Exponential Fitting

最新推荐文章于 2023-11-01 14:30:10 发布

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最新推荐文章于 2023-11-01 14:30:10 发布

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本文介绍了一种使用Python来拟合指数函数的方法。通过定义指数函数并生成数据集，利用多项式拟合找到最佳指数函数参数，进而预测未知数据点。文章展示了如何绘制原始数据与预测值之间的对比图。

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# quote from 'introduction to computation and programming     
# using Python, revised, MIT press 
import pylab
import math

#define an arbitrary exponential function
def f(x):
    return 3*(2**(1.2*x))
    
def createExpData(f, xVals):
    """assumes f is an exponential function of one argument
               xVals is an array of suitable arguments for f
       Returns array containing results of applying f to the 
               elements of xVals"""
    yVals = []
    for i in range(len(xVals)):
        yVals.append(f(xVals[i]))
    return pylab.array(xVals), pylab.array(yVals)
    
def fitExpData(xVals, yVals):
    """Assumes xVals and yVals arrays of numbers such that
         yVals[i] == f(xVals[i])
       Returns a,b, base such that log(f(x), base) == ax + b"""
    logVals = []
    for y in yVals:
        logVals.append(math.log(y, 2.0)) #get log base 2
    a, b = pylab.polyfit(xVals, logVals, 1)
    return a,b,2.0
    
xVals, yVals = createExpData(f, range(10))
pylab.plot(xVals, yVals, 'ro', label = 'Actual values')
a, b, base = fitExpData(xVals, yVals)
predictedYVals = []
for x in xVals:
    predictedYVals.append(base**(a*x + b))
pylab.plot(xVals, predictedYVals, label = 'Predicted values')
pylab.title('Fitting an Exponential Function')
pylab.legend()
#Look at a value for x not in original data
print 'f(20) = ', f(20)
print 'Predicted f(20) =', base**(a*20 + b)
pylab.show()