from __future__ import division#让/恢复为除法 import pandas import tkinter,tkinter.messagebox from tkinter.filedialog import asksaveasfile import tkinter.messagebox import sympy def Bool(n,p=False): f = ['0','n','no','NO','NOT','No','Not','不'] t = ['y', 'yes', 'Yes','YES', '不'] if p: t.append('') else: f.append('') try: _n = str(n) if _n in f: return False elif _n in t: return True except: pass return bool(n) class HS_CSV: def __init__(self,HS,name,view): if len(HS[0]) != len(HS[1]):raise Exception#个数不相等报错 print(HS) #筛查可以数字化的结果 _x = [] _y = [] for i in range(len(HS[0])):#检查 try: a_x = float(HS[0][i]) a_y = float(HS[1][i]) _x.append(a_x) _y.append(a_y) except: pass print(_x) print(_y) Iter_X = _x Iter_X = sorted(list(set(Iter_X)))#排序并且去除重复 #筛查重复 x = [] y = [] for n_x in Iter_X: try: y.append(_y[_x.index(n_x)]) x.append(n_x) except: pass print(x) print(y) #函数基本信息 self.Func_Name = name#这个是函数名字 self.View = view#绘制样式 #函数基本数据，相当于Lambda的Cul self.__x = x self.__y = y self.__ya = y self.__xy = [] self.__fx = [] self.__fy = [] for i in range(len(self.__x)): self.__xy.append(f'x:{self.__x[i]},y:{self.__y[i]}') self.__xyCSV = pandas.DataFrame((self.__x,self.__y),index=('x','y')) #函数记忆数据 self.Memore_x = [] self.Memore_y = [] self.__MemoryAnswer = [] self.YC = False self.Best_R = None self.HaveDone = False self.max_y = None self.max_x = [] self.min_y = None self.min_x = [] def __call__(self,x): return self.__y[self.__x.index(x)] def __str__(self): return f'{self.Func_Name}' def __Best_value(self): # 计算最值和极值点 if not self.HaveDone: self.Cul() # 检查Cul的计算 y = self.__y + self.Memore_y x = self.__x + self.Memore_x max_y = max(y) min_y = min(y) max_x = Find(x.copy(),y.copy(),max_y) self.max_y = max_y self.max_x = max_x min_x = Find(x.copy(),y.copy(),min_y) self.min_y = min_y self.min_x = min_x return self.max_x, self.max_y, self.min_x, self.min_y def Cul(self): if self.HaveDone:return self.__x,self.__y,self.Func_Name,self.View self.__fx = [[]] self.__fy = [[]] o_y = None p = None#单调性 0-增，1-减 _p = 1 try: for a_x in self.__x: c = 0 p2 = 1 try: y = self(a_x) if o_y != None and o_y > y: _p = 1 elif o_y != None and o_y < y: _p = 0 elif o_y != None and o_y == y: try: z_x = round(a_x - 0.5 * self.kd) z_y = self(z_x) if z_y == o_y == y: # 真实平衡 p2 = 2 elif abs(z_y - o_y) >= 10 * self.kd or abs(z_y - y) >= 10 * self.kd: p2 = 3 c += 5 except: p2 = 4 c += 9 _p = 2 if o_y != None and p != _p: if (o_y * y) < 0: c += 5 elif abs(o_y - y) >= (10 * self.kd): c += 5 if c >= 5 and (_p != 2 or p2 != 2): reason.append(c) self.__fx.append([]) self.__fy.append([]) p = _p self.__fx[-1].append(a_x) self.__fy[-1].append(y) o_y = y except: pass except (TypeError, IndexError, ValueError): pass newfx = [] newfy = [] must = False for i in range(len(self.__fx)): # 去除只有单个的组群 if len(self.__fx[i]) == 1: # 检测到有单个群组 q_r = reason[i] # 前原因 b_r = reason[i] # 后原因 if q_r < b_r: # 前原因小于后原因，连接到前面 try: newfx[-1] += self.__fx[i] newfy[-1] += self.__fy[i] except: # 按道理不应该出现这个情况 newfx.append(self.__fx[i]) newfy.append(self.__fy[i]) else: newfx.append(self.__fx[i]) newfy.append(self.__fy[i]) must = True else: if not must: newfx.append(self.__fx[i]) newfy.append(self.__fy[i]) else: newfx[-1] += self.__fx[i] newfy[-1] += self.__fy[i] must = False self.__fx = newfx self.__fy = newfy self.HaveDone = True self.__xyCSV = pandas.DataFrame((self.__x,self.__y),index=('x','y')) self.__Best_value() return self.__x,self.__y,self.Func_Name,self.View def Iterative_method_Of_Huan(self, y_in, *args,**kwargs):#保持和下一个对象相同参数 r = self.Cul_dichotomy(y_in) return r[0],r[0][0]# def Cul_dichotomy(self, y_in, *args,**kwargs):#保持和下一个对象相同参数 y = sorted(self.__y.copy()) o_y = None#o_y是比较小的，i是比较大的 q = None for i in y: try: if (o_y < y_in and i > y_in) and (abs(((i + o_y)/2) - y_in) < 0.1): q = [o_y,i] break except: pass o_y = i if q == None: for i in y: try: if abs(((i + o_y) / 2) - y_in) < 0.1: q = [o_y, i] break except: pass o_y = i if q == None:return [],[] X_o_y = Find(self.__x.copy(),self.__y.copy(),q[0]) X_y = Find(self.__x.copy(),self.__y.copy(),q[1]) l = min([len(X_y),len(X_o_y)]) answer = [] X_out = [] for i in range(l): print(X_y[i],X_o_y[i]) r = (X_y[i] + X_o_y[i])/2 print(r) self.Memore_x.append(r) self.Memore_y.append(y_in) X_out.append(r) answer.append(f'y={y_in} -> x={r}') self.