从与SciPy的单一功能的曲线拟合的多个输出

Question

好吧，我有一个使用一系列参数来计算随着时间的推移在两个不同的变量效果的功能。这些变量已经被曲线匹配到一些现有数据，以最小化变化（如下所示）

我希望能够检查以前的工作，并匹配新的数据。我一直在尝试使用scipy.optimize.curve_fit功能，通过堆叠x和从我的函数产生的Y数据（如这里建议：fit multiple parametric curves with scipy）。

它可能不是正确的方法，或者我可能只是误会，但我的代码保持运行到一个类型的错误TypeError: Improper input: N=3 must not exceed M=2

我的简化原型代码最初是采取从这里：https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html

import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit

def func(x, a, b, c):
    result = ([],[])
    for i in x:
        #set up 2 example curves
        result[0].append(a * np.exp(-b * i) + c)
        result[1].append(a * np.exp(-b * i) + c**2)
    return result #as a tuple containing 2 lists

#Define the data to be fit with some noise:
xdata = list(np.arange(0, 10, 1))
y = func(xdata, 2.5, 5, 0.5)[0]
y2 = func(xdata, 1, 1, 2)[1]

#Add some noise
y_noise = 0.1 * np.random.normal(size=len(xdata))
y2_noise = 0.1 * np.random.normal(size=len(xdata))

ydata=[]
ydata2=[]

for i in range(len(y)): #clunky
    ydata.append(y[i] + y_noise[i])
    ydata2.append(y2[i] + y2_noise[i])

plt.scatter(xdata, ydata, label='data')
plt.scatter(xdata, ydata2, label='data2')
#plt.plot(xdata, y, 'k-', label='data (original function)')
#plt.plot(xdata, y2, 'k-', label='data2 (original function)')

#stack the data
xdat = xdata+xdata
ydat = ydata+ydata2

popt, pcov = curve_fit(func, xdat, ydat)

plt.plot(xdata, func(xdata, *popt), 'r-',
         label='fit: a=%5.3f, b=%5.3f, c=%5.3f' % tuple(popt))

plt.xlabel('x')
plt.ylabel('y')
plt.legend()
plt.show()

任何帮助非常感谢！

Answer 1

下面是绘图适合与一个共享的参数的两个不同的方程，这是不是你需要什么可以很容易地适应您的特定问题的示例代码。

import numpy as np
import matplotlib
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit

y1 = np.array([ 16.00,  18.42,  20.84,  23.26])
y2 = np.array([-20.00, -25.50, -31.00, -36.50, -42.00])
comboY = np.append(y1, y2)

x1 = np.array([5.0, 6.1, 7.2, 8.3])
x2 = np.array([15.0, 16.1, 17.2, 18.3, 19.4])
comboX = np.append(x1, x2)

if len(y1) != len(x1):
    raise(Exception('Unequal x1 and y1 data length'))
if len(y2) != len(x2):
    raise(Exception('Unequal x2 and y2 data length'))


def function1(data, a, b, c): # not all parameters are used here, c is shared
        return a * data + c

def function2(data, a, b, c): # not all parameters are used here, c is shared
        return b * data + c


def combinedFunction(comboData, a, b, c):
    # single data reference passed in, extract separate data
    extract1 = comboData[:len(x1)] # first data
    extract2 = comboData[len(x1):] # second data

    result1 = function1(extract1, a, b, c)
    result2 = function2(extract2, a, b, c)

    return np.append(result1, result2)


# some initial parameter values
initialParameters = np.array([1.0, 1.0, 1.0])

# curve fit the combined data to the combined function
fittedParameters, pcov = curve_fit(combinedFunction, comboX, comboY, initialParameters)

# values for display of fitted function
a, b, c = fittedParameters

y_fit_1 = function1(x1, a, b, c) # first data set, first equation
y_fit_2 = function2(x2, a, b, c) # second data set, second equation

plt.plot(comboX, comboY, 'D') # plot the raw data
plt.plot(x1, y_fit_1) # plot the equation using the fitted parameters
plt.plot(x2, y_fit_2) # plot the equation using the fitted parameters
plt.show()

print('a, b, c:', fittedParameters)