Python Cholesky Decomposition.ipynb

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    "import numpy as np"
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a positive definite matrix"
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       "(100, 100)"
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   "source": [
    "A = np.random.randn(100,120)\n",
    "A = A.dot(A.T)\n",
    "A.shape"
   ]
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   "metadata": {},
   "source": [
    "Implementation of cholesky algorithm from:\n",
    "\n",
    "https://en.wikipedia.org/wiki/Cholesky_decomposition#The_Cholesky.E2.80.93Banachiewicz_and_Cholesky.E2.80.93Crout_algorithms"
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   "source": [
    "def cholesky_d(A):\n",
    "    L = np.zeros_like(A)\n",
    "    n = len(L)\n",
    "    for i in range(n):\n",
    "        for j in range(i+1):\n",
    "            if i==j:\n",
    "                val = A[i,i] - np.sum(np.square(L[i,:i]))\n",
    "                # if diagonal values are negative return zero - not throw exception\n",
    "                if val<0:\n",
    "                    return 0.0\n",
    "                L[i,i] = np.sqrt(val)\n",
    "            else:\n",
    "                L[i,j] = (A[i,j] - np.sum(L[i,:j]*L[j,:j]))/L[j,j]\n",
    "                \n",
    "    return L"
   ]
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      "CPU times: user 2 µs, sys: 1 µs, total: 3 µs\n",
      "Wall time: 5.01 µs\n"
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    "%time\n",
    "L1 = cholesky_d(A)"
   ]
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      "CPU times: user 2 µs, sys: 1e+03 ns, total: 3 µs\n",
      "Wall time: 6.2 µs\n"
     ]
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   "source": [
    "%time\n",
    "L2 = np.linalg.cholesky(A)"
   ]
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   "cell_type": "markdown",
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   "source": [
    "Are the values similar?"
   ]
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   "execution_count": 10,
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     "data": {
      "text/plain": [
       "True"
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     "execution_count": 10,
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   "source": [
    "np.allclose(L1,L2)"
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   "execution_count": null,
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