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    "## Numpy Example\n",
    "\n",
    "In this example, we will use numpy to perform matrix rotation using simulated annealing. We will define a fitness function that evaluates the rotation of a candidate matrix, and use simulated annealing to find the optimal rotation matrix.\n"
   ]
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   "source": [
    "from pathlib import Path\n",
    "from numpy import array, zeros, matvec, ndarray, flip\n",
    "from numpy.random import default_rng\n",
    "from numpy.linalg import norm\n",
    "from altbacken.external.neighbourhood.numeric import ArrayNeighbourhood\n",
    "from altbacken.external.annealing import SimpleSimulatedAnnealing\n",
    "from altbacken.internal.analysis.convergence import ConvergenceAnalyzer\n",
    "from altbacken.internal.analysis.acceptance import AcceptanceAnalyzer\n",
    "from altbacken.internal.report.file import JSONLineReport"
   ],
   "outputs": [],
   "execution_count": 1
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   "source": [
    "### Fitness function\n",
    "\n",
    "We will use a simple fitness function to evaluate the rotation of a candidate matrix.\n",
    "The fitness function is the sum of the absolute difference between the rotated candidate and the optimal solution. For testings, we will use 100 random vectors.\n"
   ]
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   "source": [
    "rng = default_rng(None)\n",
    "\n",
    "CANDIDATES: list[ndarray] = [\n",
    "    (v := rng.normal(size=2)) / norm(v)\n",
    "    for _ in range(100)\n",
    "]"
   ],
   "outputs": [],
   "execution_count": 2
  },
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     "start_time": "2025-12-20T19:34:55.291029Z"
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   "source": [
    "def apply_matrix(matrix: ndarray) -> float:\n",
    "    return sum(norm(flip(candidate) - matvec(matrix, candidate))**2 for candidate in CANDIDATES)\n"
   ],
   "outputs": [],
   "execution_count": 3
  },
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   "source": [
    "### Annealing strategy\n",
    "\n",
    "We choose a simple simulated annealing strategy with a temperature of 10000.0 and a neighbourhood size of 0.1."
   ]
  },
  {
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   "source": [
    "annealing: SimpleSimulatedAnnealing = SimpleSimulatedAnnealing(\n",
    "    apply_matrix,\n",
    "    ArrayNeighbourhood(0.1),\n",
    "    10000.0\n",
    ")\n",
    "\n",
    "annealing.tracer = JSONLineReport(\n",
    "    Path(\"rotation_log.json_line\"),\n",
    "    [ConvergenceAnalyzer(), AcceptanceAnalyzer(annealing.energy)],\n",
    ")"
   ],
   "outputs": [],
   "execution_count": 4
  },
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   "source": [
    "### Evaluation\n",
    "\n",
    "The best values are printed, together with the norm of the difference between the matrix obtained by annealing and the rotation matrix."
   ]
  },
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   "source": [
    "best_match, best_value = annealing.simulate(zeros((2,2)))\n",
    "annealing.tracer.close()"
   ],
   "outputs": [],
   "execution_count": 5
  },
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   },
   "source": [
    "print(\"Best match\", best_match)\n",
    "print(\"Best value\", best_value)\n",
    "print(\"Distance from optimum\", norm(best_match - array([[0,1], [1, 0]])))"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best match [[0.01098449 0.98603174]\n",
      " [0.99981828 0.00534302]]\n",
      "Best value 0.016596983069443485\n",
      "Distance from optimum 0.01855673291866348\n"
     ]
    }
   ],
   "execution_count": 6
  }
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