mirror of https://github.com/phonopy/phono3py.git
Update of LBTE document
This commit is contained in:
Atsushi Togo
parent
3a80a5ed49
commit
bac9ac8305
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@ -540,6 +540,17 @@ the results, ``--write-gamma`` option has to be specified and the
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physical properties belonging to the grid
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points are written into ``kappa-mxxx-gx(-sx).hdf5``.
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``--lbte``: Thermal conductivity with direct solution of LBTE
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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(Setting tag: ``BTERTA``, ``.TRUE.`` or ``.FALSE.``)
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Run calculation of lattice thermal conductivity tensor with a direct
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solution of linearized phonon Boltzmann equation. The basis usage of
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this option is equivalent to that of ``--br``. More detail is
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documented at :ref:`direct_solution`.
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``--isotope``: Phonon-isotope scattering
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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@ -11,15 +11,270 @@ This page explains how to use the direct solution of LBTE by
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:depth: 2
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:local:
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How to use
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----------
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Installation of collision matrix diagonalization solvers
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---------------------------------------------------------
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As written in the following sections, this calculation requires large
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memory space. When running multiple temperature points, simply the
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memory space needed is multiplied by the number of the temperature
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points. Therefore it is normally recommended to specify :ref:`--ts
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option <ts_option>`. An example to run with the direct solution of
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LBTE for ``example/Si-PBEsol`` is as follows::
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For the collision matrix diagonalization that is computationally and
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memory demanding, there are a few choices shown below. Multithreaded
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BLAS is necessary to achieve it in a reasonable computatin time with
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many cores such as 20 cores per node. This is also a memory demanding
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calculation.
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% phono3py --dim="2 2 2" --sym-fc -c POSCAR-unitcell
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...
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% phono3py --dim="2 2 2" --pa="0 1/2 1/2 1/2 0 1/2 1/2 1/2 0" -c POSCAR-unitcell --mesh="11 11 11" --fc3 --fc2 --lbte --ts=300
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...
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=================== End of collection of collisions ===================
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- Averaging collision matrix elements by phonon degeneracy [0.031s]
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- Making collision matrix symmetric (built-in) [0.000s]
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----------- Thermal conductivity (W/m-k) with tetrahedron method -----------
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Diagonalizing by lapacke dsyev... [0.111s]
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Calculating pseudo-inv with cutoff=1.0e-08 (np.dot) [0.001s]
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# T(K) xx yy zz yz xz xy
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300.0 111.588 111.588 111.588 0.000 0.000 -0.000
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(RTA) 109.009 109.009 109.009 0.000 0.000 -0.000
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----------------------------------------------------------------------------
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Thermal conductivity and related properties were written into
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"kappa-m111111.hdf5".
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Eigenvalues of collision matrix were written into "coleigs-m111111.hdf5"
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_
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___ _ __ __| |
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/ _ \ '_ \ / _` |
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| __/ | | | (_| |
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\___|_| |_|\__,_|
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Memory usage
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-------------
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The direct solution of LBTE needs diagonalization of a large collision
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matrix, which requires large memory space. This is the largest
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limitation of using this method. The memory size needed for one
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collision matrix at a temperature point is :math:`(\text{number of
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irreducible grid points} \times \text{number of bands} \times 3)^2`
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for the symmetrized collision matrix.
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..
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and :math:`(\text{number of grid
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points} \times \text{number of bands})^2` for the non-symmetrized
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collision matrix.
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These collision matrices contain real values and are supposed to be
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64bit float symmetric matrices. During the diagonalization of each
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collision matrix with LAPACK ``dsyev`` solver, around 1.2 times more
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memory space is consumed in total.
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When phono3py runs with :ref:`--wgp option <wgp_option>` together with
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``--lbte`` option, estimated memory space needed for storing collision
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matrix is presented. An example for ``example/Si-PBEsol`` is as follows::
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% phono3py --dim="2 2 2" --pa="0 1/2 1/2 1/2 0 1/2 1/2 1/2 0" -c POSCAR-unitcell --mesh="40 40 40" --wgp --lbte
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...
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Memory requirements:
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- Piece of collision matrix at each grid point, temp and sigma: 0.00 Gb
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- Full collision matrix at each temp and sigma: 7.15 Gb
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- Phonons: 0.04 Gb
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- Grid point information: 0.00 Gb
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- Phonon properties: 0.14 Gb
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...
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With :ref:`--stp option <stp_option>`, estimated
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memory space needed for ph-ph interaction strengths is shown.
