Probing hidden spin order with interpretable machine learning
These are the source codes accompanying the papers:
- Jonas Greitemann, Ke Liu, and Lode Pollet: Probing hidden spin order with interpretable machine learning, Phys. Rev. B 99, 060404(R) (2019), open access via arXiv:1804.08557;
- Ke Liu, Jonas Greitemann, and Lode Pollet: Learning multiple order parameters with interpretable machines, Phys. Rev. B 99, 104410 (2019), open access via arXiv:1810.05538;
- Jonas Greitemann, Ke Liu, Ludovic D.C. Jaubert, Han Yan, Nic Shannon, and Lode Pollet: Identification of emergent constraints and hidden order in frustrated magnets using tensorial kernel methods of machine learning, Phys. Rev. B 100, 174408 (2019), open access via arXiv:1907.12322.
They aim to provide a reusable framework that may be used to apply the TK-SVM
method to third-party Monte Carlo simulations written using ALPSCore (→ Project
structure). The gauge theory code used for the
first two papers is included as part of this repository. The simulation of the
XXZ pyrochlore model for the third paper is not openly available, yet the
present version of the framework contains many of the supporting features. While
this version is still capable of producing the results presented in the first
two papers, you may want to check out the versions of the code that were
originally published along with the first two papers. The relevant commits are
tagged PRB-99-060404(R) and PRB-99-104410, respectively, i.e. run
$ git checkout PRB-99-060404(R)
$ git checkout PRB-99-104410Additionally J. Greitemann's PhD thesis includes results for the simulation of the Kagome antiferromagnet which may also be reproduced using the present version of the code.
- Dependencies
- Project structure
- Building and installation
- Basic usage
- Runtime parameters
- Client code API
- License
A Changelog is provided separately.
These codes are based on the ALPSCore library. Refer to their website for installation instructions. ALPSCore requires the Boost and HDF5 libraries.
Further, we require a C++ compiler (tested with GCC 9 and Clang 8) with
C++14 support. For the solution of the SVM optimization problem, we rely on the
libsvm library which is included as part of our self-developed C++ wrapper
library which is kept in-tree as a git submodule. Argh! is used for
parsing command line options. Eigen 3 is used for linear algebra.
As of version 3.0, MPI is used for parallelization. A thread-safe MPI
implementation is hence required (MPI_THREAD_MULTIPLE build option enabled;
tested with Open MPI 4.0 and MPICH 3.3).
This repository contains three client codes which are for the most part regular Monte Carlo simulation codes based on the ALPSCore framework. In addition they implement the relevant API functions required by the TK-SVM framework.
The client codes are kept in their eponymous subdirectories:
ising: This is a copy of the ALPSCore demo code for the 2D Ising model. It may be used to reproduce the results presented in P. Ponte and R.G. Melko, Phys. Rev. B 96, 205146 (2017).gauge: Lattice gauge model proposed in K. Liu, J. Nissinen, R.-J. Slager, K. Wu, and J. Zaanen, PRX 6, 041025 (2016) which lets us realize arbitrary orientational orders and was used to produce the results in our first two papers.frustmag: A generic code for classical Monte Carlo simulations of models of frustrated magnets. Several lattice geometries are available to choose from, additional interactions may be included with relative ease. Supports several update schemes, including parallel tempering. This implementation was used to generate data for the study of the Kagome antiferromagnet in Ch. 9 of J. Greitemann's PhD thesis.
Additional information on the runtime parameters pertaining to these client codes are documented in the README files accompanying these respective subdirectories.
This project is designed as a generic framework that works with existing Monte
Carlo codes with minimal adaptation. Any code outside the client-code
directories is designed to be agnostic with respect to the client codes. For
each of the client codes, several executables are generated, replacing the
main function of a typical ALPSCore simulation and ending in the following
suffixes:
*-sample: Run the Monte Carlo simulations at different points in the phase diagram, occasionally sampling the spin configuration and optionally applying the monomial mapping. The point in phase diagram space is recorded along with the raw (inLAZYmode) or mapped (inEAGERmode) configuration. The resulting optimization problem is saved in a checkpoint file ending in*.clone.h5.*-learn: Read one or more checkpoint files (*.clone.h5), label the samples according to the chosen → Classifier, and perform the SVM optimization. The resultant SVM model is saved to disk in a file ending in*.out.h5.*-test: Run the Monte Carlo simulation along a set of parameter points in the phase diagram. If launched from an*.out.h5file, the SVM model is evaluated and the decision function and its variance are measured as observables. Additionally, any other predefined reference observables are measured. If launched from an*.inifile instead, only the latter observables are measured.*-coeffs: Extract the coefficient matrix from the SVM model to infer the analytical order parameter.*-segregate-phases: Carry out the graph analysis to find the phase diagram without prior knowledge of the correct phase classification.
Detailed instructions on how to build ALPSCore can be fournd in the project's wiki. The procedure revolves around the following:
$ cd alpscore
$ mkdir build.tmp && cd build.tmp
$ cmake ..
$ make -jN
$ make test
$ make installReplace N with the number of threads you want to use to build, e.g. -j8.
You may want to specify additional flags to cmake:
-DCMAKE_INSTALL_PREFIX=$HOME/.local, or another custom install location. This is required if you don't have permission to write to the default install prefix path (/usr/local). Mind that ALPSCore installs a CMake script that has to be picked up by CMake when building our codes. Thus, any non-standard install location needs to be matched by a-DCMAKE_PREFIX_PATH=<...>flag when configuring the client codes.- If a local version of boost has been installed, you may need topoint CMake
to it by specifying
-DBOOST_ROOT=/path/to/boost/install. Otherwise your local version may not be found, or be shadowed by an incompatible version.
The TK-SVM framework does not follow a traditional build model, in that it does
not provide a library for the client codes to link against. This is rooted in
the fact that it provides main functions for the five executables mentioned in
the foregoing section. Instead, the root-level
CMakeLists.txt exposes the relevant source files as CMake
variables ${TKSVM_SAMPLE_SRC} (and analogous for the other executables), the
libraries as ${TKSVM_LIBRARIES} and the include directories as
${TKSVM_INCLUDE_DIRS}.
These may then be used from the CMakeLists.txt file of each of the client
codes. It must also add the compile definitions exposed in
${TKSVM_DEFINITIONS} and additionally define a variable TKSVM_SIMINCL
holding the name of the header of the main ALPSCore simulation class which
should define a type (alias) sim_base to that class.
