

import unittest

from parameterized import parameterized

from transformers import LlamaConfig, is_torch_available, set_seed
from transformers.testing_utils import require_torch, slow, torch_device

from ...generation.test_utils import GenerationTesterMixin
from ...test_configuration_common import ConfigTester
from ...test_modeling_common import ModelTesterMixin, ids_tensor, random_attention_mask
from ...test_pipeline_mixin import PipelineTesterMixin


if is_torch_available():
       import torch

       from transformers import LlamaForCausalLM, LlamaForSequenceClassification, LlamaModel, LlamaTokenizer


class       SCREAMING_SNAKE_CASE__					:





    def __init__(      self						,   a						,   a=13						,   a=7						,   a=True						,   a=True						,   a=False						,   a=True						,   a=99						,   a=32						,   a=5						,   a=4						,   a=37						,   a="gelu"						,   a=0.1						,   a=0.1						,   a=512						,   a=16						,   a=2						,   a=0.02						,   a=3						,   a=4						,   a=None						,   ):
         lowercase__    :   List[str]      =       parent
         lowercase__    :   Dict      =       batch_size
         lowercase__    :   Tuple      =       seq_length
         lowercase__    :   int      =       is_training
         lowercase__    :   List[str]      =       use_input_mask
         lowercase__    :   Any      =       use_token_type_ids
         lowercase__    :   Tuple      =       use_labels
         lowercase__    :   List[str]      =       vocab_size
         lowercase__    :   Optional[int]      =       hidden_size
         lowercase__    :   Optional[int]      =       num_hidden_layers
         lowercase__    :   List[str]      =       num_attention_heads
         lowercase__    :   Optional[Any]      =       intermediate_size
         lowercase__    :   int      =       hidden_act
         lowercase__    :   List[Any]      =       hidden_dropout_prob
         lowercase__    :   int      =       attention_probs_dropout_prob
         lowercase__    :   str      =       max_position_embeddings
         lowercase__    :   Dict      =       type_vocab_size
         lowercase__    :   Dict      =       type_sequence_label_size
         lowercase__    :   int      =       initializer_range
         lowercase__    :   Optional[Any]      =       num_labels
         lowercase__    :   int      =       num_choices
         lowercase__    :   Tuple      =       scope





    def       snake_case_				(      self):
         lowercase__    :   Union[str, Any]      =       ids_tensor([self.batch_size, self.seq_length]						,   self.vocab_size)

         lowercase__    :   Optional[int]      =       None
         if self.use_input_mask:
              lowercase__    :   Any      =       random_attention_mask([self.batch_size, self.seq_length])

         lowercase__    :   Dict      =       None
         if self.use_token_type_ids:
              lowercase__    :   Union[str, Any]      =       ids_tensor([self.batch_size, self.seq_length]						,   self.type_vocab_size)

         lowercase__    :   Tuple      =       None
         lowercase__    :   int      =       None
         lowercase__    :   List[Any]      =       None
         if self.use_labels:
              lowercase__    :   Optional[int]      =       ids_tensor([self.batch_size]						,   self.type_sequence_label_size)
              lowercase__    :   Optional[Any]      =       ids_tensor([self.batch_size, self.seq_length]						,   self.num_labels)
              lowercase__    :   List[str]      =       ids_tensor([self.batch_size]						,   self.num_choices)

         lowercase__    :   Dict      =       self.get_config()

         return config, input_ids, token_type_ids, input_mask, sequence_labels, token_labels, choice_labels





    def       snake_case_				(      self):
         return LlamaConfig(
             vocab_size=self.vocab_size						,   hidden_size=self.hidden_size						,   num_hidden_layers=self.num_hidden_layers						,   num_attention_heads=self.num_attention_heads						,   intermediate_size=self.intermediate_size						,   hidden_act=self.hidden_act						,   hidden_dropout_prob=self.hidden_dropout_prob						,   attention_probs_dropout_prob=self.attention_probs_dropout_prob						,   max_position_embeddings=self.max_position_embeddings						,   type_vocab_size=self.type_vocab_size						,   is_decoder=a						,   initializer_range=self.initializer_range						,   )





