VERSION 3.6 DEVELOPMENT JUNE 2020

.. update build id prior to tag.

[publish binaries]

.gitignore

@@ -13,6 +13,7 @@ Makefile
 *.prl
 *.swp
 *.user
+*.AppImage
 
 # osx noise
 .DS_Store
@@ -49,4 +50,6 @@ qwt/src/Makefile.Debug
 qwt/textengines/mathml/debug/
 qwt/textengines/mathml/release/
 build.pro.user
+build.pro.user.*
 doc/contrib/WASP Packet Protocol.pdf
+

.travis.yml

@@ -1,14 +1,19 @@
 branches:
-- master
-language:
-- objective-c
-compiler:
-- clang
-- gcc
+  only:
+  - master
+  - /^[vV]\d+\.\d+(\.\d+)?(-\S*)?$/
+
+language: cpp
+
+cache:
+  directories:
+  - $HOME/Library/Caches/Homebrew
+  - qwt
+  - D2XX
+
 env:
-  matrix:
-  - BRANCH=master QT=qt5 QT_PATH=qt5 WEBKIT=0
   global:
+  - BRANCH=master
   - secure: iqYW7f3//ZkMVzeCEarYn0S0DqKjFU9juBh0KF6WTlUsKX902Jtsk7dFoJlNDYBf63HLgV+wW2Hc6MxI9sGiUkom0gY9/To/aeGIJFGEX2sLm/e0Ok3qN521FA0Q/OiCFsD0RC6J+yrHxzI+rf8Z1rujceUsz2KgsrfAjYYv+BY=
   - secure: C6f58PXwvvHeVOjCLbyDRjgyF0tk+bXjCNUDur8VJLhJEGNdnrt+rH+d3azYaX0n348ZnQZ14as4M4rHjN1A/3DRbdUdOS7PQZrkj/n363ck1tvYOG/tzYqkEcVoQyjIJ7ZoTuBXDQry/VJmLxQjM0glTa2upNFHMOMwqZNkF+I=
   - secure: mgf181ok4rJTHxAdSaeIb/OzUx7PQc6UjJYfhJQcZDjN1Nou+Um6OHpnooMHeEq0CdGuLSiv2xVmuQnRjI5MfG5re/a3l39hSzi9tPLWi1y7uOLCtQFooJw3H+LhiKZcgAtEnkTmEhUCEu5uZ7cp4lWhrQZWCR5mCDNtJrGHjiw=
@@ -23,119 +28,31 @@ env:
   - secure: QXyyyutxesRVae/WFi75dxlNw2qTyWc6WQ3vmRER9BFhlrNtt8lmE+M6ghMDOhxigzSXWxHcG9r66BLOw4DML7AXg4f3NIAIYuYQrpfsWQ1TKGC/vVvIPDlNBKL62zSOoNowjup1HfZpB575wl4JkmHjoMPDfQ4yM/JVR+MKmIM=
   - secure: lefpL3SB8yN0Vn1R2e0hAFpJgFnu4rJ/vn7DucSKQvJ61K7t3LrUHFXElDQGFZMbytx4OJDeYsJtrccrIHjcsSAEIyW8TTcwn5/JopnyeQ3ukV5AYpEoQusym09XKru9E7awqvnZrXz6mdoIum5JP7+H116mPN4vsvz5nkNWxeg=
   - secure: RAGPq/thN9x6STNueDbeJWGUN75OLNcUVUkLHI/eZwPrkMaiQPfxIaJ+8eO2PszDcBojw3eYVhzbRvLnLiXmHL3buwD6oXMTyYnxGzCZ61DeDQ2cQa8ynKmRim5JL3viKMqtdyasXVoGf/u0GqMsgaLcqN6e/vXuXMGu6kkUPEQ=
-before_install:
-## try early just to check, can delete later
-- date
-- brew update
-- sh travis/install-qt.sh
-##- brew install $QT
-- brew install libical
-##- brew install libusb libusb-compat # no longer needed?
-- brew install srmio
-- brew install libsamplerate
-- rm -rf '/usr/local/include/c++'
-- brew install r
-- brew install brewsci/science/lmfit
-## Disable KML for now
-##- brew install --HEAD travis/libkml.rb
-- sudo chmod -R +w /usr/local
-- curl -O http://www.ftdichip.com/Drivers/D2XX/MacOSX/D2XX1.2.2.dmg
-- git clone --branch 0.98 https://github.com/kypeli/kQOAuth.git kQOAuth-0.98
-- cd kQOAuth-0.98
-- CC=clang CXX=clang++ /usr/local/opt/$QT_PATH/bin/qmake -makefile -recursive QMAKE_CXXFLAGS_WARN_ON+="-Wno-unused-private-field -Wno-c++11-narrowing"
-- CC=clang CXX=clang++ make -j2 qmake_all
-- CC=clang CXX=clang++ sudo make install
-- cd ..
-- hdiutil mount D2XX1.2.2.dmg
-before_script:
-- mkdir D2XX
-- cp /Volumes/release/D2XX/Object/10.5-10.7/x86_64/libftd2xx.1.2.2.dylib D2XX
-- sudo cp /Volumes/release/D2XX/Object/10.5-10.7/x86_64/libftd2xx.1.2.2.dylib /usr/local/lib
-- cp /Volumes/release/D2XX/bin/*.h D2XX
-- sed -i "" "s|libftd2xx.dylib|@executable_path/../Frameworks/libftd2xx.1.2.2.dylib|"
-  src/FileIO/D2XX.cpp
-- cp qwt/qwtconfig.pri.in qwt/qwtconfig.pri
-- cp src/gcconfig.pri.in src/gcconfig.pri
-- /usr/local/opt/$QT_PATH/bin/lupdate src/src.pro
-- if [[ "$WEBKIT" == "0" ]]; then echo DEFINES += NOWEBKIT >> src/gcconfig.pri; fi
-- sed -i "" "s|#\(CONFIG += release.*\)|\1 static |" src/gcconfig.pri
-- sed -i "" "s|#\(QMAKE_LRELEASE\).*|\1 += /usr/local/opt/$QT_PATH/bin/lrelease|"
-  src/gcconfig.pri
-- sed -i "" "s|#\(QMAKE_CXXFLAGS\).*|\1_RELEASE += -mmacosx-version-min=10.7 -arch
-  x86_64|" src/gcconfig.pri
-- sed -i "" "s|^#CloudDB|CloudDB|" src/gcconfig.pri
-- sed -i "" "s|^#LIBZ|LIBZ|" src/gcconfig.pri
-- sed -i "" "s|#\(SRMIO_INSTALL =.*\)|\1 /usr/local|" src/gcconfig.pri
-- sed -i "" "s|#\(D2XX_INCLUDE =.*\)|\1 ../D2XX|" src/gcconfig.pri
-- sed -i "" "s|#\(D2XX_LIBS    =.*\)|\1 -L../D2XX -lftd2xx.1.2.2|" src/gcconfig.pri
-- sed -i "" "s|#\(KQOAUTH_INSTALL =.*\)|\1 /usr/local|" src/gcconfig.pri
-- sed -i "" "s|#\(KQOAUTH_INCLUDE =.*\)|\1 \$\$[QT_INSTALL_LIBS]/kqoauth.framework/Headers|"
-  src/gcconfig.pri
-- sed -i "" "s|#\(KQOAUTH_LIBS =.*\)|\1 -F\$\$[QT_INSTALL_LIBS] -framework kqoauth|"
-  src/gcconfig.pri
-## Disable KML for now
-#- sed -i "" "s|#\(KML_INSTALL =\).*|\1 /usr/local|" src/gcconfig.pri
-#- sed -i "" "s|#\(KML_LIBS    =.*\)|\1 -L/usr/local/lib -lkmlxsd -lkmlregionator -lkmldom -lkmlconvenience -lkmlengine -lkmlbase -lexpect|" src/gcconfig.pri
-- sed -i "" "s|#\(ICAL_INSTALL =.*\)|\1 /usr/local|" src/gcconfig.pri
-- sed -i "" "s|#\(ICAL_LIBS    =.*\)|\1 -L/usr/local/lib -lical|" src/gcconfig.pri
-- sed -i "" "s|#\(LIBUSB_INSTALL =\).*|\1 /usr/local|" src/gcconfig.pri
-- sed -i "" "s|#\(LIBUSB_LIBS    =.*\)|\1 -L/usr/local/lib -lusb -lusb-1.0|" src/gcconfig.pri
-- sed -i "" "s|#\(SAMPLERATE_INSTALL =\).*|\1 /usr/local|" src/gcconfig.pri
-- sed -i "" "s|#\(SAMPLERATE_LIBS =\).*|\1 -L/usr/local/lib -lsamplerate|" src/gcconfig.pri
-- sed -i "" "s|#\(LMFIT_INSTALL =\).*|\1 /usr/local|" src/gcconfig.pri
-- sed -i "" "s|#\(DEFINES += GC_HAVE_LION*\)|\1|" src/gcconfig.pri
-- sed -i "" "s|#\(HTPATH = ../httpserver.*\)|\1 |" src/gcconfig.pri
-- sed -i "" "s|#\(DEFINES += GC_WANT_ROBOT.*\)|\1 |" src/gcconfig.pri
-##- sed -i "" "s|\(DEFINES += GC_VIDEO_NONE.*\)|#\1 |" src/gcconfig.pri ## we want this for now XXX till AVKit fixup
-##- sed -i "" "s|#\(DEFINES += GC_VIDEO_QUICKTIME.*\)|\1 |" src/gcconfig.pri ## QT is deprecated, don't build with it.
-##Issues with c++11 and stdlib on travis and dependencies
-- sed -i "" "s|#\(DEFINES += GC_WANT_R.*\)|\1 |" src/gcconfig.pri
-- echo "QMAKE_CFLAGS_RELEASE += -mmacosx-version-min=10.7 -arch x86_64" >> src/gcconfig.pri
-- sed -i "" "s/__GC_GOOGLE_CALENDAR_CLIENT_SECRET__/"$GC_GOOGLE_CALENDAR_CLIENT_SECRET"/" src/Core/Secrets.h
-- sed -i "" "s/__GC_STRAVA_CLIENT_SECRET__/"$GC_STRAVA_CLIENT_SECRET"/" src/Core/Secrets.h
-- sed -i "" "s/__GC_DROPBOX_CLIENT_SECRET__/"$GC_DROPBOX_CLIENT_SECRET"/" src/Core/Secrets.h
-- sed -i "" "s/__GC_CYCLINGANALYTICS_CLIENT_SECRET__/"$GC_CYCLINGANALYTICS_CLIENT_SECRET"/" src/Core/Secrets.h
-- sed -i "" "s/__GC_TWITTER_CONSUMER_SECRET__/"$GC_TWITTER_CONSUMER_SECRET"/" src/Core/Secrets.h
-- sed -i "" "s/__GC_DROPBOX_CLIENT_ID__/"$GC_DROPBOX_CLIENT_ID"/" src/Core/Secrets.h
-- sed -i "" "s/__GC_MAPQUESTAPI_KEY__/"$GC_MAPQUESTAPI_KEY"/" src/Core/Secrets.h
-- sed -i "" "s/__GC_CLOUD_DB_BASIC_AUTH__/"$GC_CLOUD_DB_BASIC_AUTH"/" src/Core/Secrets.h
-- sed -i "" "s/__GC_CLOUD_DB_APP_NAME__/"$GC_CLOUD_DB_APP_NAME"/" src/Core/Secrets.h
-- sed -i "" "s/__GC_GOOGLE_DRIVE_CLIENT_ID__/"$GC_GOOGLE_DRIVE_CLIENT_ID"/" src/Core/Secrets.h
-- sed -i "" "s/__GC_GOOGLE_DRIVE_CLIENT_SECRET__/"$GC_GOOGLE_DRIVE_CLIENT_SECRET"/" src/Core/Secrets.h
-- sed -i "" "s/__GC_GOOGLE_DRIVE_API_KEY__/"$GC_GOOGLE_DRIVE_API_KEY"/" src/Core/Secrets.h
-- sed -i "" "s/__GC_TODAYSPLAN_CLIENT_SECRET__/"$GC_TODAYSPLAN_CLIENT_SECRET"/" src/Core/Secrets.h
-- cat src/gcconfig.pri
-script:
-- CC=clang CXX=clang++ /usr/local/opt/$QT_PATH/bin/qmake -makefile -recursive QMAKE_CXXFLAGS_WARN_ON+="-Wno-unused-private-field -Wno-c++11-narrowing"
-- CC=clang CXX=clang++ make qmake_all
-- CC=clang CXX=clang++ make -j4 sub-qwt --silent
-- CC=clang CXX=clang++ make -j4 sub-src
-after_success:
-- cd src
-- echo "Checking GoldenCheetah.app can execute"
-- GoldenCheetah.app/Contents/MacOS/GoldenCheetah --help
-- echo "About to create dmg file and fix up"
-- /usr/local/opt/$QT_PATH/bin/macdeployqt GoldenCheetah.app -verbose=2 -dmg
-- python ../travis/macdeployqtfix.py GoldenCheetah.app /usr/local/opt/$QT_PATH
-- echo "Cleaning up installed QT libraries from $QT"
-- brew remove $QT
-- echo "Renaming dmg file to branch and build number ready for deploy"
-- export FINAL_NAME=dev-prerelease-branch-master-build-${TRAVIS_BUILD_NUMBER}.dmg
-- mv GoldenCheetah.dmg $FINAL_NAME
-- ls -l $FINAL_NAME
-- echo "Mounting dmg file and testing it can execute"
-- hdiutil mount $FINAL_NAME
-- cd /Volumes/GoldenCheetah
-- GoldenCheetah.app/Contents/MacOS/GoldenCheetah --help
-- echo "Make sure we are back in the Travis build directory"
-- cd $TRAVIS_BUILD_DIR
-deploy:
-  provider: releases
-  api_key:
-    secure: KlfkRM8oGP02y5LhbdxetnhqUG3YzVylvyhT8BTYjdoJtkJr7YXYpdhj9byZ9aiy1gSWI/g7A1X6/P8/McqRtgt4dEYr4Zg8QO7Y7QdTpgNQEwu8ZrkyyG/7b/rSkfFHDjrOAHslLVXuBNwWgi8YW1aTn0rY2AqDbOri7u6tt9Q=
-  file: src/$FINAL_NAME
-  skip_cleanup: true
-  on:
-    tags: true
-    repo: GoldenCheetah/GoldenCheetah
+  - secure: Lydms45scczE9gZvkWze2fXVbEInKW48DOCIRJWziEzxKkvXUE7WPy74fLvfvL+0JW0LH/ZLZ9EbgHcJAYYs8CBrfAeOOtnyo2DZ0ouEO13RmomSZneEKSpJxRtErcPIu+B0LzcEGyAgf7bxPVevEte50CK0pZJ7z7bHMhU23pY=
+  - secure: cc0pAJjkmFNw2bO3zVACmtyHTwINAHALrtUxi+nRD+FhOO9KxuxuuwvcKCZKfp9EUOjz5PrYWKV1ZH/zt/jMix8A4Gyue2mWX8WYih7aTmJBcJWsFNTCybnClreKBCh18kHdWWhkmhk8EMINDvlqxzJZGpcNO04gxhL9wuLLrNQ=
+  - secure: em0xXIm69rMHsHXYQiizeJB7dEFBkX33PsWDHwBNrX6lFBued23eL96KJC4RVbk6A+AHFtXFATrreZ14D5JH/E/37CXhe3X2R93WqiPUSH0s7NI4fFA1BroKUNAlqO4bMqDBidtNmwMPaLTXjaOnOZyvbAG7z+QV3TKC8tOeZDU=
+  - secure: VFaSERlgsjzjiDQhKw8XFvQrjdvFzHHL7V3NQg+RfELHoT6I1pAGFdl/+lRBIVOiVkbQ6XnpBA28nlf0QydPHElRZdqmh0azQV/bkUXD4ffPE8q0iSqeqhAZ+5L05K5K+Gby/y8TZE4FX6e/7trFL7oq+h9x0gq5RQO8rAcTV84=
 
+jobs:
+  include:
+  - os: osx
+    osx_image: xcode10.1
+    compiler: clang
+  - os: linux
+    dist: xenial
+    compiler: gcc
+
+before_install:
+- travis/$TRAVIS_OS_NAME/before_install.sh
+
+before_script:
+- travis/$TRAVIS_OS_NAME/before_script.sh
+
+script:
+- travis/$TRAVIS_OS_NAME/script.sh
+
+before_cache:
+- if [[ "$TRAVIS_OS_NAME" == "osx" ]]; then brew cleanup; fi
+
+after_success:
+- travis/$TRAVIS_OS_NAME/after_success.sh

CONTRIBUTING.md

@@ -2,7 +2,7 @@
 
 #### **Do you have questions about how to use GoldenCheetah?**
 
-* Ask any question about how to use GoldenCheetah on [golden-cheetah-users mailing list](https://github.com/GoldenCheetah/GoldenCheetah/wiki), ideally after watching the corresponding [tutorials](http://www.goldencheetah.org/#section-tutorials) and/or reading the relevant parts of the [documentation](https://github.com/GoldenCheetah/GoldenCheetah/wiki).
+* Ask any question about how to use GoldenCheetah on [golden-cheetah-users mailing list](https://groups.google.com/forum/#!forum/golden-cheetah-users), ideally after watching the corresponding [tutorials](https://www.goldencheetah.org/#section-tutorials) and/or reading the relevant parts of the [documentation](https://github.com/GoldenCheetah/GoldenCheetah/wiki).
 
 #### **Do you have questions about the source code?**
 

COPYING

@@ -1,622 +1,281 @@
                     GNU GENERAL PUBLIC LICENSE
-                       Version 3, 29 June 2007
+                       Version 2, June 1991
 
- Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
+ Copyright (C) 1989, 1991 Free Software Foundation, Inc.,
+ 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
  Everyone is permitted to copy and distribute verbatim copies
  of this license document, but changing it is not allowed.
 
                             Preamble
 
-  The GNU General Public License is a free, copyleft license for
-software and other kinds of works.
-
-  The licenses for most software and other practical works are designed
-to take away your freedom to share and change the works.  By contrast,
-the GNU General Public License is intended to guarantee your freedom to
-share and change all versions of a program--to make sure it remains free
-software for all its users.  We, the Free Software Foundation, use the
-GNU General Public License for most of our software; it applies also to
-any other work released this way by its authors.  You can apply it to
+  The licenses for most software are designed to take away your
+freedom to share and change it.  By contrast, the GNU General Public
+License is intended to guarantee your freedom to share and change free
+software--to make sure the software is free for all its users.  This
+General Public License applies to most of the Free Software
+Foundation's software and to any other program whose authors commit to
+using it.  (Some other Free Software Foundation software is covered by
+the GNU Lesser General Public License instead.)  You can apply it to
 your programs, too.
 
   When we speak of free software, we are referring to freedom, not
 price.  Our General Public Licenses are designed to make sure that you
 have the freedom to distribute copies of free software (and charge for
-them if you wish), that you receive source code or can get it if you
-want it, that you can change the software or use pieces of it in new
-free programs, and that you know you can do these things.
+this service if you wish), that you receive source code or can get it
+if you want it, that you can change the software or use pieces of it
+in new free programs; and that you know you can do these things.
 
-  To protect your rights, we need to prevent others from denying you
-these rights or asking you to surrender the rights.  Therefore, you have
-certain responsibilities if you distribute copies of the software, or if
-you modify it: responsibilities to respect the freedom of others.
+  To protect your rights, we need to make restrictions that forbid
+anyone to deny you these rights or to ask you to surrender the rights.
+These restrictions translate to certain responsibilities for you if you
+distribute copies of the software, or if you modify it.
 
   For example, if you distribute copies of such a program, whether
-gratis or for a fee, you must pass on to the recipients the same
-freedoms that you received.  You must make sure that they, too, receive
-or can get the source code.  And you must show them these terms so they
-know their rights.
+gratis or for a fee, you must give the recipients all the rights that
+you have.  You must make sure that they, too, receive or can get the
+source code.  And you must show them these terms so they know their
+rights.
 
-  Developers that use the GNU GPL protect your rights with two steps:
-(1) assert copyright on the software, and (2) offer you this License
-giving you legal permission to copy, distribute and/or modify it.
+  We protect your rights with two steps: (1) copyright the software, and
+(2) offer you this license which gives you legal permission to copy,
+distribute and/or modify the software.
 
-  For the developers' and authors' protection, the GPL clearly explains
-that there is no warranty for this free software.  For both users' and
-authors' sake, the GPL requires that modified versions be marked as
-changed, so that their problems will not be attributed erroneously to
-authors of previous versions.
+  Also, for each author's protection and ours, we want to make certain
+that everyone understands that there is no warranty for this free
+software.  If the software is modified by someone else and passed on, we
+want its recipients to know that what they have is not the original, so
+that any problems introduced by others will not reflect on the original
+authors' reputations.
 
-  Some devices are designed to deny users access to install or run
-modified versions of the software inside them, although the manufacturer
-can do so.  This is fundamentally incompatible with the aim of
-protecting users' freedom to change the software.  The systematic
-pattern of such abuse occurs in the area of products for individuals to
-use, which is precisely where it is most unacceptable.  Therefore, we
-have designed this version of the GPL to prohibit the practice for those
-products.  If such problems arise substantially in other domains, we
-stand ready to extend this provision to those domains in future versions
-of the GPL, as needed to protect the freedom of users.
-
-  Finally, every program is threatened constantly by software patents.
-States should not allow patents to restrict development and use of
-software on general-purpose computers, but in those that do, we wish to
-avoid the special danger that patents applied to a free program could
-make it effectively proprietary.  To prevent this, the GPL assures that
-patents cannot be used to render the program non-free.
+  Finally, any free program is threatened constantly by software
+patents.  We wish to avoid the danger that redistributors of a free
+program will individually obtain patent licenses, in effect making the
+program proprietary.  To prevent this, we have made it clear that any
+patent must be licensed for everyone's free use or not licensed at all.
 
   The precise terms and conditions for copying, distribution and
 modification follow.
 
-                       TERMS AND CONDITIONS
-
-  0. Definitions.
-
-  "This License" refers to version 3 of the GNU General Public License.
-
-  "Copyright" also means copyright-like laws that apply to other kinds of
-works, such as semiconductor masks.
-
-  "The Program" refers to any copyrightable work licensed under this
-License.  Each licensee is addressed as "you".  "Licensees" and
-"recipients" may be individuals or organizations.
-
-  To "modify" a work means to copy from or adapt all or part of the work
-in a fashion requiring copyright permission, other than the making of an
-exact copy.  The resulting work is called a "modified version" of the
-earlier work or a work "based on" the earlier work.
-
-  A "covered work" means either the unmodified Program or a work based
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-  To "propagate" a work means to do anything with it that, without
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-  An interactive user interface displays "Appropriate Legal Notices"
-to the extent that it includes a convenient and prominently visible
-feature that (1) displays an appropriate copyright notice, and (2)
-tells the user that there is no warranty for the work (except to the
-extent that warranties are provided), that licensees may convey the
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-  1. Source Code.
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-packaging a Major Component, but which is not part of that Major
-Component, and (b) serves only to enable use of the work with that
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-Source.
-
-  The Corresponding Source for a work in source code form is that
-same work.
-
-  2. Basic Permissions.
-
-  All rights granted under this License are granted for the term of
-copyright on the Program, and are irrevocable provided the stated
-conditions are met.  This License explicitly affirms your unlimited
-permission to run the unmodified Program.  The output from running a
-covered work is covered by this License only if the output, given its
-content, constitutes a covered work.  This License acknowledges your
-rights of fair use or other equivalent, as provided by copyright law.
-
-  You may make, run and propagate covered works that you do not
-convey, without conditions so long as your license otherwise remains
-in force.  You may convey covered works to others for the sole purpose
-of having them make modifications exclusively for you, or provide you
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-for you must do so exclusively on your behalf, under your direction
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+make exceptions for this.  Our decision will be guided by the two goals
+of preserving the free status of all derivatives of our free software and
+of promoting the sharing and reuse of software generally.
 
-  Later license versions may give you additional or different
-permissions.  However, no additional obligations are imposed on any
-author or copyright holder as a result of your choosing to follow a
-later version.
+                            NO WARRANTY
 
-  15. Disclaimer of Warranty.
+  11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY
+FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW.  EXCEPT WHEN
+OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES
+PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED
+OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.  THE ENTIRE RISK AS
+TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU.  SHOULD THE
+PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING,
+REPAIR OR CORRECTION.
 
-  THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
-APPLICABLE LAW.  EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
-HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
-OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
-THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
-PURPOSE.  THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM
-IS WITH YOU.  SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
-ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
-
-  16. Limitation of Liability.
-
-  IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
-WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
-THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
-GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
-USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
-DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
-PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
-EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
-SUCH DAMAGES.
-
-  17. Interpretation of Sections 15 and 16.
-
-  If the disclaimer of warranty and limitation of liability provided
-above cannot be given local legal effect according to their terms,
-reviewing courts shall apply local law that most closely approximates
-an absolute waiver of all civil liability in connection with the
-Program, unless a warranty or assumption of liability accompanies a
-copy of the Program in return for a fee.
+  12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
+WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR
+REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES,
+INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING
+OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED
+TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY
+YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER
+PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE
+POSSIBILITY OF SUCH DAMAGES.
 
                      END OF TERMS AND CONDITIONS
 
@@ -628,15 +287,15 @@ free software which everyone can redistribute and change under these terms.
 
   To do so, attach the following notices to the program.  It is safest
 to attach them to the start of each source file to most effectively
-state the exclusion of warranty; and each file should have at least
+convey the exclusion of warranty; and each file should have at least
 the "copyright" line and a pointer to where the full notice is found.
 
     <one line to give the program's name and a brief idea of what it does.>
     Copyright (C) <year>  <name of author>
 
-    This program is free software: you can redistribute it and/or modify
+    This program is free software; you can redistribute it and/or modify
     it under the terms of the GNU General Public License as published by
-    the Free Software Foundation, either version 3 of the License, or
+    the Free Software Foundation; either version 2 of the License, or
     (at your option) any later version.
 
     This program is distributed in the hope that it will be useful,
@@ -644,32 +303,38 @@ the "copyright" line and a pointer to where the full notice is found.
     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
     GNU General Public License for more details.
 
-    You should have received a copy of the GNU General Public License
-    along with this program.  If not, see <http://www.gnu.org/licenses/>.
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
 
 Also add information on how to contact you by electronic and paper mail.
 
-  If the program does terminal interaction, make it output a short
-notice like this when it starts in an interactive mode:
+If the program is interactive, make it output a short notice like this
+when it starts in an interactive mode:
 
-    <program>  Copyright (C) <year>  <name of author>
-    This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+    Gnomovision version 69, Copyright (C) year name of author
+    Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
     This is free software, and you are welcome to redistribute it
     under certain conditions; type `show c' for details.
 
 The hypothetical commands `show w' and `show c' should show the appropriate
-parts of the General Public License.  Of course, your program's commands
-might be different; for a GUI interface, you would use an "about box".
+parts of the General Public License.  Of course, the commands you use may
+be called something other than `show w' and `show c'; they could even be
+mouse-clicks or menu items--whatever suits your program.
 
-  You should also get your employer (if you work as a programmer) or school,
-if any, to sign a "copyright disclaimer" for the program, if necessary.
-For more information on this, and how to apply and follow the GNU GPL, see
-<http://www.gnu.org/licenses/>.
+You should also get your employer (if you work as a programmer) or your
+school, if any, to sign a "copyright disclaimer" for the program, if
+necessary.  Here is a sample; alter the names:
 
-  The GNU General Public License does not permit incorporating your program
-into proprietary programs.  If your program is a subroutine library, you
-may consider it more useful to permit linking proprietary applications with
-the library.  If this is what you want to do, use the GNU Lesser General
-Public License instead of this License.  But first, please read
-<http://www.gnu.org/philosophy/why-not-lgpl.html>.
+  Yoyodyne, Inc., hereby disclaims all copyright interest in the program
+  `Gnomovision' (which makes passes at compilers) written by James Hacker.
+
+  <signature of Ty Coon>, 1 April 1989
+  Ty Coon, President of Vice
+
+This General Public License does not permit incorporating your program into
+proprietary programs.  If your program is a subroutine library, you may
+consider it more useful to permit linking proprietary applications with the
+library.  If this is what you want to do, use the GNU Lesser General
+Public License instead of this License.
 

INSTALL-LINUX

@@ -1,3 +1,12 @@
+Update Note: to build GoldenCheetah v3.6 we are using the APT Package
+Manager to install dependencies, including Qt and GSL, on Travis-ci
+Ubuntu Xenial build environment.
+You can check the travis/linux folder for the complete and updated build scripts,
+the minimum Qt version known to work is 5.13 with Qt WebEngine and Qt Charts.
+GSL - GNU Scientific Library is a mandatory dependency starting with v3.6
+
+Ale Martinez - May, 2020
+
                                  +++++++++++++++++++++++
                                  LINUX BUILD WALKTHROUGH
                                  +++++++++++++++++++++++
@@ -21,7 +30,6 @@ CONTENTS
    - FTDI D2XX
    - SRMIO
    - liboauth
-   - QwtPlot3d
    - libkml
 
 3. ADDING OPTIONAL DEPENDENCIES WHEN BUILDING VERSION 3
@@ -43,7 +51,7 @@ login and open a terminal to get a shell prompt
 Download MANDATORY DEPENDENCIES (browser)
 -----------------------------------------
 Download and install the Qt SDK from http://qt-project.org/
-Once that is completed test qmake is ok with: qmake --version (should report 4.7.0 or higher)
+Once that is completed test qmake is ok with: qmake --version (should report 4.9.8 or higher)
 
 
 DEBIAN-BASED DISTRIBUTION INSTRUCTIONS
@@ -92,6 +100,20 @@ $ make clean
 $ qmake
 $ make
 
+To compile translation you need QT tool - lrelease
+If it is not found using he defaults in src/src.pro then set the full path and filename in gcconfig.pri
+QMAKE_LRELEASE = /usr/bin/lrelease
+
+When build first time you get number of error messages on .qm files missing:
+    "RCC: Error in 'Resources/application.qrc': Cannot find file 'translations/gc_fr.qm'"
+You can ignore these messages for your build. The .qm files will be created during the
+build at a later point in time via the "lrelease" command you configured in gcconfig.pri)
+
+If your QT build includes its own local compress libs then you should comment the line below in gcconfig.pri,
+otherwise you will need to have the compress libraries installed separately. 
+#LIBZ_INCLUDE =
+#LIBZ_LIBS    = -lz
+
 You will now have a release3 binary but with none of the release3 dependencies compiled in.
 Get latest GOLDEN CHEETAH source files
 --------------------------------------
@@ -193,96 +215,6 @@ $ make
 
 You now have SRM support built in.
 
-OAUTH/CRYPT - For Tweet my ride (twitter) support
--------------------------------------------------
-
-You should be able to install liboauth and dependencies
-directly with:
-$ sudo apt-get install liboauth-dev
-
-If this does not work then:
-
-    Download the source from: http://sourceforge.net/projects/liboauth/files/liboauth-0.9.4.tar.gz/download and
-    unpack it into ~/Projects/liboauth-0.9.4 using archive manager
-
-    $ cd ~/Projects/liboauth-0.9.4
-
-    You may find that libcurl is not installed (which liboauth depends upon) so download it
-    from http://curl.haxx.se/download/curl-7.21.6.tar.gz and unpack it into ~/Projects/curl-7.21.6
-    using archive manager to drag and drop into your Projects folder
-
-    $ cd ~/Projects/curl-7.21.6
-    $ ./configure
-    $ make
-    $ sudo make install
-
-    You should now have libcurl and friends installed in /usr/local
-
-    You may find that liboauth also requires the openssl libs installed, these are available
-    pre-packaged thankfully so:
-    $ sudo apt-get install libssl-dev
-
-    This will also install zlibg which liboauth also desires.
-
-    $ cd ~/Projects/liboauth-0.9.4
-    $ ./configure
-    $ make
-    $ sudo make install
-
-Now we have liboauth and libcurl in /usr/local and libssl in /usr/lib, so we can go back to
-GoldenCheetah and update the gcconfig.pri to point at the right places:
-
-$ cd ~/Projects/Live/GoldenCheetah/src
-$ vi gcconfig.pri
-
-Make sure the following are set:
-LIBOAUTH_INSTALL = /usr/local
-LIBCRYPTO_INSTALL = -lcrypto
-LIBCURL_INSTALL=-lcurl
-
-Make clean is needed if you have previously built, since source files examine #defines before
-including this feature. You can skip it if you know why ;)
-$ make clean
-$ qmake
-$ make
-
-You can now tweet your rides and amaze your friends, or alternatively tweet your rides but
-omit to mention average power to hide your weaknesses.
-
-LIBQWTPLOT3D - For 3D plot
---------------------------
-
-Download the tarball from http://qwtplot3d.svn.sourceforge.net/viewvc/qwtplot3d/branches/maintain_0_2_x/qwtplot3d/?view=tar
-and unarchive it into your Projects directory using archive manager. There is no version number it just creates a
-subdirectory called qwtplot3d
-
-You will need to install libgl and extensions, this can be done with;
-$ sudo apt-get install libgl1-mesa-dev
-$ sudo apt-get install libglu-dev
-
-On Ubuntu 12.10 I also ran
-$ sudo apt-get install freeglut3 freeglut3-dev
-
-$ cd ~/Projects/qwtplot3d
-Edit the qwtplot3d.pri and add
-CONFIG += staticlib
-
-You will find that on modern Linuxes you also need to fix include/qwt3d_global.h by adding the line:
-#include <GL/glu.h>
-
-then build
-$ qmake
-$ make
-
-Then to let gc know where the qwtplot3d libs are you need to edit gcconfig.pri;
-$ cd ~/Projects/Live/GoldenCheetah/src
-$ vi gcconfig.pri
-
-And uncomment the following line and set the install directory to where you build
-QWT3D_INSTALL = ~/Projects/qwtplot3d
-
-
-
 LIBKML - For export to Google Earth
 -----------------------------------
 

INSTALL-MAC

@@ -1,3 +1,12 @@
+Update Note: to build GoldenCheetah v3.6 we are using the Homebrew Package
+Manager to install dependencies, including Qt and GSL, on Travis-ci
+macOS High Sierra build environment.
+You can check the travis/osx folder for the complete and updated build scripts,
+the minimum Qt version known to work is 5.13 with Qt WebEngine and Qt Charts.
+GSL - GNU Scientific Library is a mandatory dependency starting with v3.6
+
+Ale Martinez - May, 2020
+
                                  +++++++++++++++++++++++
                                 MAC OSX BUILD WALKTHROUGH
                                  +++++++++++++++++++++++
@@ -20,8 +29,6 @@ CONTENTS
 2. ADDING OPTIONAL DEPENDENCIES
    - FTDI D2XX
    - SRMIO
-   - kQOAuth
-   - QwtPlot3d
    - libkml
    - libusb
    - libical
@@ -210,6 +217,11 @@ $ cd .. #this should put you in the top level dir containing this file
 $ qmake -recursive
 $ make
 
+When build first time you get number of error messages on .qm files missing:
+    "RCC: Error in 'Resources/application.qrc': Cannot find file 'translations/gc_fr.qm'"
+You can ignore these messages for your build. The .qm files will be created during the
+build at a later point in time via the "lrelease" command you configured in gcconfig.pri)
+
 If make fails to find a Makefile then qmake is configured, by default, to create
 an xcode project file. You will need to change the qmake command above to tell it
 to create a makefile with the following:
@@ -238,8 +250,6 @@ $ open src/GoldenCheetah.app
 ===============================
 
    - SRMIO
-   - kQOAuth
-   - QwtPlot3d
    - libkml
    - libusb
    - libical
@@ -255,24 +265,7 @@ should be taken into account.
 SRMIO (git)
 ./configure CFLAGS="-isysroot /Developer/SDKs/MacOSX10.7.sdk -arch x86_64" CPPFLAGS=-I/usr/local/D2XX/ --disable-dependency-tracking
 
-2.2 kQOAuth - For OAuth Authentication
---------------------------------------
-
-kQOauth (0.98)
-
-qmake
-
-
-2.3 QwtPlot3d - For 3d plot support
------------------------------------
-
-qwtplot3d (maintain_0_2_x)
-
-Add the following to qwtplot3d.pro:
-CONFIG += x86_64 static
-QMAKE_MAC_SDK=/Developer/SDKs/MacOSX10.7.sdk
-
-2.4 libkml - For export to Google Earth
+2.2 libkml - For export to Google Earth
 ---------------------------------------
 
 expat (2.0.1)
@@ -284,7 +277,7 @@ libkml (pulled down from the svn repo)
 
 note: the added CXXFLAGS helped clear the -Werror flag that stopped compilation.
 
