# Copyright 2023 The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import math
import unittest

from parameterized import parameterized

from transformers import GPTBigCodeConfig, is_torch_available
from transformers.testing_utils import cleanup, 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 (
        AutoTokenizer,
        GPT2TokenizerFast,
        GPTBigCodeForCausalLM,
        GPTBigCodeForSequenceClassification,
        GPTBigCodeForTokenClassification,
        GPTBigCodeModel,
    )
    from transformers.models.gpt_bigcode.modeling_gpt_bigcode import GPTBigCodeAttention


class GPTBigCodeModelTester:
    def __init__(
        self,
        parent,
        batch_size=14,
        seq_length=7,
        is_training=True,
        use_token_type_ids=True,
        use_input_mask=True,
        use_labels=True,
        use_mc_token_ids=True,
        vocab_size=99,
        hidden_size=32,
        num_hidden_layers=2,
        num_attention_heads=4,
        intermediate_size=37,
        hidden_act="relu",
        hidden_dropout_prob=0.1,
        attention_probs_dropout_prob=0.1,
        max_position_embeddings=512,
        type_vocab_size=16,
        type_sequence_label_size=2,
        initializer_range=0.02,
        num_labels=3,
        num_choices=4,
        multi_query=True,
        scope=None,
    ):
        self.parent = parent
        self.batch_size = batch_size
        self.seq_length = seq_length
        self.is_training = is_training
        self.use_token_type_ids = use_token_type_ids
        self.use_input_mask = use_input_mask
        self.use_labels = use_labels
        self.use_mc_token_ids = use_mc_token_ids
        self.vocab_size = vocab_size
        self.hidden_size = hidden_size
        self.num_hidden_layers = num_hidden_layers
        self.num_attention_heads = num_attention_heads
        self.intermediate_size = intermediate_size
        self.hidden_act = hidden_act
        self.hidden_dropout_prob = hidden_dropout_prob
        self.attention_probs_dropout_prob = attention_probs_dropout_prob
        self.max_position_embeddings = max_position_embeddings
        self.type_vocab_size = type_vocab_size
        self.type_sequence_label_size = type_sequence_label_size
        self.initializer_range = initializer_range
        self.num_labels = num_labels
        self.num_choices = num_choices
        self.scope = None
        self.bos_token_id = vocab_size - 1
        self.eos_token_id = vocab_size - 2
        self.pad_token_id = vocab_size - 3
        self.multi_query = multi_query

    def prepare_config_and_inputs(
        self, gradient_checkpointing=False, scale_attn_by_inverse_layer_idx=False, reorder_and_upcast_attn=False
    ):
        input_ids = ids_tensor([self.batch_size, self.seq_length], self.vocab_size)

        input_mask = None
        if self.use_input_mask:
            input_mask = random_attention_mask([self.batch_size, self.seq_length])

        token_type_ids = None
        if self.use_token_type_ids:
            token_type_ids = ids_tensor([self.batch_size, self.seq_length], self.type_vocab_size)

        mc_token_ids = None
        if self.use_mc_token_ids:
            mc_token_ids = ids_tensor([self.batch_size, self.num_choices], self.seq_length)

        sequence_labels = None
        token_labels = None
        choice_labels = None
        if self.use_labels:
            sequence_labels = ids_tensor([self.batch_size], self.type_sequence_label_size)
            token_labels = ids_tensor([self.batch_size, self.seq_length], self.num_labels)
            choice_labels = ids_tensor([self.batch_size], self.num_choices)

        config = self.get_config(
            gradient_checkpointing=gradient_checkpointing,
            scale_attn_by_inverse_layer_idx=scale_attn_by_inverse_layer_idx,
            reorder_and_upcast_attn=reorder_and_upcast_attn,
        )

        return (
            config,
            input_ids,
            input_mask,
            token_type_ids,
            mc_token_ids,
            sequence_labels,
            token_labels,
            choice_labels,
        )

