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Include Usage_Example files; work on LiebLin (code, documentation)

This commit is contained in:
J.-S. Caux 2018-02-15 10:08:36 +01:00
parent f654f45171
commit 2677b62120
10 changed files with 549 additions and 153 deletions
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2
.gitignore vendored
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@ -4,4 +4,6 @@
*tar.gz
*out
TEST/*

9
ABACUS.org
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@ -32,15 +32,6 @@ Type your description here
TIP: Search for the string BUGRISK in the codebase
** BUGRISK Value of LiebLin ln_Density_ME
- State "BUGRISK" from "" [2018-02-11 Sun 09:11]
File: ln_Density_ME.cc
line 66
Why real?
* Priority :ABACUS:Dev:Priority:
:PROPERTIES:
:ARCHIVE: %s_archive::* Priority

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ABACUS.org_archive Normal file
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@ -0,0 +1,26 @@
# -*- mode: org -*-
Archived entries from file /Users/jscaux/WORK/_ABACUS/ABACUS/ABACUS.org
* Bugrisks
** SOLVED Value of LiebLin ln_Density_ME
CLOSED: [2018-02-15 Thu 08:42]
- State "SOLVED" from "BUGRISK" [2018-02-15 Thu 08:42] \\
No problem. Product is always real.
- State "BUGRISK" from "" [2018-02-11 Sun 09:11]
:PROPERTIES:
:ARCHIVE_TIME: 2018-02-15 Thu 08:42
:ARCHIVE_FILE: ~/WORK/_ABACUS/ABACUS/ABACUS.org
:ARCHIVE_OLPATH: Bugrisks
:ARCHIVE_CATEGORY: ABACUS
:ARCHIVE_TODO: SOLVED
:ARCHIVE_ITAGS: ABACUS Dev Bugrisks
:END:
File: ln_Density_ME.cc
line 66
Why real?

