R/pcalg_included_functions.R

In nicolagnecco/causalXtreme: Causal discovery in heavy-tailed models

# The original source for most of this comes from pcalg package
# code in https://CRAN.R-project.org/package=pcalg
# The credit goes to the authors of the package:
# Markus Kalisch, Alain Hauser , Martin Maechler, Diego Colombo,
# Doris Entner, Patrik Hoyer, Antti Hyttinen, Jonas Peters,
# Nicoletta Andri, Emilija Perkovic, Preetam Nandy, Philipp Ruetimann,
# Daniel Stekhoven, Manuel Schuerch, Marco Eigenmann.
#
# Below is the original license statement for the pcalg package.
#
# GNU GENERAL PUBLIC LICENSE
# Version 3, 29 June 2007
#
# Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
#   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
# 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.
#
# 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.
#
# 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.
#
# 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.
#
# 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.
#
# 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.
#
# 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
# on the Program.
#
# To "propagate" a work means to do anything with it that, without
# permission, would make you directly or secondarily liable for
# infringement under applicable copyright law, except executing it on a
# computer or modifying a private copy.  Propagation includes copying,
# distribution (with or without modification), making available to the
# public, and in some countries other activities as well.
#
# To "convey" a work means any kind of propagation that enables other
# parties to make or receive copies.  Mere interaction with a user through
# a computer network, with no transfer of a copy, is not conveying.
#
# 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
# work under this License, and how to view a copy of this License.  If
# the interface presents a list of user commands or options, such as a
# menu, a prominent item in the list meets this criterion.
#
# 1. Source Code.
#
# The "source code" for a work means the preferred form of the work
# for making modifications to it.  "Object code" means any non-source
# form of a work.
#
# A "Standard Interface" means an interface that either is an official
# standard defined by a recognized standards body, or, in the case of
# interfaces specified for a particular programming language, one that
# is widely used among developers working in that language.
#
# The "System Libraries" of an executable work include anything, other
# than the work as a whole, that (a) is included in the normal form of
# 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
# Major Component, or to implement a Standard Interface for which an
# implementation is available to the public in source code form.  A
# "Major Component", in this context, means a major essential component
# (kernel, window system, and so on) of the specific operating system
# (if any) on which the executable work runs, or a compiler used to
# produce the work, or an object code interpreter used to run it.
#
# The "Corresponding Source" for a work in object code form means all
# the source code needed to generate, install, and (for an executable
# work) run the object code and to modify the work, including scripts to
# control those activities.  However, it does not include the work's
# System Libraries, or general-purpose tools or generally available free
# programs which are used unmodified in performing those activities but
# which are not part of the work.  For example, Corresponding Source
# includes interface definition files associated with source files for
# the work, and the source code for shared libraries and dynamically
# linked subprograms that the work is specifically designed to require,
# such as by intimate data communication or control flow between those
# subprograms and other parts of the work.
#
# The Corresponding Source need not include anything that users
# can regenerate automatically from other parts of the Corresponding
# 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
# with facilities for running those works, provided that you comply with
# the terms of this License in conveying all material for which you do
# not control copyright.  Those thus making or running the covered works
# for you must do so exclusively on your behalf, under your direction
# and control, on terms that prohibit them from making any copies of
# your copyrighted material outside their relationship with you.
#
# Conveying under any other circumstances is permitted solely under
# the conditions stated below.  Sublicensing is not allowed; section 10
# makes it unnecessary.
#
# 3. Protecting Users' Legal Rights From Anti-Circumvention Law.
#
# No covered work shall be deemed part of an effective technological
# measure under any applicable law fulfilling obligations under article
# 11 of the WIPO copyright treaty adopted on 20 December 1996, or
# similar laws prohibiting or restricting circumvention of such
# measures.
#
# When you convey a covered work, you waive any legal power to forbid
# circumvention of technological measures to the extent such circumvention
# is effected by exercising rights under this License with respect to
# the covered work, and you disclaim any intention to limit operation or
# modification of the work as a means of enforcing, against the work's
# users, your or third parties' legal rights to forbid circumvention of
# technological measures.
