcChCZyahl3TsGsiJOUKzAmCTTdddKad1jm6aJm0qIWwXKB5ImR7+20cW7miufyQFhzwM0Ljt9n9sGhHXpq6BNQkIglOuwfevwPWvgnDLgFA03XCoqKDDneGR+AMj2j+/qZ//puw6BjiS2ph3noW7Szl0uNW+b4j3mZlemI00xOD/ybHwmdI9jV42FXnodDj7fiEDkigzm9Q4fNT7vNT7vVRHYI9p8FsDdX5DeoNSbXfT4k3NJnLkBKfBL+UeKXEH6IPfBIwJBjI5q+h0jQPpmleTCjLhZayu0Ioy/1NdjJdlqUa9e4EAJB/Haz6D7x7O2z5GPqNgn6jIWkY2A5/OSc8xtz/NzPWRZzNwneVtfj9Brpq/p8QLJpovAykFtpTlPb0yARwTMNA29J0uPh5+PRe2LEA1sxu/CEaOKPBHgmOSPOrLRx0C2hW0G1UVtWxsn4YU2+8g5MHJvDRxgIMKTlxBoQqiqIcWo9MACFfDC4uF674j3m/8gDsXwkHVkFNEdRXQkOl+bVyL/h9YHjB5yGyYjf1+9dTV3Uj04Ym8uaa/azZV9m8u5iiKMqJrEcmgC4VmWzeBp57+OMMA+P+FBId1ZTt38eknFwEcP9zyxkTFY6uC3RdQ9cEo05PBwF7NpRSsq86YKyjrguGnZKKEIKd3xVTXlCLRRdceclAomL75ogiRVF6hr6XADpL0zDih5BQuZGSA3tJGTiYAW4XyytqWV7cZqTKrA529doRvNLngVe8/Om28SGssKIoypFRCeAw9PR84vctZ+u+3QD89xeT2VNahyHNFTv9UmJ0YlRF20Nu/9cyPtxXwm8qG3BFqg5KRVG6h0oAhyH6jcKqGVir9gDm4nCD+x376prXTM7iD59u4u0Pt3HlZYOPuTxFUZSjocYzHk7yCAAmTDy61UQP5YqpmYRZdb41jn3Sk6IoytFSCeBw4vLA6oL9q0JarMtm4eIxqby/9iBlNZ6Qlq0oitJZPTIBCCEuEEI8W1HRdVsxdoqm43HnUrTkHSoKD4a06Bnj0/H4DO57ZDHS6LnLcSiK0nv1yAQgpZwnpbzR7XZ3d1XwxPTH7S+gZM+ukJY7KDmSQTFhLKioZud3xSEtW1EUpTN6ZALoSWxZJ2HT/dTsWBHysmdOy6ZUl7z5wdaQl60oitIRlQA6YMs6CQC5b2XIy/7eiBRcFo3PCiso2l0V8vIVRVEORw0D7Uj8QPxSw1q2KeRFO2063x+dyqtLdrPos11879qh1Fd7ee+p1eZuW60WAhx6cgr9xyZRXVbPJy+ub368adLxiNPSyBoRH/I6KorSe6kE0BHdSq0jhTh/eZcUf9WkTF5euptPvLU41xfga/CzWXqh9SrDEuoPVnJws05dtYeNnuDhow37KyiI0EisldSWNTBkSkqX1FdRlN5DJYBOiBh6GhHr5ppTekO8ZWH/xAjGZ8Uwb3sR87YXHfrAhaWw8DAFfVkKX8Ip7gjG7vJRUVTHhItyEEexoYSiKH2DSgCdkTwSls+C8l0QnRny4l+YOZZdJTVIaW7g4TfMTTYCdTxUdM7yvby2dA/jR/dj5ce7qSyu5/SZg7DY1ALWiqIEUwmgE2rCMggD9n3xGinT7w55+eF2C0P6HfuQ18HJbr7ZVsJr5eU8eGE2K97ZzsHtFcz8yyQAPn9pAzvWBA45DYuyc8VvxwHw0fNr2bepLCAeleji4jvGALB/SznueCdhUWr9IkXpDXpkAgjphjAh4Mgai18KjL2hHwoaSk6bzkPfH87lzy7mI28N194yIuANPSnHjW4NHPhld7W8BJJzonC4rAFtDVekDQBpSD5+fi01FR4SMiJIzHajCUFSjpvcMQkYhuSbOcHDWVMGRpM1PA6vx8+SudsDgwLSh8SQPjgWv9+g/GAtjjBrQOe3zWHBatfx+w3qq4O3dbQ7LVhsOn6fQX1NS1zXNXSbhsWiqctginIIPTIBhHxDmGOkOyIo8buxV/T88frjs2OZOTGTWd/s5NxhyUz8fksSHTypH0w69LnDp6UeOijggttGsnNNMTtWF7NpUeMS1xrkjkkAKdnwzf6g06xOnazhcfi9RlBcSghz20kfHEt1aQOv/3Fp0Pkn/6A/Q09OpXRfDW/c/21Q/PRrBzNgfBIFOyp4++Hgobrn3DSM7FHx7F5XwkfPrQ2Kn/vT4aT0j2bbikI+f2lDUPyi20cTnx7Bhm8O8PUbm0EIhAaaJhBCMP2Xo4lKdLHuq318+97OoPMvvTufMLedVZ/uZtWne4LiM+4dj81pYdn7O1j3VePvRzRuXi7gqj9OQGiCxXO3sfnbwGXHLVaNGb83hyl/9cZmdqwObN05w61cevdYAOa/spG9G0sD4hGxDi76xWgAPn5hHQU7AmfeRyeHcf7N5npY7z21htL91QHxhIxIzrphKADvPLqSyuK6gHhK/2hOvdpcR+vNh5ZRWxm47EnGsDimXt4fgNf/uBRvgy8gnpufyISLcgB4+XeLgpbVHTQxmfxzs/B6/Lz+hyW0NeyUVEaenk5dlYc5Dy4Lio8+K4MhU1KoLK7jnUeDXzvjv5dN/3FJlOyv5v2n1gTFJ12SR/bIeAp2VPLxC8GvrVNmDCRtcAx7N5Ux/+Xg19YZ1w0hKdvNzjXFfPXG5oDYadcMpl9eVNA5odYjE0BPVG1PIcG7tUs6gkPtzrMH8NnGAu6cs5oPbpuKMwR9AEIIYvuFE9svnDFnZwbFNV3jhkdPPuT5jjBru3HZ+J/aGW7lzB8NoaE28E0gOde8NBYeY+fkGQOCzk/MjATAHe9qiUuJ3y/xew1iUsLM86MdDJrYL+j8MLd5OSsyztlu3BFurv4aneRi0MR+SCmRjX000pBYHebvNjLWSfqQmKDzdYvZ4nInuNqNC100x1MHxTTviN62x8ed4Ap6Q9D1ltdhdFJY0O/O5rS0irvwewM3sHc2tu4AYlPC0Nq0lCJiHc3349LCsTsD3y6iEls2NIpPi8DltgXEo5PCWuIZkTTUBrbgoludn5gVic/rD4i7453N95Oz3UEbxEfEmnEhzNZtWxExZv01XbQbb7qUqVu1duNNvx+rTW8/HmHGbc724/Yw8/dld1najTe9dhzh1qB465Z5VxKyE+vZd5f8/Hy5bFlw5u4OW/5xDXklc5E/X4eIOswn5R7im23FzHhuCeOzYsiIdSEQCNGUuwL/o7eXz1o/pGuCy/LTGJrS/UtzKIpyeEKI5VLK/M4cq1oAneQccDJ8MxffnuVYT4AEMDEnjl+e0Z9Xl+5mV0ktEtn04TJA+/k/8MGaBj9vLNvDI5eN5JxhyV1VZUVRjjPVAugsTw08kAoTb4VJt4Gmg9BA6K0+Qjd+bfcSUavHhAb6iZN7i6sbuPGlZazYXc6vzhrAT0/JMWcqK4rS4xxJC0AlgCMgnzwJURTcmXPEhA4/fBNyph17WcdJvdfPnXPW8L/V+7lkTCr3Tx+GzaKWklKUnkZdAuoib21MJC8lhfRBQ9AECE0jzB2JJgSeulq8Hg8gzREcjVyRkSAlnvp6fF5zFIRz1XOwYR7iBEoADqvOY1eMJCc+nEc+3cyXm4sIa9O53LZV0GEbQcBJ2bFcPzmLnPjw0FZYUZQOqQRwBLwxA/lk5TpY2TIf4NaX5qDZHSyc9SwrPvhfwPFCaNz+uvnY/KcfY+38TwCYnmYndf2H2M7/+/GrfAgIIbjt9DwGJEXw4VpzGGhT+7FtQ7Iz7cp6r585y/fy6pLdnD4ogR9NyWZ8Voy6vKQox4m6BHQE6qoqKdm3B7/Xi9/nxe/zkTtmPELTKNi+lbID+wLe+AQwcJI59PHAlk2UN+4qVjrnLia518Mv1oO7by/aVlzdwEuLdvHK4l2U1nhIdjs6dWmpoxSRFuNibGYM+RnRjEyPwmVTn3WUvkH1AfRwCx+7i0ll/4SLnoaRP+ju6vQI9V4/b67Yy7