Brian Silverman | 72890c2 | 2015-09-19 14:37:37 -0400 | [diff] [blame^] | 1 | // // This file is part of Eigen, a lightweight C++ template library |
| 2 | // for linear algebra. |
| 3 | // |
| 4 | // Copyright (C) 2012 Desire Nuentsa Wakam <desire.nuentsa_wakam@inria.fr> |
| 5 | // |
| 6 | // This Source Code Form is subject to the terms of the Mozilla |
| 7 | // Public License v. 2.0. If a copy of the MPL was not distributed |
| 8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. |
| 9 | |
| 10 | // This file is modified from the colamd/symamd library. The copyright is below |
| 11 | |
| 12 | // The authors of the code itself are Stefan I. Larimore and Timothy A. |
| 13 | // Davis (davis@cise.ufl.edu), University of Florida. The algorithm was |
| 14 | // developed in collaboration with John Gilbert, Xerox PARC, and Esmond |
| 15 | // Ng, Oak Ridge National Laboratory. |
| 16 | // |
| 17 | // Date: |
| 18 | // |
| 19 | // September 8, 2003. Version 2.3. |
| 20 | // |
| 21 | // Acknowledgements: |
| 22 | // |
| 23 | // This work was supported by the National Science Foundation, under |
| 24 | // grants DMS-9504974 and DMS-9803599. |
| 25 | // |
| 26 | // Notice: |
| 27 | // |
| 28 | // Copyright (c) 1998-2003 by the University of Florida. |
| 29 | // All Rights Reserved. |
| 30 | // |
| 31 | // THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY |
| 32 | // EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK. |
| 33 | // |
| 34 | // Permission is hereby granted to use, copy, modify, and/or distribute |
| 35 | // this program, provided that the Copyright, this License, and the |
| 36 | // Availability of the original version is retained on all copies and made |
| 37 | // accessible to the end-user of any code or package that includes COLAMD |
| 38 | // or any modified version of COLAMD. |
| 39 | // |
| 40 | // Availability: |
| 41 | // |
| 42 | // The colamd/symamd library is available at |
| 43 | // |
| 44 | // http://www.cise.ufl.edu/research/sparse/colamd/ |
| 45 | |
| 46 | // This is the http://www.cise.ufl.edu/research/sparse/colamd/colamd.h |
| 47 | // file. It is required by the colamd.c, colamdmex.c, and symamdmex.c |
| 48 | // files, and by any C code that calls the routines whose prototypes are |
| 49 | // listed below, or that uses the colamd/symamd definitions listed below. |
| 50 | |
| 51 | #ifndef EIGEN_COLAMD_H |
| 52 | #define EIGEN_COLAMD_H |
| 53 | |
| 54 | namespace internal { |
| 55 | /* Ensure that debugging is turned off: */ |
| 56 | #ifndef COLAMD_NDEBUG |
| 57 | #define COLAMD_NDEBUG |
| 58 | #endif /* NDEBUG */ |
| 59 | /* ========================================================================== */ |
| 60 | /* === Knob and statistics definitions ====================================== */ |
| 61 | /* ========================================================================== */ |
| 62 | |
| 63 | /* size of the knobs [ ] array. Only knobs [0..1] are currently used. */ |
| 64 | #define COLAMD_KNOBS 20 |
| 65 | |
| 66 | /* number of output statistics. Only stats [0..6] are currently used. */ |
| 67 | #define COLAMD_STATS 20 |
| 68 | |
| 69 | /* knobs [0] and stats [0]: dense row knob and output statistic. */ |
| 70 | #define COLAMD_DENSE_ROW 0 |
| 71 | |
| 72 | /* knobs [1] and stats [1]: dense column knob and output statistic. */ |
| 73 | #define COLAMD_DENSE_COL 1 |
| 74 | |
| 75 | /* stats [2]: memory defragmentation count output statistic */ |
| 76 | #define COLAMD_DEFRAG_COUNT 2 |
| 77 | |
| 78 | /* stats [3]: colamd status: zero OK, > 0 warning or notice, < 0 error */ |
| 79 | #define COLAMD_STATUS 3 |
| 80 | |
| 81 | /* stats [4..6]: error info, or info on jumbled columns */ |
| 82 | #define COLAMD_INFO1 4 |
| 83 | #define COLAMD_INFO2 5 |
| 84 | #define COLAMD_INFO3 6 |
| 85 | |
| 86 | /* error codes returned in stats [3]: */ |
| 87 | #define COLAMD_OK (0) |
| 88 | #define COLAMD_OK_BUT_JUMBLED (1) |
| 89 | #define COLAMD_ERROR_A_not_present (-1) |
| 90 | #define COLAMD_ERROR_p_not_present (-2) |
| 91 | #define COLAMD_ERROR_nrow_negative (-3) |
| 92 | #define COLAMD_ERROR_ncol_negative (-4) |
| 93 | #define COLAMD_ERROR_nnz_negative (-5) |
| 94 | #define COLAMD_ERROR_p0_nonzero (-6) |
| 95 | #define COLAMD_ERROR_A_too_small (-7) |
| 96 | #define COLAMD_ERROR_col_length_negative (-8) |
| 97 | #define COLAMD_ERROR_row_index_out_of_bounds (-9) |
| 98 | #define COLAMD_ERROR_out_of_memory (-10) |
| 99 | #define COLAMD_ERROR_internal_error (-999) |
| 100 | |
| 101 | /* ========================================================================== */ |
| 102 | /* === Definitions ========================================================== */ |
| 103 | /* ========================================================================== */ |
| 104 | |
| 105 | #define COLAMD_MAX(a,b) (((a) > (b)) ? (a) : (b)) |
| 106 | #define COLAMD_MIN(a,b) (((a) < (b)) ? (a) : (b)) |
| 107 | |
| 108 | #define ONES_COMPLEMENT(r) (-(r)-1) |
| 109 | |
| 110 | /* -------------------------------------------------------------------------- */ |
| 111 | |
| 112 | #define COLAMD_EMPTY (-1) |
| 113 | |
| 114 | /* Row and column status */ |
| 115 | #define ALIVE (0) |
| 116 | #define DEAD (-1) |
| 117 | |
| 118 | /* Column status */ |
| 119 | #define DEAD_PRINCIPAL (-1) |
| 120 | #define DEAD_NON_PRINCIPAL (-2) |
| 121 | |
| 122 | /* Macros for row and column status update and checking. */ |
| 123 | #define ROW_IS_DEAD(r) ROW_IS_MARKED_DEAD (Row[r].shared2.mark) |
| 124 | #define ROW_IS_MARKED_DEAD(row_mark) (row_mark < ALIVE) |
| 125 | #define ROW_IS_ALIVE(r) (Row [r].shared2.mark >= ALIVE) |
| 126 | #define COL_IS_DEAD(c) (Col [c].start < ALIVE) |
| 127 | #define COL_IS_ALIVE(c) (Col [c].start >= ALIVE) |
| 128 | #define COL_IS_DEAD_PRINCIPAL(c) (Col [c].start == DEAD_PRINCIPAL) |
| 129 | #define KILL_ROW(r) { Row [r].shared2.mark = DEAD ; } |
| 130 | #define KILL_PRINCIPAL_COL(c) { Col [c].start = DEAD_PRINCIPAL ; } |
| 131 | #define KILL_NON_PRINCIPAL_COL(c) { Col [c].start = DEAD_NON_PRINCIPAL ; } |
| 132 | |
| 133 | /* ========================================================================== */ |
| 134 | /* === Colamd reporting mechanism =========================================== */ |
| 135 | /* ========================================================================== */ |
| 136 | |
| 137 | // == Row and Column structures == |
| 138 | template <typename Index> |
| 139 | struct colamd_col |
| 140 | { |
| 141 | Index start ; /* index for A of first row in this column, or DEAD */ |
| 142 | /* if column is dead */ |
| 143 | Index length ; /* number of rows in this column */ |
| 144 | union |
| 145 | { |
| 146 | Index thickness ; /* number of original columns represented by this */ |
| 147 | /* col, if the column is alive */ |
| 148 | Index parent ; /* parent in parent tree super-column structure, if */ |
| 149 | /* the column is dead */ |
| 150 | } shared1 ; |
| 151 | union |
| 152 | { |
| 153 | Index score ; /* the score used to maintain heap, if col is alive */ |
| 154 | Index order ; /* pivot ordering of this column, if col is dead */ |
| 155 | } shared2 ; |
| 156 | union |
| 157 | { |
| 158 | Index headhash ; /* head of a hash bucket, if col is at the head of */ |
