


'''simple docstring'''







def       lowercase					(_A       ):







       """simple docstring"""







       _lowerCAmelCase     :				int       =							current_set.copy()
       for row_index, row in enumerate(_A       ):
              _lowerCAmelCase     :				int       =							row[0]
              for column_index, column in enumerate(_A       ):
                     if magnitude == 0:
                            _lowerCAmelCase     :				Optional[int]       =							column
                            continue
                     _lowerCAmelCase     :				List[str]       =							column / magnitude
    # Subtract to cancel term
       _lowerCAmelCase     :				List[str]       =							current_set[0]
       _lowerCAmelCase     :				Optional[Any]       =							[first_row]
       _lowerCAmelCase     :				Dict       =							current_set[1::]
       for row in current_set:
              _lowerCAmelCase     :				Tuple       =							[]
              # 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:
              _lowerCAmelCase     :				Optional[int]       =							final_set[0]
              _lowerCAmelCase     :				str       =							[]
              _lowerCAmelCase     :				Any       =							[]
              for row in final_set[1::]:
                     current_first_column.append(row[0]       )
                     next_iteration.append(row[1::]       )
              _lowerCAmelCase     :				Tuple       =							simplify(_A       )
              for i in range(len(_A       )       ):
                     resultant[i].insert(0 ,    current_first_column[i]       )
              resultant.insert(0 ,    _A       )
              _lowerCAmelCase     :				List[str]       =							resultant
       return final_set






def       lowercase					(_A       ):







       """simple docstring"""







       if len(_A       ) == 0:
              raise IndexError('solve_simultaneous() requires n lists of length n+1'       )
       _lowerCAmelCase     :				Union[str, Any]       =							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]]
       _lowerCAmelCase     :				List[str]       =							equations.copy()
       if any(0 in row for row in data_set       ):
              _lowerCAmelCase     :				int       =							data_set.copy()
              _lowerCAmelCase     :				List[str]       =							[]
              for row_index, row in enumerate(_A       ):
                     if 0 not in row:
                            _lowerCAmelCase     :				List[Any]       =							data_set.pop(_A       )
                            break
              if not full_row:
                     raise ValueError('solve_simultaneous() requires at least 1 full equation'       )
              data_set.insert(0 ,    _A       )
       _lowerCAmelCase     :				str       =							data_set.copy()
       _lowerCAmelCase     :				Optional[int]       =							simplify(_A       )
       _lowerCAmelCase     :				Dict       =							simplified[::-1]
       _lowerCAmelCase     :				list       =							[]
       for row in simplified:
              _lowerCAmelCase     :				Optional[int]       =							row[-1]
              if not solutions:
                     if row[-2] == 0:
                            solutions.append(0       )
                            continue
                     solutions.append(current_solution / row[-2]       )
                     continue
              _lowerCAmelCase     :				List[str]       =							row.copy()[: len(_A       ) - 1 :]
              while temp_row[0] == 0:
                     temp_row.pop(0       )
              if len(_A       ) == 0:
                     solutions.append(0       )
                     continue
              _lowerCAmelCase     :				List[Any]       =							temp_row[1::]
              _lowerCAmelCase     :				Tuple       =							temp_row[::-1]
              for column_index, column in enumerate(_A       ):
                     current_solution -= column * solutions[column_index]
              solutions.append(_A       )
       _lowerCAmelCase     :				Optional[int]       =							[]
       for item in solutions:
              final.append(float(round(_A ,    5       )       )       )
       return final[::-1]


if __name__ == "__main__":
       import doctest

       doctest.testmod()
       lowerCAmelCase     :  Optional[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]]))





'''simple docstring'''







from dataclasses import dataclass
from typing import Optional, Tuple, Union

import torch
import torch.nn as nn

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput
from .embeddings import GaussianFourierProjection, TimestepEmbedding, Timesteps
from .modeling_utils import ModelMixin
from .unet_ad_blocks import get_down_block, get_mid_block, get_out_block, get_up_block
@dataclass
class 						UpperCamelCase__       (			SCREAMING_SNAKE_CASE_						):