    def       snake_case_				(      self						,   a						,   a						,   a						,   a						,   a						,   a						,   a):
         lowercase__    :   Dict      =       LlamaModel(config=a)
         model.to(a)
         model.eval()
         lowercase__    :   List[str]      =       model(a						,   attention_mask=a)
         lowercase__    :   Any      =       model(a)
         self.parent.assertEqual(result.last_hidden_state.shape						,   (self.batch_size, self.seq_length, self.hidden_size))





    def       snake_case_				(      self						,   a						,   a						,   a						,   a						,   a						,   a						,   a						,   a						,   a						,   ):
         lowercase__    :   Union[str, Any]      =       True
         lowercase__    :   int      =       LlamaModel(a)
         model.to(a)
         model.eval()
         lowercase__    :   Dict      =       model(
             a						,   attention_mask=a						,   encoder_hidden_states=a						,   encoder_attention_mask=a						,   )
         lowercase__    :   Optional[Any]      =       model(
             a						,   attention_mask=a						,   encoder_hidden_states=a						,   )
         lowercase__    :   List[Any]      =       model(a						,   attention_mask=a)
         self.parent.assertEqual(result.last_hidden_state.shape						,   (self.batch_size, self.seq_length, self.hidden_size))





    def       snake_case_				(      self						,   a						,   a						,   a						,   a						,   a						,   a						,   a						,   a						,   a						,   ):
         lowercase__    :   Optional[int]      =       LlamaForCausalLM(config=a)
         model.to(a)
         model.eval()
         lowercase__    :   Tuple      =       model(a						,   attention_mask=a						,   labels=a)
         self.parent.assertEqual(result.logits.shape						,   (self.batch_size, self.seq_length, self.vocab_size))





    def       snake_case_				(      self						,   a						,   a						,   a						,   a						,   a						,   a						,   a						,   a						,   a						,   ):
         lowercase__    :   Union[str, Any]      =       True
         lowercase__    :   List[Any]      =       True
         lowercase__    :   Optional[int]      =       LlamaForCausalLM(config=a)
         model.to(a)
         model.eval()

         # first forward pass
         lowercase__    :   List[str]      =       model(
             a						,   attention_mask=a						,   encoder_hidden_states=a						,   encoder_attention_mask=a						,   use_cache=a						,   )
         lowercase__    :   Optional[int]      =       outputs.past_key_values

         # create hypothetical multiple next token and extent to next_input_ids
         lowercase__    :   Any      =       ids_tensor((self.batch_size, 3)						,   config.vocab_size)
         lowercase__    :   Tuple      =       ids_tensor((self.batch_size, 3)						,   vocab_size=2)

         # append to next input_ids and
         lowercase__    :   Optional[int]      =       torch.cat([input_ids, next_tokens]						,   dim=-1)
         lowercase__    :   Tuple      =       torch.cat([input_mask, next_mask]						,   dim=-1)

         lowercase__    :   int      =       model(
             a						,   attention_mask=a						,   encoder_hidden_states=a						,   encoder_attention_mask=a						,   output_hidden_states=a						,   )['hidden_states'][0]
         lowercase__    :   List[Any]      =       model(
             a						,   attention_mask=a						,   encoder_hidden_states=a						,   encoder_attention_mask=a						,   past_key_values=a						,   output_hidden_states=a						,   )['hidden_states'][0]

         # select random slice
         lowercase__    :   Dict      =       ids_tensor((1,)						,   output_from_past.shape[-1]).item()
         lowercase__    :   Optional[Any]      =       output_from_no_past[:, -3:, random_slice_idx].detach()
         lowercase__    :   int      =       output_from_past[:, :, random_slice_idx].detach()

         self.parent.assertTrue(output_from_past_slice.shape[1] == next_tokens.shape[1])

