import math 
from sympy import *
x1=symbols('x1')
x2=symbols('x2')
fun=x1**2+2*x2**2-2*x1*x2-2*x2
grad1=diff(fun,x1)
grad2=diff(fun,x2)
MaxIter=100
epsilon=0.0001
iter_cnt=0
current_step_size=100
x1_value=0
x2_value=0
grad1_value=(float)(grad1.subs({x1:x1_value,x2:x2_value}).evalf())
grad2_value=(float)(grad2.subs({x1:x1_value,x2:x2_value}).evalf())
current_obj=fun.subs({x1:x1_value,x2:x2_value}).evalf()
print('iterCnt:%2d  cur_point(%3.2f,%3.2f)  cur_obj:%5.4f  grad1:%5.4f  grad2:%5.4f '
      %(iter_cnt,x1_value,x2_value,current_obj,grad1_value,grad2_value))
while(abs(grad1_value) + abs(grad2_value) >= epsilon):  
    iter_cnt += 1
    t = symbols('t')
    x1_updated = x1_value - grad1_value * t
    x2_updated = x2_value - grad2_value * t
    Fun_updated = fun.subs({x1: x1_updated, x2: x2_updated})
    grad_t = diff(Fun_updated, t)
    t_value = solve(grad_t, t)[0]  # solve grad_t == 0
    grad1_value = (float)(grad1.subs({x1: x1_value, x2: x2_value}).evalf()) 
    grad2_value = (float)(grad2.subs({x1: x1_value, x2: x2_value}).evalf()) 
    x1_value = (float)(x1_value - t_value * grad1_value)
    x2_value = (float)(x2_value - t_value * grad2_value) 
    current_obj = fun.subs({x1: x1_value, x2: x2_value}).evalf()
    current_step_size = t_value
    print('iterCnt:%2d  cur_point(%3.2f, %3.2f)  cur_obj:%5.4f  grad_1:%5.4f  grad_2 :%5.4f' 
          % (iter_cnt, x1_value, x2_value, current_obj, grad1_value, grad2_value))

import numpy as np
from sympy import *
import math
import matplotlib.pyplot as plt
import mpl_toolkits.axisartist as axisartist
x1, x2, t = symbols('x1, x2, t')
def func():
    return pow(x1, 2) + 2 * pow(x2, 2) - 2 * x1 * x2 - 2 * x2
def grad(data):
    f = func()
    grad_vec = [diff(f, x1), diff(f, x2)]  # 求偏导数,梯度向量
    grad = []
    for item in grad_vec:
        grad.append(item.subs(x1, data[0]).subs(x2, data[1]))
    return grad
def grad_len(grad):
    vec_len = math.sqrt(pow(grad[0], 2) + pow(grad[1], 2))
    return vec_len
def zhudian(f):
    t_diff = diff(f)
    t_min = solve(t_diff)
    return t_min
def main(X0, theta):
    f = func()
    grad_vec = grad(X0)
    grad_length = grad_len(grad_vec)  # 梯度向量的模长
    k = 0
    data_x = [0]
    data_y = [0]
    while grad_length > theta:  # 迭代的终止条件
        k += 1
        p = -np.array(grad_vec)
        # 迭代
        X = np.array(X0) + t*p
        t_func = f.subs(x1, X[0]).subs(x2, X[1])
        t_min = zhudian(t_func)
        X0 = np.array(X0) + t_min*p
        grad_vec = grad(X0)
        grad_length = grad_len(grad_vec)
        print('grad_length', grad_length)
        print('坐标', float(X0[0]), float(X0[1]))
        data_x.append(X0[0])
        data_y.append(X0[1])
    print(k)
    # 绘图
    fig = plt.figure()
    ax = axisartist.Subplot(fig, 111)
    fig.add_axes(ax)
    ax.axis["bottom"].set_axisline_style("-|>", size=1.5)
    ax.axis["left"].set_axisline_style("->", size=1.5)
    ax.axis["top"].set_visible(False)
    ax.axis["right"].set_visible(False)
    plt.title(r'$Gradient \ method - steepest \ descent \ method$')
    plt.plot(data_x, data_y,color='r',label=r'$f(x_1,x_2)=x_1^2+2 \cdot x_2^2-2 \cdot x_1 \cdot x_2-2 \cdot x_2$')
    plt.legend()
    plt.scatter(1, 1, marker=(3, 1), c=2, s=100)
    plt.grid()
    plt.xlabel(r'$x_1$', fontsize=20)
    plt.ylabel(r'$x_2$', fontsize=20)
    plt.show()
if __name__ == '__main__':
  # 给定初始迭代点和阈值
    main([0, 0], 0.00001)