opt_coding.ipynb

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     "input": [
      "# Import here\n",
      "%matplotlib inline\n",
      "import matplotlib.pylab as pylab\n",
      "import matplotlib.pyplot as plt\n",
      "import numpy as np\n",
      "import theano\n",
      "import theano.tensor as T\n",
      "\n",
      "pylab.rcParams['figure.figsize'] = (9.0, 6.0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def cpc(x, N):\n",
      "    n = np.arange(N, dtype=np.float32).reshape((N, 1))\n",
      "    z_matrix = np.float32(x * (N - 1)) - n\n",
      "    r = np.exp(-z_matrix ** 2 / 2)\n",
      "    r /= np.sqrt(np.sum(r ** 2, axis=0, keepdims=True))\n",
      "    return r"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n_steps = 100\n",
      "\n",
      "def t_rectify(t_x):\n",
      "    return T.maximum(t_x, 0.0)\n",
      "\n",
      "def t_one_step(t_z, t_S, t_b_eff):\n",
      "    return t_rectify(T.dot(t_S, t_z) + t_b_eff)\n",
      "\n",
      "t_x, t_nu = T.fmatrices('x', 'nu')\n",
      "t_S, t_W, t_V = T.fmatrices('S', 'W', 'V')\n",
      "t_b, t_c = T.fcols('b', 'c')\n",
      "t_y = t_rectify(T.dot(t_V, t_x) + t_c)\n",
      "t_b_eff = T.dot(t_W, t_y + t_nu) + t_b\n",
      "t_z_seq, updates = theano.scan(t_one_step,\n",
      "                               outputs_info=T.zeros_like(t_b_eff),\n",
      "                               non_sequences=[t_S, t_b_eff],\n",
      "                               n_steps=n_steps)\n",
      "t_x_hat = t_z_seq[-1]\n",
      "cost = T.mean(T.sum((t_x_hat - t_x) ** 2, axis=0))\n",
      "t_dS = T.grad(cost, t_S)\n",
      "t_dW = T.grad(cost, t_W)\n",
      "t_dV = T.grad(cost, t_V)\n",
      "t_db = T.grad(cost, t_b)\n",
      "t_dc = T.grad(cost, t_c)\n",
      "f = theano.function(inputs=[t_x, t_nu, t_S, t_W, t_V, t_b, t_c],\n",
      "                    outputs=[cost, t_x_hat, t_dS, t_dW, t_dV, t_db, t_dc],\n",
      "                    updates=updates)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dim_unit = 64\n",
      "\n",
      "# initialization\n",
      "S = np.eye(dim_unit, dtype=np.float32)\n",
      "V = np.random.randn(dim_unit, dim_unit).astype(np.float32)\n",
      "V /= np.sqrt(np.sum(V ** 2, axis=1, keepdims=True))\n",
      "W = V.T / n_steps\n",
      "b = np.zeros((dim_unit, 1), dtype=np.float32)\n",
      "c = np.zeros((dim_unit, 1), dtype=np.float32)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sigma = np.float32(1. / np.sqrt(dim_unit))\n",
      "eta_V = np.float32(0.05)\n",
      "eta_c = eta_V / dim_unit\n",
      "eta_W = eta_V / n_steps\n",
      "eta_S = eta_W / n_steps\n",