#
# 4. Conveying Verbatim Copies.
#
# You may convey verbatim copies of the Program's source code as you
# receive it, in any medium, provided that you conspicuously and
# appropriately publish on each copy an appropriate copyright notice;
# keep intact all notices stating that this License and any
# non-permissive terms added in accord with section 7 apply to the code;
# keep intact all notices of the absence of any warranty; and give all
# recipients a copy of this License along with the Program.
#
# You may charge any price or no price for each copy that you convey,
# and you may offer support or warranty protection for a fee.
#
# 5. Conveying Modified Source Versions.
#
# You may convey a work based on the Program, or the modifications to
# produce it from the Program, in the form of source code under the
# terms of section 4, provided that you also meet all of these conditions:
#
#   a) The work must carry prominent notices stating that you modified
# it, and giving a relevant date.
#
# b) The work must carry prominent notices stating that it is
# released under this License and any conditions added under section
# 7.  This requirement modifies the requirement in section 4 to
# "keep intact all notices".
#
# c) You must license the entire work, as a whole, under this
# License to anyone who comes into possession of a copy.  This
# License will therefore apply, along with any applicable section 7
# additional terms, to the whole of the work, and all its parts,
# regardless of how they are packaged.  This License gives no
# permission to license the work in any other way, but it does not
# invalidate such permission if you have separately received it.
#
# d) If the work has interactive user interfaces, each must display
# Appropriate Legal Notices; however, if the Program has interactive
# interfaces that do not display Appropriate Legal Notices, your
# work need not make them do so.
#
# A compilation of a covered work with other separate and independent
# works, which are not by their nature extensions of the covered work,
# and which are not combined with it such as to form a larger program,
# in or on a volume of a storage or distribution medium, is called an
# "aggregate" if the compilation and its resulting copyright are not
# used to limit the access or legal rights of the compilation's users
# beyond what the individual works permit.  Inclusion of a covered work
# in an aggregate does not cause this License to apply to the other
# parts of the aggregate.
#
# 6. Conveying Non-Source Forms.
#
# You may convey a covered work in object code form under the terms
# of sections 4 and 5, provided that you also convey the
# machine-readable Corresponding Source under the terms of this License,
# in one of these ways:
#
# a) Convey the object code in, or embodied in, a physical product
# (including a physical distribution medium), accompanied by the
# Corresponding Source fixed on a durable physical medium
# customarily used for software interchange.
#
# b) Convey the object code in, or embodied in, a physical product
# (including a physical distribution medium), accompanied by a
# written offer, valid for at least three years and valid for as
# long as you offer spare parts or customer support for that product
# model, to give anyone who possesses the object code either (1) a
# copy of the Corresponding Source for all the software in the
# product that is covered by this License, on a durable physical
# medium customarily used for software interchange, for a price no
# more than your reasonable cost of physically performing this
# conveying of source, or (2) access to copy the
# Corresponding Source from a network server at no charge.
#
# c) Convey individual copies of the object code with a copy of the
# written offer to provide the Corresponding Source.  This
# alternative is allowed only occasionally and noncommercially, and
# only if you received the object code with such an offer, in accord
# with subsection 6b.
#
# d) Convey the object code by offering access from a designated
# place (gratis or for a charge), and offer equivalent access to the
# Corresponding Source in the same way through the same place at no
# further charge.  You need not require recipients to copy the
# Corresponding Source along with the object code.  If the place to
# copy the object code is a network server, the Corresponding Source
# may be on a different server (operated by you or a third party)
# that supports equivalent copying facilities, provided you maintain
# clear directions next to the object code saying where to find the
# Corresponding Source.  Regardless of what server hosts the
# Corresponding Source, you remain obligated to ensure that it is
# available for as long as needed to satisfy these requirements.
#
# e) Convey the object code using peer-to-peer transmission, provided
# you inform other peers where the object code and Corresponding
# Source of the work are being offered to the general public at no
# charge under subsection 6d.
#
# A separable portion of the object code, whose source code is excluded
# from the Corresponding Source as a System Library, need not be
# included in conveying the object code work.
#
# A "User Product" is either (1) a "consumer product", which means any
# tangible personal property which is normally used for personal, family,
# or household purposes, or (2) anything designed or sold for incorporation
# into a dwelling.  In determining whether a product is a consumer product,
# doubtful cases shall be resolved in favor of coverage.  