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@ -38,7 +38,7 @@ PROJECT_NAME = ABACUS
# could be handy for archiving the generated documentation or if some version
# control system is used.
PROJECT_NUMBER =
PROJECT_NUMBER =
# Using the PROJECT_BRIEF tag one can provide an optional one line description
# for a project that appears at the top of each page and should give viewer a
@ -51,7 +51,7 @@ PROJECT_BRIEF = "Numerical tools for integrable models"
# pixels and the maximum width should not exceed 200 pixels. Doxygen will copy
# the logo to the output directory.
PROJECT_LOGO =
PROJECT_LOGO =
# The OUTPUT_DIRECTORY tag is used to specify the (relative or absolute) path
# into which the generated documentation will be written. If a relative path is
@ -162,7 +162,7 @@ FULL_PATH_NAMES = YES
# will be relative from the directory where doxygen is started.
# This tag requires that the tag FULL_PATH_NAMES is set to YES.
STRIP_FROM_PATH =
STRIP_FROM_PATH =
# The STRIP_FROM_INC_PATH tag can be used to strip a user-defined part of the
# path mentioned in the documentation of a class, which tells the reader which
@ -171,7 +171,7 @@ STRIP_FROM_PATH =
# specify the list of include paths that are normally passed to the compiler
# using the -I flag.
STRIP_FROM_INC_PATH =
STRIP_FROM_INC_PATH =
# If the SHORT_NAMES tag is set to YES, doxygen will generate much shorter (but
# less readable) file names. This can be useful is your file systems doesn't
@ -238,13 +238,13 @@ TAB_SIZE = 4
# "Side Effects:". You can put \n's in the value part of an alias to insert
# newlines.
ALIASES =
ALIASES =
# This tag can be used to specify a number of word-keyword mappings (TCL only).
# A mapping has the form "name=value". For example adding "class=itcl::class"
# will allow you to use the command class in the itcl::class meaning.
TCL_SUBST =
TCL_SUBST =
# Set the OPTIMIZE_OUTPUT_FOR_C tag to YES if your project consists of C sources
# only. Doxygen will then generate output that is more tailored for C. For
@ -291,7 +291,7 @@ OPTIMIZE_OUTPUT_VHDL = NO
# Note that for custom extensions you also need to set FILE_PATTERNS otherwise
# the files are not read by doxygen.
EXTENSION_MAPPING =
EXTENSION_MAPPING =
# If the MARKDOWN_SUPPORT tag is enabled then doxygen pre-processes all comments
# according to the Markdown format, which allows for more readable
@ -648,7 +648,7 @@ GENERATE_DEPRECATEDLIST= YES
# sections, marked by \if <section_label> ... \endif and \cond <section_label>
# ... \endcond blocks.
ENABLED_SECTIONS =
ENABLED_SECTIONS =
# The MAX_INITIALIZER_LINES tag determines the maximum number of lines that the
# initial value of a variable or macro / define can have for it to appear in the
@ -690,7 +690,7 @@ SHOW_NAMESPACES = YES
# by doxygen. Whatever the program writes to standard output is used as the file
# version. For an example see the documentation.
FILE_VERSION_FILTER =
FILE_VERSION_FILTER =
# The LAYOUT_FILE tag can be used to specify a layout file which will be parsed
# by doxygen. The layout file controls the global structure of the generated
@ -703,7 +703,7 @@ FILE_VERSION_FILTER =
# DoxygenLayout.xml, doxygen will parse it automatically even if the LAYOUT_FILE
# tag is left empty.
LAYOUT_FILE =
LAYOUT_FILE =
# The CITE_BIB_FILES tag can be used to specify one or more bib files containing
# the reference definitions. This must be a list of .bib files. The .bib
@ -713,7 +713,7 @@ LAYOUT_FILE =
# LATEX_BIB_STYLE. To use this feature you need bibtex and perl available in the
# search path. See also \cite for info how to create references.
CITE_BIB_FILES =
CITE_BIB_FILES =
#---------------------------------------------------------------------------
# Configuration options related to warning and progress messages
@ -778,7 +778,7 @@ WARN_FORMAT = "$file:$line: $text"
# messages should be written. If left blank the output is written to standard
# error (stderr).
WARN_LOGFILE =
WARN_LOGFILE =
#---------------------------------------------------------------------------
# Configuration options related to the input files
@ -873,7 +873,7 @@ RECURSIVE = YES
# Note that relative paths are relative to the directory from which doxygen is
# run.
EXCLUDE =
EXCLUDE =
# The EXCLUDE_SYMLINKS tag can be used to select whether or not files or
# directories that are symbolic links (a Unix file system feature) are excluded
@ -889,7 +889,7 @@ EXCLUDE_SYMLINKS = NO
# Note that the wildcards are matched against the file with absolute path, so to
# exclude all test directories for example use the pattern */test/*
EXCLUDE_PATTERNS =
EXCLUDE_PATTERNS =
# The EXCLUDE_SYMBOLS tag can be used to specify one or more symbol names
# (namespaces, classes, functions, etc.) that should be excluded from the
@ -900,13 +900,13 @@ EXCLUDE_PATTERNS =
# Note that the wildcards are matched against the file with absolute path, so to
# exclude all test directories use the pattern */test/*
EXCLUDE_SYMBOLS =
EXCLUDE_SYMBOLS =
# The EXAMPLE_PATH tag can be used to specify one or more files or directories
# that contain example code fragments that are included (see the \include
# command).
EXAMPLE_PATH =
EXAMPLE_PATH =
# If the value of the EXAMPLE_PATH tag contains directories, you can use the
# EXAMPLE_PATTERNS tag to specify one or more wildcard pattern (like *.cpp and
@ -926,7 +926,7 @@ EXAMPLE_RECURSIVE = NO
# that contain images that are to be included in the documentation (see the
# \image command).
IMAGE_PATH =
IMAGE_PATH =
# The INPUT_FILTER tag can be used to specify a program that doxygen should
# invoke to filter for each input file. Doxygen will invoke the filter program
@ -947,7 +947,7 @@ IMAGE_PATH =
# need to set EXTENSION_MAPPING for the extension otherwise the files are not
# properly processed by doxygen.
INPUT_FILTER =
INPUT_FILTER =
# The FILTER_PATTERNS tag can be used to specify filters on a per file pattern
# basis. Doxygen will compare the file name with each pattern and apply the
@ -960,7 +960,7 @@ INPUT_FILTER =
# need to set EXTENSION_MAPPING for the extension otherwise the files are not
# properly processed by doxygen.
FILTER_PATTERNS =
FILTER_PATTERNS =
# If the FILTER_SOURCE_FILES tag is set to YES, the input filter (if set using
# INPUT_FILTER) will also be used to filter the input files that are used for
@ -975,14 +975,14 @@ FILTER_SOURCE_FILES = NO
# *.ext= (so without naming a filter).
# This tag requires that the tag FILTER_SOURCE_FILES is set to YES.
FILTER_SOURCE_PATTERNS =
FILTER_SOURCE_PATTERNS =
# If the USE_MDFILE_AS_MAINPAGE tag refers to the name of a markdown file that
# is part of the input, its contents will be placed on the main page
# (index.html). This can be useful if you have a project on for instance GitHub
# and want to reuse the introduction page also for the doxygen output.
USE_MDFILE_AS_MAINPAGE =
USE_MDFILE_AS_MAINPAGE =
#---------------------------------------------------------------------------
# Configuration options related to source browsing
@ -1087,7 +1087,7 @@ CLANG_ASSISTED_PARSING = NO
# specified with INPUT and INCLUDE_PATH.
# This tag requires that the tag CLANG_ASSISTED_PARSING is set to YES.
CLANG_OPTIONS =
CLANG_OPTIONS =
#---------------------------------------------------------------------------
# Configuration options related to the alphabetical class index
@ -1113,7 +1113,7 @@ COLS_IN_ALPHA_INDEX = 5
# while generating the index headers.
# This tag requires that the tag ALPHABETICAL_INDEX is set to YES.
IGNORE_PREFIX =
IGNORE_PREFIX =
#---------------------------------------------------------------------------
# Configuration options related to the HTML output
@ -1157,7 +1157,7 @@ HTML_FILE_EXTENSION = .html
# of the possible markers and block names see the documentation.
# This tag requires that the tag GENERATE_HTML is set to YES.
HTML_HEADER =
HTML_HEADER =
# The HTML_FOOTER tag can be used to specify a user-defined HTML footer for each
# generated HTML page. If the tag is left blank doxygen will generate a standard
@ -1167,7 +1167,7 @@ HTML_HEADER =
# that doxygen normally uses.
# This tag requires that the tag GENERATE_HTML is set to YES.
HTML_FOOTER =
HTML_FOOTER =
# The HTML_STYLESHEET tag can be used to specify a user-defined cascading style
# sheet that is used by each HTML page. It can be used to fine-tune the look of
@ -1179,7 +1179,7 @@ HTML_FOOTER =
# obsolete.
# This tag requires that the tag GENERATE_HTML is set to YES.
HTML_STYLESHEET =
HTML_STYLESHEET =
# The HTML_EXTRA_STYLESHEET tag can be used to specify additional user-defined
# cascading style sheets that are included after the standard style sheets
@ -1192,7 +1192,7 @@ HTML_STYLESHEET =
# list). For an example see the documentation.
# This tag requires that the tag GENERATE_HTML is set to YES.
HTML_EXTRA_STYLESHEET =
HTML_EXTRA_STYLESHEET =
# The HTML_EXTRA_FILES tag can be used to specify one or more extra images or
# other source files which should be copied to the HTML output directory. Note
@ -1202,7 +1202,7 @@ HTML_EXTRA_STYLESHEET =
# files will be copied as-is; there are no commands or markers available.
# This tag requires that the tag GENERATE_HTML is set to YES.
HTML_EXTRA_FILES =
HTML_EXTRA_FILES =
# The HTML_COLORSTYLE_HUE tag controls the color of the HTML output. Doxygen
# will adjust the colors in the style sheet and background images according to
@ -1331,7 +1331,7 @@ GENERATE_HTMLHELP = NO
# written to the html output directory.
# This tag requires that the tag GENERATE_HTMLHELP is set to YES.
CHM_FILE =
CHM_FILE =
# The HHC_LOCATION tag can be used to specify the location (absolute path
# including file name) of the HTML help compiler (hhc.exe). If non-empty,
@ -1339,7 +1339,7 @@ CHM_FILE =
# The file has to be specified with full path.
# This tag requires that the tag GENERATE_HTMLHELP is set to YES.
HHC_LOCATION =
HHC_LOCATION =
# The GENERATE_CHI flag controls if a separate .chi index file is generated
# (YES) or that it should be included in the master .chm file (NO).
@ -1352,7 +1352,7 @@ GENERATE_CHI = NO
# and project file content.
# This tag requires that the tag GENERATE_HTMLHELP is set to YES.
CHM_INDEX_ENCODING =
CHM_INDEX_ENCODING =
# The BINARY_TOC flag controls whether a binary table of contents is generated
# (YES) or a normal table of contents (NO) in the .chm file. Furthermore it
@ -1383,7 +1383,7 @@ GENERATE_QHP = NO
# the HTML output folder.
# This tag requires that the tag GENERATE_QHP is set to YES.
QCH_FILE =
QCH_FILE =
# The QHP_NAMESPACE tag specifies the namespace to use when generating Qt Help
# Project output. For more information please see Qt Help Project / Namespace
@ -1408,7 +1408,7 @@ QHP_VIRTUAL_FOLDER = doc
# filters).
# This tag requires that the tag GENERATE_QHP is set to YES.
QHP_CUST_FILTER_NAME =
