Using Python's numpy for linear fitting, polynomial fitting, logarithmic fitting

Transferred from: http://blog.itpub.net/12199764/viewspace-1743145/

There are work on the trend forecast in the project, and the 3 kinds of fitting methods are sorted out:
1. Linear fit-using math
Import Math
def linefit (x, y):
N = float (len (x))
sx,sy,sxx,syy,sxy=0,0,0,0,0
For I in range (0,int (N)):
SX + = X[i]
Sy + = Y[i]
Sxx + = X[i]*x[i]
Syy + = Y[i]*y[i]
Sxy + = X[i]*y[i]
A = (sy*sx/n-sxy)/(sx*sx/n-sxx)
b = (SY-A*SX)/n
R = ABS (SY*SX/N-SXY)/math.sqrt ((sxx-sx*sx/n) * (syy-sy*sy/n))
Return A,b,r

if __name__ = = ' __main__ ':
x=[1, 2, 3, 4, 5, 6]
y=[2.5, 3.51, 4.45, 5.52, 6.47, 7.51]
A,b,r=linefit (x, y)
Print ("x=", X)
Print ("y=", Y)
Print ("fit result: Y =%10.5f x +%10.5f, r=%10.5f"% (a,b,r))
#结果为: y = 0.97222 x + 1.59056, r= 0.98591


1. Linear fit-using NumPy
Import NumPy as NP
x=[1, 2, 3, 4, 5, 6]
y=[2.5, 3.51, 4.45, 5.52, 6.47, 7.51]
Z1 = Np.polyfit (X, Y, 1) #一次多项式拟合, equivalent to linear fit
P1 = np.poly1d (z1)
Print Z1 #[1. 1.49333333]
Print P1 # 1 x + 1.493


2, two polynomial fitting
Import NumPy

def polyfit (x, Y, degree):
results = {}
Coeffs = Numpy.polyfit (x, y, degree)
results[' polynomial '] = coeffs.tolist ()

# r-squared
p = numpy.poly1d (coeffs)
# Fit values, and mean
Yhat = P (x) # or [P (z) for z in X]
Ybar = Numpy.sum (y)/len (y) # or sum (y)/len (y)
Ssreg = Numpy.sum ((yhat-ybar) **2) # or SUM ([(Yihat-ybar) **2 for Yihat in Yhat])
Sstot = Numpy.sum ((y-ybar) **2) # or SUM ([(Yi-ybar) **2 for Yi in Y])
results[' determination '] = Ssreg/sstot #准确率
return results

x=[1, 2, 3, 4, 5, 6]
y=[2.5, 3.51, 4.45, 5.52, 6.47, 7.2]
Z1 = Polyfit (x, Y, 2)
Print Z1





3, logarithmic function fitting-this is the most difficult, Baidu can not find, Google took half a day to find. Exponent, power number fitting What, use this, rewrite the func.
From scipy import log as log print Pcov
Import NumPy
From scipy import log
From scipy.optimize import Curve_fit

def func (x, A, B):
y = A * log (x) + b
Return y

def polyfit (x, Y, degree):
results = {}
#coeffs = Numpy.polyfit (x, y, degree)
popt, Pcov = Curve_fit (func, x, y)
results[' polynomial '] = popt

# r-squared
Yhat = func (x, popt[0], popt[1]) # or [P (z) for z in X]
Ybar = Numpy.sum (y)/len (y) # or sum (y)/len (y)
Ssreg = Numpy.sum ((yhat-ybar) **2) # or SUM ([(Yihat-ybar) **2 for Yihat in Yhat])
Sstot = Numpy.sum ((y-ybar) **2) # or SUM ([(Yi-ybar) **2 for Yi in Y])
results[' determination '] = Ssreg/sstot

return results


x=[1, 2, 3, 4, 5, 6]
y=[2.5, 3.51, 4.45, 5.52, 6.47, 7.51]
Z1 = Polyfit (x, Y, 2)
Print Z1

Use Python's numpy for linear fitting, polynomial fitting, and logarithmic fitting