[英]print surface fit equation in python
I'm trying to fit a surface model to a 3D data-set (x,y,z) using matplotlib. 我正在尝试使用matplotlib将表面模型拟合到3D数据集(x,y,z)。
Where z = f(x,y)
. 其中
z = f(x,y)
。
So, I'm going for the quadratic fitting with equation: 所以,我打算用方程进行二次拟合:
f(x,y) = ax^2+by^2+cxy+dx+ey+f
So far, I have successfully plotted the 3d-fitted-surface using least-square method using: 到目前为止,我使用最小二乘法成功绘制了三维拟合表面:
# best-fit quadratic curve
A = np.c_[np.ones(data.shape[0]), data[:,:2], np.prod(data[:,:2], axis=1), data[:,:2]**2]
C,_,_,_ = scipy.linalg.lstsq(A, data[:,2])
#evaluating on grid
Z = np.dot(np.c_[np.ones(XX.shape), XX, YY, XX*YY, XX**2, YY**2], C).reshape(X.shape)
But, how can I be able to print/get the fitted equation of the surface(with coefficient values) ? 但是,我怎样才能打印/获得曲面的拟合方程(系数值)?
I little help will be highly appreciated. 我会得到很少的帮助。
thank you. 谢谢。
According to the documentation of the function scipy.linalg.lstsq http://docs.scipy.org/doc/scipy-0.15.1/reference/generated/scipy.linalg.lstsq.html the estimated coefficients should be stored in your variable C (the order corresponding to columns in A). 根据函数scipy.linalg.lstsq http://docs.scipy.org/doc/scipy-0.15.1/reference/generated/scipy.linalg.lstsq.html的文档,估计的系数应该存储在你的变量中C(与A中的列对应的顺序)。
To print your equation with estimated coefficients showing 2 digits after decimal point: 要使用小数点后2位数的估计系数打印等式:
print 'f(x,y) = {:.2f}x^2+{:.2f}y^2+{:.2f}xy+{:.2f}x+{:.2f}y+{:.2f}'.format(C[4],C[5],C[3],C[1],C[2],C[0])
or: 要么:
print 'f(x,y) = {4:.2f}x^2+{5:.2f}y^2+{3:.2f}xy+{1:.2f}x+{2:.2f}y+{0:.2f}'.format(*C)
By the way, libraries pandas
and statsmodels
can be very helpful for this kind of task (eg check Run an OLS regression with Pandas Data Frame ) 顺便说一句,库
pandas
和statsmodels
对这类任务非常有用(例如,检查使用Pandas Data Frame运行OLS回归 )
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