mass_matrix_init.ipynb

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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
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    "n_dim = 100\n",
    "n_draws = 500\n",
    "\n",
    "# If mu is very far away from the initial point\n",
    "# using the identity might be better...\n",
    "# mu = np.random.randn(n_draws, n_dim) * 100\n",
    "\n",
    "mu = np.random.randn(n_draws, n_dim)\n",
    "sd = np.exp(np.random.randn(n_draws, n_dim))\n",
    "\n",
    "init_points = np.random.randn(n_draws, n_dim)"
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    "grads = -(init_points - mu) / sd**2"
   ]
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   "source": [
    "def dist(estimate, true):\n",
    "    \"\"\"Log condition number of diagonal matrix.\"\"\"\n",
    "    eigs = true / estimate\n",
    "    return np.linalg.norm(np.log(eigs), axis=-1)"
   ]
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    "# Using initial identity\n",
    "dists_identity = dist(sd*sd, np.ones(n_dim))\n",
    "dists_grad_sq = dist(sd*sd, 1 / (grads * grads))\n",
    "dists_grad = dist(sd*sd, 1 / np.abs(grads))"
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    "sns.kdeplot(dists_identity, label=\"identity\")\n",
    "sns.kdeplot(dists_grad, label=\"grad\")\n",
    "sns.kdeplot(dists_grad_sq, label=\"grad_sq\")\n",
    "plt.legend();"
   ]
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