QHP_CUST_FILTER_NAME =
# The QHP_CUST_FILTER_ATTRS tag specifies the list of the attributes of the
# custom filter to add. For more information please see Qt Help Project / Custom
@ -1416,21 +1416,21 @@ QHP_CUST_FILTER_NAME =
# filters).
# This tag requires that the tag GENERATE_QHP is set to YES.
QHP_CUST_FILTER_ATTRS =
QHP_CUST_FILTER_ATTRS =
# The QHP_SECT_FILTER_ATTRS tag specifies the list of the attributes this
# project's filter section matches. Qt Help Project / Filter Attributes (see:
# http://qt-project.org/doc/qt-4.8/qthelpproject.html#filter-attributes).
# This tag requires that the tag GENERATE_QHP is set to YES.
QHP_SECT_FILTER_ATTRS =
QHP_SECT_FILTER_ATTRS =
# The QHG_LOCATION tag can be used to specify the location of Qt's
# qhelpgenerator. If non-empty doxygen will try to run qhelpgenerator on the
# generated .qhp file.
# This tag requires that the tag GENERATE_QHP is set to YES.
QHG_LOCATION =
QHG_LOCATION =
# If the GENERATE_ECLIPSEHELP tag is set to YES, additional index files will be
# generated, together with the HTML files, they form an Eclipse help plugin. To
@ -1533,7 +1533,7 @@ FORMULA_TRANSPARENT = YES
# The default value is: NO.
# This tag requires that the tag GENERATE_HTML is set to YES.
USE_MATHJAX = NO
USE_MATHJAX = YES
# When MathJax is enabled you can set the default output format to be used for
# the MathJax output. See the MathJax site (see:
@ -1563,7 +1563,7 @@ MATHJAX_RELPATH = http://cdn.mathjax.org/mathjax/latest
# MATHJAX_EXTENSIONS = TeX/AMSmath TeX/AMSsymbols
# This tag requires that the tag USE_MATHJAX is set to YES.
MATHJAX_EXTENSIONS =
MATHJAX_EXTENSIONS =
# The MATHJAX_CODEFILE tag can be used to specify a file with javascript pieces
# of code that will be used on startup of the MathJax code. See the MathJax site
@ -1571,7 +1571,7 @@ MATHJAX_EXTENSIONS =
# example see the documentation.
# This tag requires that the tag USE_MATHJAX is set to YES.
MATHJAX_CODEFILE =
MATHJAX_CODEFILE =
# When the SEARCHENGINE tag is enabled doxygen will generate a search box for
# the HTML output. The underlying search engine uses javascript and DHTML and
@ -1631,7 +1631,7 @@ EXTERNAL_SEARCH = NO
# Searching" for details.
# This tag requires that the tag SEARCHENGINE is set to YES.
SEARCHENGINE_URL =
SEARCHENGINE_URL =
# When SERVER_BASED_SEARCH and EXTERNAL_SEARCH are both enabled the unindexed
# search data is written to a file for indexing by an external tool. With the
@ -1647,7 +1647,7 @@ SEARCHDATA_FILE = searchdata.xml
# projects and redirect the results back to the right project.
# This tag requires that the tag SEARCHENGINE is set to YES.
EXTERNAL_SEARCH_ID =
EXTERNAL_SEARCH_ID =
# The EXTRA_SEARCH_MAPPINGS tag can be used to enable searching through doxygen
# projects other than the one defined by this configuration file, but that are
@ -1657,7 +1657,7 @@ EXTERNAL_SEARCH_ID =
# EXTRA_SEARCH_MAPPINGS = tagname1=loc1 tagname2=loc2 ...
# This tag requires that the tag SEARCHENGINE is set to YES.
EXTRA_SEARCH_MAPPINGS =
EXTRA_SEARCH_MAPPINGS =
#---------------------------------------------------------------------------
# Configuration options related to the LaTeX output
@ -1721,7 +1721,7 @@ PAPER_TYPE = a4
# If left blank no extra packages will be included.
# This tag requires that the tag GENERATE_LATEX is set to YES.
EXTRA_PACKAGES =
EXTRA_PACKAGES =
# The LATEX_HEADER tag can be used to specify a personal LaTeX header for the
# generated LaTeX document. The header should contain everything until the first
@ -1737,7 +1737,7 @@ EXTRA_PACKAGES =
# to HTML_HEADER.
# This tag requires that the tag GENERATE_LATEX is set to YES.
LATEX_HEADER =
LATEX_HEADER =
# The LATEX_FOOTER tag can be used to specify a personal LaTeX footer for the
# generated LaTeX document. The footer should contain everything after the last
@ -1748,7 +1748,7 @@ LATEX_HEADER =
# Note: Only use a user-defined footer if you know what you are doing!
# This tag requires that the tag GENERATE_LATEX is set to YES.
LATEX_FOOTER =
LATEX_FOOTER =
# The LATEX_EXTRA_STYLESHEET tag can be used to specify additional user-defined
# LaTeX style sheets that are included after the standard style sheets created
@ -1759,7 +1759,7 @@ LATEX_FOOTER =
# list).
# This tag requires that the tag GENERATE_LATEX is set to YES.
LATEX_EXTRA_STYLESHEET =
LATEX_EXTRA_STYLESHEET =
# The LATEX_EXTRA_FILES tag can be used to specify one or more extra images or
# other source files which should be copied to the LATEX_OUTPUT output
@ -1767,7 +1767,7 @@ LATEX_EXTRA_STYLESHEET =
# markers available.
# This tag requires that the tag GENERATE_LATEX is set to YES.
LATEX_EXTRA_FILES =
LATEX_EXTRA_FILES =
# If the PDF_HYPERLINKS tag is set to YES, the LaTeX that is generated is
# prepared for conversion to PDF (using ps2pdf or pdflatex). The PDF file will
@ -1875,14 +1875,14 @@ RTF_HYPERLINKS = NO
# default style sheet that doxygen normally uses.
# This tag requires that the tag GENERATE_RTF is set to YES.
RTF_STYLESHEET_FILE =
RTF_STYLESHEET_FILE =
# Set optional variables used in the generation of an RTF document. Syntax is
# similar to doxygen's config file. A template extensions file can be generated
# using doxygen -e rtf extensionFile.
# This tag requires that the tag GENERATE_RTF is set to YES.
RTF_EXTENSIONS_FILE =
RTF_EXTENSIONS_FILE =
# If the RTF_SOURCE_CODE tag is set to YES then doxygen will include source code
# with syntax highlighting in the RTF output.
@ -1927,7 +1927,7 @@ MAN_EXTENSION = .3
# MAN_EXTENSION with the initial . removed.
# This tag requires that the tag GENERATE_MAN is set to YES.
MAN_SUBDIR =
MAN_SUBDIR =
# If the MAN_LINKS tag is set to YES and doxygen generates man output, then it
# will generate one additional man file for each entity documented in the real
@ -2040,7 +2040,7 @@ PERLMOD_PRETTY = YES
# overwrite each other's variables.
# This tag requires that the tag GENERATE_PERLMOD is set to YES.
PERLMOD_MAKEVAR_PREFIX =
PERLMOD_MAKEVAR_PREFIX =
#---------------------------------------------------------------------------
# Configuration options related to the preprocessor
@ -2081,7 +2081,7 @@ SEARCH_INCLUDES = YES
# preprocessor.
# This tag requires that the tag SEARCH_INCLUDES is set to YES.
INCLUDE_PATH =
INCLUDE_PATH =
# You can use the INCLUDE_FILE_PATTERNS tag to specify one or more wildcard
# patterns (like *.h and *.hpp) to filter out the header-files in the
@ -2089,7 +2089,7 @@ INCLUDE_PATH =
# used.
# This tag requires that the tag ENABLE_PREPROCESSING is set to YES.
INCLUDE_FILE_PATTERNS =
INCLUDE_FILE_PATTERNS =
# The PREDEFINED tag can be used to specify one or more macro names that are
# defined before the preprocessor is started (similar to the -D option of e.g.
@ -2099,7 +2099,7 @@ INCLUDE_FILE_PATTERNS =
# recursively expanded use the := operator instead of the = operator.
# This tag requires that the tag ENABLE_PREPROCESSING is set to YES.
PREDEFINED =
PREDEFINED =
# If the MACRO_EXPANSION and EXPAND_ONLY_PREDEF tags are set to YES then this
# tag can be used to specify a list of macro names that should be expanded. The
@ -2108,7 +2108,7 @@ PREDEFINED =
# definition found in the source code.
# This tag requires that the tag ENABLE_PREPROCESSING is set to YES.
EXPAND_AS_DEFINED =
EXPAND_AS_DEFINED =
# If the SKIP_FUNCTION_MACROS tag is set to YES then doxygen's preprocessor will
# remove all references to function-like macros that are alone on a line, have
@ -2137,13 +2137,13 @@ SKIP_FUNCTION_MACROS = YES
# the path). If a tag file is not located in the directory in which doxygen is
# run, you must also specify the path to the tagfile here.
TAGFILES =
TAGFILES =
# When a file name is specified after GENERATE_TAGFILE, doxygen will create a
# tag file that is based on the input files it reads. See section "Linking to
# external documentation" for more information about the usage of tag files.
GENERATE_TAGFILE =
GENERATE_TAGFILE =
# If the ALLEXTERNALS tag is set to YES, all external class will be listed in
# the class index. If set to NO, only the inherited external classes will be
@ -2192,14 +2192,14 @@ CLASS_DIAGRAMS = YES
# the mscgen tool resides. If left empty the tool is assumed to be found in the
# default search path.
MSCGEN_PATH =
MSCGEN_PATH =
# You can include diagrams made with dia in doxygen documentation. Doxygen will
# then run dia to produce the diagram and insert it in the documentation. The
# DIA_PATH tag allows you to specify the directory where the dia binary resides.
# If left empty dia is assumed to be found in the default search path.
DIA_PATH =
DIA_PATH =
# If set to YES the inheritance and collaboration graphs will hide inheritance
# and usage relations if the target is undocumented or is not a class.
@ -2248,7 +2248,7 @@ DOT_FONTSIZE = 10
# the path where dot can find it using this tag.
# This tag requires that the tag HAVE_DOT is set to YES.
DOT_FONTPATH =
DOT_FONTPATH =
# If the CLASS_GRAPH tag is set to YES then doxygen will generate a graph for
# each documented class showing the direct and indirect inheritance relations.
@ -2392,26 +2392,26 @@ INTERACTIVE_SVG = NO
# found. If left blank, it is assumed the dot tool can be found in the path.
# This tag requires that the tag HAVE_DOT is set to YES.
DOT_PATH =
DOT_PATH =
# The DOTFILE_DIRS tag can be used to specify one or more directories that
# contain dot files that are included in the documentation (see the \dotfile
# command).
# This tag requires that the tag HAVE_DOT is set to YES.
DOTFILE_DIRS =
DOTFILE_DIRS =
# The MSCFILE_DIRS tag can be used to specify one or more directories that
# contain msc files that are included in the documentation (see the \mscfile
# command).
MSCFILE_DIRS =
MSCFILE_DIRS =
# The DIAFILE_DIRS tag can be used to specify one or more directories that
# contain dia files that are included in the documentation (see the \diafile
# command).
DIAFILE_DIRS =
DIAFILE_DIRS =
# When using plantuml, the PLANTUML_JAR_PATH tag should be used to specify the
# path where java can find the plantuml.jar file. If left blank, it is assumed
@ -2419,17 +2419,17 @@ DIAFILE_DIRS =
# generate a warning when it encounters a \startuml command in this case and
# will not generate output for the diagram.
PLANTUML_JAR_PATH =
PLANTUML_JAR_PATH =
# When using plantuml, the PLANTUML_CFG_FILE tag can be used to specify a
# configuration file for plantuml.
PLANTUML_CFG_FILE =
PLANTUML_CFG_FILE =
# When using plantuml, the specified paths are searched for files specified by
# the !include statement in a plantuml block.
PLANTUML_INCLUDE_PATH =
PLANTUML_INCLUDE_PATH =
# The DOT_GRAPH_MAX_NODES tag can be used to set the maximum number of nodes
# that will be shown in the graph. If the number of nodes in a graph becomes

