'''simple docstring'''
# We ignore warnings about stepping the scheduler since we step it ourselves during gradient accumulation

import warnings

from .state import AcceleratorState, GradientState


warnings.filterwarnings('''ignore''', category=UserWarning, module='''torch.optim.lr_scheduler''')






class 			__lowercase		:







     """simple docstring"""






     def __init__(		self     ,			_lowerCamelCase     ,			_lowerCamelCase     ,			_lowerCamelCase = True     ,			_lowerCamelCase = False    ):
         __UpperCamelCase	:	Dict		    =  scheduler
         __UpperCamelCase	:	Optional[Any]		    =  optimizers if isinstance(_lowerCamelCase     ,			(list, tuple)    ) else [optimizers]
         __UpperCamelCase	:	Any		    =  split_batches
         __UpperCamelCase	:	Any		    =  step_with_optimizer
         __UpperCamelCase	:	List[str]		    =  GradientState()







     def lowerCAmelCase     (		self     ,			*_lowerCamelCase     ,			**_lowerCamelCase    ):
         if not self.step_with_optimizer:
             # No link between scheduler and optimizer -> just step
             self.scheduler.step(*_lowerCamelCase     ,			**_lowerCamelCase    )
             return

         # Otherwise, first make sure the optimizer was stepped.
         if not self.gradient_state.sync_gradients:
             if self.gradient_state.adjust_scheduler:
                 self.scheduler._step_count += 1
             return

         for opt in self.optimizers:
             if opt.step_was_skipped:
                 return
         if self.split_batches:
             # Split batches -> the training dataloader batch size is not changed so one step per training step
             self.scheduler.step(*_lowerCamelCase     ,			**_lowerCamelCase    )
         else:
             # Otherwise the training dataloader batch size was multiplied by `num_processes`, so we need to do
             # num_processes steps per training step
             __UpperCamelCase	:	Optional[Any]		    =  AcceleratorState().num_processes
             for _ in range(_lowerCamelCase    ):
                 # Special case when using OneCycle and `drop_last` was not used
                 if hasattr(self.scheduler     ,			'total_steps'    ):
                     if self.scheduler._step_count <= self.scheduler.total_steps:
                         self.scheduler.step(*_lowerCamelCase     ,			**_lowerCamelCase    )
                 else:
                     self.scheduler.step(*_lowerCamelCase     ,			**_lowerCamelCase    )







     def lowerCAmelCase     (		self    ):
         return self.scheduler.get_last_lr()







     def lowerCAmelCase     (		self    ):
         return self.scheduler.state_dict()







     def lowerCAmelCase     (		self     ,			_lowerCamelCase    ):
         self.scheduler.load_state_dict(_lowerCamelCase    )







     def lowerCAmelCase     (		self    ):
         return self.scheduler.get_lr()







     def lowerCAmelCase     (		self     ,			*_lowerCamelCase     ,			**_lowerCamelCase    ):
         return self.scheduler.print_lr(*_lowerCamelCase     ,			**_lowerCamelCase    )




'''simple docstring'''
from __future__ import annotations

import numpy as np
from numpy import floataa
from numpy.typing import NDArray







def  _UpperCamelCase (     _a	:	NDArray[floataa]				,     _a	:	NDArray[floataa]				,     _a	:	list[int]				,     _a	:	int				,     ):




    """simple docstring"""



    __UpperCamelCase    ,					__UpperCamelCase	:	Union[str, Any]		    =  coefficient_matrix.shape
    __UpperCamelCase    ,					__UpperCamelCase	:	Union[str, Any]		    =  constant_matrix.shape

    if rowsa != colsa:
        __UpperCamelCase	:	Tuple		    =  f"""Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"""
        raise ValueError(_a			)

    if colsa != 1:
        __UpperCamelCase	:	List[Any]		    =  f"""Constant matrix must be nx1 but received {rowsa}x{colsa}"""
        raise ValueError(_a			)

    if rowsa != rowsa:
        __UpperCamelCase	:	Optional[int]		    =  (
            'Coefficient and constant matrices dimensions must be nxn and nx1 but '
            f"""received {rowsa}x{colsa} and {rowsa}x{colsa}"""
        )
        raise ValueError(_a			)

    if len(_a			) != rowsa:
        __UpperCamelCase	:	Union[str, Any]		    =  (
            'Number of initial values must be equal to number of rows in coefficient '
            f"""matrix but received {len(_a			)} and {rowsa}"""
        )
        raise ValueError(_a			)

    if iterations <= 0:
        raise ValueError('Iterations must be at least 1'			)

    __UpperCamelCase	:	NDArray[floataa]		    =  np.concatenate(
        (coefficient_matrix, constant_matrix)				,     axis=1			)

    __UpperCamelCase    ,					__UpperCamelCase	:	Union[str, Any]		    =  table.shape

    strictly_diagonally_dominant(_a			)

    # Iterates the whole matrix for given number of times
    for _ in range(_a			):
        __UpperCamelCase	:	List[Any]		    =  []
        for row in range(_a			):
            __UpperCamelCase	:	List[Any]		    =  0
            for col in range(_a			):
                if col == row:
                    __UpperCamelCase	:	Optional[int]		    =  table[row][col]
                elif col == cols - 1:
                    __UpperCamelCase	:	str		    =  table[row][col]
                else:
                    temp += (-1) * table[row][col] * init_val[col]
            __UpperCamelCase	:	Any		    =  (temp + val) / denom
            new_val.append(_a			)
        __UpperCamelCase	:	List[Any]		    =  new_val

    return [float(_a			) for i in new_val]







def  _UpperCamelCase (     _a	:	NDArray[floataa]			):




    """simple docstring"""



    __UpperCamelCase    ,					__UpperCamelCase	:	str		    =  table.shape

    __UpperCamelCase	:	str		    =  True

    for i in range(0				,     _a			):
        __UpperCamelCase	:	Optional[Any]		    =  0
        for j in range(0				,     cols - 1			):
            if i == j:
                continue
            else:
                total += table[i][j]

        if table[i][i] <= total:
            raise ValueError('Coefficient matrix is not strictly diagonally dominant'			)

    return is_diagonally_dominant


# Test Cases
if __name__ == "__main__":
  import doctest

  doctest.testmod()