Refer to the build file of one of the client codes (e.g.
gauge/CMakeLists.txt) for an example. Third-party
client codes may rather keep this repository as a submodule in their own tree,
in which case the line
add_subdirectory(.. tksvm)
simply becomes
add_subdirectory(svm-order-params)
Refer to the READMEs of the client codes for build instructions on them
specifically, e.g. Building the gauge client
code.
Most of the behavior of the programs can be controlled through runtime parameters. However, some options have to be selected at compile time via the CMake variables listed below. To customize a variable, pass the appropriate flag on to CMake, e.g.
$ cmake -DCONFIG_MAPPING=LAZY ..or use the interactive ccmake configurator.
| Variable name | Possible values |
|---|---|
ALPSCore_DIR |
nonstandard/path/to/share/ALPSCore |
Eigen3_DIR |
nonstandard/path/to/share/eigen3/cmake |
CMAKE_BUILD_TYPE |
Release (default), Debug |
CMAKE_INSTALL_PREFIX |
path to install directory (executables will be copied into bin/) |
SVM__ENABLE_TESTS |
OFF (default), ON |
CONFIG_MAPPING |
EAGER (default), LAZY |
This section demonstrates the basic usage of the framework, drawing from the
examples provided along with the gauge client code as an example, though the
principles hold true for all applications.
Simulation parameters are stored in INI-style files.
We provide example parameter files for each client code, in their respective
params directories (e.g. for the gauge code).
Each parameter file comes with a brief comment which explains its purpose and
includes the shell commands to run that particular simulation.
They also contain estimates for the run time of the individual steps.
In the following subsections, we will give a more detailed description of some aspects of the learning, testing, and analysis stages. For a (somewhat) comprehensive listing of supported parameters, refer to the section entitled → Runtime parameters.
The *-sample binaries run the Monte Carlo simulation at a number
of points in the phase diagram. The configurations are sampled periodically and
stored as the optimization problem in a file ending in .clone.h5. For
example,
$ mpirun -n 4 gauge-sample Td-hyperplane.iniwill carry out Monte Carlo simulations of the gauge model with the tetrahedral Td symmetry group.
Note: Both the *-sample and *-test programs rely on MPI for
parallelization. Replace 4 with the number of MPI processes you want to run
in parallel.
Time limit: If the required amount of Monte Carlo steps cannot be carried
out within timelimit seconds, the simulation terminates
prematurely and the incomplete data are written to Td-hyperplane.clone.h5. One
can resume the simulation with
$ mpirun -n 4 gauge-sample Td-hyperplane.clone.h5Sweep policy: The set of parameter points at which samples are collected is determined by a so-called sweep policy. Multiple, rather flexible, options exist which are documented and elaborated in the section entitled → Sweep through the phase diagram.
EAGER vs. LAZY mode
Dependent upon the build-time option CONFIG_MAPPING, the *-sample program
may or may not already carry out the tensorial feature mapping on the data. In
EAGER mode, the mapping is carried out as soon as a snapshot is sampled and
only the tensorial features are stored. For large lattices and modest ranks,
this provides potentially huge savings in storage and memory. On the flipside,
the user commits themselves to a fixed choice of the tensorial kernel (TK) rank
and cluster choice.
In LAZY mode, the mapping to monomial features is deferred until the learning
stage and the full spin configurations are stored in the *.clone.h5 file. This
may be desirable when the Monte Carlo simulation is particularly hard and
requires long intermediate updates to generate independent configurations. In
this scenario, large lattices and huge amounts of samples are typically
unreachable anyway, so storing the full spin configurations remains feasible.
The lazy mode then helps to avoid having to run the costly simulations
separately for each choice of the TK rank or spin cluster; rather, the
corresponding parameters can be overridden when launching the *-learn program.
Note that the choice of the CONFIG_MAPPING build option modifies the internal
representation used in the *.clone.h5 files, so files generated using one
option are incompatible to programs built using the other.
The *-learn binary takes the samples stored in one or multiple *.clone.h5
files and performs the actual SVM optimization, saving the result in a file
ending in *.out.h5.
$ gauge-learn Td-hyperplane.clone.h5Labeling samples: Within the *.clone.h5 files, the samples are stored
along with the full point in parameter space they have been sampled at. Before
the data can be fed to the SVM, those points have to be mapped to discrete
(one-dimensional) labels. This labeling is done by a component called the
→ classifier. Since many different strategies for labeling are
conceivable, corresponding to varying degrees of physical prior knowledge on the
system or knowledge gained through previous analyses, the classifier policy
can be selected and configured from a range of options at runtime. For example,
the parameter file
gauge/params/Td-hyperplane.ini uses the
hyperplane classifier, mapping the phase diagram points to a binary label,
indicating if samples are from the ordered or disordered phase, respectively.
For options on the choice and configuration of the different classifiers, refer
to the dedicated section.
Multiclassification: In contrast, when using the D2h symmetry group,
$ mpirun -n 4 gauge-sample D2h-phase-diagram.ini
$ gauge-learn D2h-phase-diagram.clone.h5the phase diagram features three phases called O(3) (isotropic),
D∞h (uniaxial), and D2h (biaxial). The parameter file
gauge/params/D2h-phase-diagram.ini is
intended to be used with the phase_diagram classifier which maps the
(J1, J3) points to three labels, O(3), Dinfh, and
D2h, according to the known phase diagram. The SVM will then solve three
classification problems, yielding one decision function to distinguish between
each pair of the labels. Given that the labels indeed correspond to the physical
phases and the rank is chosen appropriately (as is the case for the
D2h example), these three decision functions can be related to the
order parameter(s).
Note that the same samples can also be used with a different classifier by
overriding the classifier.policy parameter. For example, when selecting the
fixed_from_sweep classifier, the samples will be labeled according to the grid
points in phase diagram space from which they have been sampled:
$ gauge-learn D2h-phase-diagram.clone.h5 \
--nu=0.1 \
--classifier.policy=fixed_from_sweep \
--outputfile=D2h-grid.out.h5The phase diagram has previously been sampled on a 10 x 10 grid, hence, the
samples are now assigned 100 distinct labels, resulting in 100 * 99 / 2 = 4950
decision functions. The result is written to the alternative location
D2h-grid.out.h5 to avoid overwriting the previous result. It is obviously not
feasible to interpret each of the decision functions individually, but we can
use their bias parameters for the
→ graph analysis. To that end, a
moderate regularization level is appropriate; hence ν = 0.1 is chosen.