-2.5 libusb - For Garmin USB2 stick support
+2.3 libusb - For Garmin USB2 stick support
 ------------------------------------------
 
 libusb (0.1.12)
@@ -301,7 +294,7 @@ make install
 
 note: that the sed line updates some commands in libtool.  not sure why the arch clags are not getting passed.  
 
-2.6 libical
+2.4 libical
 -----------
 
 libical (0.46)

INSTALL-WIN32

@@ -1,4 +1,11 @@
+Update Note: to build GoldenCheetah v3.6 we are using Microsoft Visual C++ 2017,
+included in Microsoft Visual Studio 2019, with pre-installed Qt and GSL
+insalled with vcpkg, on AppVeyor continuous integration platform.
+You can check the appveyor.yml for the complete and updated build script,
+the minimum Qt version known to work is 5.13 with Qt WebEngine and Qt Charts.
+GSL - GNU Scientific Library is a mandatory dependency starting with v3.6
 
+Ale Martinez - May, 2020
                                  +++++++++++++++++++++++
                                  WIN32 BUILD WALKTHROUGH
                                  +++++++++++++++++++++++
@@ -7,6 +14,7 @@
 
                                        February 2017
 
+
 This instruction will guide  you through a standard build of GoldenCheetah (without external
 dependencies or API based services included).
 
@@ -157,12 +165,6 @@ Info: I plan to provide a pre-compiled set of the dependencies for the Windows v
      The version currently used is: "CDM v2.10.00 WHQL Certified" - while there are more recent
 	 version available for download.
 	 
-- Qt Oauth library - kQoAuth
-  -- Is part of the official build as a .dll - build is done with Qt - the build uses Release 0.98
-  
-- Qt 3D plotting - qwtplot3d
-  -- Is part of the official build as a static lib - build is done with Qt - the build uses Release 0.3.0
-  
 - Google Earth .kml files (export)
   -- Is part of the official build as a static lib - build is done with MSVC2015 - the build uses Release 1.2
      (path of source code has changed to https://github.com/google/libkml)
@@ -185,7 +187,7 @@ Info: I plan to provide a pre-compiled set of the dependencies for the Windows v
 
 Building with integration to external services (via APIs)
 
-As of today a number of integrations with external services like Twitter, Strava, Cyclinganalytics, 
+As of today a number of integrations with external services like Strava, Cyclinganalytics,
 Google Calendar, Dropbox, Today's Plan, Google Drive, CloudDB) exist in the official GoldenCheetah
 builds. The permission to use API's of such services requires a dedicated registration (in this case
 for "GoldenCheetah" as the consumer of the services) where in return the GoldenCheetah team get's 
@@ -205,10 +207,3 @@ to contribute is to provide a pull-request.
 
 Cheers.
 Joern
- 
-
-
-
-
-
-  

ISSUE_TEMPLATE.md

@@ -0,0 +1 @@
+Issue tracker is **only** for Bugs and Features, before to open a new issue please read the contributing guidelines (link below), and use the forums if you need help or technical support.

README.md

@@ -29,7 +29,7 @@ INSTALL-LINUX   For building on Linux
 INSTALL-MAC     For building on Apple OS X
 
 
-OSX: [![Build Status](https://travis-ci.org/GoldenCheetah/GoldenCheetah.svg?branch=master)](https://travis-ci.org/GoldenCheetah/GoldenCheetah)
+macOS and Linux: [![Build Status](https://travis-ci.org/GoldenCheetah/GoldenCheetah.svg?branch=master)](https://travis-ci.org/GoldenCheetah/GoldenCheetah)
 
 Windows: [![Build status](https://ci.appveyor.com/api/projects/status/i6dwn4m8oyu52ihi?svg=true)](https://ci.appveyor.com/project/Joern-R/goldencheetah-knhd8)
 

appveyor.yml

@@ -1,32 +1,213 @@
 version: ci.{build}
-image: Visual Studio 2015
+image: Visual Studio 2019
 clone_depth: 1
+
+environment:
+  GC_GOOGLE_CALENDAR_CLIENT_SECRET:
+    secure: hwjHTrSAMEbKd9PA+5x/zI4x5Uk4KQm1hdfZzkwiu8k=
+  GC_GOOGLE_DRIVE_CLIENT_ID:
+    secure: mNqG+pqpMl21ZFVvAMKvhm2rfOdv42fFpnLwfrvX5QqpWVcHEeBuUFeJeUAZfTR0GQGfWfPOEmhb9CG0W1ZJ05TIyb+kTLrWF7iijCiVR6s=
+  GC_GOOGLE_DRIVE_CLIENT_SECRET:
+    secure: T+BaB/L7x4dPPf592e0kfw4sTlAslUXl10irJqiUjpY=
+  GC_GOOGLE_DRIVE_API_KEY:
+    secure: oxTAhK/kiLUsXdYvITAgzSqeB5FRcL+XANFuAYpoW5P/xBb7XaLbNnL2gyrmzQeG
+  GC_CLOUD_OPENDATA_SECRET:
+    secure: 6fPhBiHKvJeOMqXdHGqpkPS+NpUDMczEXjedx8GcjbHr82ISX+gwSuXfOUDLq/S9
+  GC_WITHINGS_CONSUMER_SECRET:
+    secure: 86xAkdoQB8mLXq964/lGCp3ElTSF4k3a27R3UUXt3618guWLyBfsEK5Q0+XSOI3Q38w80CTpmNdwejoISv8Ilg==
+  GC_NOKIA_CLIENT_SECRET:
+    secure: pvPWraDplrKeRNamt5MKga8fzDmI2+zgFx+y3lsQE6gmBadZU2xkTIc/xCaP7UPv2erNCmKivfMOh2NIcRmqvIHynDoifNVy2P61KyG5v3E=
+  GC_DROPBOX_CLIENT_SECRET:
+    secure: 7pCVnVEKKmSU4SZN6IFqUw==
+  GC_STRAVA_CLIENT_SECRET:
+    secure: n3cMS1yy709xhSnTeWABMsoAIkJzy5euh3Pw4ehv0BzszJKoWkypF0cyW8RXSm3M
+  GC_TODAYSPLAN_CLIENT_SECRET:
+    secure: 7PnFB8cfahFT6LyP64eB7N1vkbwVaULpB2ORmEkn+J75zNB1xxGClFNXSHZ7kXhB
+  GC_CYCLINGANALYTICS_CLIENT_SECRET:
+    secure: UY+m3YypNNLUzKyGdrLw8xdCvxuQWRZi9EHS3j1ubLC4qyRL7iEVW6ubumfdh6gT
+  GC_CLOUD_DB_BASIC_AUTH:
+    secure: OEBetrOnXjsY7wN8hYqmMj6482oDORmAmCq8PI7mfnfiWE6Z4jB676JvgdNlP98q
+  GC_CLOUD_DB_APP_NAME:
+    secure: bpkyuw/BsJw0OrpuBqQwZ46CHbhkbmcjcMttVtfJoZU=
+  GC_POLARFLOW_CLIENT_SECRET:
+    secure: h2JdlC1i4QOmwpkz+Xxbrw==
+  GC_SPORTTRACKS_CLIENT_SECRET:
+    secure: n6a8nJgqMyg+VsVeoIIR8TFzxyDFVi2w/ggetQk5agY=
+
 init:
-# Setup QT 5.9.4 - 64Bit
-
-- set QTDIR=C:\Qt\5.9.4\msvc2015_64
+# Setup QT 5.14 - 64Bit
+- set QTDIR=C:\Qt\5.14\msvc2017_64
 - set PATH=%QTDIR%\bin;%PATH%
+- qmake --version
 
-# Setup MSVC - VS 2015
+# Setup MSVC - VS 2019
+- call c:\"Program Files (x86)"\"Microsoft Visual Studio"\2019\Community\VC\Auxiliary\Build\vcvarsall.bat amd64
 
-- CALL "C:\Program Files (x86)\Microsoft Visual Studio 14.0\VC\vcvarsall.bat" amd64
+# Setup NSIS
+- set PATH=%PATH%;C:\"Program Files (x86)"\NSIS
 
-# Get the libraries
-
-- ps: Start-FileDownload 'https://github.com/Joern-R/gc-ci-libs/releases/download/0.0.2/gc-ci-libs.zip' -Filename 'c:/gc-ci-libs.zip'
-- 7z x c:/gc-ci-libs.zip -oC:\libs
+cache:
+- gc-ci-libs.zip
+- jom_1_1_3.zip
+- sip-4.19.8.zip
+- C:\R
+- C:\Python -> src\Python\requirements.txt
+- c:\tools\vcpkg\installed\
+- qwt
 
 install:
-# choco install winflexbison
+# Get the libraries
+- if not exist gc-ci-libs.zip appveyor DownloadFile "https://github.com/GoldenCheetah/WindowsSDK/releases/download/v0.1.1/gc-ci-libs.zip"
+- 7z x -y gc-ci-libs.zip -oC:\libs
+# GSL
+- vcpkg install gsl:x64-windows
+
+# Get config
 - copy qwt\qwtconfig.pri.in qwt\qwtconfig.pri
 - copy c:\libs\gcconfig64-Release.appveyor.pri src\gcconfig.pri
 
+# Get jom
+- if not exist jom_1_1_3.zip appveyor DownloadFile "https://download.qt.io/official_releases/jom/jom_1_1_3.zip"
+- 7z x -y jom_1_1_3.zip -oc:\jom\
+- set PATH=%PATH%;c:\jom\;
+
+# Get R and add to config
+- ps: >-
+    if (-not (Test-Path 'C:\R')) {
+      $rurl = $(ConvertFrom-JSON $(Invoke-WebRequest https://rversions.r-pkg.org/r-release-win).Content).URL
+      Start-FileDownload $rurl "R-win.exe"
+      Start-Process -FilePath .\R-win.exe -ArgumentList "/VERYSILENT /DIR=C:\R" -NoNewWindow -Wait
+    }
+- set PATH=%PATH%;c:\R\bin\;
+- R --version
+- echo DEFINES+=GC_WANT_R >> src\gcconfig.pri
+
+# Get Python embeddable and install packages
+- ps: >-
+    if (-not (Test-Path 'C:\Python')) {
+      Start-FileDownload "https://www.python.org/ftp/python/3.7.7/python-3.7.7-embed-amd64.zip" Python.zip
+      7z x Python.zip -oC:\Python\
+      echo python37.zip . '' 'import site' | Out-File C:\Python\python37._pth -Encoding ascii
+      mkdir C:\Python\lib\site-packages
+      c:\python37-x64\python -m pip install --upgrade pip
+      c:\python37-x64\python -m pip install -r src\Python\requirements.txt -t C:\Python\lib\site-packages
+    }
+
+# Get SIP and and install on Python
+- c:\python37-x64\python --version
+- if not exist sip-4.19.8.zip appveyor DownloadFile "https://sourceforge.net/projects/pyqt/files/sip/sip-4.19.8/sip-4.19.8.zip"
+- 7z x sip-4.19.8.zip
+- cd sip-4.19.8
+- c:\python37-x64\python configure.py
+- jom -j4
+- nmake install
+- cd ..
+
+# Add Python (avoiding colision between GC Context.h and Python context.h)
+- echo DEFINES+=GC_WANT_PYTHON >> src\gcconfig.pri
+- echo PYTHONINCLUDES=-ICore -I\"c:\python37-x64\include\" >> src\gcconfig.pri
+- echo PYTHONLIBS=-L\"c:\python37-x64\libs\" -lpython37 >> src\gcconfig.pri
+
+# GSL
+- echo GSL_INCLUDES=c:\tools\vcpkg\installed\x64-windows\include >> src\gcconfig.pri
+- echo GSL_LIBS=-Lc:\tools\vcpkg\installed\x64-windows\lib -lgsl -lgslcblas >> src\gcconfig.pri
+
+before_build:
+# Define GC version string, only for tagged builds
+- if %APPVEYOR_REPO_TAG% == "true" (echo DEFINES+=GC_VERSION=VERSION_STRING >> src/gcconfig.pri)
+
+# Enable CloudDB
+- echo CloudDB=active >> src\gcconfig.pri
+
+# Add Train Robot
+- echo DEFINES+=GC_WANT_ROBOT >> src\gcconfig.pri
+
+# Add debug console
+#- echo CONFIG+=console >> src\gcconfig.pri
+
+# Patch Secrets.h
+- ps: (Get-Content src\Core\Secrets.h) -replace '__GC_GOOGLE_CALENDAR_CLIENT_SECRET__', $env:GC_GOOGLE_CALENDAR_CLIENT_SECRET | Set-Content src\Core\Secrets.h
+- ps: (Get-Content src\Core\Secrets.h) -replace '__GC_GOOGLE_DRIVE_CLIENT_ID__', $env:GC_GOOGLE_DRIVE_CLIENT_ID | Set-Content src\Core\Secrets.h
+- ps: (Get-Content src\Core\Secrets.h) -replace '__GC_GOOGLE_DRIVE_CLIENT_SECRET__', $env:GC_GOOGLE_DRIVE_CLIENT_SECRET | Set-Content src\Core\Secrets.h
+- ps: (Get-Content src\Core\Secrets.h) -replace '__GC_GOOGLE_DRIVE_API_KEY__', $env:GC_GOOGLE_DRIVE_API_KEY | Set-Content src\Core\Secrets.h
+- ps: (Get-Content src\Core\Secrets.h) -replace 'OPENDATA_DISABLE', 'OPENDATA_ENABLE' | Set-Content src\Core\Secrets.h
+- ps: (Get-Content src\Core\Secrets.h) -replace '__GC_CLOUD_OPENDATA_SECRET__', $env:GC_CLOUD_OPENDATA_SECRET | Set-Content src\Core\Secrets.h
+- ps: (Get-Content src\Core\Secrets.h) -replace '__GC_WITHINGS_CONSUMER_SECRET__', $env:GC_WITHINGS_CONSUMER_SECRET | Set-Content src\Core\Secrets.h
+- ps: (Get-Content src\Core\Secrets.h) -replace '__GC_NOKIA_CLIENT_SECRET__', $env:GC_NOKIA_CLIENT_SECRET | Set-Content src\Core\Secrets.h
+- ps: (Get-Content src\Core\Secrets.h) -replace '__GC_DROPBOX_CLIENT_SECRET__', $env:GC_DROPBOX_CLIENT_SECRET | Set-Content src\Core\Secrets.h
+- ps: (Get-Content src\Core\Secrets.h) -replace '__GC_STRAVA_CLIENT_SECRET__', $env:GC_STRAVA_CLIENT_SECRET | Set-Content src\Core\Secrets.h
+- ps: (Get-Content src\Core\Secrets.h) -replace '__GC_TODAYSPLAN_CLIENT_SECRET__', $env:GC_TODAYSPLAN_CLIENT_SECRET | Set-Content src\Core\Secrets.h
+- ps: (Get-Content src\Core\Secrets.h) -replace '__GC_CYCLINGANALYTICS_CLIENT_SECRET__', $env:GC_CYCLINGANALYTICS_CLIENT_SECRET | Set-Content src\Core\Secrets.h
+- ps: (Get-Content src\Core\Secrets.h) -replace '__GC_CLOUD_DB_BASIC_AUTH__', $env:GC_CLOUD_DB_BASIC_AUTH | Set-Content src\Core\Secrets.h
+- ps: (Get-Content src\Core\Secrets.h) -replace '__GC_CLOUD_DB_APP_NAME__', $env:GC_CLOUD_DB_APP_NAME | Set-Content src\Core\Secrets.h
+- ps: (Get-Content src\Core\Secrets.h) -replace '__GC_POLARFLOW_CLIENT_SECRET__', $env:GC_POLARFLOW_CLIENT_SECRET | Set-Content src\Core\Secrets.h
+- ps: (Get-Content src\Core\Secrets.h) -replace '__GC_SPORTTRACKS_CLIENT_SECRET__', $env:GC_SPORTTRACKS_CLIENT_SECRET | Set-Content src\Core\Secrets.h
+
 build_script:
 - qmake.exe build.pro -r -spec win32-msvc
-- nmake
+- cd qwt\
+- jom -j1
+- cd ..
+- jom -j4
 
-#notifications:
-#- provider: GitHubPullRequest
-#  on_build_success: true
-#  on_build_failure: true
-#  on_build_status_changed: true
+after_build:
+- cd src\release
+
+# copy dependencies
+- windeployqt --release GoldenCheetah.exe
+- copy c:\libs\10_Precompiled_DLL\usbexpress_3.5.1\USBXpress\USBXpress_API\Host\x64\SiUSBXp.dll
+- copy c:\libs\10_Precompiled_DLL\libsamplerate64\lib\libsamplerate-0.dll
+- copy c:\libs\10_Precompiled_DLL\VLC\win64\lib\libvlc*.dll
+- xcopy /s /i /e /q c:\libs\10_Precompiled_DLL\VLC\win64\plugins plugins
+- copy c:\OpenSSL-v111-Win64\bin\lib*.dll
+- copy c:\OpenSSL-v111-Win64\license.txt "OpenSSL License.txt"
+- xcopy /s /i /e /q C:\Python .
+- copy C:\Python\LICENSE.txt "PYTHON LICENSE.txt"
+- copy c:\tools\vcpkg\installed\x64-windows\bin\gsl*.dll
+
+# ReadMe, license and icon files
+- copy ..\Resources\win32\ReadMe.txt
+- echo GoldenCheetah is licensed under the GNU General Public License v2 > license.txt
+- echo. >> license.txt
+- type ..\..\COPYING >> license.txt
+- copy ..\Resources\win32\gc.ico
+
+# Installer script
+- copy ..\Resources\win32\GC3.6-Dev-Master-W64-QT5.14.2.nsi
+
+# Build the installer
+- makensis GC3.6-Dev-Master-W64-QT5.14.2.nsi
+- move GoldenCheetah_v3.6-DEV_64bit_Windows.exe ..\..\GoldenCheetah_v3.6-DEV_x64.exe
+- cd ..\..
+- ps: Set-AppveyorBuildVariable -Name 'PUBLISH_BINARIES' -Value false
+- ps: if ($env:APPVEYOR_REPO_COMMIT_MESSAGE_EXTENDED -Match "\[publish binaries\]") { Set-AppveyorBuildVariable -Name 'PUBLISH_BINARIES' -Value true }
+
+test_script:
+# minimum test
+- src\release\GoldenCheetah --version 2>GCversionWindows.txt
+- git log -1 >> GCversionWindows.txt
+- ps: CertUtil -hashfile GoldenCheetah_v3.6-DEV_x64.exe sha256 | Select-Object -First 2 | Add-Content GCversionWindows.txt
+- type GCversionWindows.txt
+
+artifacts:
+- path: GoldenCheetah_v3.6-DEV_x64.exe
+  name: GCinstaller
+- path: GCversionWindows.txt
+  name: GCversionWindows
+
+deploy:
+# deploy continuous builds to s3
+  - provider: S3
+    access_key_id:
+      secure: RoEkfKfOnF7JHOiLZX5qfZM08X+bu4oaDzzSKgdooNM=
+    secret_access_key:
+      secure: GPAArawatirYwgpHJBthdrbvyFU5bBzPOdK7VYYPiG2YHYi/DNJZ5Q5qGK1A440p
+    bucket: goldencheetah-binaries
+    region: us-east-1
+    remove_files: true
+    set_public: true
+    folder: Windows
+    artifact: GCinstaller, GCversionWindows
+    on:
+      PUBLISH_BINARIES: true
+      APPVEYOR_REPO_NAME: "GoldenCheetah/GoldenCheetah"

build.pro

@@ -1,7 +1,4 @@
 TEMPLATE = subdirs
 SUBDIRS = qwt
-unix:!macx {
-    SUBDIRS += kqoauth
-}
 SUBDIRS += src
 CONFIG += ordered

deprecated/OverviewWindow.cpp

@@ -48,7 +48,7 @@ OverviewWindow::OverviewWindow(Context *context) :
 {
     setContentsMargins(0,0,0,0);
     setProperty("color", GColor(COVERVIEWBACKGROUND));
-    setProperty("nomenu", true);
+    //setProperty("nomenu", true);
     setShowTitle(false);
     setControls(NULL);
 
@@ -57,6 +57,7 @@ OverviewWindow::OverviewWindow(Context *context) :
     // add a view and scene and centre
     scene = new QGraphicsScene(this);
     view = new QGraphicsView(this);
+    view->viewport()->setAttribute(Qt::WA_AcceptTouchEvents, false); // stops it stealing focus on mouseover
     scrollbar = new QScrollBar(Qt::Vertical, this);
 
     // how to move etc
@@ -64,12 +65,6 @@ OverviewWindow::OverviewWindow(Context *context) :
     view->setRenderHint(QPainter::Antialiasing, true);
     view->setFrameStyle(QFrame::NoFrame);
     view->setSizePolicy(QSizePolicy::Expanding, QSizePolicy::Expanding);
-#ifdef Q_OS_LINUX
-    if (QGLFormat::openGLVersionFlags().testFlag(QGLFormat::OpenGL_Version_2_0)) {
-        view->setViewport(new QGLWidget(QGLFormat(QGL::SampleBuffers)));
-        view->setViewportUpdateMode(QGraphicsView::FullViewportUpdate);
-    }
-#endif
     view->setScene(scene);
 
     // layout
@@ -182,12 +177,12 @@ OverviewWindow::setConfiguration(QString config)
         newCard(tr("Notes"), 0, 4, 13, Card::META, "Notes");
 
         // column 1
-        newCard(tr("HRV"), 1, 0, 9, Card::METRIC, "rMSSD");
+        newCard(tr("HRV rMSSD"), 1, 0, 9, Card::METRIC, "rMSSD");
         newCard(tr("Heartrate"), 1, 1, 5, Card::METRIC, "average_hr");
         newCard(tr("Heartrate Zones"), 1, 2, 11, Card::ZONE, RideFile::hr);
         newCard(tr("Climbing"), 1, 3, 5, Card::METRIC, "elevation_gain");
         newCard(tr("Cadence"), 1, 4, 5, Card::METRIC, "average_cad");
-        newCard(tr("Equivalent Power"), 1, 5, 5, Card::METRIC, "coggan_np");
+        newCard(tr("Work"), 1, 6, 5, Card::METRIC, "total_work");
 
         // column 2
         newCard(tr("RPE"), 2, 0, 9, Card::RPE);
@@ -199,7 +194,9 @@ OverviewWindow::setConfiguration(QString config)
         newCard(tr("Intensity"), 3, 0, 9, Card::METRIC, "coggan_if");
         newCard(tr("Power"), 3, 1, 5, Card::METRIC, "average_power");
         newCard(tr("Power Zones"), 3, 2, 11, Card::ZONE, RideFile::watts);
-        newCard(tr("Power Model"), 3, 3, 17);
+        newCard(tr("Equivalent Power"), 3, 3, 5, Card::METRIC, "coggan_np");
+        newCard(tr("Peak Power Index"), 3, 4, 5, Card::METRIC, "peak_power_index");
+        newCard(tr("Variability"), 3, 5, 5, Card::METRIC, "coggam_variability_index");
 
         // column 4
         newCard(tr("Distance"), 4, 0, 9, Card::METRIC, "total_distance");
@@ -557,6 +554,8 @@ static const QStringList timeInZonesWBAL = QStringList()
 void
 Card::setData(RideItem *item)
 {
+    if (item == NULL || item->ride() == NULL) return;
+
     // use ride colors in painting?
     ridecolor = item->color;
 
@@ -2746,7 +2745,7 @@ OverviewWindow::eventFilter(QObject *, QEvent *event)
 
             // min max width
             if (setcolumn < 800) setcolumn = 800;
-            if (setcolumn > 2400) setcolumn = 2400;
+            if (setcolumn > 4400) setcolumn = 4400;
 
             columns[stateData.xresize.column] = setcolumn;
 

levmar/Axb.c

@@ -0,0 +1,75 @@
+/////////////////////////////////////////////////////////////////////////////////
+// 
+//  Solution of linear systems involved in the Levenberg - Marquardt
+//  minimization algorithm
+//  Copyright (C) 2004  Manolis Lourakis (lourakis at ics forth gr)
+//  Institute of Computer Science, Foundation for Research & Technology - Hellas
+//  Heraklion, Crete, Greece.
+//
+//  This program is free software; you can redistribute it and/or modify
+//  it under the terms of the GNU General Public License as published by
+//  the Free Software Foundation; either version 2 of the License, or
+//  (at your option) any later version.
+//
+//  This program is distributed in the hope that it will be useful,
+//  but WITHOUT ANY WARRANTY; without even the implied warranty of
+//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+//  GNU General Public License for more details.
+//
+/////////////////////////////////////////////////////////////////////////////////
+
+/******************************************************************************** 
+ * LAPACK-based implementations for various linear system solvers. The same core
+ * code is used with appropriate #defines to derive single and double precision
+ * solver versions, see also Axb_core.c
+ ********************************************************************************/
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <math.h>
+
+#include "levmar.h"
+#include "misc.h"
+
+#if !defined(LM_DBL_PREC) && !defined(LM_SNGL_PREC)
+#error At least one of LM_DBL_PREC, LM_SNGL_PREC should be defined!
+#endif
+
+
+#ifdef LM_DBL_PREC
+/* double precision definitions */
+#define LM_REAL double
+#define LM_PREFIX d
+#define LM_CNST(x) (x)
+#ifndef HAVE_LAPACK
+#include <float.h>
+#define LM_REAL_EPSILON DBL_EPSILON
+#endif
+
+#include "Axb_core.c"
+
+#undef LM_REAL
+#undef LM_PREFIX
+#undef LM_CNST
+#undef LM_REAL_EPSILON
+#endif /* LM_DBL_PREC */
+
+#ifdef LM_SNGL_PREC
+/* single precision (float) definitions */
+#define LM_REAL float
+#define LM_PREFIX s
+#define __SUBCNST(x) x##F
+#define LM_CNST(x) __SUBCNST(x) // force substitution
+#ifndef HAVE_LAPACK
+#define LM_REAL_EPSILON FLT_EPSILON
+#endif
+
+#include "Axb_core.c"
+
+#undef LM_REAL
+#undef LM_PREFIX
+#undef __SUBCNST
+#undef LM_CNST
+#undef LM_REAL_EPSILON
+#endif /* LM_SNGL_PREC */

levmar/compiler.h

@@ -0,0 +1,49 @@
+/////////////////////////////////////////////////////////////////////////////////
+// 
+//  Levenberg - Marquardt non-linear minimization algorithm
+//  Copyright (C) 2004  Manolis Lourakis (lourakis at ics forth gr)
+//  Institute of Computer Science, Foundation for Research & Technology - Hellas
+//  Heraklion, Crete, Greece.
+//
+//  This program is free software; you can redistribute it and/or modify
+//  it under the terms of the GNU General Public License as published by
+//  the Free Software Foundation; either version 2 of the License, or
+//  (at your option) any later version.
+//
+//  This program is distributed in the hope that it will be useful,
+//  but WITHOUT ANY WARRANTY; without even the implied warranty of
+//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+//  GNU General Public License for more details.
+//
+/////////////////////////////////////////////////////////////////////////////////
+
+#ifndef _COMPILER_H_
+#define _COMPILER_H_
+
+/* note: intel's icc defines both __ICC & __INTEL_COMPILER.
+ * Also, some compilers other than gcc define __GNUC__,
+ * therefore gcc should be checked last
+ */
+#ifdef _MSC_VER
+#define inline __inline // MSVC
+#elif !defined(__ICC) && !defined(__INTEL_COMPILER) && !defined(__GNUC__)
+#define inline // other than MSVC, ICC, GCC: define empty
+#endif
+
+#ifdef _MSC_VER
+#define LM_FINITE _finite // MSVC
+#elif defined(__ICC) || defined(__INTEL_COMPILER) || defined(__GNUC__)
+#define LM_FINITE finite // ICC, GCC
+#else
+#define LM_FINITE finite // other than MSVC, ICC, GCC, let's hope this will work
+#endif
+
+#ifdef _MSC_VER
+#define LM_ISINF(x) (!_finite(x) && !_isnan(x)) // MSVC
+#elif defined(__ICC) || defined(__INTEL_COMPILER) || defined(__GNUC__)
+#define LM_ISINF(x) isinf(x) // ICC, GCC
+#else
+#define LM_ISINF(x) isinf(x) // other than MSVC, ICC, GCC, let's hope this will work
+#endif
+
+#endif /* _COMPILER_H_ */

