Develop a python code to do the followings:

$1.$ Evaluate the PCA reconstruction of the dataset using $5$ PCA eigenvector and $12$ eigenvectors. For each of these cases, compare the original data with the reconstructed data for $10$ different time steps $($you pick them$).$

$2.$ Plot the eigenvalues from the PCA decomposition.

$3.$ Repeat the above process using the data associated with the first $1000$ time steps.

$4.$ Repeat the above process using the data associated with the last $1000$ time steps.

The database has the following format: first column refers to time $($minute$)1\mathrm{.}55,$ the next $11$ columns are temperature measurements $(12\mathrm{.}28,9\mathrm{.}06,4\mathrm{.}50,11\mathrm{.}51,1\mathrm{.}28,9\mathrm{.}45,11\mathrm{.}06,8\mathrm{.}07,9\mathrm{.}06,2\mathrm{.}53,3\mathrm{.}48)$ at various depths along the string. These depths are $($in meters$)16,21,23\mathrm{.}5,26,31,33\mathrm{.}5,36,41,46,51,56,$ respectively. There are $3,600$ rows equivalent to $1,500$ minutes. Thanks.