| 159 | /* a degree list */ |
| 160 | Index hash ; /* hash value, if col is not in a degree list */ |
| 161 | Index prev ; /* previous column in degree list, if col is in a */ |
| 162 | /* degree list (but not at the head of a degree list) */ |
| 163 | } shared3 ; |
| 164 | union |
| 165 | { |
| 166 | Index degree_next ; /* next column, if col is in a degree list */ |
| 167 | Index hash_next ; /* next column, if col is in a hash list */ |
| 168 | } shared4 ; |
| 169 | |
| 170 | }; |
| 171 | |
| 172 | template <typename Index> |
| 173 | struct Colamd_Row |
| 174 | { |
| 175 | Index start ; /* index for A of first col in this row */ |
| 176 | Index length ; /* number of principal columns in this row */ |
| 177 | union |
| 178 | { |
| 179 | Index degree ; /* number of principal & non-principal columns in row */ |
| 180 | Index p ; /* used as a row pointer in init_rows_cols () */ |
| 181 | } shared1 ; |
| 182 | union |
| 183 | { |
| 184 | Index mark ; /* for computing set differences and marking dead rows*/ |
| 185 | Index first_column ;/* first column in row (used in garbage collection) */ |
| 186 | } shared2 ; |
| 187 | |
| 188 | }; |
| 189 | |
| 190 | /* ========================================================================== */ |
| 191 | /* === Colamd recommended memory size ======================================= */ |
| 192 | /* ========================================================================== */ |
| 193 | |
| 194 | /* |
| 195 | The recommended length Alen of the array A passed to colamd is given by |
| 196 | the COLAMD_RECOMMENDED (nnz, n_row, n_col) macro. It returns -1 if any |
| 197 | argument is negative. 2*nnz space is required for the row and column |
| 198 | indices of the matrix. colamd_c (n_col) + colamd_r (n_row) space is |
| 199 | required for the Col and Row arrays, respectively, which are internal to |
| 200 | colamd. An additional n_col space is the minimal amount of "elbow room", |
| 201 | and nnz/5 more space is recommended for run time efficiency. |
| 202 | |
| 203 | This macro is not needed when using symamd. |
| 204 | |
| 205 | Explicit typecast to Index added Sept. 23, 2002, COLAMD version 2.2, to avoid |
| 206 | gcc -pedantic warning messages. |
| 207 | */ |
| 208 | template <typename Index> |
| 209 | inline Index colamd_c(Index n_col) |
| 210 | { return Index( ((n_col) + 1) * sizeof (colamd_col<Index>) / sizeof (Index) ) ; } |
| 211 | |
| 212 | template <typename Index> |
| 213 | inline Index colamd_r(Index n_row) |
| 214 | { return Index(((n_row) + 1) * sizeof (Colamd_Row<Index>) / sizeof (Index)); } |
| 215 | |
| 216 | // Prototypes of non-user callable routines |
| 217 | template <typename Index> |
| 218 | static Index init_rows_cols (Index n_row, Index n_col, Colamd_Row<Index> Row [], colamd_col<Index> col [], Index A [], Index p [], Index stats[COLAMD_STATS] ); |
| 219 | |
| 220 | template <typename Index> |
| 221 | static void init_scoring (Index n_row, Index n_col, Colamd_Row<Index> Row [], colamd_col<Index> Col [], Index A [], Index head [], double knobs[COLAMD_KNOBS], Index *p_n_row2, Index *p_n_col2, Index *p_max_deg); |
| 222 | |
| 223 | template <typename Index> |
| 224 | static Index find_ordering (Index n_row, Index n_col, Index Alen, Colamd_Row<Index> Row [], colamd_col<Index> Col [], Index A [], Index head [], Index n_col2, Index max_deg, Index pfree); |
| 225 | |
| 226 | template <typename Index> |
| 227 | static void order_children (Index n_col, colamd_col<Index> Col [], Index p []); |
| 228 | |
| 229 | template <typename Index> |
| 230 | static void detect_super_cols (colamd_col<Index> Col [], Index A [], Index head [], Index row_start, Index row_length ) ; |
| 231 | |
| 232 | template <typename Index> |
| 233 | static Index garbage_collection (Index n_row, Index n_col, Colamd_Row<Index> Row [], colamd_col<Index> Col [], Index A [], Index *pfree) ; |
| 234 | |
| 235 | template <typename Index> |
| 236 | static inline Index clear_mark (Index n_row, Colamd_Row<Index> Row [] ) ; |
| 237 | |
| 238 | /* === No debugging ========================================================= */ |
| 239 | |
| 240 | #define COLAMD_DEBUG0(params) ; |
| 241 | #define COLAMD_DEBUG1(params) ; |
| 242 | #define COLAMD_DEBUG2(params) ; |
| 243 | #define COLAMD_DEBUG3(params) ; |
| 244 | #define COLAMD_DEBUG4(params) ; |
| 245 | |
| 246 | #define COLAMD_ASSERT(expression) ((void) 0) |
| 247 | |
| 248 | |
| 249 | /** |
| 250 | * \brief Returns the recommended value of Alen |
| 251 | * |
| 252 | * Returns recommended value of Alen for use by colamd. |
| 253 | * Returns -1 if any input argument is negative. |
| 254 | * The use of this routine or macro is optional. |
| 255 | * Note that the macro uses its arguments more than once, |
| 256 | * so be careful for side effects, if you pass expressions as arguments to COLAMD_RECOMMENDED. |
| 257 | * |
| 258 | * \param nnz nonzeros in A |
| 259 | * \param n_row number of rows in A |
| 260 | * \param n_col number of columns in A |
| 261 | * \return recommended value of Alen for use by colamd |
| 262 | */ |
| 263 | template <typename Index> |
| 264 | inline Index colamd_recommended ( Index nnz, Index n_row, Index n_col) |
| 265 | { |
| 266 | if ((nnz) < 0 || (n_row) < 0 || (n_col) < 0) |
| 267 | return (-1); |
| 268 | else |
| 269 | return (2 * (nnz) + colamd_c (n_col) + colamd_r (n_row) + (n_col) + ((nnz) / 5)); |
| 270 | } |
| 271 | |
| 272 | /** |
| 273 | * \brief set default parameters The use of this routine is optional. |
| 274 | * |
| 275 | * Colamd: rows with more than (knobs [COLAMD_DENSE_ROW] * n_col) |
| 276 | * entries are removed prior to ordering. Columns with more than |
| 277 | * (knobs [COLAMD_DENSE_COL] * n_row) entries are removed prior to |
| 278 | * ordering, and placed last in the output column ordering. |
| 279 | * |
| 280 | * COLAMD_DENSE_ROW and COLAMD_DENSE_COL are defined as 0 and 1, |
| 281 | * respectively, in colamd.h. Default values of these two knobs |
| 282 | * are both 0.5. Currently, only knobs [0] and knobs [1] are |
| 283 | * used, but future versions may use more knobs. If so, they will |
| 284 | * be properly set to their defaults by the future version of |
| 285 | * colamd_set_defaults, so that the code that calls colamd will |
| 286 | * not need to change, assuming that you either use |
| 287 | * colamd_set_defaults, or pass a (double *) NULL pointer as the |
| 288 | * knobs array to colamd or symamd. |
| 289 | * |
| 290 | * \param knobs parameter settings for colamd |
| 291 | */ |
| 292 | |
| 293 | static inline void colamd_set_defaults(double knobs[COLAMD_KNOBS]) |
| 294 | { |
| 295 | /* === Local variables ================================================== */ |
| 296 | |
| 297 | int i ; |
| 298 | |
| 299 | if (!knobs) |
| 300 | { |
| 301 | return ; /* no knobs to initialize */ |
| 302 | } |
| 303 | for (i = 0 ; i < COLAMD_KNOBS ; i++) |
| 304 | { |
| 305 | knobs [i] = 0 ; |
| 306 | } |
| 307 | knobs [COLAMD_DENSE_ROW] = 0.5 ; /* ignore rows over 50% dense */ |
| 308 | knobs [COLAMD_DENSE_COL] = 0.5 ; /* ignore columns over 50% dense */ |
| 309 | } |
| 310 | |
| 311 | /** |
