






'''simple docstring'''





def 				snake_case  (     lowerCamelCase					):




	'''simple docstring'''







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





def 				snake_case  (     lowerCamelCase					):




	'''simple docstring'''







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


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						__UpperCamelCase      :      Union[str, Any]     						=						[
						    [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 gc
import unittest

from diffusers import FlaxDPMSolverMultistepScheduler, FlaxStableDiffusionPipeline
from diffusers.utils import is_flax_available, slow
from diffusers.utils.testing_utils import require_flax


if is_flax_available():
						import jax
						import jax.numpy as jnp
						from flax.jax_utils import replicate
						from flax.training.common_utils import shard


@slow
@require_flax
class        __UpperCamelCase    (     unittest.TestCase   ):







	def  _a   (  self      :							Union[str, Any]			)		-> Any:
		"""simple docstring"""







		super().tearDown()
		gc.collect()







	def  _a   (  self      :							List[str]			)		-> int:
		"""simple docstring"""







		__lowercase       ,						__lowercase             =  FlaxStableDiffusionPipeline.from_pretrained(
		    """stabilityai/stable-diffusion-2"""       ,				revision="""bf16"""       ,				dtype=jnp.bfloataa       ,				)

		__lowercase             =  """A painting of a squirrel eating a burger"""
		__lowercase             =  jax.device_count()
		__lowercase             =  num_samples * [prompt]
		__lowercase             =  sd_pipe.prepare_inputs(_lowerCAmelCase			)

		__lowercase             =  replicate(_lowerCAmelCase			)
		__lowercase             =  shard(_lowerCAmelCase			)

		__lowercase             =  jax.random.PRNGKey(0			)
		__lowercase             =  jax.random.split(_lowerCAmelCase       ,				jax.device_count()			)

		__lowercase             =  sd_pipe(_lowerCAmelCase       ,				_lowerCAmelCase       ,				_lowerCAmelCase       ,				num_inference_steps=25       ,				jit=_lowerCAmelCase			)[0]
		assert images.shape == (jax.device_count(), 1, 768, 768, 3)

		__lowercase             =  images.reshape((images.shape[0] * images.shape[1],) + images.shape[-3:]			)
		__lowercase             =  images[0, 253:256, 253:256, -1]

		__lowercase             =  jnp.asarray(jax.device_get(image_slice.flatten()			)			)
		__lowercase             =  jnp.array([0.4_238, 0.4_414, 0.4_395, 0.4_453, 0.4_629, 0.4_590, 0.4_531, 0.45_508, 0.4_512]			)
		print(F'output_slice: {output_slice}'			)
		assert jnp.abs(output_slice - expected_slice			).max() < 1e-2







	def  _a   (  self      :							str			)		-> List[Any]:
		"""simple docstring"""







		__lowercase             =  """stabilityai/stable-diffusion-2"""
		__lowercase       ,						__lowercase             =  FlaxDPMSolverMultistepScheduler.from_pretrained(_lowerCAmelCase       ,				subfolder="""scheduler"""			)
		__lowercase       ,						__lowercase             =  FlaxStableDiffusionPipeline.from_pretrained(
		    _lowerCAmelCase       ,				scheduler=_lowerCAmelCase       ,				revision="""bf16"""       ,				dtype=jnp.bfloataa       ,				)
		__lowercase             =  scheduler_params

		__lowercase             =  """A painting of a squirrel eating a burger"""
		__lowercase             =  jax.device_count()
		__lowercase             =  num_samples * [prompt]
		__lowercase             =  sd_pipe.prepare_inputs(_lowerCAmelCase			)

		__lowercase             =  replicate(_lowerCAmelCase			)
		__lowercase             =  shard(_lowerCAmelCase			)

		__lowercase             =  jax.random.PRNGKey(0			)
		__lowercase             =  jax.random.split(_lowerCAmelCase       ,				jax.device_count()			)

		__lowercase             =  sd_pipe(_lowerCAmelCase       ,				_lowerCAmelCase       ,				_lowerCAmelCase       ,				num_inference_steps=25       ,				jit=_lowerCAmelCase			)[0]
		assert images.shape == (jax.device_count(), 1, 768, 768, 3)

		__lowercase             =  images.reshape((images.shape[0] * images.shape[1],) + images.shape[-3:]			)
		__lowercase             =  images[0, 253:256, 253:256, -1]

		__lowercase             =  jnp.asarray(jax.device_get(image_slice.flatten()			)			)
		__lowercase             =  jnp.array([0.4_336, 0.42_969, 0.4_453, 0.4_199, 0.4_297, 0.4_531, 0.4_434, 0.4_434, 0.4_297]			)
		print(F'output_slice: {output_slice}'			)
		assert jnp.abs(output_slice - expected_slice			).max() < 1e-2

