INLAcircular copyright and licensing notices ========================================== INLAcircular is distributed under the GNU General Public License, version 3 or, at your option, any later version. The license text is in LICENSES/GPL-3 in the installed package (inst/LICENSES/GPL-3 in the source package). Original package material and adaptations ---------------------------------------- Copyright (c) 2026 Xiang Ye The permission notice for original material previously licensed under MIT is retained below. This notice applies to that material, not to the GSL-derived material described in the next section. The combined package is distributed under GPL version 3 or later. Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. GNU Scientific Library Bessel routines ------------------------------------- src/bessel_i.c adapts portions of these files from GNU Scientific Library (GSL) version 2.8: * specfunc/bessel_Inu.c Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman * specfunc/bessel.c Copyright (C) 1996,1997,1998,1999,2000,2001,2002,2003 Gerard Jungman Both files identify G. Jungman as the author and grant permission under the GNU General Public License, version 3 or any later version. Their copyright and license notices are also retained in src/bessel_i.c. The pre-existing Bessel routines in src/INLAcirc_common.h are adapted from the following GSL 2.8 sources and retain the same license: * specfunc/bessel_I0.c: bi0_data, ai0_data, ai02_data and scaled I0 evaluation Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman * specfunc/bessel_I1.c: bi1_data, ai1_data, ai12_data and scaled I1 evaluation Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman * specfunc/bessel.c: gsl_sf_bessel_I_CF1_ser continued fraction Copyright (C) 1996,1997,1998,1999,2000,2001,2002,2003 Gerard Jungman * specfunc/bessel_In.c: integer-order backward recurrence Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman These coefficients use the INLAcirc_ prefix in the package. Their numerical values are unchanged; copyright and GPL notices were added to the package header. The separate src-cloglike copy was not modified. Source release: https://ftp.gnu.org/gnu/gsl/gsl-2.8.tar.gz Archive SHA-256: 6a99eeed15632c6354895b1dd542ed5a855c0f15d9ad1326c6fe2b2c9e423190 The package includes selected Taylor-series, continued-fraction and uniform asymptotic routines, adapted to a package-local C interface. The adaptation uses the C mathematical library for the log-gamma prefactor and returns results without calling GSL's error handler. No system GSL library or headers are required. The standalone src-cloglike directory is not part of this adaptation and is excluded from the R source package. GSL 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. GSL 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. Normal quantile approximation ----------------------------- INLAcirc_qnorm in src/INLAcirc_common.h implements Peter John Acklam's rational approximation to the standard-normal quantile, using the coefficients and branch points in his original description: Peter John Acklam, "An algorithm for computing the inverse normal cumulative distribution function", first published in 2003 and last updated 2010-01-21. Original page: http://home.online.no/~pjacklam/notes/invnorm/ Archived page (permission verified 2026-10-05): https://web.archive.org/web/20151030215612/http://home.online.no/~pjacklam/notes/invnorm/ The author's Computer implementations section states: "Use them as you wish, for whatever purpose." His copyright FAQ explicitly extends this permission to the algorithm and listed implementations, and requests that credit be given. Peter John Acklam is credited here as the author of the approximation. The package does not designate this upstream permission as an MIT license or claim that Acklam waived copyright. R-INLA interface declarations and PC-prior reference formulas ------------------------------------------------------------ src/INLAcirc_cgeneric_compat.h contains the subset of declarations needed for the external cloglike ABI from R-INLA's inlaprog/src/cgeneric.h. The small-concentration and asymptotic PC-prior formulas in src/INLAcirc_common.h correspond to rinla/R/pc-vm0.R and rinla/R/pc-vminf.R. Both reference files credit Xiang Ye as their author. The package evaluates these formulas in C and does not execute R-INLA's R implementations for these calculations. Source repository: https://github.com/hrue/r-inla Verified source revision: 6afa911f01e975c4e6c921f22288e80d8e70c88f The repository's MIT license notice is retained below: Copyright 2025 Haavard Rue Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.