| 312 | * \brief Computes a column ordering using the column approximate minimum degree ordering |
| 313 | * |
| 314 | * Computes a column ordering (Q) of A such that P(AQ)=LU or |
| 315 | * (AQ)'AQ=LL' have less fill-in and require fewer floating point |
| 316 | * operations than factorizing the unpermuted matrix A or A'A, |
| 317 | * respectively. |
| 318 | * |
| 319 | * |
| 320 | * \param n_row number of rows in A |
| 321 | * \param n_col number of columns in A |
| 322 | * \param Alen, size of the array A |
| 323 | * \param A row indices of the matrix, of size ALen |
| 324 | * \param p column pointers of A, of size n_col+1 |
| 325 | * \param knobs parameter settings for colamd |
| 326 | * \param stats colamd output statistics and error codes |
| 327 | */ |
| 328 | template <typename Index> |
| 329 | static bool colamd(Index n_row, Index n_col, Index Alen, Index *A, Index *p, double knobs[COLAMD_KNOBS], Index stats[COLAMD_STATS]) |
| 330 | { |
| 331 | /* === Local variables ================================================== */ |
| 332 | |
| 333 | Index i ; /* loop index */ |
| 334 | Index nnz ; /* nonzeros in A */ |
| 335 | Index Row_size ; /* size of Row [], in integers */ |
| 336 | Index Col_size ; /* size of Col [], in integers */ |
| 337 | Index need ; /* minimum required length of A */ |
| 338 | Colamd_Row<Index> *Row ; /* pointer into A of Row [0..n_row] array */ |
| 339 | colamd_col<Index> *Col ; /* pointer into A of Col [0..n_col] array */ |
| 340 | Index n_col2 ; /* number of non-dense, non-empty columns */ |
| 341 | Index n_row2 ; /* number of non-dense, non-empty rows */ |
| 342 | Index ngarbage ; /* number of garbage collections performed */ |
| 343 | Index max_deg ; /* maximum row degree */ |
| 344 | double default_knobs [COLAMD_KNOBS] ; /* default knobs array */ |
| 345 | |
| 346 | |
| 347 | /* === Check the input arguments ======================================== */ |
| 348 | |
| 349 | if (!stats) |
| 350 | { |
| 351 | COLAMD_DEBUG0 (("colamd: stats not present\n")) ; |
| 352 | return (false) ; |
| 353 | } |
| 354 | for (i = 0 ; i < COLAMD_STATS ; i++) |
| 355 | { |
| 356 | stats [i] = 0 ; |
| 357 | } |
| 358 | stats [COLAMD_STATUS] = COLAMD_OK ; |
| 359 | stats [COLAMD_INFO1] = -1 ; |
| 360 | stats [COLAMD_INFO2] = -1 ; |
| 361 | |
| 362 | if (!A) /* A is not present */ |
| 363 | { |
| 364 | stats [COLAMD_STATUS] = COLAMD_ERROR_A_not_present ; |
| 365 | COLAMD_DEBUG0 (("colamd: A not present\n")) ; |
| 366 | return (false) ; |
| 367 | } |
| 368 | |
| 369 | if (!p) /* p is not present */ |
| 370 | { |
| 371 | stats [COLAMD_STATUS] = COLAMD_ERROR_p_not_present ; |
| 372 | COLAMD_DEBUG0 (("colamd: p not present\n")) ; |
| 373 | return (false) ; |
| 374 | } |
| 375 | |
| 376 | if (n_row < 0) /* n_row must be >= 0 */ |
| 377 | { |
| 378 | stats [COLAMD_STATUS] = COLAMD_ERROR_nrow_negative ; |
| 379 | stats [COLAMD_INFO1] = n_row ; |
| 380 | COLAMD_DEBUG0 (("colamd: nrow negative %d\n", n_row)) ; |
| 381 | return (false) ; |
| 382 | } |
| 383 | |
| 384 | if (n_col < 0) /* n_col must be >= 0 */ |
| 385 | { |
| 386 | stats [COLAMD_STATUS] = COLAMD_ERROR_ncol_negative ; |
| 387 | stats [COLAMD_INFO1] = n_col ; |
| 388 | COLAMD_DEBUG0 (("colamd: ncol negative %d\n", n_col)) ; |
| 389 | return (false) ; |
| 390 | } |
| 391 | |
| 392 | nnz = p [n_col] ; |
| 393 | if (nnz < 0) /* nnz must be >= 0 */ |
| 394 | { |
| 395 | stats [COLAMD_STATUS] = COLAMD_ERROR_nnz_negative ; |
| 396 | stats [COLAMD_INFO1] = nnz ; |
| 397 | COLAMD_DEBUG0 (("colamd: number of entries negative %d\n", nnz)) ; |
| 398 | return (false) ; |
| 399 | } |
| 400 | |
| 401 | if (p [0] != 0) |
| 402 | { |
| 403 | stats [COLAMD_STATUS] = COLAMD_ERROR_p0_nonzero ; |
| 404 | stats [COLAMD_INFO1] = p [0] ; |
| 405 | COLAMD_DEBUG0 (("colamd: p[0] not zero %d\n", p [0])) ; |
| 406 | return (false) ; |
| 407 | } |
| 408 | |
| 409 | /* === If no knobs, set default knobs =================================== */ |
| 410 | |
| 411 | if (!knobs) |
| 412 | { |
| 413 | colamd_set_defaults (default_knobs) ; |
| 414 | knobs = default_knobs ; |
| 415 | } |
| 416 | |
| 417 | /* === Allocate the Row and Col arrays from array A ===================== */ |
| 418 | |
| 419 | Col_size = colamd_c (n_col) ; |
| 420 | Row_size = colamd_r (n_row) ; |
| 421 | need = 2*nnz + n_col + Col_size + Row_size ; |
| 422 | |
| 423 | if (need > Alen) |
| 424 | { |
| 425 | /* not enough space in array A to perform the ordering */ |
| 426 | stats [COLAMD_STATUS] = COLAMD_ERROR_A_too_small ; |
| 427 | stats [COLAMD_INFO1] = need ; |
| 428 | stats [COLAMD_INFO2] = Alen ; |
| 429 | COLAMD_DEBUG0 (("colamd: Need Alen >= %d, given only Alen = %d\n", need,Alen)); |
| 430 | return (false) ; |
| 431 | } |
| 432 | |
| 433 | Alen -= Col_size + Row_size ; |
| 434 | Col = (colamd_col<Index> *) &A [Alen] ; |
| 435 | Row = (Colamd_Row<Index> *) &A [Alen + Col_size] ; |
| 436 | |
| 437 | /* === Construct the row and column data structures ===================== */ |
| 438 | |
| 439 | if (!Eigen::internal::init_rows_cols (n_row, n_col, Row, Col, A, p, stats)) |
| 440 | { |
| 441 | /* input matrix is invalid */ |
| 442 | COLAMD_DEBUG0 (("colamd: Matrix invalid\n")) ; |
| 443 | return (false) ; |
| 444 | } |
| 445 | |
| 446 | /* === Initialize scores, kill dense rows/columns ======================= */ |
| 447 | |
| 448 | Eigen::internal::init_scoring (n_row, n_col, Row, Col, A, p, knobs, |
| 449 | &n_row2, &n_col2, &max_deg) ; |
| 450 | |
| 451 | /* === Order the supercolumns =========================================== */ |
| 452 | |
| 453 | ngarbage = Eigen::internal::find_ordering (n_row, n_col, Alen, Row, Col, A, p, |
| 454 | n_col2, max_deg, 2*nnz) ; |
| 455 | |
| 456 | /* === Order the non-principal columns ================================== */ |
| 457 | |
| 458 | Eigen::internal::order_children (n_col, Col, p) ; |
| 459 | |
| 460 | /* === Return statistics in stats ======================================= */ |
| 461 | |
| 462 | stats [COLAMD_DENSE_ROW] = n_row - n_row2 ; |
| 463 | stats [COLAMD_DENSE_COL] = n_col - n_col2 ; |
| 464 | stats [COLAMD_DEFRAG_COUNT] = ngarbage ; |
| 465 | COLAMD_DEBUG0 (("colamd: done.\n")) ; |
| 466 | return (true) ; |
| 467 | } |
| 468 | |
| 469 | /* ========================================================================== */ |
| 470 | /* === NON-USER-CALLABLE ROUTINES: ========================================== */ |
| 471 | /* ========================================================================== */ |
| 472 | |
| 473 | /* There are no user-callable routines beyond this point in the file */ |
| 474 | |
| 475 | |
| 476 | /* ========================================================================== */ |
| 477 | /* === init_rows_cols ======================================================= */ |
| 478 | /* ========================================================================== */ |
| 479 | |
| 480 | /* |
| 481 | Takes the column form of the matrix in A and creates the row form of the |
| 482 | matrix. Also, row and column attributes are stored in the Col and Row |
| 483 | structs. If the columns are un-sorted or contain duplicate row indices, |
| 484 | this routine will also sort and remove duplicate row indices from the |