      "eta_b = eta_W / dim_unit\n",
      "dim_batch = 1024\n",
      "\n",
      "for t in range(100000):\n",
      "    x = np.random.uniform(size=(1, dim_batch)).astype(np.float32)\n",
      "    r = cpc(x, dim_unit)\n",
      "    nu = sigma * np.random.randn(dim_unit, dim_batch).astype(np.float32)\n",
      "    cost, x_hat, dS, dW, dV, db, dc = f(r, nu, S, W, V, b, c)\n",
      "    if (t + 1) % 10 == 0:\n",
      "        print (t + 1), ':', np.sqrt(cost)\n",
      "    S -= eta_S * dS\n",
      "    W -= eta_W * dW\n",
      "    V -= eta_V * dV\n",
      "    b -= eta_b * db\n",
      "    c -= eta_c * dc\n",
      "    V /= np.sqrt(np.sum(V ** 2, axis=1, keepdims=True))"
     ],
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     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.imshow(result_V, interpolation='None')\n",
      "plt.colorbar()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 73,
       "text": [
        "<matplotlib.colorbar.Colorbar instance at 0x12981d368>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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1/TIsle3NBdmm4X7SSszYQRoAWMEUb6ABaekbsCnj9HJ7gRy8vg7dxceeefxB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\nm+M4jhM5fHJzHMdxIodPbo7jOE7k+B99mntsIPKd8gAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x12aac8250>"
       ]
      }
     ],
     "prompt_number": 73
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(result_V[13, :].T)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 74,
       "text": [
        "[<matplotlib.lines.Line2D at 0x12aaea110>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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aG2Vr4unTK9/uvPPkti6fuPv2yW6FpncsLIUtG8GWjXumBloDvs6RsEJypCTn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\n2CzT+xJIAPdLf3fulA33XF7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       "text": [
        "<matplotlib.figure.Figure at 0x12829c650>"
       ]
      }
     ],
     "prompt_number": 74
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(np.abs(np.fft.rfft(result_V[13,:])).T)\n",
      "plt.grid()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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fZFT65CfhwAPhU59KbnwiItKcZns4GrpbrLTeQPo3IHsllUcegX/9V5g6tfmfHTNGMxwi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\nIiIikjglHCIiIpI4JRwiIiKSuP8PF/KBlJ8+UZ0AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x12aaf8290>"
       ]
      }
     ],
     "prompt_number": 75
