pca to fit plane

pca.py

# https://stackoverflow.com/questions/38754668/plane-fitting-in-a-3d-point-cloud

def PCA(data, correlation = False, sort = True):
""" Applies Principal Component Analysis to the data

Parameters
----------        
data: array
    The array containing the data. The array must have NxM dimensions, where each
    of the N rows represents a different individual record and each of the M columns
    represents a different variable recorded for that individual record.
        array([
        [V11, ... , V1m],
        ...,
        [Vn1, ... , Vnm]])

correlation(Optional) : bool
        Set the type of matrix to be computed (see Notes):
            If True compute the correlation matrix.
            If False(Default) compute the covariance matrix. 
            
sort(Optional) : bool
        Set the order that the eigenvalues/vectors will have
            If True(Default) they will be sorted (from higher value to less).
            If False they won't.   
Returns
-------
eigenvalues: (1,M) array
    The eigenvalues of the corresponding matrix.
    
eigenvector: (M,M) array
    The eigenvectors of the corresponding matrix.

Notes
-----
The correlation matrix is a better choice when there are different magnitudes
representing the M variables. Use covariance matrix in other cases.

"""

mean = np.mean(data, axis=0)

data_adjust = data - mean

#: the data is transposed due to np.cov/corrcoef syntax
if correlation:
    
    matrix = np.corrcoef(data_adjust.T)
    
else:
    matrix = np.cov(data_adjust.T) 

eigenvalues, eigenvectors = np.linalg.eig(matrix)

if sort:
    #: sort eigenvalues and eigenvectors
    sort = eigenvalues.argsort()[::-1]
    eigenvalues = eigenvalues[sort]
    eigenvectors = eigenvectors[:,sort]

return eigenvalues, eigenvectors