tests/models/sam/test_modeling_tf_sam.py

# coding=utf-8
# Copyright 2023 The HuggingFace Inc. 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.
""" Testing suite for the TensorFlow SAM model. """


from __future__ import annotations

import inspect
import unittest

import numpy as np
import requests

from transformers import SamConfig, SamMaskDecoderConfig, SamPromptEncoderConfig, SamVisionConfig
from transformers.testing_utils import require_tf, slow
from transformers.utils import is_tf_available, is_vision_available

from ...test_configuration_common import ConfigTester
from ...test_modeling_tf_common import TFModelTesterMixin, floats_tensor
from ...test_pipeline_mixin import PipelineTesterMixin


if is_tf_available():
    import tensorflow as tf

    from transformers import SamProcessor, TFSamModel

if is_vision_available():
    from PIL import Image


class TFSamPromptEncoderTester:
    def __init__(
        self,
        hidden_size=32,
        input_image_size=24,
        patch_size=2,
        mask_input_channels=4,
        num_point_embeddings=4,
        hidden_act="gelu",
    ):
        self.hidden_size = hidden_size
        self.input_image_size = input_image_size
        self.patch_size = patch_size
        self.mask_input_channels = mask_input_channels
        self.num_point_embeddings = num_point_embeddings
        self.hidden_act = hidden_act

    def get_config(self):
        return SamPromptEncoderConfig(
            image_size=self.input_image_size,
            patch_size=self.patch_size,
            mask_input_channels=self.mask_input_channels,
            hidden_size=self.hidden_size,
            num_point_embeddings=self.num_point_embeddings,
            hidden_act=self.hidden_act,
        )

    def prepare_config_and_inputs(self):
        dummy_points = floats_tensor([self.batch_size, 3, 2])
        config = self.get_config()

        return config, dummy_points


class TFSamMaskDecoderTester:
    def __init__(
        self,
        hidden_size=32,
        hidden_act="relu",
        mlp_dim=64,
        num_hidden_layers=2,
        num_attention_heads=4,
        attention_downsample_rate=2,
        num_multimask_outputs=3,
        iou_head_depth=3,
        iou_head_hidden_dim=32,
        layer_norm_eps=1e-6,
    ):
        self.hidden_size = hidden_size
        self.hidden_act = hidden_act
        self.mlp_dim = mlp_dim
        self.num_hidden_layers = num_hidden_layers
        self.num_attention_heads = num_attention_heads
        self.attention_downsample_rate = attention_downsample_rate
        self.num_multimask_outputs = num_multimask_outputs
        self.iou_head_depth = iou_head_depth
        self.iou_head_hidden_dim = iou_head_hidden_dim
        self.layer_norm_eps = layer_norm_eps

    def get_config(self):
        return SamMaskDecoderConfig(
            hidden_size=self.hidden_size,
            hidden_act=self.hidden_act,
            mlp_dim=self.mlp_dim,
            num_hidden_layers=self.num_hidden_layers,
            num_attention_heads=self.num_attention_heads,
            attention_downsample_rate=self.attention_downsample_rate,
            num_multimask_outputs=self.num_multimask_outputs,
            iou_head_depth=self.iou_head_depth,
            iou_head_hidden_dim=self.iou_head_hidden_dim,
            layer_norm_eps=self.layer_norm_eps,
        )

    def prepare_config_and_inputs(self):
        config = self.get_config()

        dummy_inputs = {
            "image_embedding": floats_tensor([self.batch_size, self.hidden_size]),
        }