For a particular
# product received by a particular user, "normally used" refers to a
# typical or common use of that class of product, regardless of the status
# of the particular user or of the way in which the particular user
# actually uses, or expects or is expected to use, the product.  A product
# is a consumer product regardless of whether the product has substantial
# commercial, industrial or non-consumer uses, unless such uses represent
# the only significant mode of use of the product.
#
# "Installation Information" for a User Product means any methods,
# procedures, authorization keys, or other information required to install
# and execute modified versions of a covered work in that User Product from
# a modified version of its Corresponding Source.  The information must
# suffice to ensure that the continued functioning of the modified object
# code is in no case prevented or interfered with solely because
# modification has been made.
#
# If you convey an object code work under this section in, or with, or
# specifically for use in, a User Product, and the conveying occurs as
# part of a transaction in which the right of possession and use of the
# User Product is transferred to the recipient in perpetuity or for a
# fixed term (regardless of how the transaction is characterized), the
# Corresponding Source conveyed under this section must be accompanied
# by the Installation Information.  But this requirement does not apply
# if neither you nor any third party retains the ability to install
# modified object code on the User Product (for example, the work has
# been installed in ROM).
#
# The requirement to provide Installation Information does not include a
# requirement to continue to provide support service, warranty, or updates
# for a work that has been modified or installed by the recipient, or for
# the User Product in which it has been modified or installed.  Access to a
# network may be denied when the modification itself materially and
# adversely affects the operation of the network or violates the rules and
# protocols for communication across the network.
#
# Corresponding Source conveyed, and Installation Information provided,
# in accord with this section must be in a format that is publicly
# documented (and with an implementation available to the public in
# source code form), and must require no special password or key for
# unpacking, reading or copying.
#
# 7. Additional Terms.
#
# "Additional permissions" are terms that supplement the terms of this
# License by making exceptions from one or more of its conditions.
# Additional permissions that are applicable to the entire Program shall
# be treated as though they were included in this License, to the extent
# that they are valid under applicable law.  If additional permissions
# apply only to part of the Program, that part may be used separately
# under those permissions, but the entire Program remains governed by
# this License without regard to the additional permissions.
#
# When you convey a copy of a covered work, you may at your option
# remove any additional permissions from that copy, or from any part of
# it.  (Additional permissions may be written to require their own
# removal in certain cases when you modify the work.)  You may place
# additional permissions on material, added by you to a covered work,
# for which you have or can give appropriate copyright permission.
#
# Notwithstanding any other provision of this License, for material you
# add to a covered work, you may (if authorized by the copyright holders of
# that material) supplement the terms of this License with terms:
#
# a) Disclaiming warranty or limiting liability differently from the
# terms of sections 15 and 16 of this License; or
#
# b) Requiring preservation of specified reasonable legal notices or
# author attributions in that material or in the Appropriate Legal
# Notices displayed by works containing it; or
#
# c) Prohibiting misrepresentation of the origin of that material, or
# requiring that modified versions of such material be marked in
# reasonable ways as different from the original version; or
#
# d) Limiting the use for publicity purposes of names of licensors or
# authors of the material; or
#
# e) Declining to grant rights under trademark law for use of some
# trade names, trademarks, or service marks; or
#
# f) Requiring indemnification of licensors and authors of that
# material by anyone who conveys the material (or modified versions of
# it) with contractual assumptions of liability to the recipient, for
# any liability that these contractual assumptions directly impose on
# those licensors and authors.
#
# All other non-permissive additional terms are considered "further
# restrictions" within the meaning of section 10.  If the Program as you
# received it, or any part of it, contains a notice stating that it is
# governed by this License along with a term that is a further
# restriction, you may remove that term.  If a license document contains
# a further restriction but permits relicensing or conveying under this
# License, you may add to a covered work material governed by the terms
# of that license document, provided that the further restriction does
# not survive such relicensing or conveying.
#
# If you add terms to a covered work in accord with this section, you
# must place, in the relevant source files, a statement of the
# additional terms that apply to those files, or a notice indicating
# where to find the applicable terms.