| 485 | column form of the matrix. Returns false if the matrix is invalid, |
| 486 | true otherwise. Not user-callable. |
| 487 | */ |
| 488 | template <typename Index> |
| 489 | static Index init_rows_cols /* returns true if OK, or false otherwise */ |
| 490 | ( |
| 491 | /* === Parameters ======================================================= */ |
| 492 | |
| 493 | Index n_row, /* number of rows of A */ |
| 494 | Index n_col, /* number of columns of A */ |
| 495 | Colamd_Row<Index> Row [], /* of size n_row+1 */ |
| 496 | colamd_col<Index> Col [], /* of size n_col+1 */ |
| 497 | Index A [], /* row indices of A, of size Alen */ |
| 498 | Index p [], /* pointers to columns in A, of size n_col+1 */ |
| 499 | Index stats [COLAMD_STATS] /* colamd statistics */ |
| 500 | ) |
| 501 | { |
| 502 | /* === Local variables ================================================== */ |
| 503 | |
| 504 | Index col ; /* a column index */ |
| 505 | Index row ; /* a row index */ |
| 506 | Index *cp ; /* a column pointer */ |
| 507 | Index *cp_end ; /* a pointer to the end of a column */ |
| 508 | Index *rp ; /* a row pointer */ |
| 509 | Index *rp_end ; /* a pointer to the end of a row */ |
| 510 | Index last_row ; /* previous row */ |
| 511 | |
| 512 | /* === Initialize columns, and check column pointers ==================== */ |
| 513 | |
| 514 | for (col = 0 ; col < n_col ; col++) |
| 515 | { |
| 516 | Col [col].start = p [col] ; |
| 517 | Col [col].length = p [col+1] - p [col] ; |
| 518 | |
| 519 | if (Col [col].length < 0) |
| 520 | { |
| 521 | /* column pointers must be non-decreasing */ |
| 522 | stats [COLAMD_STATUS] = COLAMD_ERROR_col_length_negative ; |
| 523 | stats [COLAMD_INFO1] = col ; |
| 524 | stats [COLAMD_INFO2] = Col [col].length ; |
| 525 | COLAMD_DEBUG0 (("colamd: col %d length %d < 0\n", col, Col [col].length)) ; |
| 526 | return (false) ; |
| 527 | } |
| 528 | |
| 529 | Col [col].shared1.thickness = 1 ; |
| 530 | Col [col].shared2.score = 0 ; |
| 531 | Col [col].shared3.prev = COLAMD_EMPTY ; |
| 532 | Col [col].shared4.degree_next = COLAMD_EMPTY ; |
| 533 | } |
| 534 | |
| 535 | /* p [0..n_col] no longer needed, used as "head" in subsequent routines */ |
| 536 | |
| 537 | /* === Scan columns, compute row degrees, and check row indices ========= */ |
| 538 | |
| 539 | stats [COLAMD_INFO3] = 0 ; /* number of duplicate or unsorted row indices*/ |
| 540 | |
| 541 | for (row = 0 ; row < n_row ; row++) |
| 542 | { |
| 543 | Row [row].length = 0 ; |
| 544 | Row [row].shared2.mark = -1 ; |
| 545 | } |
| 546 | |
| 547 | for (col = 0 ; col < n_col ; col++) |
| 548 | { |
| 549 | last_row = -1 ; |
| 550 | |
| 551 | cp = &A [p [col]] ; |
| 552 | cp_end = &A [p [col+1]] ; |
| 553 | |
| 554 | while (cp < cp_end) |
| 555 | { |
| 556 | row = *cp++ ; |
| 557 | |
| 558 | /* make sure row indices within range */ |
| 559 | if (row < 0 || row >= n_row) |
| 560 | { |
| 561 | stats [COLAMD_STATUS] = COLAMD_ERROR_row_index_out_of_bounds ; |
| 562 | stats [COLAMD_INFO1] = col ; |
| 563 | stats [COLAMD_INFO2] = row ; |
| 564 | stats [COLAMD_INFO3] = n_row ; |
| 565 | COLAMD_DEBUG0 (("colamd: row %d col %d out of bounds\n", row, col)) ; |
| 566 | return (false) ; |
| 567 | } |
| 568 | |
| 569 | if (row <= last_row || Row [row].shared2.mark == col) |
| 570 | { |
| 571 | /* row index are unsorted or repeated (or both), thus col */ |
| 572 | /* is jumbled. This is a notice, not an error condition. */ |
| 573 | stats [COLAMD_STATUS] = COLAMD_OK_BUT_JUMBLED ; |
| 574 | stats [COLAMD_INFO1] = col ; |
| 575 | stats [COLAMD_INFO2] = row ; |
| 576 | (stats [COLAMD_INFO3]) ++ ; |
| 577 | COLAMD_DEBUG1 (("colamd: row %d col %d unsorted/duplicate\n",row,col)); |
| 578 | } |
| 579 | |
| 580 | if (Row [row].shared2.mark != col) |
| 581 | { |
| 582 | Row [row].length++ ; |
| 583 | } |
| 584 | else |
| 585 | { |
| 586 | /* this is a repeated entry in the column, */ |
| 587 | /* it will be removed */ |
| 588 | Col [col].length-- ; |
| 589 | } |
| 590 | |
| 591 | /* mark the row as having been seen in this column */ |
| 592 | Row [row].shared2.mark = col ; |
| 593 | |
| 594 | last_row = row ; |
| 595 | } |
| 596 | } |
| 597 | |
| 598 | /* === Compute row pointers ============================================= */ |
| 599 | |
| 600 | /* row form of the matrix starts directly after the column */ |
| 601 | /* form of matrix in A */ |
| 602 | Row [0].start = p [n_col] ; |
| 603 | Row [0].shared1.p = Row [0].start ; |
| 604 | Row [0].shared2.mark = -1 ; |
| 605 | for (row = 1 ; row < n_row ; row++) |
| 606 | { |
| 607 | Row [row].start = Row [row-1].start + Row [row-1].length ; |
| 608 | Row [row].shared1.p = Row [row].start ; |
| 609 | Row [row].shared2.mark = -1 ; |
| 610 | } |
| 611 | |
| 612 | /* === Create row form ================================================== */ |
| 613 | |
| 614 | if (stats [COLAMD_STATUS] == COLAMD_OK_BUT_JUMBLED) |
| 615 | { |
| 616 | /* if cols jumbled, watch for repeated row indices */ |
| 617 | for (col = 0 ; col < n_col ; col++) |
| 618 | { |
| 619 | cp = &A [p [col]] ; |
| 620 | cp_end = &A [p [col+1]] ; |
| 621 | while (cp < cp_end) |
| 622 | { |
| 623 | row = *cp++ ; |
| 624 | if (Row [row].shared2.mark != col) |
| 625 | { |
| 626 | A [(Row [row].shared1.p)++] = col ; |
| 627 | Row [row].shared2.mark = col ; |
| 628 | } |
| 629 | } |
| 630 | } |
| 631 | } |
| 632 | else |
| 633 | { |
| 634 | /* if cols not jumbled, we don't need the mark (this is faster) */ |
| 635 | for (col = 0 ; col < n_col ; col++) |
| 636 | { |
| 637 | cp = &A [p [col]] ; |
| 638 | cp_end = &A [p [col+1]] ; |
| 639 | while (cp < cp_end) |
| 640 | { |
| 641 | A [(Row [*cp++].shared1.p)++] = col ; |
| 642 | } |
| 643 | } |
| 644 | } |
| 645 | |
| 646 | /* === Clear the row marks and set row degrees ========================== */ |
| 647 | |
| 648 | for (row = 0 ; row < n_row ; row++) |
| 649 | { |
| 650 | Row [row].shared2.mark = 0 ; |
| 651 | Row [row].shared1.degree = Row [row].length ; |
| 652 | } |
| 653 | |
| 654 | /* === See if we need to re-create columns ============================== */ |
| 655 | |
| 656 | if (stats [COLAMD_STATUS] == COLAMD_OK_BUT_JUMBLED) |
| 657 | { |
| 658 | COLAMD_DEBUG0 (("colamd: reconstructing column form, matrix jumbled\n")) ; |
| 659 | |
| 660 | |
| 661 | /* === Compute col pointers ========================================= */ |
| 662 | |
| 663 | /* col form of the matrix starts at A [0]. */ |
| 664 | /* Note, we may have a gap between the col form and the row */ |
| 665 | /* form if there were duplicate entries, if so, it will be */ |
| 666 | /* removed upon the first garbage collection */ |
| 667 | Col [0].start = 0 ; |
| 668 | p [0] = Col [0].start ; |
| 669 | for (col = 1 ; col < n_col ; col++) |
| 670 | { |
| 671 | /* note that the lengths here are for pruned columns, i.e. */ |
| 672 | /* no duplicate row indices will exist for these columns */ |
| 673 | Col [col].start = Col [col-1].start + Col [col-1].length ; |
| 674 | p [col] = Col [col].start ; |
| 675 | } |
| 676 | |
| 677 | /* === Re-create col form =========================================== */ |
| 678 | |
| 679 | for (row = 0 ; row < n_row ; row++) |