    def get_config(
        self, gradient_checkpointing=False, scale_attn_by_inverse_layer_idx=False, reorder_and_upcast_attn=False
    ):
        return GPTBigCodeConfig(
            vocab_size=self.vocab_size,
            n_embd=self.hidden_size,
            n_layer=self.num_hidden_layers,
            n_head=self.num_attention_heads,
            n_inner=self.intermediate_size,
            activation_function=self.hidden_act,
            resid_pdrop=self.hidden_dropout_prob,
            attn_pdrop=self.attention_probs_dropout_prob,
            n_positions=self.max_position_embeddings,
            type_vocab_size=self.type_vocab_size,
            initializer_range=self.initializer_range,
            use_cache=True,
            bos_token_id=self.bos_token_id,
            eos_token_id=self.eos_token_id,
            pad_token_id=self.pad_token_id,
            gradient_checkpointing=gradient_checkpointing,
            scale_attn_by_inverse_layer_idx=scale_attn_by_inverse_layer_idx,
            reorder_and_upcast_attn=reorder_and_upcast_attn,
            attention_softmax_in_fp32=False,
            scale_attention_softmax_in_fp32=False,
            multi_query=self.multi_query,
        )

    def get_pipeline_config(self):
        config = self.get_config()
        config.vocab_size = 300
        return config

    def create_and_check_gpt_bigcode_model(self, config, input_ids, input_mask, token_type_ids, *args):
        model = GPTBigCodeModel(config=config)
        model.to(torch_device)
        model.eval()

        result = model(input_ids, token_type_ids=token_type_ids)
        result = model(input_ids, token_type_ids=token_type_ids)
        result = model(input_ids)

        self.parent.assertEqual(result.last_hidden_state.shape, (self.batch_size, self.seq_length, self.hidden_size))
        self.parent.assertEqual(len(result.past_key_values), config.n_layer)

    def create_and_check_gpt_bigcode_model_past(self, config, input_ids, input_mask, token_type_ids, *args):
        model = GPTBigCodeModel(config=config)
        model.to(torch_device)
        model.eval()

        # first forward pass
        outputs = model(input_ids, token_type_ids=token_type_ids, use_cache=True)
        outputs_use_cache_conf = model(input_ids, token_type_ids=token_type_ids)
        outputs_no_past = model(input_ids, token_type_ids=token_type_ids, use_cache=False)

        self.parent.assertTrue(len(outputs) == len(outputs_use_cache_conf))
        self.parent.assertTrue(len(outputs) == len(outputs_no_past) + 1)

        output, past = outputs.to_tuple()

        # create hypothetical next token and extent to next_input_ids
        next_tokens = ids_tensor((self.batch_size, 1), config.vocab_size)
        next_token_types = ids_tensor([self.batch_size, 1], self.type_vocab_size)

        # append to next input_ids and token_type_ids
        next_input_ids = torch.cat([input_ids, next_tokens], dim=-1)
        next_token_type_ids = torch.cat([token_type_ids, next_token_types], dim=-1)

        output_from_no_past = model(next_input_ids, token_type_ids=next_token_type_ids)["last_hidden_state"]
        output_from_past = model(next_tokens, token_type_ids=next_token_types, past_key_values=past)[
            "last_hidden_state"
        ]

        # select random slice
        random_slice_idx = ids_tensor((1,), output_from_past.shape[-1]).item()
        output_from_no_past_slice = output_from_no_past[:, -1, random_slice_idx].detach()
        output_from_past_slice = output_from_past[:, 0, random_slice_idx].detach()

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

    def create_and_check_gpt_bigcode_model_attention_mask_past(
        self, config, input_ids, input_mask, token_type_ids, *args
    ):
        model = GPTBigCodeModel(config=config)
        model.to(torch_device)
        model.eval()

        # create attention mask
        attn_mask = torch.ones(input_ids.shape, dtype=torch.long, device=torch_device)
        half_seq_length = self.seq_length // 2
        attn_mask[:, half_seq_length:] = 0

        # first forward pass
        output, past = model(input_ids, attention_mask=attn_mask).to_tuple()

        # create hypothetical next token and extent to next_input_ids
        next_tokens = ids_tensor((self.batch_size, 1), config.vocab_size)