125
ABACUS_Usage_Example_Heis.cc Normal file
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@ -0,0 +1,125 @@
/**********************************************************
This software is part of J.-S. Caux's ABACUS++ library.
Copyright (c) J.-S. Caux
-----------------------------------------------------------
File: ABACUS+_Usage_Example_Heis.cc
Purpose: illustrates basic use of ABACUS for spin chains.
***********************************************************/
#include "ABACUS.h"
using namespace std;
using namespace JSC;
int main()
{
clock_t StartTime = clock();
// Refer to include/JSC_Heis.h for all class definitions
// and to src/HEIS/ for the actual implementations.
// Set basic system parameters:
DP Delta = 1.0; // anisotropy
int N = 64; // chain length
int M = 32; // number of downturned spins as compared to all spins up; must be <= N/2 (on or above equator)
// Define the chain: J, Delta, h, Nsites
Heis_Chain chain(1.0, Delta, 0.0, N);
// The Heis_Chain class so constructed contains information about all types of strings:
cout << "Delta = " << Delta << endl << "Possible string lengths and parities: ";
for (int j = 0; j < chain.Nstrings; ++j) cout << "(" << chain.Str_L[j] << ", " << chain.par[j] << ")" << "\t";
cout << endl;
// Constructing a Bethe state: start with the ground state for simplicity.
// Define the base: chain, Mdown
// A base by definition represents a partition of the M down spins into different strings.
Heis_Base gbase(chain, M); // This puts all the M down spins into one-strings.
// Define the ground state
//XXZ_Bethe_State gstate(chain, gbase); // Use this constructor for 0 < Delta < 1
XXX_Bethe_State gstate(chain, gbase); // Use this constructor for Delta == 1
//XXZ_gpd_Bethe_State gstate(chain, gbase); // Use this constructor for Delta > 1.
// Anisotropies Delta < 0 are not separately implemented.
// The assignment operator is overloaded for Bethe states:
XXX_Bethe_State gstate2 = gstate; // copies all data of gstate into new object gstate2
// Compute everything about the ground state
gstate.Compute_All(true);
// Output information about the state
cout << gstate << endl;
// Now define some excited state.
// First method:
// Start with defining a base using a base constructor with a vector of numbers of rapidities of each type as argument:
// First define Nrapidities vector:
Vect<int> Nrapidities(0, chain.Nstrings);
// Assigning the numbers that follow, you have to ensure (yourself!) the \sum_j M_j n_j = M (where n_j is the length of type j).
Nrapidities[0] = M-2; // number of one-strings
Nrapidities[1] = 1; // one two-string
// Define the base:
Heis_Base ebase(chain, Nrapidities);
// Once the base is defined, the limiting quantum numbers are automatically computed:
cout << "ebase defined, data is (Mdown, Nrap, Nraptot, Ix2_infty, Ix2_min, Ix2_max, baselabel):"
<< ebase.Mdown << endl << ebase.Nrap << endl << ebase.Nraptot << endl << ebase.Ix2_infty << endl
<< ebase.Ix2_min << endl << ebase.Ix2_max << endl << ebase.baselabel << endl;
// An excited state can then be defined using this new base:
XXX_Bethe_State estate(chain, ebase);
// Individual quantum numbers can be manipulated: this will NOT update the state label or verify range of Ix2
estate.Ix2[0][0] = M+1;
estate.Compute_All(true);
cout << endl << "estate: " << estate << endl;
// Second method of constructing a base:
Heis_Base ebase2(chain, "31"); // This is another constructor for all rapidities in one-strings
//Heis_Base ebase(chain, "29x1y1"); // one two-string (XXX)
// Construct a new Bethe state
XXX_Bethe_State estateref (chain, ebase2); // this will contain the lowest-energy quantum numbers for this base
XXX_Bethe_State estate2 (chain, ebase2); // yet another state
// Setting a state to a given label:
estate2.Set_to_Label ("31_1_nh", estateref.Ix2); // The base of estate must coincide with the base in the label. Label is relative to estateref.Ix2
estate2.Compute_All(true);
cout << "estate2: " << estate2 << endl;
// Energy and momentum of the states:
cout << "Energy and momentum of states:" << endl;
cout << "gstate.E = " << gstate.E << "\testate.E = " << estate.E << endl;
cout << "Excitation energy = estate.E - gstate.E = " << estate.E - gstate.E << endl;
cout << "Excitation momentum (mod 2 pi) = estate.K - gstate.K = " << estate.K - gstate.K << endl;
// Computing matrix elements: CAREFUL: magnetizations must be consistent with operator (error is flagged).
cout << "Matrix elements: " << endl;
// The logarithm of the matrix elements are computed as complex numbers:
cout << "ln_Sz (gstate, estate) = " << ln_Sz_ME (gstate, estate) << endl;
// The other possible matrix element call is for the Smin matrix element,
cout << "ln_Smin (gstate, estate2) = " << ln_Smin_ME (gstate, estate2) << endl;
clock_t StopTime = clock();
//cout << "Total time: " << (StopTime - StartTime)/*/CLOCKS_PER_SEC*/ << " hundreths of a second."
cout << "Total time: " << DP(StopTime - StartTime)/CLOCKS_PER_SEC << " seconds."
<< endl;
return(0);
}