levmar/levmar.h

@@ -0,0 +1,398 @@
+/* 
+////////////////////////////////////////////////////////////////////////////////////
+// 
+//  Prototypes and definitions for the Levenberg - Marquardt minimization algorithm
+//  Copyright (C) 2004  Manolis Lourakis (lourakis at ics forth gr)
+//  Institute of Computer Science, Foundation for Research & Technology - Hellas
+//  Heraklion, Crete, Greece.
+//
+//  This program is free software; you can redistribute it and/or modify
+//  it under the terms of the GNU General Public License as published by
+//  the Free Software Foundation; either version 2 of the License, or
+//  (at your option) any later version.
+//
+//  This program is distributed in the hope that it will be useful,
+//  but WITHOUT ANY WARRANTY; without even the implied warranty of
+//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+//  GNU General Public License for more details.
+//
+////////////////////////////////////////////////////////////////////////////////////
+*/
+
+#ifndef _LEVMAR_H_
+#define _LEVMAR_H_
+
+/************************************* Start of configuration options *************************************/
+/* Note that when compiling with CMake, this configuration section is automatically generated
+ * based on the user's input, see levmar.h.in
+ */
+
+/* specifies whether to use LAPACK or not. Using LAPACK is strongly recommended */
+//#define HAVE_LAPACK
+
+/* specifies whether the PLASMA parallel library for multicore CPUs is available */
+/* #undef HAVE_PLASMA */
+                      
+/* to avoid the overhead of repeated mallocs(), routines in Axb.c can be instructed to
+ * retain working memory between calls. Such a choice, however, renders these routines
+ * non-reentrant and is not safe in a shared memory multiprocessing environment.
+ * Bellow, an attempt is made to issue a warning if this option is turned on and OpenMP
+ * is being used (note that this will work only if omp.h is included before levmar.h)
+ */
+#define LINSOLVERS_RETAIN_MEMORY
+#if (defined(_OPENMP))
+# ifdef LINSOLVERS_RETAIN_MEMORY
+#  ifdef _MSC_VER
+#  pragma message("LINSOLVERS_RETAIN_MEMORY is not safe in a multithreaded environment and should be turned off!")
+#  else
+#  warning LINSOLVERS_RETAIN_MEMORY is not safe in a multithreaded environment and should be turned off!
+#  endif /* _MSC_VER */
+# endif /* LINSOLVERS_RETAIN_MEMORY */
+#endif /* _OPENMP */
+
+/* specifies whether double precision routines will be compiled or not */
+#define LM_DBL_PREC
+/* specifies whether single precision routines will be compiled or not */
+#define LM_SNGL_PREC
+
+/****************** End of configuration options, no changes necessary beyond this point ******************/
+
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* work arrays size for ?levmar_der and ?levmar_dif functions.
+ * should be multiplied by sizeof(double) or sizeof(float) to be converted to bytes
+ */
+#define LM_DER_WORKSZ(npar, nmeas) (2*(nmeas) + 4*(npar) + (nmeas)*(npar) + (npar)*(npar))
+#define LM_DIF_WORKSZ(npar, nmeas) (4*(nmeas) + 4*(npar) + (nmeas)*(npar) + (npar)*(npar))
+
+/* work arrays size for ?levmar_bc_der and ?levmar_bc_dif functions.
+ * should be multiplied by sizeof(double) or sizeof(float) to be converted to bytes
+ */
+#define LM_BC_DER_WORKSZ(npar, nmeas) (2*(nmeas) + 4*(npar) + (nmeas)*(npar) + (npar)*(npar))
+#define LM_BC_DIF_WORKSZ(npar, nmeas) LM_BC_DER_WORKSZ((npar), (nmeas)) /* LEVMAR_BC_DIF currently implemented using LEVMAR_BC_DER()! */
+
+/* work arrays size for ?levmar_lec_der and ?levmar_lec_dif functions.
+ * should be multiplied by sizeof(double) or sizeof(float) to be converted to bytes
+ */
+#define LM_LEC_DER_WORKSZ(npar, nmeas, nconstr) LM_DER_WORKSZ((npar)-(nconstr), (nmeas))
+#define LM_LEC_DIF_WORKSZ(npar, nmeas, nconstr) LM_DIF_WORKSZ((npar)-(nconstr), (nmeas))
+
+/* work arrays size for ?levmar_blec_der and ?levmar_blec_dif functions.
+ * should be multiplied by sizeof(double) or sizeof(float) to be converted to bytes
+ */
+#define LM_BLEC_DER_WORKSZ(npar, nmeas, nconstr) LM_LEC_DER_WORKSZ((npar), (nmeas)+(npar), (nconstr))
+#define LM_BLEC_DIF_WORKSZ(npar, nmeas, nconstr) LM_LEC_DIF_WORKSZ((npar), (nmeas)+(npar), (nconstr))
+
+/* work arrays size for ?levmar_bleic_der and ?levmar_bleic_dif functions.
+ * should be multiplied by sizeof(double) or sizeof(float) to be converted to bytes
+ */
+#define LM_BLEIC_DER_WORKSZ(npar, nmeas, nconstr1, nconstr2) LM_BLEC_DER_WORKSZ((npar)+(nconstr2), (nmeas)+(nconstr2), (nconstr1)+(nconstr2))
+#define LM_BLEIC_DIF_WORKSZ(npar, nmeas, nconstr1, nconstr2) LM_BLEC_DIF_WORKSZ((npar)+(nconstr2), (nmeas)+(nconstr2), (nconstr1)+(nconstr2))
+
+#define LM_OPTS_SZ    	 5 /* max(4, 5) */
+#define LM_INFO_SZ    	 10
+#define LM_ERROR         -1
+#define LM_INIT_MU    	 1E-03
+#define LM_STOP_THRESH	 1E-17
+#define LM_DIFF_DELTA    1E-06
+#define LM_VERSION       "2.6 (November 2011)"
+
+#ifdef LM_DBL_PREC
+/* double precision LM, with & without Jacobian */
+/* unconstrained minimization */
+extern int dlevmar_der(
+      void (*func)(double *p, double *hx, int m, int n, void *adata),
+      void (*jacf)(double *p, double *j, int m, int n, void *adata),
+      double *p, double *x, int m, int n, int itmax, double *opts,
+      double *info, double *work, double *covar, void *adata);
+
+extern int dlevmar_dif(
+      void (*func)(double *p, double *hx, int m, int n, void *adata),
+      double *p, double *x, int m, int n, int itmax, double *opts,
+      double *info, double *work, double *covar, void *adata);
+
+/* box-constrained minimization */
+extern int dlevmar_bc_der(
+       void (*func)(double *p, double *hx, int m, int n, void *adata),
+       void (*jacf)(double *p, double *j, int m, int n, void *adata),  
+       double *p, double *x, int m, int n, double *lb, double *ub, double *dscl,
+       int itmax, double *opts, double *info, double *work, double *covar, void *adata);
+
+extern int dlevmar_bc_dif(
+       void (*func)(double *p, double *hx, int m, int n, void *adata),
+       double *p, double *x, int m, int n, double *lb, double *ub, double *dscl,
+       int itmax, double *opts, double *info, double *work, double *covar, void *adata);
+
+#ifdef HAVE_LAPACK
+/* linear equation constrained minimization */
+extern int dlevmar_lec_der(
+      void (*func)(double *p, double *hx, int m, int n, void *adata),
+      void (*jacf)(double *p, double *j, int m, int n, void *adata),
+      double *p, double *x, int m, int n, double *A, double *b, int k,
+      int itmax, double *opts, double *info, double *work, double *covar, void *adata);
+
+extern int dlevmar_lec_dif(
+      void (*func)(double *p, double *hx, int m, int n, void *adata),
+      double *p, double *x, int m, int n, double *A, double *b, int k,
+      int itmax, double *opts, double *info, double *work, double *covar, void *adata);
+
+/* box & linear equation constrained minimization */
+extern int dlevmar_blec_der(
+      void (*func)(double *p, double *hx, int m, int n, void *adata),
+      void (*jacf)(double *p, double *j, int m, int n, void *adata),
+      double *p, double *x, int m, int n, double *lb, double *ub, double *A, double *b, int k, double *wghts,
+      int itmax, double *opts, double *info, double *work, double *covar, void *adata);
+
+extern int dlevmar_blec_dif(
+      void (*func)(double *p, double *hx, int m, int n, void *adata),
+      double *p, double *x, int m, int n, double *lb, double *ub, double *A, double *b, int k, double *wghts,
+      int itmax, double *opts, double *info, double *work, double *covar, void *adata);
+
+/* box, linear equations & inequalities constrained minimization */
+extern int dlevmar_bleic_der(
+      void (*func)(double *p, double *hx, int m, int n, void *adata),
+      void (*jacf)(double *p, double *j, int m, int n, void *adata),
+      double *p, double *x, int m, int n, double *lb, double *ub,
+      double *A, double *b, int k1, double *C, double *d, int k2,
+      int itmax, double *opts, double *info, double *work, double *covar, void *adata);
+
+extern int dlevmar_bleic_dif(
+      void (*func)(double *p, double *hx, int m, int n, void *adata),
+      double *p, double *x, int m, int n, double *lb, double *ub, 
+      double *A, double *b, int k1, double *C, double *d, int k2,
+      int itmax, double *opts, double *info, double *work, double *covar, void *adata);
+
+/* box & linear inequality constraints */
+extern int dlevmar_blic_der(
+      void (*func)(double *p, double *hx, int m, int n, void *adata),
+      void (*jacf)(double *p, double *j, int m, int n, void *adata),
+      double *p, double *x, int m, int n, double *lb, double *ub, double *C, double *d, int k2,
+      int itmax, double opts[4], double info[LM_INFO_SZ], double *work, double *covar, void *adata);
+
+extern int dlevmar_blic_dif(
+      void (*func)(double *p, double *hx, int m, int n, void *adata),
+      double *p, double *x, int m, int n, double *lb, double *ub, double *C, double *d, int k2,
+      int itmax, double opts[5], double info[LM_INFO_SZ], double *work, double *covar, void *adata);
+
+/* linear equation & inequality constraints */
+extern int dlevmar_leic_der(
+      void (*func)(double *p, double *hx, int m, int n, void *adata),
+      void (*jacf)(double *p, double *j, int m, int n, void *adata),
+      double *p, double *x, int m, int n, double *A, double *b, int k1, double *C, double *d, int k2,
+      int itmax, double opts[4], double info[LM_INFO_SZ], double *work, double *covar, void *adata);
+
+extern int dlevmar_leic_dif(
+      void (*func)(double *p, double *hx, int m, int n, void *adata),
+      double *p, double *x, int m, int n, double *A, double *b, int k1, double *C, double *d, int k2,
+      int itmax, double opts[5], double info[LM_INFO_SZ], double *work, double *covar, void *adata);
+
+/* linear inequality constraints */
+extern int dlevmar_lic_der(
+      void (*func)(double *p, double *hx, int m, int n, void *adata),
+      void (*jacf)(double *p, double *j, int m, int n, void *adata),
+      double *p, double *x, int m, int n, double *C, double *d, int k2,
+      int itmax, double opts[4], double info[LM_INFO_SZ], double *work, double *covar, void *adata);
+
+extern int dlevmar_lic_dif(
+      void (*func)(double *p, double *hx, int m, int n, void *adata),
+      double *p, double *x, int m, int n, double *C, double *d, int k2,
+      int itmax, double opts[5], double info[LM_INFO_SZ], double *work, double *covar, void *adata);
+#endif /* HAVE_LAPACK */
+
+#endif /* LM_DBL_PREC */
+
+
+#ifdef LM_SNGL_PREC
+/* single precision LM, with & without Jacobian */
+/* unconstrained minimization */
+extern int slevmar_der(
+      void (*func)(float *p, float *hx, int m, int n, void *adata),
+      void (*jacf)(float *p, float *j, int m, int n, void *adata),
+      float *p, float *x, int m, int n, int itmax, float *opts,
+      float *info, float *work, float *covar, void *adata);
+
+extern int slevmar_dif(
+      void (*func)(float *p, float *hx, int m, int n, void *adata),
+      float *p, float *x, int m, int n, int itmax, float *opts,
+      float *info, float *work, float *covar, void *adata);
+
+/* box-constrained minimization */
+extern int slevmar_bc_der(
+       void (*func)(float *p, float *hx, int m, int n, void *adata),
+       void (*jacf)(float *p, float *j, int m, int n, void *adata),  
+       float *p, float *x, int m, int n, float *lb, float *ub, float *dscl,
+       int itmax, float *opts, float *info, float *work, float *covar, void *adata);
+
+extern int slevmar_bc_dif(
+       void (*func)(float *p, float *hx, int m, int n, void *adata),
+       float *p, float *x, int m, int n, float *lb, float *ub, float *dscl,
+       int itmax, float *opts, float *info, float *work, float *covar, void *adata);
+
+#ifdef HAVE_LAPACK
+/* linear equation constrained minimization */
+extern int slevmar_lec_der(
+      void (*func)(float *p, float *hx, int m, int n, void *adata),
+      void (*jacf)(float *p, float *j, int m, int n, void *adata),
+      float *p, float *x, int m, int n, float *A, float *b, int k,
+      int itmax, float *opts, float *info, float *work, float *covar, void *adata);
+
+extern int slevmar_lec_dif(
+      void (*func)(float *p, float *hx, int m, int n, void *adata),
+      float *p, float *x, int m, int n, float *A, float *b, int k,
+      int itmax, float *opts, float *info, float *work, float *covar, void *adata);
+
+/* box & linear equation constrained minimization */
+extern int slevmar_blec_der(
+      void (*func)(float *p, float *hx, int m, int n, void *adata),
+      void (*jacf)(float *p, float *j, int m, int n, void *adata),
+      float *p, float *x, int m, int n, float *lb, float *ub, float *A, float *b, int k, float *wghts,
+      int itmax, float *opts, float *info, float *work, float *covar, void *adata);
+
+extern int slevmar_blec_dif(
+      void (*func)(float *p, float *hx, int m, int n, void *adata),
+      float *p, float *x, int m, int n, float *lb, float *ub, float *A, float *b, int k, float *wghts,
+      int itmax, float *opts, float *info, float *work, float *covar, void *adata);
+
+/* box, linear equations & inequalities constrained minimization */
+extern int slevmar_bleic_der(
+      void (*func)(float *p, float *hx, int m, int n, void *adata),
+      void (*jacf)(float *p, float *j, int m, int n, void *adata),
+      float *p, float *x, int m, int n, float *lb, float *ub,
+      float *A, float *b, int k1, float *C, float *d, int k2,
+      int itmax, float *opts, float *info, float *work, float *covar, void *adata);
+
+extern int slevmar_bleic_dif(
+      void (*func)(float *p, float *hx, int m, int n, void *adata),
+      float *p, float *x, int m, int n, float *lb, float *ub,
+      float *A, float *b, int k1, float *C, float *d, int k2,
+      int itmax, float *opts, float *info, float *work, float *covar, void *adata);
+
+/* box & linear inequality constraints */
+extern int slevmar_blic_der(
+      void (*func)(float *p, float *hx, int m, int n, void *adata),
+      void (*jacf)(float *p, float *j, int m, int n, void *adata),
+      float *p, float *x, int m, int n, float *lb, float *ub, float *C, float *d, int k2,
+      int itmax, float opts[4], float info[LM_INFO_SZ], float *work, float *covar, void *adata);
+
+extern int slevmar_blic_dif(
+      void (*func)(float *p, float *hx, int m, int n, void *adata),
+      float *p, float *x, int m, int n, float *lb, float *ub, float *C, float *d, int k2,
+      int itmax, float opts[5], float info[LM_INFO_SZ], float *work, float *covar, void *adata);
+
+/* linear equality & inequality constraints */
+extern int slevmar_leic_der(
+      void (*func)(float *p, float *hx, int m, int n, void *adata),
+      void (*jacf)(float *p, float *j, int m, int n, void *adata),
+      float *p, float *x, int m, int n, float *A, float *b, int k1, float *C, float *d, int k2,
+      int itmax, float opts[4], float info[LM_INFO_SZ], float *work, float *covar, void *adata);
+
+extern int slevmar_leic_dif(
+      void (*func)(float *p, float *hx, int m, int n, void *adata),
+      float *p, float *x, int m, int n, float *A, float *b, int k1, float *C, float *d, int k2,
+      int itmax, float opts[5], float info[LM_INFO_SZ], float *work, float *covar, void *adata);
+
+/* linear inequality constraints */
+extern int slevmar_lic_der(
+      void (*func)(float *p, float *hx, int m, int n, void *adata),
+      void (*jacf)(float *p, float *j, int m, int n, void *adata),
+      float *p, float *x, int m, int n, float *C, float *d, int k2,
+      int itmax, float opts[4], float info[LM_INFO_SZ], float *work, float *covar, void *adata);
+
+extern int slevmar_lic_dif(
+      void (*func)(float *p, float *hx, int m, int n, void *adata),
+      float *p, float *x, int m, int n, float *C, float *d, int k2,
+      int itmax, float opts[5], float info[LM_INFO_SZ], float *work, float *covar, void *adata);
+#endif /* HAVE_LAPACK */
+
+#endif /* LM_SNGL_PREC */
+
+/* linear system solvers */
+#ifdef HAVE_LAPACK
+
+#ifdef LM_DBL_PREC
+extern int dAx_eq_b_QR(double *A, double *B, double *x, int m);
+extern int dAx_eq_b_QRLS(double *A, double *B, double *x, int m, int n);
+extern int dAx_eq_b_Chol(double *A, double *B, double *x, int m);
+extern int dAx_eq_b_LU(double *A, double *B, double *x, int m);
+extern int dAx_eq_b_SVD(double *A, double *B, double *x, int m);
+extern int dAx_eq_b_BK(double *A, double *B, double *x, int m);
+#endif /* LM_DBL_PREC */
+
+#ifdef LM_SNGL_PREC
+extern int sAx_eq_b_QR(float *A, float *B, float *x, int m);
+extern int sAx_eq_b_QRLS(float *A, float *B, float *x, int m, int n);
+extern int sAx_eq_b_Chol(float *A, float *B, float *x, int m);
+extern int sAx_eq_b_LU(float *A, float *B, float *x, int m);
+extern int sAx_eq_b_SVD(float *A, float *B, float *x, int m);
+extern int sAx_eq_b_BK(float *A, float *B, float *x, int m);
+#endif /* LM_SNGL_PREC */
+
+#else /* no LAPACK */
+
+#ifdef LM_DBL_PREC
+extern int dAx_eq_b_LU_noLapack(double *A, double *B, double *x, int n);
+#endif /* LM_DBL_PREC */
+
+#ifdef LM_SNGL_PREC
+extern int sAx_eq_b_LU_noLapack(float *A, float *B, float *x, int n);
+#endif /* LM_SNGL_PREC */
+
+#endif /* HAVE_LAPACK */
+
+#ifdef HAVE_PLASMA
+#ifdef LM_DBL_PREC
+extern int dAx_eq_b_PLASMA_Chol(double *A, double *B, double *x, int m);
+#endif
+#ifdef LM_SNGL_PREC
+extern int sAx_eq_b_PLASMA_Chol(float *A, float *B, float *x, int m);
+#endif
+extern void levmar_PLASMA_setnbcores(int cores);
+#endif /* HAVE_PLASMA */
+
+/* Jacobian verification, double & single precision */
+#ifdef LM_DBL_PREC
+extern void dlevmar_chkjac(
+    void (*func)(double *p, double *hx, int m, int n, void *adata),
+    void (*jacf)(double *p, double *j, int m, int n, void *adata),
+    double *p, int m, int n, void *adata, double *err);
+#endif /* LM_DBL_PREC */
+
+#ifdef LM_SNGL_PREC
+extern void slevmar_chkjac(
+    void (*func)(float *p, float *hx, int m, int n, void *adata),
+    void (*jacf)(float *p, float *j, int m, int n, void *adata),
+    float *p, int m, int n, void *adata, float *err);
+#endif /* LM_SNGL_PREC */
+
+/* miscellaneous: standard deviation, coefficient of determination (R2),
+ *                Pearson's correlation coefficient for best-fit parameters
+ */
+#ifdef LM_DBL_PREC
+extern double dlevmar_stddev( double *covar, int m, int i);
+extern double dlevmar_corcoef(double *covar, int m, int i, int j);
+extern double dlevmar_R2(void (*func)(double *p, double *hx, int m, int n, void *adata), double *p, double *x, int m, int n, void *adata);
+
+#endif /* LM_DBL_PREC */
+
+#ifdef LM_SNGL_PREC
+extern float slevmar_stddev( float *covar, int m, int i);
+extern float slevmar_corcoef(float *covar, int m, int i, int j);
+extern float slevmar_R2(void (*func)(float *p, float *hx, int m, int n, void *adata), float *p, float *x, int m, int n, void *adata);
+
+extern void slevmar_locscale(
+        void (*func)(float *p, float *hx, int m, int n, void *adata),
+        float *p, float *x, int m, int n, void *adata,
+        int howto, float locscl[2], float **residptr);
+
+extern int slevmar_outlid(float *r, int n, float thresh, float ls[2], char *outlmap);
+
+#endif /* LM_SNGL_PREC */
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* _LEVMAR_H_ */

levmar/lm.c

@@ -0,0 +1,83 @@
+/////////////////////////////////////////////////////////////////////////////////
+// 
+//  Levenberg - Marquardt non-linear minimization algorithm
+//  Copyright (C) 2004  Manolis Lourakis (lourakis at ics forth gr)
+//  Institute of Computer Science, Foundation for Research & Technology - Hellas
+//  Heraklion, Crete, Greece.
+//
+//  This program is free software; you can redistribute it and/or modify
+//  it under the terms of the GNU General Public License as published by
+//  the Free Software Foundation; either version 2 of the License, or
+//  (at your option) any later version.
+//
+//  This program is distributed in the hope that it will be useful,
+//  but WITHOUT ANY WARRANTY; without even the implied warranty of
+//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+//  GNU General Public License for more details.
+//
+/////////////////////////////////////////////////////////////////////////////////
+
+/******************************************************************************** 
+ * Levenberg-Marquardt nonlinear minimization. The same core code is used with
+ * appropriate #defines to derive single and double precision versions, see
+ * also lm_core.c
+ ********************************************************************************/
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <float.h>
+
+#include "levmar.h"
+#include "compiler.h"
+#include "misc.h"
+
+#define EPSILON       1E-12
+#define ONE_THIRD     0.3333333334 /* 1.0/3.0 */
+
+#if !defined(LM_DBL_PREC) && !defined(LM_SNGL_PREC)
+#error At least one of LM_DBL_PREC, LM_SNGL_PREC should be defined!
+#endif
+
+
+#ifdef LM_SNGL_PREC
+/* single precision (float) definitions */
+#define LM_REAL float
+#define LM_PREFIX s
+
+#define LM_REAL_MAX FLT_MAX
+#define LM_REAL_MIN -FLT_MAX
+#define LM_REAL_EPSILON FLT_EPSILON
+#define __SUBCNST(x) x##F
+#define LM_CNST(x) __SUBCNST(x) // force substitution
+
+#include "lm_core.c" // read in core code
+
+#undef LM_REAL
+#undef LM_PREFIX
+#undef LM_REAL_MAX
+#undef LM_REAL_EPSILON
+#undef LM_REAL_MIN
+#undef __SUBCNST
+#undef LM_CNST
+#endif /* LM_SNGL_PREC */
+
+#ifdef LM_DBL_PREC
+/* double precision definitions */
+#define LM_REAL double
+#define LM_PREFIX d
+
+#define LM_REAL_MAX DBL_MAX
+#define LM_REAL_MIN -DBL_MAX
+#define LM_REAL_EPSILON DBL_EPSILON
+#define LM_CNST(x) (x)
+
+#include "lm_core.c" // read in core code
+
+#undef LM_REAL
+#undef LM_PREFIX
+#undef LM_REAL_MAX
+#undef LM_REAL_EPSILON
+#undef LM_REAL_MIN
+#undef LM_CNST
+#endif /* LM_DBL_PREC */

levmar/lm.h

@@ -0,0 +1,11 @@
+#ifndef _DEPR_LM_H_
+#define _DEPR_LM_H_
+
+#ifdef _MSC_VER
+#pragma message("lm.h is deprecated, please use levmar.h instead!")
+#else
+#error lm.h is deprecated, please use levmar.h instead!
+#endif /* _MSC_VER */
+
+#endif /* _DEPR_LM_H_ */
+

