why use pinv()?

[Ziyuan Yang]

Dear Michel,

When I check the code in results.py, I find the function use pinv() to calculate varCovar.

Here is the code in results.py line 481:

self.data.varCovar = -linalg.pinv(np.nan_to_num(self.data.H))

Why need to use pinv() here instead of inv()? And I find in some situation these 2 function returns different values, I have no idea why, but I think maybe the inv() provide a more possible right results in my experiment?

These are my codes and the result, as you can see out2 looks more like E:

import pandas as pd
import numpy as np
temp = pd.read_pickle('data/555.pickle')['self'].data.H
temp2 = np.nan_to_num(temp)
out1 = np.dot(temp2, np.linalg.pinv(temp2))
out2 = np.dot(temp2, np.linalg.inv(temp2))

[Michel Bierlaire]

pinv is the “pseudi-inverse”. It is always defined, even of the matrix is not invertible.
https://numpy.org/doc/stable/reference/generated/numpy.linalg.pinv.html

If the matrix is invertibles, and well conditioned, inv and pinv are identical.

> On 20 Sep 2023, at 17:53, Ziyuan Yang <0yang....@gmail.com> wrote:
>
> Dear Michel,
>
> When I check the code in results.py, I find the function use pinv() to calculate varCovar.
>
> Here is the code in results.py line 481:
> self.data.varCovar = -linalg.pinv(np.nan_to_num(self.data.H))
>
> Why need to use pinv() here instead of inv()? And I find in some situation these 2 function returns different values, I have no idea why, but I think maybe the inv() provide a more possible right results in my experiment?
>
> These are my codes and the result, as you can see out2 looks more like E:
> import pandas as pd
> import numpy as np
> temp = pd.read_pickle('data/555.pickle')['self'].data.H
> temp2 = np.nan_to_num(temp)
> out1 = np.dot(temp2, np.linalg.pinv(temp2))

> out2 = np.dot(temp2, np.linalg.inv(temp2))<f0848f5fd71a7482120123452e80510.png><6a3b6ea034d6a13b25a45e0c17df72f.png>
>
>
>
>
>
>
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> <f0848f5fd71a7482120123452e80510.png><6a3b6ea034d6a13b25a45e0c17df72f.png>

Michel Bierlaire
Transport and Mobility Laboratory
School of Architecture, Civil and Environmental Engineering
EPFL - Ecole Polytechnique Fédérale de Lausanne
http://transp-or.epfl.ch
http://people.epfl.ch/michel.bierlaire