         # test that outputs are equal for slice
         self.parent.assertTrue(torch.allclose(a						,   a						,   atol=1e-3))





    def       snake_case_				(      self):
         lowercase__    :   Union[str, Any]      =       self.prepare_config_and_inputs()
         (
             (
             lowercase__
         )      , (
             lowercase__
         )      , (
             lowercase__
         )      , (
             lowercase__
         )      , (
             lowercase__
         )      , (
             lowercase__
         )      , (
             lowercase__
         )      , 
         )    :   List[Any]      =       config_and_inputs
         lowercase__    :   Any      =       {'input_ids': input_ids, 'attention_mask': input_mask}
         return config, inputs_dict



@require_torch
class       SCREAMING_SNAKE_CASE__					(__snake_case		,       __snake_case		,       __snake_case		,       unittest.TestCase     ):
    __lowerCamelCase						:       Tuple														=     (LlamaModel, LlamaForCausalLM, LlamaForSequenceClassification) if is_torch_available() else ()
    __lowerCamelCase						:       List[Any]														=     (LlamaForCausalLM,) if is_torch_available() else ()
    __lowerCamelCase						:       List[Any]														=     (
        {
            """feature-extraction""": LlamaModel,
            """text-classification""": LlamaForSequenceClassification,
            """text-generation""": LlamaForCausalLM,
            """zero-shot""": LlamaForSequenceClassification,
        }
        if is_torch_available()
        else {}
    )
    __lowerCamelCase						:       str														=     False
    __lowerCamelCase						:       int														=     False





    def       snake_case_				(      self):
         lowercase__    :   List[str]      =       LlamaModelTester(self)
         lowercase__    :   Union[str, Any]      =       ConfigTester(self						,   config_class=a						,   hidden_size=37)





    def       snake_case_				(      self):
         self.config_tester.run_common_tests()





    def       snake_case_				(      self):
         lowercase__    :   Optional[Any]      =       self.model_tester.prepare_config_and_inputs()
         self.model_tester.create_and_check_model(*a)





    def       snake_case_				(      self):
         lowercase__    :   Dict      =       self.model_tester.prepare_config_and_inputs()
         for type in ["absolute", "relative_key", "relative_key_query"]:
              lowercase__    :   List[Any]      =       type
              self.model_tester.create_and_check_model(*a)





    def       snake_case_				(      self):
         lowercase__      , lowercase__    :   str      =       self.model_tester.prepare_config_and_inputs_for_common()
         lowercase__    :   int      =       3
         lowercase__    :   str      =       input_dict['input_ids']
         lowercase__    :   Tuple      =       input_ids.ne(1).to(a)
         lowercase__    :   int      =       ids_tensor([self.model_tester.batch_size]						,   self.model_tester.type_sequence_label_size)
         lowercase__    :   int      =       LlamaForSequenceClassification(a)
         model.to(a)
         model.eval()
         lowercase__    :   int      =       model(a						,   attention_mask=a						,   labels=a)
         self.assertEqual(result.logits.shape						,   (self.model_tester.batch_size, self.model_tester.num_labels))





    def       snake_case_				(      self):
         lowercase__      , lowercase__    :   List[Any]      =       self.model_tester.prepare_config_and_inputs_for_common()
         lowercase__    :   List[Any]      =       3
         lowercase__    :   Any      =       'single_label_classification'
         lowercase__    :   List[Any]      =       input_dict['input_ids']
         lowercase__    :   Dict      =       input_ids.ne(1).to(a)
         lowercase__    :   int      =       ids_tensor([self.model_tester.batch_size]						,   self.model_tester.type_sequence_label_size)
         lowercase__    :   Any      =       LlamaForSequenceClassification(a)
         model.to(a)
         model.eval()
         lowercase__    :   List[Any]      =       model(a						,   attention_mask=a						,   labels=a)
         self.assertEqual(result.logits.shape						,   (self.model_tester.batch_size, self.model_tester.num_labels))





