├── gsq ├── __init__.py ├── ci_tests.py ├── binary.py └── discrete.py ├── MANIFEST.in ├── README.md ├── setup.py └── LICENSE /gsq/__init__.py: -------------------------------------------------------------------------------- 1 | -------------------------------------------------------------------------------- /MANIFEST.in: -------------------------------------------------------------------------------- 1 | include LICENSE 2 | include README.md 3 | -------------------------------------------------------------------------------- /gsq/ci_tests.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python 2 | # -*- coding: utf-8 -*- 3 | 4 | """A collection of wrapper functions for G-square conditional 5 | independecy test functions. 6 | """ 7 | 8 | from __future__ import print_function 9 | 10 | import logging 11 | 12 | from .binary import g_square_bin 13 | from .discrete import g_square_dis 14 | 15 | _logger = logging.getLogger(__name__) 16 | 17 | def ci_test_bin(data_matrix, x, y, s, **kwargs): 18 | return g_square_bin(data_matrix, x, y, s) 19 | 20 | def ci_test_dis(data_matrix, x , y, s, **kwargs): 21 | levels = [] 22 | if 'levels' in kwargs: 23 | levels = kwargs['levels'] 24 | else: 25 | import numpy as np 26 | levels = np.amax(data_matrix, axis=0) + 1 27 | return g_square_dis(data_matrix, x, y, s, levels) 28 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # G Square Conditional Independence Test 2 | 3 | ## Overview 4 | 5 | This package contains conditional independence test functions using 6 | the G-square test. 7 | 8 | ## Acknowledgement 9 | 10 | The code fragments included in this package are logically copied and 11 | pasted from [the pcalg package for R] 12 | (http://cran.r-project.org/web/packages/pcalg/index.html) developed by 13 | Markus Kalisch, Alain Hauser, Martin Maechler, Diego Colombo, Doris 14 | Entner, Patrik Hoyer, Antti Hyttinen, and Jonas Peters. 15 | 16 | ## Code 17 | 18 | The source code is available at https://github.com/keiichishima/gsq 19 | 20 | ## Bug Reports 21 | 22 | Please submit bug reports or patches through the GitHub interface. 23 | 24 | ## Contributors 25 | 26 | - Joost H. van der Linden, https://github.com/joosthvanderlinden 27 | - Satoru Kobayashi, https://github.com/cpflat 28 | 29 | ## Author 30 | 31 | Keiichi SHIMA 32 | / IIJ Innovation Institute Inc. 33 | / WIDE project 34 | -------------------------------------------------------------------------------- /setup.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python 2 | 3 | from __future__ import print_function 4 | 5 | from setuptools import setup 6 | 7 | try: 8 | from pypandoc import convert 9 | read_md = lambda f: convert(f, 'rst') 10 | except ImportError: 11 | print('pandoc is not installed.') 12 | read_md = lambda f: open(f, 'r').read() 13 | 14 | setup(name='gsq', 15 | version='0.1.6', 16 | description='G Square Conditional Independence Test', 17 | long_description=read_md('README.md'), 18 | author='Keiichi SHIMA', 19 | author_email='keiichi@iijlab.net', 20 | url='https://github.com/keiichishima/gsq/', 21 | packages=['gsq'], 22 | install_requires=['scipy>=0.18.1','numpy>=1.12.0'], 23 | classifiers=[ 24 | 'Development Status :: 4 - Beta', 25 | 'Environment :: Console', 26 | 'Intended Audience :: Information Technology', 27 | 'Intended Audience :: Science/Research', 28 | 'License :: OSI Approved :: GNU General Public License v2 or later (GPLv2+)', 29 | 'Programming Language :: Python :: 2.7', 30 | 'Topic :: Scientific/Engineering :: Information Analysis', 31 | 'Topic :: Software Development :: Libraries :: Python Modules'], 32 | license='GNU General Public License v2 or later (GPLv2+)', 33 | ) 34 | -------------------------------------------------------------------------------- /gsq/binary.