        return config, dummy_inputs


class TFSamModelTester:
    def __init__(
        self,
        parent,
        hidden_size=36,
        intermediate_size=72,
        projection_dim=62,
        output_channels=32,
        num_hidden_layers=2,
        num_attention_heads=4,
        num_channels=3,
        image_size=24,
        patch_size=2,
        hidden_act="gelu",
        layer_norm_eps=1e-06,
        dropout=0.0,
        attention_dropout=0.0,
        initializer_range=0.02,
        initializer_factor=1.0,
        qkv_bias=True,
        mlp_ratio=4.0,
        use_abs_pos=True,
        use_rel_pos=True,
        rel_pos_zero_init=False,
        window_size=14,
        global_attn_indexes=[2, 5, 8, 11],
        num_pos_feats=16,
        mlp_dim=None,
        batch_size=2,
    ):
        self.parent = parent
        self.image_size = image_size
        self.patch_size = patch_size
        self.output_channels = output_channels
        self.num_channels = num_channels
        self.hidden_size = hidden_size
        self.projection_dim = projection_dim
        self.num_hidden_layers = num_hidden_layers
        self.num_attention_heads = num_attention_heads
        self.intermediate_size = intermediate_size
        self.dropout = dropout
        self.attention_dropout = attention_dropout
        self.initializer_range = initializer_range
        self.initializer_factor = initializer_factor
        self.hidden_act = hidden_act
        self.layer_norm_eps = layer_norm_eps
        self.qkv_bias = qkv_bias
        self.mlp_ratio = mlp_ratio
        self.use_abs_pos = use_abs_pos
        self.use_rel_pos = use_rel_pos
        self.rel_pos_zero_init = rel_pos_zero_init
        self.window_size = window_size
        self.global_attn_indexes = global_attn_indexes
        self.num_pos_feats = num_pos_feats
        self.mlp_dim = mlp_dim
        self.batch_size = batch_size

        # in ViT, the seq length equals the number of patches + 1 (we add 1 for the [CLS] token)
        num_patches = (image_size // patch_size) ** 2
        self.seq_length = num_patches + 1

        self.prompt_encoder_tester = TFSamPromptEncoderTester()
        self.mask_decoder_tester = TFSamMaskDecoderTester()

    def prepare_config_and_inputs(self):
        pixel_values = floats_tensor([self.batch_size, self.num_channels, self.image_size, self.image_size])
        config = self.get_config()

        return config, pixel_values

    def get_config(self):
        vision_config = SamVisionConfig(
            image_size=self.image_size,
            patch_size=self.patch_size,
            num_channels=self.num_channels,
            hidden_size=self.hidden_size,
            projection_dim=self.projection_dim,
            num_hidden_layers=self.num_hidden_layers,
            num_attention_heads=self.num_attention_heads,
            intermediate_size=self.intermediate_size,
            dropout=self.dropout,
            attention_dropout=self.attention_dropout,
            initializer_range=self.initializer_range,
            initializer_factor=self.initializer_factor,
            output_channels=self.output_channels,
            qkv_bias=self.qkv_bias,
            mlp_ratio=self.mlp_ratio,
            use_abs_pos=self.use_abs_pos,
            use_rel_pos=self.use_rel_pos,
            rel_pos_zero_init=self.rel_pos_zero_init,
            window_size=self.window_size,
            global_attn_indexes=self.global_attn_indexes,
            num_pos_feats=self.num_pos_feats,
            mlp_dim=self.mlp_dim,
        )

        prompt_encoder_config = self.prompt_encoder_tester.get_config()

        mask_decoder_config = self.mask_decoder_tester.get_config()

        return SamConfig(
            vision_config=vision_config,
            prompt_encoder_config=prompt_encoder_config,
            mask_decoder_config=mask_decoder_config,
        )

    def create_and_check_model(self, config, pixel_values):
        model = TFSamModel(config=config)
        result = model(pixel_values)
        self.parent.assertEqual(result.iou_scores.shape, (self.batch_size, 1, 3))
        self.parent.assertEqual(result.pred_masks.shape[:3], (self.batch_size, 1, 3))

    def create_and_check_get_image_features(self, config, pixel_values):
        model = TFSamModel(config=config)
        result = model.get_image_embeddings(pixel_values)
        self.parent.assertEqual(result[0].shape, (self.output_channels, 12, 12))

    def create_and_check_get_image_hidden_states(self, config, pixel_values):
        model = TFSamModel(config=config)
        result = model.vision_encoder(
            pixel_values,
            output_hidden_states=True,
            return_dict=True,
        )

        # after computing the convolutional features
        expected_hidden_states_shape = (self.batch_size, 12, 12, 36)
        self.parent.assertEqual(len(result[1]), self.num_hidden_layers + 1)
        self.parent.assertEqual(result[1][0].shape, expected_hidden_states_shape)

        result = model.vision_encoder(
            pixel_values,
            output_hidden_states=True,
            return_dict=False,
        )