    def       snake_case_				(      self):
         lowercase__      , lowercase__    :   Tuple      =       self.model_tester.prepare_config_and_inputs_for_common()
         lowercase__    :   Optional[Any]      =       3
         lowercase__    :   List[str]      =       'multi_label_classification'
         lowercase__    :   str      =       input_dict['input_ids']
         lowercase__    :   List[str]      =       input_ids.ne(1).to(a)
         lowercase__    :   Tuple      =       ids_tensor(
             [self.model_tester.batch_size, config.num_labels]						,   self.model_tester.type_sequence_label_size).to(torch.float)
         lowercase__    :   List[str]      =       LlamaForSequenceClassification(a)
         model.to(a)
         model.eval()
         lowercase__    :   str      =       model(a						,   attention_mask=a						,   labels=a)
         self.assertEqual(result.logits.shape						,   (self.model_tester.batch_size, self.model_tester.num_labels))





    @unittest.skip('LLaMA buffers include complex numbers, which breaks this test')
    def       snake_case_				(      self):
         pass





    @parameterized.expand([('linear',), ('dynamic',)])
    def       snake_case_				(      self						,   a):
         lowercase__      , lowercase__    :   List[Any]      =       self.model_tester.prepare_config_and_inputs_for_common()
         lowercase__    :   Tuple      =       ids_tensor([1, 10]						,   config.vocab_size)
         lowercase__    :   int      =       ids_tensor([1, int(config.max_position_embeddings * 1.5)]						,   config.vocab_size)

         set_seed(42)  # Fixed seed at init time so the two models get the same random weights
         lowercase__    :   Any      =       LlamaModel(a)
         original_model.to(a)
         original_model.eval()
         lowercase__    :   Tuple      =       original_model(a).last_hidden_state
         lowercase__    :   int      =       original_model(a).last_hidden_state

         set_seed(42)  # Fixed seed at init time so the two models get the same random weights
         lowercase__    :   List[Any]      =       {'type': scaling_type, 'factor': 10.0}
         lowercase__    :   str      =       LlamaModel(a)
         scaled_model.to(a)
         scaled_model.eval()
         lowercase__    :   int      =       scaled_model(a).last_hidden_state
         lowercase__    :   Union[str, Any]      =       scaled_model(a).last_hidden_state

         # Dynamic scaling does not change the RoPE embeddings until it receives an input longer than the original
         # maximum sequence length, so the outputs for the short input should match.
         if scaling_type == "dynamic":
              self.assertTrue(torch.allclose(a						,   a						,   atol=1e-5))
         else:
              self.assertFalse(torch.allclose(a						,   a						,   atol=1e-5))

         # The output should be different for long inputs
         self.assertFalse(torch.allclose(a						,   a						,   atol=1e-5))



@require_torch
class       SCREAMING_SNAKE_CASE__					(unittest.TestCase     ):





    @unittest.skip('Logits are not exactly the same, once we fix the instabalities somehow, will update!')
    @slow
    def       snake_case_				(      self):
         lowercase__    :   Tuple      =       [1, 306, 4658, 278, 6593, 310, 2834, 338]
         lowercase__    :   str      =       LlamaForCausalLM.from_pretrained('meta-llama/Llama-2-7b-hf'						,   device_map='auto')
         lowercase__    :   List[str]      =       model(torch.tensor([input_ids]))
         # Expected mean on dim = -1
         lowercase__    :   Tuple      =       torch.tensor([[-6.6_550, -4.1_227, -4.9_859, -3.2_406, 0.8_262, -3.0_033, 1.2_964, -3.3_699]])
         torch.testing.assert_close(out.mean(-1)						,   a						,   atol=1e-2						,   rtol=1e-2)
         # slicing logits[0, 0, 0:30]
         # fmt: off
         lowercase__    :   Dict      =       torch.tensor([-12.8_281, -7.4_453, -0.4_639, -8.0_625, -7.2_500, -8.0_000, -6.4_883, -7.7_695, -7.8_438, -7.0_312, -6.2_188, -7.1_328, -1.8_496, 1.9_961, -8.6_250, -6.7_227, -12.8_281, -6.9_492, -7.0_742, -7.7_852, -7.5_820, -7.9_062, -6.9_375, -7.9_805, -8.3_438, -8.1_562, -8.0_469, -7.6_250, -7.7_422, -7.3_398,])
         # fmt: on
         torch.testing.assert_close(out[0, 0, :30]						,   a						,   atol=1e-5						,   rtol=1e-5)





