



def 		lowerCAmelCase__     (       UpperCamelCase_					:							list[list]						)->	list[list]:
    A__					=       current_set.copy()
    for row_index, row in enumerate(UpperCamelCase_						):
        A__					=       row[0]
        for column_index, column in enumerate(UpperCamelCase_						):
            if magnitude == 0:
                A__					=       column
                continue
            A__					=       column / magnitude
    # Subtract to cancel term
    A__					=       current_set[0]
    A__					=       [first_row]
    A__					=       current_set[1::]
    for row in current_set:
        A__					=       []
        # If first term is 0, it is already in form we want, so we preserve it
        if row[0] == 0:
            final_set.append(UpperCamelCase_						)
            continue
        for column_index in range(len(UpperCamelCase_						)						):
            temp_row.append(first_row[column_index] - row[column_index]						)
        final_set.append(UpperCamelCase_						)
    # Create next recursion iteration set
    if len(final_set[0]						) != 3:
        A__					=       final_set[0]
        A__					=       []
        A__					=       []
        for row in final_set[1::]:
            current_first_column.append(row[0]						)
            next_iteration.append(row[1::]						)
        A__					=       simplify(UpperCamelCase_						)
        for i in range(len(UpperCamelCase_						)						):
            resultant[i].insert(0			,							current_first_column[i]						)
        resultant.insert(0			,							UpperCamelCase_						)
        A__					=       resultant
    return final_set



def 		lowerCAmelCase__     (       UpperCamelCase_					:							list[list]						)->	list:
    if len(UpperCamelCase_						) == 0:
        raise IndexError('''solve_simultaneous() requires n lists of length n+1'''						)
    A__					=       len(UpperCamelCase_						) + 1
    if any(len(UpperCamelCase_						) != _length for item in equations						):
        raise IndexError('''solve_simultaneous() requires n lists of length n+1'''						)
    for row in equations:
        if any(not isinstance(UpperCamelCase_			,							(int, float)						) for column in row						):
            raise ValueError('''solve_simultaneous() requires lists of integers'''						)
    if len(UpperCamelCase_						) == 1:
        return [equations[0][-1] / equations[0][0]]
    A__					=       equations.copy()
    if any(0 in row for row in data_set						):
        A__					=       data_set.copy()
        A__					=       []
        for row_index, row in enumerate(UpperCamelCase_						):
            if 0 not in row:
                A__					=       data_set.pop(UpperCamelCase_						)
                break
        if not full_row:
            raise ValueError('''solve_simultaneous() requires at least 1 full equation'''						)
        data_set.insert(0			,							UpperCamelCase_						)
    A__					=       data_set.copy()
    A__					=       simplify(UpperCamelCase_						)
    A__					=       simplified[::-1]
    A__					=       []
    for row in simplified:
        A__					=       row[-1]
        if not solutions:
            if row[-2] == 0:
                solutions.append(0						)
                continue
            solutions.append(current_solution / row[-2]						)
            continue
        A__					=       row.copy()[: len(UpperCamelCase_						) - 1 :]
        while temp_row[0] == 0:
            temp_row.pop(0						)
        if len(UpperCamelCase_						) == 0:
            solutions.append(0						)
            continue
        A__					=       temp_row[1::]
        A__					=       temp_row[::-1]
        for column_index, column in enumerate(UpperCamelCase_						):
            current_solution -= column * solutions[column_index]
        solutions.append(UpperCamelCase_						)
    A__					=       []
    for item in solutions:
        final.append(float(round(UpperCamelCase_			,							5						)						)						)
    return final[::-1]


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   _lowercase    	=		[
       [2, 1, 1, 1, 1, 4],
       [1, 2, 1, 1, 1, 5],
       [1, 1, 2, 1, 1, 6],
       [1, 1, 1, 2, 1, 7],
       [1, 1, 1, 1, 2, 8],
   ]
   print(solve_simultaneous(eq))
   print(solve_simultaneous([[4, 2]]))





import faiss  # noqa: F401 # Here to have a nice missing dependency error message early on
import numpy  # noqa: F401 # Here to have a nice missing dependency error message early on
import requests  # noqa: F401 # Here to have a nice missing dependency error message early on
import sklearn  # noqa: F401 # Here to have a nice missing dependency error message early on
import tqdm  # noqa: F401 # Here to have a nice missing dependency error message early on
from mauve import compute_mauve  # From: mauve-text

import datasets


_lowercase    	=		"\\n@inproceedings{pillutla-etal:mauve:neurips2021,\n  title={MAUVE: Measuring the Gap Between Neural Text and Human Text using Divergence Frontiers},\n  author={Pillutla, Krishna and Swayamdipta, Swabha and Zellers, Rowan and Thickstun, John and Welleck, Sean and Choi, Yejin and Harchaoui, Zaid},\n  booktitle = {NeurIPS},\n  year      = {2021}\n}\n\n"

