Hi @mortcanty,

I had two questions regarding this section.

1. The comment states that the aim of this section is to ensure sum of positive correlations between X and U is positive. What exactly is the purpose of this step and what is X in this case? From the book it is understood that U is the new multispectral image generated from the eigenvalue problem but it's unclear what X is.
2. This step appears to be missing in the iMad_tf.py script. Is there a reason for this or did I miss something?

Thanks

Hi @mortcanty

I had 2 questions about the geneiv function.

1. Is there a particular reason you went the Cholesky decomposition route?

I understand that numpy's eig function doesn't directly solve the generalised eigenproblem (Ax = λBx) as it doesn't accept a B parameter. But scipy's eig function does.

Comparing the two implementations below, you get the same eigenvalues and (scaled) eigenvectors so they are equivalent.

import scipy as sp
import numpy as np

def geneivprob(A,B):
    # Using scipy
    lamda, eigvec = sp.linalg.eig(A, B)
    return lamda, eigvec

def geneivprob2(A,B):
    """
    CRC4 method
    Reduce the problem to a standard symmetric eigenvalue problem
    Ax = λBx -> Cy = λy    
    """
    Linv = np.linalg.inv(np.linalg.cholesky(B))
    C = Linv @ A @ Linv.transpose()
    #C = np.asmatrix((C + C.transpose())*0.5,np.float32)
    lamda,V = np.linalg.eig(C)
    return lamda, Linv.transpose() @ V   

So did you go the Cholesky decomposition route becuase:

• It was more efficient
• To solve the problem in pure numpy

2. What was the purpose of this line C = np.asmatrix((C + C.transpose())*0.5,np.float32)?

Hi @mortcanty,

In numpy, the * operator in numpy corresponds to element-wise multiplication whereas np.matmul or (@ operator since Python 3.5) corresponds to matrix multiplication. So should'nt the notation be fixed in places such as this?

Hi @mortcanty,

Is this lin2pcstr function doing the 2% linear stretch and histogram equalisation?

I ask because a standard linear stretch could be done as follows:

import numpy as np

def stretch(x, lower, upper, maxout=255, minout=0):
    a = (maxout - minout) / (upper - lower)
    b = minout - a * lower
    scaled = (a * x + b)
    scaled = np.clip(scaled, minout, maxout)
    return scaled

# Standard Linear stretch
lower = img.min()
upper = img.max()
scaled = stretch(img, lower, upper)

# 2% Linear stretch
lower = np.nanpercentile(img,2)
upper = np.nanpercentile(img, 98)
scaled2 = stretch(img, lower, upper)
                

Just wanted to be sure if I'm understanding the steps correctly.

Edit: I notice you already have bytestr() for stretching to the full byte range (0 to 255). So shouldn't the 2% stretch simply be bytestr(x, rng=[np.nanpercentile(img,2), np.nanpercentile(img,98)])?

Hi~
Thanks for your book!
I want to do some exercise by using your docker config.
But when I try to authenticate earth engine, there is always a error that: urllib2.URLError: <urlopen error [Errno 99] Cannot assign requested address> after I entered authorization code.
I don't know hot to fix it, maybe I should config my docker?