#
# Additional terms, permissive or non-permissive, may be stated in the
# form of a separately written license, or stated as exceptions;
# the above requirements apply either way.
#
# 8. Termination.
#
# You may not propagate or modify a covered work except as expressly
# provided under this License.  Any attempt otherwise to propagate or
# modify it is void, and will automatically terminate your rights under
# this License (including any patent licenses granted under the third
# paragraph of section 11).
#
# However, if you cease all violation of this License, then your
# license from a particular copyright holder is reinstated (a)
# provisionally, unless and until the copyright holder explicitly and
# finally terminates your license, and (b) permanently, if the copyright
# holder fails to notify you of the violation by some reasonable means
# prior to 60 days after the cessation.
#
# Moreover, your license from a particular copyright holder is
# reinstated permanently if the copyright holder notifies you of the
# violation by some reasonable means, this is the first time you have
# received notice of violation of this License (for any work) from that
# copyright holder, and you cure the violation prior to 30 days after
# your receipt of the notice.
#
# Termination of your rights under this section does not terminate the
# licenses of parties who have received copies or rights from you under
# this License.  If your rights have been terminated and not permanently
# reinstated, you do not qualify to receive new licenses for the same
# material under section 10.
#
# 9. Acceptance Not Required for Having Copies.
#
# You are not required to accept this License in order to receive or
# run a copy of the Program.  Ancillary propagation of a covered work
# occurring solely as a consequence of using peer-to-peer transmission
# to receive a copy likewise does not require acceptance.  However,
# nothing other than this License grants you permission to propagate or
# modify any covered work.  These actions infringe copyright if you do
# not accept this License.  Therefore, by modifying or propagating a
# covered work, you indicate your acceptance of this License to do so.
#
# 10. Automatic Licensing of Downstream Recipients.
#
# Each time you convey a covered work, the recipient automatically
# receives a license from the original licensors, to run, modify and
# propagate that work, subject to this License.  You are not responsible
# for enforcing compliance by third parties with this License.
#
# An "entity transaction" is a transaction transferring control of an
# organization, or substantially all assets of one, or subdividing an
# organization, or merging organizations.  If propagation of a covered
# work results from an entity transaction, each party to that
# transaction who receives a copy of the work also receives whatever
# licenses to the work the party's predecessor in interest had or could
# give under the previous paragraph, plus a right to possession of the
# Corresponding Source of the work from the predecessor in interest, if
# the predecessor has it or can get it with reasonable efforts.
#
# You may not impose any further restrictions on the exercise of the
# rights granted or affirmed under this License.  For example, you may
# not impose a license fee, royalty, or other charge for exercise of
# rights granted under this License, and you may not initiate litigation
# (including a cross-claim or counterclaim in a lawsuit) alleging that
# any patent claim is infringed by making, using, selling, offering for
# sale, or importing the Program or any portion of it.
#
# 11. Patents.
#
# A "contributor" is a copyright holder who authorizes use under this
# License of the Program or a work on which the Program is based.  The
# work thus licensed is called the contributor's "contributor version".
#
# A contributor's "essential patent claims" are all patent claims
# owned or controlled by the contributor, whether already acquired or
# hereafter acquired, that would be infringed by some manner, permitted
# by this License, of making, using, or selling its contributor version,
# but do not include claims that would be infringed only as a
# consequence of further modification of the contributor version.  For
# purposes of this definition, "control" includes the right to grant
# patent sublicenses in a manner consistent with the requirements of
# this License.
#
# Each contributor grants you a non-exclusive, worldwide, royalty-free
# patent license under the contributor's essential patent claims, to
# make, use, sell, offer for sale, import and otherwise run, modify and
# propagate the contents of its contributor version.
#
# In the following three paragraphs, a "patent license" is any express
# agreement or commitment, however denominated, not to enforce a patent
# (such as an express permission to practice a patent or covenant not to
# sue for patent infringement).  To "grant" such a patent license to a
# party means to make such an agreement or commitment not to enforce a
# patent against the party.
#
# If you convey a covered work, knowingly relying on a patent license,
# and the Corresponding Source of the work is not available for anyone
# to copy, free of charge and under the terms of this License, through a
# publicly available network server or other readily accessible means,
# then you must either (1) cause the Corresponding Source to be so
# available, or (2) arrange to deprive yourself of the benefit of the
# patent license for this particular work, or (3) arrange, in a manner
# consistent with the requirements of this License, to extend the patent
# license to downstream recipients.  "Knowingly relying" means you have
# actual knowledge that, but for the patent license, your conveying the
# covered work in a country, or your recipient's use of the covered work
# in a country, would infringe one or more identifiable patents in that
# country that you have reason to believe are valid.
#
# If, pursuant to or in connection with a single transaction or
# arrangement, you convey, or propagate by procuring conveyance of, a
# covered work, and grant a patent license to some of the parties
# receiving the covered work authorizing them to use, propagate, modify
# or convey a specific copy of the covered work, then the patent license
# you grant is automatically extended to all recipients of the covered
# work and works based on it.
#
# A patent license is "discriminatory" if it does not include within
# the scope of its coverage, prohibits the exercise of, or is
# conditioned on the non-exercise of one or more of the rights that are
# specifically granted under this License.  You may not convey a covered
# work if you are a party to an arrangement with a third party that is
# in the business of distributing software, under which you make payment
# to the third party based on the extent of your activity of conveying
# the work, and under which the third party grants, to any of the
# parties who would receive the covered work from you, a discriminatory
# patent license (a) in connection with copies of the covered work
# conveyed by you (or copies made from those copies), or (b) primarily
# for and in connection with specific products or compilations that
# contain the covered work, unless you entered into that arrangement,
# or that patent license was granted, prior to 28 March 2007.
#
# Nothing in this License shall be construed as excluding or limiting
# any implied license or other defenses to infringement that may
# otherwise be available to you under applicable patent law.
#
# 12. No Surrender of Others' Freedom.
#
# If conditions are imposed on you (whether by court order, agreement or
# otherwise) that contradict the conditions of this License, they do not
# excuse you from the conditions of this License.  If you cannot convey a
# covered work so as to satisfy simultaneously your obligations under this
# License and any other pertinent obligations, then as a consequence you may
# not convey it at all.  For example, if you agree to terms that obligate you
# to collect a royalty for further conveying from those to whom you convey
# the Program, the only way you could satisfy both those terms and this
# License would be to refrain entirely from conveying the Program.
#
# 13. Use with the GNU Affero General Public License.
#
# Notwithstanding any other provision of this License, you have
# permission to link or combine any covered work with a work licensed
# under version 3 of the GNU Affero General Public License into a single
# combined work, and to convey the resulting work.  The terms of this
# License will continue to apply to the part which is the covered work,
# but the special requirements of the GNU Affero General Public License,
# section 13, concerning interaction through a network will apply to the
# combination as such.
#
# 14. Revised Versions of this License.
#
# The Free Software Foundation may publish revised and/or new versions of
# the GNU General Public License from time to time.  Such new versions will
# be similar in spirit to the present version, but may differ in detail to
# address new problems or concerns.
#
# Each version is given a distinguishing version number.  If the
# Program specifies that a certain numbered version of the GNU General
# Public License "or any later version" applies to it, you have the
# option of following the terms and conditions either of that numbered
# version or of any later version published by the Free Software
# Foundation.  If the Program does not specify a version number of the
# GNU General Public License, you may choose any version ever published
# by the Free Software Foundation.
#
# If the Program specifies that a proxy can decide which future
# versions of the GNU General Public License can be used, that proxy's
# public statement of acceptance of a version permanently authorizes you
# to choose that version for the Program.
#
# 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.
#
# 15. Disclaimer of Warranty.
#
# 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.
#
# END OF TERMS AND CONDITIONS
#
# How to Apply These Terms to Your New Programs
#
# If you develop a new program, and you want it to be of the greatest
# possible use to the public, the best way to achieve this is to make it
# 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
# 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
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <http://www.gnu.org/licenses/>.
#
# 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:
#
# <program>  Copyright (C) <year>  <name of author>
# This program 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".
#
#     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/>.
#
#     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>.
#
#
# changes to these functions by Nicola Gnecco
# 1. addition to estLiNGAM of the parameter 'fun' to allow for different
#    contrast functions, i.e., "logcosh" and "exp", when calling the
#    function fastICA from fastICA package.