        # change a random masked slice from input_ids
        random_seq_idx_to_change = ids_tensor((1,), half_seq_length).item() + 1
        random_other_next_tokens = ids_tensor((self.batch_size, 1), config.vocab_size).squeeze(-1)
        input_ids[:, -random_seq_idx_to_change] = random_other_next_tokens

        # append to next input_ids and attn_mask
        next_input_ids = torch.cat([input_ids, next_tokens], dim=-1)
        attn_mask = torch.cat(
            [attn_mask, torch.ones((attn_mask.shape[0], 1), dtype=torch.long, device=torch_device)],
            dim=1,
        )

        # get two different outputs
        output_from_no_past = model(next_input_ids, attention_mask=attn_mask)["last_hidden_state"]
        output_from_past = model(next_tokens, past_key_values=past, attention_mask=attn_mask)["last_hidden_state"]

        # select random slice
        random_slice_idx = ids_tensor((1,), output_from_past.shape[-1]).item()
        output_from_no_past_slice = output_from_no_past[:, -1, random_slice_idx].detach()
        output_from_past_slice = output_from_past[:, 0, random_slice_idx].detach()

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

    def create_and_check_gpt_bigcode_model_past_large_inputs(
        self, config, input_ids, input_mask, token_type_ids, *args
    ):
        model = GPTBigCodeModel(config=config)
        model.to(torch_device)
        model.eval()

        # first forward pass
        outputs = model(input_ids, token_type_ids=token_type_ids, attention_mask=input_mask, use_cache=True)

        output, past = outputs.to_tuple()

        # create hypothetical next token and extent to next_input_ids
        next_tokens = ids_tensor((self.batch_size, 3), config.vocab_size)
        next_token_types = ids_tensor([self.batch_size, 3], self.type_vocab_size)
        next_mask = ids_tensor((self.batch_size, 3), vocab_size=2)

        # append to next input_ids and token_type_ids
        next_input_ids = torch.cat([input_ids, next_tokens], dim=-1)
        next_token_type_ids = torch.cat([token_type_ids, next_token_types], dim=-1)
        next_attention_mask = torch.cat([input_mask, next_mask], dim=-1)

        output_from_no_past = model(
            next_input_ids, token_type_ids=next_token_type_ids, attention_mask=next_attention_mask
        )["last_hidden_state"]
        output_from_past = model(
            next_tokens, token_type_ids=next_token_types, attention_mask=next_attention_mask, past_key_values=past
        )["last_hidden_state"]
        self.parent.assertTrue(output_from_past.shape[1] == next_tokens.shape[1])

        # select random slice
        random_slice_idx = ids_tensor((1,), output_from_past.shape[-1]).item()
        output_from_no_past_slice = output_from_no_past[:, -3:, random_slice_idx].detach()
        output_from_past_slice = output_from_past[:, :, random_slice_idx].detach()

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

    def create_and_check_lm_head_model(self, config, input_ids, input_mask, token_type_ids, *args):
        model = GPTBigCodeForCausalLM(config)
        model.to(torch_device)
        model.eval()

        result = model(input_ids, token_type_ids=token_type_ids, labels=input_ids)
        self.parent.assertEqual(result.loss.shape, ())
        self.parent.assertEqual(result.logits.shape, (self.batch_size, self.seq_length, self.vocab_size))

    def create_and_check_forward_and_backwards(
        self,
        config,
        input_ids,
        input_mask,
        token_type_ids,
        *args,
    ):
        model = GPTBigCodeForCausalLM(config)
        model.train()
        model.to(torch_device)

        result = model(input_ids, token_type_ids=token_type_ids, labels=input_ids)
        self.parent.assertEqual(result.loss.shape, ())
        self.parent.assertEqual(result.logits.shape, (self.batch_size, self.seq_length, self.vocab_size))
        result.loss.backward()