levmar/lm_core.c

@@ -0,0 +1,858 @@
+/////////////////////////////////////////////////////////////////////////////////
+// 
+//  Levenberg - Marquardt non-linear minimization algorithm
+//  Copyright (C) 2004  Manolis Lourakis (lourakis at ics forth gr)
+//  Institute of Computer Science, Foundation for Research & Technology - Hellas
+//  Heraklion, Crete, Greece.
+//
+//  This program is free software; you can redistribute it and/or modify
+//  it under the terms of the GNU General Public License as published by
+//  the Free Software Foundation; either version 2 of the License, or
+//  (at your option) any later version.
+//
+//  This program is distributed in the hope that it will be useful,
+//  but WITHOUT ANY WARRANTY; without even the implied warranty of
+//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+//  GNU General Public License for more details.
+//
+/////////////////////////////////////////////////////////////////////////////////
+
+#ifndef LM_REAL // not included by lm.c
+#error This file should not be compiled directly!
+#endif
+
+
+/* precision-specific definitions */
+#define LEVMAR_DER LM_ADD_PREFIX(levmar_der)
+#define LEVMAR_DIF LM_ADD_PREFIX(levmar_dif)
+#define LEVMAR_FDIF_FORW_JAC_APPROX LM_ADD_PREFIX(levmar_fdif_forw_jac_approx)
+#define LEVMAR_FDIF_CENT_JAC_APPROX LM_ADD_PREFIX(levmar_fdif_cent_jac_approx)
+#define LEVMAR_TRANS_MAT_MAT_MULT LM_ADD_PREFIX(levmar_trans_mat_mat_mult)
+#define LEVMAR_L2NRMXMY LM_ADD_PREFIX(levmar_L2nrmxmy)
+#define LEVMAR_COVAR LM_ADD_PREFIX(levmar_covar)
+
+#ifdef HAVE_LAPACK
+#define AX_EQ_B_LU LM_ADD_PREFIX(Ax_eq_b_LU)
+#define AX_EQ_B_CHOL LM_ADD_PREFIX(Ax_eq_b_Chol)
+#define AX_EQ_B_QR LM_ADD_PREFIX(Ax_eq_b_QR)
+#define AX_EQ_B_QRLS LM_ADD_PREFIX(Ax_eq_b_QRLS)
+#define AX_EQ_B_SVD LM_ADD_PREFIX(Ax_eq_b_SVD)
+#define AX_EQ_B_BK LM_ADD_PREFIX(Ax_eq_b_BK)
+#else
+#define AX_EQ_B_LU LM_ADD_PREFIX(Ax_eq_b_LU_noLapack)
+#endif /* HAVE_LAPACK */
+
+#ifdef HAVE_PLASMA
+#define AX_EQ_B_PLASMA_CHOL LM_ADD_PREFIX(Ax_eq_b_PLASMA_Chol)
+#endif
+
+/* 
+ * This function seeks the parameter vector p that best describes the measurements vector x.
+ * More precisely, given a vector function  func : R^m --> R^n with n>=m,
+ * it finds p s.t. func(p) ~= x, i.e. the squared second order (i.e. L2) norm of
+ * e=x-func(p) is minimized.
+ *
+ * This function requires an analytic Jacobian. In case the latter is unavailable,
+ * use LEVMAR_DIF() bellow
+ *
+ * Returns the number of iterations (>=0) if successful, LM_ERROR if failed
+ *
+ * For more details, see K. Madsen, H.B. Nielsen and O. Tingleff's lecture notes on 
+ * non-linear least squares at http://www.imm.dtu.dk/pubdb/views/edoc_download.php/3215/pdf/imm3215.pdf
+ */
+
+int LEVMAR_DER(
+  void (*func)(LM_REAL *p, LM_REAL *hx, int m, int n, void *adata), /* functional relation describing measurements. A p \in R^m yields a \hat{x} \in  R^n */
+  void (*jacf)(LM_REAL *p, LM_REAL *j, int m, int n, void *adata),  /* function to evaluate the Jacobian \part x / \part p */ 
+  LM_REAL *p,         /* I/O: initial parameter estimates. On output has the estimated solution */
+  LM_REAL *x,         /* I: measurement vector. NULL implies a zero vector */
+  int m,              /* I: parameter vector dimension (i.e. #unknowns) */
+  int n,              /* I: measurement vector dimension */
+  int itmax,          /* I: maximum number of iterations */
+  LM_REAL opts[4],    /* I: minim. options [\mu, \epsilon1, \epsilon2, \epsilon3]. Respectively the scale factor for initial \mu,
+                       * stopping thresholds for ||J^T e||_inf, ||Dp||_2 and ||e||_2. Set to NULL for defaults to be used
+                       */
+  LM_REAL info[LM_INFO_SZ],
+					           /* O: information regarding the minimization. Set to NULL if don't care
+                      * info[0]= ||e||_2 at initial p.
+                      * info[1-4]=[ ||e||_2, ||J^T e||_inf,  ||Dp||_2, mu/max[J^T J]_ii ], all computed at estimated p.
+                      * info[5]= # iterations,
+                      * info[6]=reason for terminating: 1 - stopped by small gradient J^T e
+                      *                                 2 - stopped by small Dp
+                      *                                 3 - stopped by itmax
+                      *                                 4 - singular matrix. Restart from current p with increased mu 
+                      *                                 5 - no further error reduction is possible. Restart with increased mu
+                      *                                 6 - stopped by small ||e||_2
+                      *                                 7 - stopped by invalid (i.e. NaN or Inf) "func" values. This is a user error
+                      * info[7]= # function evaluations
+                      * info[8]= # Jacobian evaluations
+                      * info[9]= # linear systems solved, i.e. # attempts for reducing error
+                      */
+  LM_REAL *work,     /* working memory at least LM_DER_WORKSZ() reals large, allocated if NULL */
+  LM_REAL *covar,    /* O: Covariance matrix corresponding to LS solution; mxm. Set to NULL if not needed. */
+  void *adata)       /* pointer to possibly additional data, passed uninterpreted to func & jacf.
+                      * Set to NULL if not needed
+                      */
+{
+register int i, j, k, l;
+int worksz, freework=0, issolved;
+/* temp work arrays */
+LM_REAL *e,          /* nx1 */
+       *hx,         /* \hat{x}_i, nx1 */
+       *jacTe,      /* J^T e_i mx1 */
+       *jac,        /* nxm */
+       *jacTjac,    /* mxm */
+       *Dp,         /* mx1 */
+   *diag_jacTjac,   /* diagonal of J^T J, mx1 */
+       *pDp;        /* p + Dp, mx1 */
+
+register LM_REAL mu,  /* damping constant */
+                tmp; /* mainly used in matrix & vector multiplications */
+LM_REAL p_eL2, jacTe_inf, pDp_eL2; /* ||e(p)||_2, ||J^T e||_inf, ||e(p+Dp)||_2 */
+LM_REAL p_L2, Dp_L2=LM_REAL_MAX, dF, dL;
+LM_REAL tau, eps1, eps2, eps2_sq, eps3;
+LM_REAL init_p_eL2;
+int nu=2, nu2, stop=0, nfev, njev=0, nlss=0;
+const int nm=n*m;
+int (*linsolver)(LM_REAL *A, LM_REAL *B, LM_REAL *x, int m)=NULL;
+
+  mu=jacTe_inf=0.0; /* -Wall */
+
+  if(n<m){
+    fprintf(stderr, LCAT(LEVMAR_DER, "(): cannot solve a problem with fewer measurements [%d] than unknowns [%d]\n"), n, m);
+    return LM_ERROR;
+  }
+
+  if(!jacf){
+    fprintf(stderr, RCAT("No function specified for computing the Jacobian in ", LEVMAR_DER)
+        RCAT("().\nIf no such function is available, use ", LEVMAR_DIF) RCAT("() rather than ", LEVMAR_DER) "()\n");
+    return LM_ERROR;
+  }
+
+  if(opts){
+	  tau=opts[0];
+	  eps1=opts[1];
+	  eps2=opts[2];
+	  eps2_sq=opts[2]*opts[2];
+    eps3=opts[3];
+  }
+  else{ // use default values
+	  tau=LM_CNST(LM_INIT_MU);
+	  eps1=LM_CNST(LM_STOP_THRESH);
+	  eps2=LM_CNST(LM_STOP_THRESH);
+	  eps2_sq=LM_CNST(LM_STOP_THRESH)*LM_CNST(LM_STOP_THRESH);
+    eps3=LM_CNST(LM_STOP_THRESH);
+  }
+
+  if(!work){
+    worksz=LM_DER_WORKSZ(m, n); //2*n+4*m + n*m + m*m;
+    work=(LM_REAL *)malloc(worksz*sizeof(LM_REAL)); /* allocate a big chunk in one step */
+    if(!work){
+      fprintf(stderr, LCAT(LEVMAR_DER, "(): memory allocation request failed\n"));
+      return LM_ERROR;
+    }
+    freework=1;
+  }
+
+  /* set up work arrays */
+  e=work;
+  hx=e + n;
+  jacTe=hx + n;
+  jac=jacTe + m;
+  jacTjac=jac + nm;
+  Dp=jacTjac + m*m;
+  diag_jacTjac=Dp + m;
+  pDp=diag_jacTjac + m;
+
+  /* compute e=x - f(p) and its L2 norm */
+  (*func)(p, hx, m, n, adata); nfev=1;
+  /* ### e=x-hx, p_eL2=||e|| */
+#if 1
+  p_eL2=LEVMAR_L2NRMXMY(e, x, hx, n);  
+#else
+  for(i=0, p_eL2=0.0; i<n; ++i){
+    e[i]=tmp=x[i]-hx[i];
+    p_eL2+=tmp*tmp;
+  }
+#endif
+  init_p_eL2=p_eL2;
+  if(!LM_FINITE(p_eL2)) stop=7;
+
+  for(k=0; k<itmax && !stop; ++k){
+    /* Note that p and e have been updated at a previous iteration */
+
+    if(p_eL2<=eps3){ /* error is small */
+      stop=6;
+      break;
+    }
+
+    /* Compute the Jacobian J at p,  J^T J,  J^T e,  ||J^T e||_inf and ||p||^2.
+     * Since J^T J is symmetric, its computation can be sped up by computing
+     * only its upper triangular part and copying it to the lower part
+     */
+
+    (*jacf)(p, jac, m, n, adata); ++njev;
+
+    /* J^T J, J^T e */
+    if(nm<__BLOCKSZ__SQ){ // this is a small problem
+      /* J^T*J_ij = \sum_l J^T_il * J_lj = \sum_l J_li * J_lj.
+       * Thus, the product J^T J can be computed using an outer loop for
+       * l that adds J_li*J_lj to each element ij of the result. Note that
+       * with this scheme, the accesses to J and JtJ are always along rows,
+       * therefore induces less cache misses compared to the straightforward
+       * algorithm for computing the product (i.e., l loop is innermost one).
+       * A similar scheme applies to the computation of J^T e.
+       * However, for large minimization problems (i.e., involving a large number
+       * of unknowns and measurements) for which J/J^T J rows are too large to
+       * fit in the L1 cache, even this scheme incures many cache misses. In
+       * such cases, a cache-efficient blocking scheme is preferable.
+       *
+       * Thanks to John Nitao of Lawrence Livermore Lab for pointing out this
+       * performance problem.
+       *
+       * Note that the non-blocking algorithm is faster on small
+       * problems since in this case it avoids the overheads of blocking. 
+       */
+
+      /* looping downwards saves a few computations */
+      register int l;
+      register LM_REAL alpha, *jaclm, *jacTjacim;
+
+      for(i=m*m; i-->0; )
+        jacTjac[i]=0.0;
+      for(i=m; i-->0; )
+        jacTe[i]=0.0;
+
+      for(l=n; l-->0; ){
+        jaclm=jac+l*m;
+        for(i=m; i-->0; ){
+          jacTjacim=jacTjac+i*m;
+          alpha=jaclm[i]; //jac[l*m+i];
+          for(j=i+1; j-->0; ) /* j<=i computes lower triangular part only */
+            jacTjacim[j]+=jaclm[j]*alpha; //jacTjac[i*m+j]+=jac[l*m+j]*alpha
+
+          /* J^T e */
+          jacTe[i]+=alpha*e[l];
+        }
+      }
+
+      for(i=m; i-->0; ) /* copy to upper part */
+        for(j=i+1; j<m; ++j)
+          jacTjac[i*m+j]=jacTjac[j*m+i];
+
+    }
+    else{ // this is a large problem
+      /* Cache efficient computation of J^T J based on blocking
+       */
+      LEVMAR_TRANS_MAT_MAT_MULT(jac, jacTjac, n, m);
+
+      /* cache efficient computation of J^T e */
+      for(i=0; i<m; ++i)
+        jacTe[i]=0.0;
+
+      for(i=0; i<n; ++i){
+        register LM_REAL *jacrow;
+
+        for(l=0, jacrow=jac+i*m, tmp=e[i]; l<m; ++l)
+          jacTe[l]+=jacrow[l]*tmp;
+      }
+    }
+
+	  /* Compute ||J^T e||_inf and ||p||^2 */
+    for(i=0, p_L2=jacTe_inf=0.0; i<m; ++i){
+      if(jacTe_inf < (tmp=FABS(jacTe[i]))) jacTe_inf=tmp;
+
+      diag_jacTjac[i]=jacTjac[i*m+i]; /* save diagonal entries so that augmentation can be later canceled */
+      p_L2+=p[i]*p[i];
+    }
+    //p_L2=sqrt(p_L2);
+
+#if 0
+if(!(k%100)){
+  printf("Current estimate: ");
+  for(i=0; i<m; ++i)
+    printf("%.9g ", p[i]);
+  printf("-- errors %.9g %0.9g\n", jacTe_inf, p_eL2);
+}
+#endif
+
+    /* check for convergence */
+    if((jacTe_inf <= eps1)){
+      Dp_L2=0.0; /* no increment for p in this case */
+      stop=1;
+      break;
+    }
+
+   /* compute initial damping factor */
+    if(k==0){
+      for(i=0, tmp=LM_REAL_MIN; i<m; ++i)
+        if(diag_jacTjac[i]>tmp) tmp=diag_jacTjac[i]; /* find max diagonal element */
+      mu=tau*tmp;
+    }
+
+    /* determine increment using adaptive damping */
+    while(1){
+      /* augment normal equations */
+      for(i=0; i<m; ++i)
+        jacTjac[i*m+i]+=mu;
+
+      /* solve augmented equations */
+#ifdef HAVE_LAPACK
+      /* 7 alternatives are available: LU, Cholesky + Cholesky with PLASMA, LDLt, 2 variants of QR decomposition and SVD.
+       * For matrices with dimensions of at least a few hundreds, the PLASMA implementation of Cholesky is the fastest.
+       * From the serial solvers, Cholesky is the fastest but might occasionally be inapplicable due to numerical round-off;
+       * QR is slower but more robust; SVD is the slowest but most robust; LU is quite robust but
+       * slower than LDLt; LDLt offers a good tradeoff between robustness and speed
+       */
+
+      issolved=AX_EQ_B_BK(jacTjac, jacTe, Dp, m); ++nlss; linsolver=AX_EQ_B_BK;
+      //issolved=AX_EQ_B_LU(jacTjac, jacTe, Dp, m); ++nlss; linsolver=AX_EQ_B_LU;
+      //issolved=AX_EQ_B_CHOL(jacTjac, jacTe, Dp, m); ++nlss; linsolver=AX_EQ_B_CHOL;
+#ifdef HAVE_PLASMA
+      //issolved=AX_EQ_B_PLASMA_CHOL(jacTjac, jacTe, Dp, m); ++nlss; linsolver=AX_EQ_B_PLASMA_CHOL;
+#endif
+      //issolved=AX_EQ_B_QR(jacTjac, jacTe, Dp, m); ++nlss; linsolver=AX_EQ_B_QR;
+      //issolved=AX_EQ_B_QRLS(jacTjac, jacTe, Dp, m, m); ++nlss; linsolver=(int (*)(LM_REAL *A, LM_REAL *B, LM_REAL *x, int m))AX_EQ_B_QRLS;
+      //issolved=AX_EQ_B_SVD(jacTjac, jacTe, Dp, m); ++nlss; linsolver=AX_EQ_B_SVD;
+
+#else
+      /* use the LU included with levmar */
+      issolved=AX_EQ_B_LU(jacTjac, jacTe, Dp, m); ++nlss; linsolver=AX_EQ_B_LU;
+#endif /* HAVE_LAPACK */
+
+      if(issolved){
+        /* compute p's new estimate and ||Dp||^2 */
+        for(i=0, Dp_L2=0.0; i<m; ++i){
+          pDp[i]=p[i] + (tmp=Dp[i]);
+          Dp_L2+=tmp*tmp;
+        }
+        //Dp_L2=sqrt(Dp_L2);
+
+        if(Dp_L2<=eps2_sq*p_L2){ /* relative change in p is small, stop */
+        //if(Dp_L2<=eps2*(p_L2 + eps2)){ /* relative change in p is small, stop */
+          stop=2;
+          break;
+        }
+
+       if(Dp_L2>=(p_L2+eps2)/(LM_CNST(EPSILON)*LM_CNST(EPSILON))){ /* almost singular */
+       //if(Dp_L2>=(p_L2+eps2)/LM_CNST(EPSILON)){ /* almost singular */
+         stop=4;
+         break;
+       }
+
+        (*func)(pDp, hx, m, n, adata); ++nfev; /* evaluate function at p + Dp */
+        /* compute ||e(pDp)||_2 */
+        /* ### hx=x-hx, pDp_eL2=||hx|| */
+#if 1
+        pDp_eL2=LEVMAR_L2NRMXMY(hx, x, hx, n);
+#else
+        for(i=0, pDp_eL2=0.0; i<n; ++i){
+          hx[i]=tmp=x[i]-hx[i];
+          pDp_eL2+=tmp*tmp;
+        }
+#endif
+        if(!LM_FINITE(pDp_eL2)){ /* sum of squares is not finite, most probably due to a user error.
+                                  * This check makes sure that the inner loop does not run indefinitely.
+                                  * Thanks to Steve Danauskas for reporting such cases
+                                  */
+          stop=7;
+          break;
+        }
+
+        for(i=0, dL=0.0; i<m; ++i)
+          dL+=Dp[i]*(mu*Dp[i]+jacTe[i]);
+
+        dF=p_eL2-pDp_eL2;
+
+        if(dL>0.0 && dF>0.0){ /* reduction in error, increment is accepted */
+          tmp=(LM_CNST(2.0)*dF/dL-LM_CNST(1.0));
+          tmp=LM_CNST(1.0)-tmp*tmp*tmp;
+          mu=mu*( (tmp>=LM_CNST(ONE_THIRD))? tmp : LM_CNST(ONE_THIRD) );
+          nu=2;
+
+          for(i=0 ; i<m; ++i) /* update p's estimate */
+            p[i]=pDp[i];
+
+          for(i=0; i<n; ++i) /* update e and ||e||_2 */
+            e[i]=hx[i];
+          p_eL2=pDp_eL2;
+          break;
+        }
+      }
+
+      /* if this point is reached, either the linear system could not be solved or
+       * the error did not reduce; in any case, the increment must be rejected
+       */
+
+      mu*=nu;
+      nu2=nu<<1; // 2*nu;
+      if(nu2<=nu){ /* nu has wrapped around (overflown). Thanks to Frank Jordan for spotting this case */
+        stop=5;
+        break;
+      }
+      nu=nu2;
+
+      for(i=0; i<m; ++i) /* restore diagonal J^T J entries */
+        jacTjac[i*m+i]=diag_jacTjac[i];
+    } /* inner loop */
+  }
+
+  if(k>=itmax) stop=3;
+
+  for(i=0; i<m; ++i) /* restore diagonal J^T J entries */
+    jacTjac[i*m+i]=diag_jacTjac[i];
+
+  if(info){
+    info[0]=init_p_eL2;
+    info[1]=p_eL2;
+    info[2]=jacTe_inf;
+    info[3]=Dp_L2;
+    for(i=0, tmp=LM_REAL_MIN; i<m; ++i)
+      if(tmp<jacTjac[i*m+i]) tmp=jacTjac[i*m+i];
+    info[4]=mu/tmp;
+    info[5]=(LM_REAL)k;
+    info[6]=(LM_REAL)stop;
+    info[7]=(LM_REAL)nfev;
+    info[8]=(LM_REAL)njev;
+    info[9]=(LM_REAL)nlss;
+  }
+
+  /* covariance matrix */
+  if(covar){
+    LEVMAR_COVAR(jacTjac, covar, p_eL2, m, n);
+  }
+
+  if(freework) free(work);
+
+#ifdef LINSOLVERS_RETAIN_MEMORY
+  if(linsolver) (*linsolver)(NULL, NULL, NULL, 0);
+#endif
+
+  return (stop!=4 && stop!=7)?  k : LM_ERROR;
+}
+
+
+/* Secant version of the LEVMAR_DER() function above: the Jacobian is approximated with 
+ * the aid of finite differences (forward or central, see the comment for the opts argument)
+ */
+int LEVMAR_DIF(
+  void (*func)(LM_REAL *p, LM_REAL *hx, int m, int n, void *adata), /* functional relation describing measurements. A p \in R^m yields a \hat{x} \in  R^n */
+  LM_REAL *p,         /* I/O: initial parameter estimates. On output has the estimated solution */
+  LM_REAL *x,         /* I: measurement vector. NULL implies a zero vector */
+  int m,              /* I: parameter vector dimension (i.e. #unknowns) */
+  int n,              /* I: measurement vector dimension */
+  int itmax,          /* I: maximum number of iterations */
+  LM_REAL opts[5],    /* I: opts[0-4] = minim. options [\mu, \epsilon1, \epsilon2, \epsilon3, \delta]. Respectively the
+                       * scale factor for initial \mu, stopping thresholds for ||J^T e||_inf, ||Dp||_2 and ||e||_2 and
+                       * the step used in difference approximation to the Jacobian. Set to NULL for defaults to be used.
+                       * If \delta<0, the Jacobian is approximated with central differences which are more accurate
+                       * (but slower!) compared to the forward differences employed by default. 
+                       */
+  LM_REAL info[LM_INFO_SZ],
+					           /* O: information regarding the minimization. Set to NULL if don't care
+                      * info[0]= ||e||_2 at initial p.
+                      * info[1-4]=[ ||e||_2, ||J^T e||_inf,  ||Dp||_2, mu/max[J^T J]_ii ], all computed at estimated p.
+                      * info[5]= # iterations,
+                      * info[6]=reason for terminating: 1 - stopped by small gradient J^T e
+                      *                                 2 - stopped by small Dp
+                      *                                 3 - stopped by itmax
+                      *                                 4 - singular matrix. Restart from current p with increased mu 
+                      *                                 5 - no further error reduction is possible. Restart with increased mu
+                      *                                 6 - stopped by small ||e||_2
+                      *                                 7 - stopped by invalid (i.e. NaN or Inf) "func" values. This is a user error
+                      * info[7]= # function evaluations
+                      * info[8]= # Jacobian evaluations
+                      * info[9]= # linear systems solved, i.e. # attempts for reducing error
+                      */
+  LM_REAL *work,     /* working memory at least LM_DIF_WORKSZ() reals large, allocated if NULL */
+  LM_REAL *covar,    /* O: Covariance matrix corresponding to LS solution; mxm. Set to NULL if not needed. */
+  void *adata)       /* pointer to possibly additional data, passed uninterpreted to func.
+                      * Set to NULL if not needed
+                      */
+{
+register int i, j, k, l;
+int worksz, freework=0, issolved;
+/* temp work arrays */
+LM_REAL *e,          /* nx1 */
+       *hx,         /* \hat{x}_i, nx1 */
+       *jacTe,      /* J^T e_i mx1 */
+       *jac,        /* nxm */
+       *jacTjac,    /* mxm */
+       *Dp,         /* mx1 */
+   *diag_jacTjac,   /* diagonal of J^T J, mx1 */
+       *pDp,        /* p + Dp, mx1 */
+       *wrk,        /* nx1 */
+       *wrk2;       /* nx1, used only for holding a temporary e vector and when differentiating with central differences */
+
+int using_ffdif=1;
+
+register LM_REAL mu,  /* damping constant */
+                tmp; /* mainly used in matrix & vector multiplications */
+LM_REAL p_eL2, jacTe_inf, pDp_eL2; /* ||e(p)||_2, ||J^T e||_inf, ||e(p+Dp)||_2 */
+LM_REAL p_L2, Dp_L2=LM_REAL_MAX, dF, dL;
+LM_REAL tau, eps1, eps2, eps2_sq, eps3, delta;
+LM_REAL init_p_eL2;
+int nu, nu2, stop=0, nfev, njap=0, nlss=0, K=(m>=10)? m: 10, updjac, updp=1, newjac;
+const int nm=n*m;
+int (*linsolver)(LM_REAL *A, LM_REAL *B, LM_REAL *x, int m)=NULL;
+
+  mu=jacTe_inf=p_L2=0.0; /* -Wall */
+  updjac=newjac=0; /* -Wall */
+
+  if(n<m){
+    fprintf(stderr, LCAT(LEVMAR_DIF, "(): cannot solve a problem with fewer measurements [%d] than unknowns [%d]\n"), n, m);
+    return LM_ERROR;
+  }
+
+  if(opts){
+	  tau=opts[0];
+	  eps1=opts[1];
+	  eps2=opts[2];
+	  eps2_sq=opts[2]*opts[2];
+    eps3=opts[3];
+	  delta=opts[4];
+    if(delta<0.0){
+      delta=-delta; /* make positive */
+      using_ffdif=0; /* use central differencing */
+    }
+  }
+  else{ // use default values
+	  tau=LM_CNST(LM_INIT_MU);
+	  eps1=LM_CNST(LM_STOP_THRESH);
+	  eps2=LM_CNST(LM_STOP_THRESH);
+	  eps2_sq=LM_CNST(LM_STOP_THRESH)*LM_CNST(LM_STOP_THRESH);
+    eps3=LM_CNST(LM_STOP_THRESH);
+	  delta=LM_CNST(LM_DIFF_DELTA);
+  }
+
+  if(!work){
+    worksz=LM_DIF_WORKSZ(m, n); //4*n+4*m + n*m + m*m;
+    work=(LM_REAL *)malloc(worksz*sizeof(LM_REAL)); /* allocate a big chunk in one step */
+    if(!work){
+      fprintf(stderr, LCAT(LEVMAR_DIF, "(): memory allocation request failed\n"));
+      return LM_ERROR;
+    }
+    freework=1;
+  }
+
+  /* set up work arrays */
+  e=work;
+  hx=e + n;
+  jacTe=hx + n;
+  jac=jacTe + m;
+  jacTjac=jac + nm;
+  Dp=jacTjac + m*m;
+  diag_jacTjac=Dp + m;
+  pDp=diag_jacTjac + m;
+  wrk=pDp + m;
+  wrk2=wrk + n;
+
+  /* compute e=x - f(p) and its L2 norm */
+  (*func)(p, hx, m, n, adata); nfev=1;
+  /* ### e=x-hx, p_eL2=||e|| */
+#if 1
+  p_eL2=LEVMAR_L2NRMXMY(e, x, hx, n);
+#else
+  for(i=0, p_eL2=0.0; i<n; ++i){
+    e[i]=tmp=x[i]-hx[i];
+    p_eL2+=tmp*tmp;
+  }
+#endif
+  init_p_eL2=p_eL2;
+  if(!LM_FINITE(p_eL2)) stop=7;
+
+  nu=20; /* force computation of J */
+
+  for(k=0; k<itmax && !stop; ++k){
+    /* Note that p and e have been updated at a previous iteration */
+
+    if(p_eL2<=eps3){ /* error is small */
+      stop=6;
+      break;
+    }
+
+    /* Compute the Jacobian J at p,  J^T J,  J^T e,  ||J^T e||_inf and ||p||^2.
+     * The symmetry of J^T J is again exploited for speed
+     */
+
+    if((updp && nu>16) || updjac==K){ /* compute difference approximation to J */
+      if(using_ffdif){ /* use forward differences */
+        LEVMAR_FDIF_FORW_JAC_APPROX(func, p, hx, wrk, delta, jac, m, n, adata);
+        ++njap; nfev+=m;
+      }
+      else{ /* use central differences */
+        LEVMAR_FDIF_CENT_JAC_APPROX(func, p, wrk, wrk2, delta, jac, m, n, adata);
+        ++njap; nfev+=2*m;
+      }
+      nu=2; updjac=0; updp=0; newjac=1;
+    }
+
+    if(newjac){ /* Jacobian has changed, recompute J^T J, J^t e, etc */
+      newjac=0;
+
+      /* J^T J, J^T e */
+      if(nm<=__BLOCKSZ__SQ){ // this is a small problem
+        /* J^T*J_ij = \sum_l J^T_il * J_lj = \sum_l J_li * J_lj.
+         * Thus, the product J^T J can be computed using an outer loop for
+         * l that adds J_li*J_lj to each element ij of the result. Note that
+         * with this scheme, the accesses to J and JtJ are always along rows,
+         * therefore induces less cache misses compared to the straightforward
+         * algorithm for computing the product (i.e., l loop is innermost one).
+         * A similar scheme applies to the computation of J^T e.
+         * However, for large minimization problems (i.e., involving a large number
+         * of unknowns and measurements) for which J/J^T J rows are too large to
+         * fit in the L1 cache, even this scheme incures many cache misses. In
+         * such cases, a cache-efficient blocking scheme is preferable.
+         *
+         * Thanks to John Nitao of Lawrence Livermore Lab for pointing out this
+         * performance problem.
+         *
+         * Note that the non-blocking algorithm is faster on small
+         * problems since in this case it avoids the overheads of blocking. 
+         */
+        register int l;
+        register LM_REAL alpha, *jaclm, *jacTjacim;
+
+        /* looping downwards saves a few computations */
+        for(i=m*m; i-->0; )
+          jacTjac[i]=0.0;
+        for(i=m; i-->0; )
+          jacTe[i]=0.0;
+
+        for(l=n; l-->0; ){
+          jaclm=jac+l*m;
+          for(i=m; i-->0; ){
+            jacTjacim=jacTjac+i*m;
+            alpha=jaclm[i]; //jac[l*m+i];
+            for(j=i+1; j-->0; ) /* j<=i computes lower triangular part only */
+              jacTjacim[j]+=jaclm[j]*alpha; //jacTjac[i*m+j]+=jac[l*m+j]*alpha
+
+            /* J^T e */
+            jacTe[i]+=alpha*e[l];
+          }
+        }
+
+        for(i=m; i-->0; ) /* copy to upper part */
+          for(j=i+1; j<m; ++j)
+            jacTjac[i*m+j]=jacTjac[j*m+i];
+      }
+      else{ // this is a large problem
+        /* Cache efficient computation of J^T J based on blocking
+         */
+        LEVMAR_TRANS_MAT_MAT_MULT(jac, jacTjac, n, m);
+
+        /* cache efficient computation of J^T e */
+        for(i=0; i<m; ++i)
+          jacTe[i]=0.0;
+
+        for(i=0; i<n; ++i){
+          register LM_REAL *jacrow;
+
+          for(l=0, jacrow=jac+i*m, tmp=e[i]; l<m; ++l)
+            jacTe[l]+=jacrow[l]*tmp;
+        }
+      }
+      
+      /* Compute ||J^T e||_inf and ||p||^2 */
+      for(i=0, p_L2=jacTe_inf=0.0; i<m; ++i){
+        if(jacTe_inf < (tmp=FABS(jacTe[i]))) jacTe_inf=tmp;
+
+        diag_jacTjac[i]=jacTjac[i*m+i]; /* save diagonal entries so that augmentation can be later canceled */
+        p_L2+=p[i]*p[i];
+      }
+      //p_L2=sqrt(p_L2);
+    }
+
+#if 0
+if(!(k%100)){
+  printf("Current estimate: ");
+  for(i=0; i<m; ++i)
+    printf("%.9g ", p[i]);
+  printf("-- errors %.9g %0.9g\n", jacTe_inf, p_eL2);
+}
+#endif
+
+    /* check for convergence */
+    if((jacTe_inf <= eps1)){
+      Dp_L2=0.0; /* no increment for p in this case */
+      stop=1;
+      break;
+    }
+
+   /* compute initial damping factor */
+    if(k==0){
+      for(i=0, tmp=LM_REAL_MIN; i<m; ++i)
+        if(diag_jacTjac[i]>tmp) tmp=diag_jacTjac[i]; /* find max diagonal element */
+      mu=tau*tmp;
+    }
+
+    /* determine increment using adaptive damping */
+
+    /* augment normal equations */
+    for(i=0; i<m; ++i)
+      jacTjac[i*m+i]+=mu;
+
+    /* solve augmented equations */
+#ifdef HAVE_LAPACK
+    /* 7 alternatives are available: LU, Cholesky + Cholesky with PLASMA, LDLt, 2 variants of QR decomposition and SVD.
+     * For matrices with dimensions of at least a few hundreds, the PLASMA implementation of Cholesky is the fastest.
+     * From the serial solvers, Cholesky is the fastest but might occasionally be inapplicable due to numerical round-off;
+     * QR is slower but more robust; SVD is the slowest but most robust; LU is quite robust but
+     * slower than LDLt; LDLt offers a good tradeoff between robustness and speed
+     */
+
+    issolved=AX_EQ_B_BK(jacTjac, jacTe, Dp, m); ++nlss; linsolver=AX_EQ_B_BK;
+    //issolved=AX_EQ_B_LU(jacTjac, jacTe, Dp, m); ++nlss; linsolver=AX_EQ_B_LU;
+    //issolved=AX_EQ_B_CHOL(jacTjac, jacTe, Dp, m); ++nlss; linsolver=AX_EQ_B_CHOL;
+#ifdef HAVE_PLASMA
+    //issolved=AX_EQ_B_PLASMA_CHOL(jacTjac, jacTe, Dp, m); ++nlss; linsolver=AX_EQ_B_PLASMA_CHOL;
+#endif
+    //issolved=AX_EQ_B_QR(jacTjac, jacTe, Dp, m); ++nlss; linsolver=AX_EQ_B_QR;
+    //issolved=AX_EQ_B_QRLS(jacTjac, jacTe, Dp, m, m); ++nlss; linsolver=(int (*)(LM_REAL *A, LM_REAL *B, LM_REAL *x, int m))AX_EQ_B_QRLS;
+    //issolved=AX_EQ_B_SVD(jacTjac, jacTe, Dp, m); ++nlss; linsolver=AX_EQ_B_SVD;
+#else
+    /* use the LU included with levmar */
+    issolved=AX_EQ_B_LU(jacTjac, jacTe, Dp, m); ++nlss; linsolver=AX_EQ_B_LU;
+#endif /* HAVE_LAPACK */
+
+    if(issolved){
+    /* compute p's new estimate and ||Dp||^2 */
+      for(i=0, Dp_L2=0.0; i<m; ++i){
+        pDp[i]=p[i] + (tmp=Dp[i]);
+        Dp_L2+=tmp*tmp;
+      }
+      //Dp_L2=sqrt(Dp_L2);
+
+      if(Dp_L2<=eps2_sq*p_L2){ /* relative change in p is small, stop */
+      //if(Dp_L2<=eps2*(p_L2 + eps2)){ /* relative change in p is small, stop */
+        stop=2;
+        break;
+      }
+
+      if(Dp_L2>=(p_L2+eps2)/(LM_CNST(EPSILON)*LM_CNST(EPSILON))){ /* almost singular */
+      //if(Dp_L2>=(p_L2+eps2)/LM_CNST(EPSILON)){ /* almost singular */
+        stop=4;
+        break;
+      }
+
+      (*func)(pDp, wrk, m, n, adata); ++nfev; /* evaluate function at p + Dp */
+      /* compute ||e(pDp)||_2 */
+      /* ### wrk2=x-wrk, pDp_eL2=||wrk2|| */
+#if 1
+      pDp_eL2=LEVMAR_L2NRMXMY(wrk2, x, wrk, n);
+#else
+      for(i=0, pDp_eL2=0.0; i<n; ++i){
+        wrk2[i]=tmp=x[i]-wrk[i];
+        pDp_eL2+=tmp*tmp;
+      }
+#endif
+      if(!LM_FINITE(pDp_eL2)){ /* sum of squares is not finite, most probably due to a user error.
+                                * This check makes sure that the loop terminates early in the case
+                                * of invalid input. Thanks to Steve Danauskas for suggesting it
+                                */
+
+        stop=7;
+        break;
+      }
+
+      dF=p_eL2-pDp_eL2;
+      if(updp || dF>0){ /* update jac */
+        for(i=0; i<n; ++i){
+          for(l=0, tmp=0.0; l<m; ++l)
+            tmp+=jac[i*m+l]*Dp[l]; /* (J * Dp)[i] */
+          tmp=(wrk[i] - hx[i] - tmp)/Dp_L2; /* (f(p+dp)[i] - f(p)[i] - (J * Dp)[i])/(dp^T*dp) */
+          for(j=0; j<m; ++j)
+            jac[i*m+j]+=tmp*Dp[j];
+        }
+        ++updjac;
+        newjac=1;
+      }
+
+      for(i=0, dL=0.0; i<m; ++i)
+        dL+=Dp[i]*(mu*Dp[i]+jacTe[i]);
+
+      if(dL>0.0 && dF>0.0){ /* reduction in error, increment is accepted */
+        tmp=(LM_CNST(2.0)*dF/dL-LM_CNST(1.0));
+        tmp=LM_CNST(1.0)-tmp*tmp*tmp;
+        mu=mu*( (tmp>=LM_CNST(ONE_THIRD))? tmp : LM_CNST(ONE_THIRD) );
+        nu=2;
+
+        for(i=0 ; i<m; ++i) /* update p's estimate */
+          p[i]=pDp[i];
+
+        for(i=0; i<n; ++i){ /* update e, hx and ||e||_2 */
+          e[i]=wrk2[i]; //x[i]-wrk[i];
+          hx[i]=wrk[i];
+        }
+        p_eL2=pDp_eL2;
+        updp=1;
+        continue;
+      }
+    }
+
+    /* if this point is reached, either the linear system could not be solved or
+     * the error did not reduce; in any case, the increment must be rejected
+     */
+
+    mu*=nu;
+    nu2=nu<<1; // 2*nu;
+    if(nu2<=nu){ /* nu has wrapped around (overflown). Thanks to Frank Jordan for spotting this case */
+      stop=5;
+      break;
+    }
+    nu=nu2;
+
+    for(i=0; i<m; ++i) /* restore diagonal J^T J entries */
+      jacTjac[i*m+i]=diag_jacTjac[i];
+  }
+
+  if(k>=itmax) stop=3;
+
+  for(i=0; i<m; ++i) /* restore diagonal J^T J entries */
+    jacTjac[i*m+i]=diag_jacTjac[i];
+
+  if(info){
+    info[0]=init_p_eL2;
+    info[1]=p_eL2;
+    info[2]=jacTe_inf;
+    info[3]=Dp_L2;
+    for(i=0, tmp=LM_REAL_MIN; i<m; ++i)
+      if(tmp<jacTjac[i*m+i]) tmp=jacTjac[i*m+i];
+    info[4]=mu/tmp;
+    info[5]=(LM_REAL)k;
+    info[6]=(LM_REAL)stop;
+    info[7]=(LM_REAL)nfev;
+    info[8]=(LM_REAL)njap;
+    info[9]=(LM_REAL)nlss;
+  }
+
+  /* covariance matrix */
+  if(covar){
+    LEVMAR_COVAR(jacTjac, covar, p_eL2, m, n);
+  }
+
+                                                               
+  if(freework) free(work);
+
+#ifdef LINSOLVERS_RETAIN_MEMORY
+  if(linsolver) (*linsolver)(NULL, NULL, NULL, 0);
+#endif
+
+  return (stop!=4 && stop!=7)?  k : LM_ERROR;
+}
+
+/* undefine everything. THIS MUST REMAIN AT THE END OF THE FILE */
+#undef LEVMAR_DER
+#undef LEVMAR_DIF
+#undef LEVMAR_FDIF_FORW_JAC_APPROX
+#undef LEVMAR_FDIF_CENT_JAC_APPROX
+#undef LEVMAR_COVAR
+#undef LEVMAR_TRANS_MAT_MAT_MULT
+#undef LEVMAR_L2NRMXMY
+#undef AX_EQ_B_LU
+#undef AX_EQ_B_CHOL
+#undef AX_EQ_B_PLASMA_CHOL
+#undef AX_EQ_B_QR
+#undef AX_EQ_B_QRLS
+#undef AX_EQ_B_SVD
+#undef AX_EQ_B_BK

levmar/lmbc.c

@@ -0,0 +1,87 @@
+/////////////////////////////////////////////////////////////////////////////////
+// 
+//  Levenberg - Marquardt non-linear minimization algorithm
+//  Copyright (C) 2004-05  Manolis Lourakis (lourakis at ics forth gr)
+//  Institute of Computer Science, Foundation for Research & Technology - Hellas
+//  Heraklion, Crete, Greece.
+//
+//  This program is free software; you can redistribute it and/or modify
+//  it under the terms of the GNU General Public License as published by
+//  the Free Software Foundation; either version 2 of the License, or
+//  (at your option) any later version.
+//
+//  This program is distributed in the hope that it will be useful,
+//  but WITHOUT ANY WARRANTY; without even the implied warranty of
+//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+//  GNU General Public License for more details.
+//
+/////////////////////////////////////////////////////////////////////////////////
+
+/******************************************************************************** 
+ * Box-constrained Levenberg-Marquardt nonlinear minimization. The same core code
+ * is used with appropriate #defines to derive single and double precision versions,
+ * see also lmbc_core.c
+ ********************************************************************************/
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <float.h>
+
+#include "levmar.h"
+#include "compiler.h"
+#include "misc.h"
+
+#define EPSILON       1E-12
+#define ONE_THIRD     0.3333333334 /* 1.0/3.0 */
+#define _LSITMAX_     150 /* max #iterations for line search */
+#define _POW_         2.1
+
+#if !defined(LM_DBL_PREC) && !defined(LM_SNGL_PREC)
+#error At least one of LM_DBL_PREC, LM_SNGL_PREC should be defined!
+#endif
+
+
+#ifdef LM_SNGL_PREC
+/* single precision (float) definitions */
+#define LM_REAL float
+#define LM_PREFIX s
+
+#define LM_REAL_MAX FLT_MAX
+#define LM_REAL_MIN -FLT_MAX
+
+#define LM_REAL_EPSILON FLT_EPSILON
+#define __SUBCNST(x) x##F
+#define LM_CNST(x) __SUBCNST(x) // force substitution
+
+#include "lmbc_core.c" // read in core code
+
+#undef LM_REAL
+#undef LM_PREFIX
+#undef LM_REAL_MAX
+#undef LM_REAL_MIN
+#undef LM_REAL_EPSILON
+#undef __SUBCNST
+#undef LM_CNST
+#endif /* LM_SNGL_PREC */
+
+#ifdef LM_DBL_PREC
+/* double precision definitions */
+#define LM_REAL double
+#define LM_PREFIX d
+
+#define LM_REAL_MAX DBL_MAX
+#define LM_REAL_MIN -DBL_MAX
+
+#define LM_REAL_EPSILON DBL_EPSILON
+#define LM_CNST(x) (x)
+
+#include "lmbc_core.c" // read in core code
+
+#undef LM_REAL
+#undef LM_PREFIX
+#undef LM_REAL_MAX
+#undef LM_REAL_MIN
+#undef LM_REAL_EPSILON
+#undef LM_CNST
+#endif /* LM_DBL_PREC */

levmar/lmblec.c

@@ -0,0 +1,87 @@
+/////////////////////////////////////////////////////////////////////////////////
+// 
+//  Levenberg - Marquardt non-linear minimization algorithm
+//  Copyright (C) 2004-06  Manolis Lourakis (lourakis at ics forth gr)
+//  Institute of Computer Science, Foundation for Research & Technology - Hellas
+//  Heraklion, Crete, Greece.
+//
+//  This program is free software; you can redistribute it and/or modify
+//  it under the terms of the GNU General Public License as published by
+//  the Free Software Foundation; either version 2 of the License, or
+//  (at your option) any later version.
+//
+//  This program is distributed in the hope that it will be useful,
+//  but WITHOUT ANY WARRANTY; without even the implied warranty of
+//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+//  GNU General Public License for more details.
+//
+/////////////////////////////////////////////////////////////////////////////////
+
+/******************************************************************************** 
+ * combined box and linear equation constraints Levenberg-Marquardt nonlinear
+ * minimization. The same core code is used with appropriate #defines to derive
+ * single and double precision versions, see also lmblec_core.c
+ ********************************************************************************/
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <float.h>
+
+#include "levmar.h"
+#include "misc.h"
+
+#ifndef HAVE_LAPACK
+
+#ifdef _MSC_VER
+#pragma message("Combined box and linearly constrained optimization requires LAPACK and was not compiled!")
+#else
+#warning Combined box and linearly constrained optimization requires LAPACK and was not compiled!
+#endif // _MSC_VER
+
+#else // LAPACK present
+
+#if !defined(LM_DBL_PREC) && !defined(LM_SNGL_PREC)
+#error At least one of LM_DBL_PREC, LM_SNGL_PREC should be defined!
+#endif
+
+
+#ifdef LM_SNGL_PREC
+/* single precision (float) definitions */
+#define LM_REAL float
+#define LM_PREFIX s
+
+#define LM_REAL_MAX FLT_MAX
+#define LM_REAL_MIN -FLT_MAX
+#define __SUBCNST(x) x##F
+#define LM_CNST(x) __SUBCNST(x) // force substitution
+
+#include "lmblec_core.c" // read in core code
+
+#undef LM_REAL
+#undef LM_PREFIX
+#undef LM_REAL_MAX
+#undef LM_REAL_MIN
+#undef __SUBCNST
+#undef LM_CNST
+#endif /* LM_SNGL_PREC */
+
+#ifdef LM_DBL_PREC
+/* double precision definitions */
+#define LM_REAL double
+#define LM_PREFIX d
+
+#define LM_REAL_MAX DBL_MAX
+#define LM_REAL_MIN -DBL_MAX
+#define LM_CNST(x) (x)
+
+#include "lmblec_core.c" // read in core code
+
+#undef LM_REAL
+#undef LM_PREFIX
+#undef LM_REAL_MAX
+#undef LM_REAL_MIN
+#undef LM_CNST
+#endif /* LM_DBL_PREC */
+
+#endif /* HAVE_LAPACK */