Merging additional clones: One may also perform the SVM optimization on a
collection of samples drawn from a variety of different runs of the *-sample
program with different, potentially overlapping sweeps through the parameter
space. This is possible; one can provide additional *.clone.h5 files in a
colon-separated string to the merge parameter:
$ gauge-learn first.clone.h5 --merge=second.clone.h5:third.clone.h5Note that first.clone.h5 is special in that its parameters are used
subsequently, specifically they determine the selected classifier used to label
all samples, including those contributed by second.clone.h5 and
third.clone.h5.
Command line options
| Long flag | Short | Description |
|---|---|---|
--help |
-h |
Display ALPSCore help message (lists parameters) |
--merge=<clone-list> |
Specify a colon-separated list of additional *.clone.h5 files whose samples should be included in the analysis |
|
--infinite-temperature |
-i |
Include sweep.samples fictitious samples as obtained from Simulation::random_configuration() as a control group |
--statistics-only |
Collect all samples, label them by the classifer and print their statistics, but forego the actual SVM optimization |
Note that additionally runtime parameters may also be overridden using command line arguments.
$ mpirun -n 4 gauge-test Td-hyperplane.out.h5will read the SVM model that was previously learned and measure its decision
function as an observable in independent Monte Carlo simulations. Additionally,
any observables that are ordinarily measured in the simulation's measure()
function will be measured as well. It is also possible to invoke the *-test
program on an *.ini file, e.g.
$ mpirun -n 4 gauge-test Td-hyperplane.iniwhich will measure only those ordinary observables and not attempt to evaluate any SVM model. This may be useful then debugging the simulation itself.
The set of parameter points at which measurements are to be taken is again
specified by a sweep policy in much the same way this is done for the
*-sample program. Refer to the detailed explanation of the testing stage
parameters below. The example
Td-hyperplane.ini sweeps a number of points
on a line segment between two end points in the parameter space.
Output format: The results are summarized in a text file
Td-hyperplane.test.txt and full observables are stored in
Td-hyperplane.test.h5. The *.test.txt is self-documenting (generating
comments indicating the column layout at the beginning of the file) and suitable
for plotting using gnuplot. A plot of the decision function can be created
using:
gnuplot> plot 'Td.test.txt' using 2:5:6 with yerrorlines
Variances: For any observable Obs that is measured by the simulation's
measure() function and for which there exists another observable named
Obs^2, the *.test.txt will additionally contain columns giving the variance
of Obs, as calculated using the formula <Obs^2> - <Obs>^2, including an
error estimate on that variance, as obtained from jackknife resampling. This
extends to the SVM decision function(s) whose squares are also always measured.
The physical utility of the variables of decision functions, particularly some
analogies to generalized susceptibilities, are discussed in
arXiv:1907.12322.
Note: Variances are also calculated for observables of higher powers or
absolute values, e.g. when measuring all of Obs, |Obs|, Obs^2, Obs^4,
and Obs^8, the variances of Obs, |Obs|, Obs^2, and Obs^4 are all
calculated.
Command line options
| Long flag | Short | Description |
|---|---|---|
--help |
-h |
Display ALPSCore help message (lists parameters) |
--rescale |
-r |
Shift decision functions by the bias and rescale to unit interval |
Note that additionally runtime parameters may also be overridden using command line arguments.
$ gauge-coeffs Td-hyperplane.out.h5 -ureads the SVM model and contracts over the support vectors to extract the coefficient matrix, block structure, and performs miscellaneous analyses and processing steps, such as fitting and removing self-contractions or comparing to the exact result.
The three panels in Fig. 2 of arXiV:1804.08557 can be reproduced by the following invocations:
$ gauge-coeffs Td-hyperplane.out.h5 -u
$ gauge-coeffs Td-hyperplane.out.h5 -u --block=[lmn:lmn]
$ gauge-coeffs Td-hyperplane.out.h5 -u --block=[lmn:lmn] --remove-self-contractionsThese options are detailed below.
Index arrangement
-u | --unsymmetrize: coefficients involving redundant monomial (cf. Supplementary Materials) are reconstructed, i.e. the coefficient value of the corresponding non-redundant coefficient is copied.-r | --raw: the indicies are not rearranged. By default, the indices are reshuffled in the form (α1, ..., αn, a1, ..., an) and lexicographically ordered such that the color-block structure becomes apparent. Specifying this flag disables this, and indices are arranged as (α1, a1, ..., αn, an).
Extracting individual blocks
The program has two major modes: extraction of the full coefficient matrix and
single-block mode where a single block is targeted and extracted exclusively.
This is done by specifying the command line parameter --block=<block-spec>
where <block-spec> identifies a block by its color indices. E.g. in the case
of the tetrahedral (rank-3) order, the non-trival block can be found by
specifying --block=[lmn:lmn].
Contraction analysis
-c | --contraction-weights: for each block (or only the single block), perform a least-squares fit of contraction "masks" to obtain the coefficients with which each contraction contributes and output those.-s | --remove-self-contractions: perform the same analysis as above, but consequently isolate the contributions due to self-contractions and subtract them from the full coefficient matrix.
Note that "blocks" refers to the representation where indices have been
reshuffled. When the full coefficient matrix is extracted, the contraction
analysis (-c, -s) operates on the symmetrized representation where redundant
element have not been reinstated and "blocks" are actually non-local. In
single-block mode however, this would not work because the equivalents of
redundant elements are actually part of different blocks. Thus, in single-block
mode, the contraction-analysis is performed on the "unsymmetrized" (redundant)
representation. Consequently, the contraction coefficients will be different
from those obtained for the same block in full-matrix mode, as now equivalent
contractions will contribute evenly, as opposed to only those contractions that
are compatible with the symmetrization.
