"""
计算非线性方程组：
  5x1+3 = 0
  4x0^2-2sin(x1x2)=0
  x1x2-1.5=0
"""
## 误差函数
def fun(x):
  x0,x1,x2 = x.tolist()
  return[5*x1+3,4x0^2-2sin(x1x2),x1x2-1.5]

result = optimize.fsolve(fun,[1,1,1])
## result
[-0.70622057  -0.6  -2.5]

def j(x):
  x0,x1,x2 = x.tolist()
  return[[0,5,0],[8*x0,-2*x2*cos(x1*x2],[0,x2,x1]]

result = optimize.fsolve(fun,[1,1,1],fprime=j)
#result
[-0.70622057  -0.6  -2.5]

x = np.array([8.19,2.72,6.39,8.71,4.7,2.66,3.78])
y = np.array([7.01,2.78,6.47,6.71,4.1,4.23,4.05])
def residual(p):
  k,b = p
  return y-(k*x+b)
r = optimize.leastsq(residual,[1,0])
k,b = r[0]
# print k
.613495349193
# print b
.79409254326

def func(x,p):
  """
    计算的正弦波 ：A*sin(2*pi*k*x+theta)
  """
  A,k,theta = p
  return A*sin(2*np.pi*k*x+theta)

def redis(p,y,x):
  return y-func(x,p)

x = np.linspace(0,2*np.pi,100)
A,k,theta = 10,0.34,np.pi/6
y0 = func(x,[A,k,theta])
# 加入噪声
np.random.seed(0)
y1 = y0+2*np.random.randn(len(x))
p0 = [7,0.40,0]
# p0是A,k,theta的初始值，y1，x要拟合的数据
plsq = optimize.leastsq(redis, p0,args=(y1,x))
print [A,k,theta] #真是的参数值
print plsq[0]  #拟合后的参数值

def func2(x,p):
  """
    计算的正弦波 ：A*sin(2*pi*k*x+theta)
  """
  A,k,theta = p
  return A*sin(2*np.pi*k*x+theta)
ret,_=optimize.curve_fit(func2,x,y1,p0=p0)

optimize.minimize(target_fun,init_val,method,jac,hess) 
target_fun：函数的表达式计算； 
init_val：初始值； 
method：最小化的算法； 
jac：雅各比矩阵 
hess：黑塞矩阵。

def func1(x,p):
  """
    计算的正弦波 ：A*sin(2*pi*k*x+theta)
  """
  A,k,theta = p
  return A*sin(2*np.pi*k*x+theta)
def func_error(p,y,x):
  return np.sum((y-func1(x,p)**2)
result = optimize.basinhopping(func_error,[1,1,1],niter=10,
              minimizer_kwargs={"method":"L-BFGS-B",
                        "args":(y1,x1)})
## [1,1,1]是传入的初始值，args是需要拟合的数据