ToyModel.ipynb

{
 "cells": [
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "import numpy as np\nfrom snmachine.snfeatures import WaveletFeatures",
   "execution_count": 1,
   "outputs": [
    {
     "output_type": "stream",
     "text": "No module named 'pymultinest'\n\n                PyMultinest not found. If you would like to use, please install\n                Mulitnest with 'sh install/multinest_install.sh; source install/setup.sh'\n                \n",
     "name": "stdout"
    }
   ]
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "Nsamps = 75\nNfeats = 100\nNdim = 3",
   "execution_count": 12,
   "outputs": []
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "X = np.random.normal(size=(Nsamps, Ndim))\nR = np.random.random((Ndim, Nfeats))\nX = np.dot(X, R)",
   "execution_count": 13,
   "outputs": []
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "X.shape",
   "execution_count": 14,
   "outputs": [
    {
     "output_type": "execute_result",
     "execution_count": 14,
     "data": {
      "text/plain": "(75, 100)"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "wf = WaveletFeatures()",
   "execution_count": 15,
   "outputs": []
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "u, s, vh = WaveletFeatures.get_svd(X)",
   "execution_count": 35,
   "outputs": []
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "u.shape",
   "execution_count": 36,
   "outputs": [
    {
     "output_type": "execute_result",
     "execution_count": 36,
     "data": {
      "text/plain": "(75, 75)"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "s.shape",
   "execution_count": 37,
   "outputs": [
    {
     "output_type": "execute_result",
     "execution_count": 37,
     "data": {
      "text/plain": "(75,)"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "vh.shape",
   "execution_count": 38,
   "outputs": [
    {
     "output_type": "execute_result",
     "execution_count": 38,
     "data": {
      "text/plain": "(75, 100)"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "vec, Z, M, scale, vals = wf._pca(X, 95, None, method='svd', normalize_variance=False)",
   "execution_count": 39,
   "outputs": [
    {
     "output_type": "stream",
     "text": "The condition number in the SVD is 3.00878444226e+20 and the normalized one is 3.23514902654e+19\n",
     "name": "stdout"
    }
   ]
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "scale",
   "execution_count": 41,
   "outputs": []
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "Z.shape",
   "execution_count": 42,
   "outputs": [
    {
     "output_type": "execute_result",
     "execution_count": 42,
     "data": {
      "text/plain": "(75, 75)"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "vec.shape",
   "execution_count": 43,
   "outputs": [
    {
     "output_type": "execute_result",
     "execution_count": 43,
     "data": {
      "text/plain": "(100, 75)"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "u.shape",
   "execution_count": 44,
   "outputs": [
    {
     "output_type": "execute_result",
     "execution_count": 44,
     "data": {
      "text/plain": "(75, 75)"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "len(s)",
   "execution_count": 45,
   "outputs": [
    {
     "output_type": "execute_result",
     "execution_count": 45,
     "data": {
      "text/plain": "75"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "vec_low, Z_low, M_low, scale_low, vals_low = wf._pca(X, 5, None, method='svd', normalize_variance=False)",
   "execution_count": 46,
   "outputs": [
    {
     "output_type": "stream",
     "text": "The condition number in the SVD is 3.00878444226e+20 and the normalized one is 3.23514902654e+19\n",
     "name": "stdout"
    }
   ]
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "DR = WaveletFeatures.reconstruct_datamatrix_lossy(Z, vec, M)",
   "execution_count": 47,
   "outputs": []
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "Delta = DR - X",
   "execution_count": 48,
   "outputs": []
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "var = np.sum(Delta**2, axis=1)",
   "execution_count": 49,
   "outputs": []
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "var",
   "execution_count": 50,
   "outputs": [
    {
     "output_type": "execute_result",
     "execution_count": 50,
     "data": {