__MemoryAnswer += answer return answer,X_out def __Parity(self,ro=False): if not self.HaveDone: self.Cul() # 检查Cul的计算 y = self.__y.copy() x = self.__x.copy() a = sorted(x)[0] b = sorted(x)[1] a = -min([abs(a),abs(b)]) b = -a flat = None#0-偶函数，1-奇函数 for i in range(len(x)): _x = x[i]#正项x if _x < a or _x > b:continue#x不在区间内 try: _y = self(_x) o_y = self(-_x) if o_y == _y == 0: continue elif o_y == _y: if flat == None: flat = 0 elif flat == 1: raise Exception elif o_y == -_y: if flat == None: flat = 1 elif flat == 0: raise Exception else: raise Exception except: flat = None break return flat,[a,b] def __Monotonic(self): if not self.HaveDone: self.Cul() # 运行Cul计算 fy = self.__fy.copy() fx = self.__fx.copy() Increase_interval = []#增区间 Minus_interval = []#减区间 Interval = []#不增不减 for i in range(len(fx)): x = fx[i] y = fx[i] o_x = None o_y = None start_x = None flat = None#当前研究反围:0-增区间,1-减区间,2-不增不减 for i in range(len(x)): _x = x[i]#正项x _y = y[i]#正项y if start_x == None: start_x = _x else: if o_y > _y:#减区间 if flat == None or flat == 1:#减区间 pass elif flat == 0:#增区间 Increase_interval.append((start_x,o_x)) start_x = o_x elif flat == 2: Interval.append((start_x, o_x)) start_x = o_x flat = 1 elif o_y < _y:#增区间 if flat == None or flat == 0: # 增区间 pass elif flat == 1: # 减区间 Minus_interval.append((start_x, o_x)) start_x = o_x elif flat == 2: Interval.append((start_x, o_x)) start_x = o_x flat = 0 else:#水平区间 if flat == None or flat == 2: pass elif flat == 1: # 减区间 Minus_interval.append((start_x, o_x)) start_x = o_x elif flat == 0: # 增区间 Increase_interval.append((start_x, o_x)) start_x = o_x flat = 2 o_x = _x o_y = _y if flat == 2: Interval.append((start_x, o_x)) elif flat == 1: # 减区间 Minus_interval.append((start_x, o_x)) elif flat == 0: # 增区间 Increase_interval.append((start_x, o_x)) return Increase_interval,Minus_interval,Interval def Nature(self,addNews=lambda x:x): answer = [] P = self.__Parity() M = self.__Monotonic() ZQ = self.Periodic(addNews)[0] DCZ = self.Symmetry_axis(addNews)[0] DCZX = self.Center_of_symmetry(addNews)[0] if P[0] == 1: answer.append(f'奇函数 区间:[{P[1][0]},{P[1][0]}]') elif P[0] == 0: answer.append(f'偶函数 区间:[{P[1][0]},{P[1][0]}]') for i in M[0]: answer.append(f'增区间:[{i[0]},{i[1]}]') for i in M[1]: answer.append(f'减区间:[{i[0]},{i[1]}]') for i in M[2]: answer.append(f'水平区间:[{i[0]},{i[1]}]') if ZQ != None: answer.append(f'最小正周期：{ZQ}') if DCZ != None: answer.append(f'对称轴：x={DCZ}') if DCZX != None: answer.append(f'对称中心：{DCZX}') return answer def YC_On_Off(self): if self.YC: if tkinter.messagebox.askokcancel('提示', f'是否显示{self}的记忆数据？'): # addNews('记忆显示完毕') self.YC = False else: if tkinter.messagebox.askokcancel('提示', f'是否隐藏{self}的记忆数据？'): # addNews('记忆隐藏完毕') self.YC = True def Out(self): if not self.HaveDone: self.Cul() # 检查Cul的计算 if tkinter.messagebox.askokcancel('提示', f'是否确认导出函数:\n{str(self)}'): try: Dic = tkinter.filedialog.asksaveasfilename(title='选择导出位置', filetypes=[("CSV", ".csv")]) + '.csv' if Dic == '.csv':raise Exception self.__xyCSV.to_csv(Dic) return True except: pass return False def returnList(self): # 最值和极值点设计 # if not self.HaveDone: self.Cul() # 检查Cul的计算 a = [] for i in self.min_x: a.append(f'极值点：{i}>最小值{self.min_y}') for i in self.max_x: a.append(f'极值点：{i}>最大值{self.max_y}') return a + self.__MemoryAnswer +self.__xy def Best_value(self): if not self.HaveDone: self.Cul() # 检查Cul的计算 return self.max_x, self.max_y, self.min_x, self.min_y def getMemory(self): if self.YC: return [], [] return self.Memore_x, self.Memore_y def Clear_Memory(self): self.Memore_x = [] self.Memore_y = [] self.__MemoryAnswer = [] def Draw_Cul(self): if not self.HaveDone:self.Cul() return self.__fx,self.__fy,self.Func_Name,self.View def Cul_Y(self,x_in): answer = [] for i in x_in: try: i = float(i) y = self(i) answer.append(f'x={i} -> y={y}') if i not in self.Memore_x: self.Memore_x.append(i) self.Memore_y.append(y) except:#捕捉运算错误 continue self.__MemoryAnswer += answer self.__Best_value() return answer def Periodic(self,addNews=lambda x:x):#计算周期 if not tkinter.messagebox.askokcancel('提示', f'计算周期需要一定时间，是否执行？(计算过程程序可能无响应)'): return None,[]#无结果 if not self.HaveDone: self.Cul() p = []#可能的周期 ran = len(self.