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python 2 | # -*- coding: utf-8 -*- 3 | 4 | """A conditional independency test function for binary data. 5 | 6 | The code included in this package is logically copied and pasted from 7 | the pcalg package for R developed by Markus Kalisch, Alain Hauser, 8 | Martin Maechler, Diego Colombo, Doris Entner, Patrik Hoyer, Antti 9 | Hyttinen, and Jonas Peters. 10 | 11 | License: GPLv2 12 | """ 13 | 14 | from __future__ import print_function 15 | 16 | import logging 17 | from math import pow 18 | 19 | from scipy.stats import chi2 20 | import numpy as np 21 | 22 | _logger = logging.getLogger(__name__) 23 | 24 | def g_square_bin(dm, x, y, s): 25 | """G square test for a binary data. 26 | 27 | Args: 28 | dm: the data matrix to be used (as a numpy.ndarray). 29 | x: the first node (as an integer). 30 | y: the second node (as an integer). 31 | s: the set of neibouring nodes of x and y (as a set()). 32 | 33 | Returns: 34 | p_val: the p-value of conditional independence. 35 | """ 36 | 37 | def _calculate_tlog(x, y, s, dof, dm): 38 | nijk = np.zeros((2, 2, dof)) 39 | s_size = len(s) 40 | z = [] 41 | for z_index in range(s_size): 42 | z.append(s.pop()) 43 | pass 44 | for row_index in range(0, dm.shape[0]): 45 | i = dm[row_index, x] 46 | j = dm[row_index, y] 47 | k = [] 48 | k_index = 0 49 | for z_index in range(s_size): 50 | k_index += dm[row_index, z[z_index]] * int(pow(2, z_index)) 51 | pass 52 | nijk[i, j, k_index] += 1 53 | pass 54 | nik = np.ndarray((2, dof)) 55 | njk = np.ndarray((2, dof)) 56 | for k_index in range(dof): 57 | nik[:, k_index] = nijk[:, :, k_index].sum(axis = 1) 58 | njk[:, k_index] = nijk[:, :, k_index].sum(axis = 0) 59 | pass 60 | nk = njk.sum(axis = 0) 61 | tlog = np.zeros((2, 2 , dof)) 62 | tlog.fill(np.nan) 63 | for k in range(dof): 64 | tx = np.array([nik[:,k]]).T 65 | ty = np.array([njk[:,k]]) 66 | tdijk = tx.dot(ty) 67 | tlog[:,:,k] = nijk[:,:,k] * nk[k] / tdijk 68 | pass 69 | return (nijk, tlog) 70 | 71 | _logger.debug('Edge %d -- %d with subset: %s' % (x, y, s)) 72 | row_size = dm.shape[0] 73 | s_size = len(s) 74 | dof = int(pow(2, s_size)) 75 | row_size_required = 10 * dof 76 | if row_size < row_size_required: 77 | _logger.warning('Not enough samples. %s is too small. Need %s.' 78 | % (str(row_size), str(row_size_required))) 79 | return 1 80 | nijk = None 81 | if s_size < 6: 82 | if s_size == 0: 83 | nijk = np.zeros((2, 2)) 84 | for row_index in range(0, dm.shape[0]): 85 | i = dm[row_index, x] 86 | j = dm[row_index, y] 87 | nijk[i, j] += 1 88 | pass 89 | tx = np.array([nijk.sum(axis = 1)]).T 90 | ty = np.array([nijk.sum(axis = 0)]) 91 | tdij = tx.dot(ty) 92 | tlog = nijk * row_size / tdij 93 | pass 94 | if s_size > 0: 95 | nijk, tlog = _calculate_tlog(x, y, s, dof, dm) 96 | pass 97 | pass 98 | else: 99 | # s_size >= 6 100 | nijk = np.zeros((2, 2, 1)) 101 | i = dm[0, x] 102 | j = dm[0, y] 103 | k = [] 104 | for z in s: 105 | k.append(dm[:,z]) 106 | pass 107 | k = np.array(k).T 108 | parents_count = 1 109 | parents_val = np.array([k[0,:]]) 110 | nijk[i, j, parents_count - 1] = 1 111 | for it_sample in range(1, row_size): 112 | is_new = True 113 | i = dm[it_sample, x] 114 | j = dm[it_sample, y] 115 | tcomp = parents_val[:parents_count,:] == k[it_sample,:] 116 | for it_parents in range(parents_count): 117 | if np.all(tcomp[it_parents,:]): 118 | nijk[i, j, it_parents] += 1 119 | is_new = False 120 | break 121 | pass 122 | if is_new is True: 123 | parents_count += 1 124 | parents_val = np.r_[parents_val, [k[it_sample,:]]] 125 | nnijk = np.zeros((2,2,parents_count)) 126 | for p in range(parents_count - 1): 127 | nnijk[:,:,p] = nijk[:,:,p] 128 | nnijk[i, j, parents_count - 1] = 1 129 | nijk = nnijk 130 | pass 131 | pass 132 | nik = np.ndarray((2, parents_count)) 133 | njk = np.ndarray((2, parents_count)) 134 | for k_index in range(parents_count): 135 | nik[:, k_index] = nijk[:, :, k_index].sum(axis = 1) 136 | njk[:, k_index] = nijk[:, :, k_index].sum(axis = 0) 137 | pass 