| 680 | { |
| 681 | rp = &A [Row [row].start] ; |
| 682 | rp_end = rp + Row [row].length ; |
| 683 | while (rp < rp_end) |
| 684 | { |
| 685 | A [(p [*rp++])++] = row ; |
| 686 | } |
| 687 | } |
| 688 | } |
| 689 | |
| 690 | /* === Done. Matrix is not (or no longer) jumbled ====================== */ |
| 691 | |
| 692 | return (true) ; |
| 693 | } |
| 694 | |
| 695 | |
| 696 | /* ========================================================================== */ |
| 697 | /* === init_scoring ========================================================= */ |
| 698 | /* ========================================================================== */ |
| 699 | |
| 700 | /* |
| 701 | Kills dense or empty columns and rows, calculates an initial score for |
| 702 | each column, and places all columns in the degree lists. Not user-callable. |
| 703 | */ |
| 704 | template <typename Index> |
| 705 | static void init_scoring |
| 706 | ( |
| 707 | /* === Parameters ======================================================= */ |
| 708 | |
| 709 | Index n_row, /* number of rows of A */ |
| 710 | Index n_col, /* number of columns of A */ |
| 711 | Colamd_Row<Index> Row [], /* of size n_row+1 */ |
| 712 | colamd_col<Index> Col [], /* of size n_col+1 */ |
| 713 | Index A [], /* column form and row form of A */ |
| 714 | Index head [], /* of size n_col+1 */ |
| 715 | double knobs [COLAMD_KNOBS],/* parameters */ |
| 716 | Index *p_n_row2, /* number of non-dense, non-empty rows */ |
| 717 | Index *p_n_col2, /* number of non-dense, non-empty columns */ |
| 718 | Index *p_max_deg /* maximum row degree */ |
| 719 | ) |
| 720 | { |
| 721 | /* === Local variables ================================================== */ |
| 722 | |
| 723 | Index c ; /* a column index */ |
| 724 | Index r, row ; /* a row index */ |
| 725 | Index *cp ; /* a column pointer */ |
| 726 | Index deg ; /* degree of a row or column */ |
| 727 | Index *cp_end ; /* a pointer to the end of a column */ |
| 728 | Index *new_cp ; /* new column pointer */ |
| 729 | Index col_length ; /* length of pruned column */ |
| 730 | Index score ; /* current column score */ |
| 731 | Index n_col2 ; /* number of non-dense, non-empty columns */ |
| 732 | Index n_row2 ; /* number of non-dense, non-empty rows */ |
| 733 | Index dense_row_count ; /* remove rows with more entries than this */ |
| 734 | Index dense_col_count ; /* remove cols with more entries than this */ |
| 735 | Index min_score ; /* smallest column score */ |
| 736 | Index max_deg ; /* maximum row degree */ |
| 737 | Index next_col ; /* Used to add to degree list.*/ |
| 738 | |
| 739 | |
| 740 | /* === Extract knobs ==================================================== */ |
| 741 | |
| 742 | dense_row_count = COLAMD_MAX (0, COLAMD_MIN (knobs [COLAMD_DENSE_ROW] * n_col, n_col)) ; |
| 743 | dense_col_count = COLAMD_MAX (0, COLAMD_MIN (knobs [COLAMD_DENSE_COL] * n_row, n_row)) ; |
| 744 | COLAMD_DEBUG1 (("colamd: densecount: %d %d\n", dense_row_count, dense_col_count)) ; |
| 745 | max_deg = 0 ; |
| 746 | n_col2 = n_col ; |
| 747 | n_row2 = n_row ; |
| 748 | |
| 749 | /* === Kill empty columns =============================================== */ |
| 750 | |
| 751 | /* Put the empty columns at the end in their natural order, so that LU */ |
| 752 | /* factorization can proceed as far as possible. */ |
| 753 | for (c = n_col-1 ; c >= 0 ; c--) |
| 754 | { |
| 755 | deg = Col [c].length ; |
| 756 | if (deg == 0) |
| 757 | { |
| 758 | /* this is a empty column, kill and order it last */ |
| 759 | Col [c].shared2.order = --n_col2 ; |
| 760 | KILL_PRINCIPAL_COL (c) ; |
| 761 | } |
| 762 | } |
| 763 | COLAMD_DEBUG1 (("colamd: null columns killed: %d\n", n_col - n_col2)) ; |
| 764 | |
| 765 | /* === Kill dense columns =============================================== */ |
| 766 | |
| 767 | /* Put the dense columns at the end, in their natural order */ |
| 768 | for (c = n_col-1 ; c >= 0 ; c--) |
| 769 | { |
| 770 | /* skip any dead columns */ |
| 771 | if (COL_IS_DEAD (c)) |
| 772 | { |
| 773 | continue ; |
| 774 | } |
| 775 | deg = Col [c].length ; |
| 776 | if (deg > dense_col_count) |
| 777 | { |
| 778 | /* this is a dense column, kill and order it last */ |
| 779 | Col [c].shared2.order = --n_col2 ; |
| 780 | /* decrement the row degrees */ |
| 781 | cp = &A [Col [c].start] ; |
| 782 | cp_end = cp + Col [c].length ; |
| 783 | while (cp < cp_end) |
| 784 | { |
| 785 | Row [*cp++].shared1.degree-- ; |
| 786 | } |
| 787 | KILL_PRINCIPAL_COL (c) ; |
| 788 | } |
| 789 | } |
| 790 | COLAMD_DEBUG1 (("colamd: Dense and null columns killed: %d\n", n_col - n_col2)) ; |
| 791 | |
| 792 | /* === Kill dense and empty rows ======================================== */ |
| 793 | |
| 794 | for (r = 0 ; r < n_row ; r++) |
| 795 | { |
| 796 | deg = Row [r].shared1.degree ; |
| 797 | COLAMD_ASSERT (deg >= 0 && deg <= n_col) ; |
| 798 | if (deg > dense_row_count || deg == 0) |
| 799 | { |
| 800 | /* kill a dense or empty row */ |
| 801 | KILL_ROW (r) ; |
| 802 | --n_row2 ; |
| 803 | } |
| 804 | else |
| 805 | { |
| 806 | /* keep track of max degree of remaining rows */ |
| 807 | max_deg = COLAMD_MAX (max_deg, deg) ; |
| 808 | } |
| 809 | } |
| 810 | COLAMD_DEBUG1 (("colamd: Dense and null rows killed: %d\n", n_row - n_row2)) ; |
| 811 | |
| 812 | /* === Compute initial column scores ==================================== */ |
| 813 | |
| 814 | /* At this point the row degrees are accurate. They reflect the number */ |
| 815 | /* of "live" (non-dense) columns in each row. No empty rows exist. */ |
| 816 | /* Some "live" columns may contain only dead rows, however. These are */ |
| 817 | /* pruned in the code below. */ |
| 818 | |
| 819 | /* now find the initial matlab score for each column */ |
| 820 | for (c = n_col-1 ; c >= 0 ; c--) |
| 821 | { |
| 822 | /* skip dead column */ |
| 823 | if (COL_IS_DEAD (c)) |
| 824 | { |
| 825 | continue ; |
| 826 | } |
| 827 | score = 0 ; |
| 828 | cp = &A [Col [c].start] ; |
| 829 | new_cp = cp ; |
| 830 | cp_end = cp + Col [c].length ; |
| 831 | while (cp < cp_end) |
| 832 | { |
| 833 | /* get a row */ |
| 834 | row = *cp++ ; |
| 835 | /* skip if dead */ |
| 836 | if (ROW_IS_DEAD (row)) |
| 837 | { |
| 838 | continue ; |
| 839 | } |
| 840 | /* compact the column */ |
| 841 | *new_cp++ = row ; |
| 842 | /* add row's external degree */ |
| 843 | score += Row [row].shared1.degree - 1 ; |
| 844 | /* guard against integer overflow */ |
| 845 | score = COLAMD_MIN (score, n_col) ; |
| 846 | } |
| 847 | /* determine pruned column length */ |
| 848 | col_length = (Index) (new_cp - &A [Col [c].start]) ; |
| 849 | if (col_length == 0) |
| 850 | { |
| 851 | /* a newly-made null column (all rows in this col are "dense" */ |
| 852 | /* and have already been killed) */ |
| 853 | COLAMD_DEBUG2 (("Newly null killed: %d\n", c)) ; |
| 854 | Col [c].shared2.order = --n_col2 ; |
| 855 | KILL_PRINCIPAL_COL (c) ; |
| 856 | } |
| 857 | else |
| 858 | { |
| 859 | /* set column length and set score */ |
| 860 | COLAMD_ASSERT (score >= 0) ; |
| 861 | COLAMD_ASSERT (score <= n_col) ; |
| 862 | Col [c].length = col_length ; |
| 863 | Col [c].shared2.score = score ; |
| 864 | } |