108
ABACUS_Usage_Example_LiebLin.cc Normal file
View File

@ -0,0 +1,108 @@
/**********************************************************
This software is part of J.-S. Caux's ABACUS library.
Copyright (c) J.-S. Caux.
-----------------------------------------------------------
File: ABACUS_Usage_Example_LiebLin.cc
Purpose: examples of calculations for Lieb-Liniger
***********************************************************/
#include "ABACUS.h"
using namespace std;
using namespace ABACUS;
int main()
{
clock_t StartTime = clock();
DP c_int = 2.0;
DP L = 3.0;
int N = 3;
DP nbar_required = 1.0;
DP kBT = 4.0;
int Npts = 4*N;
DP req_diff = 1.0e-4;
int Max_Secs = 60;
if (true) { // State-by-state checks
DP c_int = 4.0;
DP L = 16.0;
int N = 16;
LiebLin_Bethe_State gstate (c_int, L, N);
gstate.Compute_All(true);
cout << setprecision(16) << gstate << endl;
LiebLin_Bethe_State estate (c_int, L, N-1);
//estate.Set_to_ids (1LL, 1LL, 2LL, 0LL);
//estate.Set_to_Label ("64_2_028ysn1", gstate.Ix2);
//for (int i = 0; i < N; ++i) estate.Ix2[i] += 2;
// estate.Ix2[0] -= 8;
// estate.Ix2[1] -= 4;
// estate.Ix2[N-3] += 2;
// estate.Ix2[N-2] += 4;
// estate.Ix2[N-1] += 6;
// estate.Set_Label_from_Ix2(gstate.Ix2);
estate.Compute_All(true);
cout << setprecision(16) << estate << endl;
//Scan_LiebLin ('o', estate, "28_3_i3y55yf3", -2*N, 2*N, 60, 1.0e+6, 0, 0, 1);
//stringstream filenameprefix;
//Data_File_Name (filenameprefix, 'd', -2*N, 2*N, 0.0, estate, estate, "28_3_i3y55yf3");
//string prefix = filenameprefix.str();
DP ommin = 0.0; DP ommax = 10.0; DP gwidth = 1.0;// meaningless
int Nom = 10;
DP normalization = twoPI * L;
//Smoothen_RAW_into_SF (filenameprefix.str(), -2*N, 2*N, 0, ommin, ommax, Nom, gwidth, normalization, L);
//Density-density matrix elements:
// cout << setprecision(16) << "omega = " << estate.E - gstate.E << "\t"
// << exp(real(ln_Density_ME(gstate, estate))) << "\t" << exp(real(ln_Density_ME(estate, gstate))) << endl;
//Field operator matrix elements:
cout << "omega\tiK\t< estate | Psi | gstate > matrix element:" << endl;
cout << setprecision(16) << estate.E - gstate.E << "\t" << estate.iK - gstate.iK << "\t"
<< exp(ln_Psi_ME(estate, gstate)) << endl;
//LiebLin_Bethe_State flipstate = estate;
//flipstate.Parity_Flip();
//cout << "Flipping: " << endl;
//cout << "omega = " << flipstate.E - gstate.E << "\t" << exp(real(ln_Density_ME(gstate, flipstate))) << endl;
// Finite T checks:
DP kBT = 1.0;
// Delta is the number of sites involved in the smoothing of the entropy
//int Delta = int(sqrt(N))/2;//6;//N/20;
//DP epsilon = log(L)/L;
DP epsilon = log(L)/L;
// Construct the finite-size saddle-point state:
//LiebLin_Bethe_State spstate = Canonical_Saddle_Point_State (c_int, L, N, kBT, Delta);
//LiebLin_Bethe_State spstate = Canonical_Saddle_Point_State (c_int, L, N, kBT, epsilon);
//spstate.Compute_All(true);
//cout << spstate << endl;
}
clock_t StopTime = clock();
//cout << "Total time: " << (StopTime - StartTime)/*/CLOCKS_PER_SEC*/ << " hundreths of a second."
cout << "Total time: " << DP(StopTime - StartTime)/CLOCKS_PER_SEC << " seconds."
<< endl;
return(0);
}