138 | nk = njk.sum(axis = 0) 139 | tlog = np.zeros((2, 2 , parents_count)) 140 | tlog.fill(np.nan) 141 | for k in range(parents_count): 142 | tX = np.array([nik[:,k]]).T 143 | tY = np.array([njk[:,k]]) 144 | tdijk = tX.dot(tY) 145 | tlog[:,:,k] = nijk[:,:,k] * nk[k] / tdijk 146 | pass 147 | pass 148 | log_tlog = np.log(tlog) 149 | G2 = np.nansum(2 * nijk * log_tlog) 150 | # _logger.debug('dof = %d' % dof) 151 | # _logger.debug('nijk = %s' % nijk) 152 | # _logger.debug('tlog = %s' % tlog) 153 | # _logger.debug('log(tlog) = %s' % log_tlog) 154 | _logger.debug('G2 = %f' % G2) 155 | p_val = chi2.sf(G2, dof) 156 | _logger.info('p_val = %s' % str(p_val)) 157 | return p_val 158 | 159 | 160 | if __name__ == '__main__': 161 | from math import frexp 162 | 163 | import gsq_testdata 164 | 165 | dm = np.array([gsq_testdata.bin_data]).reshape((5000,5)) 166 | x = 0 167 | y = 1 168 | 169 | sets = [[], [2], [2, 3], [3, 4], [2, 3, 4]] 170 | for idx in range(len(sets)): 171 | print('x =', x, ', y =', y, ', s =', sets[idx], end='') 172 | p = g_square_bin(dm, 0, 1, set(sets[idx])) 173 | print(', p =', p, end='') 174 | fr_p = frexp(p) 175 | fr_a = frexp(gsq_testdata.bin_answer[idx]) 176 | if (round(fr_p[0] - fr_a[0], 7) == 0 177 | and fr_p[1] == fr_a[1]): 178 | print(' => GOOD') 179 | else: 180 | print(' => WRONG') 181 | print('p =', fr_p) 182 | print('a =', fr_a) 183 | -------------------------------------------------------------------------------- /gsq/discrete.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python 2 | # -*- coding: utf-8 -*- 3 | 4 | """A conditional independency test function for discrete data. 5 | 6 | The code included in this package is logically copied and pasted from 7 | the pcalg package for R developed by Markus Kalisch, Alain Hauser, 8 | Martin Maechler, Diego Colombo, Doris Entner, Patrik Hoyer, Antti 9 | Hyttinen, and Jonas Peters. 10 | 11 | License: GPLv2 12 | """ 13 | 14 | from __future__ import print_function 15 | 16 | import logging 17 | 18 | from scipy.stats import chi2 19 | import numpy as np 20 | 21 | _logger = logging.getLogger(__name__) 22 | 23 | def g_square_dis(dm, x, y, s, levels): 24 | """G square test for discrete data. 25 | 26 | Args: 27 | dm: the data matrix to be used (as a numpy.ndarray). 28 | x: the first node (as an integer). 29 | y: the second node (as an integer). 30 | s: the set of neibouring nodes of x and y (as a set()). 31 | levels: levels of each column in the data matrix 32 | (as a list()). 33 | 34 | Returns: 35 | p_val: the p-value of conditional independence. 36 | """ 37 | 38 | def _calculate_tlog(x, y, s, dof, levels, dm): 39 | prod_levels = np.prod(list(map(lambda x: levels[x], s))) 40 | nijk = np.zeros((levels[x], levels[y], prod_levels)) 41 | s_size = len(s) 42 | z = [] 43 | for z_index in range(s_size): 44 | z.append(s.pop()) 45 | pass 46 | for row_index in range(dm.shape[0]): 47 | i = dm[row_index, x] 48 | j = dm[row_index, y] 49 | k = [] 50 | k_index = 0 51 | for s_index in range(s_size): 52 | if s_index == 0: 53 | k_index += dm[row_index, z[s_index]] 54 | else: 55 | lprod = np.prod(list(map(lambda x: levels[x], z[:s_index]))) 56 | k_index += (dm[row_index, z[s_index]] * lprod) 57 | pass 58 | pass 59 | nijk[i, j, k_index] += 1 60 | pass 61 | nik = np.ndarray((levels[x], prod_levels)) 62 | njk = np.ndarray((levels[y], prod_levels)) 63 | for k_index in range(prod_levels): 64 | nik[:, k_index] = nijk[:, :, k_index].sum(axis = 1) 65 | njk[:, k_index] = nijk[:, :, k_index].sum(axis = 0) 66 | pass 67 | nk = njk.sum(axis = 0) 68 | tlog = np.zeros((levels[x], levels[y], prod_levels)) 69 | tlog.fill(np.nan) 70 | for k in range(prod_levels): 71 | tx = np.array([nik[:, k]]).T 72 | ty = np.array([njk[:, k]]) 73 | tdijk = tx.dot(ty) 74 | tlog[:, :, k] = nijk[:, :, k] * nk[k] / tdijk 75 | pass 76 | return (nijk, tlog) 77 | 78 | _logger.debug('Edge %d -- %d with subset: %s' % (x, y, s)) 79 | row_size = dm.shape[0] 80 | s_size = len(s) 81 | dof = ((levels[x] - 1) * (levels[y] - 1) 82 | * np.prod(list(map(lambda x: levels[x], s)))) 83 | row_size_required = 10 * dof 84 | if row_size < row_size_required: 85 | _logger.warning('Not enough samples. %s is too small. Need %s.' 86 | % (str(row_size), str(row_size_required))) 87 | return 1 88 | nijk = None 89 | if s_size < 5: 90 | if s_size == 0: 91 | nijk = np.zeros((levels[x], levels[y])) 92 | for row_index in range(row_size): 93 | i = dm[row_index, x] 94 | j = dm[row_index, y] 95 | nijk[i, j] += 1 96 | pass 97 | tx = np.array([nijk.sum(axis = 1)]).T 98 | ty = np.array([nijk.sum(axis = 0)]) 99 | tdij = tx.dot(ty) 100 | tlog = nijk * row_size / tdij 101 | pass 102 | if s_size > 0: 103 | nijk, tlog = _calculate_tlog(x, y, s, dof, levels, dm) 104 | pass 105 | pass 106 | else: 107 | # s_size >= 5 108 | nijk = np.zeros((levels[x], levels[y], 1)) 109 | i = dm[0, x] 110 | j = dm[0, y] 111 | k = [] 112 | for z in s: 113 | k.append(dm[:, z]) 114 | pass 115 | k = np.array(k).T 116 | parents_count = 1 117 | parents_val = np.array([k[0, :]]) 118 | nijk[i, j, parents_count - 1] = 1 119 | for it_sample in range(1, row_size): 120 | is_new = True 121 | i = dm[it_sample, x] 122 | j = dm[it_sample, y] 123 | tcomp = parents_val[:parents_count, :] == k[it_sample, :] 124 | for it_parents in range(parents_count): 125 | if np.all(tcomp[it_parents, :]): 126 | nijk[i, j, it_parents] += 1 127 | is_new = False 128 | break 129 | pass 130 | if is_new is True: 131 | parents_count += 1 132 | parents_val = np.r_[parents_val, [k[it_sample, :]]] 133 | nnijk = np.zeros((levels[x], levels[y], parents_count)) 134 | for p in range(parents_count - 1): 135 | nnijk[:, :, p] = nijk[:, :, p] 136 | pass 137 | nnijk[i, j, parents_count - 1] = 1 138 | nijk = nnijk 139 | pass 140 | pass 141 | nik = np.ndarray((levels[x], parents_count)) 142 | njk = np.ndarray((levels[y], parents_count)) 143 | for k_index in range(parents_count): 144 | nik[:, k_index] = nijk[:, :, k_index].sum(axis = 1) 145 | njk[:, k_index] = nijk[:, :, k_index].sum(axis = 0) 146 | pass 147 | nk = njk.sum(axis = 0) 148 | tlog = np.zeros((levels[x], levels[y], parents_count)) 149 | tlog.fill(np.nan) 150 | for k in range(parents_count): 151 | tx = np.array([nik[:, k]]).T 152 | ty = np.array([njk[:, k]]) 153 | tdijk = tx.dot(ty) 154 | tlog[:, :, k] = nijk[:, :, k] * nk[k] / tdijk 155 | pass 156 | pass 157 | log_tlog = np.log(tlog) 158 | G2 = np.nansum(2 * nijk * log_tlog) 159 | # _logger.debug('dof = %d' % dof) 160 | # _logger.debug('nijk = %s' % nijk) 161 | # _logger.debug('tlog = %s' % tlog) 162 | # _logger.debug('log(tlog) = %s' % log_tlog) 163 | _logger.debug('G2 = %f' % G2) 164 | if dof == 0: 165 | # dof can be 0 when levels[x] or levels[y] is 1, which is 166 | # the case that the values of columns x or y are all 0. 167 | p_val = 1 168 | else: 169 | p_val = chi2.sf(G2, dof) 170 | _logger.info('p_val = %s' % str(p_val)) 171 | return p_val 172 | 173 | 174 | if __name__ == '__main__': 175 | from math import frexp 176 | 177 | import gsq_testdata 178 | 179 | dm = np.array([gsq_testdata.dis_data]).reshape((10000,5)) 180 | x = 0 181 | y = 1 182 | 183 | sets = [[], [2], [2, 3], [3, 4], [2, 3, 4]] 184 | for idx in range(len(sets)): 185 | print('x =', x, ', y =', y, ', s =', sets[idx], end='') 186 | p = g_square_dis(dm, 0, 1, set(sets[idx]), [3,2,3,4,2]) 187 | print(', p =', p, end='') 188 | fr_p = frexp(p) 189 | fr_a = frexp(gsq_testdata.dis_answer[idx]) 190 | if (round(fr_p[0] - fr_a[0], 7) == 0 191 | and fr_p[1] == fr_a[1]): 192 | print(' => GOOD') 193 | else: 194 | print(' => WRONG') 195 | print('p =', fr_p) 196 | print('a =', fr_a) 197 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 2, June 1991 3 | 4 | Copyright (C) 1989, 1991 Free Software Foundation, Inc., 5 | 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA 6 | Everyone is permitted to copy and distribute verbatim copies 7 | of this license document, but changing it is not allowed. 