__x) k = int(ran/20) addNews('正在预测可能的周期') for i in range(0,ran,k): start = self.__x[i] try: y = self(start) x_list = self.Cul_dichotomy(y)[1] # print(x_list) q = [] for o_x in x_list: a = abs(o_x - start) if a == 0:continue if a:q.append(a) p.extend(list(set(q))) except: pass p_c = list(set(p)) a = []#a的可能列表 c = 0 addNews('正在筛选结果') for i in p_c: n_c = p.count(i) if n_c > c: a = [i] c = n_c elif n_c == c: a.append(i) try: a.sort()# addNews('计算完毕') return a[0],a except: addNews('无周期') return None,[]#无结果 def Symmetry_axis(self,addNews=lambda x:x):#计算对称轴 if not tkinter.messagebox.askokcancel('提示', f'计算对称轴需要一定时间，是否执行？(计算过程程序可能无响应)'): return None,[]#无结果 if not self.HaveDone: self.Cul() p = []#可能的对称轴 ran = len(self.__x) k = int(ran / 20) addNews('正在预测可能的对称轴') for i in range(0, ran, k): start = self.__x[i] try: y = self(start) x_list = self.Cul_dichotomy(y)[1] print(x_list) q = [] for o_x in x_list: a = (o_x + start)/2 if a:q.append(a) p.extend(list(set(q))) except: pass p_c = list(set(p)) a = []#a的可能列表 c = 0 addNews('正在筛选结果') for i in p_c: n_c = p.count(i) if n_c > c: a = [i] c = n_c elif n_c == c: a.append(i) try: a.sort() # addNews('计算完毕') return a[0], a except: addNews('无对称轴') return None, [] # 无结果 def Center_of_symmetry(self,addNews=lambda x:x): # 计算对称中心 if not tkinter.messagebox.askokcancel('提示', f'计算对称中心需要一定时间，是否执行？(计算过程程序可能无响应)'): return None, [] # 无结果 if not self.HaveDone: self.Cul() point = [] # 可能的对称轴 ran = len(self.__x) k = int(ran / 20) addNews('正在计算坐标点') for i in range(0, ran, k): start = self.__x[i] try: y = self(start) x = start point.append((x,y)) except: pass p = [] addNews('正在预测对称中心') for i in point: for o in point: x = i[0] + o[0] / 2 y = i[1] + o[1] / 2 if i == o:continue # print(f'i={i},o={o},x={x},y={y}') p.append((x,y)) p_c = list(set(p)) a = [] # a的可能列表 c = 0 addNews('正在筛选结果') for i in p_c: n_c = p.count(i) if n_c > c: a = [i] c = n_c elif n_c == c: a.append(i) try: if c < 5:raise Exception addNews('计算完毕') a.sort() # return a[int(len(a)/2)], a except: addNews('无对称中心') return None, [] # 无结果 class HS_lambda: def __init__(self,HS,name,view,start = -10,end = 10,kd = 0.1,JD = 2,a = 1,a_start=-10,a_end=10,a_kd=1,c_Son = False): self.x = sympy.Symbol('x') Name = {'a':a,'x': self.x, 'Pi': sympy.pi, 'e': sympy.E, 'log': sympy.log, 'sin': sympy.sin, 'cos': sympy.cos, 'tan': sympy.tan, 'cot': lambda x: 1 / sympy.tan(x), 'csc': lambda x: 1 / sympy.sin(x), 'sec': lambda x: 1 / sympy.cos(x), 'sinh': sympy.sinh, 'cosh': sympy.cosh, 'tanh': sympy.tanh, 'asin': sympy.asin, 'acos': sympy.acos, 'atan': sympy.atan,'abs':abs} # 这个是函数命名域 self.HS = eval(HS.replace(' ', ''), Name)#函数解析式 self.str_HS = HS.replace(' ', '') #函数基本信息 self.View = view#绘制样式 #数据辨析 try: start = float(start) end = float(end) if start > end:#使用float确保输入是数字，否则诱发ValueError start, end = end, start kd = abs(float(kd)) start = (start//kd)*kd#确保start可以恰好被kd整除 end = (end//kd+1)*kd JD = abs(int(JD)) if JD >= 3:JD = 3 except ValueError: start,end,kd,JD = -10,10,0.1,2#保底设置 #基本数据存储 self.JD = JD self.start = start self.end = end self.kd = kd #x和y数据存储 self.__x = [] self.__y = [] self.__ya = [] self.__fx = [[]] self.__fy = [[]] #记忆数据存储 self.Memore_x = [] self.Memore_y = [] self.__MemoryAnswer = [] #最值和极值点 self.max_y = None self.max_x = [] self.min_y = None self.min_x = [] self.YC = False self.Best_R = None#是否计算最值 self.HaveDone = False#是否已经计算过xy #函数求导 try: self.DHS = sympy.diff(self.HS, self.x) except: self.DHS = None #儿子函数 try: a_start = float(a_start) a_end = float(a_end) if a_start > a_end:#使用float确保输入是数字，否则诱发ValueError a_start, a_end = a_end, a_start a_kd = abs(float(a_kd)) except ValueError: a_start,a_end,a_kd = -10,10,1#保底设置 if c_Son: self.Son_List = [] while a_start <= a_end: try: self.Son_List.append(HS_lambda_Son(HS,name,view,start,end,kd,JD,a_start)) except:pass#不应该出现 a_start += a_kd self.Func_Name = f'{name}:y={HS} a={a}({a_start},{a_end},{a_kd})' # 这个是函数名字 else: self.Son_List = [] self.Func_Name = f'{name}:y={HS} a={a})' # 这个是函数名字 def Return_Son(self): return self.Son_List def __call__(self,x): return self.HS.subs({self.x:x}) def __str__(self): return f'{self.Func_Name} {self.start,self.end,self.kd}' def __Best_value(self):#计算最值和极值点 #使用ya解决了因计算器误差而没计算到的最值，但是同时本不是最值的与最值相近的数字也被当为了最值，所以使用群组击破 if not self.HaveDone: self.Cul()#检查Cul的计算 if len(self.