nanotools.eig module
This module defines the Eig
class.
- class nanotools.eig.Eig(abstol=-1.0, algo='x', elpa_solver='ELPA_SOLVER_2STAGE', elpa_complex_kernel='ELPA_2STAGE_COMPLEX_DEFAULT', elpa_real_kernel='ELPA_2STAGE_REAL_DEFAULT', inclband: List[int] = None, lwork=-1, orfac=1e-06, reduAlgo=2, target_irange: List[int] = None)[source]
Bases:
Base
Eig
class.- abstol
The absolute error tolerance for the eigenvalues.
- Type:
float
- algo
Determine the algorithm used to diagonalize the Kohn-Sham Hamiltonian, or its projection. For projected (dense) eigenvalue problems:
In our experience “x” is both fast and robust. “elpa” is the fastest, especially when solving large systems (i.e. > 1000 orbitals) and when using a lot of processes (i.e. > 100). However, “elpa” requires that
mpidist.orbblk
*mpidist.orbprc
< n, where n is the number of orbitals.Examples:
eig.algo = "elpa"
- Type:
string
- elpa_solver
Sets the ELPA library solver. Allowed values are:
ELPA_SOLVER_1STAGE
ELPA_SOLVER_2STAGE
- Type:
string
- elpa_complex_kernel
Sets the ELPA solver complex kernel. For all allowed values, see ELPA documentation. Some allowed values are:
ELPA_2STAGE_COMPLEX_GENERIC
ELPA_2STAGE_COMPLEX_SSE_BLOCK1
ELPA_2STAGE_COMPLEX_AVX_BLOCK1
ELPA_2STAGE_COMPLEX_AVX2_BLOCK1
ELPA_2STAGE_COMPLEX_AVX512_BLOCK1
ELPA_2STAGE_COMPLEX_DEFAULT
- Type:
string
- elpa_real_kernel
Sets the ELPA solver real kernel. For all allowed values, see ELPA documentation. Some allowed values are:
ELPA_2STAGE_REAL_GENERIC
ELPA_2STAGE_REAL_SSE_BLOCK2
ELPA_2STAGE_REAL_AVX_BLOCK2
ELPA_2STAGE_REAL_AVX2_BLOCK2
ELPA_2STAGE_REAL_AVX512_BLOCK2
ELPA_2STAGE_REAL_DEFAULT
- Type:
string
- inclband
Index range of the energy bands included in the calculation. If
eig.inclband = [il,iu]
, the eigensolver will seek the eigenvalues and/or eigenvectors with an index between il and iu. il <= iu is required; not all eigenpairs need to converge (seetarget_irange
).Examples:
eig.inclband = [430,470]
- Type:
1D array
- lwork
Size of the work array in ScaLAPACK. If
lwork
is -1, then ScaLAPACK estimates the optimal work array size. Iflwork
is too small ScaLAPACK will compromise on precision or crash. Don’t worry, it will throw at least a warning. If that happends, just increase the value oflwork
by a factor 2 until the message disappear.Examples:
eig.lwork = 2000000
- Type:
integer
- orfac
Specifies which eigenvectors should be reorthogonalized. Eigenvectors that correspond to eigenvalues which are within
tol=orfac*norm(A)
of each other are to be reorthogonalized. However, if the workspace is insufficient (seelwork
), tolerance may be decreased until all eigenvectors to be reorthogonalized can be stored in one process. No reorthogonalization will be done iforfac
equals zero. A default value of 1e-3 is used iforfac
is negative.orfac
should be identical on all processes.Examples:
eig.orfac = 1e-8
- Type:
float
- reduAlgo
- Switch between triangular inverse (1) and ScaLAPACK’s sygst (2) to reduce the
eigenvalue problem from general to standard form. If
algo=elpa
thenreduAlgo=3
uses ELPA’s Cannon algorithm if the number of process rows divides the number of process columns (seempidist.orbprc
). This parameter impacts performance.Examples:
eig.reduAlgo = 2
- Type:
integer
- target_irange
Index range of the energy bands that are forced to converge according to the tolerance given by
abstol
.Examples:
eig.target_irange = [440,460]
- Type:
1D array
- get_number_of_bands()[source]
Returns the number of bands.
The total number of bands usually include some bands that act as a buffer and hence they are not necessarily accurate. For bands satifying the prescribed tolerance, refer to
target_irange
.
- set_abstol(abstol)[source]
Sets the parameter abstol.
The absolute error tolerance for the eigenvalues.
- set_algo(algo)[source]
Sets the parameter algo.
Determine the algorithm used to diagonalize the Kohn-Sham Hamiltonian, or its projection. For projected (dense) eigenvalue problems:
In our experience “x” is both fast and robust. “elpa” is the fastest, especially when solving large systems (i.e. > 1000 orbitals) and when using a lot of processes (i.e. > 100). However, “elpa” requires that
mpidist.orbblk
*mpidist.orbprc
< n, where n is the number of orbitals.
- set_elpa_complex_kernel(elpa_complex_kernel)[source]
Sets the parameter elpa_complex_kernel.
For all allowed values, see ELPA documentation. Some allowed values are:
ELPA_2STAGE_COMPLEX_GENERIC
ELPA_2STAGE_COMPLEX_SSE_BLOCK1
ELPA_2STAGE_COMPLEX_AVX_BLOCK1
ELPA_2STAGE_COMPLEX_AVX2_BLOCK1
ELPA_2STAGE_COMPLEX_AVX512_BLOCK1
ELPA_2STAGE_COMPLEX_DEFAULT
- set_elpa_real_kernel(elpa_real_kernel)[source]
Sets the parameter elpa_real_kernel.
For all allowed values, see ELPA documentation. Some allowed values are:
ELPA_2STAGE_REAL_GENERIC
ELPA_2STAGE_REAL_SSE_BLOCK2
ELPA_2STAGE_REAL_AVX_BLOCK2
ELPA_2STAGE_REAL_AVX2_BLOCK2
ELPA_2STAGE_REAL_AVX512_BLOCK2
ELPA_2STAGE_REAL_DEFAULT
- set_elpa_solver(elpa_solver)[source]
Sets the parameter elpa_solver.
Allowed values are:
ELPA_SOLVER_1STAGE
ELPA_SOLVER_2STAGE
- set_lwork(lwork)[source]
Sets the parameter lwork.
Size of the work array in ScaLAPACK. If
lwork
is -1, then ScaLAPACK estimates the optimal work array size. Iflwork
is too small ScaLAPACK will compromise on precision or crash. Don’t worry, it will throw at least a warning. If that happends, just increase the value oflwork
by a factor 2 until the message disappear.
- set_orfac(orfac)[source]
Sets the parameter orfac.
Specifies which eigenvectors should be reorthogonalized. Eigenvectors that correspond to eigenvalues which are within
tol=orfac*norm(A)
of each other are to be reorthogonalized. However, if the workspace is insufficient (seelwork
), tolerance may be decreased until all eigenvectors to be reorthogonalized can be stored in one process. No reorthogonalization will be done iforfac
equals zero. A default value of 1e-3 is used iforfac
is negative.orfac
should be identical on all processes.
- set_reduAlgo(reduAlgo)[source]
Sets the parameter reduAlgo.
Switch between triangular inverse (1) and ScaLAPACK’s sygst (2) to reduce the eigenvalue problem from general to standard form. If
algo=elpa
thenreduAlgo=3
uses ELPA’s Cannon algorithm if the number of process rows divides the number of process columns (seempidist.orbprc
). This parameter impacts performance.