41
include/ABACUS_LiebLin.h
View File

@ -29,6 +29,14 @@ namespace ABACUS {
//***********************************************************************
/**
Eigenstates of the Lieb-Liniger model in the repulsive \f$(c > 0)\f$ regime.
For numerical convenience, rapidities are rescaled by the interaction parameter \f$c\f$.
In equations throughout this documentation, \f$\tilde{\lambda} \equiv \lambda/c\f$.
In the code, these rescaled rapidities are denoted `lambdaoc` (read: "lambda over c").
*/
class LiebLin_Bethe_State {
public:
@ -104,7 +112,8 @@ namespace ABACUS {
};
inline bool Is_Inner_Skeleton (LiebLin_Bethe_State& State) {
return (State.N >= 2 && (State.Ix2[0] == State.Ix2[1] - 2 || State.Ix2[State.N-1] == State.Ix2[State.N-2] + 2));
return (State.N >= 2 && (State.Ix2[0] == State.Ix2[1] - 2
|| State.Ix2[State.N-1] == State.Ix2[State.N-2] + 2));
};
inline bool Is_Outer_Skeleton (LiebLin_Bethe_State& State) {
return (State.N >= 2 && State.Ix2[0] == LIEBLIN_Ix2_MIN + (State.N % 2) + 1
@ -115,12 +124,14 @@ namespace ABACUS {
&& State.Ix2[State.N-1] == LIEBLIN_Ix2_MAX - (State.N % 2) - 1);
};
inline bool Force_Descent (char whichDSF, LiebLin_Bethe_State& ScanState, LiebLin_Bethe_State& RefState,
inline bool Force_Descent (char whichDSF, LiebLin_Bethe_State& ScanState,
LiebLin_Bethe_State& RefState,
int desc_type_required, int iKmod, DP Chem_Pot)
{
bool forcedesc = false;
// Force descent if we're computing density-density, we're at zero momentum and we're descending with momentum preserved:
// Force descent if we're computing density-density, we're at zero momentum
// and we're descending with momentum preserved:
if (whichDSF == 'd' && ScanState.iK == RefState.iK && desc_type_required > 8) forcedesc = true;
// For BEC to c > 0 quench, g2(x=0): force first step
@ -135,7 +146,8 @@ namespace ABACUS {
// FUNCTION DECLARATIONS:
DP Chemical_Potential (LiebLin_Bethe_State& RefState);
DP Sumrule_Factor (char whichDSF, LiebLin_Bethe_State& RefState, DP Chem_Pot, int iKmin, int iKmax);
DP Sumrule_Factor (char whichDSF, LiebLin_Bethe_State& RefState, DP Chem_Pot,
int iKmin, int iKmax);
void Evaluate_F_Sumrule (char whichDSF, const LiebLin_Bethe_State& RefState, DP Chem_Pot,
int iKmin, int iKmax, const char* RAW_Cstr, const char* FSR_Cstr);
void Evaluate_F_Sumrule (std::string prefix, char whichDSF, const LiebLin_Bethe_State& RefState,
@ -157,14 +169,23 @@ namespace ABACUS {
std::complex<DP> ln_Psi_ME (LiebLin_Bethe_State& lstate, LiebLin_Bethe_State& rstate);
std::complex<DP> ln_g2_ME (LiebLin_Bethe_State& mu, LiebLin_Bethe_State& lambda);
DP Compute_Matrix_Element_Contrib (char whichDSF, int iKmin, int iKmax, LiebLin_Bethe_State& LeftState,
LiebLin_Bethe_State& RefState, DP Chem_Pot, std::stringstream& DAT_outfile);
DP Compute_Matrix_Element_Contrib (char whichDSF, int iKmin, int iKmax,
LiebLin_Bethe_State& LeftState,
LiebLin_Bethe_State& RefState, DP Chem_Pot,
std::stringstream& DAT_outfile);
DP LiebLin_Twisted_lnnorm (Vect<std::complex<DP> >& lambdaoc, double cxL);
std::complex<DP> LiebLin_Twisted_ln_Overlap (DP expbeta, Vect<DP> lstate_lambdaoc, DP lstate_lnnorm, LiebLin_Bethe_State& rstate);
std::complex<DP> LiebLin_Twisted_ln_Overlap (std::complex<DP> expbeta, Vect<std::complex<DP> > lstate_lambdaoc, DP lstate_lnnorm, LiebLin_Bethe_State& rstate);
std::complex<DP> LiebLin_ln_Overlap (Vect<DP> lstate_lambdaoc, DP lstate_lnnorm, LiebLin_Bethe_State& rstate);
std::complex<DP> LiebLin_ln_Overlap (Vect<std::complex<DP> > lstate_lambdaoc, DP lstate_lnnorm, LiebLin_Bethe_State& rstate);
std::complex<DP> LiebLin_Twisted_ln_Overlap (DP expbeta, Vect<DP> lstate_lambdaoc,
DP lstate_lnnorm,
LiebLin_Bethe_State& rstate);
std::complex<DP> LiebLin_Twisted_ln_Overlap (std::complex<DP> expbeta,
Vect<std::complex<DP> > lstate_lambdaoc,
DP lstate_lnnorm,
LiebLin_Bethe_State& rstate);
std::complex<DP> LiebLin_ln_Overlap (Vect<DP> lstate_lambdaoc, DP lstate_lnnorm,
LiebLin_Bethe_State& rstate);
std::complex<DP> LiebLin_ln_Overlap (Vect<std::complex<DP> > lstate_lambdaoc, DP lstate_lnnorm,
LiebLin_Bethe_State& rstate);
// In src/LiebLin_Tgt0.cc:
DP Entropy (LiebLin_Bethe_State& RefState);

