Testing methods to set the diagonal of a scipy sparse matrix to zero.

set_diag_zero

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     "source": [
      "Set the Diagonal of a Sparse Matrix to Zero"
     ]
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    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy\n",
      "import scipy.sparse as sp"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "one_dim = int(1E03)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Construct a fairly sparse matrix."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mat = sp.csr_matrix((scipy.random.random_sample((one_dim, one_dim)) > 0.8).astype(float))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
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    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mat.nnz / float(one_dim * one_dim)"
     ],
     "language": "python",
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        "0.199934"
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     "cell_type": "code",
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     "input": [
      "(mat.diagonal() > 0.0).sum()"
     ],
     "language": "python",
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     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "First naive attempt, `setdiag` will also set elements that were not previously present."
     ]
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     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%timeit\n",
      "cpy = mat.copy()\n",
      "cpy.setdiag(scipy.zeros(one_dim))\n",
      "assert (cpy.diagonal() > 0.0).sum() == 0"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
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       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1 loops, best of 3: 816 ms per loop\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/home/moritz/.virtualenvs/test-diag/lib/python2.7/site-packages/scipy/sparse/compressed.py:728: SparseEfficiencyWarning: Changing the sparsity structure of a csr_matrix is expensive. lil_matrix is more efficient.\n",
        "  SparseEfficiencyWarning)\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "At least convert to a sparse format where modification isn't as expensive."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%timeit\n",
      "lil = mat.tolil()\n",
      "lil.setdiag(scipy.zeros(one_dim))\n",
      "cpy = lil.tocsr()\n",
      "assert (cpy.diagonal() > 0.0).sum() == 0"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "10 loops, best of 3: 111 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Implement a function that sets only diagonal elements that are actually present."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def csr_setdiag_val(csr, value=0):\n",
      "    \"\"\"Set all diagonal nonzero elements\n",
      "    (elements currently in the sparsity pattern)\n",
      "    to the given value. Useful to set to 0 mostly.\n",
      "    \"\"\"\n",
      "    if csr.format != \"csr\":\n",
      "        raise ValueError('Matrix given must be of CSR format.')\n",
      "    csr.sort_indices()\n",
      "    pointer = csr.indptr\n",
      "    indices = csr.indices\n",
      "    data = csr.data\n",
      "    for i in range(min(csr.shape)):\n",
      "        ind = indices[pointer[i]: pointer[i + 1]]\n",
      "        j =  ind.searchsorted(i)\n",
      "        # matrix has only elements up until diagonal (in row i)\n",
      "        if j == len(ind):\n",
      "            continue\n",
      "        j += pointer[i]\n",
      "        # in case matrix has only elements after diagonal (in row i)\n",
      "        if indices[j] == i:\n",
      "            data[j] = value"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
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     "cell_type": "code",
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     "input": [
      "%%timeit\n",
      "cpy = mat.copy()\n",
      "csr_setdiag_val(cpy)\n",
      "assert (cpy.diagonal() > 0.0).sum() == 0"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
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       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "100 loops, best of 3: 9.87 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Create a sparse matrix from the diagonal and subtract it from the original."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%timeit\n",
      "cpy = mat.copy() - sp.dia_matrix((mat.diagonal()[scipy.newaxis, :], [0]), shape=(one_dim, one_dim))\n",
      "assert (cpy.diagonal() > 0.0).sum() == 0"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1000 loops, best of 3: 1.99 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 10
    }
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