Monitoring optimization of spread function

The output during optimization steps is printed to the 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  |   18.371525257652|   18.371525257652|  ---> DISE
  |     2  |   17.955767336391|   -0.415757921261|  ---> DISE
  |     3  |   17.659503060694|   -0.296264275698|  ---> DISE
  |     4  |   17.454033576174|   -0.205469484520|  ---> DISE
  |     5  |   17.311180447271|   -0.142853128902|  ---> DISE
  |     6  |   17.210945408916|   -0.100235038355|  ---> DISE
  |     7  |   17.139778800398|   -0.071166608519|  ---> DISE
  |     8  |   17.088603102826|   -0.051175697572|  ---> DISE
  |     9  |   17.051329329614|   -0.037273773211|  ---> DISE
  |    10  |   17.023842837298|   -0.027486492316|  ---> 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 |Mode of Gradient|d_Omega_in_steps|     d_Omega   | (in Angs^2) ---> CONV 
  | SD    1 | 6.52434844E-01 | 5.41612774E-04 |-5.41340331E-04|  ---> CONV 
  | SD    2 | 6.51123660E-01 | 5.40524307E-04 |-5.40253165E-04|  ---> CONV 
  .....
  .....
  | SD  200 | 4.77499752E-01 | 3.96392019E-04 |-3.96271308E-04|  ---> CONV 
  |Opt Step |Mode of Gradient|     d_Omega    | (Angs^2) ---> CONV 
  | CG    1 | 8.61043764E-01 | -3.24716990E-01|  ---> CONV 
  .....
  .....
  | CG   58 | 1.67083857E-12 | -5.37225101E-13|  ---> CONV 
  | CG   59 | 5.44431651E-13 | -1.98972260E-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

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

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. [122]. On the other hand, 'd_Omega' is given by

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

where

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 |   16.93053479  |    0.13727387  |    6.57748455 |   23.64529321 |  ---> SPRD 
  | SD    2 |   16.93053479  |    0.13724827  |    6.57696989 |   23.64475295 |  ---> SPRD 
  | SD    3 |   16.93053479  |    0.13722279  |    6.57645620 |   23.64421378 |  ---> SPRD 
  | SD    4 |   16.93053479  |    0.13719743  |    6.57594347 |   23.64367569 |  ---> SPRD 
  .....
  .....
  | SD  199 |   16.93053479  |    0.13399285  |    6.48989479 |   23.55442243 |  ---> SPRD 
  | SD  200 |   16.93053479  |    0.13398326  |    6.48950811 |   23.55402616 |  ---> SPRD 
  |Opt Step |     Omega_I    |     Omega_D    |     Omega_OD  |    Tot_Omega  | (Angs^2) ---> SPRD 
  | CG    1 |    16.93053479 |     0.15480701 |    6.14396737 |   23.22930917 |  ---> SPRD 
  | CG    2 |    16.93053479 |     0.17172507 |    5.87830203 |   22.98056189 |  ---> SPRD 
  | CG    3 |    16.93053479 |     0.17012089 |    5.78940789 |   22.89006357 |  ---> SPRD 
  .....
  .....
  | CG   57 |    16.93053479 |     0.16557875 |    5.73752928 |   22.83364282 |  ---> SPRD 
  | CG   58 |    16.93053479 |     0.16557876 |    5.73752928 |   22.83364282 |  ---> SPRD 
  | CG   59 |    16.93053479 |     0.16557876 |    5.73752928 |   22.83364282 |  ---> 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 ( 1.14164289, 1.14164298, 1.14164266) |   2.95573380  --->CENT
  WF   2 ( 1.55716251, 1.55716342, 1.14164203) |   2.95572597  --->CENT
  WF   3 ( 1.55716191, 1.14164295, 1.55716190) |   2.95572978  --->CENT
  WF   4 ( 1.14164389, 1.55716087, 1.55716055) |   2.95572957  --->CENT
  WF   5 ( 0.20775982, 0.20775967, 0.20775893) |   2.95572677  --->CENT
  WF   6 ( 0.20776045,-0.20775959,-0.20775914) |   2.95572605  --->CENT
  WF   7 (-0.20775851, 0.20775981,-0.20775888) |   2.95572925  --->CENT
  WF   8 (-0.20775787,-0.20775767, 0.20775933) |   2.95573335  --->CENT
  Total Center ( 5.39761509, 5.39761243, 5.39760738) sum_spread  23.64583455 --->CENT
  SD     1 ------------------------------------------------------------------------> CENT
  WF   1 ( 1.14164582, 1.14164592, 1.14164559) |   2.95566613  --->CENT
  WF   2 ( 1.55715957, 1.55716049, 1.14164497) |   2.95565831  --->CENT
  WF   3 ( 1.55715897, 1.14164588, 1.55715897) |   2.95566211  --->CENT
  WF   4 ( 1.14164683, 1.55715794, 1.55715761) |   2.95566190  --->CENT
  WF   5 ( 0.20775689, 0.20775673, 0.20775599) |   2.95565910  --->CENT
  WF   6 ( 0.20775752,-0.20775666,-0.20775620) |   2.95565838  --->CENT
  WF   7 (-0.20775558, 0.20775687,-0.20775594) |   2.95566158  --->CENT
  WF   8 (-0.20775493,-0.20775474, 0.20775639) |   2.95566569  --->CENT
  Total Center ( 5.39761509, 5.39761243, 5.39760738) sum_spread  23.64529321 --->CENT
  SD     2 ------------------------------------------------------------------------> CENT
  .....
  .....
  CG    59 ------------------------------------------------------------------------> CENT
  WF   1 ( 1.14585349, 1.14584696, 1.14584386) |   2.85421846  --->CENT
  WF   2 ( 1.55295615, 1.55294970, 1.14584792) |   2.85422167  --->CENT
  WF   3 ( 1.55296133, 1.14584610, 1.55295139) |   2.85421070  --->CENT
  WF   4 ( 1.14584053, 1.55296761, 1.55296391) |   2.85417080  --->CENT
  WF   5 ( 0.20356211, 0.20355857, 0.20355600) |   2.85418933  --->CENT
  WF   6 ( 0.20355119,-0.20355008,-0.20355192) |   2.85422458  --->CENT
  WF   7 (-0.20355306, 0.20355395,-0.20355905) |   2.85420611  --->CENT
  WF   8 (-0.20355603,-0.20356000, 0.20355520) |   2.85420117  --->CENT
  Total Center ( 5.39761571, 5.39761281, 5.39760730) sum_spread  22.83364282 --->CENT

where the optimization method and step are indicated by starting with 'SD' or 'CG'. Lines starting with 'WF' show the center of each Wannier function with (

) coordinates in Å unit. and its spread in Å $^{2}$ . The sum up of all the Wannier functions center and spread are given in the line starting with 'Total Center'.