Multiclassification
When analyzing the result of a multiclassification problem (see the D2h example above), the analysis is performed for each decision function separately. Because of the quadratic growth of the number of decision functions, this can get messy for big multiclassification problems. Instead, one can list the decision functions and their biases without extracting the coefficient matrices using:
$ gauge-coeffs D2h-hyperplane.out.h5 --list
0: O(3) -- Dinfh rho = -1.0052
1: O(3) -- D2h rho = -1.00266
2: Dinfh -- D2h rho = -0.659734In this lists, the decision functions are given a running number. This number can be used to select a single decision function and extract only its coefficient matrix. For example, to limit the analysis to the O(3) / D2h transition:
$ gauge-coeffs D2h-hyperplane.out.h5 -u --transition=1Command line options
| Long flag | Short | Description |
|---|---|---|
--help |
-h |
Display ALPSCore help message (lists parameters) |
--verbose |
-v |
Print information on currently running step |
--list |
-l |
List the transitions between labels and their bias value, but do not write any files |
--transition=<num> |
-t |
Rather than extracting coefficients for all transitions in a multiclassification setting, only consider the transition numbered <num> (as listed using the --list option) |
--unsymmetrize |
-u |
Assign the extracted coefficient to all equivalent monomials, rather than only to a single representative |
--raw |
-r |
Indicies are not rearranged; redundant monomials are not included in the output pattern |
--blocks-only |
-b |
Skip output of the full coefficient matrix and only output block structure; unavailable (and pointless) in single-block mode. |
--block=<block-spec> |
Only output the coefficient matrix block identified by <block-spec> |
|
--contraction-weights |
-c |
For each block (or only the single block), perform a least-squares fit of contraction "masks" to obtain the contributions of each contraction and output those. |
--remove-self-contractions |
-s |
Perform the same analysis as above, but consequently isolate the contributions due to self-contractions and subtract them from the full coefficient matrix. |
--exact |
-e |
Calculate and output the exact result (as specified by --result) for the coefficient matrix (if available) |
--diff |
-d |
Output the deviation from the exact result (as specified by --result) for the coefficient matrix and print total relative deviation δ |
--result=<name> |
The name of the exact result to look up; hardcoded values: Cinfv, Dinfh, D2h; required when using --exact or --diff |
Short flags may be combined into one multi-flag, as is customary for POSIX-compatible programs.
The *-segregate-phases program is intended to be used in conjunction with
massive multiclassification programs (such as the previously constructed file
D2h-grid.out.h5) to infer the topology of the phase diagram based on the bias
criterion.
The rationale is, that if the bias of a decision function between two points is far from one (the ideal value expected for a physical transitions), those two points are either in the same phase, or the phase transition could not be captured at the rank considered. We then go ahead and construct an undirected simple graph by adding an edge connecting those two points (vertices). On the other hand, if the bias is "close" to one, we assume there is a phase transition taking place between the points and we don't put an edge. The threshold value ρc can be tuned to control the inclusivity of the criterion: an edge is included in the graph if the deviation of corresponding unoriented bias |ρ| from unity exceeds ρc: ||ρ| - 1| > ρc.
The resulting graph can be subjected to a spectral partitioning analysis. To that end, the eigendecomposition of the Laplacian of the graph is calculated. The degeneracy of the lowest eigenvalue (zero) indicates the number of connected components within the graph. We recommend to choose ρc such that the graph consists of a single connected component, i.e. a slightly larger value of ρc would lead to a degeneracy of eigenvalue zero. For the above example of the D2h symmetry, this sweet spot happens to be achieved at around ρc=0.9, but your mileage may vary:
$ gauge-segregate-phases D2h-grid.out.h5 --rhoc=1.0
Degeneracy of smallest eval: 2
$ gauge-segregate-phases D2h-grid.out.h5 --rhoc=0.9
Degeneracy of smallest eval: 1Then, the second largest eigenvalue is the so-called algebraic connectivity and its corresponding eigenvector, the Fiedler vector can be used to infer the phase diagram: if the graph features regions which are strongly intraconnected, but weakly interconnected, the algebraic connectivity will be small and the entries of the Fiedler vector will cluster such that the entries corresponding to intraconnected regions will have a similar value.
Thus, the Fiedler vector can be visualized and will be reminiscient of the phase
diagram. To that end, the *-segregate-phases program outputs two files,
edges.txt and phases.txt. The former lists pairs of points corresponding to
the edges of the graph, the latter gives all the eigenvectors of the Laplacian
matrix such that the second dataset (index 1) is the Fiedler vector. Using
gnuplot, we can see that we achieve a decent approximation of the
D2h phase diagram:
gnuplot> plot 'edges.txt' using 2:1 with lines, \
'phases.txt' index 1 using 2:1:3 with points pt 7 lc palette
Weighted graphs
Rather than making a binary decision on whether or not to include an edge into
the graph, one can in some situations obtain better results by constructing a
weighted graph whose edges have weights which are calculated from their biases
by means of a weighting function w(ρ). Three options are provided which may be
selected using the --weight flag:
<weight-func-name> |
Equation w(ρ) | Default value of ρc |
|---|---|---|
box (default) |
 |
1 |
gaussian |
 |
standard deviation of the distribution of ρ values |
lorentzian |
 |
half interquartile spacing of the distribution of ρ values |
In each of these, the parameter ρc constitutes a characteristic
scale. The default box option corresponds to the strategy using unweighted
graphs outlined above.
Masks
In phase diagrams where multiple different transitions occur at different ranks,
it may be desirable to exclude a region of the parameter space which has been
identified to exhibit order at a certain rank from the subsequent analysis of
the remaining parameter space at higher ranks. An example of this can be found
in the easy-plane antiferromagnetic (AF) phase in the pyrochlore XXZ model
studied in arXiv:1907.12322. To this end, the *-segregate-phases program
allows for the creation and application of "masks". Sticking with the example of
the AF phase, one first performs a graph analysis of the whole parameter space
at rank 1. The resulting Fiedler vector clearly reflects the bipartition of the
parameter space into the AF phase and "the rest". By specifying the option
--threshold=0, a file mask.txt will be written which identifies all those
parameter points whose associated Fiedler vector entry is larger than 0; in
the example, this would correspond to the AF phase. Since we want to further
analyze the remainder of the parameter space, the flag --invert-mask is
provided. Now mask.txt identifies all those points which are not in the AF
phase.
Subsequently, we perform a graph analysis at rank 2, passing the flag
--mask=mask.txt on the command line. This way, the previously created mask is
applied and the parameter points belonging to the AF phase are ignored in the
construction of the graph. They are also omitted from the output files
phases.txt and edges.txt. Particularly when visualizing the Fiedler vector
(phases.txt) using e.g. gnuplot this can be a problem as each row of the
"image" may have a different number of pixels due to the omitted points. As a
remedy, the additional flag --masked-value=42 will cause these ignored points
to be included yet again in the output but with the value 42 in lieu of their
Fiedler vector element. When rendering the result, the color palette may be
chosen such that pixels with the value 42 are shown in gray, indicating their
absence from the analysis.