      "text/plain": "array([  3.61334069e-29,   1.97038220e-27,   3.70003108e-28,\n         3.21005529e-28,   3.13092268e-28,   6.48730880e-28,\n         2.84261867e-28,   1.44137108e-28,   7.80813047e-28,\n         5.53711215e-28,   7.27289695e-28,   4.53586932e-28,\n         2.47728033e-28,   4.20654716e-28,   6.04215838e-28,\n         1.89750322e-28,   1.39045979e-28,   5.56755592e-29,\n         1.32745211e-28,   1.08653456e-28,   1.00203246e-28,\n         6.99838269e-29,   1.43667633e-28,   1.07038660e-28,\n         2.33246779e-28,   1.47377600e-28,   6.42852094e-29,\n         1.33263760e-28,   8.24466150e-28,   1.16888733e-28,\n         7.35756549e-29,   8.15152979e-29,   6.60656549e-29,\n         8.15284436e-29,   2.48794519e-28,   1.25180710e-28,\n         6.26512715e-29,   1.45344495e-28,   1.00709516e-28,\n         8.80873579e-29,   5.33962327e-29,   3.70869396e-28,\n         2.80650363e-28,   1.13848652e-28,   1.33748131e-28,\n         9.29117432e-29,   9.49903345e-29,   7.77342407e-29,\n         1.12623424e-28,   1.63889959e-28,   7.86948005e-29,\n         1.03198717e-28,   9.38810440e-29,   1.40090414e-28,\n         6.15775392e-29,   9.10440439e-29,   9.57557322e-29,\n         1.77974416e-28,   2.70956002e-28,   9.97260970e-29,\n         1.23650865e-28,   1.00301276e-28,   2.14835945e-28,\n         9.12501440e-29,   2.05834967e-28,   1.56441548e-28,\n         6.16060031e-29,   1.00873698e-28,   2.07772404e-28,\n         5.70759879e-29,   8.59917035e-29,   2.20133022e-28,\n         7.07895442e-29,   1.32546520e-28,   1.17119844e-28])"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "## For the low dimensional case"
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "DR_low = WaveletFeatures.reconstruct_datamatrix_lossy(Z_low, vec_low, M_low)",
   "execution_count": 51,
   "outputs": []
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "Delta_low = DR_low - X",
   "execution_count": 53,
   "outputs": []
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "var_low = np.sum(Delta_low**2, axis=1)",
   "execution_count": 56,
   "outputs": []
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "var_low",
   "execution_count": 57,
   "outputs": [
    {
     "output_type": "execute_result",
     "execution_count": 57,
     "data": {
      "text/plain": "array([  1.02018676e-29,   1.83388553e-27,   2.55519260e-28,\n         1.35160223e-28,   2.01543176e-28,   2.71240872e-28,\n         5.92662570e-29,   5.88263555e-29,   6.85497302e-28,\n         4.21438924e-28,   6.23455879e-28,   9.86053983e-29,\n         2.38527063e-29,   3.50035428e-29,   4.21905769e-28,\n         9.89781621e-29,   6.08200973e-29,   1.01965412e-29,\n         8.84407932e-29,   4.86016125e-29,   4.83783611e-29,\n         1.51602329e-29,   7.25162698e-29,   5.87110595e-29,\n         1.07950959e-28,   5.35734488e-29,   9.69681954e-30,\n         6.35289177e-29,   5.06130730e-28,   2.22799280e-29,\n         1.35943858e-29,   3.92752245e-29,   9.79483437e-30,\n         1.06864870e-29,   1.64575384e-28,   6.16092189e-29,\n         6.22672410e-30,   6.87409205e-29,   4.92372085e-29,\n         3.49570024e-29,   9.08208733e-31,   2.04598471e-28,\n         2.44543799e-28,   6.20858184e-29,   6.27608569e-29,\n         3.49886659e-29,   3.73008274e-29,   2.19991893e-29,\n         6.31703698e-29,   1.04437465e-28,   4.08710892e-29,\n         5.17688404e-29,   4.16320091e-29,   6.42548158e-29,\n         6.90327696e-30,   5.82264625e-29,   1.76611026e-29,\n         8.84641253e-29,   9.87285616e-29,   2.38954943e-29,\n         6.60917527e-29,   4.91313034e-29,   8.68247738e-29,\n         4.08338842e-29,   5.50985446e-29,   9.61540446e-29,\n         1.60263251e-30,   4.07055766e-29,   4.23396439e-29,\n         7.80952029e-30,   3.15867491e-29,   8.55860156e-29,\n         1.58418481e-29,   5.29962586e-29,   5.41766019e-29])"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "np.allclose(var, 0.)",
   "execution_count": 58,
   "outputs": [
    {
     "output_type": "execute_result",
     "execution_count": 58,
     "data": {
      "text/plain": "True"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "np.allclose(vals_low, 0.)",
   "execution_count": 59,
   "outputs": [
    {
     "output_type": "execute_result",
     "execution_count": 59,
     "data": {
      "text/plain": "False"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "max(var)",
   "execution_count": 61,
   "outputs": [
    {
     "output_type": "execute_result",
     "execution_count": 61,
     "data": {
      "text/plain": "1.8338855273361544e-27"
     },
     "metadata": {}
    }
   ]
  },
  {
   "metadata": {
    "trusted": true
   },
   "cell_type": "code",
   "source": "max(var_low)",
   "execution_count": 62,
   "outputs": [
    {
     "output_type": "execute_result",
     "execution_count": 62,
     "data": {
      "text/plain": "1.8338855273361544e-27"
     },
     "metadata": {}
    }
   ]
  }
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