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Work load distribution
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-----------------------
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The other difficulty compared with RTA is the workload
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distribution. Currently there are two ways to distribute the
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calculation: (1) Collision matrix is divided and the pieces are
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distributed into computing nodes. (2) Ph-ph interaction strengths at
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grid points are distributed into computing nodes. These two can not be
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mixed, so one of them has to be chosen. In either case, the
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distribution is done simply running a set of phono3py calculations
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over grid points and optionally band indices. The data computed on
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each computing node are stored in an hdf5 file. Increasing the
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calculation size, e.g., larger mesh numbers or larger number of atoms
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in the primitive cell, large files are created.
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.. _distribution_colmat:
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Distribution of collision matrix
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^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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A full collision matrix is divided into pieces at grid points of
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irreducible part of Brillouin zone. Each piece is calculated
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independently from the other pieces. After finishing the calculations
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of these pieces, the full collision matrix is diagonzalized to obtain
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the thermal conductivity.
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File size of Each piece of the collision matrix can be
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large. Therefore it is recommended to use :ref:`--ts option
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<ts_option>` to limit the number of temperature points, e.g.,
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``--ts="100 200 300 400 500``, depending on the memory size installed
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on each computing node. To write them into files,
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``--write-collision`` option must be specified, and to read them from
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files, ``--read-collision`` option is used. These are similarly used
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as :ref:`--write-gamma <write_gamma_option>` and :ref:`--read-gamma
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<read_gamma_option>` options for RTA calculation as shown in
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:ref:`workload_distribution`.
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``--read-collision`` option collects the pieces and make one full
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collision matrix, then starts to diagonalize it. This option requires
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one argument to specify an index to read the collision matrix at one
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temperature point, e.g., the collision matrix at 200K is read with
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``--read-collision=1`` for the (pieces of) collision matrices created
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with ``--ts="100 200 300 400 500"`` (corresponding to 0, 1, 2, 3,
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4). The temperature (e.g. 200K) is also read from the file, so it is
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unnecessary to specify :ref:`--ts option <ts_option>` when reading.
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The summary of the procedure is as follows:
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1. Running at each grid point with :ref:`--gp <gp_option>` (or
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:ref:`--ga <ga_option>`) option and
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saving the piece of the collision matrix to an hdf5 file with
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``--write-collision`` option. It is probably OK to calculate and
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store the pieces of the collision matrices at multiple temperatures
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though it depends on memory size of the computer node. This
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calculation has to be done at all irreducible grid points.
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2. Collecting and creating all necessary pieces of the collision
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matrix with ``--read-collision=num`` (``num``: index of
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temperature). By this one full collision matrix at the selected
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temperature is created and then diagonalized. An option ``-o num``
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may be used together with ``--read-collision`` to distinguish the
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file names of the results at different temperatures.
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Examples of command options are shown below using ``Si-PBE`` example.
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Irreducible grid point indices are obtained by :ref:`--wgp option<wgp_option>`::
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% phono3py --dim="2 2 2" --pa="0 1/2 1/2 1/2 0 1/2 1/2 1/2 0" -c POSCAR-unitcell --mesh="19 19 19" --lbte --wgp
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and the information is given in ``ir_grid_points.yaml``. For
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distribution of collision matrix calculation (see also :ref:`workload_distribution`)::
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% phono3py --dim="2 2 2" --pa="0 1/2 1/2 1/2 0 1/2 1/2 1/2 0" -c POSCAR-unitcell --mesh="19 19 19" --fc3 --fc2 --lbte --ts=300 --write-collision --gp="grid_point_numbers..."
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To collect distributed pieces of the collision matrix::
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% phono3py --dim="2 2 2" --pa="0 1/2 1/2 1/2 0 1/2 1/2 1/2 0" -c POSCAR-unitcell --mesh="19 19 19" --fc3 --fc2 --lbte --ts=300 --read-collision=0
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Distribution of phonon-phonon interaction strengths
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^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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The distribution of pieces of collision matrix is straightforward and
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is recommended to use if the number of temperature points is
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small. However increasing data file size, network communication
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becomes to require long time to send the files from a master node to
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computation nodes. In this case, the distribution over ph-ph
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interaction strengths can be another choice. Since, without using
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:ref:`--full-pp option <full_pp_option>`, the tetrahedron method or
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smearing approach with :ref:`--sigma-cutoff option
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<sigma_cutoff_option>` results in the sparse ph-ph interaction
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strength data array, i.e., most of the elements are zero, the data
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size can be reduced by only storing non-zero elements. Not like the
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collision matrix, the ph-ph interaction strengths in phono3py are
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independent from temperature though it is not the case if the force
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constants provided are temperature dependent. Once
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stored, they are used to create the collision matrices at
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temperatures. Using ``--write-pp`` and ``--read-pp``, they are written
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into and read from hdf5 files at grid points.