Command line options
| Long flag | Short | Description |
|---|---|---|
--help |
-h |
Display ALPSCore help message (lists parameters) |
--verbose |
-v |
Print information on currently running step |
--weight=<weight-func-name> |
-w |
Specify the weighting function used to mapping biases to edge weights; <weight-func-name must be one of: box (default), gaussian, lorentzian (see below) |
--rhoc=<number> |
-r |
Specify the characteristics bias scale ρc used to rescale the weighting function; default value depends on choice of weighting function (see below) |
--radius=<max-distance> |
-R |
Specify a cutoff radius: edges between parameters points farther than <max-distance> apart from oneanother will not be included in the graph; defaults to infinity |
--threshold=<tval> |
-t |
Trigger the output of a mask.txt file, identifying all parameter points with Fiedler vector elements larger or equal to <tval> |
--invert-mask |
Inverts the behavior of the --threshold option, i.e. identifies points with Fiedler vector elements less than <tval> |
|
--mask=<mask-filename> |
-m |
Applies a previously saved mask, i.e. ignores all parameter points not included in the mask from the graph analysis |
--masked-value=<mval> |
When outputting the results of the graph analysis, specifically phases.txt, replace the would-be Fiedler vector element of those parameter points which have been ignored due to the --mask with <mval>; otherwise omit the point entirely |
This section lists all parameters that can be used to control the behavior of the simulations with respect to runtime duration and output, regularization of the SVM optimization, the way the parameter space is swept, and the way samples are labeled (classified) before being fed to the SVM. These parameters are shared by all client codes.
Client codes may define parameters of their own, conventionally pertaining to
the physical parameters of the simulated model (lattice size, coupling, etc.),
the MC update scheme (number of sweeps, update attempt probabilities, etc.),
and the choice of the tensorial kernel that is to be used (rank, cluster choice,
etc.).
For the three client codes shipped as part of this repository, those parameters
are documented in the READMEs of each of the corresponding subdirectories.
Note that some of these parameters appear in each of these cases (e.g. rank,
total_sweeps); however no assumption is made on part of the shared framework
that any of them need to be present.
Most parameters feature a hierarchical name where levels in the hierarchy are
separated by dots. These parameters can also be grouped by hierarchical prefix.
The following three specification of the parameter sweep.grid.N1 are
equivalent:
sweep.grid.N1 = 42
[sweep]
grid.N1 = 42
[sweep.grid]
N1 = 42Note that the hierarchical prefix has to be specified in full and cannot be nested. I.e., the following version does not work:
[sweep]
[grid]
N1 = 42 # this won't work!The following parameters control the runtime behavior of the *-sample and
*-test programs. In general, the program will run until either it finished the
specified amount of Monte Carlo sweeps (as specified by the client codes), or
until the wallclock timelimit is exceed. In both cases, the program will write
a checkpoint file *.clone.h5 to disk which the simulation can be resumed from
(to complete the required number of sweeps, or to perform additional sampling).
| Parameter name | Default | Description |
|---|---|---|
SEED |
42 |
Seed of the master thread PRNG |
timelimit |
0 |
Time limit before termination in sec (0 = indefinite) |
outputfile |
*.out.h5 |
HDF5 output file name for SVM model |
checkpoint |
*.clone.h5 |
HDF5 checkpoint file name |
batch.index |
0 |
Index of the phase point dimension used for → PT |
Depending on the physical model simulated by the client codes, the phase diagram
space (i.e. parameter space) may be different. For example, the ising
code uses only the temperature, so the parameter space is
one-dimensional. The gauge client code has a two-dimensional phase
diagram spanned by the J1 and J3 coupling constants.
Both the sweep policies and the
classifiers which define traversals and regions in the phase
diagram thus have parameters which depend on the (dimensionality of the) model's
phase diagram. In the relevant subsection, these will invoke the placeholder
<phase-diag-point-spec>.
In the ising client code, <phase-diag-point-spec> has to be
replaced by a single parameter:
temperature phase diagram point |
Default | Description |
|---|---|---|
temp |
1 |
Temperature |
For example, the start point of a line scan sweep, specified as
sweep.line_scan.a.<phase-diag-point-spec> would be satisfied by setting the
single parameter sweep.line_scan.a.temp. On the implementation side, the
definition of the phase diagram points is detailed below.
At the sampling stage, the simulation performs a sweep through the phase diagram
space. The sweep policy determines the strategy followed to generate these
points. Some are deterministic, such as cycle and grid, others are
nondeterministic and use pseudorandom numbers, like uniform and
uniform_line. The sweep policy can be selected at runtime through the
sweep.policy parameter.
Regardless of the sweep policy selected, it will be used to generate a certain
number (possibly repeated) points. At each point, sweep.samples spin
configurations are sampled. These samples are evenly spaced throughout the
progress of the simulation as reported by the simulation's
fraction_completed() function. Note that simply increasing sweep.samples
reduces the number of MC update between consecutive samples.
| Parameter name | Default | Description |
|---|---|---|
sweep.samples |
1000 |
Number of spin samples per phase diagram point |
sweep.policy |
cycle |
Name of sweep policy; see below |
sweep.<sweep-spec> |
required | Specification of the chosen sweep; see below |
Possible values for the sweep policy are: cycle, grid, nonuniform_grid,
sweep_grid, uniform, line_scan, log_scan, or uniform_line. The effects
of, and parameters associated with, each of these are detailed below.
Cycling through a set of predefined phase diagram points
The cycle sweep policy can be used to probe the phase diagram at a set of up
to 8 points P1, ..., P8 which are manually provided as individual
parameters.
cycle sweep policy |
Default | Description |
|---|---|---|
sweep.cycle.P<i>.<phase-diag-point-spec> |
optional | ith phase diagram point in cycle sweep |
Equidistant rectangular grid
The grid sweep policy imposes a regular grid on the rectangular region of the phase
diagram spanned by the two points a and b. The spacing of the grid points is
equidistant within each dimension of the phase diagram, where the spacing is
determined by the number of grid points in that dimension, N1, N2, ... .
