2.json

{
  "id": "2",
  "title": "Transpose of a Matrix",
  "difficulty": "easy",
  "category": "Linear Algebra",
  "video": "https://youtu.be/fj0ZJ2gTSmI?si=vG8VSqASjyG0eNLY",
  "likes": "0",
  "dislikes": "0",
  "contributor": [
    {
      "profile_link": "https://github.com/moe18",
      "name": "Moe Chabot"
    }
  ],
  "tinygrad_difficulty": "easy",
  "pytorch_difficulty": "easy",
  "description": "Write a Python function that computes the transpose of a given matrix.",
  "learn_section": "\n## Transpose of a Matrix\n\nLet's consider a matrix $M$ and its transpose $M^T$:\n\n**Original Matrix $M$:**\n$$\nM = \\begin{pmatrix} \na & b & c \\\\ \nd & e & f \n\\end{pmatrix}\n$$\n\n**Transposed Matrix $M^T$:**\n$$\nM^T = \\begin{pmatrix} \na & d \\\\ \nb & e \\\\ \nc & f \n\\end{pmatrix}\n$$\n\n### Explanation:\nTransposing a matrix involves converting its rows into columns and vice versa. This operation is fundamental in linear algebra for various computations and transformations.",
  "starter_code": "def transpose_matrix(a: list[list[int|float]]) -> list[list[int|float]]:\n\treturn b",
  "solution": "def transpose_matrix(a: list[list[int|float]]) -> list[list[int|float]]:\n    return [list(i) for i in zip(*a)]",
  "example": {
    "input": "a = [[1,2,3],[4,5,6]]",
    "output": "[[1,4],[2,5],[3,6]]",
    "reasoning": "The transpose of a matrix is obtained by flipping rows and columns."
  },
  "test_cases": [
    {
      "test": "print(transpose_matrix([[1,2],[3,4],[5,6]]))",
      "expected_output": "[[1, 3, 5], [2, 4, 6]]"
    },
    {
      "test": "print(transpose_matrix([[1,2,3],[4,5,6]]))",
      "expected_output": "[[1, 4], [2, 5], [3, 6]]"
    }
  ],
  "tinygrad_starter_code": "from tinygrad.tensor import Tensor\n\ndef transpose_matrix_tg(a:Tensor) -> Tensor:\n    \"\"\"\n    Transpose a 2D matrix `a` using tinygrad.\n    Inputs are tinygrad Tensors.\n    Returns a transposed Tensor.\n    \"\"\"\n    pass",
  "tinygrad_solution": "from tinygrad.tensor import Tensor\n\ndef transpose_matrix_tg(a) -> Tensor:\n    \"\"\"\n    Transpose a 2D matrix `a` using tinygrad.\n    Inputs are tinygrad Tensors.\n    Returns a transposed Tensor.\n    \"\"\"\n    return a.T",
  "tinygrad_test_cases": [
    {
      "test": "from tinygrad.tensor import Tensor\nres = transpose_matrix_tg(Tensor([[1,2,3],[4,5,6]]))\nprint(res.numpy().tolist())",
      "expected_output": "[[1, 4], [2, 5], [3, 6]]"
    },
    {
      "test": "from tinygrad.tensor import Tensor\nres = transpose_matrix_tg(Tensor([[1,2],[3,4]]))\nprint(res.numpy().tolist())",
      "expected_output": "[[1, 3], [2, 4]]"
    }
  ],
  "pytorch_starter_code": "import torch\n\ndef transpose_matrix(a) -> torch.Tensor:\n    \"\"\"\n    Transpose a 2D matrix `a` using PyTorch.\n    Inputs can be Python lists, NumPy arrays, or torch Tensors.\n    Returns a transposed tensor.\n    \"\"\"\n    a_t = torch.as_tensor(a)\n    # Your implementation here\n    pass",
  "pytorch_solution": "import torch\n\ndef transpose_matrix(a) -> torch.Tensor:\n    \"\"\"\n    Transpose a 2D matrix `a` using PyTorch.\n    Inputs can be Python lists, NumPy arrays, or torch Tensors.\n    Returns a transposed tensor.\n    \"\"\"\n    a_t = torch.as_tensor(a)\n    return a_t.T",
  "pytorch_test_cases": [
    {
      "test": "import torch\nres = transpose_matrix(torch.tensor([[1,2,3],[4,5,6]]))\nprint(res.numpy().tolist())",
      "expected_output": "[[1, 4], [2, 5], [3, 6]]"
    },
    {
      "test": "import torch\nres = transpose_matrix(torch.tensor([[1,2],[3,4]]))\nprint(res.numpy().tolist())",
      "expected_output": "[[1, 3], [2, 4]]"
    }
  ]
}