    def create_and_check_gpt_bigcode_for_sequence_classification(
        self, config, input_ids, input_mask, token_type_ids, mc_token_ids, sequence_labels, *args
    ):
        config.num_labels = self.num_labels
        model = GPTBigCodeForSequenceClassification(config)
        model.to(torch_device)
        model.eval()
        result = model(input_ids, attention_mask=input_mask, token_type_ids=token_type_ids, labels=sequence_labels)
        self.parent.assertEqual(result.logits.shape, (self.batch_size, self.num_labels))

    def create_and_check_gpt_bigcode_for_token_classification(
        self, config, input_ids, input_mask, token_type_ids, mc_token_ids, sequence_labels, *args
    ):
        config.num_labels = self.num_labels
        model = GPTBigCodeForTokenClassification(config)
        model.to(torch_device)
        model.eval()
        result = model(input_ids, attention_mask=input_mask, token_type_ids=token_type_ids)
        self.parent.assertEqual(result.logits.shape, (self.batch_size, self.seq_length, self.num_labels))

    def create_and_check_gpt_bigcode_weight_initialization(self, config, *args):
        model = GPTBigCodeModel(config)
        model_std = model.config.initializer_range / math.sqrt(2 * model.config.n_layer)
        for key in model.state_dict():
            if "c_proj" in key and "weight" in key:
                self.parent.assertLessEqual(abs(torch.std(model.state_dict()[key]) - model_std), 0.001)
                self.parent.assertLessEqual(abs(torch.mean(model.state_dict()[key]) - 0.0), 0.01)

    def prepare_config_and_inputs_for_common(self):
        config_and_inputs = self.prepare_config_and_inputs()

        (
            config,
            input_ids,
            input_mask,
            token_type_ids,
            mc_token_ids,
            sequence_labels,
            token_labels,
            choice_labels,
        ) = config_and_inputs

        inputs_dict = {
            "input_ids": input_ids,
            "token_type_ids": token_type_ids,
        }

        return config, inputs_dict


@require_torch
class GPTBigCodeModelTest(ModelTesterMixin, GenerationTesterMixin, PipelineTesterMixin, unittest.TestCase):
    # TODO: Update the tests to use valid pretrained models.
    all_model_classes = (
        (
            GPTBigCodeModel,
            GPTBigCodeForCausalLM,
            GPTBigCodeForSequenceClassification,
            GPTBigCodeForTokenClassification,
        )
        if is_torch_available()
        else ()
    )
    pipeline_model_mapping = (
        {
            "feature-extraction": GPTBigCodeModel,
            "text-classification": GPTBigCodeForSequenceClassification,
            "text-generation": GPTBigCodeForCausalLM,
            "token-classification": GPTBigCodeForTokenClassification,
            "zero-shot": GPTBigCodeForSequenceClassification,
        }
        if is_torch_available()
        else {}
    )
    test_missing_keys = False

    multi_query = True

    # special case for DoubleHeads model
    def _prepare_for_class(self, inputs_dict, model_class, return_labels=False):
        inputs_dict = super()._prepare_for_class(inputs_dict, model_class, return_labels=return_labels)

        return inputs_dict

    def setUp(self):
        self.model_tester = GPTBigCodeModelTester(self, multi_query=self.multi_query)
        self.config_tester = ConfigTester(self, config_class=GPTBigCodeConfig, n_embd=37)

    def tearDown(self):
        super().tearDown()
        # clean-up as much as possible GPU memory occupied by PyTorch
        cleanup(torch_device)

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

    @unittest.skip(reason="MQA models does not support retain_grad")
    def test_retain_grad_hidden_states_attentions(self):
        pass

    @unittest.skip(reason="CPU offload seems to be broken for some reason - tiny models keep hitting corner cases")
    def test_cpu_offload(self):
        pass

    @unittest.skip(reason="Disk offload seems to be broken for some reason - tiny models keep hitting corner cases")
    def test_disk_offload(self):
        pass

    @unittest.skip(reason="BigCodeGPT has a non-standard KV cache format.")
    def test_past_key_values_format(self):
        pass