levmar/lmblec_core.c

@@ -0,0 +1,413 @@
+/////////////////////////////////////////////////////////////////////////////////
+// 
+//  Levenberg - Marquardt non-linear minimization algorithm
+//  Copyright (C) 2004-06  Manolis Lourakis (lourakis at ics forth gr)
+//  Institute of Computer Science, Foundation for Research & Technology - Hellas
+//  Heraklion, Crete, Greece.
+//
+//  This program is free software; you can redistribute it and/or modify
+//  it under the terms of the GNU General Public License as published by
+//  the Free Software Foundation; either version 2 of the License, or
+//  (at your option) any later version.
+//
+//  This program is distributed in the hope that it will be useful,
+//  but WITHOUT ANY WARRANTY; without even the implied warranty of
+//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+//  GNU General Public License for more details.
+//
+/////////////////////////////////////////////////////////////////////////////////
+
+/*******************************************************************************
+ * This file implements combined box and linear equation constraints.
+ *
+ * Note that the algorithm implementing linearly constrained minimization does
+ * so by a change in parameters that transforms the original program into an
+ * unconstrained one. To employ the same idea for implementing box & linear
+ * constraints would require the transformation of box constraints on the
+ * original parameters to box constraints for the new parameter set. This
+ * being impossible, a different approach is used here for finding the minimum.
+ * The trick is to remove the box constraints by augmenting the function to
+ * be fitted with penalty terms and then solve the resulting problem (which
+ * involves linear constrains only) with the functions in lmlec.c
+ *
+ * More specifically, for the constraint a<=x[i]<=b to hold, the term C[i]=
+ * (2*x[i]-(a+b))/(b-a) should be within [-1, 1]. This is enforced by adding
+ * the penalty term w[i]*max((C[i])^2-1, 0) to the objective function, where
+ * w[i] is a large weight. In the case of constraints of the form a<=x[i],
+ * the term C[i]=a-x[i] has to be non positive, thus the penalty term is
+ * w[i]*max(C[i], 0). If x[i]<=b, C[i]=x[i]-b has to be non negative and
+ * the penalty is w[i]*max(C[i], 0). The derivatives needed for the Jacobian
+ * are as follows:
+ * For the constraint a<=x[i]<=b: 4*(2*x[i]-(a+b))/(b-a)^2 if x[i] not in [a, b],
+ *                                0 otherwise
+ * For the constraint a<=x[i]: -1 if x[i]<=a, 0 otherwise
+ * For the constraint x[i]<=b: 1 if b<=x[i], 0 otherwise
+ *
+ * Note that for the above to work, the weights w[i] should be large enough;
+ * depending on your minimization problem, the default values might need some
+ * tweaking (see arg "wghts" below).
+ *******************************************************************************/
+
+#ifndef LM_REAL // not included by lmblec.c
+#error This file should not be compiled directly!
+#endif
+
+
+#define __MAX__(x, y)   (((x)>=(y))? (x) : (y))
+#define __BC_WEIGHT__   LM_CNST(1E+04)
+
+#define __BC_INTERVAL__ 0
+#define __BC_LOW__      1
+#define __BC_HIGH__     2
+
+/* precision-specific definitions */
+#define LEVMAR_BOX_CHECK LM_ADD_PREFIX(levmar_box_check)
+#define LMBLEC_DATA LM_ADD_PREFIX(lmblec_data)
+#define LMBLEC_FUNC LM_ADD_PREFIX(lmblec_func)
+#define LMBLEC_JACF LM_ADD_PREFIX(lmblec_jacf)
+#define LEVMAR_LEC_DER LM_ADD_PREFIX(levmar_lec_der)
+#define LEVMAR_LEC_DIF LM_ADD_PREFIX(levmar_lec_dif)
+#define LEVMAR_BLEC_DER LM_ADD_PREFIX(levmar_blec_der)
+#define LEVMAR_BLEC_DIF LM_ADD_PREFIX(levmar_blec_dif)
+#define LEVMAR_COVAR LM_ADD_PREFIX(levmar_covar)
+
+struct LMBLEC_DATA{
+  LM_REAL *x, *lb, *ub, *w;
+  int *bctype;
+  void (*func)(LM_REAL *p, LM_REAL *hx, int m, int n, void *adata);
+  void (*jacf)(LM_REAL *p, LM_REAL *jac, int m, int n, void *adata);
+  void *adata;
+};
+
+/* augmented measurements */
+static void LMBLEC_FUNC(LM_REAL *p, LM_REAL *hx, int m, int n, void *adata)
+{
+struct LMBLEC_DATA *data=(struct LMBLEC_DATA *)adata;
+int nn;
+register int i, j, *typ;
+register LM_REAL *lb, *ub, *w, tmp;
+
+  nn=n-m;
+  lb=data->lb;
+  ub=data->ub;
+  w=data->w;
+  typ=data->bctype;
+  (*(data->func))(p, hx, m, nn, data->adata);
+
+  for(i=nn, j=0; i<n; ++i, ++j){
+    switch(typ[j]){
+      case __BC_INTERVAL__:
+        tmp=(LM_CNST(2.0)*p[j]-(lb[j]+ub[j]))/(ub[j]-lb[j]);
+        hx[i]=w[j]*__MAX__(tmp*tmp-LM_CNST(1.0), LM_CNST(0.0));
+      break;
+
+      case __BC_LOW__:
+        hx[i]=w[j]*__MAX__(lb[j]-p[j], LM_CNST(0.0));
+      break;
+
+      case __BC_HIGH__:
+        hx[i]=w[j]*__MAX__(p[j]-ub[j], LM_CNST(0.0));
+      break;
+    }
+  }
+}
+
+/* augmented Jacobian */
+static void LMBLEC_JACF(LM_REAL *p, LM_REAL *jac, int m, int n, void *adata)
+{
+struct LMBLEC_DATA *data=(struct LMBLEC_DATA *)adata;
+int nn, *typ;
+register int i, j;
+register LM_REAL *lb, *ub, *w, tmp;
+
+  nn=n-m;
+  lb=data->lb;
+  ub=data->ub;
+  w=data->w;
+  typ=data->bctype;
+  (*(data->jacf))(p, jac, m, nn, data->adata);
+
+  /* clear all extra rows */
+  for(i=nn*m; i<n*m; ++i)
+    jac[i]=0.0;
+
+  for(i=nn, j=0; i<n; ++i, ++j){
+    switch(typ[j]){
+      case __BC_INTERVAL__:
+        if(lb[j]<=p[j] && p[j]<=ub[j])
+          continue; // corresp. jac element already 0
+
+        /* out of interval */
+        tmp=ub[j]-lb[j];
+        tmp=LM_CNST(4.0)*(LM_CNST(2.0)*p[j]-(lb[j]+ub[j]))/(tmp*tmp);
+        jac[i*m+j]=w[j]*tmp;
+      break;
+
+      case __BC_LOW__: // (lb[j]<=p[j])? 0.0 : -1.0;
+        if(lb[j]<=p[j])
+          continue; // corresp. jac element already 0
+
+        /* smaller than lower bound */
+        jac[i*m+j]=-w[j];
+      break;
+
+      case __BC_HIGH__: // (p[j]<=ub[j])? 0.0 : 1.0;
+        if(p[j]<=ub[j])
+          continue; // corresp. jac element already 0
+
+        /* greater than upper bound */
+        jac[i*m+j]=w[j];
+      break;
+    }
+  }
+}
+
+/* 
+ * This function seeks the parameter vector p that best describes the measurements
+ * vector x under box & linear constraints.
+ * More precisely, given a vector function  func : R^m --> R^n with n>=m,
+ * it finds p s.t. func(p) ~= x, i.e. the squared second order (i.e. L2) norm of
+ * e=x-func(p) is minimized under the constraints lb[i]<=p[i]<=ub[i] and A p=b;
+ * A is kxm, b kx1. Note that this function DOES NOT check the satisfiability of
+ * the specified box and linear equation constraints.
+ * If no lower bound constraint applies for p[i], use -DBL_MAX/-FLT_MAX for lb[i];
+ * If no upper bound constraint applies for p[i], use DBL_MAX/FLT_MAX for ub[i].
+ *
+ * This function requires an analytic Jacobian. In case the latter is unavailable,
+ * use LEVMAR_BLEC_DIF() bellow
+ *
+ * Returns the number of iterations (>=0) if successful, LM_ERROR if failed
+ *
+ * For more details on the algorithm implemented by this function, please refer to
+ * the comments in the top of this file.
+ *
+ */
+int LEVMAR_BLEC_DER(
+  void (*func)(LM_REAL *p, LM_REAL *hx, int m, int n, void *adata), /* functional relation describing measurements. A p \in R^m yields a \hat{x} \in  R^n */
+  void (*jacf)(LM_REAL *p, LM_REAL *j, int m, int n, void *adata),  /* function to evaluate the Jacobian \part x / \part p */ 
+  LM_REAL *p,         /* I/O: initial parameter estimates. On output has the estimated solution */
+  LM_REAL *x,         /* I: measurement vector. NULL implies a zero vector */
+  int m,              /* I: parameter vector dimension (i.e. #unknowns) */
+  int n,              /* I: measurement vector dimension */
+  LM_REAL *lb,        /* I: vector of lower bounds. If NULL, no lower bounds apply */
+  LM_REAL *ub,        /* I: vector of upper bounds. If NULL, no upper bounds apply */
+  LM_REAL *A,         /* I: constraints matrix, kxm */
+  LM_REAL *b,         /* I: right hand constraints vector, kx1 */
+  int k,              /* I: number of constraints (i.e. A's #rows) */
+  LM_REAL *wghts,     /* mx1 weights for penalty terms, defaults used if NULL */
+  int itmax,          /* I: maximum number of iterations */
+  LM_REAL opts[4],    /* I: minim. options [\mu, \epsilon1, \epsilon2, \epsilon3]. Respectively the scale factor for initial \mu,
+                       * stopping thresholds for ||J^T e||_inf, ||Dp||_2 and ||e||_2. Set to NULL for defaults to be used
+                       */
+  LM_REAL info[LM_INFO_SZ],
+					           /* O: information regarding the minimization. Set to NULL if don't care
+                      * info[0]= ||e||_2 at initial p.
+                      * info[1-4]=[ ||e||_2, ||J^T e||_inf,  ||Dp||_2, mu/max[J^T J]_ii ], all computed at estimated p.
+                      * info[5]= # iterations,
+                      * info[6]=reason for terminating: 1 - stopped by small gradient J^T e
+                      *                                 2 - stopped by small Dp
+                      *                                 3 - stopped by itmax
+                      *                                 4 - singular matrix. Restart from current p with increased mu 
+                      *                                 5 - no further error reduction is possible. Restart with increased mu
+                      *                                 6 - stopped by small ||e||_2
+                      *                                 7 - stopped by invalid (i.e. NaN or Inf) "func" values. This is a user error
+                      * info[7]= # function evaluations
+                      * info[8]= # Jacobian evaluations
+                      * info[9]= # linear systems solved, i.e. # attempts for reducing error
+                      */
+  LM_REAL *work,     /* working memory at least LM_BLEC_DER_WORKSZ() reals large, allocated if NULL */
+  LM_REAL *covar,    /* O: Covariance matrix corresponding to LS solution; mxm. Set to NULL if not needed. */
+  void *adata)       /* pointer to possibly additional data, passed uninterpreted to func & jacf.
+                      * Set to NULL if not needed
+                      */
+{
+  struct LMBLEC_DATA data;
+  int ret;
+  LM_REAL locinfo[LM_INFO_SZ];
+  register int i;
+
+  if(!jacf){
+    fprintf(stderr, RCAT("No function specified for computing the Jacobian in ", LEVMAR_BLEC_DER)
+      RCAT("().\nIf no such function is available, use ", LEVMAR_BLEC_DIF) RCAT("() rather than ", LEVMAR_BLEC_DER) "()\n");
+    return LM_ERROR;
+  }
+
+  if(!lb && !ub){
+    fprintf(stderr, RCAT(LCAT(LEVMAR_BLEC_DER, "(): lower and upper bounds for box constraints cannot be both NULL, use "),
+          LEVMAR_LEC_DER) "() in this case!\n");
+    return LM_ERROR;
+  }
+
+  if(!LEVMAR_BOX_CHECK(lb, ub, m)){
+    fprintf(stderr, LCAT(LEVMAR_BLEC_DER, "(): at least one lower bound exceeds the upper one\n"));
+    return LM_ERROR;
+  }
+
+  /* measurement vector needs to be extended by m */
+  if(x){ /* nonzero x */
+    data.x=(LM_REAL *)malloc((n+m)*sizeof(LM_REAL));
+    if(!data.x){
+      fprintf(stderr, LCAT(LEVMAR_BLEC_DER, "(): memory allocation request #1 failed\n"));
+      return LM_ERROR;
+    }
+
+    for(i=0; i<n; ++i)
+      data.x[i]=x[i];
+    for(i=n; i<n+m; ++i)
+      data.x[i]=0.0;
+  }
+  else
+    data.x=NULL;
+
+  data.w=(LM_REAL *)malloc(m*sizeof(LM_REAL) + m*sizeof(int)); /* should be arranged in that order for proper doubles alignment */
+  if(!data.w){
+    fprintf(stderr, LCAT(LEVMAR_BLEC_DER, "(): memory allocation request #2 failed\n"));
+    if(data.x) free(data.x);
+    return LM_ERROR;
+  }
+  data.bctype=(int *)(data.w+m);
+
+  /* note: at this point, one of lb, ub are not NULL */
+  for(i=0; i<m; ++i){
+    data.w[i]=(!wghts)? __BC_WEIGHT__ : wghts[i];
+    if(!lb) data.bctype[i]=__BC_HIGH__;
+    else if(!ub) data.bctype[i]=__BC_LOW__;
+    else if(ub[i]!=LM_REAL_MAX && lb[i]!=LM_REAL_MIN) data.bctype[i]=__BC_INTERVAL__;
+    else if(lb[i]!=LM_REAL_MIN) data.bctype[i]=__BC_LOW__;
+    else data.bctype[i]=__BC_HIGH__;
+  }
+
+  data.lb=lb;
+  data.ub=ub;
+  data.func=func;
+  data.jacf=jacf;
+  data.adata=adata;
+
+  if(!info) info=locinfo; /* make sure that LEVMAR_LEC_DER() is called with non-null info */
+  ret=LEVMAR_LEC_DER(LMBLEC_FUNC, LMBLEC_JACF, p, data.x, m, n+m, A, b, k, itmax, opts, info, work, covar, (void *)&data);
+
+  if(data.x) free(data.x);
+  free(data.w);
+
+  return ret;
+}
+
+/* Similar to the LEVMAR_BLEC_DER() function above, except that the Jacobian is approximated
+ * with the aid of finite differences (forward or central, see the comment for the opts argument)
+ */
+int LEVMAR_BLEC_DIF(
+  void (*func)(LM_REAL *p, LM_REAL *hx, int m, int n, void *adata), /* functional relation describing measurements. A p \in R^m yields a \hat{x} \in  R^n */
+  LM_REAL *p,         /* I/O: initial parameter estimates. On output has the estimated solution */
+  LM_REAL *x,         /* I: measurement vector. NULL implies a zero vector */
+  int m,              /* I: parameter vector dimension (i.e. #unknowns) */
+  int n,              /* I: measurement vector dimension */
+  LM_REAL *lb,        /* I: vector of lower bounds. If NULL, no lower bounds apply */
+  LM_REAL *ub,        /* I: vector of upper bounds. If NULL, no upper bounds apply */
+  LM_REAL *A,         /* I: constraints matrix, kxm */
+  LM_REAL *b,         /* I: right hand constraints vector, kx1 */
+  int k,              /* I: number of constraints (i.e. A's #rows) */
+  LM_REAL *wghts,     /* mx1 weights for penalty terms, defaults used if NULL */
+  int itmax,          /* I: maximum number of iterations */
+  LM_REAL opts[5],    /* I: opts[0-3] = minim. options [\mu, \epsilon1, \epsilon2, \epsilon3, \delta]. Respectively the
+                       * scale factor for initial \mu, stopping thresholds for ||J^T e||_inf, ||Dp||_2 and ||e||_2 and
+                       * the step used in difference approximation to the Jacobian. Set to NULL for defaults to be used.
+                       * If \delta<0, the Jacobian is approximated with central differences which are more accurate
+                       * (but slower!) compared to the forward differences employed by default. 
+                       */
+  LM_REAL info[LM_INFO_SZ],
+					           /* O: information regarding the minimization. Set to NULL if don't care
+                      * info[0]= ||e||_2 at initial p.
+                      * info[1-4]=[ ||e||_2, ||J^T e||_inf,  ||Dp||_2, mu/max[J^T J]_ii ], all computed at estimated p.
+                      * info[5]= # iterations,
+                      * info[6]=reason for terminating: 1 - stopped by small gradient J^T e
+                      *                                 2 - stopped by small Dp
+                      *                                 3 - stopped by itmax
+                      *                                 4 - singular matrix. Restart from current p with increased mu 
+                      *                                 5 - no further error reduction is possible. Restart with increased mu
+                      *                                 6 - stopped by small ||e||_2
+                      *                                 7 - stopped by invalid (i.e. NaN or Inf) "func" values. This is a user error
+                      * info[7]= # function evaluations
+                      * info[8]= # Jacobian evaluations
+                      * info[9]= # linear systems solved, i.e. # attempts for reducing error
+                      */
+  LM_REAL *work,     /* working memory at least LM_BLEC_DIF_WORKSZ() reals large, allocated if NULL */
+  LM_REAL *covar,    /* O: Covariance matrix corresponding to LS solution; mxm. Set to NULL if not needed. */
+  void *adata)       /* pointer to possibly additional data, passed uninterpreted to func.
+                      * Set to NULL if not needed
+                      */
+{
+  struct LMBLEC_DATA data;
+  int ret;
+  register int i;
+  LM_REAL locinfo[LM_INFO_SZ];
+
+  if(!lb && !ub){
+    fprintf(stderr, RCAT(LCAT(LEVMAR_BLEC_DIF, "(): lower and upper bounds for box constraints cannot be both NULL, use "),
+          LEVMAR_LEC_DIF) "() in this case!\n");
+    return LM_ERROR;
+  }
+
+  if(!LEVMAR_BOX_CHECK(lb, ub, m)){
+    fprintf(stderr, LCAT(LEVMAR_BLEC_DER, "(): at least one lower bound exceeds the upper one\n"));
+    return LM_ERROR;
+  }
+
+  /* measurement vector needs to be extended by m */
+  if(x){ /* nonzero x */
+    data.x=(LM_REAL *)malloc((n+m)*sizeof(LM_REAL));
+    if(!data.x){
+      fprintf(stderr, LCAT(LEVMAR_BLEC_DER, "(): memory allocation request #1 failed\n"));
+      return LM_ERROR;
+    }
+
+    for(i=0; i<n; ++i)
+      data.x[i]=x[i];
+    for(i=n; i<n+m; ++i)
+      data.x[i]=0.0;
+  }
+  else
+    data.x=NULL;
+
+  data.w=(LM_REAL *)malloc(m*sizeof(LM_REAL) + m*sizeof(int)); /* should be arranged in that order for proper doubles alignment */
+  if(!data.w){
+    fprintf(stderr, LCAT(LEVMAR_BLEC_DER, "(): memory allocation request #2 failed\n"));
+    if(data.x) free(data.x);
+    return LM_ERROR;
+  }
+  data.bctype=(int *)(data.w+m);
+
+  /* note: at this point, one of lb, ub are not NULL */
+  for(i=0; i<m; ++i){
+    data.w[i]=(!wghts)? __BC_WEIGHT__ : wghts[i];
+    if(!lb) data.bctype[i]=__BC_HIGH__;
+    else if(!ub) data.bctype[i]=__BC_LOW__;
+    else if(ub[i]!=LM_REAL_MAX && lb[i]!=LM_REAL_MIN) data.bctype[i]=__BC_INTERVAL__;
+    else if(lb[i]!=LM_REAL_MIN) data.bctype[i]=__BC_LOW__;
+    else data.bctype[i]=__BC_HIGH__;
+  }
+
+  data.lb=lb;
+  data.ub=ub;
+  data.func=func;
+  data.jacf=NULL;
+  data.adata=adata;
+
+  if(!info) info=locinfo; /* make sure that LEVMAR_LEC_DIF() is called with non-null info */
+  ret=LEVMAR_LEC_DIF(LMBLEC_FUNC, p, data.x, m, n+m, A, b, k, itmax, opts, info, work, covar, (void *)&data);
+
+  if(data.x) free(data.x);
+  free(data.w);
+
+  return ret;
+}
+
+/* undefine all. THIS MUST REMAIN AT THE END OF THE FILE */
+#undef LEVMAR_BOX_CHECK
+#undef LMBLEC_DATA
+#undef LMBLEC_FUNC
+#undef LMBLEC_JACF
+#undef LEVMAR_COVAR
+#undef LEVMAR_LEC_DER
+#undef LEVMAR_LEC_DIF
+#undef LEVMAR_BLEC_DER
+#undef LEVMAR_BLEC_DIF

levmar/lmbleic.c

@@ -0,0 +1,89 @@
+/////////////////////////////////////////////////////////////////////////////////
+// 
+//  Levenberg - Marquardt non-linear minimization algorithm
+//  Copyright (C) 2009  Manolis Lourakis (lourakis at ics forth gr)
+//  Institute of Computer Science, Foundation for Research & Technology - Hellas
+//  Heraklion, Crete, Greece.
+//
+//  This program is free software; you can redistribute it and/or modify
+//  it under the terms of the GNU General Public License as published by
+//  the Free Software Foundation; either version 2 of the License, or
+//  (at your option) any later version.
+//
+//  This program is distributed in the hope that it will be useful,
+//  but WITHOUT ANY WARRANTY; without even the implied warranty of
+//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+//  GNU General Public License for more details.
+//
+/////////////////////////////////////////////////////////////////////////////////
+
+/*******************************************************************************
+ * Wrappers for linear inequality constrained Levenberg-Marquardt minimization.
+ * The same core code is used with appropriate #defines to derive single and
+ * double precision versions, see also lmbleic_core.c
+ *******************************************************************************/
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <float.h>
+
+#include "levmar.h"
+#include "misc.h"
+
+
+#ifndef HAVE_LAPACK
+
+#ifdef _MSC_VER
+#pragma message("Linear inequalities constrained optimization requires LAPACK and was not compiled!")
+#else
+#warning Linear inequalities constrained optimization requires LAPACK and was not compiled!
+#endif // _MSC_VER
+
+#else // LAPACK present
+
+#if !defined(LM_DBL_PREC) && !defined(LM_SNGL_PREC)
+#error At least one of LM_DBL_PREC, LM_SNGL_PREC should be defined!
+#endif
+
+
+#ifdef LM_SNGL_PREC
+/* single precision (float) definitions */
+#define LM_REAL float
+#define LM_PREFIX s
+
+#define LM_REAL_MAX FLT_MAX
+#define LM_REAL_MIN -FLT_MAX
+#define __SUBCNST(x) x##F
+#define LM_CNST(x) __SUBCNST(x) // force substitution
+
+#include "lmbleic_core.c" // read in core code
+
+#undef LM_REAL
+#undef LM_PREFIX
+#undef LM_REAL_MAX
+#undef LM_REAL_MIN
+#undef __SUBCNST
+#undef LM_CNST
+#endif /* LM_SNGL_PREC */
+
+#ifdef LM_DBL_PREC
+/* double precision definitions */
+#define LM_REAL double
+#define LM_PREFIX d
+
+#define LM_REAL_MAX DBL_MAX
+#define LM_REAL_MIN -DBL_MAX
+#define LM_CNST(x) (x)
+
+#include "lmbleic_core.c" // read in core code
+
+#undef LM_REAL
+#undef LM_PREFIX
+#undef LM_REAL_MAX
+#undef LM_REAL_MIN
+#undef LM_CNST
+#endif /* LM_DBL_PREC */
+
+#endif /* HAVE_LAPACK */
+

