# [gmx-users] help me in understanding PCA

Upendra N nupendra90 at gmail.com
Sat Jun 16 15:47:36 CEST 2018

```Dear gromacs users,

Earlier mail contains spread sheet calculation for first element. But I
have mentioned 1row 2column please ignore that. My intension is to
understand the meaning of all elements.

Thank you

With Regards
Upendra N
Research Scholar
Department of Studies in Physics,Manasagangotri
University of Mysore, Mysuru

On Sat, Jun 16, 2018 at 7:13 PM, Upendra N <nupendra90 at gmail.com> wrote:

> Dear gromacs users,
>
> I am trying to understand covariance matrix produced in the covariance
> analysis.
>
> For understanding purpose, I have simulated 4 residue peptide (10ps, 6
> frames ) and constructed covariance matrix for c-alpha atoms.
>
> matrix is in 48x3 form (but it is supposed to be 16x16 as per the formula
> in the manual
>
> , where i,j runs from 1 to 3N)
>
>
> I would like to understand the meaning of elements in the matrix.
>
> for example: 1st row 2nd column may be the covariance of x and y
> components of 1st c-alpha atom.
>
> Please enlighten me whether I am thinking in a right way. I also tried to
> reproduce* 1st row 2 column element using manual calculation from spread
> sheet but i didn't get the value which is in covariance matrix.
>
> Kindly help me in understanding the meaning of elements in matrix. Also
> how to visualize in 3Nx3N form, since covar.dat is in (3NN)X(3) FORM
>
> * I have extracted co-ordinates of individual frames using gmx dump.
>  Then I used spread sheet to reproduce the covariance element.
>
> *****************First 3 rows of covar.dat*****************
>
> 0.000231868   -0.000110616    6.46952e-05
> -0.000275112   -3.07266e-05   -1.78349e-05
> -0.000104521   0.000100497   -7.23912e-05
> 0.000147767    4.08451e-05    2.55278e-05
> ****************************************************************
> ***************** Variance caluculation for 1st element************
> *Frames* *X-coordinates of 1st atom* *X-avg* *<(x-<x>)^2>*
> 1 1.75345 1.749638333 1.45288053188883E-05
> 2 1.821 1.749638333 0.0050924875
> 3 1.76899 1.749638333 0.000374487
> 4 1.67863 1.749638333 0.0050421834
> 5 1.75432 1.749638333 0.000021918
> 6 1.72144 1.749638333 0.000795146
> *sum * 10.49783
> 0.0113407507
> *average* 1.7496383333
> 0.0018901251
> ************************************************************
> ****************
>
> ******************* Trajectory frames************************
> ***************
> prod_ca.trr frame 0:
>    natoms=         4  step=         0  time=0.0000000e+00  lambda=
> 0
>    box (3x3):
>       box[    0]={ 3.35198e+00,  0.00000e+00,  0.00000e+00}
>       box[    1]={ 0.00000e+00,  3.35198e+00,  0.00000e+00}
>       box[    2]={ 0.00000e+00,  0.00000e+00,  3.35198e+00}
>    x (4x3):
>       x[    0]={ 1.75345e+00,  2.11837e+00,  1.48333e+00}
>       x[    1]={ 1.66725e+00,  1.74678e+00,  1.55009e+00}
>       x[    2]={ 1.87095e+00,  1.45219e+00,  1.68827e+00}
>       x[    3]={ 1.83285e+00,  1.07340e+00,  1.72068e+00}