__fx) != 1:#没有计算的必要 if self.Best_R == None: self.Best_R = not tkinter.messagebox.askokcancel('建议不计算最值', f'{self}的最值计算不精确，函数可能无最值，是否不计算最值') if not self.Best_R: pass return self.max_x,self.max_y,self.min_x,self.min_y y = self.__ya + self.Memore_y#x和y数据对齐(因为是加法，所以y的修改不影响self.__ya) _y = self.__y + self.Memore_y x = self.__x + self.Memore_x max_y = max(y) min_y = min(y) max_x = Find(x.copy(),y,max_y) min_x = Find(x.copy(),y,min_y) #处理最大值极值点重复 max_x = sorted(list(set(max_x)))#处理重复 n = [] o_a = None flat = False b = max_x.copy() #可处理列表 for i in range(len(max_x)): #迭代选择 g_a = max_x[i] if o_a == None or abs(g_a - o_a) >= 1:#1-连续系数 flat = False else: if flat:#加入群组 n[-1].append(g_a) else:#新键群组 n.append([o_a, g_a]) del b[b.index(o_a)] flat = True del b[b.index(g_a)]#删除可处理列表 o_a = g_a for i in n:#逐个攻破群组 y_For_X = []#群组中x的y值 for Qx in i: num = x.index(Qx) y_For_X.append(_y[num])#找到对应y值 n_max = max(y_For_X)#求解最大y值 n_x = Find(i,y_For_X,n_max) n_max_x = n_x[int(len(n_x)/2)] b.append(n_max_x)#取中间个 self.max_y = max_y self.max_x = b # 处理最小值极值点重复 min_x = sorted(list(set(min_x))) # 处理重复 n = [] o_a = None flat = False b = min_x.copy() # 可处理列表 for i in range(len(min_x)): # 迭代选择 g_a = min_x[i] if o_a == None or abs(g_a - o_a) >= 1: # 1-连续系数 flat = False else: if flat: # 加入群组 n[-1].append(g_a) else: # 新键群组 n.append([o_a, g_a]) del b[b.index(o_a)] flat = True del b[b.index(g_a)] # 删除可处理列表 o_a = g_a for i in n: # 逐个攻破群组 y_For_X = [] # 群组中x的y值 for Qx in i: num = x.index(Qx) y_For_X.append(_y[num]) # 找到对应y值 n_min = min(y_For_X) # 求解最大y值 n_x = Find(i,y_For_X,n_min) n_min_x = n_x[int(len(n_x) / 2)] b.append(n_min_x) # 取中间个 self.min_y = min_y self.min_x = b return self.max_x,self.max_y,self.min_x,self.min_y def Cul(self,it=float): if self.HaveDone: return self.__x,self.__y,self.Func_Name,self.View #混合存储 self.__y = [] self.__ya = [] self.__x = [] self.__xy = [] self.__fx = [[]] self.__fy = [[]] reason = [30] o_y = None p = None#单调性 0-增，1-减 _p = 1 try: a = int(self.start) while a <= int(self.end): # 因为range不接受小数 p2 = 1 try: c = 0 a_x = round(a, self.JD) y = self(a_x) y = it(y)#数字处理方案 a_y=round(y,self.JD) if o_y != None and o_y > y: _p = 1 elif o_y != None and o_y < y: _p = 0 elif o_y != None and o_y == y: try: z_x = round(a_x - 0.5 * self.kd) z_y = self(z_x) if z_y == o_y == y: # 真实平衡 p2 = 2 elif abs(z_y - o_y) >= 10 * self.kd or abs(z_y - y) >= 10 * self.kd: p2 = 3 c += 5 except: p2 = 4 c += 9 _p = 2 if o_y != None and p != _p: if (o_y * y) < 0: c += 5 elif abs(o_y - y) >= (10 * self.kd): c += 5 if c >= 5 and (_p != 2 or p2 != 2): reason.append(c) self.__fx.append([]) self.__fy.append([]) p = _p self.__x.append(a_x)#四舍五入减少计算量 self.__y.append(y)#不四舍五入 self.__ya.append(a_y) # 四舍五入(用于求解最值) self.__xy.append(f'x:{a_x},y:{a_y}') self.__fx[-1].append(a_x) self.__fy[-1].append(y) o_y = y except: reason.append(0) self.__fx.append([]) self.__fy.append([]) a += self.kd except (TypeError, IndexError, ValueError): pass newfx = [] newfy = [] must = False for i in range(len(self.__fx)):#去除只有单个的组群 if len(self.__fx[i]) <= 1:#检测到有单个群组 q_r = reason[i]#前原因 b_r = reason[i]#后原因 if q_r < b_r:#前原因小于后原因，连接到前面 try: newfx[-1] += self.__fx[i] newfy[-1] += self.__fy[i] except:#按道理不应该出现这个情况 newfx.append(self.__fx[i]) newfy.append(self.__fy[i]) else: newfx.append(self.__fx[i]) newfy.append(self.__fy[i]) must = True else: if not must: newfx.append(self.__fx[i]) newfy.append(self.__fy[i]) else: newfx[-1] += self.__fx[i] newfy[-1] += self.__fy[i] must = False self.__fx = newfx self.__fy = newfy self.HaveDone = True self.__xyCSV = pandas.DataFrame((self.__x,self.__y),index=('x','y')) self.__Best_value() return self.__x,self.