    @unittest.skip(reason="BigCodeGPT has a non-standard KV cache format and breaks this test.")
    def test_generate_continue_from_inputs_embeds(self):
        pass

    def test_gpt_bigcode_model(self):
        config_and_inputs = self.model_tester.prepare_config_and_inputs()
        self.model_tester.create_and_check_gpt_bigcode_model(*config_and_inputs)

    def test_gpt_bigcode_model_past(self):
        config_and_inputs = self.model_tester.prepare_config_and_inputs()
        self.model_tester.create_and_check_gpt_bigcode_model_past(*config_and_inputs)

    def test_gpt_bigcode_model_att_mask_past(self):
        config_and_inputs = self.model_tester.prepare_config_and_inputs()
        self.model_tester.create_and_check_gpt_bigcode_model_attention_mask_past(*config_and_inputs)

    def test_gpt_bigcode_model_past_large_inputs(self):
        config_and_inputs = self.model_tester.prepare_config_and_inputs()
        self.model_tester.create_and_check_gpt_bigcode_model_past_large_inputs(*config_and_inputs)

    def test_gpt_bigcode_lm_head_model(self):
        config_and_inputs = self.model_tester.prepare_config_and_inputs()
        self.model_tester.create_and_check_lm_head_model(*config_and_inputs)

    def test_gpt_bigcode_sequence_classification_model(self):
        config_and_inputs = self.model_tester.prepare_config_and_inputs()
        self.model_tester.create_and_check_gpt_bigcode_for_sequence_classification(*config_and_inputs)

    def test_gpt_bigcode_token_classification_model(self):
        config_and_inputs = self.model_tester.prepare_config_and_inputs()
        self.model_tester.create_and_check_gpt_bigcode_for_token_classification(*config_and_inputs)

    def test_gpt_bigcode_scale_attn_by_inverse_layer_idx(self):
        config_and_inputs = self.model_tester.prepare_config_and_inputs(scale_attn_by_inverse_layer_idx=True)
        self.model_tester.create_and_check_forward_and_backwards(*config_and_inputs)

    def test_gpt_bigcode_reorder_and_upcast_attn(self):
        config_and_inputs = self.model_tester.prepare_config_and_inputs(reorder_and_upcast_attn=True)
        self.model_tester.create_and_check_forward_and_backwards(*config_and_inputs)

    def test_gpt_bigcode_weight_initialization(self):
        config_and_inputs = self.model_tester.prepare_config_and_inputs()
        self.model_tester.create_and_check_gpt_bigcode_weight_initialization(*config_and_inputs)


@require_torch
class GPTBigCodeMHAModelTest(GPTBigCodeModelTest):
    # `parameterized_class` breaks with mixins, so we use inheritance instead
    multi_query = False


@slow
@require_torch
class GPTBigCodeModelLanguageGenerationTest(unittest.TestCase):
    def test_generate_simple(self):
        model = GPTBigCodeForCausalLM.from_pretrained("bigcode/gpt_bigcode-santacoder").to(torch_device)
        tokenizer = GPT2TokenizerFast.from_pretrained("bigcode/gpt_bigcode-santacoder")

        input_ids = tokenizer("def print_hello_world():", return_tensors="pt").input_ids.to(torch_device)

        output_sequence = model.generate(input_ids)
        output_sentence = tokenizer.decode(output_sequence[0], skip_special_tokens=True)

        expected_output = 'def print_hello_world():\n    print("Hello World!")\n\n\ndef print_hello_world_with_args(name'  # fmt: skip
        self.assertEqual(output_sentence, expected_output)

    def test_generate_batched(self):
        tokenizer = GPT2TokenizerFast.from_pretrained("bigcode/gpt_bigcode-santacoder")
        tokenizer.pad_token = tokenizer.eos_token
        tokenizer.padding_side = "left"

        model = GPTBigCodeForCausalLM.from_pretrained("bigcode/gpt_bigcode-santacoder").to(torch_device)

        inputs = tokenizer(["def print_hello_world():", "def say_hello():"], return_tensors="pt", padding=True).to(
            torch_device
        )
        outputs = model.generate(**inputs)
        outputs = tokenizer.batch_decode(outputs, skip_special_tokens=True)