levmar/lmbleic_core.c

@@ -0,0 +1,506 @@
+/////////////////////////////////////////////////////////////////////////////////
+// 
+//  Levenberg - Marquardt non-linear minimization algorithm
+//  Copyright (C) 2009  Manolis Lourakis (lourakis at ics forth gr)
+//  Institute of Computer Science, Foundation for Research & Technology - Hellas
+//  Heraklion, Crete, Greece.
+//
+//  This program is free software; you can redistribute it and/or modify
+//  it under the terms of the GNU General Public License as published by
+//  the Free Software Foundation; either version 2 of the License, or
+//  (at your option) any later version.
+//
+//  This program is distributed in the hope that it will be useful,
+//  but WITHOUT ANY WARRANTY; without even the implied warranty of
+//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+//  GNU General Public License for more details.
+//
+/////////////////////////////////////////////////////////////////////////////////
+
+#ifndef LM_REAL // not included by lmbleic.c
+#error This file should not be compiled directly!
+#endif
+
+
+/* precision-specific definitions */
+#define LMBLEIC_DATA LM_ADD_PREFIX(lmbleic_data)
+#define LMBLEIC_ELIM LM_ADD_PREFIX(lmbleic_elim)
+#define LMBLEIC_FUNC LM_ADD_PREFIX(lmbleic_func)
+#define LMBLEIC_JACF LM_ADD_PREFIX(lmbleic_jacf)
+#define LEVMAR_BLEIC_DER LM_ADD_PREFIX(levmar_bleic_der)
+#define LEVMAR_BLEIC_DIF LM_ADD_PREFIX(levmar_bleic_dif)
+#define LEVMAR_BLIC_DER LM_ADD_PREFIX(levmar_blic_der)
+#define LEVMAR_BLIC_DIF LM_ADD_PREFIX(levmar_blic_dif)
+#define LEVMAR_LEIC_DER LM_ADD_PREFIX(levmar_leic_der)
+#define LEVMAR_LEIC_DIF LM_ADD_PREFIX(levmar_leic_dif)
+#define LEVMAR_LIC_DER LM_ADD_PREFIX(levmar_lic_der)
+#define LEVMAR_LIC_DIF LM_ADD_PREFIX(levmar_lic_dif)
+#define LEVMAR_BLEC_DER LM_ADD_PREFIX(levmar_blec_der)
+#define LEVMAR_BLEC_DIF LM_ADD_PREFIX(levmar_blec_dif)
+#define LEVMAR_TRANS_MAT_MAT_MULT LM_ADD_PREFIX(levmar_trans_mat_mat_mult)
+#define LEVMAR_COVAR LM_ADD_PREFIX(levmar_covar)
+#define LEVMAR_FDIF_FORW_JAC_APPROX LM_ADD_PREFIX(levmar_fdif_forw_jac_approx)
+
+struct LMBLEIC_DATA{
+  LM_REAL *jac;
+  int nineqcnstr; // #inequality constraints
+  void (*func)(LM_REAL *p, LM_REAL *hx, int m, int n, void *adata);
+  void (*jacf)(LM_REAL *p, LM_REAL *jac, int m, int n, void *adata);
+  void *adata;
+};
+
+
+/* wrapper ensuring that the user-supplied function is called with the right number of variables (i.e. m) */
+static void LMBLEIC_FUNC(LM_REAL *pext, LM_REAL *hx, int mm, int n, void *adata)
+{
+struct LMBLEIC_DATA *data=(struct LMBLEIC_DATA *)adata;
+int m;
+
+  m=mm-data->nineqcnstr;
+  (*(data->func))(pext, hx, m, n, data->adata);
+}
+
+
+/* wrapper for computing the Jacobian at pext. The Jacobian is nxmm */
+static void LMBLEIC_JACF(LM_REAL *pext, LM_REAL *jacext, int mm, int n, void *adata)
+{
+struct LMBLEIC_DATA *data=(struct LMBLEIC_DATA *)adata;
+int m;
+register int i, j;
+LM_REAL *jac, *jacim, *jacextimm;
+
+  m=mm-data->nineqcnstr;
+  jac=data->jac;
+
+  (*(data->jacf))(pext, jac, m, n, data->adata);
+
+  for(i=0; i<n; ++i){
+    jacextimm=jacext+i*mm;
+    jacim=jac+i*m;
+    for(j=0; j<m; ++j)
+      jacextimm[j]=jacim[j]; //jacext[i*mm+j]=jac[i*m+j];
+
+    for(j=m; j<mm; ++j)
+      jacextimm[j]=0.0; //jacext[i*mm+j]=0.0;
+  }
+}
+
+
+/* 
+ * This function is similar to LEVMAR_DER except that the minimization is
+ * performed subject to the box constraints lb[i]<=p[i]<=ub[i], the linear
+ * equation constraints A*p=b, A being k1xm, b k1x1, and the linear inequality
+ * constraints C*p>=d, C being k2xm, d k2x1. 
+ *
+ * The inequalities are converted to equations by introducing surplus variables,
+ * i.e. c^T*p >= d becomes c^T*p - y = d, with y>=0. To transform all inequalities
+ * to equations, a total of k2 surplus variables are introduced; a problem with only
+ * box and linear constraints results then and is solved with LEVMAR_BLEC_DER()
+ * Note that opposite direction inequalities should be converted to the desired
+ * direction by negating, i.e. c^T*p <= d becomes -c^T*p >= -d
+ *
+ * This function requires an analytic Jacobian. In case the latter is unavailable,
+ * use LEVMAR_BLEIC_DIF() bellow
+ *
+ */
+int LEVMAR_BLEIC_DER(
+  void (*func)(LM_REAL *p, LM_REAL *hx, int m, int n, void *adata), /* functional relation describing measurements. A p \in R^m yields a \hat{x} \in  R^n */
+  void (*jacf)(LM_REAL *p, LM_REAL *j, int m, int n, void *adata),  /* function to evaluate the Jacobian \part x / \part p */ 
+  LM_REAL *p,         /* I/O: initial parameter estimates. On output has the estimated solution */
+  LM_REAL *x,         /* I: measurement vector. NULL implies a zero vector */
+  int m,              /* I: parameter vector dimension (i.e. #unknowns) */
+  int n,              /* I: measurement vector dimension */
+  LM_REAL *lb,        /* I: vector of lower bounds. If NULL, no lower bounds apply */
+  LM_REAL *ub,        /* I: vector of upper bounds. If NULL, no upper bounds apply */
+  LM_REAL *A,         /* I: equality constraints matrix, k1xm. If NULL, no linear equation constraints apply */
+  LM_REAL *b,         /* I: right hand constraints vector, k1x1 */
+  int k1,             /* I: number of constraints (i.e. A's #rows) */
+  LM_REAL *C,         /* I: inequality constraints matrix, k2xm */
+  LM_REAL *d,         /* I: right hand constraints vector, k2x1 */
+  int k2,             /* I: number of inequality constraints (i.e. C's #rows) */
+  int itmax,          /* I: maximum number of iterations */
+  LM_REAL opts[4],    /* I: minim. options [\mu, \epsilon1, \epsilon2, \epsilon3]. Respectively the scale factor for initial \mu,
+                       * stopping thresholds for ||J^T e||_inf, ||Dp||_2 and ||e||_2. Set to NULL for defaults to be used
+                       */
+  LM_REAL info[LM_INFO_SZ],
+					           /* O: information regarding the minimization. Set to NULL if don't care
+                      * info[0]= ||e||_2 at initial p.
+                      * info[1-4]=[ ||e||_2, ||J^T e||_inf,  ||Dp||_2, mu/max[J^T J]_ii ], all computed at estimated p.
+                      * info[5]= # iterations,
+                      * info[6]=reason for terminating: 1 - stopped by small gradient J^T e
+                      *                                 2 - stopped by small Dp
+                      *                                 3 - stopped by itmax
+                      *                                 4 - singular matrix. Restart from current p with increased mu 
+                      *                                 5 - no further error reduction is possible. Restart with increased mu
+                      *                                 6 - stopped by small ||e||_2
+                      *                                 7 - stopped by invalid (i.e. NaN or Inf) "func" values. This is a user error
+                      * info[7]= # function evaluations
+                      * info[8]= # Jacobian evaluations
+                      * info[9]= # linear systems solved, i.e. # attempts for reducing error
+                      */
+  LM_REAL *work,     /* working memory at least LM_BLEIC_DER_WORKSZ() reals large, allocated if NULL */
+  LM_REAL *covar,    /* O: Covariance matrix corresponding to LS solution; mxm. Set to NULL if not needed. */
+  void *adata)       /* pointer to possibly additional data, passed uninterpreted to func & jacf.
+                      * Set to NULL if not needed
+                      */
+{
+  struct LMBLEIC_DATA data;
+  LM_REAL *ptr, *pext, *Aext, *bext, *covext; /* corresponding to p, A, b, covar for the full set of variables;
+                                                 pext=[p, surplus], pext is mm, Aext is (k1+k2)xmm, bext (k1+k2), covext is mmxmm
+                                               */
+  LM_REAL *lbext, *ubext; // corresponding to lb, ub for the full set of variables
+  int mm, ret, k12;
+  register int i, j, ii;
+  register LM_REAL tmp;
+  LM_REAL locinfo[LM_INFO_SZ];
+
+  if(!jacf){
+    fprintf(stderr, RCAT("No function specified for computing the Jacobian in ", LEVMAR_BLEIC_DER)
+      RCAT("().\nIf no such function is available, use ", LEVMAR_BLEIC_DIF) RCAT("() rather than ", LEVMAR_BLEIC_DER) "()\n");
+    return LM_ERROR;
+  }
+
+  if(!C || !d){
+    fprintf(stderr, RCAT(LCAT(LEVMAR_BLEIC_DER, "(): missing inequality constraints, use "), LEVMAR_BLEC_DER) "() in this case!\n");
+    return LM_ERROR;
+  }
+
+  if(!A || !b) k1=0; // sanity check
+
+  mm=m+k2;
+
+  if(n<m-k1){
+    fprintf(stderr, LCAT(LEVMAR_BLEIC_DER, "(): cannot solve a problem with fewer measurements + equality constraints [%d + %d] than unknowns [%d]\n"), n, k1, m);
+    return LM_ERROR;
+  }
+
+  k12=k1+k2;
+  ptr=(LM_REAL *)malloc((3*mm + k12*mm + k12 + n*m + (covar? mm*mm : 0))*sizeof(LM_REAL));
+  if(!ptr){
+    fprintf(stderr, LCAT(LEVMAR_BLEIC_DER, "(): memory allocation request failed\n"));
+    return LM_ERROR;
+  }
+  pext=ptr;
+  lbext=pext+mm;
+  ubext=lbext+mm;
+  Aext=ubext+mm;
+  bext=Aext+k12*mm;
+  data.jac=bext+k12;
+  covext=covar? data.jac+n*m : NULL;
+  data.nineqcnstr=k2;
+  data.func=func;
+  data.jacf=jacf;
+  data.adata=adata;
+
+  /* compute y s.t. C*p - y=d, i.e. y=C*p-d.
+   * y is stored in the last k2 elements of pext
+   */
+  for(i=0; i<k2; ++i){
+    for(j=0, tmp=0.0; j<m; ++j)
+      tmp+=C[i*m+j]*p[j];
+    pext[j=i+m]=tmp-d[i];
+
+    /* surplus variables must be >=0 */
+    lbext[j]=0.0;
+    ubext[j]=LM_REAL_MAX;
+  }
+  /* set the first m elements of pext equal to p */
+  for(i=0; i<m; ++i){
+    pext[i]=p[i];
+    lbext[i]=lb? lb[i] : LM_REAL_MIN;
+    ubext[i]=ub? ub[i] : LM_REAL_MAX;
+  }
+
+  /* setup the constraints matrix */
+  /* original linear equation constraints */
+  for(i=0; i<k1; ++i){
+    for(j=0; j<m; ++j)
+      Aext[i*mm+j]=A[i*m+j];
+
+    for(j=m; j<mm; ++j)
+      Aext[i*mm+j]=0.0;
+
+    bext[i]=b[i];
+  }
+  /* linear equation constraints resulting from surplus variables */
+  for(i=0, ii=k1; i<k2; ++i, ++ii){
+    for(j=0; j<m; ++j)
+      Aext[ii*mm+j]=C[i*m+j];
+
+    for(j=m; j<mm; ++j)
+      Aext[ii*mm+j]=0.0;
+
+    Aext[ii*mm+m+i]=-1.0;
+
+    bext[ii]=d[i];
+  }
+
+  if(!info) info=locinfo; /* make sure that LEVMAR_BLEC_DER() is called with non-null info */
+  /* note that the default weights for the penalty terms are being used below */
+  ret=LEVMAR_BLEC_DER(LMBLEIC_FUNC, LMBLEIC_JACF, pext, x, mm, n, lbext, ubext, Aext, bext, k12, NULL, itmax, opts, info, work, covext, (void *)&data);
+
+  /* copy back the minimizer */
+  for(i=0; i<m; ++i)
+    p[i]=pext[i];
+
+#if 0
+printf("Surplus variables for the minimizer:\n");
+for(i=m; i<mm; ++i)
+  printf("%g ", pext[i]);
+printf("\n\n");
+#endif
+
+  if(covar){
+    for(i=0; i<m; ++i){
+      for(j=0; j<m; ++j)
+        covar[i*m+j]=covext[i*mm+j];
+    }
+  }
+
+  free(ptr);
+
+  return ret;
+}
+
+/* Similar to the LEVMAR_BLEIC_DER() function above, except that the Jacobian is approximated
+ * with the aid of finite differences (forward or central, see the comment for the opts argument)
+ */
+int LEVMAR_BLEIC_DIF(
+  void (*func)(LM_REAL *p, LM_REAL *hx, int m, int n, void *adata), /* functional relation describing measurements. A p \in R^m yields a \hat{x} \in  R^n */
+  LM_REAL *p,         /* I/O: initial parameter estimates. On output has the estimated solution */
+  LM_REAL *x,         /* I: measurement vector. NULL implies a zero vector */
+  int m,              /* I: parameter vector dimension (i.e. #unknowns) */
+  int n,              /* I: measurement vector dimension */
+  LM_REAL *lb,        /* I: vector of lower bounds. If NULL, no lower bounds apply */
+  LM_REAL *ub,        /* I: vector of upper bounds. If NULL, no upper bounds apply */
+  LM_REAL *A,         /* I: equality constraints matrix, k1xm. If NULL, no linear equation constraints apply */
+  LM_REAL *b,         /* I: right hand constraints vector, k1x1 */
+  int k1,             /* I: number of constraints (i.e. A's #rows) */
+  LM_REAL *C,         /* I: inequality constraints matrix, k2xm */
+  LM_REAL *d,         /* I: right hand constraints vector, k2x1 */
+  int k2,             /* I: number of inequality constraints (i.e. C's #rows) */
+  int itmax,          /* I: maximum number of iterations */
+  LM_REAL opts[5],    /* I: opts[0-3] = minim. options [\mu, \epsilon1, \epsilon2, \epsilon3, \delta]. Respectively the
+                       * scale factor for initial \mu, stopping thresholds for ||J^T e||_inf, ||Dp||_2 and ||e||_2 and
+                       * the step used in difference approximation to the Jacobian. Set to NULL for defaults to be used.
+                       * If \delta<0, the Jacobian is approximated with central differences which are more accurate
+                       * (but slower!) compared to the forward differences employed by default. 
+                       */
+  LM_REAL info[LM_INFO_SZ],
+					           /* O: information regarding the minimization. Set to NULL if don't care
+                      * info[0]= ||e||_2 at initial p.
+                      * info[1-4]=[ ||e||_2, ||J^T e||_inf,  ||Dp||_2, mu/max[J^T J]_ii ], all computed at estimated p.
+                      * info[5]= # iterations,
+                      * info[6]=reason for terminating: 1 - stopped by small gradient J^T e
+                      *                                 2 - stopped by small Dp
+                      *                                 3 - stopped by itmax
+                      *                                 4 - singular matrix. Restart from current p with increased mu 
+                      *                                 5 - no further error reduction is possible. Restart with increased mu
+                      *                                 6 - stopped by small ||e||_2
+                      *                                 7 - stopped by invalid (i.e. NaN or Inf) "func" values. This is a user error
+                      * info[7]= # function evaluations
+                      * info[8]= # Jacobian evaluations
+                      * info[9]= # linear systems solved, i.e. # attempts for reducing error
+                      */
+  LM_REAL *work,     /* working memory at least LM_BLEIC_DIF_WORKSZ() reals large, allocated if NULL */
+  LM_REAL *covar,    /* O: Covariance matrix corresponding to LS solution; mxm. Set to NULL if not needed. */
+  void *adata)       /* pointer to possibly additional data, passed uninterpreted to func.
+                      * Set to NULL if not needed
+                      */
+{
+  struct LMBLEIC_DATA data;
+  LM_REAL *ptr, *pext, *Aext, *bext, *covext; /* corresponding to p, A, b, covar for the full set of variables;
+                                                 pext=[p, surplus], pext is mm, Aext is (k1+k2)xmm, bext (k1+k2), covext is mmxmm
+                                               */
+  LM_REAL *lbext, *ubext; // corresponding to lb, ub for the full set of variables
+  int mm, ret, k12;
+  register int i, j, ii;
+  register LM_REAL tmp;
+  LM_REAL locinfo[LM_INFO_SZ];
+
+  if(!C || !d){
+    fprintf(stderr, RCAT(LCAT(LEVMAR_BLEIC_DIF, "(): missing inequality constraints, use "), LEVMAR_BLEC_DIF) "() in this case!\n");
+    return LM_ERROR;
+  }
+  if(!A || !b) k1=0; // sanity check
+
+  mm=m+k2;
+
+  if(n<m-k1){
+    fprintf(stderr, LCAT(LEVMAR_BLEIC_DIF, "(): cannot solve a problem with fewer measurements + equality constraints [%d + %d] than unknowns [%d]\n"), n, k1, m);
+    return LM_ERROR;
+  }
+
+  k12=k1+k2;
+  ptr=(LM_REAL *)malloc((3*mm + k12*mm + k12 + (covar? mm*mm : 0))*sizeof(LM_REAL));
+  if(!ptr){
+    fprintf(stderr, LCAT(LEVMAR_BLEIC_DIF, "(): memory allocation request failed\n"));
+    return LM_ERROR;
+  }
+  pext=ptr;
+  lbext=pext+mm;
+  ubext=lbext+mm;
+  Aext=ubext+mm;
+  bext=Aext+k12*mm;
+  data.jac=NULL;
+  covext=covar? bext+k12 : NULL;
+  data.nineqcnstr=k2;
+  data.func=func;
+  data.jacf=NULL;
+  data.adata=adata;
+
+  /* compute y s.t. C*p - y=d, i.e. y=C*p-d.
+   * y is stored in the last k2 elements of pext
+   */
+  for(i=0; i<k2; ++i){
+    for(j=0, tmp=0.0; j<m; ++j)
+      tmp+=C[i*m+j]*p[j];
+    pext[j=i+m]=tmp-d[i];
+
+    /* surplus variables must be >=0 */
+    lbext[j]=0.0;
+    ubext[j]=LM_REAL_MAX;
+  }
+  /* set the first m elements of pext equal to p */
+  for(i=0; i<m; ++i){
+    pext[i]=p[i];
+    lbext[i]=lb? lb[i] : LM_REAL_MIN; 
+    ubext[i]=ub? ub[i] : LM_REAL_MAX;
+  }
+
+  /* setup the constraints matrix */
+  /* original linear equation constraints */
+  for(i=0; i<k1; ++i){
+    for(j=0; j<m; ++j)
+      Aext[i*mm+j]=A[i*m+j];
+
+    for(j=m; j<mm; ++j)
+      Aext[i*mm+j]=0.0;
+
+    bext[i]=b[i];
+  }
+  /* linear equation constraints resulting from surplus variables */
+  for(i=0, ii=k1; i<k2; ++i, ++ii){
+    for(j=0; j<m; ++j)
+      Aext[ii*mm+j]=C[i*m+j];
+
+    for(j=m; j<mm; ++j)
+      Aext[ii*mm+j]=0.0;
+
+    Aext[ii*mm+m+i]=-1.0;
+
+    bext[ii]=d[i];
+  }
+
+  if(!info) info=locinfo; /* make sure that LEVMAR_BLEC_DIF() is called with non-null info */
+  /* note that the default weights for the penalty terms are being used below */
+  ret=LEVMAR_BLEC_DIF(LMBLEIC_FUNC, pext, x, mm, n, lbext, ubext, Aext, bext, k12, NULL, itmax, opts, info, work, covext, (void *)&data);
+
+  /* copy back the minimizer */
+  for(i=0; i<m; ++i)
+    p[i]=pext[i];
+
+#if 0
+printf("Surplus variables for the minimizer:\n");
+for(i=m; i<mm; ++i)
+  printf("%g ", pext[i]);
+printf("\n\n");
+#endif
+
+  if(covar){
+    for(i=0; i<m; ++i){
+      for(j=0; j<m; ++j)
+        covar[i*m+j]=covext[i*mm+j];
+    }
+  }
+
+  free(ptr);
+
+  return ret;
+}
+
+
+/* convenience wrappers to LEVMAR_BLEIC_DER/LEVMAR_BLEIC_DIF */
+
+/* box & linear inequality constraints */
+int LEVMAR_BLIC_DER(
+  void (*func)(LM_REAL *p, LM_REAL *hx, int m, int n, void *adata),
+  void (*jacf)(LM_REAL *p, LM_REAL *j, int m, int n, void *adata),
+  LM_REAL *p, LM_REAL *x, int m, int n,
+  LM_REAL *lb, LM_REAL *ub,
+  LM_REAL *C, LM_REAL *d, int k2,
+  int itmax, LM_REAL opts[4], LM_REAL info[LM_INFO_SZ], LM_REAL *work, LM_REAL *covar, void *adata)
+{
+  return LEVMAR_BLEIC_DER(func, jacf, p, x, m, n, lb, ub, NULL, NULL, 0, C, d, k2, itmax, opts, info, work, covar, adata);
+}
+
+int LEVMAR_BLIC_DIF(
+  void (*func)(LM_REAL *p, LM_REAL *hx, int m, int n, void *adata),
+  LM_REAL *p, LM_REAL *x, int m, int n,
+  LM_REAL *lb, LM_REAL *ub,
+  LM_REAL *C, LM_REAL *d, int k2,
+  int itmax, LM_REAL opts[5], LM_REAL info[LM_INFO_SZ], LM_REAL *work, LM_REAL *covar, void *adata)
+{
+  return LEVMAR_BLEIC_DIF(func, p, x, m, n, lb, ub, NULL, NULL, 0, C, d, k2, itmax, opts, info, work, covar, adata);
+}
+
+/* linear equation & inequality constraints */
+int LEVMAR_LEIC_DER(
+  void (*func)(LM_REAL *p, LM_REAL *hx, int m, int n, void *adata),
+  void (*jacf)(LM_REAL *p, LM_REAL *j, int m, int n, void *adata),
+  LM_REAL *p, LM_REAL *x, int m, int n,
+  LM_REAL *A, LM_REAL *b, int k1,
+  LM_REAL *C, LM_REAL *d, int k2,
+  int itmax, LM_REAL opts[4], LM_REAL info[LM_INFO_SZ], LM_REAL *work, LM_REAL *covar, void *adata)
+{
+  return LEVMAR_BLEIC_DER(func, jacf, p, x, m, n, NULL, NULL, A, b, k1, C, d, k2, itmax, opts, info, work, covar, adata);
+}
+
+int LEVMAR_LEIC_DIF(
+  void (*func)(LM_REAL *p, LM_REAL *hx, int m, int n, void *adata),
+  LM_REAL *p, LM_REAL *x, int m, int n,
+  LM_REAL *A, LM_REAL *b, int k1,
+  LM_REAL *C, LM_REAL *d, int k2,
+  int itmax, LM_REAL opts[5], LM_REAL info[LM_INFO_SZ], LM_REAL *work, LM_REAL *covar, void *adata)
+{
+  return LEVMAR_BLEIC_DIF(func, p, x, m, n, NULL, NULL, A, b, k1, C, d, k2, itmax, opts, info, work, covar, adata);
+}
+
+/* linear inequality constraints */
+int LEVMAR_LIC_DER(
+  void (*func)(LM_REAL *p, LM_REAL *hx, int m, int n, void *adata),
+  void (*jacf)(LM_REAL *p, LM_REAL *j, int m, int n, void *adata),
+  LM_REAL *p, LM_REAL *x, int m, int n,
+  LM_REAL *C, LM_REAL *d, int k2,
+  int itmax, LM_REAL opts[4], LM_REAL info[LM_INFO_SZ], LM_REAL *work, LM_REAL *covar, void *adata)
+{
+  return LEVMAR_BLEIC_DER(func, jacf, p, x, m, n, NULL, NULL, NULL, NULL, 0, C, d, k2, itmax, opts, info, work, covar, adata);
+}
+
+int LEVMAR_LIC_DIF(
+  void (*func)(LM_REAL *p, LM_REAL *hx, int m, int n, void *adata),
+  LM_REAL *p, LM_REAL *x, int m, int n,
+  LM_REAL *C, LM_REAL *d, int k2,
+  int itmax, LM_REAL opts[5], LM_REAL info[LM_INFO_SZ], LM_REAL *work, LM_REAL *covar, void *adata)
+{
+  return LEVMAR_BLEIC_DIF(func, p, x, m, n, NULL, NULL, NULL, NULL, 0, C, d, k2, itmax, opts, info, work, covar, adata);
+}
+
+/* undefine all. THIS MUST REMAIN AT THE END OF THE FILE */
+#undef LMBLEIC_DATA
+#undef LMBLEIC_ELIM
+#undef LMBLEIC_FUNC
+#undef LMBLEIC_JACF
+#undef LEVMAR_FDIF_FORW_JAC_APPROX
+#undef LEVMAR_COVAR
+#undef LEVMAR_TRANS_MAT_MAT_MULT
+#undef LEVMAR_BLEIC_DER
+#undef LEVMAR_BLEIC_DIF
+#undef LEVMAR_BLIC_DER
+#undef LEVMAR_BLIC_DIF
+#undef LEVMAR_LEIC_DER
+#undef LEVMAR_LEIC_DIF
+#undef LEVMAR_LIC_DER
+#undef LEVMAR_LIC_DIF
+#undef LEVMAR_BLEC_DER
+#undef LEVMAR_BLEC_DIF

levmar/lmlec.c

@@ -0,0 +1,80 @@
+/////////////////////////////////////////////////////////////////////////////////
+// 
+//  Levenberg - Marquardt non-linear minimization algorithm
+//  Copyright (C) 2004-05  Manolis Lourakis (lourakis at ics forth gr)
+//  Institute of Computer Science, Foundation for Research & Technology - Hellas
+//  Heraklion, Crete, Greece.
+//
+//  This program is free software; you can redistribute it and/or modify
+//  it under the terms of the GNU General Public License as published by
+//  the Free Software Foundation; either version 2 of the License, or
+//  (at your option) any later version.
+//
+//  This program is distributed in the hope that it will be useful,
+//  but WITHOUT ANY WARRANTY; without even the implied warranty of
+//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+//  GNU General Public License for more details.
+//
+/////////////////////////////////////////////////////////////////////////////////
+
+/*******************************************************************************
+ * Wrappers for linearly constrained Levenberg-Marquardt minimization. The same
+ * core code is used with appropriate #defines to derive single and double
+ * precision versions, see also lmlec_core.c
+ *******************************************************************************/
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+
+#include "levmar.h"
+#include "misc.h"
+
+
+#ifndef HAVE_LAPACK
+
+#ifdef _MSC_VER
+#pragma message("Linearly constrained optimization requires LAPACK and was not compiled!")
+#else
+#warning Linearly constrained optimization requires LAPACK and was not compiled!
+#endif // _MSC_VER
+
+#else // LAPACK present
+
+#if !defined(LM_DBL_PREC) && !defined(LM_SNGL_PREC)
+#error At least one of LM_DBL_PREC, LM_SNGL_PREC should be defined!
+#endif
+
+
+#ifdef LM_SNGL_PREC
+/* single precision (float) definitions */
+#define LM_REAL float
+#define LM_PREFIX s
+
+#define __SUBCNST(x) x##F
+#define LM_CNST(x) __SUBCNST(x) // force substitution
+
+#include "lmlec_core.c" // read in core code
+
+#undef LM_REAL
+#undef LM_PREFIX
+#undef __SUBCNST
+#undef LM_CNST
+#endif /* LM_SNGL_PREC */
+
+#ifdef LM_DBL_PREC
+/* double precision definitions */
+#define LM_REAL double
+#define LM_PREFIX d
+
+#define LM_CNST(x) (x)
+
+#include "lmlec_core.c" // read in core code
+
+#undef LM_REAL
+#undef LM_PREFIX
+#undef LM_CNST
+#endif /* LM_DBL_PREC */
+
+#endif /* HAVE_LAPACK */
+

levmar/lmlec_core.c

@@ -0,0 +1,656 @@
+/////////////////////////////////////////////////////////////////////////////////
+// 
+//  Levenberg - Marquardt non-linear minimization algorithm
+//  Copyright (C) 2004-05  Manolis Lourakis (lourakis at ics forth gr)
+//  Institute of Computer Science, Foundation for Research & Technology - Hellas
+//  Heraklion, Crete, Greece.
+//
+//  This program is free software; you can redistribute it and/or modify
+//  it under the terms of the GNU General Public License as published by
+//  the Free Software Foundation; either version 2 of the License, or
+//  (at your option) any later version.
+//
+//  This program is distributed in the hope that it will be useful,
+//  but WITHOUT ANY WARRANTY; without even the implied warranty of
+//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+//  GNU General Public License for more details.
+//
+/////////////////////////////////////////////////////////////////////////////////
+
+#ifndef LM_REAL // not included by lmlec.c
+#error This file should not be compiled directly!
+#endif
+
+
+/* precision-specific definitions */
+#define LMLEC_DATA LM_ADD_PREFIX(lmlec_data)
+#define LMLEC_ELIM LM_ADD_PREFIX(lmlec_elim)
+#define LMLEC_FUNC LM_ADD_PREFIX(lmlec_func)
+#define LMLEC_JACF LM_ADD_PREFIX(lmlec_jacf)
+#define LEVMAR_LEC_DER LM_ADD_PREFIX(levmar_lec_der)
+#define LEVMAR_LEC_DIF LM_ADD_PREFIX(levmar_lec_dif)
+#define LEVMAR_DER LM_ADD_PREFIX(levmar_der)
+#define LEVMAR_DIF LM_ADD_PREFIX(levmar_dif)
+#define LEVMAR_TRANS_MAT_MAT_MULT LM_ADD_PREFIX(levmar_trans_mat_mat_mult)
+#define LEVMAR_COVAR LM_ADD_PREFIX(levmar_covar)
+#define LEVMAR_FDIF_FORW_JAC_APPROX LM_ADD_PREFIX(levmar_fdif_forw_jac_approx)
+
+#define GEQP3 LM_MK_LAPACK_NAME(geqp3)
+#define ORGQR LM_MK_LAPACK_NAME(orgqr)
+#define TRTRI LM_MK_LAPACK_NAME(trtri)
+
+struct LMLEC_DATA{
+  LM_REAL *c, *Z, *p, *jac;
+  int ncnstr;
+  void (*func)(LM_REAL *p, LM_REAL *hx, int m, int n, void *adata);
+  void (*jacf)(LM_REAL *p, LM_REAL *jac, int m, int n, void *adata);
+  void *adata;
+};
+
+/* prototypes for LAPACK routines */
+#ifdef __cplusplus
+extern "C" {
+#endif
+extern int GEQP3(int *m, int *n, LM_REAL *a, int *lda, int *jpvt,
+                   LM_REAL *tau, LM_REAL *work, int *lwork, int *info);
+
+extern int ORGQR(int *m, int *n, int *k, LM_REAL *a, int *lda, LM_REAL *tau,
+                   LM_REAL *work, int *lwork, int *info);
+
+extern int TRTRI(char *uplo, char *diag, int *n, LM_REAL *a, int *lda, int *info);
+#ifdef __cplusplus
+}
+#endif
+
+/*
+ * This function implements an elimination strategy for linearly constrained
+ * optimization problems. The strategy relies on QR decomposition to transform
+ * an optimization problem constrained by Ax=b to an equivalent, unconstrained
+ * one. Also referred to as "null space" or "reduced Hessian" method.
+ * See pp. 430-433 (chap. 15) of "Numerical Optimization" by Nocedal-Wright
+ * for details.
+ *
+ * A is mxn with m<=n and rank(A)=m
+ * Two matrices Y and Z of dimensions nxm and nx(n-m) are computed from A^T so that
+ * their columns are orthonormal and every x can be written as x=Y*b + Z*x_z=
+ * c + Z*x_z, where c=Y*b is a fixed vector of dimension n and x_z is an
+ * arbitrary vector of dimension n-m. Then, the problem of minimizing f(x)
+ * subject to Ax=b is equivalent to minimizing f(c + Z*x_z) with no constraints.
+ * The computed Y and Z are such that any solution of Ax=b can be written as
+ * x=Y*x_y + Z*x_z for some x_y, x_z. Furthermore, A*Y is nonsingular, A*Z=0
+ * and Z spans the null space of A.
+ *
+ * The function accepts A, b and computes c, Y, Z. If b or c is NULL, c is not
+ * computed. Also, Y can be NULL in which case it is not referenced.
+ * The function returns LM_ERROR in case of error, A's computed rank if successful
+ *
+ */
+static int LMLEC_ELIM(LM_REAL *A, LM_REAL *b, LM_REAL *c, LM_REAL *Y, LM_REAL *Z, int m, int n)
+{
+static LM_REAL eps=LM_CNST(-1.0);
+
+LM_REAL *buf=NULL;
+LM_REAL *a, *tau, *work, *r, aux;
+register LM_REAL tmp;
+int a_sz, jpvt_sz, tau_sz, r_sz, Y_sz, worksz;
+int info, rank, *jpvt, tot_sz, mintmn, tm, tn;
+register int i, j, k;
+
+  if(m>n){
+    fprintf(stderr, RCAT("matrix of constraints cannot have more rows than columns in", LMLEC_ELIM) "()!\n");
+    return LM_ERROR;
+  }
+
+  tm=n; tn=m; // transpose dimensions
+  mintmn=m;
+
+  /* calculate required memory size */
+  worksz=-1; // workspace query. Optimal work size is returned in aux
+  //ORGQR((int *)&tm, (int *)&tm, (int *)&mintmn, NULL, (int *)&tm, NULL, (LM_REAL *)&aux, &worksz, &info);
+  GEQP3((int *)&tm, (int *)&tn, NULL, (int *)&tm, NULL, NULL, (LM_REAL *)&aux, (int *)&worksz, &info);
+  worksz=(int)aux;
+  a_sz=tm*tm; // tm*tn is enough for xgeqp3()
+  jpvt_sz=tn;
+  tau_sz=mintmn;
+  r_sz=mintmn*mintmn; // actually smaller if a is not of full row rank
+  Y_sz=(Y)? 0 : tm*tn;
+
+  tot_sz=(a_sz + tau_sz + r_sz + worksz + Y_sz)*sizeof(LM_REAL) + jpvt_sz*sizeof(int); /* should be arranged in that order for proper doubles alignment */
+  buf=(LM_REAL *)malloc(tot_sz); /* allocate a "big" memory chunk at once */
+  if(!buf){
+    fprintf(stderr, RCAT("Memory allocation request failed in ", LMLEC_ELIM) "()\n");
+    return LM_ERROR;
+  }
+
+  a=buf;
+  tau=a+a_sz;
+  r=tau+tau_sz;
+  work=r+r_sz;
+  if(!Y){
+    Y=work+worksz;
+    jpvt=(int *)(Y+Y_sz);
+  }
+  else
+    jpvt=(int *)(work+worksz);
+
+  /* copy input array so that LAPACK won't destroy it. Note that copying is
+   * done in row-major order, which equals A^T in column-major
+   */
+  for(i=0; i<tm*tn; ++i)
+      a[i]=A[i];
+
+  /* clear jpvt */
+  for(i=0; i<jpvt_sz; ++i) jpvt[i]=0;
+
+  /* rank revealing QR decomposition of A^T*/
+  GEQP3((int *)&tm, (int *)&tn, a, (int *)&tm, jpvt, tau, work, (int *)&worksz, &info);
+  //dgeqpf_((int *)&tm, (int *)&tn, a, (int *)&tm, jpvt, tau, work, &info);
+  /* error checking */
+  if(info!=0){
+    if(info<0){
+      fprintf(stderr, RCAT(RCAT("LAPACK error: illegal value for argument %d of ", GEQP3) " in ", LMLEC_ELIM) "()\n", -info);
+    }
+    else if(info>0){
+      fprintf(stderr, RCAT(RCAT("unknown LAPACK error (%d) for ", GEQP3) " in ", LMLEC_ELIM) "()\n", info);
+    }
+    free(buf);
+    return LM_ERROR;
+  }
+  /* the upper triangular part of a now contains the upper triangle of the unpermuted R */
+
+  if(eps<0.0){
+    LM_REAL aux;
+
+    /* compute machine epsilon. DBL_EPSILON should do also */
+    for(eps=LM_CNST(1.0); aux=eps+LM_CNST(1.0), aux-LM_CNST(1.0)>0.0; eps*=LM_CNST(0.5))
+                              ;
+    eps*=LM_CNST(2.0);
+  }
+
+  tmp=tm*LM_CNST(10.0)*eps*FABS(a[0]); // threshold. tm is max(tm, tn)
+  tmp=(tmp>LM_CNST(1E-12))? tmp : LM_CNST(1E-12); // ensure that threshold is not too small
+  /* compute A^T's numerical rank by counting the non-zeros in R's diagonal */
+  for(i=rank=0; i<mintmn; ++i)
+    if(a[i*(tm+1)]>tmp || a[i*(tm+1)]<-tmp) ++rank; /* loop across R's diagonal elements */
+    else break; /* diagonal is arranged in absolute decreasing order */
+
+  if(rank<tn){
+    fprintf(stderr, RCAT("\nConstraints matrix in ",  LMLEC_ELIM) "() is not of full row rank (i.e. %d < %d)!\n"
+            "Make sure that you do not specify redundant or inconsistent constraints.\n\n", rank, tn);
+    free(buf);
+    return LM_ERROR;
+  }
+
+  /* compute the permuted inverse transpose of R */
+  /* first, copy R from the upper triangular part of a to the lower part of r (thus transposing it). R is rank x rank */
+  for(j=0; j<rank; ++j){
+    for(i=0; i<=j; ++i)
+      r[j+i*rank]=a[i+j*tm];
+    for(i=j+1; i<rank; ++i)
+      r[j+i*rank]=0.0; // upper part is zero
+  }
+  /* r now contains R^T */
+
+  /* compute the inverse */
+  TRTRI("L", "N", (int *)&rank, r, (int *)&rank, &info);
+  /* error checking */
+  if(info!=0){
+    if(info<0){
+      fprintf(stderr, RCAT(RCAT("LAPACK error: illegal value for argument %d of ", TRTRI) " in ", LMLEC_ELIM) "()\n", -info);
+    }
+    else if(info>0){
+      fprintf(stderr, RCAT(RCAT("A(%d, %d) is exactly zero for ", TRTRI) " (singular matrix) in ", LMLEC_ELIM) "()\n", info, info);
+    }
+    free(buf);
+    return LM_ERROR;
+  }
+
+  /* finally, permute R^-T using Y as intermediate storage */
+  for(j=0; j<rank; ++j)
+    for(i=0, k=jpvt[j]-1; i<rank; ++i)
+      Y[i+k*rank]=r[i+j*rank];
+
+  for(i=0; i<rank*rank; ++i) // copy back to r
+    r[i]=Y[i];
+
+  /* resize a to be tm x tm, filling with zeroes */
+  for(i=tm*tn; i<tm*tm; ++i)
+    a[i]=0.0;
+
+  /* compute Q in a as the product of elementary reflectors. Q is tm x tm */
+  ORGQR((int *)&tm, (int *)&tm, (int *)&mintmn, a, (int *)&tm, tau, work, &worksz, &info);
+  /* error checking */
+  if(info!=0){
+    if(info<0){
+      fprintf(stderr, RCAT(RCAT("LAPACK error: illegal value for argument %d of ", ORGQR) " in ", LMLEC_ELIM) "()\n", -info);
+    }
+    else if(info>0){
+      fprintf(stderr, RCAT(RCAT("unknown LAPACK error (%d) for ", ORGQR) " in ", LMLEC_ELIM) "()\n", info);
+    }
+    free(buf);
+    return LM_ERROR;
+  }
+
+  /* compute Y=Q_1*R^-T*P^T. Y is tm x rank */
+  for(i=0; i<tm; ++i)
+    for(j=0; j<rank; ++j){
+      for(k=0, tmp=0.0; k<rank; ++k)
+        tmp+=a[i+k*tm]*r[k+j*rank];
+      Y[i*rank+j]=tmp;
+    }
+
+  if(b && c){
+    /* compute c=Y*b */
+    for(i=0; i<tm; ++i){
+      for(j=0, tmp=0.0; j<rank; ++j)
+        tmp+=Y[i*rank+j]*b[j];
+
+      c[i]=tmp;
+    }
+  }
+
+  /* copy Q_2 into Z. Z is tm x (tm-rank) */
+  for(j=0; j<tm-rank; ++j)
+    for(i=0, k=j+rank; i<tm; ++i)
+      Z[i*(tm-rank)+j]=a[i+k*tm];
+
+  free(buf);
+
+  return rank;
+}
+
+/* constrained measurements: given pp, compute the measurements at c + Z*pp */
+static void LMLEC_FUNC(LM_REAL *pp, LM_REAL *hx, int mm, int n, void *adata)
+{
+struct LMLEC_DATA *data=(struct LMLEC_DATA *)adata;
+int m;
+register int i, j;
+register LM_REAL sum;
+LM_REAL *c, *Z, *p, *Zimm;
+
+  m=mm+data->ncnstr;
+  c=data->c;
+  Z=data->Z;
+  p=data->p;
+  /* p=c + Z*pp */
+  for(i=0; i<m; ++i){
+    Zimm=Z+i*mm;
+    for(j=0, sum=c[i]; j<mm; ++j)
+      sum+=Zimm[j]*pp[j]; // sum+=Z[i*mm+j]*pp[j];
+    p[i]=sum;
+  }
+
+  (*(data->func))(p, hx, m, n, data->adata);
+}
+
+/* constrained Jacobian: given pp, compute the Jacobian at c + Z*pp
+ * Using the chain rule, the Jacobian with respect to pp equals the
+ * product of the Jacobian with respect to p (at c + Z*pp) times Z
+ */
+static void LMLEC_JACF(LM_REAL *pp, LM_REAL *jacjac, int mm, int n, void *adata)
+{
+struct LMLEC_DATA *data=(struct LMLEC_DATA *)adata;
+int m;
+register int i, j, l;
+register LM_REAL sum, *aux1, *aux2;
+LM_REAL *c, *Z, *p, *jac; 
+
+  m=mm+data->ncnstr;
+  c=data->c;
+  Z=data->Z;
+  p=data->p;
+  jac=data->jac;
+  /* p=c + Z*pp */
+  for(i=0; i<m; ++i){
+    aux1=Z+i*mm;
+    for(j=0, sum=c[i]; j<mm; ++j)
+      sum+=aux1[j]*pp[j]; // sum+=Z[i*mm+j]*pp[j];
+    p[i]=sum;
+  }
+
+  (*(data->jacf))(p, jac, m, n, data->adata);
+
+  /* compute jac*Z in jacjac */
+  if(n*m<=__BLOCKSZ__SQ){ // this is a small problem
+    /* This is the straightforward way to compute jac*Z. However, due to
+     * its noncontinuous memory access pattern, it incures many cache misses when
+     * applied to large minimization problems (i.e. problems involving a large
+     * number of free variables and measurements), in which jac is too large to
+     * fit in the L1 cache. For such problems, a cache-efficient blocking scheme
+     * is preferable. On the other hand, the straightforward algorithm is faster
+     * on small problems since in this case it avoids the overheads of blocking.
+     */
+
+    for(i=0; i<n; ++i){
+      aux1=jac+i*m;
+      aux2=jacjac+i*mm;
+      for(j=0; j<mm; ++j){
+        for(l=0, sum=0.0; l<m; ++l)
+          sum+=aux1[l]*Z[l*mm+j]; // sum+=jac[i*m+l]*Z[l*mm+j];
+
+        aux2[j]=sum; // jacjac[i*mm+j]=sum;
+      }
+    }
+  }
+  else{ // this is a large problem
+    /* Cache efficient computation of jac*Z based on blocking
+     */
+#define __MIN__(x, y) (((x)<=(y))? (x) : (y))
+    register int jj, ll;
+
+    for(jj=0; jj<mm; jj+=__BLOCKSZ__){
+      for(i=0; i<n; ++i){
+        aux1=jacjac+i*mm;
+        for(j=jj; j<__MIN__(jj+__BLOCKSZ__, mm); ++j)
+          aux1[j]=0.0; //jacjac[i*mm+j]=0.0;
+      }
+
+      for(ll=0; ll<m; ll+=__BLOCKSZ__){
+        for(i=0; i<n; ++i){
+          aux1=jacjac+i*mm; aux2=jac+i*m;
+          for(j=jj; j<__MIN__(jj+__BLOCKSZ__, mm); ++j){
+            sum=0.0;
+            for(l=ll; l<__MIN__(ll+__BLOCKSZ__, m); ++l)
+              sum+=aux2[l]*Z[l*mm+j]; //jac[i*m+l]*Z[l*mm+j];
+            aux1[j]+=sum; //jacjac[i*mm+j]+=sum;
+          }
+        }
+      }
+    }
+  }
+}
+#undef __MIN__
+
+
+/* 
+ * This function is similar to LEVMAR_DER except that the minimization
+ * is performed subject to the linear constraints A p=b, A is kxm, b kx1
+ *
+ * This function requires an analytic Jacobian. In case the latter is unavailable,
+ * use LEVMAR_LEC_DIF() bellow
+ *
+ */
+int LEVMAR_LEC_DER(
+  void (*func)(LM_REAL *p, LM_REAL *hx, int m, int n, void *adata), /* functional relation describing measurements. A p \in R^m yields a \hat{x} \in  R^n */
+  void (*jacf)(LM_REAL *p, LM_REAL *j, int m, int n, void *adata),  /* function to evaluate the Jacobian \part x / \part p */ 
+  LM_REAL *p,         /* I/O: initial parameter estimates. On output has the estimated solution */
+  LM_REAL *x,         /* I: measurement vector. NULL implies a zero vector */
+  int m,              /* I: parameter vector dimension (i.e. #unknowns) */
+  int n,              /* I: measurement vector dimension */
+  LM_REAL *A,         /* I: constraints matrix, kxm */
+  LM_REAL *b,         /* I: right hand constraints vector, kx1 */
+  int k,              /* I: number of constraints (i.e. A's #rows) */
+  int itmax,          /* I: maximum number of iterations */
+  LM_REAL opts[4],    /* I: minim. options [\mu, \epsilon1, \epsilon2, \epsilon3]. Respectively the scale factor for initial \mu,
+                       * stopping thresholds for ||J^T e||_inf, ||Dp||_2 and ||e||_2. Set to NULL for defaults to be used
+                       */
+  LM_REAL info[LM_INFO_SZ],
+					           /* O: information regarding the minimization. Set to NULL if don't care
+                      * info[0]= ||e||_2 at initial p.
+                      * info[1-4]=[ ||e||_2, ||J^T e||_inf,  ||Dp||_2, mu/max[J^T J]_ii ], all computed at estimated p.
+                      * info[5]= # iterations,
+                      * info[6]=reason for terminating: 1 - stopped by small gradient J^T e
+                      *                                 2 - stopped by small Dp
+                      *                                 3 - stopped by itmax
+                      *                                 4 - singular matrix. Restart from current p with increased mu 
+                      *                                 5 - no further error reduction is possible. Restart with increased mu
+                      *                                 6 - stopped by small ||e||_2
+                      *                                 7 - stopped by invalid (i.e. NaN or Inf) "func" values. This is a user error
+                      * info[7]= # function evaluations
+                      * info[8]= # Jacobian evaluations
+                      * info[9]= # linear systems solved, i.e. # attempts for reducing error
+                      */
+  LM_REAL *work,     /* working memory at least LM_LEC_DER_WORKSZ() reals large, allocated if NULL */
+  LM_REAL *covar,    /* O: Covariance matrix corresponding to LS solution; mxm. Set to NULL if not needed. */
+  void *adata)       /* pointer to possibly additional data, passed uninterpreted to func & jacf.
+                      * Set to NULL if not needed
+                      */
+{
+  struct LMLEC_DATA data;
+  LM_REAL *ptr, *Z, *pp, *p0, *Zimm; /* Z is mxmm */
+  int mm, ret;
+  register int i, j;
+  register LM_REAL tmp;
+  LM_REAL locinfo[LM_INFO_SZ];
+
+  if(!jacf){
+    fprintf(stderr, RCAT("No function specified for computing the Jacobian in ", LEVMAR_LEC_DER)
+      RCAT("().\nIf no such function is available, use ", LEVMAR_LEC_DIF) RCAT("() rather than ", LEVMAR_LEC_DER) "()\n");
+    return LM_ERROR;
+  }
+
+  mm=m-k;
+
+  if(n<mm){
+    fprintf(stderr, LCAT(LEVMAR_LEC_DER, "(): cannot solve a problem with fewer measurements + equality constraints [%d + %d] than unknowns [%d]\n"), n, k, m);
+    return LM_ERROR;
+  }
+
+  ptr=(LM_REAL *)malloc((2*m + m*mm + n*m + mm)*sizeof(LM_REAL));
+  if(!ptr){
+    fprintf(stderr, LCAT(LEVMAR_LEC_DER, "(): memory allocation request failed\n"));
+    return LM_ERROR;
+  }
+  data.p=p;
+  p0=ptr;
+  data.c=p0+m;
+  data.Z=Z=data.c+m;
+  data.jac=data.Z+m*mm;
+  pp=data.jac+n*m;
+  data.ncnstr=k;
+  data.func=func;
+  data.jacf=jacf;
+  data.adata=adata;
+
+  ret=LMLEC_ELIM(A, b, data.c, NULL, Z, k, m); // compute c, Z
+  if(ret==LM_ERROR){
+    free(ptr);
+    return LM_ERROR;
+  }
+
+  /* compute pp s.t. p = c + Z*pp or (Z^T Z)*pp=Z^T*(p-c)
+   * Due to orthogonality, Z^T Z = I and the last equation
+   * becomes pp=Z^T*(p-c). Also, save the starting p in p0
+   */
+  for(i=0; i<m; ++i){
+    p0[i]=p[i];
+    p[i]-=data.c[i];
+  }
+
+  /* Z^T*(p-c) */
+  for(i=0; i<mm; ++i){
+    for(j=0, tmp=0.0; j<m; ++j)
+      tmp+=Z[j*mm+i]*p[j];
+    pp[i]=tmp;
+  }
+
+  /* compute the p corresponding to pp (i.e. c + Z*pp) and compare with p0 */
+  for(i=0; i<m; ++i){
+    Zimm=Z+i*mm;
+    for(j=0, tmp=data.c[i]; j<mm; ++j)
+      tmp+=Zimm[j]*pp[j]; // tmp+=Z[i*mm+j]*pp[j];
+    if(FABS(tmp-p0[i])>LM_CNST(1E-03))
+      fprintf(stderr, RCAT("Warning: component %d of starting point not feasible in ", LEVMAR_LEC_DER) "()! [%.10g reset to %.10g]\n",
+                      i, p0[i], tmp);
+  }
+
+  if(!info) info=locinfo; /* make sure that LEVMAR_DER() is called with non-null info */
+  /* note that covariance computation is not requested from LEVMAR_DER() */
+  ret=LEVMAR_DER(LMLEC_FUNC, LMLEC_JACF, pp, x, mm, n, itmax, opts, info, work, NULL, (void *)&data);
+
+  /* p=c + Z*pp */
+  for(i=0; i<m; ++i){
+    Zimm=Z+i*mm;
+    for(j=0, tmp=data.c[i]; j<mm; ++j)
+      tmp+=Zimm[j]*pp[j]; // tmp+=Z[i*mm+j]*pp[j];
+    p[i]=tmp;
+  }
+
+  /* compute the covariance from the Jacobian in data.jac */
+  if(covar){
+    LEVMAR_TRANS_MAT_MAT_MULT(data.jac, covar, n, m); /* covar = J^T J */
+    LEVMAR_COVAR(covar, covar, info[1], m, n);
+  }
+
+  free(ptr);
+
+  return ret;
+}
+
+/* Similar to the LEVMAR_LEC_DER() function above, except that the Jacobian is approximated
+ * with the aid of finite differences (forward or central, see the comment for the opts argument)
+ */
+int LEVMAR_LEC_DIF(
+  void (*func)(LM_REAL *p, LM_REAL *hx, int m, int n, void *adata), /* functional relation describing measurements. A p \in R^m yields a \hat{x} \in  R^n */
+  LM_REAL *p,         /* I/O: initial parameter estimates. On output has the estimated solution */
+  LM_REAL *x,         /* I: measurement vector. NULL implies a zero vector */
+  int m,              /* I: parameter vector dimension (i.e. #unknowns) */
+  int n,              /* I: measurement vector dimension */
+  LM_REAL *A,         /* I: constraints matrix, kxm */
+  LM_REAL *b,         /* I: right hand constraints vector, kx1 */
+  int k,              /* I: number of constraints (i.e. A's #rows) */
+  int itmax,          /* I: maximum number of iterations */
+  LM_REAL opts[5],    /* I: opts[0-3] = minim. options [\mu, \epsilon1, \epsilon2, \epsilon3, \delta]. Respectively the
+                       * scale factor for initial \mu, stopping thresholds for ||J^T e||_inf, ||Dp||_2 and ||e||_2 and
+                       * the step used in difference approximation to the Jacobian. Set to NULL for defaults to be used.
+                       * If \delta<0, the Jacobian is approximated with central differences which are more accurate
+                       * (but slower!) compared to the forward differences employed by default. 
+                       */
+  LM_REAL info[LM_INFO_SZ],
+					           /* O: information regarding the minimization. Set to NULL if don't care
+                      * info[0]= ||e||_2 at initial p.
+                      * info[1-4]=[ ||e||_2, ||J^T e||_inf,  ||Dp||_2, mu/max[J^T J]_ii ], all computed at estimated p.
+                      * info[5]= # iterations,
+                      * info[6]=reason for terminating: 1 - stopped by small gradient J^T e
+                      *                                 2 - stopped by small Dp
+                      *                                 3 - stopped by itmax
+                      *                                 4 - singular matrix. Restart from current p with increased mu 
+                      *                                 5 - no further error reduction is possible. Restart with increased mu
+                      *                                 6 - stopped by small ||e||_2
+                      *                                 7 - stopped by invalid (i.e. NaN or Inf) "func" values. This is a user error
+                      * info[7]= # function evaluations
+                      * info[8]= # Jacobian evaluations
+                      * info[9]= # linear systems solved, i.e. # attempts for reducing error
+                      */
+  LM_REAL *work,     /* working memory at least LM_LEC_DIF_WORKSZ() reals large, allocated if NULL */
+  LM_REAL *covar,    /* O: Covariance matrix corresponding to LS solution; mxm. Set to NULL if not needed. */
+  void *adata)       /* pointer to possibly additional data, passed uninterpreted to func.
+                      * Set to NULL if not needed
+                      */
+{
+  struct LMLEC_DATA data;
+  LM_REAL *ptr, *Z, *pp, *p0, *Zimm; /* Z is mxmm */
+  int mm, ret;
+  register int i, j;
+  register LM_REAL tmp;
+  LM_REAL locinfo[LM_INFO_SZ];
+
+  mm=m-k;
+
+  if(n<mm){
+    fprintf(stderr, LCAT(LEVMAR_LEC_DIF, "(): cannot solve a problem with fewer measurements + equality constraints [%d + %d] than unknowns [%d]\n"), n, k, m);
+    return LM_ERROR;
+  }
+
+  ptr=(LM_REAL *)malloc((2*m + m*mm + mm)*sizeof(LM_REAL));
+  if(!ptr){
+    fprintf(stderr, LCAT(LEVMAR_LEC_DIF, "(): memory allocation request failed\n"));
+    return LM_ERROR;
+  }
+  data.p=p;
+  p0=ptr;
+  data.c=p0+m;
+  data.Z=Z=data.c+m;
+  data.jac=NULL;
+  pp=data.Z+m*mm;
+  data.ncnstr=k;
+  data.func=func;
+  data.jacf=NULL;
+  data.adata=adata;
+
+  ret=LMLEC_ELIM(A, b, data.c, NULL, Z, k, m); // compute c, Z
+  if(ret==LM_ERROR){
+    free(ptr);
+    return LM_ERROR;
+  }
+
+  /* compute pp s.t. p = c + Z*pp or (Z^T Z)*pp=Z^T*(p-c)
+   * Due to orthogonality, Z^T Z = I and the last equation
+   * becomes pp=Z^T*(p-c). Also, save the starting p in p0
+   */
+  for(i=0; i<m; ++i){
+    p0[i]=p[i];
+    p[i]-=data.c[i];
+  }
+
+  /* Z^T*(p-c) */
+  for(i=0; i<mm; ++i){
+    for(j=0, tmp=0.0; j<m; ++j)
+      tmp+=Z[j*mm+i]*p[j];
+    pp[i]=tmp;
+  }
+
+  /* compute the p corresponding to pp (i.e. c + Z*pp) and compare with p0 */
+  for(i=0; i<m; ++i){
+    Zimm=Z+i*mm;
+    for(j=0, tmp=data.c[i]; j<mm; ++j)
+      tmp+=Zimm[j]*pp[j]; // tmp+=Z[i*mm+j]*pp[j];
+    if(FABS(tmp-p0[i])>LM_CNST(1E-03))
+      fprintf(stderr, RCAT("Warning: component %d of starting point not feasible in ", LEVMAR_LEC_DIF) "()! [%.10g reset to %.10g]\n",
+                      i, p0[i], tmp);
+  }
+
+  if(!info) info=locinfo; /* make sure that LEVMAR_DIF() is called with non-null info */
+  /* note that covariance computation is not requested from LEVMAR_DIF() */
+  ret=LEVMAR_DIF(LMLEC_FUNC, pp, x, mm, n, itmax, opts, info, work, NULL, (void *)&data);
+
+  /* p=c + Z*pp */
+  for(i=0; i<m; ++i){
+    Zimm=Z+i*mm;
+    for(j=0, tmp=data.c[i]; j<mm; ++j)
+      tmp+=Zimm[j]*pp[j]; // tmp+=Z[i*mm+j]*pp[j];
+    p[i]=tmp;
+  }
+
+  /* compute the Jacobian with finite differences and use it to estimate the covariance */
+  if(covar){
+    LM_REAL *hx, *wrk, *jac;
+
+    hx=(LM_REAL *)malloc((2*n+n*m)*sizeof(LM_REAL));
+    if(!hx){
+      fprintf(stderr, LCAT(LEVMAR_LEC_DIF, "(): memory allocation request failed\n"));
+      free(ptr);
+      return LM_ERROR;
+    }
+
+    wrk=hx+n;
+    jac=wrk+n;
+
+    (*func)(p, hx, m, n, adata); /* evaluate function at p */
+    LEVMAR_FDIF_FORW_JAC_APPROX(func, p, hx, wrk, (LM_REAL)LM_DIFF_DELTA, jac, m, n, adata); /* compute the Jacobian at p */
+    LEVMAR_TRANS_MAT_MAT_MULT(jac, covar, n, m); /* covar = J^T J */
+    LEVMAR_COVAR(covar, covar, info[1], m, n);
+    free(hx);
+  }
+
+  free(ptr);
+
+  return ret;
+}
+
+/* undefine all. THIS MUST REMAIN AT THE END OF THE FILE */
+#undef LMLEC_DATA
+#undef LMLEC_ELIM
+#undef LMLEC_FUNC
+#undef LMLEC_JACF
+#undef LEVMAR_FDIF_FORW_JAC_APPROX
+#undef LEVMAR_COVAR
+#undef LEVMAR_TRANS_MAT_MAT_MULT
+#undef LEVMAR_LEC_DER
+#undef LEVMAR_LEC_DIF
+#undef LEVMAR_DER
+#undef LEVMAR_DIF
+
+#undef GEQP3
+#undef ORGQR
+#undef TRTRI