8 | 9 | Preamble 10 | 11 | The licenses for most software are designed to take away your 12 | freedom to share and change it. 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For example, if a patent 205 | license would not permit royalty-free redistribution of the Program by 206 | all those who receive copies directly or indirectly through you, then 207 | the only way you could satisfy both it and this License would be to 208 | refrain entirely from distribution of the Program. 209 | 210 | If any portion of this section is held invalid or unenforceable under 211 | any particular circumstance, the balance of the section is intended to 212 | apply and the section as a whole is intended to apply in other 213 | circumstances. 214 | 215 | It is not the purpose of this section to induce you to infringe any 216 | patents or other property right claims or to contest validity of any 217 | such claims; this section has the sole purpose of protecting the 218 | integrity of the free software distribution system, which is 219 | implemented by public license practices. Many people have made 220 | generous contributions to the wide range of software distributed 221 | through that system in reliance on consistent application of that 222 | system; it is up to the author/donor to decide if he or she is willing 223 | to distribute software through any other system and a licensee cannot 224 | impose that choice. 225 | 226 | This section is intended to make thoroughly clear what is believed to 227 | be a consequence of the rest of this License. 228 | 229 | 8. If the distribution and/or use of the Program is restricted in 230 | certain countries either by patents or by copyrighted interfaces, the 231 | original copyright holder who places the Program under this License 232 | may add an explicit geographical distribution limitation excluding 233 | those countries, so that distribution is permitted only in or among 234 | countries not thus excluded. In such case, this License incorporates 235 | the limitation as if written in the body of this License. 236 | 237 | 9. The Free Software Foundation may publish revised and/or new versions 238 | of the General Public License from time to time. Such new versions will 239 | be similar in spirit to the present version, but may differ in detail to 240 | address new problems or concerns. 241 | 242 | Each version is given a distinguishing version number. If the Program 243 | specifies a version number of this License which applies to it and "any 244 | later version", you have the option of following the terms and conditions 245 | either of that version or of any later version published by the Free 246 | Software Foundation. If the Program does not specify a version number of 247 | this License, you may choose any version ever published by the Free Software 248 | Foundation. 249 | 250 | 10. If you wish to incorporate parts of the Program into other free 251 | programs whose distribution conditions are different, write to the author 252 | to ask for permission. For software which is copyrighted by the Free 253 | Software Foundation, write to the Free Software Foundation; we sometimes 254 | make exceptions for this. Our decision will be guided by the two goals 255 | of preserving the free status of all derivatives of our free software and 256 | of promoting the sharing and reuse of software generally. 257 | 258 | NO WARRANTY 259 | 260 | 11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY 261 | FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN 262 | OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES 263 | PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED 264 | OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF 265 | MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS 266 | TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE 267 | PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, 268 | REPAIR OR CORRECTION. 