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.imshow(r, interpolation='None')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "<matplotlib.image.AxesImage at 0x12031f410>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ux2fivfX33JdoTLtnkhr+iviWEm7GS5BoSke3545k3tlCDqp0/j4d/9JbXb0e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\nMp/eJeitzzkAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11f7ad790>"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.imshow(x_hat, interpolation='None')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "<matplotlib.image.AxesImage at 0x12088ef10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Cw5OHG95JSOu3oW14X8PUskFetVtCfn6/Nt31DZT3+c8Xeb33uE4r0lV4+j3I\nd4nOF4WvNPeupO+rBujGlmVFAH5bMCq8GCDd3Ul/Er40HvH52rGAtRPaAwAmlFKeUJO2ZsMbYCOZ\n466ctMVlqbqRk0zGkRa7mViRmNpSZQsYIgCzC9B6NFUQ2i1IH3mPz5Ohz0XRlBwlhZB0SF44S+Ni\nA+ZPGmChNVEJqEcwj1dllMnM5zJzFwBLIS5aeIyZOwJ4GMAUCCHjJgAvQ3jPtGA5gtMIv8gN1WT2\nrfQ7+GFbiY1EfD9WGLvskDsK9+fE6r2fZzobL03eqiMcLZ4B/tgk2Av4KwJjPVGEZ5cYEcvn54t6\nMtaKXw08ZUgH6D2zlr2hAVlXaADQdtXnMDfYwHmTvreXL+Ghgn+ZVRz9vAS7gDIk3t8s6I876W4Y\nNYxEQ72fYPfcwWGsLXSxFAEu9XzElrhtwjg+yt45Y66YgWNy0ftTAODe3BLpSVrdPiK+f37O7nzp\nqhrZ8lzHqCq4CmHeqDVV+J5YAxyZU+4DCcyDolfESHgcOKkhxRaJJuwtTb13uRSn+reWhryEq9/z\nPGk8SbXCg6RVNDuxe9LztQknFMXfwUVNrA+AEyegrLXyv3lEaStgZ7+dJ2hQE5F04sbHVTVn2zU9\ngZdXC+gSlJ11jc+bxtNzlWd1MRJqLI4qdZQWYcE2k3lgvCNnWr3Lp9uSZ9RepYGo/VLVZvsLGFu7\n/FD9Np/d/WcBmBEVojVkppQN+iUeny4m8huhZ+Ov1pB/zKZGquszG4AHg3Ty0dzqhPLUl4PBt4v1\nf1+Ciq4vz4YFXg9gX9NFRXdA7MfWh0FzusRizT04ML5UC2p1Ocw7Oo9U4NsRFD4BwBENmFgn+Ltk\nxyJKU/shlYFhXUHhRqp5jelCGY1xafacuovLvytpC2vbp1C3Gjp7w6FB3g3YoEZ3wx8wN5fd58aw\nHtOincH/Lu8gXT0x4rYkJ8Zu4+NDdCuB1X76wJraVoCKS3GdxgPASi9+auDxGoN/hlSq12tRFgAO\nMK1muiPCHIfCmd6gSj9hxqrZUBykYzwwD9JuldkyAaaV5PtN5PeHY2HpVqCn3tHVlTlZaJAGRQYu\nzMsCblP482XzRLztTe/CqCWcLtLtk5PdattsNqTv8L+5La0tD+pXjEvwFJfQl69edJzx3eKS5M2Q\nG5CyoRnB+8nlrz/1dF5JrXd1C3k5go+69YLR0XgExIW+FH4kAgTCbEKZ9aS3LIbF+jJaVvoj8PIG\nhiSinxXj/bDrAAAPE0lEQVQGn41QoNIxUUn5Hx5Jqu1zPlatkk7cpD0tRAQcGNRZaNdkyift3EKc\nYkOJiD4E8AWAEoAbmPkmIlrFzO399wRxcVh7JR1nu9o5ljPo8fFgg1GdLr6x8ugsgNXlUxDfki4L\nCFHDxexeRbKhrihu3fxvAFHy5qYpzpJzgW0uRupyHl4E7i5mZBCItJOeBeAtXbtsprbU7MjIF/n/\npd5wPgbiup8KYGLt/ALowobm3fM21psNWwHUHdbr0StGB1R27be5PqlbAbx4gvF9i6Ca/lt1n7Gl\nr7R8fcq0CcTl2gH9AtQLt5q1z/ctiLtw3isC3R8G8BqwQ9F3iKXkE5RnRdlXxnO7djVYs+b3YMNR\ntbQaij2YeScII4jRRLSn/NJumNkI4/XlM5OEDQYPuighTjS+EZtvaIkf/B2hiZMx+4zGlYWSfmUP\nAHilqAkkBOed6z4yuBj+N0Cn0lGR59El39CNCIBv9JNyuzyMI3cmoEfJdzsrCxOUwu5jbWWdf9dS\nv/BBnpQiXSsd7RGlCq+w1meqx512VazOODq0js8iTADCkW6FYNIvgf4woTphQvd9qYWJcH9+V297\ngJ9GXenw9HmnWdERcIO3QArI4l7fXDCc5KdHweleTYpYCV4umQHjFd1SHCBa18OLCPuuptASl8b2\niXG0ZxlfrTQFmAMtpkBnb4kmvpL/jGIFefqY5P89jtHZ6wEAaDtfuHkKLnqUmNNmDwCYGm3725YC\nx3nBXSLqoteGJjSXUWaANUR0H4DnAGwJ4BCk9pbZHxFPmRJqB6Y5LmXxqKeDrnxeLpSNlOxIMOQM\nYDtOxeqDfURsqBlpfrlLMR5GQHDeOeJi2NouKt0XG5syaXwgWZmfGnm+brh/FI8ZgH+OnrNKFNHo\nb9fsEk/La6PbETr+VWtyLeLGpHmTn4gKPFpOO1rjbEiDstCUYMWuxZEiTV1pBHD4+BiJrVeo586B\nuJCdFkWFP0LE/sOGLH4fshT1NVSFnWa4P/9ybg4AYGlt3N7FiMTiI4CB43PbSWEG242KviHOQKeS\nfj/1j0POCx/qTGNbstdIsGWsHiXRlaTEfn+KXWAiQe+HIgJjPxALi+tyG2ve6QxR02FZzuAPRfYi\n/JjyLkv9+RfZYV4DluWEcfba9tcAANb9aJIpVQxtDgjb0s9Lg/Bh28CuKnr5YnxLVGfoWo9mMcoU\nGdKGAK6DKKbeABYDmINqvGX6qMhRjg1E+sF9kfK8b6XbMGLiPG7MVZY4yt6f5T6ITb85AeFpE9kO\nYCz0q5WeyqqRtT9j0HW6FJti/bx5qeaVS7xlGpJppHauzjBfvhFwRFDODMjjPhMqyyR+k+b8XOCF\nTh2QKlhG39aQ6k6Xd8b5Z/PVT4hlqWln64sAgKU17YQxutI3/pa7p/qDEQCEgTQkWr/2+btWCTeA\ny/8lI9a/LT4jDmuoSNgznm5aYxBENSc3ElHuk+bvDpwxNVMlYe03hu96JPyuoR/djXDhZ8g3afz0\nk8lauPun6i+xmpuXnHTFiuKZ5Gahvi+zHNhmxA06+3hJN0fbMmWt079hhbvCh6lFlE+PDCs0485T\nekLrOl1Z/v3G8bv5XkrjxiaqBrD2y70Byu7XKUAaDUVXCI3EKRBLy0eY+UFU4i1zesqOd16FE75p\n50V1h/tOpR1USOA35iwXq6onLeTz4MplM19s+LKU7AjpzUToVysZ3UCXr+Jtir9LoUuem3sxMQ4A\nnJ3raCVZvjBJYy0Nrk+VRwQ6YeghKSxic1Nlb47UmU/rtYQLeYxoijyNz9VKT/o2ycHFeQn1lfvs\nG/FjqKbv8M2+AZZKw6QZyIYBpXd9csE3zIjmxQBgMq7Wo65k2n6MMpyzOoU1aQh/mpC7ZFCYZqj4\nXQXjia3c/Zspn88vB1Av1b1hXExyGggARPgyxQJOeEts8tMYmOyd8L1+smk1oYfaYbldNRGbMm6r\npYBhvSVjfm6e/kUSfO3N3TWKkSYR7s/9NRLU9vMBAIBuM96002xO77emI9eBjwmdSV/XAuRxSSzy\nFUP9qSnal480AkUOwF8g7vD4FsC2RLQRKvCWSW8DaXwb9J8g1GBh+RBmevMjcc6PHAsDnvaeknPS\n0h3u+ZLl0qL4qxt8I5qBAh7z5toHlaQb6d4PJ7dbPlEHSckaf+fgdEAxEkPnt/8Jz7yPNcn7LHwo\nN5ymctAE72tc7ZlcugKoqUSYi/ZccRUyyuU29jXRQDfrHFdi0X2jMuQj140g/onna4tkj4c6/pSO\nm7Yf3/LJiPhuw862vGz0m+J8lROk4yeC58K68ra8EsBIDHsg5bZdBMFK0nLB2jBduxAau8aawA5A\nGcHL39QB95aGZvrGT0ZrvMBqwFtFz8zf5gVbFaNAFO453+KFako64y943UvpzCyNhuPFrEaecSzw\nZpR/U3lt8QH28wKV/aE435O2JiS2tpv4TtX5R+FvYZa/Pfjrn3C5KDpB3eEZ8medozS5PJtS8BJt\nB+FtrsE261gA4fHwh734XRYnear9XGVCzAEf+XXEGoeCCv71QyG0LM6rHpmBchmMKzSvQGUl1UHK\nK4x41qIGROuB4zwd9QDSIo1AUQOhx7+emXsB+BqKz4m0Rpl84ZGIHSeK+FHwU+Rf8rcYAxUN46Bc\ntGL+kPOlxHfFQDfwerkhqQOboHN3LnoF8M0zj0AcvmZgXAEDvEex/3bP2geVZQYHWWXtQMjL0Xnz\nFcRc3n8sRsLzbeL79vtub/ZDcFpuR5lq7P34XC1O2esmY3qsTxgcj7cJHOKbj9x1eiR79vcF/7mh\n5JlwkVix6o9zmuDXjdTctto8jQV33B6ibKR8p+57wn1EXZ2lGQM4q4SQaWARE//efaX7FHgdsHgb\n3F+jG+ySJudAwDSX5aQZJyohbTC8JJx7mFkXZXBd6XUcmt8ZeolC7xiIp8TbxYhS3PBT5B3S/b9c\noH243bfOB0CEo3P7h2mueAE75UaU39mRpl6qnxR650JbKpbuO5qdC7SSK8IxT8Ffc/eFD+XPURZu\nukqaaOjLUwNNojoBPR2hFWQ1cmubk8Co8XGWeyEEgvZ8EjCzgIu8c3w6Yrx80esDIJzwhuSk+WS2\n+L5rc9/EqI4tEcyXeenbxCO5d/XRtfc8ve7/0Cbws0k7RpiMXVV7h3hmA0qBNlXfty9LIwHwQqQ1\nykw8NkpEnQHMZ+Zt/Oe+AM4BsC2AAcy8jIi2ADCHmXdQ0nKvXndCyCB65J4cCW8fnWfAwHq3K2KX\ntkg4fsG/cENvu2dA7Wkl8v8zfP+kBa/jtN69UPFgYTc+zgDT94+E8MWRjE8/nYUtt/xVFTzsCuAd\nAF/j4AWb4IHetj3IdMe0dliwKxb2fjkxXjpsAiFsDAKQ4pr5MrbBLgva4ZXe6kDxAwCVXHJmR/X1\nkIQDATzYQrQ1DZqOBdginJbjHQew5BsBPwKwIjsLI44Hpt0GUTdSXSf2tWiESD1EBoctAej2ULoA\n+Dg7v/8WGABh8hbHHgu64c+9dSfFjgNwoya8eZG1P4RjRtg/6XfHga/X87r9gl9gUe8XtO+wzXHA\nkub+xuqOqIrrsh6Hvg1WCPoNwPcogTsDCO+DyVIPbdvW4IUXjjEeG03rh+I5AMcw8yIiKgIIdEj/\nYOZLiehsAJsx89lKumbeIHNwcHBwcHD4LlGtQPFzCK81G0DcOHokgDyAewH8GGIT5lBmtlkrOjg4\nODg4OPyXIpVA4eDg4ODg4OBgQ5a7PBwcHBwcHBwctGgxgYKIBhHRQiJaTETxoxwOzQIi6kJEc4jo\nHSJ6m4hO8cM7+NfLLyKiJ+Xr5YnoHL9eFhLRPt8d9/99IKI8Eb1ORLP8Z1cPrQwi2oyI7iOi94jo\nXSLazdVD68Mv13eI6C0i+hMR/cDVQ+uAiG4louVE9JYUlrnsiWhnv/4WE5HNoyOAFhIoiCgP4R1j\nEIQXmcOIyHJ5vUMVWAfgNGb+GYDdIe5a6Q5xtPcp30/IM/4ziOinAH4DUS+DAFxPRE5T1XwYA+Bd\nhMcKXD20Pq4C8BgzdwfwPwAWwtVDq4KI6gEcC6AXM/eEsLkbDlcPrYWpEOUoI0vZB0aXkwEczczd\nAHQjIpVmBC1VYbsC+ICZm1g4WLgbwNAWyut7DWZexsx/8X9/BXEJwVYAhgC43Y92O8Lr5YcCmM7M\n65i5CeJMqs6NnUNGEFEdgP0hDJiDDunqoRVBRJsC2JOZbwUAZl7PzF/A1UNrYzXEYmdDIqqBOBn4\nKVw9tAqYeR7E9RgyspT9br47iI2ZOTjff4eURouWEii2QvTg9lKoHk4cmh3+qmAnCBfpmzNz4Mh+\nOYDN/d9bQtRHAFc3zYdJEK77PCnM1UPrYhuIiwunEtFrRHST79nX1UMrgpk/B3AFgI8gBIl/MvNT\ncPXwXSJr2avhnyChTlpKoHBHR1oZRFQL4H4AY7jsIlDA7slURGlJ3r4PIKIDAKxg4SJPe0bb1UOr\noErPviJKy7H3/QARbQfgVIibxraEuPcp4prY1cN3hxRlXxFaSqD4BMK9XIAuiEo6Ds0IImoDIUzc\n6V/cBgDLfS+n8FVXgWtCtW7qEPpedqgcvwAwhIiWAJgOYG8iuhOuHlobSwEsZeZX/Of7IASMZa4e\nWhW9AbzAzP9g5vUQ/rH7wNXDd4ksY9FSP7xOCbfWSUsJFAsgDDjqiWgDCIOPh1sor+81fOOZWwC8\ny8xXSq8eBhDcvDUKoU/mhwEMJ6INiGgbiMu+m8sH9vcWzHwuM3fxXdQPB/AsM/8Wrh5aFcy8DMDH\nRBRcwjIQwm/8LLh6aE0sBLA7EbXzx6iBEMbKrh6+O2Qai/y+tNo/JUUAfosE3/41LcE1M68nopMA\nPAFh3XsLM7+XkMyhMuwB4AgAbxKRfyMNzgFwCYB7ieho+J5MAYCZ3yWieyE693oAv2Pn3awlEJSp\nq4fWx8kApvmLmYhnX1cPrQNmfoOI7oBYXHoQVyvfCGBjuHpocRDRdAD9AHQkoo8BjEdlY9HvANwG\ncdvcY8xsvSzJecp0cHBwcHBwqBrunK+Dg4ODg4ND1XAChYODg4ODg0PVcAKFg4ODg4ODQ9VwAoWD\ng4ODg4ND1XAChYODg4ODg0PVcAKFg4ODg4ODQ9VwAoWDg4ODg4ND1XAChYODg4ODg0PV+H/GzdbY\n9DSAgQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x12032d910>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def create_decoder():\n",
      "    A, y = T.fmatrices('A', 'y')\n",
      "    x = T.nnet.sigmoid(T.dot(A, y))\n",
      "    return theano.function(inputs=[A, y],\n",
      "                           outputs=x)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "decoder = create_decoder()\n",
      "dec_mat = np.load('/Users/chayut/Dropbox/data/grid_cells/cpc_decoding_vector.npy')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "decoder(dec_mat, result_x_hat)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "array([[ 0.27246067,  0.17158265,  0.59323031, ...,  0.48518836,\n",
        "         0.68330532,  0.4247331 ]], dtype=float32)"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}