Valid values for N<d> include 1; 0 is not permitted.
grid sweep policy |
Default | Description |
|---|---|---|
sweep.grid.N<d> |
1 |
Number of grid points along the dth dimension |
sweep.grid.a.<phase-diag-point-spec> |
required | Lower-left corner of rectangular uniform grid |
sweep.grid.b.<phase-diag-point-spec> |
required | Upper-right corner of rectangular uniform grid |
Nonuniform rectangular grid
The nonuniform_grid sweep policy is a crossover between both the cycle and
grid policies. One manually specifies a series of up to 10 phase points,
stop1 through stop10, as well as a number of points in each dimension of the
phase diagram space, N1, ..., N<D>, where <D> is the dimension of the
space. The policy will then generate a regular grid of N1 × ... × N<D>
points, i.e. the cartesian product where the factor set w.r.t. each dimension
<d> is formed from the values of the associated parameter as specified by the
stops, stop<i> with <i> = 1, ..., N<d>.
nonuniform_grid sweep policy |
Default | Description |
|---|---|---|
sweep.nonuniform_grid.N<d> |
1 |
Number of grid points along the dth dimension |
sweep.nonuniform_grid.stop<i>.<phase-diag-point-spec> |
required | Specification of the <i>th "stop", <i> < 10 |
Example: for a two-dimensional phase diagram (with parameters X and Y),
the following sweep:
sweep.policy = nonuniform_grid
[sweep.nonuniform_grid]
N1 = 3
stop1.X = 1
stop2.X = 3
stop3.X = 7
N2 = 2
stop1.Y = 2
stop2.Y = 4results in the six points: (1,2), (1,4), (3,2), (3,4), (7,2), (7,4). Note that
the value of stop3.Y — while implicitly defaulted — is not taken into
account.
Regular grid made from other sweeps
The sweep_grid sweep policy is yet another way of creating a nonuniform
regular grid by using sweep policies for each dimension to generate the
coordinates before again forming the cartesian product. Each of the individual
subsweeps is specified in the same manner as the sweep policy in general but
with a prefix sweep.sweep_grid.sweep<d> where <d> = 1, ..., <D> enumerates
the dimension. Note that for each of the subsweeps only the "hot" coordinate of
the generated points is relevant.
sweep_grid sweep policy |
Default | Description |
|---|---|---|
sweep.sweep_grid.sweep<d>.policy |
cycle |
Name of the sweep policy used to generate the cartian product set for the <d>th coordinate |
sweep.sweep_grid.sweep<d>.<sweep-spec> |
required | Nested specification of the sweep used to generate the cartesian product set for the <d>th coordinate |
Example: The following parameters result in the same six points as the
previous example for nonuniform_grid, using cycle subsweeps (the default):
sweep.policy = sweep_grid
[sweep.sweep_grid.sweep1.cycle]
P1.X = 1
P2.X = 3
P3.X = 7
[sweep.sweep_grid.sweep2.cycle]
P1.Y = 2
P2.Y = 4Uniform rectangular region
The uniform sweep policy generates points which are uniformly, yet randomly,
distributed in the rectangular region spanned by the two points a and b.
uniform sweep policy |
Default | Description |
|---|---|---|
sweep.uniform.N |
10 |
Number of points to sample uniformly from the rectangle |
sweep.uniform.a.<phase-diag-point-spec> |
required | Lower-left corner of rectangular region |
sweep.uniform.b.<phase-diag-point-spec> |
required | Upper-right corner of rectangular region |
Equidistant points on a line segment
The line_scan sweep policy generates N equidistant points on a line through
the phase diagram, connecting the points a and b. For one-dimensional
parameter spaces, it is equivalent to grid.
line_scan sweep policy |
Default | Description |
|---|---|---|
sweep.line_scan.N |
8 |
Number of points |
sweep.line_scan.a.<phase-diag-point-spec> |
required | Start point of the line segment |
sweep.line_scan.b.<phase-diag-point-spec> |
required | End point of the line segment |
Logarithmically-spaced points on a line segment
The log_scan sweep policy is similar to line_scan but for each dimension,
the coordinates are either linearly or logarithmically (default) spaced.
log_scan sweep policy |
Default | Description |
|---|---|---|
sweep.log_scan.N |
8 |
Number of points |
sweep.log_scan.log<d> |
true |
Booleans, indicating if points are to be spaced logarithmically in the <d>th dimension |
sweep.log_scan.a.<phase-diag-point-spec> |
required | Start point of the line segment |
sweep.log_scan.b.<phase-diag-point-spec> |
required | End point of the line segment |
Uniform line segment
The uniform_line sweep policy generates random points uniformly on the line
segment connecting the points a and b. For one-dimensional phase diagrams,
it is identical to the uniform sweep policy.
uniform_line sweep policy |
Default | Description |
|---|---|---|
sweep.uniform_line.N |
10 |
Number of points to be drawn from the line |
sweep.uniform_line.a.<phase-diag-point-spec> |
required | Start point of the uniformly sampled line |
sweep.uniform_line.b.<phase-diag-point-spec> |
required | End point of the uniformly sampled line |
Simulation samples need to be labeled in some fashion and these labels are exposed to the SVM. Thus, some sort of classification or mapping of phase diagram space points to a finite number of labels needs to be specified. Depending on the model and the available physical information, different choices for this classifier might be appropriate. A number of those are documented in this section and users may define additional ones without too much effort.
Previous versions of the framework required the classifier to be selected at compile time. In the present version, this has been changed in favor of policies which may be selected by name using runtime parameters in a way that is similar to the selection of the sweep policy. The behavior of the selected classifier may also be customized by runtime parameters. These are detailed below.
Since the classification step happens only after sampling (*-sample) and
immediately prior to the SVM optimization (*-learn), one can override the
selected classifier policy and/or parameters governing its behavior when
invoking the *-learn program, without the need to resample. A common scenario
where this may be useful is to use the fixed_from_sweep classifier in the
absence of information on the phase diagram to perform the graph analysis and
infer a phase diagram and subsequently "pool" those same samples accordingly
using the phase_diagram classifier into a handful of labels ostensibly
corresponding to the identified phases and/or spin liquid regimes.
Note that the above mentioned deferred selection of the classifier holds true
irrespective of the configuration mapping mode (EAGER vs. LAZY). However,
after the learning stage (*-learn) the classifer policy must not be altered
when invoking any of the subsequent programs (*-coeffs, *-segregate-phases,
or *-test). Parameters that have been overridden upon invocation of *-learn
will be stored in the *.out.h5 file, so it is not necessary to specify those
in the subsequent stages.
| Parameter name | Default | Description |
|---|---|---|
classifier.policy |
fixed_from_sweep |
Name of the known phase diagram to retrieve |
classifier.<classifier-spec> |
required | Specification of the chosen classifier; see below |
Possible values for the classifier policy are: fixed_from_sweep,
phase_diagram, hyperplane, and critical_temperature. The effects of, and
parameters associated with, each of those are detailed below.