269 | 270 | 12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 271 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR 272 | REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, 273 | INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING 274 | OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED 275 | TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY 276 | YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER 277 | PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE 278 | POSSIBILITY OF SUCH DAMAGES. 279 | 280 | END OF TERMS AND CONDITIONS 281 | 282 | How to Apply These Terms to Your New Programs 283 | 284 | If you develop a new program, and you want it to be of the greatest 285 | possible use to the public, the best way to achieve this is to make it 286 | free software which everyone can redistribute and change under these terms. 287 | 288 | To do so, attach the following notices to the program. It is safest 289 | to attach them to the start of each source file to most effectively 290 | convey the exclusion of warranty; and each file should have at least 291 | the "copyright" line and a pointer to where the full notice is found. 292 | 293 | {description} 294 | Copyright (C) {year} {fullname} 295 | 296 | This program is free software; you can redistribute it and/or modify 297 | it under the terms of the GNU General Public License as published by 298 | the Free Software Foundation; either version 2 of the License, or 299 | (at your option) any later version. 300 | 301 | This program is distributed in the hope that it will be useful, 302 | but WITHOUT ANY WARRANTY; without even the implied warranty of 303 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 304 | GNU General Public License for more details. 305 | 306 | You should have received a copy of the GNU General Public License along 307 | with this program; if not, write to the Free Software Foundation, Inc., 308 | 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. 309 | 310 | Also add information on how to contact you by electronic and paper mail. 311 | 312 | If the program is interactive, make it output a short notice like this 313 | when it starts in an interactive mode: 314 | 315 | Gnomovision version 69, Copyright (C) year name of author 316 | Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 317 | This is free software, and you are welcome to redistribute it 318 | under certain conditions; type `show c' for details. 319 | 320 | The hypothetical commands `show w' and `show c' should show the appropriate 321 | parts of the General Public License. Of course, the commands you use may 322 | be called something other than `show w' and `show c'; they could even be 323 | mouse-clicks or menu items--whatever suits your program. 324 | 325 | You should also get your employer (if you work as a programmer) or your 326 | school, if any, to sign a "copyright disclaimer" for the program, if 327 | necessary. Here is a sample; alter the names: 328 | 329 | Yoyodyne, Inc., hereby disclaims all copyright interest in the program 330 | `Gnomovision' (which makes passes at compilers) written by James Hacker. 331 | 332 | {signature of Ty Coon}, 1 April 1989 333 | Ty Coon, President of Vice 334 | 335 | This General Public License does not permit incorporating your program into 336 | proprietary programs. If your program is a subroutine library, you may 337 | consider it more useful to permit linking proprietary applications with the 338 | library. If this is what you want to do, use the GNU Lesser General 339 | Public License instead of this License. 340 | 341 | --------------------------------------------------------------------------------