/usr/include/rcond.h is in libalglib-dev 2.6.0-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 | /*************************************************************************
Copyright (c) 1992-2007 The University of Tennessee. All rights reserved.
Contributors:
* Sergey Bochkanov (ALGLIB project). Translation from FORTRAN to
pseudocode.
See subroutines comments for additional copyrights.
>>> SOURCE LICENSE >>>
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 (www.fsf.org); 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.
A copy of the GNU General Public License is available at
http://www.fsf.org/licensing/licenses
>>> END OF LICENSE >>>
*************************************************************************/
#ifndef _rcond_h
#define _rcond_h
#include "ap.h"
#include "ialglib.h"
#include "reflections.h"
#include "creflections.h"
#include "hqrnd.h"
#include "matgen.h"
#include "ablasf.h"
#include "ablas.h"
#include "trfac.h"
#include "trlinsolve.h"
#include "safesolve.h"
/*************************************************************************
Estimate of a matrix condition number (1-norm)
The algorithm calculates a lower bound of the condition number. In this case,
the algorithm does not return a lower bound of the condition number, but an
inverse number (to avoid an overflow in case of a singular matrix).
Input parameters:
A - matrix. Array whose indexes range within [0..N-1, 0..N-1].
N - size of matrix A.
Result: 1/LowerBound(cond(A))
NOTE:
if k(A) is very large, then matrix is assumed degenerate, k(A)=INF,
0.0 is returned in such cases.
*************************************************************************/
double rmatrixrcond1(ap::real_2d_array a, int n);
/*************************************************************************
Estimate of a matrix condition number (infinity-norm).
The algorithm calculates a lower bound of the condition number. In this case,
the algorithm does not return a lower bound of the condition number, but an
inverse number (to avoid an overflow in case of a singular matrix).
Input parameters:
A - matrix. Array whose indexes range within [0..N-1, 0..N-1].
N - size of matrix A.
Result: 1/LowerBound(cond(A))
NOTE:
if k(A) is very large, then matrix is assumed degenerate, k(A)=INF,
0.0 is returned in such cases.
*************************************************************************/
double rmatrixrcondinf(ap::real_2d_array a, int n);
/*************************************************************************
Condition number estimate of a symmetric positive definite matrix.
The algorithm calculates a lower bound of the condition number. In this case,
the algorithm does not return a lower bound of the condition number, but an
inverse number (to avoid an overflow in case of a singular matrix).
It should be noted that 1-norm and inf-norm of condition numbers of symmetric
matrices are equal, so the algorithm doesn't take into account the
differences between these types of norms.
Input parameters:
A - symmetric positive definite matrix which is given by its
upper or lower triangle depending on the value of
IsUpper. Array with elements [0..N-1, 0..N-1].
N - size of matrix A.
IsUpper - storage format.
Result:
1/LowerBound(cond(A)), if matrix A is positive definite,
-1, if matrix A is not positive definite, and its condition number
could not be found by this algorithm.
NOTE:
if k(A) is very large, then matrix is assumed degenerate, k(A)=INF,
0.0 is returned in such cases.
*************************************************************************/
double spdmatrixrcond(ap::real_2d_array a, int n, bool isupper);
/*************************************************************************
Triangular matrix: estimate of a condition number (1-norm)
The algorithm calculates a lower bound of the condition number. In this case,
the algorithm does not return a lower bound of the condition number, but an
inverse number (to avoid an overflow in case of a singular matrix).
Input parameters:
A - matrix. Array[0..N-1, 0..N-1].
N - size of A.
IsUpper - True, if the matrix is upper triangular.
IsUnit - True, if the matrix has a unit diagonal.
Result: 1/LowerBound(cond(A))
NOTE:
if k(A) is very large, then matrix is assumed degenerate, k(A)=INF,
0.0 is returned in such cases.
*************************************************************************/
double rmatrixtrrcond1(const ap::real_2d_array& a,
int n,
bool isupper,
bool isunit);
/*************************************************************************
Triangular matrix: estimate of a matrix condition number (infinity-norm).
The algorithm calculates a lower bound of the condition number. In this case,
the algorithm does not return a lower bound of the condition number, but an
inverse number (to avoid an overflow in case of a singular matrix).
Input parameters:
A - matrix. Array whose indexes range within [0..N-1, 0..N-1].
N - size of matrix A.
IsUpper - True, if the matrix is upper triangular.
IsUnit - True, if the matrix has a unit diagonal.