| 865 | } |
| 866 | COLAMD_DEBUG1 (("colamd: Dense, null, and newly-null columns killed: %d\n", |
| 867 | n_col-n_col2)) ; |
| 868 | |
| 869 | /* At this point, all empty rows and columns are dead. All live columns */ |
| 870 | /* are "clean" (containing no dead rows) and simplicial (no supercolumns */ |
| 871 | /* yet). Rows may contain dead columns, but all live rows contain at */ |
| 872 | /* least one live column. */ |
| 873 | |
| 874 | /* === Initialize degree lists ========================================== */ |
| 875 | |
| 876 | |
| 877 | /* clear the hash buckets */ |
| 878 | for (c = 0 ; c <= n_col ; c++) |
| 879 | { |
| 880 | head [c] = COLAMD_EMPTY ; |
| 881 | } |
| 882 | min_score = n_col ; |
| 883 | /* place in reverse order, so low column indices are at the front */ |
| 884 | /* of the lists. This is to encourage natural tie-breaking */ |
| 885 | for (c = n_col-1 ; c >= 0 ; c--) |
| 886 | { |
| 887 | /* only add principal columns to degree lists */ |
| 888 | if (COL_IS_ALIVE (c)) |
| 889 | { |
| 890 | COLAMD_DEBUG4 (("place %d score %d minscore %d ncol %d\n", |
| 891 | c, Col [c].shared2.score, min_score, n_col)) ; |
| 892 | |
| 893 | /* === Add columns score to DList =============================== */ |
| 894 | |
| 895 | score = Col [c].shared2.score ; |
| 896 | |
| 897 | COLAMD_ASSERT (min_score >= 0) ; |
| 898 | COLAMD_ASSERT (min_score <= n_col) ; |
| 899 | COLAMD_ASSERT (score >= 0) ; |
| 900 | COLAMD_ASSERT (score <= n_col) ; |
| 901 | COLAMD_ASSERT (head [score] >= COLAMD_EMPTY) ; |
| 902 | |
| 903 | /* now add this column to dList at proper score location */ |
| 904 | next_col = head [score] ; |
| 905 | Col [c].shared3.prev = COLAMD_EMPTY ; |
| 906 | Col [c].shared4.degree_next = next_col ; |
| 907 | |
| 908 | /* if there already was a column with the same score, set its */ |
| 909 | /* previous pointer to this new column */ |
| 910 | if (next_col != COLAMD_EMPTY) |
| 911 | { |
| 912 | Col [next_col].shared3.prev = c ; |
| 913 | } |
| 914 | head [score] = c ; |
| 915 | |
| 916 | /* see if this score is less than current min */ |
| 917 | min_score = COLAMD_MIN (min_score, score) ; |
| 918 | |
| 919 | |
| 920 | } |
| 921 | } |
| 922 | |
| 923 | |
| 924 | /* === Return number of remaining columns, and max row degree =========== */ |
| 925 | |
| 926 | *p_n_col2 = n_col2 ; |
| 927 | *p_n_row2 = n_row2 ; |
| 928 | *p_max_deg = max_deg ; |
| 929 | } |
| 930 | |
| 931 | |
| 932 | /* ========================================================================== */ |
| 933 | /* === find_ordering ======================================================== */ |
| 934 | /* ========================================================================== */ |
| 935 | |
| 936 | /* |
| 937 | Order the principal columns of the supercolumn form of the matrix |
| 938 | (no supercolumns on input). Uses a minimum approximate column minimum |
| 939 | degree ordering method. Not user-callable. |
| 940 | */ |
| 941 | template <typename Index> |
| 942 | static Index find_ordering /* return the number of garbage collections */ |
| 943 | ( |
| 944 | /* === Parameters ======================================================= */ |
| 945 | |
| 946 | Index n_row, /* number of rows of A */ |
| 947 | Index n_col, /* number of columns of A */ |
| 948 | Index Alen, /* size of A, 2*nnz + n_col or larger */ |
| 949 | Colamd_Row<Index> Row [], /* of size n_row+1 */ |
| 950 | colamd_col<Index> Col [], /* of size n_col+1 */ |
| 951 | Index A [], /* column form and row form of A */ |
| 952 | Index head [], /* of size n_col+1 */ |
| 953 | Index n_col2, /* Remaining columns to order */ |
| 954 | Index max_deg, /* Maximum row degree */ |
| 955 | Index pfree /* index of first free slot (2*nnz on entry) */ |
| 956 | ) |
| 957 | { |
| 958 | /* === Local variables ================================================== */ |
| 959 | |
| 960 | Index k ; /* current pivot ordering step */ |
| 961 | Index pivot_col ; /* current pivot column */ |
| 962 | Index *cp ; /* a column pointer */ |
| 963 | Index *rp ; /* a row pointer */ |
| 964 | Index pivot_row ; /* current pivot row */ |
| 965 | Index *new_cp ; /* modified column pointer */ |
| 966 | Index *new_rp ; /* modified row pointer */ |
| 967 | Index pivot_row_start ; /* pointer to start of pivot row */ |
| 968 | Index pivot_row_degree ; /* number of columns in pivot row */ |
| 969 | Index pivot_row_length ; /* number of supercolumns in pivot row */ |
| 970 | Index pivot_col_score ; /* score of pivot column */ |
| 971 | Index needed_memory ; /* free space needed for pivot row */ |
| 972 | Index *cp_end ; /* pointer to the end of a column */ |
| 973 | Index *rp_end ; /* pointer to the end of a row */ |
| 974 | Index row ; /* a row index */ |
| 975 | Index col ; /* a column index */ |
| 976 | Index max_score ; /* maximum possible score */ |
| 977 | Index cur_score ; /* score of current column */ |
| 978 | unsigned int hash ; /* hash value for supernode detection */ |
| 979 | Index head_column ; /* head of hash bucket */ |
| 980 | Index first_col ; /* first column in hash bucket */ |
| 981 | Index tag_mark ; /* marker value for mark array */ |
| 982 | Index row_mark ; /* Row [row].shared2.mark */ |
| 983 | Index set_difference ; /* set difference size of row with pivot row */ |
| 984 | Index min_score ; /* smallest column score */ |
| 985 | Index col_thickness ; /* "thickness" (no. of columns in a supercol) */ |
| 986 | Index max_mark ; /* maximum value of tag_mark */ |
| 987 | Index pivot_col_thickness ; /* number of columns represented by pivot col */ |
| 988 | Index prev_col ; /* Used by Dlist operations. */ |
| 989 | Index next_col ; /* Used by Dlist operations. */ |
| 990 | Index ngarbage ; /* number of garbage collections performed */ |
| 991 | |
| 992 | |
| 993 | /* === Initialization and clear mark ==================================== */ |
| 994 | |
| 995 | max_mark = INT_MAX - n_col ; /* INT_MAX defined in <limits.h> */ |
| 996 | tag_mark = Eigen::internal::clear_mark (n_row, Row) ; |
| 997 | min_score = 0 ; |
| 998 | ngarbage = 0 ; |
| 999 | COLAMD_DEBUG1 (("colamd: Ordering, n_col2=%d\n", n_col2)) ; |
| 1000 | |
| 1001 | /* === Order the columns ================================================ */ |
| 1002 | |
| 1003 | for (k = 0 ; k < n_col2 ; /* 'k' is incremented below */) |
| 1004 | { |
| 1005 | |
| 1006 | /* === Select pivot column, and order it ============================ */ |
| 1007 | |
| 1008 | /* make sure degree list isn't empty */ |
| 1009 | COLAMD_ASSERT (min_score >= 0) ; |
| 1010 | COLAMD_ASSERT (min_score <= n_col) ; |
| 1011 | COLAMD_ASSERT (head [min_score] >= COLAMD_EMPTY) ; |
| 1012 | |
| 1013 | /* get pivot column from head of minimum degree list */ |
| 1014 | while (head [min_score] == COLAMD_EMPTY && min_score < n_col) |
| 1015 | { |
| 1016 | min_score++ ; |
| 1017 | } |
| 1018 | pivot_col = head [min_score] ; |
| 1019 | COLAMD_ASSERT (pivot_col >= 0 && pivot_col <= n_col) ; |
| 1020 | next_col = Col [pivot_col].shared4.degree_next ; |
| 1021 | head [min_score] = next_col ; |
| 1022 | if (next_col != COLAMD_EMPTY) |
| 1023 | { |
| 1024 | Col [next_col].shared3.prev = COLAMD_EMPTY ; |
| 1025 | } |