> prod_ca.trr frame 1:
>    natoms=         4  step=      1000  time=2.0000000e+00  lambda=
> 0
>    box (3x3):
>       box[    0]={ 3.35023e+00,  0.00000e+00,  0.00000e+00}
>       box[    1]={ 0.00000e+00,  3.35023e+00,  0.00000e+00}
>       box[    2]={ 0.00000e+00,  0.00000e+00,  3.35023e+00}
>    x (4x3):
>       x[    0]={ 1.82100e+00,  2.09153e+00,  1.47850e+00}
>       x[    1]={ 1.66768e+00,  1.74522e+00,  1.52569e+00}
>       x[    2]={ 1.81584e+00,  1.50417e+00,  1.77563e+00}
>       x[    3]={ 1.75791e+00,  1.12533e+00,  1.80000e+00}
> prod_ca.trr frame 2:
>    natoms=         4  step=      2000  time=4.0000000e+00  lambda=
> 0
>    box (3x3):
>       box[    0]={ 3.34566e+00,  0.00000e+00,  0.00000e+00}
>       box[    1]={ 0.00000e+00,  3.34566e+00,  0.00000e+00}
>       box[    2]={ 0.00000e+00,  0.00000e+00,  3.34566e+00}
>    x (4x3):
>       x[    0]={ 1.76899e+00,  2.08417e+00,  1.42760e+00}
>       x[    1]={ 1.60314e+00,  1.73896e+00,  1.50322e+00}
>       x[    2]={ 1.74817e+00,  1.49365e+00,  1.75878e+00}
>       x[    3]={ 1.60434e+00,  1.14668e+00,  1.80072e+00}
> prod_ca.trr frame 3:
>    natoms=         4  step=      3000  time=6.0000000e+00  lambda=
> 0
>    box (3x3):
>       box[    0]={ 3.34446e+00,  0.00000e+00,  0.00000e+00}
>       box[    1]={ 0.00000e+00,  3.34446e+00,  0.00000e+00}
>       box[    2]={ 0.00000e+00,  0.00000e+00,  3.34446e+00}
>    x (4x3):
>       x[    0]={ 1.67863e+00,  2.06560e+00,  1.49634e+00}
>       x[    1]={ 1.54220e+00,  1.72828e+00,  1.61010e+00}
>       x[    2]={ 1.69418e+00,  1.44080e+00,  1.80575e+00}
>       x[    3]={ 1.50439e+00,  1.11635e+00,  1.84362e+00}
> prod_ca.trr frame 4:
>    natoms=         4  step=      4000  time=8.0000000e+00  lambda=
> 0
>    box (3x3):
>       box[    0]={ 3.34345e+00,  0.00000e+00,  0.00000e+00}
>       box[    1]={ 0.00000e+00,  3.34345e+00,  0.00000e+00}
>       box[    2]={ 0.00000e+00,  0.00000e+00,  3.34345e+00}
>    x (4x3):
>       x[    0]={ 1.75432e+00,  2.06958e+00,  1.33725e+00}
>       x[    1]={ 1.63294e+00,  1.74710e+00,  1.51241e+00}
>       x[    2]={ 1.77183e+00,  1.43452e+00,  1.68678e+00}
>       x[    3]={ 1.57508e+00,  1.13509e+00,  1.82323e+00}
> prod_ca.trr frame 5:
>    natoms=         4  step=      5000  time=1.0000000e+01  lambda=
> 0
>    box (3x3):
>       box[    0]={ 3.34616e+00,  0.00000e+00,  0.00000e+00}
>       box[    1]={ 0.00000e+00,  3.34616e+00,  0.00000e+00}
>       box[    2]={ 0.00000e+00,  0.00000e+00,  3.34616e+00}
>    x (4x3):
>       x[    0]={ 1.72144e+00,  1.99902e+00,  1.42431e+00}
>       x[    1]={ 1.60459e+00,  1.70278e+00,  1.63203e+00}
>       x[    2]={ 1.71879e+00,  1.35945e+00,  1.75611e+00}
>       x[    3]={ 1.51826e+00,  1.05315e+00,  1.85289e+00}
>
> ************************************************************************
>
>
>
>
> With Regards
> Upendra N
> Research Scholar
> Department of Studies in Physics,Manasagangotri
> University of Mysore, Mysuru
>
>
```