{"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":"64ea4f53-7131-5638-9609-4486c88c3081","task_key":"dev--9030474a-b5b5-5851-8469-165589d3b509--29~2e3","task_revision_id":"3","upstream_id":"29.3","short_description":"With the previous functions, provide a function that performs Gram-Schmidt…","config":"","split":"dev","body":"{\"step_background\":\"Background\\nThe Gram-Schmidt orthogonalization is defined as\\n\\n$$\\n\\\\begin{aligned}\\n& \\\\varepsilon_1=\\\\alpha_1, \\\\\\\\\\n& \\\\varepsilon_2=\\\\alpha_2-\\\\frac{\\\\left(\\\\alpha_2, \\\\varepsilon_1\\\\right)}{\\\\left(\\\\varepsilon_1, \\\\varepsilon_1\\\\right)} \\\\varepsilon_1, \\\\\\\\\\n& \\\\varepsilon_3=\\\\alpha_3-\\\\frac{\\\\left(\\\\alpha_3, \\\\varepsilon_1\\\\right)}{\\\\left(\\\\varepsilon_1, \\\\varepsilon_1\\\\right)} \\\\varepsilon_1-\\\\frac{\\\\left(\\\\alpha_3, \\\\varepsilon_2\\\\right)}{\\\\left(\\\\varepsilon_2, \\\\varepsilon_2\\\\right)} \\\\varepsilon_2, \\\\\\\\\\n& \\\\ldots \\\\ldots \\\\ldots \\\\ldots \\\\\\\\\\n& \\\\varepsilon_{\\\\mathrm{i}+1}=\\\\alpha_{\\\\mathrm{i}+1}-\\\\sum_{\\\\mathrm{k}=1}^{\\\\mathrm{i}} \\\\frac{\\\\left(\\\\alpha_{\\\\mathrm{i}+1}, \\\\varepsilon_{\\\\mathrm{k}}\\\\right)}{\\\\left(\\\\varepsilon_{\\\\mathrm{k}}, \\\\varepsilon_{\\\\mathrm{k}}\\\\right)} \\\\varepsilon_{\\\\mathrm{k}} \\\\\\\\\\n& \\\\ldots \\\\ldots \\\\ldots \\\\ldots \\\\ldots \\\\\\\\\\n& \\\\varepsilon_{\\\\mathrm{n}}=\\\\alpha_{\\\\mathrm{n}}-\\\\sum_{\\\\mathrm{k}=1}^{n-1} \\\\frac{\\\\left(\\\\alpha_{\\\\mathrm{n}}, \\\\varepsilon_{\\\\mathrm{k}}\\\\right)}{\\\\left(\\\\varepsilon_{\\\\mathrm{k}}, \\\\varepsilon_{\\\\mathrm{k}}\\\\right)} \\\\varepsilon_{\\\\mathrm{k}}\\n\\\\end{aligned}\\n$$\\n\\nand this function wants to not only do the orthogonalization but also the normalization for all the vectors.\",\"step_description_prompt\":\"With the previous functions, provide a function that performs Gram-Schmidt orthogonalization on N linearly independent vectors in N-dimension space. The input is an $N\\\\times N$ numpy array, containing N vectors in the shape of $N\\\\times1$. The output should also be an $N\\\\times N$ numpy array, containing the orthogonal and normalized vectors.\"}","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":[]}