172
src/LIEBLIN/LiebLin_Bethe_State.cc
View File

@ -24,18 +24,18 @@ namespace ABACUS {
LiebLin_Bethe_State::LiebLin_Bethe_State ()
: c_int (0.0), L(0.0), cxL(0.0), N(0),
Ix2_available(Vect<int>(0, 1)), index_first_hole_to_right (Vect<int>(0,1)), displacement (Vect<int>(0,1)),
Ix2(Vect<int>(0, 1)), lambdaoc(Vect<DP>(0.0, 1)),
S(Vect<DP>(0.0, 1)), dSdlambdaoc(Vect<DP>(0.0, 1)),
diffsq(0.0), prec(ITER_REQ_PREC_LIEBLIN), conv(0), iter_Newton(0), E(0.0), iK(0), K(0.0), lnnorm(-100.0)
Ix2_available(Vect<int>(0, 1)), index_first_hole_to_right (Vect<int>(0,1)),
displacement (Vect<int>(0,1)), Ix2(Vect<int>(0, 1)), lambdaoc(Vect<DP>(0.0, 1)),
S(Vect<DP>(0.0, 1)), dSdlambdaoc(Vect<DP>(0.0, 1)), diffsq(0.0), prec(ITER_REQ_PREC_LIEBLIN),
conv(0), iter_Newton(0), E(0.0), iK(0), K(0.0), lnnorm(-100.0)
{
stringstream Nout; Nout << N; label = Nout.str() + LABELSEP + ABACUScoding[0] + LABELSEP;
}
LiebLin_Bethe_State::LiebLin_Bethe_State (DP c_int_ref, DP L_ref, int N_ref)
: c_int(c_int_ref), L(L_ref), cxL(c_int_ref * L_ref), N(N_ref),
Ix2_available(Vect<int>(0, 2)), index_first_hole_to_right (Vect<int>(0,N)), displacement (Vect<int>(0,N)),
Ix2(Vect<int>(0, N)), lambdaoc(Vect<DP>(0.0, N)),
Ix2_available(Vect<int>(0, 2)), index_first_hole_to_right (Vect<int>(0,N)),
displacement (Vect<int>(0,N)), Ix2(Vect<int>(0, N)), lambdaoc(Vect<DP>(0.0, N)),
S(Vect<DP>(0.0, N)), dSdlambdaoc(Vect<DP>(0.0, N)),
diffsq(0.0), prec(ABACUS::max(1.0, 1.0/(c_int * c_int)) * ITER_REQ_PREC_LIEBLIN),
conv(0), iter_Newton(0), E(0.0), iK(0), K(0.0), lnnorm(-100.0)
@ -93,7 +93,8 @@ namespace ABACUS {
if (N != OriginStateIx2.size()) {
cout << label_ref << endl;
cout << labeldata.M << endl;
ABACUSerror("Trying to set an incorrect label on LiebLin_Bethe_State: N != OriginStateIx2.size().");
ABACUSerror("Trying to set an incorrect label on LiebLin_Bethe_State: "
"N != OriginStateIx2.size().");
}
label = label_ref;
@ -106,7 +107,8 @@ namespace ABACUS {
// Now set the excitations:
for (int iexc = 0; iexc < labeldata.nexc[0]; ++iexc)
for (int i = 0; i < N; ++i) if (Ix2[i] == labeldata.Ix2old[0][iexc]) Ix2[i] = labeldata.Ix2exc[0][iexc];
for (int i = 0; i < N; ++i)
if (Ix2[i] == labeldata.Ix2old[0][iexc]) Ix2[i] = labeldata.Ix2exc[0][iexc];
// Now reorder the Ix2 to follow convention:
Ix2.QuickSort();
@ -143,10 +145,13 @@ namespace ABACUS {
Ix2old_ref[0] = Vect<int>(ABACUS::max(nexc_ref[0],1));
Ix2exc_ref[0] = Vect<int>(ABACUS::max(nexc_ref[0],1));
int nexccheck = 0;
for (int i = 0; i < N; ++i) if (!OriginStateIx2.includes(Ix2[i])) Ix2exc_ref[0][nexccheck++] = Ix2[i];
if (nexccheck != nexc_ref[0]) ABACUSerror("Counting excitations wrong (1) in LiebLin_Bethe_State::Set_Label_from_Ix2");
for (int i = 0; i < N; ++i)
if (!OriginStateIx2.includes(Ix2[i])) Ix2exc_ref[0][nexccheck++] = Ix2[i];
if (nexccheck != nexc_ref[0])
ABACUSerror("Counting excitations wrong (1) in LiebLin_Bethe_State::Set_Label_from_Ix2");
nexccheck = 0;
for (int i = 0; i < N; ++i) if (!Ix2.includes (OriginStateIx2[i])) Ix2old_ref[0][nexccheck++] = OriginStateIx2[i];
for (int i = 0; i < N; ++i)
if (!Ix2.includes (OriginStateIx2[i])) Ix2old_ref[0][nexccheck++] = OriginStateIx2[i];
if (nexccheck != nexc_ref[0]) {
cout << "nexc_ref[0] = " << nexc_ref[0] << "\tnexccheck = " << nexccheck << endl;
cout << OriginStateIx2 << endl;
@ -167,7 +172,8 @@ namespace ABACUS {
void LiebLin_Bethe_State::Set_Label_Internals_from_Ix2 (const Vect<int>& OriginStateIx2)
{
if (N != OriginStateIx2.size()) ABACUSerror("N != OriginStateIx2.size() in Set_Label_Internals_from_Ix2.");
if (N != OriginStateIx2.size())
ABACUSerror("N != OriginStateIx2.size() in Set_Label_Internals_from_Ix2.");
Vect<int> OriginStateIx2ordered = OriginStateIx2;
OriginStateIx2ordered.QuickSort();
@ -207,7 +213,8 @@ namespace ABACUS {
for (int j = 0; j < N; ++j) {
int i = 0;
while (Ix2_available[i] < OriginStateIx2ordered[j]) i++;
// We now have Ix2_available[i] == OriginStateIx2[j]. Shift all Ix2_available to the right of this by 2;
// We now have Ix2_available[i] == OriginStateIx2[j].
// Shift all Ix2_available to the right of this by 2;
for (int i1 = i; i1 < navailable; ++i1) Ix2_available[i1] += 2;
index_first_hole_to_right[j] = i;
}
@ -218,10 +225,12 @@ namespace ABACUS {
// Set displacement vector from the Ix2:
for (int j = 0; j < N; ++j) {
if (Ix2[j] < OriginStateIx2ordered[j]) {
// Ix2[j] must be equal to some OriginState_Ix2_available[i] for i < OriginState_index_first_hole_to_right[j]
// Ix2[j] must be equal to some OriginState_Ix2_available[i]
// for i < OriginState_index_first_hole_to_right[j]
while (Ix2[j] != Ix2_available[index_first_hole_to_right[j] + displacement[j] ]) {
if (index_first_hole_to_right[j] + displacement[j] == 0) {
cout << label << endl << j << endl << OriginStateIx2 << endl << Ix2 << endl << Ix2_available
cout << label << endl << j << endl << OriginStateIx2 << endl
<< Ix2 << endl << Ix2_available
<< endl << index_first_hole_to_right << endl << displacement << endl;
ABACUSerror("Going down too far in Set_Label_Internals...");
}
@ -233,7 +242,8 @@ namespace ABACUS {
displacement[j] = 1; // start with this value to prevent segfault
while (Ix2[j] != Ix2_available[index_first_hole_to_right[j] - 1 + displacement[j] ]) {
if (index_first_hole_to_right[j] + displacement[j] == Ix2_available.size() - 1) {
cout << label << endl << j << endl << OriginStateIx2 << endl << Ix2 << endl << Ix2_available
cout << label << endl << j << endl << OriginStateIx2 << endl
<< Ix2 << endl << Ix2_available
<< endl << index_first_hole_to_right << endl << displacement << endl;
ABACUSerror("Going up too far in Set_Label_Internals...");
}
@ -245,7 +255,8 @@ namespace ABACUS {
bool LiebLin_Bethe_State::Check_Admissibility (char whichDSF)
{
//if (Ix2.min() < -13 || Ix2.max() > 13) return(false); // For testing with restricted Hilbert space
// For testing with restricted Hilbert space:
//if (Ix2.min() < -13 || Ix2.max() > 13) return(false);
return(true);
}
@ -253,7 +264,8 @@ namespace ABACUS {
{
// This function finds the rapidities of the eigenstate
lnnorm = -100.0; // sentinel value, recalculated if Newton method used in the last step of iteration.
// sentinel value, recalculated if Newton method used in the last step of iteration.
lnnorm = -100.0;
diffsq = 1.0;
@ -289,15 +301,20 @@ namespace ABACUS {
return nonan;
}
/**
For the repulsive Lieb-Liniger model, all eigenstates have real rapidities
(there are no strings). All string deviations are thus set to zero.
*/
DP LiebLin_Bethe_State::String_delta()
{
return(0.0); // no strings (thus no deviations) in replusive LiebLin
return(0.0);
}
/**
Checks whether the quantum numbers are symmetrically distributed: \f$\{ I \} = \{ -I \}\f$.
*/
bool LiebLin_Bethe_State::Check_Symmetry ()
{
// Checks whether the I's are symmetrically distributed.
bool symmetric_state = true;
Vect<int> Ix2check = Ix2;
@ -309,6 +326,18 @@ namespace ABACUS {
return(symmetric_state);
}
/**
This function computes the log of the norm of a `LiebLin_Bethe_State` instance.
This is obtained from the Gaudin-Korepin norm formula
\f{eqnarray*}{
\langle 0 | \prod_{j=0}^{N-1} C(\lambda_j) \prod_{j=0}^{N-1} B(\lambda_j) | 0 \rangle
= \prod_{j=0}^{N-2}\prod_{k=j+1}^{N-1}
\frac{(\lambda_j - \lambda_k )^2 + c^2}{(\lambda_j - \lambda_k)^2}
\times ~\mbox{Det}_N G
\f}
in which \f$G\f$ is the Gaudin matrix computed by
LiebLin_Bethe_State::Build_Reduced_Gaudin_Matrix.
*/
void LiebLin_Bethe_State::Compute_lnnorm ()
{
if (lnnorm == -100.0) { // else Gaudin part already calculated by Newton method
@ -317,7 +346,13 @@ namespace ABACUS {
(*this).Build_Reduced_Gaudin_Matrix(Gaudin_Red);
lnnorm = real(lndet_LU_dstry(Gaudin_Red));
complex<DP> lnnorm_CX = lndet_LU_dstry(Gaudin_Red);
if (abs(imag(lnnorm_CX)) > 1.0e-6) {
cout << "lnnorm_CX = " << lnnorm_CX << endl;
ABACUSerror("Gaudin norm of LiebLin_Bethe_State should be real and positive.");
}
lnnorm = real(lnnorm_CX);
// Add the pieces outside of Gaudin determinant
@ -329,7 +364,15 @@ namespace ABACUS {
return;
}
void LiebLin_Bethe_State::Compute_All (bool reset_rapidities) // solves BAE, computes E, K and lnnorm
/**
This function solves the Bethe equations, computes the energy, momentum and state norm.
It calls LiebLin_Bethe_State::Find_Rapidities, LiebLin_Bethe_State::Compute_Energy,
LiebLin_Bethe_State::Compute_Momentum and LiebLin_Bethe_State::Compute_lnnorm.
Assumptions:
- the set of quantum numbers is admissible.
*/
void LiebLin_Bethe_State::Compute_All (bool reset_rapidities)
{
(*this).Find_Rapidities (reset_rapidities);
if (conv == 1) {
@ -345,7 +388,8 @@ namespace ABACUS {
if (cxL >= 1.0)
for (int a = 0; a < N; ++a) lambdaoc[a] = PI * Ix2[a]/cxL;
// For small values of c, use better approximation using approximate zeroes of Hermite polynomials: see Gaudin eqn 4.71.
// For small values of c, use better approximation using approximate
// zeroes of Hermite polynomials: see Gaudin eqn 4.71.
if (cxL < 1.0) {
DP oneoversqrtcLN = 1.0/pow(cxL * N, 0.5);
for (int a = 0; a < N; ++a) lambdaoc[a] = oneoversqrtcLN * PI * Ix2[a];
@ -403,7 +447,8 @@ namespace ABACUS {
dSdlambdaoc[j] += 1.0/((lambdaoc[j] - lambdaoc[k]) * (lambdaoc[j] - lambdaoc[k]) + 1.0);
dSdlambdaoc[j] *= 2.0/(PI * cxL);
dlambdaoc[j] = (PI*Ix2[j]/cxL - S[j] + lambdaoc[j] * dSdlambdaoc[j])/(1.0 + dSdlambdaoc[j]) - lambdaoc[j];
dlambdaoc[j] = (PI*Ix2[j]/cxL - S[j] + lambdaoc[j] * dSdlambdaoc[j])
/(1.0 + dSdlambdaoc[j]) - lambdaoc[j];
}
@ -421,16 +466,18 @@ namespace ABACUS {
return;
}
/**
Performs one step of the matrix Newton method on the rapidities.
*/
void LiebLin_Bethe_State::Iterate_BAE_Newton (DP damping)
{
// does one step of a Newton method on the rapidities...
Vect_DP RHSBAE (0.0, N); // contains RHS of BAEs
Vect_DP dlambdaoc (0.0, N); // contains delta lambdaoc computed from Newton's method
SQMat_DP Gaudin (0.0, N);
Vect_INT indx (N);
DP sumtheta = 0.0;
int atanintshift = 0; // for large |lambda|, use atan (lambda) = sgn(lambda) pi/2 - atan(1/lambda)
// for large |lambda|, use atan (lambda) = sgn(lambda) pi/2 - atan(1/lambda)
int atanintshift = 0;
DP lambdahere = 0.0;
// Compute the RHS of the BAEs:
@ -463,11 +510,13 @@ namespace ABACUS {
lubksb (Gaudin, indx, dlambdaoc);
bool ordering_changed = false;
for (int j = 0; j < N-1; ++j) if (lambdaoc[j] + dlambdaoc[j] > lambdaoc[j+1] + dlambdaoc[j+1]) ordering_changed = true;
for (int j = 0; j < N-1; ++j)
if (lambdaoc[j] + dlambdaoc[j] > lambdaoc[j+1] + dlambdaoc[j+1]) ordering_changed = true;
// To prevent Newton from diverging, we limit the size of the rapidity changes.
// The leftmost and rightmost rapidities can grow by one order of magnitude per iteration step.
if (ordering_changed) { // We explicitly ensure that the ordering remains correct after the iteration step.
if (ordering_changed) {
// We explicitly ensure that the ordering remains correct after the iteration step.
bool ordering_still_changed = false;
DP maxdlambdaoc = 0.0;
do {
@ -552,16 +601,38 @@ namespace ABACUS {
K = 2.0 * iK * PI/L;
}
/**
The fundamental scattering kernel for Lieb-Liniger,
\f[
K (\tilde{\lambda}) = \frac{ 2 }{\tilde{\lambda}^2 + 1}
\f]
given two indices for the rapidities as arguments.
*/
DP LiebLin_Bethe_State::Kernel (int a, int b)
{
return(2.0/(pow(lambdaoc[a] - lambdaoc[b], 2.0) + 1.0));
}
/**
The fundamental scattering kernel for Lieb-Liniger,
\f[
K (\tilde{\lambda}) = \frac{ 2 }{\tilde{\lambda}^2 + 1}
\f]
given the rapidity difference as argument.
*/
DP LiebLin_Bethe_State::Kernel (DP lambdaoc_ref)
{
return(2.0/(lambdaoc_ref * lambdaoc_ref + 1.0));
}
/**
This function constructs the Gaudin matrix \f$G\f$
which is defined as the Hessian of the Yang-Yang action \f$S^{YY}\f$,
\f[
G_{jk} = \delta_{jk} \left\{ cL + \sum_{l} K (\tilde{\lambda}_j - \tilde{\lambda}_l) \right\}
- K (\tilde{\lambda}_j - \tilde{\lambda}_k).
\f]
*/
void LiebLin_Bethe_State::Build_Reduced_Gaudin_Matrix (SQMat<DP>& Gaudin_Red)
{
@ -575,7 +646,8 @@ namespace ABACUS {
if (j == k) {
sum_Kernel = 0.0;
for (int kp = 0; kp < N; ++kp) if (j != kp) sum_Kernel += Kernel (lambdaoc[j] - lambdaoc[kp]);
for (int kp = 0; kp < N; ++kp)
if (j != kp) sum_Kernel += Kernel (lambdaoc[j] - lambdaoc[kp]);
Gaudin_Red[j][k] = cxL + sum_Kernel;
}
@ -586,6 +658,11 @@ namespace ABACUS {
return;
}
/**
For a summetric `LiebLin_Bethe_State`, this function computes the Gaudin matrix
as an \f$N/2 \times N/2\f$ matrix to accelerate computations.
*/
void LiebLin_Bethe_State::Build_Reduced_BEC_Quench_Gaudin_Matrix (SQMat<DP>& Gaudin_Red)
{
// Passing a matrix of dimension N/2
@ -612,7 +689,8 @@ namespace ABACUS {
sum_Kernel = 0.0;
for (int kp = N/2; kp < N; ++kp)
if (j + N/2 != kp)
sum_Kernel += Kernel (lambdaoc[j+N/2] - lambdaoc[kp]) + Kernel (lambdaoc[j+N/2] + lambdaoc[kp]);
sum_Kernel += Kernel (lambdaoc[j+N/2] - lambdaoc[kp])
+ Kernel (lambdaoc[j+N/2] + lambdaoc[kp]);
Gaudin_Red[j][k] = cxL + sum_Kernel;
}
@ -625,10 +703,13 @@ namespace ABACUS {
}
void LiebLin_Bethe_State::Annihilate_ph_pair (int ipart, int ihole, const Vect<int>& OriginStateIx2)
/**
This function changes the Ix2 of a given state by annihilating a particle and hole
pair specified by ipart and ihole (counting from the left, starting with index 0).
*/
void LiebLin_Bethe_State::Annihilate_ph_pair (int ipart, int ihole,
const Vect<int>& OriginStateIx2)
{
// This function changes the Ix2 of a given state by annihilating a particle and hole
// pair specified by ipart and ihole (counting from the left, starting with index 0).
State_Label_Data currentdata = Read_State_Label ((*this).label, OriginStateIx2);
@ -645,8 +726,10 @@ namespace ABACUS {
int ntypespresent = 1; // only one type for LiebLin
Vect<Vect<int> > Ix2old_new(ntypespresent);
Vect<Vect<int> > Ix2exc_new(ntypespresent);
for (int it = 0; it < ntypespresent; ++it) Ix2old_new[it] = Vect<int>(ABACUS::max(nexc_new[it],1));
for (int it = 0; it < ntypespresent; ++it) Ix2exc_new[it] = Vect<int>(ABACUS::max(nexc_new[it],1));
for (int it = 0; it < ntypespresent; ++it)
Ix2old_new[it] = Vect<int>(ABACUS::max(nexc_new[it],1));
for (int it = 0; it < ntypespresent; ++it)
Ix2exc_new[it] = Vect<int>(ABACUS::max(nexc_new[it],1));
// Copy earlier data in, leaving out ipart and ihole:
for (int it = 0; it < ntypespresent; ++it) {
@ -661,9 +744,12 @@ namespace ABACUS {
(*this).Set_to_Label (Return_State_Label(newdata, OriginStateIx2));
}
/**
Performs a spatial inversion of a `LiebLin_Bethe_State`, mapping all quantum numbers
and rapidities to minus themselves.
*/
void LiebLin_Bethe_State::Parity_Flip ()
{
// For simplicity, we don't redo base_id, type_id, id.
Vect_INT Ix2buff = Ix2;
Vect_DP lambdaocbuff = lambdaoc;
for (int i = 0; i < N; ++i) Ix2[i] = -Ix2buff[N - 1 - i];
@ -672,16 +758,20 @@ namespace ABACUS {
K = -K;
}
/**
Send information about a `LiebLin_Bethe_State` to the output stream.
*/
std::ostream& operator<< (std::ostream& s, const LiebLin_Bethe_State& state)
{
s << endl << "******** State for c = " << state.c_int << " L = " << state.L << " N = " << state.N
<< " with label " << state.label << " ********" << endl;
s << endl << "******** State for c = " << state.c_int << " L = " << state.L
<< " N = " << state.N << " with label " << state.label << " ********" << endl;
s << "Ix2:" << endl;
for (int j = 0; j < state.N; ++j) s << state.Ix2[j] << " ";
s << endl << "lambdaocs:" << endl;
for (int j = 0; j < state.N; ++j) s << state.lambdaoc[j] << " ";
s << endl << "conv = " << state.conv << " iter_Newton = " << state.iter_Newton << endl;
s << "E = " << state.E << " iK = " << state.iK << " K = " << state.K << " lnnorm = " << state.lnnorm << endl;
s << "E = " << state.E << " iK = " << state.iK << " K = " << state.K
<< " lnnorm = " << state.lnnorm << endl;
return(s);
}

