Here, Dragon results for the 3 molecules: I've included both  Whim and 3D 
descriptors but I don't have access to PMi!


I found the second document in agreement with Peter answer...


BR,

Dr. Guillaume GODIN
Principal Scientist
Chemoinformatic & Datamining
Innovation
CORPORATE R&D DIVISION
DIRECT LINE +41 (0)22 780 3645
MOBILE          +41 (0)79 536 1039
        Firmenich SA
        RUE DES JEUNES 1 | CASE POSTALE 239 | CH-1211 GENEVE 8

________________________________
De : Peter Gedeck <peter.ged...@gmail.com>
Envoyé : dimanche 15 janvier 2017 15:07
À : Greg Landrum; RDKit Discuss; Guillaume GODIN
Objet : Re: [Rdkit-discuss] PMI API

According to this:
https://en.wikipedia.org/wiki/List_of_moments_of_inertia
The moments of inertia of a disk (something like benzene) are:

Iz = mr^2/2
Ix = Iy = mr^2/4

None of them is zero. The smallest moment of inertia of a rod-like molecule 
(e.g. C#C) is zero.

Best,

Peter



On Sun, Jan 15, 2017 at 8:15 AM Greg Landrum 
<greg.land...@gmail.com<mailto:greg.land...@gmail.com>> wrote:
Hi Guillaume,

I think it this case it's something else. According to the Todeschini article 
the smallest moment of inertia of a planar molecule like benzene should be 
zero. The eigenvalues of the inertia matrix for benzene, however, are 
definitely not zero (and not close enough that it's likely to be round-off 
error).
It would be very nice if you could run the three files I mention through Dragon 
and let me know what it calculates for those descriptors.

-greg


_____________________________
From: Guillaume GODIN 
<guillaume.go...@firmenich.com<mailto:guillaume.go...@firmenich.com>>
Sent: Sunday, January 15, 2017 1:11 PM
Subject: RE: [Rdkit-discuss] PMI API
To: Greg Landrum <greg.land...@gmail.com<mailto:greg.land...@gmail.com>>, RDKit 
Discuss 
<rdkit-discuss@lists.sourceforge.net<mailto:rdkit-discuss@lists.sourceforge.net>>,
 Chris Earnshaw <cgearns...@gmail.com<mailto:cgearns...@gmail.com>>




Dear Greg,


I  suspect that it's a precision error or eigen algorithm shift between rdkit 
c++ & dragon.


To obtain good value, I suggest to try to implement a test on the eigen values 
like i did in gateway.cpp implementation.



JacobiSVD<MatrixXd> getSVD(MatrixXd A) {

    JacobiSVD<MatrixXd> mysvd(A,  ComputeThinU | ComputeThinV);

    return mysvd;

}


// get the A-1 matrix using

MatrixXd GetPinv(MatrixXd A){

    JacobiSVD<MatrixXd> svd = getSVD(A);

    double  pinvtoler=1.e-2;// choose your tolerance wisely!

    VectorXd vs=svd.singularValues();

    VectorXd vsinv=svd.singularValues();


    for (unsignedint i=0; i<A.cols(); ++i) {

        if ( vs(i) > pinvtoler )

           vsinv(i)=1.0/vs(i);

       else vsinv(i)=0.0;

    }


    MatrixXd S =  vsinv.asDiagonal();

    MatrixXd Ap = svd.matrixV() * S * svd.matrixU().transpose();

    return Ap;

}


If it's not solve the problem, I would like to test it in Matlab. can you 
provide me the 3 (3d xyz matrix) of your example please ?


