python实现三维拟合的方法
如下所示：
frommatplotlibimportpyplotasplt
importnumpyasnp
frommpl_toolkits.mplot3dimportAxes3D
fig=plt.figure()
ax=Axes3D(fig)
#列出实验数据
point=[[2,3,48],[4,5,50],[5,7,51],[8,9,55],[9,12,56]]
plt.xlabel("X1")
plt.ylabel("X2")
#表示矩阵中的值
ISum=0.0
X1Sum=0.0
X2Sum=0.0
X1_2Sum=0.0
X1X2Sum=0.0
X2_2Sum=0.0
YSum=0.0
X1YSum=0.0
X2YSum=0.0
#在图中显示各点的位置
foriinrange(0,len(point)):
x1i=point[i][0]
x2i=point[i][1]
yi=point[i][2]
ax.scatter(x1i,x2i,yi,color="red")
show_point="["+str(x1i)+","+str(x2i)+","+str(yi)+"]"
ax.text(x1i,x2i,yi,show_point)
ISum=ISum+1
X1Sum=X1Sum+x1i
X2Sum=X2Sum+x2i
X1_2Sum=X1_2Sum+x1i**2
X1X2Sum=X1X2Sum+x1i*x2i
X2_2Sum=X2_2Sum+x2i**2
YSum=YSum+yi
X1YSum=X1YSum+x1i*yi
X2YSum=X2YSum+x2i*yi
#进行矩阵运算
#_mat1设为mat1的逆矩阵
m1=[[ISum,X1Sum,X2Sum],[X1Sum,X1_2Sum,X1X2Sum],[X2Sum,X1X2Sum,X2_2Sum]]
mat1=np.matrix(m1)
m2=[[YSum],[X1YSum],[X2YSum]]
mat2=np.matrix(m2)
_mat1=mat1.getI()
mat3=_mat1*mat2
#用list来提取矩阵数据
m3=mat3.tolist()
a0=m3[0][0]
a1=m3[1][0]
a2=m3[2][0]
#绘制回归线
x1=np.linspace(0,9)
x2=np.linspace(0,12)
y=a0+a1*x1+a2*x2
ax.plot(x1,x2,y)
show_line="y="+str(a0)+"+"+str(a1)+"x1"+"+"+str(a2)+"x2"
plt.title(show_line)
plt.show()
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