Result: 1/LowerBound(cond(A))
NOTE:
if k(A) is very large, then matrix is assumed degenerate, k(A)=INF,
0.0 is returned in such cases.
*************************************************************************/
double rmatrixtrrcondinf(const ap::real_2d_array& a,
int n,
bool isupper,
bool isunit);
/*************************************************************************
Condition number estimate of a Hermitian positive definite matrix.
The algorithm calculates a lower bound of the condition number. In this case,
the algorithm does not return a lower bound of the condition number, but an
inverse number (to avoid an overflow in case of a singular matrix).
It should be noted that 1-norm and inf-norm of condition numbers of symmetric
matrices are equal, so the algorithm doesn't take into account the
differences between these types of norms.
Input parameters:
A - Hermitian positive definite matrix which is given by its
upper or lower triangle depending on the value of
IsUpper. Array with elements [0..N-1, 0..N-1].
N - size of matrix A.
IsUpper - storage format.
Result:
1/LowerBound(cond(A)), if matrix A is positive definite,
-1, if matrix A is not positive definite, and its condition number
could not be found by this algorithm.
NOTE:
if k(A) is very large, then matrix is assumed degenerate, k(A)=INF,
0.0 is returned in such cases.
*************************************************************************/
double hpdmatrixrcond(ap::complex_2d_array a, int n, bool isupper);
/*************************************************************************
Estimate of a matrix condition number (1-norm)
The algorithm calculates a lower bound of the condition number. In this case,
the algorithm does not return a lower bound of the condition number, but an
inverse number (to avoid an overflow in case of a singular matrix).
Input parameters:
A - matrix. Array whose indexes range within [0..N-1, 0..N-1].
N - size of matrix A.
Result: 1/LowerBound(cond(A))
NOTE:
if k(A) is very large, then matrix is assumed degenerate, k(A)=INF,
0.0 is returned in such cases.
*************************************************************************/
double cmatrixrcond1(ap::complex_2d_array a, int n);
/*************************************************************************
Estimate of a matrix condition number (infinity-norm).
The algorithm calculates a lower bound of the condition number. In this case,
the algorithm does not return a lower bound of the condition number, but an
inverse number (to avoid an overflow in case of a singular matrix).
Input parameters:
A - matrix. Array whose indexes range within [0..N-1, 0..N-1].
N - size of matrix A.
Result: 1/LowerBound(cond(A))
NOTE:
if k(A) is very large, then matrix is assumed degenerate, k(A)=INF,
0.0 is returned in such cases.
*************************************************************************/
double cmatrixrcondinf(ap::complex_2d_array a, int n);
/*************************************************************************
Estimate of the condition number of a matrix given by its LU decomposition (1-norm)
The algorithm calculates a lower bound of the condition number. In this case,
the algorithm does not return a lower bound of the condition number, but an
inverse number (to avoid an overflow in case of a singular matrix).
Input parameters:
LUA - LU decomposition of a matrix in compact form. Output of
the RMatrixLU subroutine.
N - size of matrix A.
Result: 1/LowerBound(cond(A))
NOTE:
if k(A) is very large, then matrix is assumed degenerate, k(A)=INF,
0.0 is returned in such cases.
*************************************************************************/
double rmatrixlurcond1(const ap::real_2d_array& lua, int n);
/*************************************************************************
Estimate of the condition number of a matrix given by its LU decomposition
(infinity norm).
The algorithm calculates a lower bound of the condition number. In this case,
the algorithm does not return a lower bound of the condition number, but an
inverse number (to avoid an overflow in case of a singular matrix).
Input parameters:
LUA - LU decomposition of a matrix in compact form. Output of
the RMatrixLU subroutine.
N - size of matrix A.
Result: 1/LowerBound(cond(A))
NOTE:
if k(A) is very large, then matrix is assumed degenerate, k(A)=INF,
0.0 is returned in such cases.
*************************************************************************/
double rmatrixlurcondinf(const ap::real_2d_array& lua, int n);
/*************************************************************************
Condition number estimate of a symmetric positive definite matrix given by
Cholesky decomposition.
The algorithm calculates a lower bound of the condition number. In this
case, the algorithm does not return a lower bound of the condition number,
but an inverse number (to avoid an overflow in case of a singular matrix).
It should be noted that 1-norm and inf-norm condition numbers of symmetric
matrices are equal, so the algorithm doesn't take into account the
differences between these types of norms.
Input parameters:
CD - Cholesky decomposition of matrix A,
output of SMatrixCholesky subroutine.