__y,self.Func_Name,self.View def Iterative_method_Of_Huan(self,y_in,start,end,k=100,kx=0.00001):#梯度计算(kx表示精度) try: y_in = float(y_in) start = float(start) end = float(end) except: return '',None try: k = int(k) kx = float(kx) except: k = 100 kx = 0.00001 a = start b = end o_a = [] o_b = [] c = 0 o_c = None _a = 0 _b = 0 _c = 0 flat = 0#收缩方向1=a往b，2=b往a，0=未知 p = 0#增or减 q = 0#增减预测1增，0减 for i in range(k): #a,b,c确定 if a > b: a, b = b, a # a是小的数字，b是大的数字，c是中间 o_a.append(a)#赋值a的回退值 o_b.append(b) c = (a + b) / 2 _a = self(a) _b = self(b) _c = self(c) #增减预测 if abs(_c - y_in) x={c}') print(f'y={y_in} -> x={c}',c) return f'y={y_in} -> x={c}',c def Cul_dichotomy(self, y_in, k=100, d=0.0001, ky=0.1, dx=0.5, r_Cul=False,H_Cul=True, deep=1000, cx=0.1, kx=0.1,f_On=False,f=None,all=False): #y_in输入的参数,k最大迭代数,r_Cul允许使用原来的数值,d精度,ky最值允许偏移量,kx新区间偏移量,cx扩张限制,dx两零点的最小范围,deep扩张深度 #H_Cul允许扩展计算,f_On开启二级验证,f二级验证效果 if f == None:f = d try:#参数处理 r_Cul = Bool(r_Cul) H_Cul = Bool(H_Cul,True) f_On = Bool(f_On) k = abs(int(k)) d = abs(float(d)) ky = abs(float(ky)) kx = abs(float(kx)) cx = abs(float(cx)) dx = abs(float(dx)) deep = abs(int(deep)) f = abs(float(f)) except: r_Cul = False H_Cul = True f_On = False k = 100 d = 0.0001 ky = 0.1 kx = 0.1 cx = 0.5 dx = 0.5 deep = 100 f = d if not self.HaveDone: self.Cul() x = self.__x + self.Memore_x y = self.__y + self.Memore_x try:#y_in是否为数字 y_in = float(y_in) except: return [], [] try: if y_in < self.min_y-ky or y_in > self.max_y+ky: return [],[] # 返回空值 if r_Cul and y_in in y: # 如果已经计算过 num = y.index(y_in) return x[num] except: pass iter_list = [[self.start, self.end]] # 准备迭代的列表 c_list = [] c_o_list = [] c = 0 for ab in iter_list: a = ab[0] b = ab[1] c = None br = False for i in range(k): # 限定次数的迭代 try: if a > b:a,b=b,a#a是小的数字，b是大的数字，c是中间 if a == b:#如果相等，作废 c=None break _a = self(a) - y_in#计算a _b = self(b) - y_in#计算b c = (a + b) / 2#计算c try: _c = self(c) - y_in#计算c except: if deep > 0: # 尝试向两边扩张，前提是有deep余额（扩张限制）而且新去见大于cx if abs(a - (c - kx)) > cx: iter_list.append([a, c - kx]) # 增加区间（新区间不包括c，增加了一个偏移kx） deep -= 1 # 余额减一 if abs((c + kx) - b) > cx: iter_list.append([c + kx, b]) # 增加区间 deep -= 1 c = None break # print(f'a={a},b={b},c={c},_a={_a},_b={_b}') q = _a * _c#a,c之间零点 p = _b * _c#b,c之间零点 if _c == 0:#如果c就是零点 if deep > 0:#尝试向两边扩张，前提是有deep余额（扩张限制）而且新去见大于cx if abs(a - (c-kx)) > cx: iter_list.append([a, c-kx])#增加区间（新区间不包括c，增加了一个偏移kx） deep -= 1#余额减一 if abs((c+kx) - b) > cx: iter_list.append([c+kx, b])#增加区间 deep -= 1 break#这个区间迭代完成，跳出返回c elif q * p == 0:#a或者b之间有一个是零点 if q == 0:#a是零点 c = a if deep > 0 and abs((a+kx) - b) > cx:#尝试往b方向扩张 iter_list.append([a+kx, b]) deep -= 1 break else: c = b#同上 if deep > 0 and abs(a - (b-kx)) > cx: iter_list.append([a, b-kx]) deep -= 1 break elif q * p > 0:#q和p都有或都没用零点 if q > 0 and abs(a - b) < dx:#如果ab足够小反围，则认为a和b之间不存在零点 if H_Cul: # addNews('进入梯度运算') c = self.Iterative_method_Of_Huan(y_in, a, b)[1] if c != None: break c = None break iter_list.append([b, c])#其中一个方向继续迭代，另一个方向加入候选 b = c _b = self(b) - y_in elif q < 0:#往一个方向收缩，同时另一个方向增加新的区间 if deep > 0 and abs(c - b) > cx: iter_list.append([c,b]) deep -= 1 b = c _b = self(b) - y_in elif p < 0:#同上 if deep > 0 and abs(a - c) > cx: iter_list.append([a,c]) deep -= 1 a = c _a = self(a) - y_in if abs(a - b) < d:#a和b足够小，认为找到零点 c = (a + b) / 2 _c = self(c) if f_On and abs(y_in - _c) > f:#_c不是目标输出 print("A") c = None break except: break else:#证明没有break br = True if c == None: continue#去除c不存在的选项 if not br: c_list.append(c) else: c_o_list.append(c) answer = [] for i in c_list: self.Memore_x.append(i) self.Memore_y.append(y_in) answer.append(f'y={y_in} -> x={i}') if all: for i in c_o_list: answer.append(f'(误差)y={y_in} -> x={i}') self.__MemoryAnswer += answer return answer, c_list def __Parity(self,ro=False):#启动round处理 if not self.HaveDone: self.Cul()#运行Cul计算 if len(self.__fx) != 1: m = True#通过self计算y else: m = False y = self.__y.copy() x = self.__x.copy() a = self.start b = self.end a = -min([abs(a),abs(b)]) b = -a flat = None#0-偶函数，1-奇函数 for i in range(len(x)): _x = x[i]#正项x if _x < a or _x > b:continue#x不在区间内 try: if m: _y = self(_x) else: _y = y[i] # 求得x的y if m: o_y = self(-_x) else: o_y = y[x.index(-_x)]#求得-x的y if ro: _y = round(_y,self.JD) o_y = round(o_y, self.JD) if o_y == _y == 0: continue elif o_y == _y: if flat == None: flat = 0 elif flat == 1: raise Exception elif o_y == -_y: if flat == None: flat = 1 elif flat == 0: raise Exception else: raise Exception except: flat = None break return flat,[a,b] def __Monotonic(self): if not self.HaveDone: self.Cul() # 运行Cul计算 fy = self.__fy.copy() fx = self.