| 1026 | |
| 1027 | COLAMD_ASSERT (COL_IS_ALIVE (pivot_col)) ; |
| 1028 | COLAMD_DEBUG3 (("Pivot col: %d\n", pivot_col)) ; |
| 1029 | |
| 1030 | /* remember score for defrag check */ |
| 1031 | pivot_col_score = Col [pivot_col].shared2.score ; |
| 1032 | |
| 1033 | /* the pivot column is the kth column in the pivot order */ |
| 1034 | Col [pivot_col].shared2.order = k ; |
| 1035 | |
| 1036 | /* increment order count by column thickness */ |
| 1037 | pivot_col_thickness = Col [pivot_col].shared1.thickness ; |
| 1038 | k += pivot_col_thickness ; |
| 1039 | COLAMD_ASSERT (pivot_col_thickness > 0) ; |
| 1040 | |
| 1041 | /* === Garbage_collection, if necessary ============================= */ |
| 1042 | |
| 1043 | needed_memory = COLAMD_MIN (pivot_col_score, n_col - k) ; |
| 1044 | if (pfree + needed_memory >= Alen) |
| 1045 | { |
| 1046 | pfree = Eigen::internal::garbage_collection (n_row, n_col, Row, Col, A, &A [pfree]) ; |
| 1047 | ngarbage++ ; |
| 1048 | /* after garbage collection we will have enough */ |
| 1049 | COLAMD_ASSERT (pfree + needed_memory < Alen) ; |
| 1050 | /* garbage collection has wiped out the Row[].shared2.mark array */ |
| 1051 | tag_mark = Eigen::internal::clear_mark (n_row, Row) ; |
| 1052 | |
| 1053 | } |
| 1054 | |
| 1055 | /* === Compute pivot row pattern ==================================== */ |
| 1056 | |
| 1057 | /* get starting location for this new merged row */ |
| 1058 | pivot_row_start = pfree ; |
| 1059 | |
| 1060 | /* initialize new row counts to zero */ |
| 1061 | pivot_row_degree = 0 ; |
| 1062 | |
| 1063 | /* tag pivot column as having been visited so it isn't included */ |
| 1064 | /* in merged pivot row */ |
| 1065 | Col [pivot_col].shared1.thickness = -pivot_col_thickness ; |
| 1066 | |
| 1067 | /* pivot row is the union of all rows in the pivot column pattern */ |
| 1068 | cp = &A [Col [pivot_col].start] ; |
| 1069 | cp_end = cp + Col [pivot_col].length ; |
| 1070 | while (cp < cp_end) |
| 1071 | { |
| 1072 | /* get a row */ |
| 1073 | row = *cp++ ; |
| 1074 | COLAMD_DEBUG4 (("Pivot col pattern %d %d\n", ROW_IS_ALIVE (row), row)) ; |
| 1075 | /* skip if row is dead */ |
| 1076 | if (ROW_IS_DEAD (row)) |
| 1077 | { |
| 1078 | continue ; |
| 1079 | } |
| 1080 | rp = &A [Row [row].start] ; |
| 1081 | rp_end = rp + Row [row].length ; |
| 1082 | while (rp < rp_end) |
| 1083 | { |
| 1084 | /* get a column */ |
| 1085 | col = *rp++ ; |
| 1086 | /* add the column, if alive and untagged */ |
| 1087 | col_thickness = Col [col].shared1.thickness ; |
| 1088 | if (col_thickness > 0 && COL_IS_ALIVE (col)) |
| 1089 | { |
| 1090 | /* tag column in pivot row */ |
| 1091 | Col [col].shared1.thickness = -col_thickness ; |
| 1092 | COLAMD_ASSERT (pfree < Alen) ; |
| 1093 | /* place column in pivot row */ |
| 1094 | A [pfree++] = col ; |
| 1095 | pivot_row_degree += col_thickness ; |
| 1096 | } |
| 1097 | } |
| 1098 | } |
| 1099 | |
| 1100 | /* clear tag on pivot column */ |
| 1101 | Col [pivot_col].shared1.thickness = pivot_col_thickness ; |
| 1102 | max_deg = COLAMD_MAX (max_deg, pivot_row_degree) ; |
| 1103 | |
| 1104 | |
| 1105 | /* === Kill all rows used to construct pivot row ==================== */ |
| 1106 | |
| 1107 | /* also kill pivot row, temporarily */ |
| 1108 | cp = &A [Col [pivot_col].start] ; |
| 1109 | cp_end = cp + Col [pivot_col].length ; |
| 1110 | while (cp < cp_end) |
| 1111 | { |
| 1112 | /* may be killing an already dead row */ |
| 1113 | row = *cp++ ; |
| 1114 | COLAMD_DEBUG3 (("Kill row in pivot col: %d\n", row)) ; |
| 1115 | KILL_ROW (row) ; |
| 1116 | } |
| 1117 | |
| 1118 | /* === Select a row index to use as the new pivot row =============== */ |
| 1119 | |
| 1120 | pivot_row_length = pfree - pivot_row_start ; |
| 1121 | if (pivot_row_length > 0) |
| 1122 | { |
| 1123 | /* pick the "pivot" row arbitrarily (first row in col) */ |
| 1124 | pivot_row = A [Col [pivot_col].start] ; |
| 1125 | COLAMD_DEBUG3 (("Pivotal row is %d\n", pivot_row)) ; |
| 1126 | } |
| 1127 | else |
| 1128 | { |
| 1129 | /* there is no pivot row, since it is of zero length */ |
| 1130 | pivot_row = COLAMD_EMPTY ; |
| 1131 | COLAMD_ASSERT (pivot_row_length == 0) ; |
| 1132 | } |
| 1133 | COLAMD_ASSERT (Col [pivot_col].length > 0 || pivot_row_length == 0) ; |
| 1134 | |
| 1135 | /* === Approximate degree computation =============================== */ |
| 1136 | |
| 1137 | /* Here begins the computation of the approximate degree. The column */ |
| 1138 | /* score is the sum of the pivot row "length", plus the size of the */ |
| 1139 | /* set differences of each row in the column minus the pattern of the */ |
| 1140 | /* pivot row itself. The column ("thickness") itself is also */ |
| 1141 | /* excluded from the column score (we thus use an approximate */ |
| 1142 | /* external degree). */ |
| 1143 | |
| 1144 | /* The time taken by the following code (compute set differences, and */ |
| 1145 | /* add them up) is proportional to the size of the data structure */ |
| 1146 | /* being scanned - that is, the sum of the sizes of each column in */ |
| 1147 | /* the pivot row. Thus, the amortized time to compute a column score */ |
| 1148 | /* is proportional to the size of that column (where size, in this */ |
| 1149 | /* context, is the column "length", or the number of row indices */ |
| 1150 | /* in that column). The number of row indices in a column is */ |
| 1151 | /* monotonically non-decreasing, from the length of the original */ |
| 1152 | /* column on input to colamd. */ |
| 1153 | |
| 1154 | /* === Compute set differences ====================================== */ |
| 1155 | |
| 1156 | COLAMD_DEBUG3 (("** Computing set differences phase. **\n")) ; |
| 1157 | |
| 1158 | /* pivot row is currently dead - it will be revived later. */ |
| 1159 | |
| 1160 | COLAMD_DEBUG3 (("Pivot row: ")) ; |
| 1161 | /* for each column in pivot row */ |
| 1162 | rp = &A [pivot_row_start] ; |
| 1163 | rp_end = rp + pivot_row_length ; |
| 1164 | while (rp < rp_end) |
| 1165 | { |
| 1166 | col = *rp++ ; |
| 1167 | COLAMD_ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ; |
| 1168 | COLAMD_DEBUG3 (("Col: %d\n", col)) ; |
| 1169 | |
| 1170 | /* clear tags used to construct pivot row pattern */ |
| 1171 | col_thickness = -Col [col].shared1.thickness ; |
| 1172 | COLAMD_ASSERT (col_thickness > 0) ; |
| 1173 | Col [col].shared1.thickness = col_thickness ; |
| 1174 | |
| 1175 | /* === Remove column from degree list =========================== */ |
| 1176 | |
| 1177 | cur_score = Col [col].shared2.score ; |
| 1178 | prev_col = Col [col].shared3.prev ; |
| 1179 | next_col = Col [col].shared4.degree_next ; |
| 1180 | COLAMD_ASSERT (cur_score >= 0) ; |
| 1181 | COLAMD_ASSERT (cur_score <= n_col) ; |
| 1182 | COLAMD_ASSERT (cur_score >= COLAMD_EMPTY) ; |
| 1183 | if (prev_col == COLAMD_EMPTY) |
| 1184 | { |
| 1185 | head [cur_score] = next_col ; |
| 1186 | } |
| 1187 | else |
| 1188 | { |
| 1189 | Col [prev_col].shared4.degree_next = next_col ; |
| 1190 | } |
| 1191 | if (next_col != COLAMD_EMPTY) |
| 1192 | { |
| 1193 | Col [next_col].shared3.prev = prev_col ; |
| 1194 | } |
| 1195 | |
| 1196 | /* === Scan the column ========================================== */ |
