{"task": {"agent_timeout": 1800, "task": "scicode-4", "verifier_timeout": 1800, "instruction": "# SciCode Problem 4\n\nCreate a function to compute the incomplete Cholesky factorization of an input matrix.\n\n\"\"\"\nInputs:\nA : Matrix, 2d array M * M\n\nOutputs:\nA : Matrix, 2d array M * M\n\"\"\"\n\n## Required Dependencies\n\n```python\nimport numpy as np\n```\n\nYou must implement 1 functions sequentially. Each step builds on previous steps. Write ALL functions in a single file `/app/solution.py`.\n\n## Step 1 (Step ID: 4.1)\n\nCreate a function to compute the incomplete Cholesky factorization of an input matrix.\n\n### Function to Implement\n\n```python\ndef ichol(A):\n    '''Inputs:\n    A : Matrix, 2d array M * M\n    Outputs:\n    A : Matrix, 2d array M * M\n    '''\n\nreturn A\n```\n\n---\n\n## Instructions\n\n1. Create `/app/solution.py` containing ALL functions above.\n2. Include the required dependencies at the top of your file.\n3. Each function must match the provided header exactly (same name, same parameters).\n4. Later steps may call functions from earlier steps \u2014 ensure they are all in the same file.\n5. Do NOT include test code, example usage, or __main__ blocks.\n", "memory": "", "runnable": false, "difficulty": "hard", "language": "", "cpus": "", "instruction_truncated": false, "category": "scientific_computing", "compose": true, "has_solution": true, "oracle": null, "docker_image": "", "taskset": "scicode", "tags": ["scicode", "scientific-computing", "python"]}, "runs": []}