levmar/misc.c

@@ -0,0 +1,70 @@
+/////////////////////////////////////////////////////////////////////////////////
+// 
+//  Levenberg - Marquardt non-linear minimization algorithm
+//  Copyright (C) 2004-05  Manolis Lourakis (lourakis at ics forth gr)
+//  Institute of Computer Science, Foundation for Research & Technology - Hellas
+//  Heraklion, Crete, Greece.
+//
+//  This program is free software; you can redistribute it and/or modify
+//  it under the terms of the GNU General Public License as published by
+//  the Free Software Foundation; either version 2 of the License, or
+//  (at your option) any later version.
+//
+//  This program is distributed in the hope that it will be useful,
+//  but WITHOUT ANY WARRANTY; without even the implied warranty of
+//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+//  GNU General Public License for more details.
+//
+/////////////////////////////////////////////////////////////////////////////////
+
+/******************************************************************************** 
+ * Miscelaneous functions for Levenberg-Marquardt nonlinear minimization. The
+ * same core code is used with appropriate #defines to derive single and double
+ * precision versions, see also misc_core.c
+ ********************************************************************************/
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <float.h>
+
+#include "levmar.h"
+#include "misc.h"
+
+#if !defined(LM_DBL_PREC) && !defined(LM_SNGL_PREC)
+#error At least one of LM_DBL_PREC, LM_SNGL_PREC should be defined!
+#endif
+
+#ifdef LM_SNGL_PREC
+/* single precision (float) definitions */
+#define LM_REAL float
+#define LM_PREFIX s
+
+#define LM_REAL_EPSILON FLT_EPSILON
+#define __SUBCNST(x) x##F
+#define LM_CNST(x) __SUBCNST(x) // force substitution
+
+#include "misc_core.c" // read in core code
+
+#undef LM_REAL
+#undef LM_PREFIX
+#undef LM_REAL_EPSILON
+#undef __SUBCNST
+#undef LM_CNST
+#endif /* LM_SNGL_PREC */
+
+#ifdef LM_DBL_PREC
+/* double precision definitions */
+#define LM_REAL double
+#define LM_PREFIX d
+
+#define LM_REAL_EPSILON DBL_EPSILON
+#define LM_CNST(x) (x)
+
+#include "misc_core.c" // read in core code
+
+#undef LM_REAL
+#undef LM_PREFIX
+#undef LM_REAL_EPSILON
+#undef LM_CNST
+#endif /* LM_DBL_PREC */

levmar/misc.h

@@ -0,0 +1,114 @@
+/////////////////////////////////////////////////////////////////////////////////
+// 
+//  Levenberg - Marquardt non-linear minimization algorithm
+//  Copyright (C) 2004  Manolis Lourakis (lourakis at ics forth gr)
+//  Institute of Computer Science, Foundation for Research & Technology - Hellas
+//  Heraklion, Crete, Greece.
+//
+//  This program is free software; you can redistribute it and/or modify
+//  it under the terms of the GNU General Public License as published by
+//  the Free Software Foundation; either version 2 of the License, or
+//  (at your option) any later version.
+//
+//  This program is distributed in the hope that it will be useful,
+//  but WITHOUT ANY WARRANTY; without even the implied warranty of
+//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+//  GNU General Public License for more details.
+//
+/////////////////////////////////////////////////////////////////////////////////
+
+#ifndef _MISC_H_
+#define _MISC_H_
+
+/* common suffix for LAPACK subroutines. Define empty in case of no prefix. */
+#define LM_LAPACK_SUFFIX _
+//#define LM_LAPACK_SUFFIX  // define empty
+
+/* common prefix for BLAS subroutines. Leave undefined in case of no prefix.
+ * You might also need to modify LM_BLAS_PREFIX below
+ */
+/* f2c'd BLAS */
+//#define LM_BLAS_PREFIX f2c_
+/* C BLAS */
+//#define LM_BLAS_PREFIX cblas_
+
+/* common suffix for BLAS subroutines */
+//#define LM_BLAS_SUFFIX  // define empty if a f2c_ or cblas_ prefix was defined for LM_BLAS_PREFIX above
+#define LM_BLAS_SUFFIX _ // use this in case of no BLAS prefix
+
+
+#define LCAT_(a, b)    #a b
+#define LCAT(a, b)    LCAT_(a, b) // force substitution
+#define RCAT_(a, b)    a #b
+#define RCAT(a, b)    RCAT_(a, b) // force substitution
+
+#define LM_MK_LAPACK_NAME(s)  LM_ADD_PREFIX(LM_CAT_(s, LM_LAPACK_SUFFIX))
+
+#ifdef LM_BLAS_PREFIX
+#define LM_MK_BLAS_NAME(s) LM_CAT_(LM_BLAS_PREFIX, LM_ADD_PREFIX(LM_CAT_(s, LM_BLAS_SUFFIX)))
+#else
+#define LM_MK_BLAS_NAME(s) LM_ADD_PREFIX(LM_CAT_(s, LM_BLAS_SUFFIX))
+#endif
+
+
+#define __BLOCKSZ__       32 /* block size for cache-friendly matrix-matrix multiply. It should be
+                              * such that __BLOCKSZ__^2*sizeof(LM_REAL) is smaller than the CPU (L1)
+                              * data cache size. Notice that a value of 32 when LM_REAL=double assumes
+                              * an 8Kb L1 data cache (32*32*8=8K). This is a concervative choice since
+                              * newer Pentium 4s have a L1 data cache of size 16K, capable of holding
+                              * up to 45x45 double blocks.
+                              */
+#define __BLOCKSZ__SQ    (__BLOCKSZ__)*(__BLOCKSZ__)
+
+/* add a prefix in front of a token */
+#define LM_CAT__(a, b) a ## b
+#define LM_CAT_(a, b) LM_CAT__(a, b) // force substitution
+#define LM_ADD_PREFIX(s) LM_CAT_(LM_PREFIX, s)
+
+#define FABS(x) (((x)>=0.0)? (x) : -(x))
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* blocking-based matrix multiply */
+extern void slevmar_trans_mat_mat_mult(float *a, float *b, int n, int m);
+extern void dlevmar_trans_mat_mat_mult(double *a, double *b, int n, int m);
+
+/* forward finite differences */
+extern void slevmar_fdif_forw_jac_approx(void (*func)(float *p, float *hx, int m, int n, void *adata),
+					float *p, float *hx, float *hxx, float delta,
+					float *jac, int m, int n, void *adata);
+extern void dlevmar_fdif_forw_jac_approx(void (*func)(double *p, double *hx, int m, int n, void *adata),
+					double *p, double *hx, double *hxx, double delta,
+					double *jac, int m, int n, void *adata);
+
+/* central finite differences */
+extern void slevmar_fdif_cent_jac_approx(void (*func)(float *p, float *hx, int m, int n, void *adata),
+          float *p, float *hxm, float *hxp, float delta,
+          float *jac, int m, int n, void *adata);
+extern void dlevmar_fdif_cent_jac_approx(void (*func)(double *p, double *hx, int m, int n, void *adata),
+          double *p, double *hxm, double *hxp, double delta,
+          double *jac, int m, int n, void *adata);
+
+/* e=x-y and ||e|| */
+extern float  slevmar_L2nrmxmy(float *e, float *x, float *y, int n);
+extern double dlevmar_L2nrmxmy(double *e, double *x, double *y, int n);
+
+/* covariance of LS fit */
+extern int slevmar_covar(float *JtJ, float *C, float sumsq, int m, int n);
+extern int dlevmar_covar(double *JtJ, double *C, double sumsq, int m, int n);
+
+/* box constraints consistency check */
+extern int slevmar_box_check(float *lb, float *ub, int m);
+extern int dlevmar_box_check(double *lb, double *ub, int m);
+
+/* Cholesky */
+extern int slevmar_chol(float *C, float *W, int m);
+extern int dlevmar_chol(double *C, double *W, int m);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* _MISC_H_ */

