Monitoring Optimization of Spread Function

The output during optimization steps is printed to standard output. To monitor the optimization progress, the following method may be helpful. For convenient, we assume the standard output is stored in a file 'stdout.std'. The following example is for Si.dat which can be found in openmx*.*/work/wf_example, and each user can trace the same calculation.

DISE

Monitor the self-consistent loops for disentangling progress (the first step of optimization):

    % grep "DISE" stdout.std

    |  Iter  | Omega_I (Angs^2) | Delta_I (Angs^2) |  ---> DISE
    |     1  |   15.729405734992|   15.729405734992|  ---> DISE
    |     2  |   15.472899644675|   -0.256506090316|  ---> DISE
    |     3  |   15.298904204761|   -0.173995439915|  ---> DISE 
    |     4  |   15.184358975818|   -0.114545228943|  ---> DISE
    |     5  |   15.109144558995|   -0.075214416823|  ---> DISE
    |     6  |   15.059536215864|   -0.049608343132|  ---> DISE
    |     7  |   15.026555029591|   -0.032981186273|  ---> DISE
    |     8  |   15.004405549290|   -0.022149480301|  ---> DISE
    |     9  |   14.989360674543|   -0.015044874747|  ---> DISE
    |    10  |   14.979019019700|   -0.010341654843|  ---> DISE
    ........
    .....
    ...
    .

where 'Iter', 'Omega_I', and 'Delta_I' mean the iteration number, the gauge invariant part of the spread function, and its difference between two neighboring steps. The criterion given by the keyword 'Wannier.Dis.Conv.Criterion' is applied to 'Delta_I'.

CONV

Monitor the optimization of the gauge dependent part of the spread function (the second step of optimization):

    % grep "CONV" stdout.std

   |Opt Step |Modu.of Gradient|d_Omega_in_steps|     d_Omega   | (in Angs^2) ---> CONV 
   | SD    1 | 1.01158918E+00 | 1.49290922E-03 |-1.49143228E-03|  ---> CONV 
   | SD    2 | 1.00759578E+00 | 1.48701574E-03 |-1.48555300E-03|  ---> CONV 
    .....
    .....
   | SD  200 | 5.84949196E-01 | 8.63271441E-04 |-8.62809578E-04|  ---> CONV 
   |Opt Step |Mode of Gradient|     d_Omega    | (Angs^2) ---> CONV 
   | CG    1 | 3.60406914E-01 | -4.00536821E-01|  ---> CONV 
    .....
    .....
   | CG   55 | 1.00046240E-12 | -4.85492314E-13|  ---> CONV 
   | CG   56 | 3.40196568E-13 | -2.46725602E-13|  ---> CONV 
   ************************************************************* ---> CONV
                     CONVERGENCE ACHIEVED !                      ---> CONV
   ************************************************************* ---> CONV
                     CONVERGENCE ACHIEVED !                      ---> SPRD

where 'Opt Step' and 'Modu.of Gradient' are the optimization step in either 'SD' or 'CG' method and the modulus of gradient of the spread function. The difference between two neighboring steps in the gauge dependent spread functions is calculated in two different way in the SD method, giving 'd_Omega_in_steps' and 'd_Omega'. 'd_Omega_in_steps' is given by

$$d\Omega = \epsilon \sum_{\bf k} \vert\vert G^{\bf (k)} \vert\vert^2,$$

where $\epsilon$ is the step length, $G^{\bf (k)}$ is the gradient of the spread function. The details of the equation can be found in Ref. [74]. On the other hand, 'd_Omega' is given by

$$d\Omega = \Omega^{(n+1)} - \Omega^{(n)},$$

where $n$ is the iteration number. In the CG method, only 'd_Omega' is evaluated. The criterion given by the keyword 'Wannier.Minimizing.Conv.Criterion' is applied to 'Modu.of Gradient'.

SPRD

Monitor the variation of spread of the Wannier functions:

     % grep "SPRD" stdout.std
     
     |Opt Step |     Omega_I    |     Omega_D    |     Omega_OD  |    Tot_Omega  | (in Angs^2) ---> SPRD 
     | SD    1 |   14.95330056  |    0.13750102  |    6.49032814 |   21.58112972 |  ---> SPRD 
     | SD    2 |   14.95330056  |    0.13744541  |    6.48889820 |   21.57964416 |  ---> SPRD 
     | SD    3 |   14.95330056  |    0.13739052  |    6.48747336 |   21.57816443 |  ---> SPRD 
     | SD    4 |   14.95330056  |    0.13733636  |    6.48605355 |   21.57669047 |  ---> SPRD 
     .....
     .....
     | SD  199 |   14.95330056  |    0.13449510  |    6.27229121 |   21.36008687 |  ---> SPRD 
     | SD  200 |   14.95330056  |    0.13450210  |    6.27142140 |   21.35922406 |  ---> SPRD 
     |Opt Step |     Omega_I    |     Omega_D    |     Omega_OD  |    Tot_Omega  | (Angs^2) ---> SPRD 
     | CG    1 |    14.95330056 |     0.16848639 |    5.83690029 |   20.95868724 |  ---> SPRD 
     | CG    2 |    14.95330056 |     0.16421934 |    5.78500985 |   20.90252974 |  ---> SPRD 
     | CG    3 |    14.95330056 |     0.16106859 |    5.77547389 |   20.88984303 |  ---> SPRD 
     .....
     .....
     | CG   55 |    14.95330056 |     0.15987820 |    5.77203385 |   20.88521260 |  ---> SPRD 
     | CG   56 |    14.95330056 |     0.15987820 |    5.77203385 |   20.88521260 |  ---> SPRD 
     ************************************************************* ---> SPRD
                       CONVERGENCE ACHIEVED !                      ---> SPRD
     ************************************************************* ---> SPRD

where 'Opt Step' is the optimization step in either 'SD' or 'CG' method. 'Omega_I' is the gauge invariant part of spread function. 'Omega_D' and 'Omega_OD' are the gauge dependent diagonal and off-diagonal contribution, respectively. 'Tot_Omega' is the sum up of all the above three components of the spread function.

CENT

Monitor the variation of Wannier function center:

    % grep "CENT" stdout.std
    WF   1 ( 1.14465704, 1.14465689, 1.14465697) |   2.69781828  --->CENT
    WF   2 ( 1.55414640, 1.55414634, 1.14465803) |   2.69783245  --->CENT
    WF   3 ( 1.55414741, 1.14465636, 1.55414731) |   2.69783410  --->CENT
    WF   4 ( 1.14465805, 1.55414638, 1.55414610) |   2.69781605  --->CENT
    WF   5 ( 0.20474553, 0.20474549, 0.20474559) |   2.69782821  --->CENT
    WF   6 ( 0.20474381,-0.20474431,-0.20474417) |   2.69782871  --->CENT
    WF   7 (-0.20474538, 0.20474519,-0.20474564) |   2.69783184  --->CENT
    WF   8 (-0.20474446,-0.20474477, 0.20474501) |   2.69783151  --->CENT
    Total Center ( 5.39760841, 5.39760756, 5.39760921) sum_spread  21.58262115 --->CENT
    SD     1 ------------------------------------------------------------------------> CENT
    WF   1 ( 1.14466694, 1.14466679, 1.14466688) |   2.69763185  --->CENT
    WF   2 ( 1.55413650, 1.55413644, 1.14466794) |   2.69764602  --->CENT
    WF   3 ( 1.55413751, 1.14466626, 1.55413741) |   2.69764767  --->CENT
    WF   4 ( 1.14466796, 1.55413647, 1.55413620) |   2.69762962  --->CENT
    WF   5 ( 0.20473563, 0.20473559, 0.20473568) |   2.69764178  --->CENT
    WF   6 ( 0.20473391,-0.20473440,-0.20473426) |   2.69764228  --->CENT
    WF   7 (-0.20473548, 0.20473528,-0.20473574) |   2.69764541  --->CENT
    WF   8 (-0.20473455,-0.20473487, 0.20473510) |   2.69764508  --->CENT
    Total Center ( 5.39760841, 5.39760756, 5.39760921) sum_spread  21.58112972 --->CENT
    SD     2 ------------------------------------------------------------------------> CENT
     .....
     .....
    CG    56 ------------------------------------------------------------------------> CENT
    WF   1 ( 1.14827796, 1.14827609, 1.14827941) |   2.61064261  --->CENT
    WF   2 ( 1.55052871, 1.55052733, 1.14827518) |   2.61064883  --->CENT
    WF   3 ( 1.55052569, 1.14827674, 1.55052521) |   2.61066105  --->CENT
    WF   4 ( 1.14827660, 1.55052607, 1.55052876) |   2.61063511  --->CENT
    WF   5 ( 0.20111752, 0.20112435, 0.20112008) |   2.61067382  --->CENT
    WF   6 ( 0.20113239,-0.20112644,-0.20113155) |   2.61063347  --->CENT
    WF   7 (-0.20112056, 0.20112674,-0.20111898) |   2.61067162  --->CENT
    WF   8 (-0.20112985,-0.20112333, 0.20113122) |   2.61064610  --->CENT
    Total Center ( 5.39760846, 5.39760756, 5.39760933) sum_spread  20.88521260 --->CENT

where the optimization method and step is indicated by starting with 'SD' or 'CG'. Lines starting with 'WF' show the center of each Wannier function with (x, y, z) coordinates in $\AA$ unit. and its spread in $\AA^{2}$. The sum up of all the Wannier functions center and spread are given in the the line starting with 'Total Center'.