estLiNGAM <- function (X, only.perm = FALSE, fastICA.tol = 1e-14, pmax.nz.brute = 8,
                       pmax.slt.brute = 8, verbose = FALSE, fun = c("logcosh","exp")) {
  p <- ncol(X)
  fun <- match.arg(fun)
  icares <- fastICA::fastICA(X, n.comp = p, tol = fastICA.tol, verbose = if (verbose >=
                                                                             1)
    verbose - 1L
    else FALSE, fun = fun)
  W <- t(icares$K %*% icares$W)
  if (verbose)
    cat("Performing row permutation, nzdiag*() ...\n  ")
  nzd <- if (p <= pmax.nz.brute) {
    if (verbose)
      cat("(Small dimensionality, using brute-force method.): ")
    nzdiagbruteforce(W)
  }
  else {
    if (verbose)
      cat("(Using the Hungarian algorithm.): ")
    nzdiaghungarian(W)
  }
  Wp <- nzd$Wopt
  if (verbose)
    cat("Done!\n")
  if (!only.perm)
    estdisturbancestd <- 1/diag(abs(Wp))
  Wp <- Wp/diag(Wp)
  Best <- diag(p) - Wp
  if (!only.perm)
    cest <- Wp %*% colMeans(X)
  if (verbose)
    cat("Performing permutation for causal order...\n  ")
  slt <- if (p <= pmax.slt.brute) {
    if (verbose)
      cat("(Small dimensionality, using brute-force method.): ")
    sltbruteforce(Best)
  }
  else {
    if (verbose)
      cat("(Using pruning algorithm.): ")
    sltprune(Best)
  }
  causalperm <- slt$optperm
  if (verbose)
    cat("Done!\n")
  if (only.perm && !verbose)
    return(list(k = causalperm))
  Bestcausal <- slt$Bopt
  if (verbose)
    print(Bestcausal)
  percentinupper <- sltscore(Bestcausal)/sum(Bestcausal^2)
  if (verbose) {
    if (percentinupper > 0.2)
      cat("WARNING: Causal B not really triangular at all!!\n")
    else if (percentinupper > 0.05)
      cat("WARNING: Causal B only somewhat triangular!\n")
    else cat("Causal B nicely triangular. No problems to report here.\n")
    if (only.perm)
      return(list(k = causalperm))
  }
  Bestcausal[upper.tri(Bestcausal, diag = FALSE)] <- 0
  icausal <- iperm(causalperm)
  list(B = Bestcausal[icausal, icausal], stde = estdisturbancestd,
       ci = cest, k = causalperm, W = W, pinup = percentinupper)
}

