{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "6aa2f949",
   "metadata": {},
   "source": [
    "# Choosing a Backend\n",
    "\n",
    "LightGP picks the fastest available backend automatically with `Backend.Auto`.\n",
    "This tutorial shows the available choices, what `Auto` does, and how to force\n",
    "a specific backend when benchmarking or debugging."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2c0d1275",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-15T06:51:25.680120Z",
     "iopub.status.busy": "2026-05-15T06:51:25.679898Z",
     "iopub.status.idle": "2026-05-15T06:51:25.892129Z",
     "shell.execute_reply": "2026-05-15T06:51:25.891752Z"
    }
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import sys\n",
    "\n",
    "# Make the locally-built lightgp importable. Real users install via 'pip install lightgp'.\n",
    "sys.path.insert(0, os.path.abspath(os.path.join(\"..\", \"..\", \"..\", \"python\")))\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import lightgp as gp\n",
    "\n",
    "rng = np.random.default_rng(0)\n",
    "plt.rcParams.update({\"figure.figsize\": (8, 3.5), \"figure.dpi\": 90})"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a182b37c",
   "metadata": {},
   "source": [
    "## Available backends\n",
    "\n",
    "| Backend | Library | Available on |\n",
    "|---------|---------|--------------|\n",
    "| `Backend.CPU` | reference C++ + Accelerate (macOS) / OpenBLAS (Linux) | always |\n",
    "| `Backend.Metal` | Apple Metal Shading Language compute shaders | macOS builds |\n",
    "| `Backend.CUDA` | cuBLAS + cuSOLVER + cuFFT + custom kernels | CUDA-enabled builds |\n",
    "| `Backend.Auto` | resolves at fit time based on problem shape | always |"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89bd4473",
   "metadata": {},
   "source": [
    "## Forcing a specific backend"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "687d4af3",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-15T06:51:25.893569Z",
     "iopub.status.busy": "2026-05-15T06:51:25.893472Z",
     "iopub.status.idle": "2026-05-15T06:51:26.040372Z",
     "shell.execute_reply": "2026-05-15T06:51:26.039986Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU     fit ok\n",
      "Metal   fit ok\n",
      "Auto    fit ok\n"
     ]
    }
   ],
   "source": [
    "N, D = 1500, 4\n",
    "X = rng.standard_normal((N, D)).astype(np.float32)\n",
    "y = (np.sin(X[:, 0]) + 0.1 * rng.standard_normal(N)).astype(np.float32)\n",
    "\n",
    "for name, backend in [\n",
    "    (\"CPU\",   gp.Backend.CPU),\n",
    "    (\"Metal\", gp.Backend.Metal),\n",
    "    (\"Auto\",  gp.Backend.Auto),\n",
    "]:\n",
    "    try:\n",
    "        m = gp.GPExact(gp.RBF(), backend=backend, noise_var=0.05)\n",
    "        m.fit(X, y)\n",
    "        print(f\"{name:<6}  fit ok\")\n",
    "    except Exception as e:\n",
    "        print(f\"{name:<6}  not available: {e}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85ce7509",
   "metadata": {},
   "source": [
    "## Quick wall-time comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "27228492",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-15T06:51:26.041499Z",
     "iopub.status.busy": "2026-05-15T06:51:26.041423Z",
     "iopub.status.idle": "2026-05-15T06:51:26.216006Z",
     "shell.execute_reply": "2026-05-15T06:51:26.215707Z"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 540x306 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import time\n",
    "results = {}\n",
    "for name, backend in [\n",
    "    (\"CPU\",   gp.Backend.CPU),\n",
    "    (\"Metal\", gp.Backend.Metal),\n",
    "    (\"Auto\",  gp.Backend.Auto),\n",
    "]:\n",
    "    try:\n",
    "        m = gp.GPExact(gp.RBF(), backend=backend, noise_var=0.05)\n",
    "        m.fit(X, y); m.predict(X[:16])   # warmup\n",
    "        t0 = time.perf_counter()\n",
    "        m.fit(X, y); m.predict(X[:16])\n",
    "        results[name] = (time.perf_counter() - t0) * 1000.0\n",
    "    except Exception:\n",
    "        pass\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(6, 3.4))\n",
    "names = list(results.keys()); vals = list(results.values())\n",
    "ax.bar(names, vals, color=[\"#2563EB\", \"#10B981\", \"#F59E0B\"][: len(names)])\n",
    "for n, v in zip(names, vals):\n",
    "    ax.text(n, v, f\"{v:.1f}\", ha=\"center\", va=\"bottom\", fontsize=9)\n",
    "ax.set_ylabel(\"fit + predict (ms)\")\n",
    "ax.set_title(f\"GPExact at N={N}, D={D}\")\n",
    "plt.tight_layout(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "464c1f26",
   "metadata": {},
   "source": [
    "## How `Backend.Auto` chooses\n",
    "\n",
    "The dispatch heuristic, derived empirically and baked into\n",
    "`resolve_auto_backend`:\n",
    "\n",
    "```text\n",
    "Solver.SKI                           → CPU (vDSP, on macOS)\n",
    "Solver.CG, N > 2000                  → Metal (matrix-free matvec)\n",
    "D ≥ 16 and N ≥ 2000                  → Metal (kernel construction)\n",
    "otherwise                            → CPU (AMX Cholesky wins)\n",
    "```\n",
    "\n",
    "A surprising finding: for moderate-N **dense Cholesky** on Apple Silicon, the\n",
    "CPU (with its AMX matrix coprocessor) **beats** the integrated Metal GPU.\n",
    "`Auto` reflects that.\n",
    "\n",
    "## Cross-platform code\n",
    "\n",
    "The same Python script runs unchanged on macOS and Linux. With `Backend.Auto`,\n",
    "LightGP picks the Metal / CUDA / OpenBLAS path that fits the host."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "lightgp-docs",
   "language": "python",
   "name": "lightgp-docs"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}