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It is also recommended to use :ref:`--write-phonon option
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<write_phonon_option>` and :ref:`--read-phonon option
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<read_phonon_option>` to use identical phonon eigenvectors among the
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distributed nodes.
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The summary of the procedure is as follows:
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1. Running at each grid point with :ref:`--gp <gp_option>` (or
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:ref:`--ga <ga_option>`) option and storing the ph-ph interaction
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strengths to an hdf5 file with ``--write-pp`` option. This calculation
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has to be done at all irreducible grid points.
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2. Running with ``--read-pp`` option and without :ref:`--gp <gp_option>` (or
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:ref:`--ga <ga_option>`) option. By this one full collision matrix at the
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selected temperature is created and then diagonalized. An option
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``-o num`` may be used together with ``--read-collision`` to
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distinguish the file names of the results at different
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temperatures.
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Examples of command options are shown below using ``Si-PBE`` example.
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Irreducible grid point indices are obtained by :ref:`--wgp option<wgp_option>`::
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% phono3py --dim="2 2 2" --pa="0 1/2 1/2 1/2 0 1/2 1/2 1/2 0" -c POSCAR-unitcell --mesh="19 19 19" --lbte --wgp
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and the grid point information is provided in
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``ir_grid_points.yaml``. All phonons on mesh grid points are saved
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by::
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% phono3py --dim="2 2 2" --pa="0 1/2 1/2 1/2 0 1/2 1/2 1/2 0" -c POSCAR-unitcell --mesh="19 19 19" --fc2 --write-phonon
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For distribution of ph-ph interaction strength calculation (see also
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:ref:`workload_distribution`)::
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% phono3py --dim="2 2 2" --pa="0 1/2 1/2 1/2 0 1/2 1/2 1/2 0" -c POSCAR-unitcell --mesh="19 19 19" --fc3 --fc2 --lbte --ts=300 --write-pp --gp="grid_point_numbers..." --read-phonon
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Here one temperature has to be specified but any one of temperatures
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is OK since ph-ph interaction strength computed here is assumed to be
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temperature independent. Then the computed ph-ph interaction strengths
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are read and used to compute collision matrix and lattice thermal
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conductivity at a temperature by
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::
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% phono3py --dim="2 2 2" --pa="0 1/2 1/2 1/2 0 1/2 1/2 1/2 0" -c POSCAR-unitcell --mesh="19 19 19" --fc3 --fc2 --lbte --ts=300 --read-pp --read-phonon
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This last command is repeated at different temperatures to obtain the
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properties at multiple temperatures.
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.. _diagonzalization_solver:
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Cutoff parameter of pseudo inversion
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-------------------------------------
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To achieve a pseudo inversion, a cutoff parameter is used to find null
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space, i.e., to select the nearly zero eigenvalues. The default cutoff
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value is ``1e-8``, and this hopefully works in many cases. But if a
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collision matrix is numerically not very accurate, we may have to
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carefully choose the value by ``--pinv-cutoff`` option. It is safer to
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plot the absolute values of eigenvalues in log scale to see if there
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is clear gap between non-zero eigenvalue and nearly-zero eigenvalues.
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After running the direct solution of LBTE, ``coleigs-mxxx.hdf5`` is
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created. This contains the eigenvalues of the collision matrix (either
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symmetrized or non-symmetrized). The eigenvalues are plotted using
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``phono3py-coleigplot`` in the phono3py package::
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phono3py-coleigplot coleigs-mxxx.hdf5
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It is assumed that only one set of eigenvalues at a temperature point
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is contained.
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.. figure:: Si-coleigplot.png
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:width: 50%
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:name: coleigplot
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Eigenvalues are plotted in log scale (Si-PBEsol exmaple with
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15x15x15 mesh). The number in x-axis is just the index where each
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eigenvalue is stored. Normally the eigenvalues are stored ascending
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order. The bule points show the positive values, and
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the red points show the negative values as positive values
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(absolute values) to be able to plot in log scale. In this plot, we
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can see the gap between :math:`10^{-4}` and :math:`10^{-16}`, which
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is a good sign. The values whose absolute values are smaller than
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:math:`10^{-8}` are treated as 0 and those solutions are considered
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as null spaces.
