4.3.13. Lanczos_Step.dat

(For the Lanczos method) This file is outputted to show the process information for calculating the eigenvector by Lanczos method. An example of the file format for the Lanczos method is shown as follows.
For method="Lanczos"
LanczosStep  E[1] E[2] E[3] E[4] Target:E[3] E_Max/Nsite
stp = 2 1.2149586211 14.6560471044 xxxxxxxxxx xxxxxxxxx 0.0000000000 xxxxxxxxx
stp=4 -5.6626980051 3.1523174817 12.4860778911 21.2322666770 12.4860778911 2.6540333346
stp=6 -8.5113374325 -2.3219709559 4.3459108959 11.5079386600 4.3459108959 3.0307814358
stp=8 -9.5061025854 -5.2757708534 -0.1734100333 5.2236216333 -0.1734100333 3.2049774861
stp=10 -9.7541889139 -6.6054773893 -2.9493235242 1.2364826532 -2.9493235242 3.2686702753
...
stp=84 -10.4543987874 -9.8960493865 -9.7550111859 -9.7407358084 -9.7550111859 3.3731105157
stp=86 -10.4543987874 -9.8960493865 -9.7550111859 -9.7407358084 -9.7550111859 3.3731105157
stp=88 -10.4543987874 -9.8960493865 -9.7550111859 -9.7407358084 -9.7550111859 3.3731105157
For method="CG"
  Step   Residual-2-norm     Threshold      Energy
      1     6.79819e+00     8.19743e-07    7.86586e+00     8.19743e+00     8.02804e+00
      2     7.47402e+00     3.69905e-07    3.35827e+00     3.63546e+00     3.69905e+00
      3     5.30943e+00     2.44472e-07   -2.44472e+00    -2.23296e+00    -1.95487e+00
      4     4.52737e+00     5.10297e-07   -5.10297e+00    -4.92390e+00    -4.58682e+00
      5     3.66168e+00     7.14105e-07   -7.14105e+00    -6.91226e+00    -6.44532e+00
      6     3.12717e+00     8.27201e-07   -8.27201e+00    -7.93262e+00    -7.44680e+00
...
    152     1.05602e-06     1.04544e-06   -1.04544e+01    -9.89605e+00    -9.89605e+00
    153     1.07401e-06     1.04544e-06   -1.04544e+01    -9.89605e+00    -9.89605e+00
    154     9.45018e-07     1.04544e-06   -1.04544e+01    -9.89605e+00    -9.89605e+00

File name

  • ##_Lanczos_Step.dat

## indicates a header defined by [string02] in a ModPara file.

File format

  • For``method=”Lanczos”``

    stp= [int01] [double01] [double02] [double03] [double04] [double-a] [double-b]

  • For method="CG"

    [int01] [double-c] [double-d] [double01] [double02] …

Parameters

  • [int01]

    Type : Int

    Description : The iteration number of the Lanczos and LOBCG method.

  • [double01], [double02], [double03], [double04] …

    Type : Double

    Description : Eigenvalues computed with the Lanczos or LOBCG method (ascending order). Four and exct eigenvalues are printed for the Lanczos and LOBCG method, respectively (in the above case, exct=3). While the degenerate eigenstates are printed as a single state in the Lanczos method, they are printed separately in LOBCG method. In the above case, we can find there is a degeneracy in the first excited state.

  • [double-a]

    Type : Double

    Description : (Only for the Lanczos method) The eigenvalue used for the convergence check. It was specified by LanczosTarget (in the above case, LanczosTarget=3).

  • [double-b]

    Type : Double

    Description : (Only for the Lanczos method) The maximum eigenvalue divided by the number of sites. It is the lower limit of LargeValue in TPQ method.

  • [double-c]

    Type : Double

    Description : (Only for LOBCG method) The maximum of the 2-norm of each residual vector. It is used for the convergence check.

  • [double-d]

    Type : Double

    Description : (Only for LOBCG method) The convergence threshold. This is obtained by the value specified with LanczosEps times the absolute value of the energy of the ground state.