KdZXT0muzoFWtI2FJQxaaCKqQ0h7FmxLqwhGBGsNtpJSXKSb/GW3yEHS0ELRabRSPSYSHCYSXSaSHMZglJuZoGNl1Trao+5IRPAK2Wgrhhy5Yt3V2dkJOGH/G3PMg7E6Y/3d3V6bUq6rys2F3Gsp2lbC+qOebypISyWg/7K+o4UF6P7wTay9lu0bBZNOwWjU70znRICLBoAl0TWDRhzow+9moCoAmBJprmrYSu3KZ5MM1zYkJUbsAPIHTl/vfHE7DqRz7Q4oTvBO5pS0GEmtB0yJyC3PEl4gSYWXyicjutTBuQwLQBCSEv229IiqoaKK4O3pvhSEkJDT4/VfU+Kuu9VNb7qGmzLMLR8huSBp9Bg89Pg9fA4zc6PqkTZOOqtT6j5WtoCgaJxDDMlXFDm2MbZ3DLtnOKQ1CybPoJJ5YemQD6go0HYGDlfijZBnE9Y9E7pfN0TZDkdpDkdnR8sKL0UGogdzepiTEX2fJs/Liba6IoSl+lEkA3SR53NpVeOw3fvdvdVVEUpY9SCaCbJOUNYF9DHPbClWCE5rqsoijKkVAJoJtomk59wmhsshZZ8F13V0dRlD5IJYBuFDf1KgCMrfO7uSaKovRFKgF0o7STzoLYPPRdX3d3VRRF6YNUAuhmvrSJGDu+Bn/wfreKoihdSSWAbra5UEfz1+HZploBiqIcX2oiWDdzj70UOfdFqpe8RkzqiMa56o3T9YNmCHcwY1jTweo8/DGKoiiNVALoZknDxlH4RiSJ22bDQ7OPuTzPeU9gG3tVCGqmKEpvpxJAN9MtFnZm/Yj1q98DaTD1ypnommDLkoXs27S++TiBuQHN1BkzAdi46CsKtgUulDc6oQTX8hdAJQBFUTqhR64G2qS3LgfdGYbhRxoSmjZzlwZIidVurj3j83qRfn/AOdq3z6B/dg/8dDEkDOqGWiuK0t2OZDXQHtkJLIS4QAjxbEVFRXdXpdtomo5usaBbrFisVqw2e/ObP2A+5nAE3PTRVyI1K9ue/xlVpcXdWHtFUU4EPTIBSCnnSSlvdLvd3V2VE0tYHN7MafSrW8Xnzz7W4cYqiqL0bT0yAShHzzbxJpy6F23rx6xf8Hl3V0dRlB5MJYDeJnsaMjKF/JRq5s96Vl0KUhTlkNQooN5G0xGjriLpywdxkcGWJYsYfc4FHNiyiQ//+ShAwP6wp13/E9IGD2PPujV8PuvZ5sebjjjzx7eRlJOHp64WITSsDrUBiqL0FioB9EajrkR8+SDTz8imNtvcbcxqtxOXltG8d13Tpng2hzlxzGK3E5WY3FhAS9+BxWoFYNGbr7Phq/lMvOxKhp5yBpquH6cnoyhKV1HDQHurly6Ckq1w22pzhvAx2r95A1+8/AIHNm8kNjWdEWeeS2JWDv36D8Iw/Kz74rOgc+IzskjKycPn8bBh4ReAuSF3k8TsXOIzso65boqitDjhN4VXQmD01TDnWtg+H3JPP+bi+vUfxA/+8Fe2LP2Gr16dxecvPs2osy8wE4Df4ONnHg86Z/z0y8zLR/V1fPx0cHzyFVcTn5FFZXEhs39/F/EZ2UQlJTdfoho0+RQSMrMpO7ifNZ9+GHT+0FPOIDY1jeI9u1j3ZWACstrtDDn5dNwJidSUl1Gydzdtl9JIys3D5nBSVVJM2YH9QeUn9x+A1WansqiQ8oKDAGiahmbR0S1W4tIz0S0WaivKqauqCjo/pl8KQtOoKS+jvro6KB6bmgZAdWkJDbW1CE0ghEAIDU3XiYw3N7OvKS/D5wncfF5oGpFxh45ruoWI2Diz/LJS/F5vy6U/AbrFSlhUdHPc8AduQt86XlVajGyzaZHFZscV6W4VD/wgabXbcUZEAlBZXBT03G0OJ47wcKSUVJUE91PZnE4cYeFIw6CqtCQobne5sLvCMPx+qstKg+KOsDBsThd+n4+a8rLgeHg4NocTn9dLbUV5UNwZEYHV7sDn8VBbGTwc3RkZidVmx9tQH/S3F0LgjHRjsVrx1tdTXxP8t3e53egWK576OhpqaoLiYVHRx6WVrRJAbzXwPHDGwHt3QPzAxnWF2ltfiPYfa023waSfI5KH03/8JHLHnkR1aWnz5SPdYuGGJ//V5iSJzekCzP9sNzz5YusrSwDYw8IA8Pt8JOcNpGjndnatWdkcT8rpT0JmNtUlxaz66L2gaqUPGU5sahoVhQWBcSnxeT1kDB+NOyGRnatX8OFTjwSdf9WDj5OQmc3WZYv5/MWng+LXP/48UYlJbPxmAV+9Oiso/pPn/oMr0s2KD+ax5O3gZTxue/ktLDYbS+a+wcoP5gXEhKZx+2v/A+Dr2S+z7otPg343t7xolvn5i0+zecnCgHhEbDw3PmX+zj986hF2rl4REI9NTWfmw08BMO/vD7B/84aAeHLuAGb8+WEA3rr/Hop27wyIpw8dwaW/+zMAs+/9NRWFBQHx3LEnceEdvwXg5Ttvpa6qMiA+eMo0zrnllwC8+PMb8XsDV7sdceZ5nH79T5CGwXM3X0tbYy+8hKkzZtJQW9tufNJlP+Sk719BdVkJz918XVB82jU3MPrcCyk7sI9/33FzUPzMH9/KsGlnUrhjG6/97o6g+Pk/v4sBEyazb+N65vz5t0Hxi+++j6yRY9i5egX/e/j+oPjl9z1I6sAhbF6y8LCvvXVffnbY115XU5eAerOlz8GKlwDZ+OYrm/sAWnTi71+xD8Li4CcLT5jF5gzDnCWtaTo15WWU7t8bdExidh739IUAAAifSURBVK7ZAigtpvzggaB4Um5/swVQXNj8BigNA8Pnw+/3kTliNLrFStHunY0tjED9T5qEpukUbN9K2cHAFoYQggETpgBwYOsmKgoOmn8Jw0BKidB1Bk06GYA969YEfYq22u30P2kyADvXrKSmzadgm8tF3tgJAGxf+S215ean3Ka+H1ekm5wx4wHYsvSboE+p4dGxZI0cA8CmRV/jqa8NiEfGJZAxbCQAG76aj6/NG3xUUjJpg4cBsPaLT4NaEDEpaaQMGIQ0DNa2SX4A8emZJOX2x+f1suGr4A2TErNzScjMxlNfx6ZvvgqKJ+cNIC4tg/rqarYs/SYonjJwCDH9UqitKGfb8qVB8fShw3EnJFFVWszOVSuC4pkjRhMRG0dFYQG7165ufrzp/fT/27v7GKmuOozj32d3yy5vy9IWDJU3KRSKxgKNlJVqaq0ISNtEG2OjCX+gRtMoVRNT0sRoNKbGRlsTYuJLW02aaqTWEppYCVITidJCC3aBrttaKEuRRVKkrQXc5fjHPRumu8Pu7DLjPTPzfJKbmXtm9s6Tydn97T3nzpkrr13K+LbJvHb0CIf3dwz6+XlL2xk7sZUT3a9wpPPAoMfnt3+A5nHjBrWXYiRDQC4ANrx/PAW/vBWu/wrc9M2cw5jZUKp+KQhLzJwbYPFnYMeP4Oje4Z5tZlXCBcBKs+I7MO4y2PwlGDBhaGbVyQXASjN2Mqz+fnYG8NeNeacxszJwAbDSLbwVFqyB7d+FEy/lncbMLpIvA7XSSbD6Xth4HTzwURg/dfDjb28ocozC+w2wZC28b125k5pZCVwAbGRap8EnH4JdD1L8stKoaPuAttePwhNfzc4mVny7LJ9YNrPSuQDYyF15Y7ZdrHN98OTd2ZzCyUPw8Z/CmNFd+2xmI+c5AMtPQyOsugdW3gMvPAG/WANv9OSdyqxu+AzA8rfsi9A2Ezatg3uvyuYGChVdqmKY5StmLoPl67N1kIZb6sKsTrkAWBoWfAw+uxX2Pz5g/qDIXMJwn17vOwv7HoOHb4Op74blX4b3fAIaLylrZLNql+RSEJJuBm6eO3fu57q6uvKOY9Wo9yx0PAo77ofjB6CpBRoGFIDRnBlMmgGz2mFmO8x6P7ReUZ68ZmXitYDM+oUAXVvh5T8Nf2Yx7LHOwfFO6H4GzsbF08ZPGVxYRqOlFSZNzwpM2wyYOA1UwlVRpazk2tIKzZOgZRI0Txg8xFb8wEM/3NCYHbupBRo9kJASfx+AWT8JrlqRbeXS1wvHnodDf8nOLi76n6gAb52Ek6/Akd3w1uD165OmRmhqZtiiUdKxlBWXhqbzWzmOC1nhU1wSXQ1lPG7hUusXWHJ9NL7w54oPW7oAmI1UYxNcsTjbKuHMG/BmTxkKC9B7Gk6fgtP/hjOn4MzrDHv2U8rrnuuDvjPQ27+dvvis/a8d+uBcb7aVbd2p+JmVcO78Vjb9xw2M6swyRy4AZqlpnpBtZhXmzwGYmdUpFwAzszrlAmBmVqdcAMzM6pQLgJlZnXIBMDOrUy4AZmZ1ygXAzKxOJb0WkKTjwKFR/vjlwL/KGKfSnLeynLeyqi0vVF/mUvPOCiFMKeWASReAiyFpV6kLIqXAeSvLeSur2vJC9WWuRF4PAZmZ1SkXADOzOlXLBeAneQcYIeetLOetrGrLC9WXuex5a3YOwMzMhlbLZwBmZjaEmisAklZK6pT0oqS78s5TjKQHJPVI6ihou1TSVkld8XZynhkLSZohabukA5L2SVof25PMLKlF0tOS9sa834rt75K0M+b9taQxeWctJKlR0nOStsT9ZPNKOijpeUl7JO2KbUn2BwBJbZI2SXoh9uP2VPNKmh/f1/7tlKQ7K5G3pgqApEZgI7AKWAjcLmlhvqmKeghYOaDtLmBbCGEesC3up6IX+FoI4WpgGXBHfF9TzXwGuDGEcA2wCFgpaRnwPeCHMe9rwLocMxazHjhQsJ963g+FEBYVXJqYan8AuB/4fQhhAXAN2fucZN4QQmd8XxcB1wL/AR6jEnlDCDWzAe3AkwX7G4ANeee6QNbZQEfBficwLd6fBnTmnXGI7I8DH6mGzMA44FngOrIP0TQV6yt5b8D0+Et9I7CF7AtrU857ELh8QFuS/QFoBV4mznmmnndAxhXAjkrlrakzAOCdwOGC/e7YVg3eEUI4ChBvp+acpyhJs4HFwE4SzhyHU/YAPcBW4CXgZAih/0tmU+sb9wFfB/q/rPYy0s4bgD9I2i3p87Et1f4wBzgOPBiH2H4maTzp5i30KeCReL/seWutAKhImy9zKhNJE4BHgTtDCKfyzjOUEEJfyE6hpwNLgauLPe3/m6o4SWuAnhDC7sLmIk9NIm+0PISwhGy49Q5JH8w70BCagCXAj0MIi4E3SWS4ZyhxzucW4DeVeo1aKwDdwIyC/enAqzllGaljkqYBxNuenPO8jaRLyP74PxxC+G1sTjozQAjhJPAU2dxFm6Sm+FBKfWM5cIukg8CvyIaB7iPdvIQQXo23PWTj00tJtz90A90hhJ1xfxNZQUg1b79VwLMhhGNxv+x5a60APAPMi1dPjCE7fdqcc6ZSbQbWxvtrycbZkyBJwM+BAyGEHxQ8lGRmSVMktcX7Y4GbyCb9tgO3xaclkzeEsCGEMD2EMJusz/4xhPBpEs0rabykif33ycapO0i0P4QQ/gkcljQ/Nn0Y2E+ieQvczvnhH6hE3rwnOSowabIa+DvZmO/deee5QMZHgKPAf8n+O1lHNua7DeiKt5fmnbMg7/Vkww9/A/bEbXWqmYH3As/FvB3AN2L7HOBp4EWy0+rmvLMWyX4DsCXlvDHX3rjt6/89S7U/xGyLgF2xT/wOmJx43nHACWBSQVvZ8/qTwGZmdarWhoDMzKxELgBmZnXKBcDMrE65AJiZ1SkXADOzOuUCYGZWp1wAzMzqlAuAmVmd+h/mwD89EuVMxAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b6a049b0f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.semilogy(np.array([sum([__['loss'] for __ in _],[]) for _ in hists]).T, '--')\n",