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Installation of diagonalization solvers with multithreaded BLAS
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---------------------------------------------------------------
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Multithreaded BLAS is recommended to use for the calculation of the
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direct solution of LBTE since the diagonalization of the collision
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matrix is computationally demanding. A few examples of how to install
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multithreded BLAS libraries are presented below.
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MKL linked scipy
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^^^^^^^^^^^^^^^^^^
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@ -90,212 +345,3 @@ chosen:
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The solver choices other than ``--pinv-solver=1`` and
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``--pinv-solver=4`` are dangerous and not recommend. They exist just
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for the tests.
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Memory usage
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-------------
|
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|
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The direct solution of LBTE needs diagonalization of a large collision
|
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matrix, which requires large memory space. This is the largest
|
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limitation of using this method. The memory size needed for one
|
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collision matrix at one temperature point is :math:`(\text{number of
|
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irreducible grid points} \times \text{number of bands} \times 3)^2`
|
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for the symmetrized collision matrix.
|
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|
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..
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and :math:`(\text{number of grid
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points} \times \text{number of bands})^2` for the non-symmetrized
|
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collision matrix.
|
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|
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These collision matrices contain real values and are supposed to be
|
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64bit float symmetric matrices. During the diagonalization with LAPACK
|
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``dsyev`` solver, around 1.2 times more memory space of that needed
|
||||
for the collision matrix is required.
|
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|
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When phono3py runs with :ref:`--wgp option <wgp_option>` together with
|
||||
``--lbte`` option, estimated memory space needed for storing collision
|
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matrix is presented. With :ref:`--stp option <stp_option>`, estimated
|
||||
memory space needed for ph-ph interaction strengths is shown.
|
||||
|
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Work load distribution
|
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-----------------------
|
||||
|
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The other difficulty compared with RTA is the workload
|
||||
distribution. Currently there are two ways to distribute the
|
||||
calculation: (1) Collision matrix is divided and the pieces are
|
||||
distributed into computing nodes. (2) Ph-ph interaction strengths at
|
||||
grid points are distributed into computing nodes. These two can not be
|
||||
mixed, so one of them has to be chosen. In either case, the
|
||||
distribution is done simply running a set of phono3py calculations
|
||||
over grid points and optionally band indices. The data computed on
|
||||
each computing node are stored in an hdf5 file. Increasing the
|
||||
calculation size, e.g., larger mesh numbers or larger number of atoms
|
||||
in the primitive cell, large files are created.
|
||||
|
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.. _distribution_colmat:
|
||||
|
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Distribution of collision matrix
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^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
|
||||
|
||||
A full collision matrix is divided into pieces at grid points of
|
||||
irreducible part of Brillouin zone. Each piece is calculated
|
||||
independently from the other pieces. After finishing the calculations
|
||||
of these pieces, the full collision matrix is diagonzalized to obtain
|
||||
the thermal conductivity.
|
||||
|
||||
File size of Each piece of the collision matrix can be
|
||||
large. Therefore it is recommended to use :ref:`--ts option
|
||||
<ts_option>` to limit the number of temperature points, e.g.,
|
||||
``--ts="100 200 300 400 500``, depending on the memory size installed
|
||||
on each computing node. To write them into files,
|
||||
``--write-collision`` option must be specified, and to read them from
|
||||
files, ``--read-collision`` option is used. These are similarly used
|
||||
as :ref:`--write-gamma <write_gamma_option>` and :ref:`--read-gamma
|
||||
<read_gamma_option>` options for RTA calculation as shown in
|
||||
:ref:`workload_distribution`.
|
||||
``--read-collision`` option collects the pieces and make one full
|
||||
collision matrix, then starts to diagonalize it. This option requires
|
||||
one argument to specify an index to read the collision matrix at one
|
||||
temperature point, e.g., the collision matrix at 200K is read with
|
||||
``--read-collision=1`` for the (pieces of) collision matrices created
|
||||
with ``--ts="100 200 300 400 500"`` (corresponding to 0, 1, 2, 3,
|
||||
4). The temperature (e.g. 200K) is also read from the file, so it is
|
||||
unnecessary to specify :ref:`--ts option <ts_option>` when reading.