Classification according to sweep policy
When the phase diagram is not yet known, the easiest approach is to sweep the parameter space exhaustively, covering the space somewhat uniformly and then classify the samples with a running label according to which point they have been sampled from. Thus, no two different points in the phase diagram will be given the same label, ruling out wrong assumptions on the tentative phase diagram. One arrives at a (potentially huge) multiclassification problem and can use the result to decide which phase diagram points should in fact be given the same label, either through manual inspection (cf. Sec. VI.A of arXiv:1810.05538) or on a larger scale using the → graph analysis (cf. Sec. VII of arXiv:1810.05538; Secs. II.D and III of arXiv:1907.12322).
The corresponding classifier policy is called fixed_from_sweep. No further
customization by means of runtime parameters is needed.
Classification based on known phase diagram
When the phase diagram is already known, the user will likely want to label
points in the phase diagram space accordingly. This can be achieved with the
phase_diagram classifier. The phase diagram is encoded as a collection of
disjoint polygons which correspond to the phases and cover the relevant parts of
the phase diagram space. The polygons are labeled by strings; each point is
given the label associated with the polygon it is contained in. Should a point
not be contained in any of the polygons, it is mapped to an "invalid" label and
subsequently excluded from the analysis.
The available phase diagrams are hard-coded but additional ones can be added
relatively easily in user client codes by injection of a template specialization
of the tksvm::phase_space::classifier::phase_diagram_database<> template.
Both the gauge and frustmag built-in client codes demonstrate this.
The
desired diagram is selected from the "database" by specifying its name:
phase_diagram classifier parameters |
Default | Description |
|---|---|---|
classifier.phase_diagram.name |
required | Name of the known phase diagram to retrieve |
Because this classifier policy relies on a description in terms of polygons, it is only capable of handling parameter spaces of one or two dimensions. In higher-dimensional spaces, only the first two dimensions are considered.
Binary classification using a hyperplane through the phase diagram
When samples from multiple (possibly random) points in the phase diagram are
used to analyze a particular transition, the hyperplane classifier allows for
a binary classification by partitioning the phase diagram space into two regions
on either side of a "hyperplane" (a single point in 1d phase diagrams, a line in
2d, a plane in 3d, ...). The hyperplane is specified by any one "support" point
on the plane (fixing its offset from the origin) and a normal vector which is
orthogonal to the plane and does not need to be normalized.
The resulting label has the two values ORDERED and
DISORDERED. The normal vector is pointing into the half space that is
ORDERED.
hyperplane classifier parameters |
Default | Description |
|---|---|---|
classifier.hyperplane.support.<phase-diag-point-spec> |
required | A point somewhere on the desired hyperplane |
classifier.hyperplane.normal.<phase-diag-point-spec> |
required | The normal vector defining the orientation |
Classifiers for temperature phase diagram points
One special instance of binary classification is the in one-dimensional
temperature phase diagram space which is used in the ising and frustmag built-in client codes.
The critical_temperature classifier does pretty much the same as a
hyperplane classifier but is more simple and less versatile.
critical_temperature classifier parameters |
Default | Description |
|---|---|---|
classifier.critical_temperature.temp_crit |
1 |
Critical temperature |
| Parameter name | Default | Description |
|---|---|---|
nu |
0.5 |
Regularization parameter ν in [0, 1] |
merge |
"" |
Colon-separated list of paths to *.clone.h5 files whose samples are to be merged |
Naturally, further parameters such as the choice of the tensorial kernel rank
or cluster determine the success of the SVM optimization. These are specific
to the client codes and documented therein.
During the testing stage (programs *-test) the SVM
decision function along with any analytical reference quantities are measured on a set of points which is obtained through a sweep policy, selectable by the parameter test.policy.
| Parameter name | Default | Description |
|---|---|---|
test.filename |
*.test.h5 |
HDF5 test file name |
test.txtname |
*.test.txt |
Human-readable ASCII test result file name |
test.policy |
cycle |
Name of the sweep policy that is to be used for testing; analogous to sweep.policy |
test.<sweep-spec> |
required | Specification of the chosen sweep policy; analogous to the sampling sweep |
Note that at each point, the simulation performs the regular amount of Monte Carlo sweeps as determined by the client code parameters which control the simulation runtime (e.g. number of MC updates, thermalization time, etc.). One may want to override these parameters from the command line if the amount necessary for testing differs from that used in sampling stage.
Client codes have to conform to ALPSCore's model for Monte Carlo simulations.
They must also encode their entire set of variable parameters which determine
the location in the parameter space (phase diagram) in a member type
phase_point. As an example, if the parameter space is spanned exclusively by
temperature, one may use the built-in type temperature:
using phase_point = tksvm::phase_space::point::temperature;The requirements on the type phase_point are summarized in a
section below.
Rather than deriving from alps::mcbase, TKSVM-compliant simulation classes are
now required to be derived from either
tksvm::embarrassing_adapter<phase_point> or
tksvm::pt_adapter<phase_point>, the latter enabling support for
→ Parallel Tempering while the former supports
embarrassingly simple parallelization.
Any use of measurements (in ALPSCore's alps::mcbase formerly a protected
member variable) is to be replaced by a function call to measurements().
In the simulation's overrides of the load / save functions, rather than
calling mcbase::load / mcbase::save, make sure to call the tksvm base
class's load / save function.
In addition, the simulation class must implement the following member functions:
decltype(auto) configuration() const;returns the raw spin configuration as an implementation-defined type. Can return either by value or by reference to const.
Note: By design, the type returned by configuration() is relatively
unconstrained and the framework does not impose any one way of accessing the
spin components. It can be a container of sorts, but it doesn't have to be. For
example, in the frustmag client code, the function returns references to the
lattice class, a relatively complicated class which encodes the lattice
geometry, including nearest neighbor relations. It is up to the configuration
policy (see below) to map the configuration objects to the feature vectors which
are subsequently fed to the SVM.
Note: As one of the few requirements, configurations need to be serializable.
This is done by providing a template specialization of
tksvm::config::serializer<> which implements the following functions:
template <>
struct serializer<Config> {
template <typename OutputIterator>
void serialize(Config const& conf, OutputIterator it) const;
template <typename InputIterator>
void deserialize(InputIterator it, Config & conf) const;
};where Config is the return type (without references) of configuration() and
the OutputIterator and InputIterator types abide by the eponymous concepts
with respect to value_type double. In case the configuration type is
iterable (i.e. provides begin() and end() functions) over the spin
components, e.g. a std::vector<double>, the default implementation of the
serializer template can be used and no user-defined specialization needs to be
provided.
auto random_configuration();returns a raw spin configuration corresponding to the infinite temperature
state. Note that the method is not const to allow for the use of the RNG.