        # after computing the convolutional features
        expected_hidden_states_shape = (self.batch_size, 12, 12, 36)
        self.parent.assertEqual(len(result[1]), self.num_hidden_layers + 1)
        self.parent.assertEqual(result[1][0].shape, expected_hidden_states_shape)

    def prepare_config_and_inputs_for_common(self):
        config_and_inputs = self.prepare_config_and_inputs()
        config, pixel_values = config_and_inputs
        inputs_dict = {"pixel_values": pixel_values}
        return config, inputs_dict


@require_tf
class TFSamModelTest(TFModelTesterMixin, PipelineTesterMixin, unittest.TestCase):
    """
    Here we also overwrite some of the tests of test_modeling_common.py, as SAM's vision encoder does not use input_ids, inputs_embeds,
    attention_mask and seq_length.
    """

    all_model_classes = (TFSamModel,) if is_tf_available() else ()
    pipeline_model_mapping = (
        {"feature-extraction": TFSamModel, "mask-generation": TFSamModel} if is_tf_available() else {}
    )
    test_pruning = False
    test_resize_embeddings = False
    test_head_masking = False
    test_onnx = False

    # TODO: Fix me @Arthur: `run_batch_test` in `tests/test_pipeline_mixin.py` not working
    def is_pipeline_test_to_skip(
        self, pipeline_test_casse_name, config_class, model_architecture, tokenizer_name, processor_name
    ):
        return True

    def setUp(self):
        self.model_tester = TFSamModelTester(self)
        self.vision_config_tester = ConfigTester(self, config_class=SamVisionConfig, has_text_modality=False)
        self.prompt_encoder_config_tester = ConfigTester(
            self,
            config_class=SamPromptEncoderConfig,
            has_text_modality=False,
            num_attention_heads=12,
            num_hidden_layers=2,
        )
        self.mask_decoder_config_tester = ConfigTester(
            self, config_class=SamMaskDecoderConfig, has_text_modality=False
        )

    def test_config(self):
        self.vision_config_tester.run_common_tests()
        self.prompt_encoder_config_tester.run_common_tests()
        self.mask_decoder_config_tester.run_common_tests()

    @unittest.skip(reason="SAM's vision encoder does not use inputs_embeds")
    def test_inputs_embeds(self):
        pass

    def test_model_common_attributes(self):
        config, _ = self.model_tester.prepare_config_and_inputs_for_common()

        for model_class in self.all_model_classes:
            model = model_class(config)
            self.assertIsInstance(model.get_input_embeddings(), (tf.keras.layers.Layer))
            x = model.get_output_embeddings()
            self.assertTrue(x is None or isinstance(x, tf.keras.layers.Dense))

    def test_forward_signature(self):
        config, _ = self.model_tester.prepare_config_and_inputs_for_common()

        for model_class in self.all_model_classes:
            model = model_class(config)
            signature = inspect.signature(model.call)
            # signature.parameters is an OrderedDict => so arg_names order is deterministic
            arg_names = [*signature.parameters.keys()]

            expected_arg_names = ["pixel_values"]
            self.assertListEqual(arg_names[:1], expected_arg_names)

    def test_model(self):
        config_and_inputs = self.model_tester.prepare_config_and_inputs()
        self.model_tester.create_and_check_model(*config_and_inputs)

    def test_get_image_features(self):
        config_and_inputs = self.model_tester.prepare_config_and_inputs()
        self.model_tester.create_and_check_get_image_features(*config_and_inputs)

    def test_image_hidden_states(self):
        config_and_inputs = self.model_tester.prepare_config_and_inputs()
        self.model_tester.create_and_check_get_image_hidden_states(*config_and_inputs)

    def test_attention_outputs(self):
        config, inputs_dict = self.model_tester.prepare_config_and_inputs_for_common()
        config.return_dict = True

        expected_vision_attention_shape = (
            self.model_tester.batch_size * self.model_tester.num_attention_heads,
            196,
            196,
        )
        expected_mask_decoder_attention_shape = (self.model_tester.batch_size, 1, 144, 32)

        for model_class in self.all_model_classes:
            inputs_dict["output_attentions"] = True
            inputs_dict["output_hidden_states"] = False
            config.return_dict = True
            model = model_class(config)
            outputs = model(**self._prepare_for_class(inputs_dict, model_class))

            vision_attentions = outputs.vision_attentions
            self.assertEqual(len(vision_attentions), self.model_tester.num_hidden_layers)

            mask_decoder_attentions = outputs.mask_decoder_attentions
            self.assertEqual(len(mask_decoder_attentions), self.model_tester.mask_decoder_tester.num_hidden_layers)