|
||||
|
||||
The summary of the procedure is as follows:
|
||||
|
||||
1. Running at each grid point with :ref:`--gp <gp_option>` (or
|
||||
:ref:`--ga <ga_option>`) option and
|
||||
saving the piece of the collision matrix to an hdf5 file with
|
||||
``--write-collision`` option. It is probably OK to calculate and
|
||||
store the pieces of the collision matrices at multiple temperatures
|
||||
though it depends on memory size of the computer node. This
|
||||
calculation has to be done at all irreducible grid points.
|
||||
2. Collecting and creating all necessary pieces of the collision
|
||||
matrix with ``--read-collision=num`` (``num``: index of
|
||||
temperature). By this one full collision matrix at the selected
|
||||
temperature is created and then diagonalized. An option ``-o num``
|
||||
may be used together with ``--read-collision`` to distinguish the
|
||||
file names of the results at different temperatures.
|
||||
|
||||
Examples of command options are shown below using ``Si-PBE`` example.
|
||||
Irreducible grid point indices are obtained by :ref:`--wgp option<wgp_option>`::
|
||||
|
||||
phono3py --dim="2 2 2" --pa="0 1/2 1/2 1/2 0 1/2 1/2 1/2 0" -c POSCAR-unitcell --mesh="19 19 19" --fc3 --fc2 --lbte --ts=300 --wgp
|
||||
|
||||
and the information is given in ``ir_grid_points.yaml``. For
|
||||
distribution of collision matrix calculation (see also :ref:`workload_distribution`)::
|
||||
|
||||
phono3py --dim="2 2 2" --pa="0 1/2 1/2 1/2 0 1/2 1/2 1/2 0" -c POSCAR-unitcell --mesh="19 19 19" --fc3 --fc2 --lbte --ts=300 --write-collision --gp="grid_point_numbers..."
|
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|
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To collect distributed pieces of the collision matrix::
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|
||||
phono3py --dim="2 2 2" --pa="0 1/2 1/2 1/2 0 1/2 1/2 1/2 0" -c POSCAR-unitcell --mesh="19 19 19" --fc3 --fc2 --lbte --ts=300 --read-collision=0
|
||||
|
||||
Distribution of phonon-phonon interaction strengths
|
||||
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
|
||||
|
||||
The distribution of pieces of collision matrix is straightforward and
|
||||
is recommended to use if the number of temperature points is
|
||||
small. However increasing data file size, time taking for network
|
||||
communication becomes non-negligible. In this case, the distribution
|
||||
over ph-ph interaction strengths can be another choice. Since, without
|
||||
using :ref:`--full-pp option <full_pp_option>`, the tetrahedron method
|
||||
or smearing approach with :ref:`--sigma-cutoff option
|
||||
<sigma_cutoff_option>` results in the sparse ph-ph interaction
|
||||
strength data array, i.e., most of the elements are zero, the file
|
||||
size can be reduced by only storing non-zero elements. Not like the
|
||||
collision matrix, the ph-ph interaction strengths in phono3py are
|
||||
independent from temperature. Once stored, they are used to create the
|
||||
collision matrices at temperatures. Using ``--write-pp`` and
|
||||
``--read-pp``, they are written into and read from hdf5 files at grid
|
||||
points.
|
||||
|
||||
In this approach, the computer environment for writing and reading the
|
||||
hdf5 files should be almost the same. If they are different, phonon
|
||||
eigenvectors for degenerate bands are often computed differently,
|
||||
although with almost the same eigenvalues, and these different
|
||||
eigenvectors would induce slightly different results. Probably the
|
||||
difference will be negligible, but if most secured results are
|
||||
expected, it is recommended to use :ref:`--write-phonon option
|
||||
<write_phonon_option>` and :ref:`--read-phonon option
|
||||
<read_phonon_option>` by which the same phonon eigenvectors are
|
||||
employed throughout the calculation.
|
||||
|
||||
The summary of the procedure is as follows:
|
||||
|
||||
1. Running at each grid point with :ref:`--gp <gp_option>` (or
|
||||
:ref:`--ga <ga_option>`) option and saving the ph-ph interaction
|
||||
strengths to an hdf5 file with ``--write-pp`` option. This calculation
|
||||
has to be done at all irreducible grid points.
|
||||
2. Running with ``--read-pp`` option and without :ref:`--gp <gp_option>` (or
|
||||
:ref:`--ga <ga_option>`) option. By this one full collision matrix at the
|
||||
selected temperature is created and then diagonalized. An option
|
||||
``-o num`` may be used together with ``--read-collision`` to
|
||||
distinguish the file names of the results at different
|
||||
temperatures.
|
||||
|
||||
Examples of command options are shown below using ``Si-PBE`` example.