     """simple docstring"""






     __magic_name__           =     42
class 						UpperCamelCase__       (			SCREAMING_SNAKE_CASE_     ,       SCREAMING_SNAKE_CASE_						):



     """simple docstring"""






     @register_to_config
     def __init__(			self   ,						snake_case__ = 6_5536   ,						snake_case__ = None   ,						snake_case__ = 2   ,						snake_case__ = 2   ,						snake_case__ = 0   ,						snake_case__ = "fourier"   ,						snake_case__ = True   ,						snake_case__ = False   ,						snake_case__ = 0.0   ,						snake_case__ = ("DownBlock1DNoSkip", "DownBlock1D", "AttnDownBlock1D")   ,						snake_case__ = ("AttnUpBlock1D", "UpBlock1D", "UpBlock1DNoSkip")   ,						snake_case__ = "UNetMidBlock1D"   ,						snake_case__ = None   ,						snake_case__ = (32, 32, 64)   ,						snake_case__ = None   ,						snake_case__ = 8   ,						snake_case__ = 1   ,						snake_case__ = False   ,						):

            '''simple docstring'''

            super().__init__()
            _lowerCAmelCase     :				Optional[int]       =							sample_size

            # time
            if time_embedding_type == "fourier":
                   _lowerCAmelCase     :				Tuple       =							GaussianFourierProjection(
                       embedding_size=8   ,						set_W_to_weight=snake_case__   ,						log=snake_case__   ,						flip_sin_to_cos=snake_case__ )
                   _lowerCAmelCase     :				List[Any]       =							2 * block_out_channels[0]
            elif time_embedding_type == "positional":
                   _lowerCAmelCase     :				Optional[Any]       =							Timesteps(
                       block_out_channels[0]   ,						flip_sin_to_cos=snake_case__   ,						downscale_freq_shift=snake_case__ )
                   _lowerCAmelCase     :				Optional[int]       =							block_out_channels[0]

            if use_timestep_embedding:
                   _lowerCAmelCase     :				Any       =							block_out_channels[0] * 4
                   _lowerCAmelCase     :				List[str]       =							TimestepEmbedding(
                       in_channels=snake_case__   ,						time_embed_dim=snake_case__   ,						act_fn=snake_case__   ,						out_dim=block_out_channels[0]   ,						)

            _lowerCAmelCase     :				Tuple       =							nn.ModuleList([] )
            _lowerCAmelCase     :				Tuple       =							None
            _lowerCAmelCase     :				Optional[Any]       =							nn.ModuleList([] )
            _lowerCAmelCase     :				str       =							None

            # down
            _lowerCAmelCase     :				List[str]       =							in_channels
            for i, down_block_type in enumerate(snake_case__ ):
                   _lowerCAmelCase     :				str       =							output_channel
                   _lowerCAmelCase     :				Any       =							block_out_channels[i]

                   if i == 0:
                          input_channel += extra_in_channels

                   _lowerCAmelCase     :				Tuple       =							i == len(snake_case__ ) - 1

                   _lowerCAmelCase     :				List[str]       =							get_down_block(
                       snake_case__   ,						num_layers=snake_case__   ,						in_channels=snake_case__   ,						out_channels=snake_case__   ,						temb_channels=block_out_channels[0]   ,						add_downsample=not is_final_block or downsample_each_block   ,						)
                   self.down_blocks.append(snake_case__ )

            # mid
            _lowerCAmelCase     :				List[str]       =							get_mid_block(
                snake_case__   ,						in_channels=block_out_channels[-1]   ,						mid_channels=block_out_channels[-1]   ,						out_channels=block_out_channels[-1]   ,						embed_dim=block_out_channels[0]   ,						num_layers=snake_case__   ,						add_downsample=snake_case__   ,						)