__fx.copy() Increase_interval = []#增区间 Minus_interval = []#减区间 Interval = []#不增不减 for i in range(len(fx)): x = fx[i] y = fx[i] o_x = None o_y = None start_x = None flat = None#当前研究反围:0-增区间,1-减区间,2-不增不减 for i in range(len(x)): _x = x[i]#正项x _y = y[i]#正项y if start_x == None: start_x = _x else: if o_y > _y:#减区间 if flat == None or flat == 1:#减区间 pass elif flat == 0:#增区间 Increase_interval.append((start_x,o_x)) start_x = o_x elif flat == 2: Interval.append((start_x, o_x)) start_x = o_x flat = 1 elif o_y < _y:#增区间 if flat == None or flat == 0: # 增区间 pass elif flat == 1: # 减区间 Minus_interval.append((start_x, o_x)) start_x = o_x elif flat == 2: Interval.append((start_x, o_x)) start_x = o_x flat = 0 else:#水平区间 if flat == None or flat == 2: pass elif flat == 1: # 减区间 Minus_interval.append((start_x, o_x)) start_x = o_x elif flat == 0: # 增区间 Increase_interval.append((start_x, o_x)) start_x = o_x flat = 2 o_x = _x o_y = _y if flat == 2: Interval.append((start_x, o_x)) elif flat == 1: # 减区间 Minus_interval.append((start_x, o_x)) elif flat == 0: # 增区间 Increase_interval.append((start_x, o_x)) return Increase_interval,Minus_interval,Interval def Nature(self,addNews=lambda x:x,all=False,JD=None,must=False): try: if not must:JD = float(JD) except: JD = None answer = [] P = self.__Parity() M = self.__Monotonic() ZQ = self.Periodic(addNews,JD) DCZ = self.Symmetry_axis(addNews,JD) DCZX = self.Center_of_symmetry(addNews,JD) if P[0] == 1: answer.append(f'奇函数 区间:[{P[1][0]},{P[1][0]}]') elif P[0] == 0: answer.append(f'偶函数 区间:[{P[1][0]},{P[1][0]}]') for i in M[0]: answer.append(f'增区间:[{i[0]},{i[1]}]') for i in M[1]: answer.append(f'减区间:[{i[0]},{i[1]}]') for i in M[2]: answer.append(f'水平区间:[{i[0]},{i[1]}]') if self.DHS: answer.append(f'导函数：{self.DHS}') if ZQ[0] != None: answer.append(f'最小正周期：{ZQ[0]}') if DCZ[0] != None: answer.append(f'对称轴：x={DCZ[0]}') if DCZX[0] != None: answer.append(f'对称中心：{DCZX[0]}') if all: try: for i in ZQ[1][1:]: answer.append(f'可能的最小正周期：{i}') except: pass try: for i in DCZ[1][1:]: answer.append(f'可能的对称轴：{i}') except: pass try: for i in DCZX[1][1:]: answer.append(f'可能的对称中心：{i}') except: pass return answer def YC_On_Off(self):#记忆数据显示和隐藏 if self.YC: if tkinter.messagebox.askokcancel('提示', f'是否显示{self}的记忆数据？'): # addNews('记忆显示完毕') self.YC = False else: if tkinter.messagebox.askokcancel('提示', f'是否隐藏{self}的记忆数据？'): # addNews('记忆隐藏完毕') self.YC = True def Out(self): if not self.HaveDone: self.Cul() if tkinter.messagebox.askokcancel('提示', f'是否确认导出函数:\n{str(self)}'): try: Dic = tkinter.filedialog.asksaveasfilename(title='选择导出位置', filetypes=[("CSV", ".csv")]) + '.csv' if Dic == '.csv':raise Exception self.__xyCSV.to_csv(Dic) return True except: pass return False def returnList(self):#导出列表 if not self.HaveDone:self.Cul() #最值和极值点设计 a = [] for i in self.min_x: a.append(f'极值点：{i}>最小值{self.min_y}') for i in self.max_x: a.append(f'极值点：{i}>最大值{self.max_y}') return a + self.__MemoryAnswer +self.__xy def Best_value(self): return self.max_x, self.max_y, self.min_x, self.min_y def getMemory(self): if self.YC:return [],[] return self.Memore_x,self.Memore_y def Clear_Memory(self): self.Memore_x = [] self.Memore_y = [] self.__MemoryAnswer = [] def Draw_Cul(self): if not self.HaveDone:self.Cul() return self.__fx,self.__fy,self.Func_Name,self.View def Cul_Y(self,x_in): answer = [] for i in x_in: try: i = float(i) y = self(i) answer.append(f'x={i} -> y={y}={float(y)}') if i not in self.Memore_x: self.Memore_x.append(i) self.Memore_y.append(y) except:#捕捉运算错误 continue self.__Best_value() self.__xyCSV = pandas.DataFrame((self.__x+self.Memore_x, self.__y+self.Memore_y), index=('x', 'y')) self.__MemoryAnswer += answer return answer def Periodic(self,addNews=lambda x:x,JD=None):#计算周期 if not tkinter.messagebox.askokcancel('提示', f'计算周期需要一定时间，是否执行？(计算过程程序可能无响应)'): return None,[]#无结果 if not self.HaveDone: self.Cul() p = []#可能的周期 start = self.start end = self.end if JD != None: k = JD else: k = abs(start - end) / 20 addNews('正在预测可能的周期') print(start,end,k) while start <= end: try: y = self(start) x_list = self.Cul_dichotomy(y)[1] addNews('迭代运算...') # print(x_list) q = [] for o_x in x_list: a = round(abs(o_x - start),self.JD) if a == 0: start += k continue if a:q.append(round(a,self.JD)) p.extend(list(set(q))) except: pass start += k print(start) p_c = list(set(p)) a = []#a的可能列表 c = 0 addNews('正在筛选结果') for i in p_c: n_c = p.count(i) if n_c > c: a = [i] c = n_c elif n_c == c: a.append(i) try: a.sort()# addNews('计算完毕') return a[0],a except: addNews('无周期') return None,[]#无结果 def Symmetry_axis(self,addNews=lambda x:x,JD=None):#计算对称轴 if not tkinter.messagebox.askokcancel('提示', f'计算对称轴需要一定时间，是否执行？