nzdiagbruteforce <- function(W) {
  stopifnot((n <- nrow(W)) >= 1)
  allperms <- all.perm(n)
  I.n <- diag(n)
  bestval <- Inf
  besti <- 0
  nperms <- nrow(allperms)
  for (i in 1:nperms) {
    Pr <- I.n[, allperms[i, ]]
    Wtilde <- Pr %*% W
    c <- nzdiagscore(Wtilde)
    if (c < bestval) {
      bestWtilde <- Wtilde
      bestval <- c
      besti <- i
    }
  }
  list(Wopt = bestWtilde, rowp = iperm(allperms[besti, ]))
}

nzdiaghungarian <- function(W) {
  n <- nrow(W)
  S <- matrix(1, n, n)/abs(W)
  c <- as.integer(clue::solve_LSAP(S))
  Pr <- diag(n)[, c]
  Wopt <- Pr %*% W
  list(Wopt = Wopt, rowp = iperm(c))
}

nzdiagscore <- function (W) {
  sum(1/diag(abs(W)))
}

all.perm <- function (n) {
  p <- matrix(1L, 1L, 1L)
  if (n > 1L)
    for (i in 2L:n) {
      p <- pp <- cbind(p, i, deparse.level = 0L)
      ii <- seq_len(i)
      v <- c(ii, seq_len(i - 1L))
      for (j in 2L:i) {
        v <- v[-1L]
        p <- rbind(p, pp[, v[ii]], deparse.level = 0L)
      }
    }
  p
}

iperm <- function (p) {
  sort.list(p, method = "radix")
}

sltbruteforce <- function (B) {
  n <- nrow(B)
  bestval <- Inf
  besti <- 0
  allperms <- all.perm(n)
  nperms <- nrow(allperms)
  for (i in 1:nperms) {
    p.i <- allperms[i, ]
    Btilde <- B[p.i, p.i]
    c <- sltscore(Btilde)
    if (c < bestval) {
      bestBtilde <- Btilde
      bestval <- c
      besti <- i
    }
  }
  list(Bopt = bestBtilde, optperm = allperms[besti, ])
}

sltscore <- function (B) {
  sum((B[upper.tri(B, diag = TRUE)])^2)
}

sltprune <- function (B) {
  n <- nrow(B)
  ind <- sort.list(abs(B))
  for (i in ((n * (n + 1)/2):(n * n))) {
    Bi <- B
    Bi[ind[1:i]] <- 0
    p <- slttestperm(Bi)
    if (any(p != 0)) {
      Bopt <- B[p, p, drop = FALSE]
      break
    }
  }
  list(Bopt = Bopt, optperm = p)
}

slttestperm <- function (B, rowS.tol = 1e-12) {
  stopifnot((n <- nrow(B)) >= 1, rowS.tol >= 0)
  p <- integer(0)
  remnodes <- 1:n
  Brem <- abs(B)
  for (ii in 1:n) {
    rowS <- if (length(Brem) > 1)
      rowSums(Brem)
    else Brem
    therow <- which(rowS < rowS.tol)
    if (length(therow) == 0L)
      return(0L)
    if (ii == n)
      return(c(p, remnodes))
    therow <- therow[1]
    Brem <- Brem[-therow, -therow, drop = FALSE]
    p <- c(p, remnodes[therow])
    remnodes <- remnodes[-therow]
  }
  stop("the program flow should never get here [please report!]")
}