I also have Dragon 6


best regards,

Dr. Guillaume GODIN
Principal Scientist
Chemoinformatic & Datamining
Innovation
CORPORATE R&D DIVISION
DIRECT LINE +41 (0)22 780 3645<tel:022%20780%2036%2045>
MOBILE          +41 (0)79 536 1039<tel:079%20536%2010%2039>
        Firmenich SA
        RUE DES JEUNES 1 | CASE POSTALE 239 | CH-1211 GENEVE 8

________________________________
De : Greg Landrum <greg.land...@gmail.com<mailto:greg.land...@gmail.com>>
Envoyé : dimanche 15 janvier 2017 11:50
À : Chris Earnshaw; RDKit Discuss
Objet : Re: [Rdkit-discuss] PMI API

I managed to make some time to look into this this weekend and I've found a bug 
and something I don't understand. Hopefully the community can help out here.
On Sun, Jan 8, 2017 at 11:17 AM, Chris Earnshaw 
<cgearns...@gmail.com<mailto:cgearns...@gmail.com>> wrote:
4) The big one! The returned results look very odd. They appear to relate more 
to the dimensions of the molecule than the moments of inertia. For a rod-like 
molecule (dimethylacetylene) I'd expect two large and one small PMI (e.g. PMI1: 
6.61651   PMI2: 150.434   PMI3: 150.434  NPR1: 0.0439828  NPR2: 0.999998) but 
actually get PMI1: 0.061647  PMI2: 0.061652  PMI3: 25.3699  NPR1: 0.002430  
NPR2: 0.002430.
For disk-like (benzene) the result should be one large and two medium (e.g. 
PMI1: 89.1448  PMI2: 89.1495  PMI3: 178.294  NPR1: 0.499987  NPR2: 0.500013) 
but get PMI1: 2.37457e-10  PMI2: 11.0844  PMI3: 11.0851  NPR1: 2.14213e-11  
NPR2: 0.999933.
Finally for a roughly spherical molecule (neopentane) the NPR values look 
reasonable (no great surprise) but the absolute PMI values may be too small: 
old program - PMI1: 114.795  PMI2: 114.797  PMI3: 114.799
NPR1: 0.999966  NPR2: 0.999988, new program - PMI1: 6.59466  PMI2: 6.59488  
PMI3: 6.59531  NPR1: 0.999902  NPR2: 0.999935

Your expectations are correct: the current RDKit implementation is wrong. The 
corresponding github entry is here: https://github.com/rdkit/rdkit/issues/1262
This is due to a mistake in the way the principal moments are calculated (which 
is due to the fact that I don't spend a lot of time working with/thinking about 
3D descriptors). Instead of using the eigenvectors/eigenvalues of the inertia 
matrix (the tensor of inertia) the RDKit is currently using the covariance 
matrix. There's some more on the relationship between these two here: 
http://number-none.com/blow/inertia/deriving_i.html

The problem is easy to fix (and I have something working here: 
https://github.com/greglandrum/rdkit/tree/fix/github1262), but it screws up the 
values of the descriptors that are derived from here:
Todeschini and Consoni "Descriptors from Molecular Geometry" Handbook of 
Chemoinformaticshttp://dx.doi.org/10.1002/9783527618279.ch37
These include the radius of gyration, inertial shape factor, etc.
Within that article they state that Ic = 0 for planar molecules. Ignoring the 
inequality on page 1010, which says that Ic is the largest moment and is 
contradicted by the rest of the text (particularly the inequalities on page 
1011), Ic corresponds to the smallest principal moment : PMI1.

So now I'm confused, but I'm hoping this is obvious to someone versed in the 
field: I'd like to reproduce the descriptors described in the Todeschini 
article, but I clearly can't do that using the actual moments of inertia. I 
could keep using the eigenvalues of the covariance matrix there, but that 
doesn't match what's described in the text.

Two things that would be extremely helpful:
1) an explanation of the disconnect here from someone who knows this stuff, I 
would guess that it's pretty simple
2) The results of running the files github1262_1.mol, github1262_2.mol, and 
github1262_3.mol from here: 
https://github.com/greglandrum/rdkit/tree/fix/github1262/Code/GraphMol/MolTransforms/test_data
 through Dragon and calculating the radius of gyration, inertial shape factor, 
eccentricity, molecular asphericity, and spherocity index.

Best,
-greg




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