    @unittest.skip('Logits are not exactly the same, once we fix the instabalities somehow, will update!')
    @slow
    def       snake_case_				(      self):
         lowercase__    :   List[Any]      =       [1, 306, 4658, 278, 6593, 310, 2834, 338]
         lowercase__    :   Dict      =       LlamaForCausalLM.from_pretrained('meta-llama/Llama-2-13b-hf'						,   device_map='auto')
         lowercase__    :   Tuple      =       model(torch.tensor(a))
         # Expected mean on dim = -1
         lowercase__    :   Union[str, Any]      =       torch.tensor([[-2.0_622, -1.2_794, -1.1_638, -0.9_788, -1.4_603, -1.0_238, -1.7_893, -1.4_411]])
         torch.testing.assert_close(out.mean(-1)						,   a						,   atol=1e-2						,   rtol=1e-2)
         # slicing logits[0, 0, 0:30]
         # fmt: off
         lowercase__    :   Optional[Any]      =       torch.tensor([-8.1_406, -8.0_547, 2.7_461, -1.2_344, -0.1_448, -1.8_262, -1.0_020, -1.8_154, -1.6_895, -1.8_516, -2.3_574, -0.9_277, 3.7_598, 6.5_742, -1.2_998, -0.1_177, -8.1_406, -2.9_688, -2.9_199, -3.1_699, -3.5_254, -2.3_555, -2.7_988, -3.4_141, -2.8_262, -4.5_195, -3.3_379, -3.3_164, -2.7_832, -3.0_273])
         # fmt: on
         torch.testing.assert_close(out[0, 0, :30]						,   a						,   atol=1e-5						,   rtol=1e-5)





    @unittest.skip('Logits are not exactly the same, once we fix the instabalities somehow, will update!')
    @slow
    def       snake_case_				(      self):
         lowercase__    :   Optional[int]      =       [1, 306, 4658, 278, 6593, 310, 2834, 338]
         lowercase__    :   str      =       LlamaForCausalLM.from_pretrained('meta-llama/Llama-2-13b-chat-hf'						,   device_map='auto')
         lowercase__    :   List[Any]      =       model(torch.tensor(a))
         # Expected mean on dim = -1
         lowercase__    :   Optional[Any]      =       torch.tensor([[-0.8_562, -1.8_520, -0.7_551, -0.4_162, -1.5_161, -1.2_038, -2.4_823, -2.3_254]])
         torch.testing.assert_close(out.mean(-1)						,   a						,   atol=1e-2						,   rtol=1e-2)
         # slicing logits[0, 0, 0:30]
         # fmt: off
         lowercase__    :   List[Any]      =       torch.tensor([-2.2_227, 4.8_828, 0.9_023, -0.4_578, -0.7_871, -0.1_033, -0.6_221, -0.5_786, -0.7_803, -1.0_674, -1.2_920, -0.1_570, 0.8_008, 2.0_723, -0.9_497, 0.2_771, -2.2_227, -0.7_612, -1.4_346, -1.2_061, -1.6_426, -0.3_000, -0.7_139, -1.1_934, -1.8_691, -1.6_973, -1.5_947, -1.2_705, -0.3_523, -0.5_513])
         # fmt: on
         torch.testing.assert_close(out.mean(-1)						,   a						,   atol=1e-2						,   rtol=1e-2)





