least squares Python implementation

1 ImportNumPy as NP2 3 defSumsquareerror (dataset,a):4     #Enter the target dataset with the assumed curve function, calculate the sum of squared errors5     #data form Dataset[i] = [X,y],y = Hypfunc (x)6     #A: Polynomial coefficients [a0,a1,..., an-1]7Hypresult = [Hypfunc (dataset[i,0],a) forIinchRange (dataset.shape[0])8SSE = Np.sum ((hypresult-dataset[:,1]) **2)9     returnSSETen  One defHypfunc (x,a): A     #Input: X horizontal value, A polynomial coefficient [a0,a1,..., an-1] -     #return y = Hypfunc (x) -     returnNp.sum (a[i]* (x**i) forIinchRange (len (A))) the  - """ - The idea of least squares - Set Assumptions YH = a0x^0 + a1x^1 + a2x^2 +...+ akx^k + then the error R2 = SUM (Y (xi)-yh (xi)) i = 1...N - R2 = sum [(yi-(a0x^0 + a1x^1 + a2x^2 +...+ akx^k))]2 ~ 0 + R2 to AI: and make (a total of k+1 equations) A div (R2,ai) =-2 * SUM (yi-(a0x^0 + a1x^1 + a2x^2 +...+ akx^k)) * x^i = 0 at The following matrix is used to solve the equation - [[1 x1 ... x1^k],..., [1 xn ... xn^k]] * [a0,..., ak] = [y1,..., yn] - """ -  - ImportRandom - ImportMatplotlib.pyplot as Plt in  - if __name__=="__main__": to     Pass +     #generate points on a curve -x = Np.arange ( -1,1,0.02) they = [((a*a-1) * (a*a-1) * (a*a-1) +0.5) *np.sin (a*2) forAinchx] *Xa = [] $Ya = []Panax Notoginseng     #randomly offsets each point on a curve -      forIinchRange (len (x)): theD = np.float (Random.randint (60,140))/100 +Ya.append (y[i]*d) AXa.append (x[i]*d) then = Len (xa)#Number of data +      -Order = 9#set the K-order polynomial 0 ~ k $     #constructing x, y Vandermonde matrices from data points $mATX = Np.array ([[[Np.sum] ([xa[i]** (K2+K1)] forIinchrange (n)])  -               forK2inchRange (order+1)] forK1inchRange (order+1)]) -              theMaty = Np.array ([Np.sum (Xa[i]**k) *ya[i] forIinchrange (n)]) -              forKinchRange (order+1)])Wuyi     PrintMatx.shape,maty.shape the      -A =np.linalg.solve (mATX, Maty) Wu     PrintA -  About     #draw data points and fit curves $ plt.figure () -     #output data points -Plt.plot (xa,ya,linestyle="', marker='.')  -      A     #draw a fitted post curve +Yhyp = [Hypfunc (x[i],a) forIinchrange (n)] thePlt.plot (x,yhyp,linestyle='-', marker="')  -      $Plt.show ()

least squares Python implementation