
'''simple docstring'''

# limitations under the License.

# NOTE: This file is deprecated and will be removed in a future version.
# It only exists so that temporarely `from diffusers.pipelines import DiffusionPipeline` works

from .pipelines import DiffusionPipeline, ImagePipelineOutput  # noqa: F401
from .utils import deprecate


deprecate(
    """pipelines_utils""",
    """0.22.0""",
    """Importing `DiffusionPipeline` or `ImagePipelineOutput` from diffusers.pipeline_utils is deprecated. Please import from diffusers.pipelines.pipeline_utils instead.""",
    standard_warn=False,
    stacklevel=3,
)







'''simple docstring'''

def        UpperCAmelCase_ (  lowerCamelCase_			):







 """simple docstring"""


 lowerCAmelCase__     :   str     		=	len(lowerCamelCase_			)
 lowerCAmelCase__     :   Optional[Any]     		=	len(matrix[0]			)
 lowerCAmelCase__     :   Any     		=	min(lowerCamelCase_      ,			lowerCamelCase_			)

 for row in range(lowerCamelCase_			):
  # Check if diagonal element is not zero
  if matrix[row][row] != 0:
   # Eliminate all the elements below the diagonal
   for col in range(row + 1      ,			lowerCamelCase_			):
    lowerCAmelCase__     :   Tuple     		=	matrix[col][row] / matrix[row][row]
    for i in range(lowerCamelCase_      ,			lowerCamelCase_			):
     matrix[col][i] -= multiplier * matrix[row][i]
  else:
   # Find a non-zero diagonal element to swap rows
   lowerCAmelCase__     :   Dict     		=	True
   for i in range(row + 1      ,			lowerCamelCase_			):
    if matrix[i][row] != 0:
     lowerCAmelCase__		,     lowerCAmelCase__     :   Optional[Any]     		=	matrix[i], matrix[row]
     lowerCAmelCase__     :   Optional[Any]     		=	False
     break
   if reduce:
    rank -= 1
    for i in range(lowerCamelCase_			):
     lowerCAmelCase__     :   Union[str, Any]     		=	matrix[i][rank]

            # Reduce the row pointer by one to stay on the same row
   row -= 1

 return rank


if __name__ == "__main__":
     import doctest

     doctest.testmod()