    @unittest.skip(
        'Logits are not exactly the same, once we fix the instabalities somehow, will update! Also it is gonna be a `too_slow` test')
    @slow
    def       snake_case_				(      self):
         lowercase__    :   Dict      =       [1, 306, 4658, 278, 6593, 310, 2834, 338]
         lowercase__    :   str      =       LlamaForCausalLM.from_pretrained('meta-llama/Llama-2-70b-hf'						,   device_map='auto')
         lowercase__    :   List[str]      =       model(torch.tensor(a))

         lowercase__    :   int      =       torch.tensor(
             [[-4.2_327, -3.3_360, -4.6_665, -4.7_631, -1.8_180, -3.4_170, -1.4_211, -3.1_810]]						,   dtype=torch.floataa)
         torch.testing.assert_close(out.mean(-1)						,   a						,   atol=1e-2						,   rtol=1e-2)
         # fmt: off
         lowercase__    :   str      =       torch.tensor([-9.4_922, -3.9_551, 1.7_998, -5.6_758, -5.1_055, -5.8_984, -4.8_320, -6.8_086, -6.5_391, -5.6_172, -5.5_820, -5.5_352, 1.7_881, 3.6_289, -6.5_117, -3.4_785, -9.5_000, -6.0_352, -6.8_125, -6.0_195, -6.6_836, -5.4_727, -6.2_812, -6.0_391, -7.3_398, -7.4_297, -7.4_844, -6.5_820, -5.8_789, -5.5_312])
         # fmt: on
         torch.testing.assert_close(out[0, 0, :30]						,   a						,   atol=1e-5						,   rtol=1e-5)





    @unittest.skip('Model is curently gated')
    @slow
    def       snake_case_				(      self):
         lowercase__    :   List[str]      =       'Simply put, the theory of relativity states that 1) the laws of physics are the same everywhere in the universe and 2) the passage of time and the length of objects can vary depending on the observer\'s frame of reference.\n\nThe first part of the theory, that the laws of physics are the same everywhere, is known as the "princi'
         lowercase__    :   Union[str, Any]      =       'Simply put, the theory of relativity states that '
         lowercase__    :   Any      =       LlamaTokenizer.from_pretrained('meta-llama/Llama-2-13b-chat-hf')
         lowercase__    :   str      =       tokenizer.encode(a						,   return_tensors='pt')
         lowercase__    :   List[str]      =       LlamaForCausalLM.from_pretrained(
             'meta-llama/Llama-2-13b-chat-hf'						,   device_map='sequential'						,   use_safetensors=a)

         # greedy generation outputs
         lowercase__    :   Tuple      =       model.generate(a						,   max_new_tokens=64						,   top_p=a						,   temperature=1						,   do_sample=a)
         lowercase__    :   Union[str, Any]      =       tokenizer.decode(generated_ids[0]						,   skip_special_tokens=a)
         self.assertEqual(a						,   a)




from __future__ import annotations

from typing import Any


class       SCREAMING_SNAKE_CASE__					:





    def __init__(      self						,   a						,   a						,   a = 0):
         lowercase__      , lowercase__    :   Dict      =       row, column
         lowercase__    :   Optional[Any]      =       [[default_value for c in range(a)] for r in range(a)]





    def __str__(      self):
         lowercase__    :   Tuple      =       f"""Matrix consist of {self.row} rows and {self.column} columns\n"""

         # Make string identifier
         lowercase__    :   Optional[int]      =       0
         for row_vector in self.array:
              for obj in row_vector:
                   lowercase__    :   List[str]      =       max(a						,   len(str(a)))
         lowercase__    :   Optional[int]      =       f"""%{max_element_length}s"""