    "plt.semilogy(np.array([sum([__['loss'] for __ in _],[]) for _ in hists_opt]).T)\n",
    "plt.gcf()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b6a04bd1d68>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b6a04bd1d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.semilogy(np.array([sum([__['val_loss'] for __ in _],[]) for _ in hists]).T, '--')\n",
    "plt.semilogy(np.array([sum([__['val_loss'] for __ in _],[]) for _ in hists_opt]).T)\n",
    "plt.gcf()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b4f7f541d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.loglog(avgs[:6], [_[-1]['val_loss'][-1] for _ in hists],'o-')\n",
    "plt.loglog(avgs[:6], [_[-1]['val_loss'][-1] for _ in hists_opt],'o-')\n",
    "plt.loglog(avgs[:6], [_[-1]['loss'][-1] for _ in hists],'o--',color='C0')\n",
    "plt.loglog(avgs[:6], [_[-1]['loss'][-1] for _ in hists_opt],'o--',color='C1')\n",
    "plt.xlabel('Number of Samples, S')\n",
    "plt.ylabel('Validation and Cost functions')\n",
    "l1 = plt.legend(['random','optimized'])\n",
    "xlim = plt.xlim()\n",
    "ylim = plt.ylim()\n",
    "p1, = plt.plot([1,2],[1,2],'k--')\n",
    "p2, = plt.plot([1,2],[1,2],'k-')\n",
    "plt.xlim(*xlim)\n",
    "plt.ylim(*ylim)\n",
    "plt.legend([p1,p2],['cost','validation'],loc=(0.75,0.65))\n",
    "plt.gca().add_artist(l1)\n",
    "plt.title('Gains from D-design')\n",
    "plt.tight_layout()\n",
    "plt.savefig('FI_ddesign.png',dpi=400,bbox_inches='tight')\n",
    "plt.gcf();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2b635dd67d68>"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.semilogx(avgs[:6], [_[-1]['val_loss'][-1]/_o[-1]['val_loss'][-1] for _,_o in zip(hists,hists_opt)])\n",
    "plt.semilogx(avgs[:6], [_[-1]['loss'][-1]/_o[-1]['loss'][-1] for _,_o in zip(hists,hists_opt)],'--',color='C0')\n",
    "plt.gcf()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "avgs = [1,2,4,8,16,32,64,128]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}