prune <- function (X, k, method = "resampling", prunefactor = 1, npieces = 10,
                   verbose = FALSE) {
  if (verbose)
    cat("Pruning the network connections...\n")
  stopifnot(length(k) == (p <- nrow(X)))
  ndata <- ncol(X)
  X.k <- X[k, ]
  ik <- iperm(k)
  method <- match.arg(method)
  switch(method, resampling = {
    stopifnot(is.numeric(npieces), length(npieces) == 1,
              npieces%%1 == 0, 1 <= npieces, npieces <= ndata)
    piecesize <- floor(ndata/npieces)
    Bpieces <- array(0, c(p, p, npieces))
    diststdpieces <- array(0, c(p, npieces))
    cpieces <- array(0, c(p, npieces))
    Bfinal <- matrix(0, p, p)
    I.p <- diag(p)
    for (i in 1:npieces) {
      Xp <- X.k[, ((i - 1) * piecesize + 1):(i * piecesize)]
      Xpm <- rowMeans(Xp)
      Xp <- Xp - Xpm
      C <- (Xp %*% t(Xp))/ncol(Xp)
      if (TRUE) {
        C <- C + diag(10^(-10), dim(C)[1])
      }
      while (min(eigen(C, only.values = TRUE)$values) <
             0) {
        C <- C + diag(10^(-10), dim(C)[1])
      }
      L <- tridecomp(invsqrtm(C), choice = "ql", only.B = TRUE)
      diag.L <- diag(L)
      newestdisturbancestd <- 1/abs(diag.L)
      L <- L/diag.L
      Bnewest <- I.p - L
      cnewest <- L %*% Xpm
      Bnewest <- Bnewest[ik, ik]
      newestdisturbancestd <- newestdisturbancestd[ik]
      cnewest <- cnewest[ik]
      Bpieces[, , i] <- Bnewest
      diststdpieces[, i] <- newestdisturbancestd
      cpieces[, i] <- cnewest
    }
    for (i in 1:p) {
      Bp.i <- Bpieces[i, , ]
      for (j in 1:p) {
        themean <- mean(Bp.i[j, ])
        thestd <- stats::sd(Bp.i[j, ])
        Bfinal[i, j] <- if (abs(themean) < prunefactor *
                            thestd) 0 else themean
      }
    }
    stde <- rowMeans(diststdpieces)
    cfinal <- rowMeans(cpieces)
  }, olsboot = {
    stop(gettextf("Method '%s' not implemented yet!", method),
         domain = NA)
  }, wald = {
    stop(gettextf("Method '%s' not implemented yet!", method),
         domain = NA)
  }, bonferroni = {
    stop(gettextf("Method '%s' not implemented yet!", method),
         domain = NA)
  }, hochberg = {
    stop(gettextf("Method '%s' not implemented yet!", method),
         domain = NA)
  }, modelfit = {
    stop(gettextf("Method '%s' not implemented yet!", method),
         domain = NA)
  })
  if (verbose)
    cat("Done!\n")
  list(Bpruned = Bfinal, stde = stde, ci = cfinal)
}

tridecomp <- function (W, choice = "qr", only.B = FALSE) {
  stopifnot(1 <= (m <- nrow(W)), 1 <= (n <- ncol(W)))
  Jm <- matrix(0, m, m)
  Jm[m:1, ] <- diag(m)
  Jn <- matrix(0, n, n)
  Jn[n:1, ] <- diag(n)
  switch(choice, qr = {
    r <- qr(W)
    if (only.B) qr.R(r) else list(A = qr.Q(r), B = qr.R(r))
  }, lq = {
    r <- qr(t(W))
    if (only.B) t(qr.Q(r)) else list(A = t(qr.R(r)), B = t(qr.Q(r)))
  }, ql = {
    r <- qr(Jm %*% W %*% Jn)
    if (only.B) Jm %*% qr.R(r) %*% Jn else list(A = Jm %*%
                                                  qr.Q(r) %*% Jm, B = Jm %*% qr.R(r) %*% Jn)
  }, rq = {
    r <- qr(Jn %*% t(W) %*% Jm)
    if (only.B) t(Jn %*% qr.Q(r) %*% Jn) else list(A = t(Jn %*%
                                                           qr.R(r) %*% Jm), B = t(Jn %*% qr.Q(r) %*% Jn))
  }, stop("invalid 'choice': ", choice))
}

invsqrtm <- function (A){
  e <- eigen(A)
  V <- e$vectors
  lam.m.5 <- 1/sqrt(e$values)
  tcrossprod(V * rep(lam.m.5, each = nrow(V)), V)
}