            # check that output_attentions also work using config
            del inputs_dict["output_attentions"]
            config.output_attentions = True
            model = model_class(config)
            outputs = model(**self._prepare_for_class(inputs_dict, model_class))
            vision_attentions = outputs.vision_attentions
            self.assertEqual(len(vision_attentions), self.model_tester.num_hidden_layers)

            mask_decoder_attentions = outputs.mask_decoder_attentions
            self.assertEqual(len(mask_decoder_attentions), self.model_tester.mask_decoder_tester.num_hidden_layers)

            self.assertListEqual(
                list(vision_attentions[0].shape[-4:]),
                list(expected_vision_attention_shape),
            )

            self.assertListEqual(
                list(mask_decoder_attentions[0].shape[-4:]),
                list(expected_mask_decoder_attention_shape),
            )

    @unittest.skip(reason="Hidden_states is tested in create_and_check_model tests")
    def test_hidden_states_output(self):
        pass

    @slow
    def test_model_from_pretrained(self):
        model = TFSamModel.from_pretrained("facebook/sam-vit-base")  # sam-vit-huge blows out our memory
        self.assertIsNotNone(model)

    def check_pt_tf_outputs(self, tf_outputs, pt_outputs, model_class, tol=5e-4, name="outputs", attributes=None):
        super().check_pt_tf_outputs(
            tf_outputs=tf_outputs,
            pt_outputs=pt_outputs,
            model_class=model_class,
            tol=tol,
            name=name,
            attributes=attributes,
        )


def prepare_image():
    img_url = "https://huggingface.co/ybelkada/segment-anything/resolve/main/assets/car.png"
    raw_image = Image.open(requests.get(img_url, stream=True).raw).convert("RGB")
    return raw_image


def prepare_dog_img():
    img_url = "https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/transformers/model_doc/dog-sam.png"
    raw_image = Image.open(requests.get(img_url, stream=True).raw).convert("RGB")
    return raw_image


@slow
class SamModelIntegrationTest(unittest.TestCase):
    def test_inference_mask_generation_no_point(self):
        model = TFSamModel.from_pretrained("facebook/sam-vit-base")
        processor = SamProcessor.from_pretrained("facebook/sam-vit-base")

        raw_image = prepare_image()
        inputs = processor(images=raw_image, return_tensors="tf")

        outputs = model(**inputs)
        scores = tf.squeeze(outputs.iou_scores)
        masks = outputs.pred_masks[0, 0, 0, 0, :3]
        self.assertTrue(np.allclose(scores[-1].numpy(), np.array(0.4515), atol=2e-4))
        self.assertTrue(np.allclose(masks.numpy(), np.array([-4.1807, -3.4949, -3.4483]), atol=1e-2))

    def test_inference_mask_generation_one_point_one_bb(self):
        model = TFSamModel.from_pretrained("facebook/sam-vit-base")
        processor = SamProcessor.from_pretrained("facebook/sam-vit-base")

        raw_image = prepare_image()
        input_boxes = [[[650, 900, 1000, 1250]]]
        input_points = [[[820, 1080]]]

        inputs = processor(images=raw_image, input_boxes=input_boxes, input_points=input_points, return_tensors="tf")

        outputs = model(**inputs)
        scores = tf.squeeze(outputs.iou_scores)
        masks = outputs.pred_masks[0, 0, 0, 0, :3]

        self.assertTrue(np.allclose(scores[-1], np.array(0.9566), atol=2e-4))
        self.assertTrue(np.allclose(masks.numpy(), np.array([-12.7657, -12.3683, -12.5985]), atol=2e-2))

    def test_inference_mask_generation_batched_points_batched_images(self):
        model = TFSamModel.from_pretrained("facebook/sam-vit-base")
        processor = SamProcessor.from_pretrained("facebook/sam-vit-base")

        raw_image = prepare_image()
        input_points = [
            [[[820, 1080]], [[820, 1080]], [[820, 1080]], [[820, 1080]]],
            [[[510, 1080]], [[820, 1080]], [[820, 1080]], [[820, 1080]]],
        ]

        inputs = processor(images=[raw_image, raw_image], input_points=input_points, return_tensors="tf")

        outputs = model(**inputs)
        scores = tf.squeeze(outputs.iou_scores)
        masks = outputs.pred_masks[0, 0, 0, 0, :3]

