Comparison of numpy division by zero handling approaches

numpy_divide_demo_executed.ipynb

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   "source": [
    "# Comparing Division by Zero Handling Approaches\n",
    "\n",
    "This notebook demonstrates three approaches to handling division by zero in numpy arrays:\n",
    "1. The `where` approach (causes warnings)\n",
    "2. The mask approach (current PolicyEngine standard)\n",
    "3. The `np.divide` approach (potential alternative)"
   ]
  },
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Income: [ 50000  75000      0 100000      0  25000]\n",
      "Tax: [ 5000 10000     0 15000   100  2000]\n",
      "\n",
      "Expected effective tax rates:\n",
      "[0.1, 0.133, 0.0, 0.15, 0.0, 0.08]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import warnings\n",
    "\n",
    "# Create test data with zeros that would cause division by zero\n",
    "income = np.array([50000, 75000, 0, 100000, 0, 25000])\n",
    "tax = np.array([5000, 10000, 0, 15000, 100, 2000])\n",
    "\n",
    "print(\"Income:\", income)\n",
    "print(\"Tax:\", tax)\n",
    "print(\"\\nExpected effective tax rates:\")\n",
    "print(\"[0.1, 0.133, 0.0, 0.15, 0.0, 0.08]\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. The `where` Approach (Causes Warnings)"
   ]
  },
  {
   "cell_type": "code",
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "⚠️ Warning raised: divide by zero encountered in divide\n",
      "\n",
      "Result: [0.1        0.13333333 0.         0.15       0.         0.08      ]\n",
      "Correct values: True\n"
     ]
    }
   ],
   "source": [
    "# This approach evaluates the division for ALL values before selecting\n",
    "with warnings.catch_warnings(record=True) as w:\n",
    "    warnings.simplefilter(\"always\")\n",
    "    \n",
    "    effective_rate_where = np.where(income > 0, tax / income, 0)\n",
    "    \n",
    "    if w:\n",
    "        print(f\"⚠️ Warning raised: {w[0].message}\")\n",
    "    else:\n",
    "        print(\"✓ No warnings\")\n",
    "        \n",
    "print(\"\\nResult:\", effective_rate_where)\n",
    "print(\"Correct values:\", np.allclose(effective_rate_where, [0.1, 0.133333, 0, 0.15, 0, 0.08], atol=1e-6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. The Mask Approach (Current PolicyEngine Standard)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "✓ No warnings\n",
      "\n",
      "Result: [0.1        0.13333333 0.         0.15       0.         0.08      ]\n",
      "Correct values: True\n"
     ]
    }
   ],
   "source": [
    "# This approach only divides where the mask is True\n",
    "with warnings.catch_warnings(record=True) as w:\n",
    "    warnings.simplefilter(\"always\")\n",
    "    \n",
    "    effective_rate_mask = np.zeros_like(income, dtype=float)\n",
    "    mask = income != 0\n",
    "    effective_rate_mask[mask] = tax[mask] / income[mask]\n",
    "    \n",
    "    if w:\n",
    "        print(f\"⚠️ Warning raised: {w[0].message}\")\n",
    "    else:\n",
    "        print(\"✓ No warnings\")\n",
    "        \n",
    "print(\"\\nResult:\", effective_rate_mask)\n",
    "print(\"Correct values:\", np.allclose(effective_rate_mask, [0.1, 0.133333, 0, 0.15, 0, 0.08], atol=1e-6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. The `np.divide` Approach (Potential Alternative)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "✓ No warnings\n",
      "\n",
      "Result: [0.1        0.13333333 0.         0.15       0.         0.08      ]\n",
      "Correct values: True\n"
     ]
    }
   ],
   "source": [
    "# This approach uses np.divide with out and where parameters\n",
    "with warnings.catch_warnings(record=True) as w:\n",
    "    warnings.simplefilter(\"always\")\n",
    "    \n",
    "    effective_rate_divide = np.divide(\n",
    "        tax, \n",
    "        income,\n",
    "        out=np.zeros_like(income, dtype=float),\n",
    "        where=income != 0\n",
    "    )\n",
    "    \n",
    "    if w:\n",
    "        print(f\"⚠️ Warning raised: {w[0].message}\")\n",
    "    else:\n",
    "        print(\"✓ No warnings\")\n",
    "        \n",
    "print(\"\\nResult:\", effective_rate_divide)\n",
    "print(\"Correct values:\", np.allclose(effective_rate_divide, [0.1, 0.133333, 0, 0.15, 0, 0.08], atol=1e-6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Performance Comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
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    "execution": {
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing with 1,000,000 elements..."
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of zeros in income: 4\n"
     ]
    }
   ],
   "source": [
    "# Create larger arrays for performance testing\n",
    "np.random.seed(42)\n",
    "large_income = np.random.randint(0, 200000, size=1_000_000)\n",
    "large_tax = np.random.randint(0, 50000, size=1_000_000)\n",
    "\n",
    "print(f\"Testing with {len(large_income):,} elements...\")\n",
    "print(f\"Number of zeros in income: {(large_income == 0).sum():,}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mask approach: 10.50 ms\n",
      "np.divide approach: 1.90 ms\n",
      "\n",
      "np.divide reduces runtime by 82%\n"
     ]
    }
   ],
   "source": [
    "import timeit\n",
    "\n",
    "# Time the mask approach\n",
    "def mask_approach():\n",
    "    result = np.zeros_like(large_income, dtype=float)\n",
    "    mask = large_income != 0\n",
    "    result[mask] = large_tax[mask] / large_income[mask]\n",
    "    return result\n",
    "\n",
    "# Time the np.divide approach\n",
    "def divide_approach():\n",
    "    return np.divide(\n",
    "        large_tax, \n",
    "        large_income,\n",
    "        out=np.zeros_like(large_income, dtype=float),\n",
    "        where=large_income != 0\n",
    "    )\n",
    "\n",
    "# Run timing tests\n",
    "mask_time = timeit.timeit(mask_approach, number=100) / 100\n",
    "divide_time = timeit.timeit(divide_approach, number=100) / 100\n",
    "\n",
    "print(f\"Mask approach: {mask_time*1000:.2f} ms\")\n",
    "print(f\"np.divide approach: {divide_time*1000:.2f} ms\")\n",
    "\n",
    "runtime_reduction = (mask_time - divide_time) / mask_time * 100\n",
    "print(f\"\\nnp.divide reduces runtime by {runtime_reduction:.0f}%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "Both the mask approach and `np.divide` approach:\n",
    "- ✅ Avoid division by zero warnings\n",
    "- ✅ Produce correct results\n",
    "- ✅ Have similar performance\n",
    "\n",
    "The `np.divide` approach offers:\n",
    "- More concise, single-expression syntax\n",
    "- Built-in numpy function designed for this use case\n",
    "- Already used in some parts of PolicyEngine codebase\n",
    "\n",
    "The mask approach:\n",
    "- Is the current PolicyEngine standard\n",
    "- Is more explicit about what's happening\n",
    "- Has been thoroughly tested in the codebase"
   ]
  }
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