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Lemma 2の分岐条件の導出 （Claude.aiと相談しながら得た導出）

目標： $X \to 0$ の近傍で $F(X) \gtrless X$ のどちらが成り立つかを判定し、ゼロ固定点の局所安定性を決める分岐条件を導く。

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準備：登場する関数の定義

$$G(X) := 2\Phi(\sqrt{X}) - 1, \quad g(Y) := G'(Y) = \frac{\phi(\sqrt{Y})}{\sqrt{Y}}$$

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from pyknp import Juman
import torch
from pytorch_transformers import *

config = BertConfig.from_json_file('Japanese_L-12_H-768_A-12_E-30_BPE/bert_config.json')
model = BertForMaskedLM.from_pretrained('Japanese_L-12_H-768_A-12_E-30_BPE/pytorch_model.bin',
                                        config=config)
tokenizer = BertTokenizer('Japanese_L-12_H-768_A-12_E-30_BPE/vocab.txt',
                          do_lower_case=False, do_basic_tokenize=False)

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# -*- coding: utf-8 -*-
from lxml import etree
import os
import sys
from io import TextIOWrapper
from nltk.tokenize import RegexpTokenizer

#
# USAGE:
#

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import sys
import torch
import torch.nn
import torch.nn.functional as F
import torch.optim as optim
from torch.autograd import Variable
import numpy as np
import matplotlib
matplotlib.use('agg')
import matplotlib.pyplot as plt

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import io, sys, math, random
import numpy as np
import matplotlib.pyplot as plt

import torch
import torch.nn
from torch.autograd import Variable
from torch import optim

sys.stdout = io.TextIOWrapper(sys.stdout.buffer, encoding='utf-8')

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import torch
from torch.autograd import Variable
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import axes3d

torch.manual_seed(102)
np.random.seed(22)

fig = plt.figure()