{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "initial_id",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2024-06-03T03:34:30.787475200Z",
     "start_time": "2024-06-03T03:34:28.159120700Z"
    }
   },
   "outputs": [],
   "source": [
    "from algorithm.neat.gene.conn.bspline import BSplineConn\n",
    "from algorithm.neat.gene.conn.cache_bspline import CacheBSplineConn\n",
    "import jax, jax.numpy as jnp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "outputs": [],
   "source": [
    "normal_gene = BSplineConn(grid_cnt=6, spline_order=3, grid_init_range=[-1, 1])\n",
    "cache_gene = CacheBSplineConn(grid_cnt=6, spline_order=3, grid_range=[-1, 1], cache_num=1000000)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-06-03T03:41:35.807924900Z",
     "start_time": "2024-06-03T03:41:35.793415500Z"
    }
   },
   "id": "a09d6ccf956606b3"
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "outputs": [
    {
     "data": {
      "text/plain": "State ({'kan_initial_grids': Array([-1.        , -0.6       , -0.20000002,  0.20000005,  0.6       ,\n        1.        ], dtype=float32), 'bspline_cache': Array([[0.16666666, 0.6666666 , 0.16666667, ..., 0.        , 0.        ,\n        0.        ],\n       [0.16666412, 0.6666665 , 0.1666692 , ..., 0.        , 0.        ,\n        0.        ],\n       [0.16666159, 0.66666657, 0.16667175, ..., 0.        , 0.        ,\n        0.        ],\n       ...,\n       [0.        , 0.        , 0.        , ..., 0.1666717 , 0.6666666 ,\n        0.16666172],\n       [0.        , 0.        , 0.        , ..., 0.16666915, 0.6666666 ,\n        0.16666426],\n       [0.        , 0.        , 0.        , ..., 0.16666675, 0.6666665 ,\n        0.16666663]], dtype=float32)})"
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "state = normal_gene.setup()\n",
    "state = cache_gene.setup(state)\n",
    "state"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-06-03T03:41:37.462678200Z",
     "start_time": "2024-06-03T03:41:36.459771900Z"
    }
   },
   "id": "57fbeab2e4d4c511"
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "outputs": [
    {
     "data": {
      "text/plain": "Array([ 0.08086783, -0.38624713, -0.37565565,  1.6689739 , -1.2758198 ,\n        2.1192005 , -0.85821223,  1.1305932 ], dtype=float32)"
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "key = jax.random.PRNGKey(0)\n",
    "normal_attrs = normal_gene.new_random_attrs(state, key)\n",
    "normal_attrs\n",
    "weights = normal_attrs[normal_gene.grid_cnt:]\n",
    "weights"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-06-03T03:41:38.867812Z",
     "start_time": "2024-06-03T03:41:38.789154200Z"
    }
   },
   "id": "9d9cacf5af5f38c3"
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "outputs": [
    {
     "data": {
      "text/plain": "(Array(-0.0304966, dtype=float32), Array(-0.03049916, dtype=float32))"
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = 0.99999\n",
    "normal_res = normal_gene.forward(state, normal_attrs, t)\n",
    "cache_res = cache_gene.forward(state, weights, t)\n",
    "normal_res, cache_res"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-06-03T03:43:23.083384100Z",
     "start_time": "2024-06-03T03:43:23.002384100Z"
    }
   },
   "id": "9177b012b7ab25cd"
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "outputs": [],
   "source": [
    "batch = 100000\n",
    "t = jnp.linspace(-1, 1, batch)\n",
    "batch_normal_forward = jax.jit(jax.vmap(normal_gene.forward, in_axes=(None, None, 0)))\n",
    "batch_cache_forward = jax.jit(jax.vmap(cache_gene.forward, in_axes=(None, None, 0)))"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-06-03T03:50:05.806318700Z",
     "start_time": "2024-06-03T03:50:05.785312900Z"
    }
   },
   "id": "878f5eda35df17f7"
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.34 ms ± 99.2 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit batch_normal_forward(state, normal_attrs, t).block_until_ready()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-06-03T03:52:23.070679300Z",
     "start_time": "2024-06-03T03:52:21.768451Z"
    }
   },
   "id": "2f649d81e1945757"
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "134 µs ± 28.3 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit batch_cache_forward(state, weights, t).block_until_ready()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-06-03T03:52:43.066619300Z",
     "start_time": "2024-06-03T03:52:42.599706100Z"
    }
   },
   "id": "cac106d6792ea53b"
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "outputs": [],
   "source": [
    "normal_res = batch_normal_forward(state, normal_attrs, t).block_until_ready()\n",
    "cache_res = batch_cache_forward(state, weights, t).block_until_ready()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-06-03T03:53:15.153532800Z",
     "start_time": "2024-06-03T03:53:15.145531800Z"
    }
   },
   "id": "27bc7e5abf9b65d4"
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false
   },
   "id": "1b25ee5a2fe153c4"
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "outputs": [
    {
     "data": {
      "text/plain": "[<matplotlib.lines.Line2D at 0x7f5b32908a30>]"
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "plt.plot(t, normal_res, color='blue')\n",
    "plt.plot(t, cache_res, color='red')"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-06-03T03:53:58.803332700Z",
     "start_time": "2024-06-03T03:53:57.867105200Z"
    }
   },
   "id": "97ace2f9183fef16"
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false
   },
   "id": "4edc26eea7760479"
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}