levmar/misc_core.c

@@ -0,0 +1,826 @@
+/////////////////////////////////////////////////////////////////////////////////
+// 
+//  Levenberg - Marquardt non-linear minimization algorithm
+//  Copyright (C) 2004-05  Manolis Lourakis (lourakis at ics forth gr)
+//  Institute of Computer Science, Foundation for Research & Technology - Hellas
+//  Heraklion, Crete, Greece.
+//
+//  This program is free software; you can redistribute it and/or modify
+//  it under the terms of the GNU General Public License as published by
+//  the Free Software Foundation; either version 2 of the License, or
+//  (at your option) any later version.
+//
+//  This program is distributed in the hope that it will be useful,
+//  but WITHOUT ANY WARRANTY; without even the implied warranty of
+//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+//  GNU General Public License for more details.
+//
+/////////////////////////////////////////////////////////////////////////////////
+
+#ifndef LM_REAL // not included by misc.c
+#error This file should not be compiled directly!
+#endif
+
+
+/* precision-specific definitions */
+#define LEVMAR_CHKJAC LM_ADD_PREFIX(levmar_chkjac)
+#define LEVMAR_FDIF_FORW_JAC_APPROX LM_ADD_PREFIX(levmar_fdif_forw_jac_approx)
+#define LEVMAR_FDIF_CENT_JAC_APPROX LM_ADD_PREFIX(levmar_fdif_cent_jac_approx)
+#define LEVMAR_TRANS_MAT_MAT_MULT LM_ADD_PREFIX(levmar_trans_mat_mat_mult)
+#define LEVMAR_COVAR LM_ADD_PREFIX(levmar_covar)
+#define LEVMAR_STDDEV LM_ADD_PREFIX(levmar_stddev)
+#define LEVMAR_CORCOEF LM_ADD_PREFIX(levmar_corcoef)
+#define LEVMAR_R2 LM_ADD_PREFIX(levmar_R2)
+#define LEVMAR_BOX_CHECK LM_ADD_PREFIX(levmar_box_check)
+#define LEVMAR_L2NRMXMY LM_ADD_PREFIX(levmar_L2nrmxmy)
+
+#ifdef HAVE_LAPACK
+#define LEVMAR_PSEUDOINVERSE LM_ADD_PREFIX(levmar_pseudoinverse)
+static int LEVMAR_PSEUDOINVERSE(LM_REAL *A, LM_REAL *B, int m);
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+/* BLAS matrix multiplication, LAPACK SVD & Cholesky routines */
+#define GEMM LM_MK_BLAS_NAME(gemm)
+/* C := alpha*op( A )*op( B ) + beta*C */
+extern void GEMM(char *transa, char *transb, int *m, int *n, int *k,
+          LM_REAL *alpha, LM_REAL *a, int *lda, LM_REAL *b, int *ldb, LM_REAL *beta, LM_REAL *c, int *ldc);
+
+#define GESVD LM_MK_LAPACK_NAME(gesvd)
+#define GESDD LM_MK_LAPACK_NAME(gesdd)
+extern int GESVD(char *jobu, char *jobvt, int *m, int *n, LM_REAL *a, int *lda, LM_REAL *s, LM_REAL *u, int *ldu,
+                 LM_REAL *vt, int *ldvt, LM_REAL *work, int *lwork, int *info);
+
+/* lapack 3.0 new SVD routine, faster than xgesvd() */
+extern int GESDD(char *jobz, int *m, int *n, LM_REAL *a, int *lda, LM_REAL *s, LM_REAL *u, int *ldu, LM_REAL *vt, int *ldvt,
+                 LM_REAL *work, int *lwork, int *iwork, int *info);
+
+/* Cholesky decomposition */
+#define POTF2 LM_MK_LAPACK_NAME(potf2)
+extern int POTF2(char *uplo, int *n, LM_REAL *a, int *lda, int *info);
+#ifdef __cplusplus
+}
+#endif
+
+#define LEVMAR_CHOLESKY LM_ADD_PREFIX(levmar_chol)
+
+#else /* !HAVE_LAPACK */
+#define LEVMAR_LUINVERSE LM_ADD_PREFIX(levmar_LUinverse_noLapack)
+
+static int LEVMAR_LUINVERSE(LM_REAL *A, LM_REAL *B, int m);
+#endif /* HAVE_LAPACK */
+
+/* blocked multiplication of the transpose of the nxm matrix a with itself (i.e. a^T a)
+ * using a block size of bsize. The product is returned in b.
+ * Since a^T a is symmetric, its computation can be sped up by computing only its
+ * upper triangular part and copying it to the lower part.
+ *
+ * More details on blocking can be found at 
+ * http://www-2.cs.cmu.edu/afs/cs/academic/class/15213-f02/www/R07/section_a/Recitation07-SectionA.pdf
+ */
+void LEVMAR_TRANS_MAT_MAT_MULT(LM_REAL *a, LM_REAL *b, int n, int m)
+{
+#ifdef HAVE_LAPACK /* use BLAS matrix multiply */
+
+LM_REAL alpha=LM_CNST(1.0), beta=LM_CNST(0.0);
+  /* Fool BLAS to compute a^T*a avoiding transposing a: a is equivalent to a^T in column major,
+   * therefore BLAS computes a*a^T with a and a*a^T in column major, which is equivalent to
+   * computing a^T*a in row major!
+   */
+  GEMM("N", "T", &m, &m, &n, &alpha, a, &m, a, &m, &beta, b, &m);
+
+#else /* no LAPACK, use blocking-based multiply */
+
+register int i, j, k, jj, kk;
+register LM_REAL sum, *bim, *akm;
+const int bsize=__BLOCKSZ__;
+
+#define __MIN__(x, y) (((x)<=(y))? (x) : (y))
+#define __MAX__(x, y) (((x)>=(y))? (x) : (y))
+
+  /* compute upper triangular part using blocking */
+  for(jj=0; jj<m; jj+=bsize){
+    for(i=0; i<m; ++i){
+      bim=b+i*m;
+      for(j=__MAX__(jj, i); j<__MIN__(jj+bsize, m); ++j)
+        bim[j]=0.0; //b[i*m+j]=0.0;
+    }
+
+    for(kk=0; kk<n; kk+=bsize){
+      for(i=0; i<m; ++i){
+        bim=b+i*m;
+        for(j=__MAX__(jj, i); j<__MIN__(jj+bsize, m); ++j){
+          sum=0.0;
+          for(k=kk; k<__MIN__(kk+bsize, n); ++k){
+            akm=a+k*m;
+            sum+=akm[i]*akm[j]; //a[k*m+i]*a[k*m+j];
+          }
+          bim[j]+=sum; //b[i*m+j]+=sum;
+        }
+      }
+    }
+  }
+
+  /* copy upper triangular part to the lower one */
+  for(i=0; i<m; ++i)
+    for(j=0; j<i; ++j)
+      b[i*m+j]=b[j*m+i];
+
+#undef __MIN__
+#undef __MAX__
+
+#endif /* HAVE_LAPACK */
+}
+
+/* forward finite difference approximation to the Jacobian of func */
+void LEVMAR_FDIF_FORW_JAC_APPROX(
+    void (*func)(LM_REAL *p, LM_REAL *hx, int m, int n, void *adata),
+													   /* function to differentiate */
+    LM_REAL *p,              /* I: current parameter estimate, mx1 */
+    LM_REAL *hx,             /* I: func evaluated at p, i.e. hx=func(p), nx1 */
+    LM_REAL *hxx,            /* W/O: work array for evaluating func(p+delta), nx1 */
+    LM_REAL delta,           /* increment for computing the Jacobian */
+    LM_REAL *jac,            /* O: array for storing approximated Jacobian, nxm */
+    int m,
+    int n,
+    void *adata)
+{
+register int i, j;
+LM_REAL tmp;
+register LM_REAL d;
+
+  for(j=0; j<m; ++j){
+    /* determine d=max(1E-04*|p[j]|, delta), see HZ */
+    d=LM_CNST(1E-04)*p[j]; // force evaluation
+    d=FABS(d);
+    if(d<delta)
+      d=delta;
+
+    tmp=p[j];
+    p[j]+=d;
+
+    (*func)(p, hxx, m, n, adata);
+
+    p[j]=tmp; /* restore */
+
+    d=LM_CNST(1.0)/d; /* invert so that divisions can be carried out faster as multiplications */
+    for(i=0; i<n; ++i){
+      jac[i*m+j]=(hxx[i]-hx[i])*d;
+    }
+  }
+}
+
+/* central finite difference approximation to the Jacobian of func */
+void LEVMAR_FDIF_CENT_JAC_APPROX(
+    void (*func)(LM_REAL *p, LM_REAL *hx, int m, int n, void *adata),
+													   /* function to differentiate */
+    LM_REAL *p,              /* I: current parameter estimate, mx1 */
+    LM_REAL *hxm,            /* W/O: work array for evaluating func(p-delta), nx1 */
+    LM_REAL *hxp,            /* W/O: work array for evaluating func(p+delta), nx1 */
+    LM_REAL delta,           /* increment for computing the Jacobian */
+    LM_REAL *jac,            /* O: array for storing approximated Jacobian, nxm */
+    int m,
+    int n,
+    void *adata)
+{
+register int i, j;
+LM_REAL tmp;
+register LM_REAL d;
+
+  for(j=0; j<m; ++j){
+    /* determine d=max(1E-04*|p[j]|, delta), see HZ */
+    d=LM_CNST(1E-04)*p[j]; // force evaluation
+    d=FABS(d);
+    if(d<delta)
+      d=delta;
+
+    tmp=p[j];
+    p[j]-=d;
+    (*func)(p, hxm, m, n, adata);
+
+    p[j]=tmp+d;
+    (*func)(p, hxp, m, n, adata);
+    p[j]=tmp; /* restore */
+
+    d=LM_CNST(0.5)/d; /* invert so that divisions can be carried out faster as multiplications */
+    for(i=0; i<n; ++i){
+      jac[i*m+j]=(hxp[i]-hxm[i])*d;
+    }
+  }
+}
+
+/* 
+ * Check the Jacobian of a n-valued nonlinear function in m variables
+ * evaluated at a point p, for consistency with the function itself.
+ *
+ * Based on fortran77 subroutine CHKDER by
+ * Burton S. Garbow, Kenneth E. Hillstrom, Jorge J. More
+ * Argonne National Laboratory. MINPACK project. March 1980.
+ *
+ *
+ * func points to a function from R^m --> R^n: Given a p in R^m it yields hx in R^n
+ * jacf points to a function implementing the Jacobian of func, whose correctness
+ *     is to be tested. Given a p in R^m, jacf computes into the nxm matrix j the
+ *     Jacobian of func at p. Note that row i of j corresponds to the gradient of
+ *     the i-th component of func, evaluated at p.
+ * p is an input array of length m containing the point of evaluation.
+ * m is the number of variables
+ * n is the number of functions
+ * adata points to possible additional data and is passed uninterpreted
+ *     to func, jacf.
+ * err is an array of length n. On output, err contains measures
+ *     of correctness of the respective gradients. if there is
+ *     no severe loss of significance, then if err[i] is 1.0 the
+ *     i-th gradient is correct, while if err[i] is 0.0 the i-th
+ *     gradient is incorrect. For values of err between 0.0 and 1.0,
+ *     the categorization is less certain. In general, a value of
+ *     err[i] greater than 0.5 indicates that the i-th gradient is
+ *     probably correct, while a value of err[i] less than 0.5
+ *     indicates that the i-th gradient is probably incorrect.
+ *
+ *
+ * The function does not perform reliably if cancellation or
+ * rounding errors cause a severe loss of significance in the
+ * evaluation of a function. therefore, none of the components
+ * of p should be unusually small (in particular, zero) or any
+ * other value which may cause loss of significance.
+ */
+
+void LEVMAR_CHKJAC(
+    void (*func)(LM_REAL *p, LM_REAL *hx, int m, int n, void *adata),
+    void (*jacf)(LM_REAL *p, LM_REAL *j, int m, int n, void *adata),
+    LM_REAL *p, int m, int n, void *adata, LM_REAL *err)
+{
+LM_REAL factor=LM_CNST(100.0);
+LM_REAL one=LM_CNST(1.0);
+LM_REAL zero=LM_CNST(0.0);
+LM_REAL *fvec, *fjac, *pp, *fvecp, *buf;
+
+register int i, j;
+LM_REAL eps, epsf, temp, epsmch;
+LM_REAL epslog;
+int fvec_sz=n, fjac_sz=n*m, pp_sz=m, fvecp_sz=n;
+
+  epsmch=LM_REAL_EPSILON;
+  eps=(LM_REAL)sqrt(epsmch);
+
+  buf=(LM_REAL *)malloc((fvec_sz + fjac_sz + pp_sz + fvecp_sz)*sizeof(LM_REAL));
+  if(!buf){
+    fprintf(stderr, LCAT(LEVMAR_CHKJAC, "(): memory allocation request failed\n"));
+    exit(1);
+  }
+  fvec=buf;
+  fjac=fvec+fvec_sz;
+  pp=fjac+fjac_sz;
+  fvecp=pp+pp_sz;
+
+  /* compute fvec=func(p) */
+  (*func)(p, fvec, m, n, adata);
+
+  /* compute the Jacobian at p */
+  (*jacf)(p, fjac, m, n, adata);
+
+  /* compute pp */
+  for(j=0; j<m; ++j){
+    temp=eps*FABS(p[j]);
+    if(temp==zero) temp=eps;
+    pp[j]=p[j]+temp;
+  }
+
+  /* compute fvecp=func(pp) */
+  (*func)(pp, fvecp, m, n, adata);
+
+  epsf=factor*epsmch;
+  epslog=(LM_REAL)log10(eps);
+
+  for(i=0; i<n; ++i)
+    err[i]=zero;
+
+  for(j=0; j<m; ++j){
+    temp=FABS(p[j]);
+    if(temp==zero) temp=one;
+
+    for(i=0; i<n; ++i)
+      err[i]+=temp*fjac[i*m+j];
+  }
+
+  for(i=0; i<n; ++i){
+    temp=one;
+    if(fvec[i]!=zero && fvecp[i]!=zero && FABS(fvecp[i]-fvec[i])>=epsf*FABS(fvec[i]))
+        temp=eps*FABS((fvecp[i]-fvec[i])/eps - err[i])/(FABS(fvec[i])+FABS(fvecp[i]));
+    err[i]=one;
+    if(temp>epsmch && temp<eps)
+        err[i]=((LM_REAL)log10(temp) - epslog)/epslog;
+    if(temp>=eps) err[i]=zero;
+  }
+
+  free(buf);
+
+  return;
+}
+
+#ifdef HAVE_LAPACK
+/*
+ * This function computes the pseudoinverse of a square matrix A
+ * into B using SVD. A and B can coincide
+ * 
+ * The function returns 0 in case of error (e.g. A is singular),
+ * the rank of A if successful
+ *
+ * A, B are mxm
+ *
+ */
+static int LEVMAR_PSEUDOINVERSE(LM_REAL *A, LM_REAL *B, int m)
+{
+LM_REAL *buf=NULL;
+int buf_sz=0;
+static LM_REAL eps=LM_CNST(-1.0);
+
+register int i, j;
+LM_REAL *a, *u, *s, *vt, *work;
+int a_sz, u_sz, s_sz, vt_sz, tot_sz;
+LM_REAL thresh, one_over_denom;
+int info, rank, worksz, *iwork, iworksz;
+   
+  /* calculate required memory size */
+  worksz=5*m; // min worksize for GESVD
+  //worksz=m*(7*m+4); // min worksize for GESDD
+  iworksz=8*m;
+  a_sz=m*m;
+  u_sz=m*m; s_sz=m; vt_sz=m*m;
+
+  tot_sz=(a_sz + u_sz + s_sz + vt_sz + worksz)*sizeof(LM_REAL) + iworksz*sizeof(int); /* should be arranged in that order for proper doubles alignment */
+
+    buf_sz=tot_sz;
+    buf=(LM_REAL *)malloc(buf_sz);
+    if(!buf){
+      fprintf(stderr, RCAT("memory allocation in ", LEVMAR_PSEUDOINVERSE) "() failed!\n");
+      return 0; /* error */
+    }
+
+  a=buf;
+  u=a+a_sz;
+  s=u+u_sz;
+  vt=s+s_sz;
+  work=vt+vt_sz;
+  iwork=(int *)(work+worksz);
+
+  /* store A (column major!) into a */
+  for(i=0; i<m; i++)
+    for(j=0; j<m; j++)
+      a[i+j*m]=A[i*m+j];
+
+  /* SVD decomposition of A */
+  GESVD("A", "A", (int *)&m, (int *)&m, a, (int *)&m, s, u, (int *)&m, vt, (int *)&m, work, (int *)&worksz, &info);
+  //GESDD("A", (int *)&m, (int *)&m, a, (int *)&m, s, u, (int *)&m, vt, (int *)&m, work, (int *)&worksz, iwork, &info);
+
+  /* error treatment */
+  if(info!=0){
+    if(info<0){
+      fprintf(stderr, RCAT(RCAT(RCAT("LAPACK error: illegal value for argument %d of ", GESVD), "/" GESDD) " in ", LEVMAR_PSEUDOINVERSE) "()\n", -info);
+    }
+    else{
+      fprintf(stderr, RCAT("LAPACK error: dgesdd (dbdsdc)/dgesvd (dbdsqr) failed to converge in ", LEVMAR_PSEUDOINVERSE) "() [info=%d]\n", info);
+    }
+    free(buf);
+    return 0;
+  }
+
+  if(eps<0.0){
+    LM_REAL aux;
+
+    /* compute machine epsilon */
+    for(eps=LM_CNST(1.0); aux=eps+LM_CNST(1.0), aux-LM_CNST(1.0)>0.0; eps*=LM_CNST(0.5))
+                                          ;
+    eps*=LM_CNST(2.0);
+  }
+
+  /* compute the pseudoinverse in B */
+	for(i=0; i<a_sz; i++) B[i]=0.0; /* initialize to zero */
+  for(rank=0, thresh=eps*s[0]; rank<m && s[rank]>thresh; rank++){
+    one_over_denom=LM_CNST(1.0)/s[rank];
+
+    for(j=0; j<m; j++)
+      for(i=0; i<m; i++)
+        B[i*m+j]+=vt[rank+i*m]*u[j+rank*m]*one_over_denom;
+  }
+
+  free(buf);
+
+	return rank;
+}
+#else // no LAPACK
+
+/*
+ * This function computes the inverse of A in B. A and B can coincide
+ *
+ * The function employs LAPACK-free LU decomposition of A to solve m linear
+ * systems A*B_i=I_i, where B_i and I_i are the i-th columns of B and I.
+ *
+ * A and B are mxm
+ *
+ * The function returns 0 in case of error, 1 if successful
+ *
+ */
+static int LEVMAR_LUINVERSE(LM_REAL *A, LM_REAL *B, int m)
+{
+void *buf=NULL;
+int buf_sz=0;
+
+register int i, j, k, l;
+int *idx, maxi=-1, idx_sz, a_sz, x_sz, work_sz, tot_sz;
+LM_REAL *a, *x, *work, max, sum, tmp;
+
+  /* calculate required memory size */
+  idx_sz=m;
+  a_sz=m*m;
+  x_sz=m;
+  work_sz=m;
+  tot_sz=(a_sz + x_sz + work_sz)*sizeof(LM_REAL) + idx_sz*sizeof(int); /* should be arranged in that order for proper doubles alignment */
+
+  buf_sz=tot_sz;
+  buf=(void *)malloc(tot_sz);
+  if(!buf){
+    fprintf(stderr, RCAT("memory allocation in ", LEVMAR_LUINVERSE) "() failed!\n");
+    return 0; /* error */
+  }
+
+  a=buf;
+  x=a+a_sz;
+  work=x+x_sz;
+  idx=(int *)(work+work_sz);
+
+  /* avoid destroying A by copying it to a */
+  for(i=0; i<a_sz; ++i) a[i]=A[i];
+
+  /* compute the LU decomposition of a row permutation of matrix a; the permutation itself is saved in idx[] */
+	for(i=0; i<m; ++i){
+		max=0.0;
+		for(j=0; j<m; ++j)
+			if((tmp=FABS(a[i*m+j]))>max)
+        max=tmp;
+		  if(max==0.0){
+        fprintf(stderr, RCAT("Singular matrix A in ", LEVMAR_LUINVERSE) "()!\n");
+        free(buf);
+
+        return 0;
+      }
+		  work[i]=LM_CNST(1.0)/max;
+	}
+
+	for(j=0; j<m; ++j){
+		for(i=0; i<j; ++i){
+			sum=a[i*m+j];
+			for(k=0; k<i; ++k)
+        sum-=a[i*m+k]*a[k*m+j];
+			a[i*m+j]=sum;
+		}
+		max=0.0;
+		for(i=j; i<m; ++i){
+			sum=a[i*m+j];
+			for(k=0; k<j; ++k)
+        sum-=a[i*m+k]*a[k*m+j];
+			a[i*m+j]=sum;
+			if((tmp=work[i]*FABS(sum))>=max){
+				max=tmp;
+				maxi=i;
+			}
+		}
+		if(j!=maxi){
+			for(k=0; k<m; ++k){
+				tmp=a[maxi*m+k];
+				a[maxi*m+k]=a[j*m+k];
+				a[j*m+k]=tmp;
+			}
+			work[maxi]=work[j];
+		}
+		idx[j]=maxi;
+		if(a[j*m+j]==0.0)
+      a[j*m+j]=LM_REAL_EPSILON;
+		if(j!=m-1){
+			tmp=LM_CNST(1.0)/(a[j*m+j]);
+			for(i=j+1; i<m; ++i)
+        a[i*m+j]*=tmp;
+		}
+	}
+
+  /* The decomposition has now replaced a. Solve the m linear systems using
+   * forward and back substitution
+   */
+  for(l=0; l<m; ++l){
+    for(i=0; i<m; ++i) x[i]=0.0;
+    x[l]=LM_CNST(1.0);
+
+	  for(i=k=0; i<m; ++i){
+		  j=idx[i];
+		  sum=x[j];
+		  x[j]=x[i];
+		  if(k!=0)
+			  for(j=k-1; j<i; ++j)
+          sum-=a[i*m+j]*x[j];
+		  else
+        if(sum!=0.0)
+			    k=i+1;
+		  x[i]=sum;
+	  }
+
+	  for(i=m-1; i>=0; --i){
+		  sum=x[i];
+		  for(j=i+1; j<m; ++j)
+        sum-=a[i*m+j]*x[j];
+		  x[i]=sum/a[i*m+i];
+	  }
+
+    for(i=0; i<m; ++i)
+      B[i*m+l]=x[i];
+  }
+
+  free(buf);
+
+  return 1;
+}
+#endif /* HAVE_LAPACK */
+
+/*
+ * This function computes in C the covariance matrix corresponding to a least
+ * squares fit. JtJ is the approximate Hessian at the solution (i.e. J^T*J, where
+ * J is the Jacobian at the solution), sumsq is the sum of squared residuals
+ * (i.e. goodnes of fit) at the solution, m is the number of parameters (variables)
+ * and n the number of observations. JtJ can coincide with C.
+ * 
+ * if JtJ is of full rank, C is computed as sumsq/(n-m)*(JtJ)^-1
+ * otherwise and if LAPACK is available, C=sumsq/(n-r)*(JtJ)^+
+ * where r is JtJ's rank and ^+ denotes the pseudoinverse
+ * The diagonal of C is made up from the estimates of the variances
+ * of the estimated regression coefficients.
+ * See the documentation of routine E04YCF from the NAG fortran lib
+ *
+ * The function returns the rank of JtJ if successful, 0 on error
+ *
+ * A and C are mxm
+ *
+ */
+int LEVMAR_COVAR(LM_REAL *JtJ, LM_REAL *C, LM_REAL sumsq, int m, int n)
+{
+register int i;
+int rnk;
+LM_REAL fact;
+
+#ifdef HAVE_LAPACK
+   rnk=LEVMAR_PSEUDOINVERSE(JtJ, C, m);
+   if(!rnk) return 0;
+#else
+#ifdef _MSC_VER
+#pragma message("LAPACK not available, LU will be used for matrix inversion when computing the covariance; this might be unstable at times")
+#else
+#warning LAPACK not available, LU will be used for matrix inversion when computing the covariance; this might be unstable at times
+#endif // _MSC_VER
+
+   rnk=LEVMAR_LUINVERSE(JtJ, C, m);
+   if(!rnk) return 0;
+
+   rnk=m; /* assume full rank */
+#endif /* HAVE_LAPACK */
+
+   fact=sumsq/(LM_REAL)(n-rnk);
+   for(i=0; i<m*m; ++i)
+     C[i]*=fact;
+
+   return rnk;
+}
+
+/*  standard deviation of the best-fit parameter i.
+ *  covar is the mxm covariance matrix of the best-fit parameters (see also LEVMAR_COVAR()).
+ *
+ *  The standard deviation is computed as \sigma_{i} = \sqrt{C_{ii}} 
+ */
+LM_REAL LEVMAR_STDDEV(LM_REAL *covar, int m, int i)
+{
+   return (LM_REAL)sqrt(covar[i*m+i]);
+}
+
+/* Pearson's correlation coefficient of the best-fit parameters i and j.
+ * covar is the mxm covariance matrix of the best-fit parameters (see also LEVMAR_COVAR()).
+ *
+ * The coefficient is computed as \rho_{ij} = C_{ij} / sqrt(C_{ii} C_{jj})
+ */
+LM_REAL LEVMAR_CORCOEF(LM_REAL *covar, int m, int i, int j)
+{
+   return (LM_REAL)(covar[i*m+j]/sqrt(covar[i*m+i]*covar[j*m+j]));
+}
+
+/* coefficient of determination.
+ * see  http://en.wikipedia.org/wiki/Coefficient_of_determination
+ */
+LM_REAL LEVMAR_R2(void (*func)(LM_REAL *p, LM_REAL *hx, int m, int n, void *adata),
+                  LM_REAL *p, LM_REAL *x, int m, int n, void *adata)
+{
+register int i;
+register LM_REAL tmp;
+LM_REAL SSerr,  // sum of squared errors, i.e. residual sum of squares \sum_i (x_i-hx_i)^2 
+        SStot, // \sum_i (x_i-xavg)^2
+        *hx, xavg;
+
+
+  if((hx=(LM_REAL *)malloc(n*sizeof(LM_REAL)))==NULL){
+    fprintf(stderr, RCAT("memory allocation request failed in ", LEVMAR_R2) "()\n");
+    exit(1);
+  }
+
+  /* hx=f(p) */
+  (*func)(p, hx, m, n, adata);
+
+  for(i=n, tmp=0.0; i-->0; )
+    tmp+=x[i];
+  xavg=tmp/(LM_REAL)n;
+  
+  if(x)
+    for(i=n, SSerr=SStot=0.0; i-->0; ){
+      tmp=x[i]-hx[i];
+      SSerr+=tmp*tmp;
+
+      tmp=x[i]-xavg;
+      SStot+=tmp*tmp;
+    }
+  else /* x==0 */
+    for(i=n, SSerr=SStot=0.0; i-->0; ){
+      tmp=-hx[i];
+      SSerr+=tmp*tmp;
+
+      tmp=-xavg;
+      SStot+=tmp*tmp;
+    }
+
+  free(hx);
+
+  return LM_CNST(1.0) - SSerr/SStot;
+}
+
+/* check box constraints for consistency */
+int LEVMAR_BOX_CHECK(LM_REAL *lb, LM_REAL *ub, int m)
+{
+register int i;
+
+  if(!lb || !ub) return 1;
+
+  for(i=0; i<m; ++i)
+    if(lb[i]>ub[i]) return 0;
+
+  return 1;
+}
+
+#ifdef HAVE_LAPACK
+
+/* compute the Cholesky decomposition of C in W, s.t. C=W^t W and W is upper triangular */
+int LEVMAR_CHOLESKY(LM_REAL *C, LM_REAL *W, int m)
+{
+register int i, j;
+int info;
+
+  /* copy weights array C to W so that LAPACK won't destroy it;
+   * C is assumed symmetric, hence no transposition is needed
+   */
+  for(i=0, j=m*m; i<j; ++i)
+    W[i]=C[i];
+
+  /* Cholesky decomposition */
+  POTF2("L", (int *)&m, W, (int *)&m, (int *)&info);
+  /* error treatment */
+  if(info!=0){
+		if(info<0){
+      fprintf(stderr, "LAPACK error: illegal value for argument %d of dpotf2 in %s\n", -info, LCAT(LEVMAR_CHOLESKY, "()"));
+		}
+		else{
+			fprintf(stderr, "LAPACK error: the leading minor of order %d is not positive definite,\n%s()\n", info,
+						RCAT("and the Cholesky factorization could not be completed in ", LEVMAR_CHOLESKY));
+		}
+    return LM_ERROR;
+  }
+
+  /* the decomposition is in the lower part of W (in column-major order!).
+   * zeroing the upper part makes it lower triangular which is equivalent to
+   * upper triangular in row-major order
+   */
+  for(i=0; i<m; i++)
+    for(j=i+1; j<m; j++)
+      W[i+j*m]=0.0;
+
+  return 0;
+}
+#endif /* HAVE_LAPACK */
+
+
+/* Compute e=x-y for two n-vectors x and y and return the squared L2 norm of e.
+ * e can coincide with either x or y; x can be NULL, in which case it is assumed
+ * to be equal to the zero vector.
+ * Uses loop unrolling and blocking to reduce bookkeeping overhead & pipeline
+ * stalls and increase instruction-level parallelism; see http://www.abarnett.demon.co.uk/tutorial.html
+ */
+
+LM_REAL LEVMAR_L2NRMXMY(LM_REAL *e, LM_REAL *x, LM_REAL *y, int n)
+{
+const int blocksize=8, bpwr=3; /* 8=2^3 */
+register int i;
+int j1, j2, j3, j4, j5, j6, j7;
+int blockn;
+register LM_REAL sum0=0.0, sum1=0.0, sum2=0.0, sum3=0.0;
+
+  /* n may not be divisible by blocksize, 
+   * go as near as we can first, then tidy up.
+   */ 
+  blockn = (n>>bpwr)<<bpwr; /* (n / blocksize) * blocksize; */
+
+  /* unroll the loop in blocks of `blocksize'; looping downwards gains some more speed */
+  if(x){
+    for(i=blockn-1; i>0; i-=blocksize){
+              e[i ]=x[i ]-y[i ]; sum0+=e[i ]*e[i ];
+      j1=i-1; e[j1]=x[j1]-y[j1]; sum1+=e[j1]*e[j1];
+      j2=i-2; e[j2]=x[j2]-y[j2]; sum2+=e[j2]*e[j2];
+      j3=i-3; e[j3]=x[j3]-y[j3]; sum3+=e[j3]*e[j3];
+      j4=i-4; e[j4]=x[j4]-y[j4]; sum0+=e[j4]*e[j4];
+      j5=i-5; e[j5]=x[j5]-y[j5]; sum1+=e[j5]*e[j5];
+      j6=i-6; e[j6]=x[j6]-y[j6]; sum2+=e[j6]*e[j6];
+      j7=i-7; e[j7]=x[j7]-y[j7]; sum3+=e[j7]*e[j7];
+    }
+
+   /*
+    * There may be some left to do.
+    * This could be done as a simple for() loop, 
+    * but a switch is faster (and more interesting) 
+    */ 
+
+    i=blockn;
+    if(i<n){ 
+      /* Jump into the case at the place that will allow
+       * us to finish off the appropriate number of items. 
+       */ 
+
+      switch(n - i){ 
+        case 7 : e[i]=x[i]-y[i]; sum0+=e[i]*e[i]; ++i;
+        case 6 : e[i]=x[i]-y[i]; sum1+=e[i]*e[i]; ++i;
+        case 5 : e[i]=x[i]-y[i]; sum2+=e[i]*e[i]; ++i;
+        case 4 : e[i]=x[i]-y[i]; sum3+=e[i]*e[i]; ++i;
+        case 3 : e[i]=x[i]-y[i]; sum0+=e[i]*e[i]; ++i;
+        case 2 : e[i]=x[i]-y[i]; sum1+=e[i]*e[i]; ++i;
+        case 1 : e[i]=x[i]-y[i]; sum2+=e[i]*e[i]; //++i;
+      }
+    }
+  }
+  else{ /* x==0 */
+    for(i=blockn-1; i>0; i-=blocksize){
+              e[i ]=-y[i ]; sum0+=e[i ]*e[i ];
+      j1=i-1; e[j1]=-y[j1]; sum1+=e[j1]*e[j1];
+      j2=i-2; e[j2]=-y[j2]; sum2+=e[j2]*e[j2];
+      j3=i-3; e[j3]=-y[j3]; sum3+=e[j3]*e[j3];
+      j4=i-4; e[j4]=-y[j4]; sum0+=e[j4]*e[j4];
+      j5=i-5; e[j5]=-y[j5]; sum1+=e[j5]*e[j5];
+      j6=i-6; e[j6]=-y[j6]; sum2+=e[j6]*e[j6];
+      j7=i-7; e[j7]=-y[j7]; sum3+=e[j7]*e[j7];
+    }
+
+   /*
+    * There may be some left to do.
+    * This could be done as a simple for() loop, 
+    * but a switch is faster (and more interesting) 
+    */ 
+
+    i=blockn;
+    if(i<n){ 
+      /* Jump into the case at the place that will allow
+       * us to finish off the appropriate number of items. 
+       */ 
+
+      switch(n - i){ 
+        case 7 : e[i]=-y[i]; sum0+=e[i]*e[i]; ++i;
+        case 6 : e[i]=-y[i]; sum1+=e[i]*e[i]; ++i;
+        case 5 : e[i]=-y[i]; sum2+=e[i]*e[i]; ++i;
+        case 4 : e[i]=-y[i]; sum3+=e[i]*e[i]; ++i;
+        case 3 : e[i]=-y[i]; sum0+=e[i]*e[i]; ++i;
+        case 2 : e[i]=-y[i]; sum1+=e[i]*e[i]; ++i;
+        case 1 : e[i]=-y[i]; sum2+=e[i]*e[i]; //++i;
+      }
+    }
+  }
+
+  return sum0+sum1+sum2+sum3;
+}
+
+/* undefine everything. THIS MUST REMAIN AT THE END OF THE FILE */
+#undef POTF2
+#undef GESVD
+#undef GESDD
+#undef GEMM
+#undef LEVMAR_PSEUDOINVERSE
+#undef LEVMAR_LUINVERSE
+#undef LEVMAR_BOX_CHECK
+#undef LEVMAR_CHOLESKY
+#undef LEVMAR_COVAR
+#undef LEVMAR_STDDEV
+#undef LEVMAR_CORCOEF
+#undef LEVMAR_R2
+#undef LEVMAR_CHKJAC
+#undef LEVMAR_FDIF_FORW_JAC_APPROX
+#undef LEVMAR_FDIF_CENT_JAC_APPROX
+#undef LEVMAR_TRANS_MAT_MAT_MULT
+#undef LEVMAR_L2NRMXMY

lmfit/COPYING

@@ -0,0 +1,30 @@
+The package lmfit is distributed under the FreeBSD License:
+
+--
+  Copyright (c) 1980-1999 University of Chicago,
+                          as operator of Argonne National Laboratory
+  Copyright (c) 2004-2015 Joachim Wuttke, Forschungszentrum Juelich GmbH
+
+  All rights reserved.
+
+  Redistribution and use in source and binary forms, with or without
+  modification, are permitted provided that the following conditions are met:
+
+  - Redistributions of source code must retain the above copyright notice,
+    this list of conditions and the following disclaimer.
+  - Redistributions in binary form must reproduce the above copyright notice,
+    this list of conditions and the following disclaimer in the documentation
+    and/or other materials provided with the distribution.
+
+  This software is provided by the copyright holders and contributors "as is"
+  and any express or implied warranties, including, but not limited to, the
+  implied warranties of merchantability and fitness for a particular purpose
+  are disclaimed. In no event shall the copyright holder or contributors
+  be liable for any direct, indirect, incidental, special, exemplary, or
+  consequential damages (including, but not limited to, procurement of
+  substitute goods or services; loss of use, data, or profits; or business
+  interruption) however caused and on any theory of liability, whether in
+  contract, strict liability, or tort (including negligence or otherwise)
+  arising in any way out of the use of this software, even if advised of the
+  possibility of such damage.
+--

lmfit/lmcurve.c

@@ -0,0 +1,52 @@
+/*
+ * Library:   lmfit (Levenberg-Marquardt least squares fitting)
+ *
+ * File:      lmcurve.c
+ *
+ * Contents:  Implements lmcurve, a simplified API for curve fitting
+ *            using the generic Levenberg-Marquardt routine lmmin.
+ *
+ * Copyright: Joachim Wuttke, Forschungszentrum Juelich GmbH (2004-2013)
+ *
+ * License:   see ../COPYING (FreeBSD)
+ *
+ * Homepage:  apps.jcns.fz-juelich.de/lmfit
+ *
+ * Note to programmers: Don't patch and fork, but copy and modify!
+ *   If you need to compute residues differently, then please do not patch
+ * lmcurve.h and lmcurve.c, but copy them, and create differently named
+ * versions of lmcurve_data_struct, lmcurve_evaluate, and lmcurve of your own.
+ */
+
+#include "lmmin.h"
+
+
+typedef struct {
+    const double *const t;
+    const double *const y;
+    double (*const g) (const double t, const double *par);
+} lmcurve_data_struct;
+
+
+void lmcurve_evaluate(
+    const double *const par, const int m_dat, const void *const data,
+    double *const fvec, int *const info)
+{
+    for (int i = 0; i < m_dat; i++ )
+        fvec[i] =
+            ((lmcurve_data_struct*)data)->y[i] -
+            ((lmcurve_data_struct*)data)->g(
+                ((lmcurve_data_struct*)data)->t[i], par );
+}
+
+
+void lmcurve(
+    const int n_par, double *const par, const int m_dat,
+    const double *const t, const double *const y,
+    double (*const g)(const double t, const double *const par),
+    const lm_control_struct *const control, lm_status_struct *const status)
+{
+    lmcurve_data_struct data = {t, y, g};
+    lmmin(n_par, par, m_dat, NULL, (const void *const) &data,
+          lmcurve_evaluate, control, status);
+}

lmfit/lmcurve.h

@@ -0,0 +1,45 @@
+/*
+ * Library:   lmfit (Levenberg-Marquardt least squares fitting)
+ *
+ * File:      lmcurve.h
+ *
+ * Contents:  Declares lmcurve, a simplified API for curve fitting
+ *            using the generic Levenberg-Marquardt routine lmmin.
+ *
+ * Copyright: Joachim Wuttke, Forschungszentrum Juelich GmbH (2004-2013)
+ *
+ * License:   see ../COPYING (FreeBSD)
+ *
+ * Homepage:  apps.jcns.fz-juelich.de/lmfit
+ *
+ * Note to programmers: Don't patch and fork, but copy and variate!
+ *   If you need to compute residues differently, then please do not patch
+ * lmcurve.h, but copy it to a differently named file, and change lmcurve()
+ * into a differently named function declaration, like we have done in
+ * lmcurve_tyd.h.
+ */
+
+#ifndef LMCURVE_H
+#define LMCURVE_H
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+#define __BEGIN_DECLS extern "C" {
+#define __END_DECLS }
+#else
+#define __BEGIN_DECLS /* empty */
+#define __END_DECLS   /* empty */
+#endif
+
+#include<lmstruct.h>
+
+__BEGIN_DECLS
+
+void lmcurve(
+    const int n_par, double* par, const int m_dat,
+    const double* t, const double* y,
+    double (*g)(const double t, const double* par),
+    const lm_control_struct* control, lm_status_struct* status);
+
+__END_DECLS
+#endif /* LMCURVE_H */

lmfit/lmcurve_tyd.h

@@ -0,0 +1,39 @@
+/*
+ * Library:   lmfit (Levenberg-Marquardt least squares fitting)
+ *
+ * File:      lmcurve_tyd.h
+ *
+ * Contents:  Declares lmcurve_tyd(), a variant of lmcurve() that weighs
+ *            data points y(t) with the inverse of the standard deviations dy.
+ *
+ * Copyright: Joachim Wuttke, Forschungszentrum Juelich GmbH (2004-2013)
+ *
+ * License:   see ../COPYING (FreeBSD)
+ *
+ * Homepage:  apps.jcns.fz-juelich.de/lmfit
+ */
+
+#ifndef LMCURVETYD_H
+#define LMCURVETYD_H
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+#define __BEGIN_DECLS extern "C" {
+#define __END_DECLS }
+#else
+#define __BEGIN_DECLS /* empty */
+#define __END_DECLS   /* empty */
+#endif
+
+#include <lmstruct.h>
+
+__BEGIN_DECLS
+
+void lmcurve_tyd(
+    const int n_par, double* par, const int m_dat,
+    const double* t, const double* y, const double* dy,
+    double (*f)(double t, const double* par),
+    const lm_control_struct* control, lm_status_struct* status);
+
+__END_DECLS
+#endif /* LMCURVETYD_H */

lmfit/lmmin.h

@@ -0,0 +1,84 @@
+/*
+ * Library:   lmfit (Levenberg-Marquardt least squares fitting)
+ *
+ * File:      lmmin.h
+ *
+ * Contents:  Declarations for Levenberg-Marquardt minimization.
+ *
+ * Copyright: Joachim Wuttke, Forschungszentrum Juelich GmbH (2004-2013)
+ *
+ * License:   see ../COPYING (FreeBSD)
+ *
+ * Homepage:  apps.jcns.fz-juelich.de/lmfit
+ */
+
+#ifndef LMMIN_H
+#define LMMIN_H
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+#define __BEGIN_DECLS extern "C" {
+#define __END_DECLS }
+#else
+#define __BEGIN_DECLS /* empty */
+#define __END_DECLS   /* empty */
+#endif
+
+#include "lmstruct.h"
+
+__BEGIN_DECLS
+
+/* Levenberg-Marquardt minimization. */
+void lmmin(
+    const int n_par, double* par, const int m_dat, const double* y,
+    const void* data,
+    void (*evaluate)(
+        const double* par, const int m_dat, const void* data,
+        double* fvec, int* userbreak),
+    const lm_control_struct* control, lm_status_struct* status);
+/*
+ *   This routine contains the core algorithm of our library.
+ *
+ *   It minimizes the sum of the squares of m nonlinear functions
+ *   in n variables by a modified Levenberg-Marquardt algorithm.
+ *   The function evaluation is done by the user-provided routine 'evaluate'.
+ *   The Jacobian is then calculated by a forward-difference approximation.
+ *
+ *   Parameters:
+ *
+ *      n_par is the number of variables (INPUT, positive integer).
+ *
+ *      par is the solution vector (INPUT/OUTPUT, array of length n).
+ *        On input it must be set to an estimated solution.
+ *        On output it yields the final estimate of the solution.
+ *
+ *      m_dat is the number of functions to be minimized (INPUT, positive integer).
+ *        It must fulfill m>=n.
+ *
+ *      y contains data to be fitted. Use a null pointer if there are no data.
+ *
+ *      data is a pointer that is ignored by lmmin; it is however forwarded
+ *        to the user-supplied functions evaluate and printout.
+ *        In a typical application, it contains experimental data to be fitted.
+ *
+ *      evaluate is a user-supplied function that calculates the m functions.
+ *        Parameters:
+ *          n, x, m, data as above.
+ *          fvec is an array of length m; on OUTPUT, it must contain the
+ *            m function values for the parameter vector x.
+ *          userbreak is an integer pointer. When *userbreak is set to a
+ *            nonzero value, lmmin will terminate.
+ *
+ *      control contains INPUT variables that control the fit algorithm,
+ *        as declared and explained in lmstruct.h
+ *
+ *      status contains OUTPUT variables that inform about the fit result,
+ *        as declared and explained in lmstruct.h
+ */
+
+/* Refined calculation of Eucledian norm. */
+double lm_enorm(const int, const double*);
+double lm_fnorm(const int, const double*, const double*);
+
+__END_DECLS
+#endif /* LMMIN_H */

lmfit/lmstruct.h

@@ -0,0 +1,81 @@
+/*
+ * Library:   lmfit (Levenberg-Marquardt least squares fitting)
+ *
+ * File:      lmstruct.h
+ *
+ * Contents:  Declarations of parameter records, used in lmmin.h and lmcurve.h
+ *
+ * Copyright: Joachim Wuttke, Forschungszentrum Juelich GmbH (2004-2013)
+ *
+ * License:   see ../COPYING (FreeBSD)
+ *
+ * Homepage:  apps.jcns.fz-juelich.de/lmfit
+ */
+
+#ifndef LMSTRUCT_H
+#define LMSTRUCT_H
+#undef __BEGIN_DECLS
+#undef __END_DECLS
+#ifdef __cplusplus
+#define __BEGIN_DECLS extern "C" {
+#define __END_DECLS }
+#else
+#define __BEGIN_DECLS /* empty */
+#define __END_DECLS   /* empty */
+#endif
+__BEGIN_DECLS
+
+#include <stdio.h>
+
+/* Collection of input parameters for fit control. */
+typedef struct {
+    double ftol;      /* Relative error desired in the sum of squares.
+                         Termination occurs when both the actual and
+                         predicted relative reductions in the sum of squares
+                         are at most ftol. */
+    double xtol;      /* Relative error between last two approximations.
+                         Termination occurs when the relative error between
+                         two consecutive iterates is at most xtol. */
+    double gtol;      /* Orthogonality desired between fvec and its derivs.
+                         Termination occurs when the cosine of the angle
+                         between fvec and any column of the Jacobian is at
+                         most gtol in absolute value. */
+    double epsilon;   /* Step used to calculate the Jacobian, should be
+                         slightly larger than the relative error in the
+                         user-supplied functions. */
+    double stepbound; /* Used in determining the initial step bound. This
+                         bound is set to the product of stepbound and the
+                         Euclidean norm of diag*x if nonzero, or else to
+                         stepbound itself. In most cases stepbound should lie
+                         in the interval (0.1,100.0). Generally, the value
+                         100.0 is recommended. */
+    int patience;     /* Used to set the maximum number of function evaluations
+                         to patience*(number_of_parameters+1). */
+    int scale_diag;   /* If 1, the variables will be rescaled internally.
+                         Recommended value is 1. */
+    FILE* msgfile;    /* Progress messages will be written to this file. */
+    int verbosity;    /* OR'ed: 1: print some messages; 2: print Jacobian. */
+    int n_maxpri;     /* -1, or max number of parameters to print. */
+    int m_maxpri;     /* -1, or max number of residuals to print. */
+} lm_control_struct;
+
+/* Collection of output parameters for status info. */
+typedef struct {
+    double fnorm;  /* norm of the residue vector fvec. */
+    int nfev;      /* actual number of iterations. */
+    int outcome;   /* Status indicator. Nonnegative values are used as index
+                      for the message text lm_infmsg, set in lmmin.c. */
+    int userbreak; /* Set when function evaluation requests termination. */
+} lm_status_struct;
+
+/* Preset (and recommended) control parameter settings. */
+extern const lm_control_struct lm_control_double;
+extern const lm_control_struct lm_control_float;
+
+/* Preset message texts. */
+
+extern const char* lm_infmsg[];
+extern const char* lm_shortmsg[];
+
+__END_DECLS
+#endif /* LMSTRUCT_H */

qtsolutions/qwtcurve/qwt_plot_gapped_curve.cpp

@@ -29,7 +29,7 @@ void QwtPlotGappedCurve::drawSeries(QPainter *painter, const QwtScaleMap &xMap,
         return;
 
     if (to < 0)
-        to = dataSize() - 1;
+        to = dataSize();
 
     int i = from;
     double last = 0;
@@ -38,7 +38,11 @@ void QwtPlotGappedCurve::drawSeries(QPainter *painter, const QwtScaleMap &xMap,
         // First non-missed point will be the start of curve section.
         double x = sample(i).x();
         double y = sample(i).y();
-        if ((y < (naValue_ + -0.001) || y > (naValue_ + 0.001)) && x - last <= gapValue_) {
+        double yprev = 0;
+        if (i>0) yprev = sample(i-1).y();
+
+        if ((y < (naValue_ + -0.001) || y > (naValue_ + 0.001)) && (x - last <= gapValue_) &&
+            (yprev < (naValue_ + -0.001) || yprev > (naValue_ + 0.001))) {
 
             int start = i-1;
             int end = i;