[CSSチュートリアル】波動効果を生み出すCSSのアイデア

"""


import numpy as np


from scipy.optimize import leastsq




def func(x, p): 


"""

"""


return y - func(x, p)




x = np.linspace(-2*np.pi, 0, 100)


A, k, theta = 10, 0.34, np.pi/6 # function arguments for real data


y0 = func(x, [A, k, theta]) # real data


# Experimental data after adding noise


y1 = y0 + 2 * np.random.randn(len(x)) 




p0 = [7, 0.2, 0] # First-guess function fit parameters
# call leastsq to fit the data, residuals is the function that calculates the error


# p0 is the initial value of the fit parameters, # args is the experimental data to be fitted


plsq = leastsq(residuals, p0, args=(y1, x)) 


# In addition to the initial values, the args argument is called to specify the other parameters used in the residuals (the global variables for x,y are used directly in the linear fit), again returning a tuple with the first element being the array of parameters after the fit.
Here (y1, x) is passed to the args argument. leastsq() will pass these two additional arguments to residuals(). Thus residuals() has three arguments, p for the sine function, and y and x for the array representing the experimental data.


print u"Real Parameters:", [A, k, theta]  


print u "Fitted parameters", plsq[0] # Parameters after fitting to experimental data 




import pylab as pl 


pl.plot(x, y0, label=u"real data") 


pl.plot(x, y1, label=u"Experimental data with noise") 


pl.plot(x, func(x, plsq[0]), label=u"Fitted data") 


pl.legend() 


pl.show() 
>>> Real Parameters: [10, 0.340000000000000000002, 0.52359877559829882]


>>> Fitted parameters [-9.84152775 0.33829767 -2.68899335]

minimize(fun, x0[, args, method, jac, hess, ...]) Minimization of scalar function of one or more variables.
Note: The parameter bounds=((0,None), (0,None)) represents the bounds corresponding to each dimension of x. If there is only one dimension, write bounds= ((0, None), ) as well, or use the following minimize_scalar function.
bounds= ((0, None), (0, None)) corresponds to the initial value x0 of x, which should be two-dimensional, as in (1, 0). 
For example see [ 
scipy.optimize.minimize
]


 minimize_scalar(fun[, bracket, bounds, ...]) Minimization of scalar function of one variable.
Note: These functions, such as minimize_scalar, return an OptimizeResult object, and print() results like this.    
 fun: -2.3627208257312922 


    nfev: 9 


     nit: 8 


 success: True 


       x: 1.333333333395553

def test():
    import math
    from scipy import optimize
    func = lambda x: x * math.log(x, 2)
    a = optimize.optimize_scalar(func, bounds=[0.1, 1], method='bounded')
    print(a)

     fun: -0.5307378454230427 



 message: 'Solution found.' 


    nfev: 9 


  status: 0 


 success: True 


       x: 0.3678794534141907 

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