        EXPECTED_SCORES = np.array(
            [
                [
                    [0.6765, 0.9379, 0.8803],
                    [0.6765, 0.9379, 0.8803],
                    [0.6765, 0.9379, 0.8803],
                    [0.6765, 0.9379, 0.8803],
                ],
                [
                    [0.3317, 0.7264, 0.7646],
                    [0.6765, 0.9379, 0.8803],
                    [0.6765, 0.9379, 0.8803],
                    [0.6765, 0.9379, 0.8803],
                ],
            ]
        )
        EXPECTED_MASKS = np.array([-2.8552, -2.7990, -2.9612])
        self.assertTrue(np.allclose(scores.numpy(), EXPECTED_SCORES, atol=1e-3))
        self.assertTrue(np.allclose(masks.numpy(), EXPECTED_MASKS, atol=3e-2))

    def test_inference_mask_generation_one_point_one_bb_zero(self):
        model = TFSamModel.from_pretrained("facebook/sam-vit-base")
        processor = SamProcessor.from_pretrained("facebook/sam-vit-base")

        raw_image = prepare_image()
        input_boxes = [[[620, 900, 1000, 1255]]]
        input_points = [[[820, 1080]]]
        labels = [[0]]

        inputs = processor(
            images=raw_image,
            input_boxes=input_boxes,
            input_points=input_points,
            input_labels=labels,
            return_tensors="tf",
        )

        outputs = model(**inputs)
        scores = tf.squeeze(outputs.iou_scores)
        self.assertTrue(np.allclose(scores[-1].numpy(), np.array(0.7894), atol=1e-4))

    def test_inference_mask_generation_one_point(self):
        model = TFSamModel.from_pretrained("facebook/sam-vit-base")
        processor = SamProcessor.from_pretrained("facebook/sam-vit-base")

        raw_image = prepare_image()

        input_points = [[[400, 650]]]
        input_labels = [[1]]

        inputs = processor(images=raw_image, input_points=input_points, input_labels=input_labels, return_tensors="tf")

        outputs = model(**inputs)
        scores = tf.squeeze(outputs.iou_scores)

        self.assertTrue(np.allclose(scores[-1], np.array(0.9675), atol=1e-4))

        # With no label
        input_points = [[[400, 650]]]

        inputs = processor(images=raw_image, input_points=input_points, return_tensors="tf")

        outputs = model(**inputs)
        scores = tf.squeeze(outputs.iou_scores)

        self.assertTrue(np.allclose(scores[-1].numpy(), np.array(0.9675), atol=1e-4))

    def test_inference_mask_generation_two_points(self):
        model = TFSamModel.from_pretrained("facebook/sam-vit-base")
        processor = SamProcessor.from_pretrained("facebook/sam-vit-base")
        raw_image = prepare_image()

        input_points = [[[400, 650], [800, 650]]]
        input_labels = [[1, 1]]

        inputs = processor(images=raw_image, input_points=input_points, input_labels=input_labels, return_tensors="tf")

        outputs = model(**inputs)
        scores = tf.squeeze(outputs.iou_scores)

        self.assertTrue(np.allclose(scores[-1].numpy(), np.array(0.9762), atol=1e-4))