(计算过程程序可能无响应)'): return None,[]#无结果 if not self.HaveDone: self.Cul() p = []#可能的对称轴 start = self.start end = self.end if JD != None: k = JD else: k = abs(start - end) / 20 addNews('正在预测对称轴') while start <= end: try: y = self(start) x_list = self.Cul_dichotomy(y)[1] addNews('迭代运算...') # print(x_list) q = [] for o_x in x_list: a = (o_x + start)/2 if a:q.append(round(a,self.JD)) p.extend(list(set(q))) except: pass start += k p_c = list(set(p)) a = []#a的可能列表 c = 0 addNews('正在筛选结果') for i in p_c: n_c = p.count(i) if n_c > c: a = [i] c = n_c elif n_c == c: a.append(i) try: a.sort() # addNews('计算完毕') return a[0], a except: addNews('无对称轴') return None, [] # 无结果 def Center_of_symmetry(self,addNews=lambda x:x,JD=None): # 计算对称中心 if not tkinter.messagebox.askokcancel('提示', f'计算对称中心需要一定时间，是否执行？(计算过程程序可能无响应)'): return None, [] # 无结果 if not self.HaveDone: self.Cul() point = [] # 可能的对称轴 start = self.start end = self.end addNews('正在计算坐标点') if JD != None: k = JD else: k = 1 while start <= end: try: y = self(start) x = start point.append((x,y)) except: pass start += k p = [] addNews('正在预测对称中心') for i in point: for o in point: x = round((i[0] + o[0])/2,self.JD) y = round((i[1] + o[1]) / 2, self.JD) if i == o:continue # print(f'i={i},o={o},x={x},y={y}') p.append((x,y)) p_c = list(set(p)) a = [] # a的可能列表 c = 0 addNews('正在筛选结果') for i in p_c: n_c = p.count(i) if n_c > c: a = [i] c = n_c elif n_c == c: a.append(i) try: if c < 5:raise Exception addNews('计算完毕') a.sort() # return a[int(len(a)/2)], a except: addNews('无对称中心') return None, [] # 无结果 def Check_Monotonic(self,cs,addNews=lambda x:x,JD = None):#检查单调性 test = True#预测结果 try: cd = cs.split(',') start = float(cd[0]) end = float(cd[1]) flat = float(cd[2]) # 当前研究反围:0-增区间,1-减区间,2-不增不减 except: return False,'' if start > end: start,end = end,start o_y = None if JD != None: k = JD else: k = self.kd while start<= end: try: addNews('迭代运算...') y = round(self(start),self.JD) except: start += k continue start += k if o_y == None:continue if flat == 0 and o_y > y:#增区间，o_y不小于y test = False break elif flat == 1 and o_y < y:#减小区间，o_y不小于y test = False break elif flat == 2 and o_y != y: test = False break o_y = y #Start+=k在上面 key = {0:'单调递增',1:'单调递减',2:'平行'} keys = {True: '成立', False: '不成立'} return test,f'{self}在[{cd[0]},{cd[1]}]{key[flat]}{keys[test]}' def Check_Periodic(self,cs,addNews=lambda x:x,JD = None):#检查周期性 test = True try: cs = float(cs) except: return False,'' start = self.start end = self.end if JD != None: k = JD else: k = self.kd while start <= end: try: addNews('迭代运算...') y = round(self(start),self.JD) o_y = round(self(start + cs),self.JD) if y != o_y: test = False except: pass start += k key = {True:'是',False:'不是'} return test,f'{self}的周期{key[test]}{cs}' def Check_Symmetry_axis(self,cs,addNews=lambda x:x,JD=None):#检查对称轴 test = True try: cs = 2 * float(cs) except: return False,'' start = self.start end = self.end if JD != None: k = JD else: k = self.kd while start <= end: try: addNews('迭代运算...') y = round(self(start),self.JD) o_y = round(self(cs-start),self.JD)#(a+b)/2=c >>> b = 2c-a if y != o_y: test = False except: pass start += k key = {True:'是',False:'不是'} return test,f'{self}的对称轴{key[test]}{cs}' def Check_Center_of_symmetry(self,in_cs,addNews=lambda x:x,JD=None):#检查对称中心 test = True try: cs = [] for i in in_cs.split(','): cs.append(float(i)) except: return False,'' start = self.start end = self.end if JD != None: k = JD else: k = self.kd while start <= end: try: addNews('迭代运算...') y = round(self(start),self.JD) o_y = round(self(2*cs[0]-start),self.JD)#(a+b)/2=c >>> b = 2c-a if round((y+o_y)/2,self.JD) != cs[1]: test = False except: pass start += k key = {True:'是',False:'不是'} return test,f'{self}的对称中心{key[test]}{cs}' def Sympy_Cul(self,y_in):#利用Sympy解方程 try: f = self.HS - float(y_in) x_list = sympy.solve(f,self.x) answer = [] for x