_lowercase    	=		"\\nMAUVE is a library built on PyTorch and HuggingFace Transformers to measure the gap between neural text and human text with the eponymous MAUVE measure.\n\nMAUVE summarizes both Type I and Type II errors measured softly using Kullback–Leibler (KL) divergences.\n\nFor details, see the MAUVE paper: https://arxiv.org/abs/2102.01454 (Neurips, 2021).\n\nThis metrics is a wrapper around the official implementation of MAUVE:\nhttps://github.com/krishnap25/mauve\n"

_lowercase    	=		"\nCalculates MAUVE scores between two lists of generated text and reference text.\nArgs:\n    predictions: list of generated text to score. Each predictions\n        should be a string with tokens separated by spaces.\n    references: list of reference for each prediction. Each\n        reference should be a string with tokens separated by spaces.\nOptional Args:\n    num_buckets: the size of the histogram to quantize P and Q. Options: 'auto' (default) or an integer\n    pca_max_data: the number data points to use for PCA dimensionality reduction prior to clustering. If -1, use all the data. Default -1\n    kmeans_explained_var: amount of variance of the data to keep in dimensionality reduction by PCA. Default 0.9\n    kmeans_num_redo: number of times to redo k-means clustering (the best objective is kept). Default 5\n    kmeans_max_iter: maximum number of k-means iterations. Default 500\n    featurize_model_name: name of the model from which features are obtained. Default 'gpt2-large' Use one of ['gpt2', 'gpt2-medium', 'gpt2-large', 'gpt2-xl'].\n    device_id: Device for featurization. Supply a GPU id (e.g. 0 or 3) to use GPU. If no GPU with this id is found, use CPU\n    max_text_length: maximum number of tokens to consider. Default 1024\n    divergence_curve_discretization_size: Number of points to consider on the divergence curve. Default 25\n    mauve_scaling_factor: \"c\" from the paper. Default 5.\n    verbose: If True (default), print running time updates\n    seed: random seed to initialize k-means cluster assignments.\nReturns:\n    mauve: MAUVE score, a number between 0 and 1. Larger values indicate that P and Q are closer,\n    frontier_integral: Frontier Integral, a number between 0 and 1. Smaller values indicate that P and Q are closer,\n    divergence_curve: a numpy.ndarray of shape (m, 2); plot it with matplotlib to view the divergence curve,\n    p_hist: a discrete distribution, which is a quantized version of the text distribution p_text,\n    q_hist: same as above, but with q_text.\nExamples:\n\n    >>> # faiss segfaults in doctest for some reason, so the .compute call is not tested with doctest\n    >>> import datasets\n    >>> mauve = datasets.load_metric('mauve')\n    >>> predictions = [\"hello there\", \"general kenobi\"]\n    >>> references = [\"hello there\", \"general kenobi\"]\n    >>> out = mauve.compute(predictions=predictions, references=references) # doctest: +SKIP\n    >>> print(out.mauve) # doctest: +SKIP\n    1.0\n"



@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION      ,   _KWARGS_DESCRIPTION  )
class      _UpperCAmelCase      (							datasets.Metric  ):




     def 		snake_case_		(					self):
         return datasets.MetricInfo(
             description=_DESCRIPTION			,    citation=_CITATION			,    homepage='''https://github.com/krishnap25/mauve'''			,    inputs_description=_KWARGS_DESCRIPTION			,    features=datasets.Features(
                 {
                     '''predictions''': datasets.Value('''string'''			,    id='''sequence'''),
                     '''references''': datasets.Value('''string'''			,    id='''sequence'''),
                 })			,    codebase_urls=['''https://github.com/krishnap25/mauve''']			,    reference_urls=[
                 '''https://arxiv.org/abs/2102.01454''',
                 '''https://github.com/krishnap25/mauve''',
             ]			,    )




     def 		snake_case_		(					self			,    a__			,    a__			,    a__=None			,    a__=None			,    a__=None			,    a__=None			,    a__="auto"			,    a__=-1			,    a__=0.9			,    a__=5			,    a__=5_0_0			,    a__="gpt2-large"			,    a__=-1			,    a__=1_0_2_4			,    a__=2_5			,    a__=5			,    a__=True			,    a__=2_5			,    ):
         A__					=       compute_mauve(
             p_text=a__			,    q_text=a__			,    p_features=a__			,    q_features=a__			,    p_tokens=a__			,    q_tokens=a__			,    num_buckets=a__			,    pca_max_data=a__			,    kmeans_explained_var=a__			,    kmeans_num_redo=a__			,    kmeans_max_iter=a__			,    featurize_model_name=a__			,    device_id=a__			,    max_text_length=a__			,    divergence_curve_discretization_size=a__			,    mauve_scaling_factor=a__			,    verbose=a__			,    seed=a__			,    )
         return out