        # no labels
        inputs = processor(images=raw_image, input_points=input_points, return_tensors="tf")

        outputs = model(**inputs)
        scores = tf.squeeze(outputs.iou_scores)

        self.assertTrue(np.allclose(scores[-1].numpy(), np.array(0.9762), atol=1e-4))

    def test_inference_mask_generation_two_points_batched(self):
        model = TFSamModel.from_pretrained("facebook/sam-vit-base")
        processor = SamProcessor.from_pretrained("facebook/sam-vit-base")

        raw_image = prepare_image()

        input_points = [[[400, 650], [800, 650]], [[400, 650]]]
        input_labels = [[1, 1], [1]]

        inputs = processor(
            images=[raw_image, raw_image], input_points=input_points, input_labels=input_labels, return_tensors="tf"
        )

        outputs = model(**inputs)
        scores = tf.squeeze(outputs.iou_scores)

        self.assertTrue(np.allclose(scores[0][-1].numpy(), np.array(0.9762), atol=1e-4))
        self.assertTrue(np.allclose(scores[1][-1], np.array(0.9637), atol=1e-4))

    def test_inference_mask_generation_one_box(self):
        model = TFSamModel.from_pretrained("facebook/sam-vit-base")
        processor = SamProcessor.from_pretrained("facebook/sam-vit-base")

        raw_image = prepare_image()

        input_boxes = [[[75, 275, 1725, 850]]]

        inputs = processor(images=raw_image, input_boxes=input_boxes, return_tensors="tf")

        outputs = model(**inputs)
        scores = tf.squeeze(outputs.iou_scores)

        self.assertTrue(np.allclose(scores[-1].numpy(), np.array(0.7937), atol=1e-4))

    def test_inference_mask_generation_batched_image_one_point(self):
        model = TFSamModel.from_pretrained("facebook/sam-vit-base")
        processor = SamProcessor.from_pretrained("facebook/sam-vit-base")

        raw_image = prepare_image()
        raw_dog_image = prepare_dog_img()

        input_points = [[[820, 1080]], [[220, 470]]]

        inputs = processor(images=[raw_image, raw_dog_image], input_points=input_points, return_tensors="tf")

        outputs = model(**inputs)
        scores_batched = tf.squeeze(outputs.iou_scores)

        input_points = [[[220, 470]]]

        inputs = processor(images=raw_dog_image, input_points=input_points, return_tensors="tf")

        outputs = model(**inputs)
        scores_single = tf.squeeze(outputs.iou_scores)
        self.assertTrue(np.allclose(scores_batched[1, :].numpy(), scores_single.numpy(), atol=1e-4))

    def test_inference_mask_generation_two_points_point_batch(self):
        model = TFSamModel.from_pretrained("facebook/sam-vit-base")
        processor = SamProcessor.from_pretrained("facebook/sam-vit-base")

        raw_image = prepare_image()

        # fmt: off
        input_points = tf.convert_to_tensor([[[400, 650]], [[220, 470]]])
        # fmt: on

        input_points = tf.expand_dims(input_points, 0)

        inputs = processor(raw_image, input_points=input_points, return_tensors="tf")

        outputs = model(**inputs)

        iou_scores = outputs.iou_scores
        self.assertTrue(iou_scores.shape == (1, 2, 3))
        self.assertTrue(
            np.allclose(
                iou_scores.numpy(),
                np.array([[[0.9105, 0.9825, 0.9675], [0.7646, 0.7943, 0.7774]]]),
                atol=1e-4,
                rtol=1e-4,
            )
        )

    def test_inference_mask_generation_three_boxes_point_batch(self):
        model = TFSamModel.from_pretrained("facebook/sam-vit-base")
        processor = SamProcessor.from_pretrained("facebook/sam-vit-base")

        raw_image = prepare_image()

        # fmt: off
        input_boxes = tf.convert_to_tensor([[[620, 900, 1000, 1255]], [[75, 275, 1725, 850]],  [[75, 275, 1725, 850]]])
        EXPECTED_IOU = np.array([[[0.9773, 0.9881, 0.9522],
         [0.5996, 0.7661, 0.7937],
         [0.5996, 0.7661, 0.7937]]])
        # fmt: on
        input_boxes = tf.expand_dims(input_boxes, 0)

        inputs = processor(raw_image, input_boxes=input_boxes, return_tensors="tf")

        outputs = model(**inputs)

        iou_scores = outputs.iou_scores
        self.assertTrue(iou_scores.shape == (1, 3, 3))
        self.assertTrue(np.allclose(iou_scores.numpy(), EXPECTED_IOU, atol=1e-4, rtol=1e-4))