in x_list: self.Memore_x.append(x)#可能需要修复成float(x) self.Memore_y.append(y_in) answer.append(f'y={y_in} -> x={x}') return answer,x_list except: return [],[] def Sympy_DHS(self,x_in,dx=0.1,must=False):#可导函数求导，不可导函数逼近 DHS = self.DHS try: dx = abs(float(dx)) except: dx = 0.1 try: x_in = float(x_in) if DHS != None and not must:#导函数法 get = DHS.evalf(subs ={self.x:x_in}) a = '导函数求值' else: x1 = x_in - dx/2 x2 = x_in + dx/2 y1 = self(x1) y2 = self(x2) dy = y2 - y1 get = dy/dx a = '逼近法求值' except: return None,None answer = f'({a})x:{x_in} -> {get}' return answer, get def Find(x,y,in_y):#输入x和y照除In_Y的所有对应x值 m = [] while True: try: num = y.index(in_y) m.append(x[num]) del x[num] del y[num] except ValueError: break return m class HS_lambda_Son: def __init__(self,HS,name,view,start = -10,end = 10,kd = 0.1,JD = 2,a=1): self.x = sympy.Symbol('x') Name = {'a':a,'x': self.x, 'Pi': sympy.pi, 'e': sympy.E, 'log': sympy.log, 'sin': sympy.sin, 'cos': sympy.cos, 'tan': sympy.tan, 'cot': lambda x: 1 / sympy.tan(x), 'csc': lambda x: 1 / sympy.sin(x), 'sec': lambda x: 1 / sympy.cos(x), 'sinh': sympy.sinh, 'cosh': sympy.cosh, 'tanh': sympy.tanh, 'asin': sympy.asin, 'acos': sympy.acos, 'atan': sympy.atan,'abs':abs} # 这个是函数命名域 self.HS = eval(HS.replace(' ', ''), Name)#函数解析式 self.str_HS = HS.replace(' ', '') #函数基本信息 self.Func_Name = f'y={HS} a={a}'#这个是函数名字 self.View = view#绘制样式 #数据辨析 try: start = float(start) end = float(end) if start > end:#使用float确保输入是数字，否则诱发ValueError start, end = end, start kd = abs(float(kd)) start = (start//kd)*kd#确保start可以恰好被kd整除 end = (end//kd+1)*kd JD = abs(int(JD)) if JD >= 3:JD = 3 except ValueError: start,end,kd,JD = -10,10,0.1,2#保底设置 #基本数据存储 self.JD = JD self.start = start self.end = end self.kd = kd #x和y数据存储 self.__x = [] self.__y = [] self.__ya = [] self.__fx = [[]] self.__fy = [[]] #最值和极值点 self.HaveDone = False#是否已经计算过xy #函数求导 try: self.DHS = sympy.diff(self.HS, self.x) except: self.DHS = None def __call__(self,x): return self.HS.evalf(subs={self.x:x}) def __str__(self): return f'{self.Func_Name} {self.start,self.end,self.kd}' def Creat_Son(self,a_start = -10,a_end = 10,a_kd = 0.1): self.Son_List = [] while a_start <= a_end: self.Son_List.append(HS_lambda_Son()) def Cul(self,it=float): if self.HaveDone: return self.__x, self.__y, self.Func_Name, self.View # 混合存储 self.__y = [] self.__ya = [] self.__x = [] self.__xy = [] self.__fx = [[]] self.__fy = [[]] reason = [30] o_y = None p = None # 单调性 0-增，1-减 _p = 1 try: a = int(self.start) while a <= int(self.end): # 因为range不接受小数 p2 = 1 try: c = 0 a_x = round(a, self.JD) y = self(a_x) y = it(y) # 数字处理方案 a_y = round(y, self.JD) if o_y != None and o_y > y: _p = 1 elif o_y != None and o_y < y: _p = 0 elif o_y != None and o_y == y: try: z_x = round(a_x - 0.5 * self.kd) z_y = self(z_x) if z_y == o_y == y: # 真实平衡 p2 = 2 elif abs(z_y - o_y) >= 10 * self.kd or abs(z_y - y) >= 10 * self.kd: p2 = 3 c += 5 except: p2 = 4 c += 9 _p = 2 if o_y != None and p != _p: if (o_y * y) < 0: c += 5 elif abs(o_y - y) >= (10 * self.kd): c += 5 if c >= 5 and (_p != 2 or p2 != 2): reason.append(c) self.__fx.append([]) self.__fy.append([]) p = _p self.__x.append(a_x) # 四舍五入减少计算量 self.__y.append(y) # 不四舍五入 self.__ya.append(a_y) # 四舍五入(用于求解最值) self.__xy.append(f'x:{a_x},y:{a_y}') self.__fx[-1].append(a_x) self.__fy[-1].append(y) o_y = y except: reason.append(0) self.__fx.append([]) self.__fy.append([]) a += self.kd except (TypeError, IndexError, ValueError): pass newfx = [] newfy = [] must = False for i in range(len(self.__fx)): # 去除只有单个的组群 if len(self.__fx[i]) <= 1: # 检测到有单个群组 q_r = reason[i] # 前原因 b_r = reason[i] # 后原因 if q_r < b_r: # 前原因小于后原因，连接到前面 try: newfx[-1] += self.__fx[i] newfy[-1] += self.__fy[i] except: # 按道理不应该出现这个情况 newfx.append(self.__fx[i]) newfy.append(self.__fy[i]) else: newfx.append(self.__fx[i]) newfy.append(self.__fy[i]) must = True else: if not must: newfx.append(self.__fx[i]) newfy.append(self.__fy[i]) else: newfx[-1] += self.__fx[i] newfy[-1] += self.__fy[i] must = False self.__fx = newfx self.__fy = newfy self.HaveDone = True return self.__x, self.__y, self.Func_Name, self.View def Draw_Cul(self): if not self.HaveDone:self.Cul() return self.__fx,self.__fy,self.Func_Name,self.View