            # up
            _lowerCAmelCase     :				Union[str, Any]       =							list(reversed(snake_case__ ) )
            _lowerCAmelCase     :				List[Any]       =							reversed_block_out_channels[0]
            if out_block_type is None:
                   _lowerCAmelCase     :				Tuple       =							out_channels
            else:
                   _lowerCAmelCase     :				Tuple       =							block_out_channels[0]

            for i, up_block_type in enumerate(snake_case__ ):
                   _lowerCAmelCase     :				int       =							output_channel
                   _lowerCAmelCase     :				Dict       =							(
                       reversed_block_out_channels[i + 1] if i < len(snake_case__ ) - 1 else final_upsample_channels
                   )

                   _lowerCAmelCase     :				Union[str, Any]       =							i == len(snake_case__ ) - 1

                   _lowerCAmelCase     :				Tuple       =							get_up_block(
                       snake_case__   ,						num_layers=snake_case__   ,						in_channels=snake_case__   ,						out_channels=snake_case__   ,						temb_channels=block_out_channels[0]   ,						add_upsample=not is_final_block   ,						)
                   self.up_blocks.append(snake_case__ )
                   _lowerCAmelCase     :				List[str]       =							output_channel

            # out
            _lowerCAmelCase     :				Tuple       =							norm_num_groups if norm_num_groups is not None else min(block_out_channels[0] // 4   ,						32 )
            _lowerCAmelCase     :				Any       =							get_out_block(
                out_block_type=snake_case__   ,						num_groups_out=snake_case__   ,						embed_dim=block_out_channels[0]   ,						out_channels=snake_case__   ,						act_fn=snake_case__   ,						fc_dim=block_out_channels[-1] // 4   ,						)







     def a						(			self   ,						snake_case__   ,						snake_case__   ,						snake_case__ = True   ,						):

            '''simple docstring'''

            _lowerCAmelCase     :				Optional[int]       =							timestep
            if not torch.is_tensor(snake_case__ ):
                   _lowerCAmelCase     :				Optional[int]       =							torch.tensor([timesteps]   ,						dtype=torch.long   ,						device=sample.device )
            elif torch.is_tensor(snake_case__ ) and len(timesteps.shape ) == 0:
                   _lowerCAmelCase     :				List[Any]       =							timesteps[None].to(sample.device )

            _lowerCAmelCase     :				int       =							self.time_proj(snake_case__ )
            if self.config.use_timestep_embedding:
                   _lowerCAmelCase     :				Optional[int]       =							self.time_mlp(snake_case__ )
            else:
                   _lowerCAmelCase     :				List[str]       =							timestep_embed[..., None]
                   _lowerCAmelCase     :				Dict       =							timestep_embed.repeat([1, 1, sample.shape[2]] ).to(sample.dtype )
                   _lowerCAmelCase     :				Tuple       =							timestep_embed.broadcast_to((sample.shape[:1] + timestep_embed.shape[1:]) )

            # 2. down
            _lowerCAmelCase     :				str       =							()
            for downsample_block in self.down_blocks:
                   _lowerCAmelCase      ,  _lowerCAmelCase     :				Union[str, Any]       =							downsample_block(hidden_states=snake_case__   ,						temb=snake_case__ )
                   down_block_res_samples += res_samples

            # 3. mid
            if self.mid_block:
                   _lowerCAmelCase     :				Any       =							self.mid_block(snake_case__   ,						snake_case__ )

            # 4. up
            for i, upsample_block in enumerate(self.up_blocks ):
                   _lowerCAmelCase     :				Union[str, Any]       =							down_block_res_samples[-1:]
                   _lowerCAmelCase     :				Union[str, Any]       =							down_block_res_samples[:-1]
                   _lowerCAmelCase     :				Union[str, Any]       =							upsample_block(snake_case__   ,						res_hidden_states_tuple=snake_case__   ,						temb=snake_case__ )

            # 5. post-process
            if self.out_block:
                   _lowerCAmelCase     :				Optional[Any]       =							self.out_block(snake_case__   ,						snake_case__ )

            if not return_dict:
                   return (sample,)

            return UNetaDOutput(sample=snake_case__ )

