{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"scicode","formal_name":"SciCode","introduction":"SciCode evaluates the ability to solve scientific research problems through code. Problems are decomposed into subproblems; this dev import preserves the relationships between 15 parent problems and 50 subproblems.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/SciCode1/SciCode","indexing_mode":"noindex","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"6025f40a-ed3d-5bdf-9873-5787989e7daa","task_key":"dev--831ff049-2748-5e6d-ba9b-f8252555cd23--78~2e2","task_revision_id":"3","upstream_id":"78.2","short_description":"Write a fourth-order fixed-time-step Runge-Kutta (RK4) integrator from scratch…","config":"","split":"dev","body":"{\"step_background\":\"Background\\n\\nGiven an initial value problem of the form:\\n\\n$$\\n\\\\frac{dy}{dt} = f(t, y), \\\\quad y(t_0) = y_0\\n$$\\n\\nthe RK4 method updates the solution $y$ from time $t$ to $t + \\\\Delta t$ using the following steps:\\n\\n**2.1 Calculate intermediate slopes:**\\n   - $k_1 = f(t, y)$\\n   - $k_2 = f(t + \\\\frac{\\\\Delta t}{2}, y + \\\\frac{k_1 \\\\Delta t}{2})$\\n   - $k_3 = f(t + \\\\frac{\\\\Delta t}{2}, y + \\\\frac{k_2 \\\\Delta t}{2})$\\n   - $k_4 = f(t + \\\\Delta t, y + k_3 \\\\Delta t)$\\n\\n**2.2 Update the solution:**\\n\\n   $$\\n   y(t + \\\\Delta t) = y(t) + \\\\frac{\\\\Delta t}{6} (k_1 + 2k_2 + 2k_3 + k_4)\\n   $$\\n\\nIn our case, *$y$* represents the state vector of the system, which includes the angle *$\\\\theta$* and the angular velocity *$\\\\omega$*.\",\"step_description_prompt\":\"Write a fourth-order fixed-time-step Runge-Kutta (RK4) integrator from scratch in Python, to calculate $\\\\theta$ and $\\\\omega$ at any certain timepoint. The output of this procedure — a series of state vectors representing the n-point state-space trajectory emanating from ~x(t0). Do not use any canned numerical integration routines, commands, functions.\"}","display_format":"scicode-step","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/SciCode1/SciCode","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}