
'''simple docstring'''
def      UpperCamelCase_				(      A__						):
	a_      				=						current_set.copy()
	for row_index, row in enumerate(A__						):
		a_      				=						row[0]
		for column_index, column in enumerate(A__						):
			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(A__						)
			continue
		for column_index in range(len(A__						)						):
			temp_row.append(first_row[column_index] - row[column_index]						)
		final_set.append(A__						)
	# 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(A__						)
		for i in range(len(A__						)						):
			resultant[i].insert(0  ,      current_first_column[i]						)
		resultant.insert(0  ,      A__						)
		a_      				=						resultant
	return final_set






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


'''simple docstring'''
from unittest.mock import patch

import pyspark

from datasets.packaged_modules.spark.spark import (
    Spark,
    SparkExamplesIterable,
    _generate_iterable_examples,
)

from ..utils import (
    require_dill_gt_0_3_2,
    require_not_windows,
)






def      UpperCamelCase_				(      A__  ,      A__						):
	a_      				=						[]
	for part_id in partition_order:
		a_      				=						df.where(F'''SPARK_PARTITION_ID() = {part_id}'''						).collect()
		for row_idx, row in enumerate(A__						):
			expected_row_ids_and_row_dicts.append((F'''{part_id}_{row_idx}''', row.asDict())						)
	return expected_row_ids_and_row_dicts






@require_not_windows
@require_dill_gt_0_3_2
def      UpperCamelCase_				(      ):
	a_      				=						pyspark.sql.SparkSession.builder.master("""local[*]"""						).appName("""pyspark"""						).getOrCreate()
	a_      				=						spark.range(1_00						).repartition(1						)
	a_      				=						Spark(A__						)
	# The id ints will be converted to Pyarrow int64s, so each row will be 8 bytes. Setting a max_shard_size of 16 means
	# that each partition can hold 2 rows.
	spark_builder._repartition_df_if_needed(max_shard_size=16						)
	# Given that the dataframe has 100 rows and each partition has 2 rows, we expect 50 partitions.
	assert spark_builder.df.rdd.getNumPartitions() == 50






@require_not_windows
@require_dill_gt_0_3_2
def      UpperCamelCase_				(      ):
	a_      				=						pyspark.sql.SparkSession.builder.master("""local[*]"""						).appName("""pyspark"""						).getOrCreate()
	a_      				=						spark.range(10						).repartition(2						)
	a_      				=						[1, 0]
	a_      				=						_generate_iterable_examples(A__  ,      A__						)  # Reverse the partitions.
	a_      				=						_get_expected_row_ids_and_row_dicts_for_partition_order(A__  ,      A__						)

	for i, (row_id, row_dict) in enumerate(generate_fn()						):
		a_				,  a_      				=						expected_row_ids_and_row_dicts[i]
		assert row_id == expected_row_id
		assert row_dict == expected_row_dict






@require_not_windows
@require_dill_gt_0_3_2
def      UpperCamelCase_				(      ):
	a_      				=						pyspark.sql.SparkSession.builder.master("""local[*]"""						).appName("""pyspark"""						).getOrCreate()
	a_      				=						spark.range(10						).repartition(1						)
	a_      				=						SparkExamplesIterable(A__						)
	assert it.n_shards == 1
	for i, (row_id, row_dict) in enumerate(A__						):
		assert row_id == F'''0_{i}'''
		assert row_dict == {"id": i}






@require_not_windows
@require_dill_gt_0_3_2
def      UpperCamelCase_				(      ):
	a_      				=						pyspark.sql.SparkSession.builder.master("""local[*]"""						).appName("""pyspark"""						).getOrCreate()
	a_      				=						spark.range(30						).repartition(3						)
	# Mock the generator so that shuffle reverses the partition indices.
	with patch("""numpy.random.Generator"""						) as generator_mock:
		a_      				=						lambda A__						: x.reverse()
		a_      				=						_get_expected_row_ids_and_row_dicts_for_partition_order(A__  ,      [2, 1, 0]						)

		a_      				=						SparkExamplesIterable(A__						).shuffle_data_sources(A__						)
		assert shuffled_it.n_shards == 3
		for i, (row_id, row_dict) in enumerate(A__						):
			a_				,  a_      				=						expected_row_ids_and_row_dicts[i]
			assert row_id == expected_row_id
			assert row_dict == expected_row_dict






@require_not_windows
@require_dill_gt_0_3_2
def      UpperCamelCase_				(      ):
	a_      				=						pyspark.sql.SparkSession.builder.master("""local[*]"""						).appName("""pyspark"""						).getOrCreate()
	a_      				=						spark.range(20						).repartition(4						)

	# Partitions 0 and 2
	a_      				=						SparkExamplesIterable(A__						).shard_data_sources(worker_id=0  ,      num_workers=2						)
	assert shard_it_a.n_shards == 2
	a_      				=						_get_expected_row_ids_and_row_dicts_for_partition_order(A__  ,      [0, 2]						)
	for i, (row_id, row_dict) in enumerate(A__						):
		a_				,  a_      				=						expected_row_ids_and_row_dicts_a[i]
		assert row_id == expected_row_id
		assert row_dict == expected_row_dict

	# Partitions 1 and 3
	a_      				=						SparkExamplesIterable(A__						).shard_data_sources(worker_id=1  ,      num_workers=2						)
	assert shard_it_a.n_shards == 2
	a_      				=						_get_expected_row_ids_and_row_dicts_for_partition_order(A__  ,      [1, 3]						)
	for i, (row_id, row_dict) in enumerate(A__						):
		a_				,  a_      				=						expected_row_ids_and_row_dicts_a[i]
		assert row_id == expected_row_id
		assert row_dict == expected_row_dict






@require_not_windows
@require_dill_gt_0_3_2
def      UpperCamelCase_				(      ):
	a_      				=						pyspark.sql.SparkSession.builder.master("""local[*]"""						).appName("""pyspark"""						).getOrCreate()
	a_      				=						spark.range(1_00						).repartition(1						)
	a_      				=						Spark(A__						)
	# Choose a small max_shard_size for maximum partitioning.
	spark_builder._repartition_df_if_needed(max_shard_size=1						)
	# The new number of partitions should not be greater than the number of rows.
	assert spark_builder.df.rdd.getNumPartitions() == 1_00
