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   "source": [
    "# Statistics\n",
    "\n",
    "This notebook shows show the do some basic statistics on Neuropixels `ChannelMap` and its blueprint."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "921caa08-2269-4da0-9cc8-1b6ce2b6e4ed",
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   "source": [
    "## Number of selected electrodes\n",
    "\n",
    "For a channelmap"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c083f032-a2d3-4ac9-945b-8ca8da728236",
   "metadata": {},
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      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from neurocarto.probe_npx import ChannelMap\n",
    "\n",
    "chmap = ChannelMap(24)\n",
    "len(chmap) # empty map"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "d2a6a7df-f4ef-48d6-a5f7-c25633c4d347",
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "1"
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     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "chmap.add_electrode((0,0,0))\n",
    "len(chmap)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e382835d-6f7c-4137-899a-bff5cb10e853",
   "metadata": {},
   "source": [
    "For a blueprint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "4862e95a-fe6e-4967-bd39-0a9694fea459",
   "metadata": {},
   "outputs": [
    {
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       "0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from neurocarto.probe_npx import NpxProbeDesp\n",
    "\n",
    "D = NpxProbeDesp()\n",
    "\n",
    "# all electrodes, chmap here used as a probe type reference, we do not use its content inside.\n",
    "blueprint = D.all_electrodes(chmap)\n",
    "len([e for e in blueprint if e.state == D.STATE_USED])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "a2234e64-5896-48ce-b62f-9c3918adc931",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get selected electrodes\n",
    "# This function will read the content of chmap\n",
    "len(D.all_channels(chmap))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c67a834c-4c43-4e08-8667-38687690f981",
   "metadata": {},
   "source": [
    "## Number of electrode set with full-density category"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c31ff57c-18c3-42e8-9979-6913d87808ab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "66"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "blueprint = D.load_blueprint('Fig3_example.blueprint.npy', chmap)\n",
    "\n",
    "len([e for e in blueprint if e.category == D.CATE_FULL])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8a2b16b-0c0f-4f13-afd3-77876fa086a4",
   "metadata": {},
   "source": [
    "## Area Efficiency\n",
    "\n",
    "we define the area efficiency $Aeff$ of a given blueprint $Q$ and its outcomes channel map $S$ as\n",
    "\n",
    "$Aeff(S|Q) = \\cfrac{selected(S|Q)}{request(Q)}$, $0$ if $request(Q)=0$ \n",
    "\n",
    "Where $selected$ and $request$ are defined below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "21f5c7d1-ee78-43c3-ac0e-7a8b9aafbf68",
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   "source": [
    "def selected(S, Q):\n",
    "    \"\"\"How many electrodes are selected in density-category.\"\"\"\n",
    "    # we do not use S here, because Q contains the selecting information.\n",
    "    v1 = len([e for e in Q if e.state == D.STATE_USED and e.category == D.CATE_SET])\n",
    "    v2 = len([e for e in Q if e.state == D.STATE_USED and e.category == D.CATE_FULL])\n",
    "    v3 = len([e for e in Q if e.state == D.STATE_USED and e.category == D.CATE_HALF])\n",
    "    v4 = len([e for e in Q if e.state == D.STATE_USED and e.category == D.CATE_QUARTER])\n",
    "    return v1 + v2 + v3 + v4\n",
    "\n",
    "def request(Q):\n",
    "    \"\"\"How many electrodes are requested in density-category.\"\"\"\n",
    "    v1 = len([e for e in Q if e.category == D.CATE_SET])\n",
    "    v2 = len([e for e in Q if e.category == D.CATE_FULL])\n",
    "    v3 = len([e for e in Q if e.category == D.CATE_HALF])\n",
    "    v4 = len([e for e in Q if e.category == D.CATE_QUARTER])\n",
    "    return v1 + v2 + v3/2 + v4/4"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "When $Aeff < 1$ , it means area are not well used on average. When $Aeff > 1$ , it means area are over-used on average."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "37ac4df0-2045-4a25-827e-7a67cb9ef06f",
   "metadata": {},
   "source": [
    "## Channel Efficiency\n",
    "\n",
    "We define the channel efficiency $Ceff$ of a given blueprint $Q$ and its outcomes channel map $S$ as\n",
    "\n",
    "$Ceff(S|Q) = min \\{ Aeff(S|Q), \\cfrac{1}{Aeff(S|Q)} \\}$, $0$ if $Aeff(S|Q) = 0$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6730b582-5da9-445b-8ced-113385cdf5c5",
   "metadata": {},
   "source": [
    "We define the channel efficiency $Ceff$ of a blueprint $Q$ as\n",
    "\n",
    "$Ceff(Q) = max \\{ Ceff(S|Q) | S \\in \\mathcal{S} \\}$\n",
    "\n",
    "where $\\mathcal{S}$ is all possible outcomes from the given blueprint $Q$."
   ]
  }
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