         # Make string and return
         def single_line(a) -> str:
              nonlocal string_format_identifier
              lowercase__    :   Tuple      =       '['
              line += ", ".join(string_format_identifier % (obj,) for obj in row_vector)
              line += "]"
              return line

         s += "\n".join(single_line(a) for row_vector in self.array)
         return s





    def __repr__(      self):
         return str(self)





    def       snake_case_				(      self						,   a):
         if not (isinstance(a						,   (list, tuple)) and len(a) == 2):
              return False
         elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
              return False
         else:
              return True





    def __getitem__(      self						,   a):
         assert self.validate_indicies(a)
         return self.array[loc[0]][loc[1]]





    def __setitem__(      self						,   a						,   a):
         assert self.validate_indicies(a)
         lowercase__    :   List[str]      =       value





    def __add__(      self						,   a):
         assert isinstance(a						,   a)
         assert self.row == another.row and self.column == another.column

         # Add
         lowercase__    :   List[str]      =       Matrix(self.row						,   self.column)
         for r in range(self.row):
              for c in range(self.column):
                   lowercase__    :   Dict      =       self[r, c] + another[r, c]
         return result





    def __neg__(      self):
         lowercase__    :   List[Any]      =       Matrix(self.row						,   self.column)
         for r in range(self.row):
              for c in range(self.column):
                   lowercase__    :   int      =       -self[r, c]
         return result





    def __sub__(      self						,   a):
         return self + (-another)





    def __mul__(      self						,   a):

         if isinstance(a						,   (int, float)):  # Scalar multiplication
              lowercase__    :   Optional[Any]      =       Matrix(self.row						,   self.column)
              for r in range(self.row):
                   for c in range(self.column):
                        lowercase__    :   Union[str, Any]      =       self[r, c] * another
              return result
         elif isinstance(a						,   a):  # Matrix multiplication
              assert self.column == another.row
              lowercase__    :   List[Any]      =       Matrix(self.row						,   another.column)
              for r in range(self.row):
                   for c in range(another.column):
                        for i in range(self.column):
                             result[r, c] += self[r, i] * another[i, c]
              return result
         else:
              lowercase__    :   Optional[Any]      =       f"""Unsupported type given for another ({type(a)})"""
              raise TypeError(a)





    def       snake_case_				(      self):
         lowercase__    :   Optional[int]      =       Matrix(self.column						,   self.row)
         for r in range(self.row):
              for c in range(self.column):
                   lowercase__    :   str      =       self[r, c]
         return result





    def       snake_case_				(      self						,   a						,   a):
         assert isinstance(a						,   a) and isinstance(a						,   a)
         assert self.row == self.column == u.row == v.row  # u, v should be column vector
         assert u.column == v.column == 1  # u, v should be column vector

         # Calculate
         lowercase__    :   int      =       v.transpose()
         lowercase__    :   Tuple      =       (v_t * self * u)[0, 0] + 1
         if numerator_factor == 0:
              return None  # It's not invertable
         return self - ((self * u) * (v_t * self) * (1.0 / numerator_factor))


# Testing
if __name__ == "__main__":

       def 	snake_case__			(    ):



            '''simple docstring'''





            lowercase__    :   Any      =       Matrix(3	,     3	,     0			)
            for i in range(3			):
                 lowercase__    :   str      =       1
            print(f"""a^(-1) is {ainv}"""			)
            # u, v
            lowercase__    :   Optional[Any]      =       Matrix(3	,     1	,     0			)
            lowercase__      , lowercase__      , lowercase__    :   List[Any]      =       1, 2, -3
            lowercase__    :   Union[str, Any]      =       Matrix(3	,     1	,     0			)
            lowercase__      , lowercase__      , lowercase__    :   Any      =       4, -2, 5
            print(f"""u is {u}"""			)
            print(f"""v is {v}"""			)
            print(f"""uv^T is {u * v.transpose()}"""			)
            # Sherman Morrison
            print(f"""(a + uv^T)^(-1) is {ainv.sherman_morrison(SCREAMING_SNAKE_CASE_	,     SCREAMING_SNAKE_CASE_			)}"""			)

       def 	snake_case__			(    ):



            '''simple docstring'''





            import doctest

            doctest.testmod()

       testa()