|
||||
Irreducible grid point indices are obtained by :ref:`--wgp option<wgp_option>`::
|
||||
|
||||
phono3py --dim="2 2 2" --pa="0 1/2 1/2 1/2 0 1/2 1/2 1/2 0" -c POSCAR-unitcell --mesh="19 19 19" --fc3 --fc2 --lbte --ts=300 --wgp
|
||||
|
||||
and the information is given in ``ir_grid_points.yaml``. Optionally
|
||||
all phonons on mesh grid points are saved by::
|
||||
|
||||
phono3py --dim="2 2 2" --pa="0 1/2 1/2 1/2 0 1/2 1/2 1/2 0" -c POSCAR-unitcell --mesh="19 19 19" --fc2 --write-phonon
|
||||
|
||||
For distribution of collision matrix calculation (see also :ref:`workload_distribution`)::
|
||||
|
||||
phono3py --dim="2 2 2" --pa="0 1/2 1/2 1/2 0 1/2 1/2 1/2 0" -c POSCAR-unitcell --mesh="19 19 19" --fc3 --fc2 --lbte --ts=300 --write-pp --gp="grid_point_numbers..."
|
||||
|
||||
If the phonon data file was created by ``--write-phonon`` option in
|
||||
the previous step::
|
||||
|
||||
phono3py --dim="2 2 2" --pa="0 1/2 1/2 1/2 0 1/2 1/2 1/2 0" -c POSCAR-unitcell --mesh="19 19 19" --fc3 --fc2 --lbte --ts=300 --write-pp --gp="grid_point_numbers..." --read-phonon
|
||||
|
||||
not to recalculate phonons but read from the file. To collect
|
||||
distributed pieces of the collision matrix::
|
||||
|
||||
phono3py --dim="2 2 2" --pa="0 1/2 1/2 1/2 0 1/2 1/2 1/2 0" -c POSCAR-unitcell --mesh="19 19 19" --fc3 --fc2 --lbte --ts=300 --read-pp
|
||||
|
||||
Again if the phonon data file exists::
|
||||
|
||||
phono3py --dim="2 2 2" --pa="0 1/2 1/2 1/2 0 1/2 1/2 1/2 0" -c POSCAR-unitcell --mesh="19 19 19" --fc3 --fc2 --lbte --ts=300 --read-pp --read-phonon
|
||||
|
||||
.. _diagonzalization_solver:
|
||||
|
||||
Cutoff parameter of pseudo inversion
|
||||
-------------------------------------
|
||||
|
||||
To achieve a pseudo inversion, a cutoff parameter is used to find null
|
||||
space, i.e., to select the nearly zero eigenvalues. The default cutoff
|
||||
value is ``1e-8``, and this hopefully works in many cases. But if a
|
||||
collision matrix is numerically not very accurate, we may have to
|
||||
carefully choose the value by ``--pinv-cutoff`` option. It is safer to
|
||||
plot the absolute values of eigenvalues in log scale to see if there
|
||||
is clear gap between non-zero eigenvalue and nearly-zero eigenvalues.
|
||||
After running the direct solution of LBTE, ``coleigs-mxxx.hdf5`` is
|
||||
created. This contains the eigenvalues of the collision matrix (either
|
||||
symmetrized or non-symmetrized). The eigenvalues are plotted using
|
||||
``phono3py-coleigplot`` in the phono3py package::
|
||||
|
||||
phono3py-coleigplot coleigs-mxxx.hdf5
|
||||
|
||||
It is assumed that only one set of eigenvalues at a temperature point
|
||||
is contained.
|
||||
|
||||
.. figure:: Si-coleigplot.png
|
||||
:width: 50%
|
||||
:name: coleigplot
|
||||
|
||||
Eigenvalues are plotted in log scale (Si-PBEsol exmaple with
|
||||
15x15x15 mesh). The number in x-axis is just the index where each
|
||||
eigenvalue is stored. Normally the eigenvalues are stored ascending
|
||||
order. The bule points show the positive values, and
|
||||
the red points show the negative values as positive values
|
||||
(absolute values) to be able to plot in log scale. In this plot, we
|
||||
can see the gap between :math:`10^{-4}` and :math:`10^{-16}`, which
|
||||
is a good sign. The values whose absolute values are smaller than
|
||||
:math:`10^{-8}` are treated as 0 and those solutions are considered
|
||||
as null spaces.
|
||||
|
|
|
|||
Loading…
Reference in New Issue