N - size of matrix A.
Result: 1/LowerBound(cond(A))
NOTE:
if k(A) is very large, then matrix is assumed degenerate, k(A)=INF,
0.0 is returned in such cases.
*************************************************************************/
double spdmatrixcholeskyrcond(const ap::real_2d_array& a, int n, bool isupper);
/*************************************************************************
Condition number estimate of a Hermitian positive definite matrix given by
Cholesky decomposition.
The algorithm calculates a lower bound of the condition number. In this
case, the algorithm does not return a lower bound of the condition number,
but an inverse number (to avoid an overflow in case of a singular matrix).
It should be noted that 1-norm and inf-norm condition numbers of symmetric
matrices are equal, so the algorithm doesn't take into account the
differences between these types of norms.
Input parameters:
CD - Cholesky decomposition of matrix A,
output of SMatrixCholesky subroutine.
N - size of matrix A.
Result: 1/LowerBound(cond(A))
NOTE:
if k(A) is very large, then matrix is assumed degenerate, k(A)=INF,
0.0 is returned in such cases.
*************************************************************************/
double hpdmatrixcholeskyrcond(const ap::complex_2d_array& a,
int n,
bool isupper);
/*************************************************************************
Estimate of the condition number of a matrix given by its LU decomposition (1-norm)
The algorithm calculates a lower bound of the condition number. In this case,
the algorithm does not return a lower bound of the condition number, but an
inverse number (to avoid an overflow in case of a singular matrix).
Input parameters:
LUA - LU decomposition of a matrix in compact form. Output of
the CMatrixLU subroutine.
N - size of matrix A.
Result: 1/LowerBound(cond(A))
NOTE:
if k(A) is very large, then matrix is assumed degenerate, k(A)=INF,
0.0 is returned in such cases.
*************************************************************************/
double cmatrixlurcond1(const ap::complex_2d_array& lua, int n);
/*************************************************************************
Estimate of the condition number of a matrix given by its LU decomposition
(infinity norm).
The algorithm calculates a lower bound of the condition number. In this case,
the algorithm does not return a lower bound of the condition number, but an
inverse number (to avoid an overflow in case of a singular matrix).
Input parameters:
LUA - LU decomposition of a matrix in compact form. Output of
the CMatrixLU subroutine.
N - size of matrix A.
Result: 1/LowerBound(cond(A))
NOTE:
if k(A) is very large, then matrix is assumed degenerate, k(A)=INF,
0.0 is returned in such cases.
*************************************************************************/
double cmatrixlurcondinf(const ap::complex_2d_array& lua, int n);
/*************************************************************************
Triangular matrix: estimate of a condition number (1-norm)
The algorithm calculates a lower bound of the condition number. In this case,
the algorithm does not return a lower bound of the condition number, but an
inverse number (to avoid an overflow in case of a singular matrix).
Input parameters:
A - matrix. Array[0..N-1, 0..N-1].
N - size of A.
IsUpper - True, if the matrix is upper triangular.
IsUnit - True, if the matrix has a unit diagonal.
Result: 1/LowerBound(cond(A))
NOTE:
if k(A) is very large, then matrix is assumed degenerate, k(A)=INF,
0.0 is returned in such cases.
*************************************************************************/
double cmatrixtrrcond1(const ap::complex_2d_array& a,
int n,
bool isupper,
bool isunit);
/*************************************************************************
Triangular matrix: estimate of a matrix condition number (infinity-norm).
The algorithm calculates a lower bound of the condition number. In this case,
the algorithm does not return a lower bound of the condition number, but an
inverse number (to avoid an overflow in case of a singular matrix).
Input parameters:
A - matrix. Array whose indexes range within [0..N-1, 0..N-1].
N - size of matrix A.
IsUpper - True, if the matrix is upper triangular.
IsUnit - True, if the matrix has a unit diagonal.
Result: 1/LowerBound(cond(A))
NOTE:
if k(A) is very large, then matrix is assumed degenerate, k(A)=INF,
0.0 is returned in such cases.
*************************************************************************/
double cmatrixtrrcondinf(const ap::complex_2d_array& a,
int n,
bool isupper,
bool isunit);
/*************************************************************************
Threshold for rcond: matrices with condition number beyond this threshold
are considered singular.
Threshold must be far enough from underflow, at least Sqr(Threshold) must
be greater than underflow.
*************************************************************************/
double rcondthreshold();
#endif
|