The return type needs to be the same as for configuration(), though it may
differ by value category (must return by value while configuration() may
return by reference to constant).
virtual phase_point phase_space_point() const override;returns the current location in the phase diagram space.
virtual bool update_phase_point(phase_point const&) override;updates (or attempts to do so) the current location in the phase diagram space. Returns a boolean indicating if the new point differs from the old one (and so thermalization steps need to be allowed for).
Note: The override must call the overridden base class member!
virtual void reset_sweeps(bool skip_therm = false) override;resets the internal counter of the simulation progress; called after phase point update. The optional argument indicates if the phase point in fact has not changed and thus no intermediate thermalization phase is necessary.
Note: The override must call the overridden base class member!
bool is_thermalized() const;returns whether the simulation is thermalized.
std::vector<std::string> order_param_names() const;returns a vector of names of registered observables (which have been registered
with the accumulator set returned by measurements() upon construction) which
are to be considered as reference observables to compare to. These are then
measured in the *-test program. For any of the names in the returned vector,
the presence of an observable corresponding to the its square (by appending
^2, doubling the power, etc.) is checked. If such a square is present, it is
used to compute the variance of that observable. The squared observable itself
does not need to be listed in the vector returned by this function.
template <typename Introspector>
static auto config_policy_from_parameters(alps::params const& parameters,
bool unsymmetrize = true)
-> std::unique_ptr<tksvm::config::policy<phase_point, Introspector>>This static factory function returns a unique pointer to the configuration
policy. The config policy must be derived from the abstract
tksvm::config::policy<phase_point, Introspector> where phase_point is the
phase space (parameter) point defined by the simulation class and Introspector
is a template parameter that is passed on.
Most configuration policies will actually derive from (or alias)
tksvm::config::clustered_policy.
This function is tasked with initializing the config policy according to the
simulation-defined parameters.
The optional second boolean argument indicates if the configuration policy
should "unsymmetrize" the coefficient matrix. (If the configuration policy
derives from tksvm::config::monomial_policy, as most do, this argument can
simply be passed on to the base policy constructor.)
The phase_point member type of the simulation class encodes a point in the
parameter space (phase diagram) of the simulation model. It must meet the
following requirements:
- It must be iterable, i.e. provide functions
begin()andend(), returning (mutable and constant)RandomAccessIterators which dereference todouble. These iterator types must also be exposed as member typesiteratorandconst_iterator. - Its dimension (i.e. number of independent parameters) is exposed as a
static const size_t label_dimmember, such thatphase_point::label_dim == p.end() - p.begin()(forpan instance ofphase_point). - It is constructible from a single
InputIteratorwhich dereferences todouble.label_dimelements will be read. - It is constructible from ALPSCore parameters, i.e. it has a constructor with
signature
where the
phase_point(alps::params const& params, std::string prefix="");
prefixargument is used to enable hierarchical parameter names. A typical prefix might besweep.cycle.P1.. (Note the trailing dot.) It also implements the static member functionswhich define the parameters and check whether the parameters for the point are fully supplied by the user.static void define_parameters(alps::params & params, std::string prefix=""); static bool supplied(alps::params const& params, std::string prefix="");
Parallel tempering (PT) can be a last resort to combat long autocorrelation times which are common in frustrated spin systems and exacerbated at low temperature which is also where most of the interesting physics takes place. In essense, multiple simulation instances run at a range of different parameters (e.g. different temperatures); an additional update is proposed which would amount to exchanging the whole configuration with Metropolis probability. In practice, rather than exchanging configurations, it is more convenient to exchange the current simulation parameters (e.g. temperature). This way, each worker process performs a random walk through parameter space which allows it to "heat up" and move relatively freely through configuration space and consequently cool down again, relaxing into a new local energy minimum, thus helping reduce autocorrelation. Details on the PT update with a focus on frustrated spin systems can be found in J. Greitemann's PhD thesis, Sec. 3.4 and references therein.
To enable parallel tempering, the simulation class has to be derived from
tksvm::pt_adapter<phase_point>. The PT adapter takes care of most of the
bookkeeping necessary for PT. In particular, it launches a "manager" thread
which coordinates between worker processes. When a PT update is accepted, it
issues the exchange of the respective parameter points by calling
update_phase_point. It will also rebind the measurements() object to
redirect further measurements to the appropriate accumulators. Each worker
locally keeps a set of accumulators for each parameter point it ever visited.
When alps::collect_results is called, collective communication between the
workers merges all the local measurement sets.
At some point during the update() member function, the PT update can be
initiated by invoking the negotiate_update member function of the
pt_adapter. This can be done on every update, or only when a certain condition
is met. Note that PT should generally be used sparingly as it can
incur significant latency. negotiate_update takes three arguments:
- A C++11-style random number generator. The simulation can either provide one
specifically for PT, or, preferably, retire the use of
mcbase::randomaltogether in favor of the superior C++11<random>API. - A
boolindicating if it should only check if another replica has requested a PT update and engage in it only if that is the case (false), or if it should proactively seek a PT update with another replica. Depending on the node interconnect, it may be beneficial to check more often in order to not keep the other replica waiting. For slow interconnects, any additional communication is to be avoided and, hence, no additional checking is advisable. - A callable which calculates the logarithmic weight of the current
simulation state (spin configuration) with respect to a different phase
point, relative to the current phase point. E.g., for an Ising model where
only the (inverse) temperature changes (from beta to beta') and the energy
is left invariant, this would amount to
log_weight(beta') = -(beta' - beta) * E
In order to allow for synchronization between simulations at different
parameters, they must be run at the same time. To this end, all the parameter
points are obtained from the sweep policy and then "batched" into batches which
must run concurrently. For simulations which do not use PT (and are derived from
tksvm::embarrassing_adapter<phase_point>), each parameter point constitutes
its own batch of size one. When using PT, the runtime parameter batch.index is
used to identify the index of the phase_point dimension over which PT should
be performed. For example, if the parameter space is spanned by the temperature
(index 0) and a coupling (index 1), batch.index = 0 (the default) will cause
all points to be organized into batches where points within each batch share the
same coupling and differ only by temperature. The number of MPI processes
(workers) must at least equal the size of the largest batch. If it exceeds the
batch size by more, it is also possible for multiple PT batches to run
simultaneously, yet independently.
Of the built-in client codes, only the frustmag code makes use
of PT.
Copyright © 2018-2019 Jonas Greitemann, Ke Liu, and Lode Pollet
This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
A copy of the GNU General Public License is available in the file LICENSE.