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Both test functions I wrote are above, but when I want to test I get wrong results. System It doesn't accept my code. I don't know exactly where my problem is. I share the problem and my solution.

def PCA(X, num_components):

"""

Args:

X: ndarray of size (N, D), where D is the dimension of the data,

and N is the number of datapoints

num_components: the number of principal components to use.

Returns:

the reconstructed data, the sample mean of the X, principal values

and principal components

"""

N, D = X.shape

# YOUR CODE HERE

# your solution should take advantage of the functions you have implemented above.

### Uncomment and modify the code below

# first perform normalization on the digits so that they have zero mean and unit variance

X_normalized, mean = normalize(X) # EDIT THIS

# Then compute the data covariance matrix S

S = np.cov(X_normalized, rowvar = False, bias = True) # EDIT THIS

# Next find eigenvalues and corresponding eigenvectors for S

eig_vals, eig_vecs = eig(S)

# Take the top `num_components` of eig_vals and eig_vecs,

# This will be the corresponding principal values and components

principal_vals, principal_components = eig_vals[:num_components], eig_vecs[:,:num_components]

principal_components = np.real(principal_components)

principal_components = np.real(principal_components)

# reconstruct the data from the using the basis spanned by the principal components

# Notice that we have subtracted the mean from X so make sure that you add it back

# to the reconstructed data

P = projection_matrix(principal_components)

reconst = (P @ X_normalized.T).T + mean

return reconst, mean, principal_vals, principal_components

and

**def PCA_high_dim(X, num_components):
"""Compute PCA for small sample size but high-dimensional features.
Args:
X: ndarray of size (N, D), where D is the dimension of the sample,
and N is the number of samples
num_components: the number of principal components to use.
Returns:
X_reconstruct: (N, D) ndarray. the reconstruction
of X from the first `num_components` pricipal components.
"""
# YOUR CODE HERE
# Uncomment and modify the code belo
N, D = X.shape
# # Normalize the dataset
#X_normalized, mean = normalize(X)
X_normalized, mean = normalize(X)**

**# # Find the covariance matrix
M = np.dot(X_normalized, X_normalized.T) / N
#S = np.cov(X_normalized.T, rowvar=False, bias=True)
#cov = np.cov(X_centered, rowvar=False)
eig_vals, eig_vecs = eig(M)**

**# # Next find eigenvalues and corresponding eigenvectors for S
# # Make sure that you only take the first D eigenvalues/vectors
# # You can also take a look at the eigenvalues beyond column (D-1) and they should be
# # zero (or a very small number due to finite floating point precision)
# eig_vals, eig_vecs = None, None
principal_values = eig_vals[:num_components]
principal_components = eig_vecs[:, :num_components]**

**# # Compute the eigenvalues and eigenvectors for the original system
# # eig_vecs = None
#eig_vals, eig_vecs = eig(S)
#eig_vals = eig_vals[0:D]
#eig_vecs = eig_vecs[:, 0:D]
# Normalize the eigenvectors to have unit-length
# # Take the top `num_components` of the eigenvalues / eigenvectors
# # as the principal values and principal components
# principal_values = None
# principal_components = None
principal_components = np.real(principal_components)**

**
# Due to precision errors, the eigenvectors might come out to be complex, so only take their real parts
# principal_components = np.real(principal_components)
#principal_values = eig_vals[:num_components]
#principal_components = eig_vecs[:, :num_components]**

**# # reconstruct the images from the lower dimensional representation
# # Remember to add back the sample mean
# reconst = None
# return reconst, mean, principal_values, principal_components
#P = projection_matrix(principal_components)
# reconst = (P @ X_normalized.T).T + mean
# return reconst, mean, principal_values, principal_components
reconst = (projection_matrix(principal_components)@ X_normalized) + mean
return reconst, mean, principal_values, principal_components**

???????here my error what am ? mss??

ERROR: test_PCA (week4_tests.Test) ---------------------------------------------------------------------- Traceback (most recent call last): File "/tmp/autograde_5q4slzm7/week4_tests.py", line 185, in test_PCA np.testing.assert_allclose(result[0], expected[0]) TypeError: 'PCA' object is not subscriptable

There are a few things that you could try to debug your code. Here are some suggestions: Make sure that you are calling the correct test function. You