        expected_output = [
            'def print_hello_world():\n    print("Hello World!")\n\n\ndef print_hello_world_with_args(name',
            'def say_hello():\n    print("Hello, World!")\n\n\nsay_hello()\n',
        ]
        self.assertListEqual(outputs, expected_output)

    def test_newline_regression(self):
        """Added to prevent regressions regarding attention (scaling) indicated by excessive newlines"""
        tokenizer = AutoTokenizer.from_pretrained("bigcode/tiny_starcoder_py")
        model = GPTBigCodeForCausalLM.from_pretrained("bigcode/tiny_starcoder_py").to(torch_device)

        input_ids = tokenizer(
            "Analyze the impact of the COVID-19 pandemic on global economic structures and future business models.\n",
            return_tensors="pt",
        ).input_ids.to(torch_device)

        output_sequence = model.generate(input_ids, max_new_tokens=20, do_sample=False)
        output_sentence = tokenizer.decode(output_sequence[0], skip_special_tokens=True)

        expected_output = 'Analyze the impact of the COVID-19 pandemic on global economic structures and future business models.\n\nThe impact of the COVID-19 pandemic on global economic structures and future business'  # fmt: skip
        self.assertEqual(output_sentence, expected_output)


@require_torch
class GPTBigCodeMQATest(unittest.TestCase):
    def get_attention(self, multi_query):
        config = GPTBigCodeConfig.from_pretrained(
            "bigcode/gpt_bigcode-santacoder",
            multi_query=multi_query,
            attn_pdrop=0,
            resid_pdrop=0,
        )
        # We need to set it here as it's normally set by the Model's __init__
        config._attn_implementation = "sdpa"
        return GPTBigCodeAttention(config)

    @parameterized.expand([(seed, is_train_mode) for seed in range(5) for is_train_mode in [True, False]])
    def test_mqa_reduces_to_mha(self, seed, is_train_mode=True):
        torch.manual_seed(seed)

        # CREATE MQA AND MHA ATTENTIONS
        attention_mqa = self.get_attention(True)
        attention_mha = self.get_attention(False)

        # ENFORCE MATCHING WEIGHTS
        num_heads = attention_mqa.num_heads
        embed_dim = attention_mqa.embed_dim
        head_dim = attention_mqa.head_dim

        with torch.no_grad():
            mqa_q_weight = attention_mqa.c_attn.weight[:embed_dim, :].view(num_heads, 1, head_dim, embed_dim)
            mqa_kv_weight = attention_mqa.c_attn.weight[embed_dim:, :].view(1, 2, head_dim, embed_dim)
            mha_c_weight = torch.cat(
                [mqa_q_weight, mqa_kv_weight.expand(num_heads, 2, head_dim, embed_dim)], dim=1
            ).view(3 * num_heads * head_dim, embed_dim)

            mqa_q_bias = attention_mqa.c_attn.bias[:embed_dim].view(num_heads, 1, head_dim)
            mqa_kv_bias = attention_mqa.c_attn.bias[embed_dim:].view(1, 2, head_dim)
            mha_c_bias = torch.cat([mqa_q_bias, mqa_kv_bias.expand(num_heads, 2, head_dim)], dim=1).view(
                3 * num_heads * head_dim
            )

            attention_mha.c_attn.weight.copy_(mha_c_weight)
            attention_mha.c_attn.bias.copy_(mha_c_bias)
            attention_mha.c_proj.weight.copy_(attention_mqa.c_proj.weight)
            attention_mha.c_proj.bias.copy_(attention_mqa.c_proj.bias)

        # PUT THE MODEL INTO THE CORRECT MODE
        attention_mha.train(is_train_mode)
        attention_mqa.train(is_train_mode)

        # RUN AN INPUT THROUGH THE MODELS
        num_tokens = 5
        hidden_states = torch.randn(1, num_tokens, embed_dim)
        attention_mha_result = attention_mha(hidden_states)[0]
        attention_mqa_result = attention_mqa(hidden_states)[0]

        # CHECK THAT ALL OUTPUTS ARE THE SAME
        torch.testing.assert_close(attention_mha_result, attention_mqa_result, rtol=1e-5, atol=1e-5)
