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

.gitignore

@@ -4,4 +4,6 @@
 
 *tar.gz
 
+*out
+
 TEST/*

ABACUS.org

@@ -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

ABACUS.org_archive

@@ -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?

ABACUS_Doxyfile

@@ -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

ABACUS_Usage_Example_Heis.cc

@@ -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);
+}

ABACUS_Usage_Example_LiebLin.cc

@@ -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);
+}

include/ABACUS_LiebLin.h

@@ -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);

src/LIEBLIN/LiebLin_Bethe_State.cc

@@ -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);
   }

src/LIEBLIN/ln_Density_ME.cc

@@ -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);
 

src/LIEBLIN/ln_Psi_ME.cc

@@ -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));
   }