35
src/LIEBLIN/ln_Density_ME.cc
View File

@ -19,35 +19,51 @@ using namespace ABACUS;
namespace ABACUS {
/**
Given a index \f$j\f$ together with a bra and ket respectively parametrized
by sets of rapidities \f$\{ \mu \}\f$ and \f$\{ \lambda \}\f$,
this function returns the product (see e.g.
[J.-S. Caux et al, JSTAT P01008 (2007)](https://doi.org/10.1088/1742-5468/2007/01/P01008))
\f[
V_j^+ \equiv \prod_l
\frac{\tilde{\mu}_l - \tilde{\lambda}_j + i}{\tilde{\lambda}_l - \tilde{\lambda}_j + i}.
\f]
*/
complex<DP> Fn_V (int j, LiebLin_Bethe_State& lstate, LiebLin_Bethe_State& rstate)
{
complex<DP> result = 1.0;
for (int m = 0; m < lstate.N; ++m) {
result *= (lstate.lambdaoc[m] - rstate.lambdaoc[j] + II)/(rstate.lambdaoc[m] - rstate.lambdaoc[j] + II);
result *= (lstate.lambdaoc[m] - rstate.lambdaoc[j] + II)
/(rstate.lambdaoc[m] - rstate.lambdaoc[j] + II);
}
return(result);
}
/**
Computes the log of the density operator \f$\hat{\rho}(x = 0)\f$ matrix element
between lstate (bra) and rstate (ket). If lstate == rstate, density matrix element = N/L;
if momentum difference is zero but states are different, then matrix element is zero
(but this function then returns the log artificially set to -200.0).
*/
complex<DP> ln_Density_ME (LiebLin_Bethe_State& lstate, LiebLin_Bethe_State& rstate)
{
// Computes the log of the density operator \rho(x = 0) matrix element between lstate and rstate.
// If we have lstate == rstate, density matrix element = N/L:
if (lstate.Ix2 == rstate.Ix2) return(log(lstate.N/lstate.L));
// If momentum difference is zero but states are different, then matrix element is zero:
else if (lstate.iK == rstate.iK) return(-200.0); // so exp(.) is zero
SQMat_DP one_plus_U (0.0, lstate.N);
Vect_CX Vplus (0.0, lstate.N); // contains V^+_j; V^-_j is the conjugate
Vect_CX ln_Fn_Prod (0.0, lstate.N); // product_{m\neq j} (\mu_m - \lambdaoc_j)/(\lambdaoc_m - \lambdaoc_j)
// prod_{m\neq j} (\mu_m - \lambdaoc_j)/(\lambdaoc_m - \lambdaoc_j):
Vect_CX ln_Fn_Prod (0.0, lstate.N);
Vect_DP rKern (0.0, lstate.N); // K(lambdaoc_j - lambdaoc_(p == arbitrary))
// "Phantom" rapidity in ME expression. Choice doesn't matter, see 1990_Slavnov_TMP_82
// after (3.8). Choose rapidity around the middle.
//int p = 0;
int p = rstate.N/2-1; // choice doesn't matter, see 1990_Slavnov_TMP_82 after (3.8). Choose rapidity around the middle.
int p = rstate.N/2-1;
DP Kout = lstate.K - rstate.K;
@ -62,8 +78,9 @@ namespace ABACUS {
for (int a = 0; a < lstate.N; ++a)
for (int b = 0; b < lstate.N; ++b)
one_plus_U[a][b] = (a == b ? 1.0 : 0.0) + 0.5 * ((lstate.lambdaoc[a] - rstate.lambdaoc[a])/imag(Vplus[a]))
* real(exp(ln_Fn_Prod[a])) * (rstate.Kernel(a,b) - rKern[b]); // BUGRISK: why real here?
one_plus_U[a][b] = (a == b ? 1.0 : 0.0)
+ 0.5 * ((lstate.lambdaoc[a] - rstate.lambdaoc[a])/imag(Vplus[a]))
* real(exp(ln_Fn_Prod[a])) * (rstate.Kernel(a,b) - rKern[b]);
complex<DP> ln_ddalpha_sigma = lndet_LU_dstry(one_plus_U);

50
src/LIEBLIN/ln_Psi_ME.cc
View File

@ -19,62 +19,78 @@ using namespace ABACUS;
namespace ABACUS {
/**
Given a index \f$j\f$ together with a bra and ket respectively parametrized
by sets of rapidities \f$\{ \mu \}\f$ and \f$\{ \lambda \}\f$,
this function returns the product (see e.g.
[J.-S. Caux et al, JSTAT P01008 (2007)](https://doi.org/10.1088/1742-5468/2007/01/P01008))
\f[
V_j^+ \equiv \prod_l
\frac{\tilde{\mu}_l - \tilde{\lambda}_j + i}{\tilde{\lambda}_l - \tilde{\lambda}_j + i}.
\f]
*/
complex<DP> Fn_V_Psi (int j, LiebLin_Bethe_State& lstate, LiebLin_Bethe_State& rstate)
{
// lstate has one particle less than rstate
complex<DP> result_num = 1.0;
complex<DP> result_den = 1.0;
complex<DP> result = 1.0;
for (int m = 0; m < lstate.N; ++m)
result_num *= (lstate.lambdaoc[m] - rstate.lambdaoc[j] + II);
result *= (lstate.lambdaoc[m] - rstate.lambdaoc[j] + II)
/(rstate.lambdaoc[m] - rstate.lambdaoc[j] + II);
result /= (rstate.lambdaoc[rstate.N - 1] - rstate.lambdaoc[j] + II);
for (int m = 0; m < rstate.N; ++m)
result_den *= (rstate.lambdaoc[m] - rstate.lambdaoc[j] + II);
return(result_num/result_den);
return(result);
}
/**
Computes the log of the annihilation operator matrix element between lstate and rstate.
*/
complex<DP> ln_Psi_ME (LiebLin_Bethe_State& lstate, LiebLin_Bethe_State& rstate)
{
// Computes the log of the annihilation operator matrix element between lstate and rstate.
if (lstate.N + 1 != rstate.N) ABACUSerror("Wrong particle numbers in left and right states for Psi FF.");
if (lstate.N + 1 != rstate.N)
ABACUSerror("Wrong particle numbers in left and right states for Psi FF.");
SQMat_DP U_Psi (0.0, lstate.N);
Vect_CX Vplus (0.0, lstate.N); // contains V^+_j; V^-_j is the conjugate
Vect_DP Fn_Prod (0.0, lstate.N); // product_{m} (\mu_m - \lambdaoc_j)/product_{m neq j} (\lambdaoc_m - \lambdaoc_j)
// product_{m} (\mu_m - \lambdaoc_j)/product_{m neq j} (\lambdaoc_m - \lambdaoc_j)
Vect_DP Fn_Prod (0.0, lstate.N);
Vect_DP rKern (0.0, lstate.N); // K(lambdaoc_j - lambdaoc_(p == N))
int p = rstate.N - 1;
for (int a = 0; a < lstate.N; ++a) {
Vplus[a] = Fn_V_Psi (a, lstate, rstate);
Fn_Prod[a] = (lstate.lambdaoc[a] - rstate.lambdaoc[a])/(rstate.lambdaoc[rstate.N - 1] - rstate.lambdaoc[a]);
Fn_Prod[a] = (lstate.lambdaoc[a] - rstate.lambdaoc[a])
/(rstate.lambdaoc[rstate.N - 1] - rstate.lambdaoc[a]);
for (int m = 0; m < lstate.N; ++m)
if (m != a) Fn_Prod[a] *= (lstate.lambdaoc[m] - rstate.lambdaoc[a])/(rstate.lambdaoc[m] - rstate.lambdaoc[a]);
if (m != a) Fn_Prod[a] *= (lstate.lambdaoc[m] - rstate.lambdaoc[a])
/(rstate.lambdaoc[m] - rstate.lambdaoc[a]);
rKern[a] = rstate.Kernel (a, p);
}
for (int a = 0; a < lstate.N; ++a)
for (int b = 0; b < lstate.N; ++b)
U_Psi[a][b] = (a == b ? 2.0 * imag(Vplus[a]) : 0.0) + Fn_Prod[a] * (rstate.Kernel(a,b) - rKern[b]);
U_Psi[a][b] = (a == b ? 2.0 * imag(Vplus[a]) : 0.0)
+ Fn_Prod[a] * (rstate.Kernel(a,b) - rKern[b]);
complex<DP> ln_det_U_Psi = lndet_LU_dstry(U_Psi);
complex<DP> ln_prod_lambdaocsq_plus_one = 0.0;
for (int a = 0; a < rstate.N - 1; ++a)
for (int b = a; b < rstate.N; ++b)
ln_prod_lambdaocsq_plus_one += log(complex<DP>((rstate.lambdaoc[a] - rstate.lambdaoc[b])
* (rstate.lambdaoc[a] - rstate.lambdaoc[b])) + 1.0);
ln_prod_lambdaocsq_plus_one +=
log(complex<DP>((rstate.lambdaoc[a] - rstate.lambdaoc[b])
* (rstate.lambdaoc[a] - rstate.lambdaoc[b])) + 1.0);
complex<DP> ln_prod_lambdaoca_min_mub = 0.0;
for (int a = 0; a < rstate.N; ++a)
for (int b = 0; b < lstate.N; ++b)
ln_prod_lambdaoca_min_mub += log(complex<DP>(rstate.lambdaoc[a] - lstate.lambdaoc[b]));
return (ln_det_U_Psi + 0.5 * log(lstate.c_int) + ln_prod_lambdaocsq_plus_one - ln_prod_lambdaoca_min_mub
return (ln_det_U_Psi + 0.5 * log(lstate.c_int)
+ ln_prod_lambdaocsq_plus_one - ln_prod_lambdaoca_min_mub
- 0.5 * (lstate.lnnorm + rstate.lnnorm));
}