| 1197 | |
| 1198 | cp = &A [Col [col].start] ; |
| 1199 | cp_end = cp + Col [col].length ; |
| 1200 | while (cp < cp_end) |
| 1201 | { |
| 1202 | /* get a row */ |
| 1203 | row = *cp++ ; |
| 1204 | row_mark = Row [row].shared2.mark ; |
| 1205 | /* skip if dead */ |
| 1206 | if (ROW_IS_MARKED_DEAD (row_mark)) |
| 1207 | { |
| 1208 | continue ; |
| 1209 | } |
| 1210 | COLAMD_ASSERT (row != pivot_row) ; |
| 1211 | set_difference = row_mark - tag_mark ; |
| 1212 | /* check if the row has been seen yet */ |
| 1213 | if (set_difference < 0) |
| 1214 | { |
| 1215 | COLAMD_ASSERT (Row [row].shared1.degree <= max_deg) ; |
| 1216 | set_difference = Row [row].shared1.degree ; |
| 1217 | } |
| 1218 | /* subtract column thickness from this row's set difference */ |
| 1219 | set_difference -= col_thickness ; |
| 1220 | COLAMD_ASSERT (set_difference >= 0) ; |
| 1221 | /* absorb this row if the set difference becomes zero */ |
| 1222 | if (set_difference == 0) |
| 1223 | { |
| 1224 | COLAMD_DEBUG3 (("aggressive absorption. Row: %d\n", row)) ; |
| 1225 | KILL_ROW (row) ; |
| 1226 | } |
| 1227 | else |
| 1228 | { |
| 1229 | /* save the new mark */ |
| 1230 | Row [row].shared2.mark = set_difference + tag_mark ; |
| 1231 | } |
| 1232 | } |
| 1233 | } |
| 1234 | |
| 1235 | |
| 1236 | /* === Add up set differences for each column ======================= */ |
| 1237 | |
| 1238 | COLAMD_DEBUG3 (("** Adding set differences phase. **\n")) ; |
| 1239 | |
| 1240 | /* for each column in pivot row */ |
| 1241 | rp = &A [pivot_row_start] ; |
| 1242 | rp_end = rp + pivot_row_length ; |
| 1243 | while (rp < rp_end) |
| 1244 | { |
| 1245 | /* get a column */ |
| 1246 | col = *rp++ ; |
| 1247 | COLAMD_ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ; |
| 1248 | hash = 0 ; |
| 1249 | cur_score = 0 ; |
| 1250 | cp = &A [Col [col].start] ; |
| 1251 | /* compact the column */ |
| 1252 | new_cp = cp ; |
| 1253 | cp_end = cp + Col [col].length ; |
| 1254 | |
| 1255 | COLAMD_DEBUG4 (("Adding set diffs for Col: %d.\n", col)) ; |
| 1256 | |
| 1257 | while (cp < cp_end) |
| 1258 | { |
| 1259 | /* get a row */ |
| 1260 | row = *cp++ ; |
| 1261 | COLAMD_ASSERT(row >= 0 && row < n_row) ; |
| 1262 | row_mark = Row [row].shared2.mark ; |
| 1263 | /* skip if dead */ |
| 1264 | if (ROW_IS_MARKED_DEAD (row_mark)) |
| 1265 | { |
| 1266 | continue ; |
| 1267 | } |
| 1268 | COLAMD_ASSERT (row_mark > tag_mark) ; |
| 1269 | /* compact the column */ |
| 1270 | *new_cp++ = row ; |
| 1271 | /* compute hash function */ |
| 1272 | hash += row ; |
| 1273 | /* add set difference */ |
| 1274 | cur_score += row_mark - tag_mark ; |
| 1275 | /* integer overflow... */ |
| 1276 | cur_score = COLAMD_MIN (cur_score, n_col) ; |
| 1277 | } |
| 1278 | |
| 1279 | /* recompute the column's length */ |
| 1280 | Col [col].length = (Index) (new_cp - &A [Col [col].start]) ; |
| 1281 | |
| 1282 | /* === Further mass elimination ================================= */ |
| 1283 | |
| 1284 | if (Col [col].length == 0) |
| 1285 | { |
| 1286 | COLAMD_DEBUG4 (("further mass elimination. Col: %d\n", col)) ; |
| 1287 | /* nothing left but the pivot row in this column */ |
| 1288 | KILL_PRINCIPAL_COL (col) ; |
| 1289 | pivot_row_degree -= Col [col].shared1.thickness ; |
| 1290 | COLAMD_ASSERT (pivot_row_degree >= 0) ; |
| 1291 | /* order it */ |
| 1292 | Col [col].shared2.order = k ; |
| 1293 | /* increment order count by column thickness */ |
| 1294 | k += Col [col].shared1.thickness ; |
| 1295 | } |
| 1296 | else |
| 1297 | { |
| 1298 | /* === Prepare for supercolumn detection ==================== */ |
| 1299 | |
| 1300 | COLAMD_DEBUG4 (("Preparing supercol detection for Col: %d.\n", col)) ; |
| 1301 | |
| 1302 | /* save score so far */ |
| 1303 | Col [col].shared2.score = cur_score ; |
| 1304 | |
| 1305 | /* add column to hash table, for supercolumn detection */ |
| 1306 | hash %= n_col + 1 ; |
| 1307 | |
| 1308 | COLAMD_DEBUG4 ((" Hash = %d, n_col = %d.\n", hash, n_col)) ; |
| 1309 | COLAMD_ASSERT (hash <= n_col) ; |
| 1310 | |
| 1311 | head_column = head [hash] ; |
| 1312 | if (head_column > COLAMD_EMPTY) |
| 1313 | { |
| 1314 | /* degree list "hash" is non-empty, use prev (shared3) of */ |
| 1315 | /* first column in degree list as head of hash bucket */ |
| 1316 | first_col = Col [head_column].shared3.headhash ; |
| 1317 | Col [head_column].shared3.headhash = col ; |
| 1318 | } |
| 1319 | else |
| 1320 | { |
| 1321 | /* degree list "hash" is empty, use head as hash bucket */ |
| 1322 | first_col = - (head_column + 2) ; |
| 1323 | head [hash] = - (col + 2) ; |
| 1324 | } |
| 1325 | Col [col].shared4.hash_next = first_col ; |
| 1326 | |
| 1327 | /* save hash function in Col [col].shared3.hash */ |
| 1328 | Col [col].shared3.hash = (Index) hash ; |
| 1329 | COLAMD_ASSERT (COL_IS_ALIVE (col)) ; |
| 1330 | } |
| 1331 | } |
| 1332 | |
| 1333 | /* The approximate external column degree is now computed. */ |
| 1334 | |
| 1335 | /* === Supercolumn detection ======================================== */ |
| 1336 | |
| 1337 | COLAMD_DEBUG3 (("** Supercolumn detection phase. **\n")) ; |
| 1338 | |
| 1339 | Eigen::internal::detect_super_cols (Col, A, head, pivot_row_start, pivot_row_length) ; |
| 1340 | |
| 1341 | /* === Kill the pivotal column ====================================== */ |
| 1342 | |
| 1343 | KILL_PRINCIPAL_COL (pivot_col) ; |
| 1344 | |
| 1345 | /* === Clear mark =================================================== */ |
| 1346 | |
| 1347 | tag_mark += (max_deg + 1) ; |
| 1348 | if (tag_mark >= max_mark) |
| 1349 | { |
| 1350 | COLAMD_DEBUG2 (("clearing tag_mark\n")) ; |
| 1351 | tag_mark = Eigen::internal::clear_mark (n_row, Row) ; |
| 1352 | } |
| 1353 | |
| 1354 | /* === Finalize the new pivot row, and column scores ================ */ |
| 1355 | |
| 1356 | COLAMD_DEBUG3 (("** Finalize scores phase. **\n")) ; |
| 1357 | |
| 1358 | /* for each column in pivot row */ |
| 1359 | rp = &A [pivot_row_start] ; |
| 1360 | /* compact the pivot row */ |
| 1361 | new_rp = rp ; |
| 1362 | rp_end = rp + pivot_row_length ; |
| 1363 | while (rp < rp_end) |
| 1364 | { |
| 1365 | col = *rp++ ; |
| 1366 | /* skip dead columns */ |
| 1367 | if (COL_IS_DEAD (col)) |
| 1368 | { |
| 1369 | continue ; |
| 1370 | } |
| 1371 | *new_rp++ = col ; |
| 1372 | /* add new pivot row to column */ |
| 1373 | A [Col [col].start + (Col [col].length++)] = pivot_row ; |
| 1374 | |
| 1375 | /* retrieve score so far and add on pivot row's degree. */ |
| 1376 | /* (we wait until here for this in case the pivot */ |
| 1377 | /* row's degree was reduced due to mass elimination). */ |
| 1378 | cur_score = Col [col].shared2.score + pivot_row_degree ; |
| 1379 | |
| 1380 | /* calculate the max possible score as the number of */ |
| 1381 | /* external columns minus the 'k' value minus the */ |
| 1382 | /* columns thickness */ |
| 1383 | max_score = n_col - k - Col [col].shared1.thickness ; |
| 1384 | |
| 1385 | /* make the score the external degree of the union-of-rows */ |
| 1386 | cur_score -= Col [col].shared1.thickness ; |
| 1387 | |
| 1388 | /* make sure score is less or equal than the max score */ |
| 1389 | cur_score = COLAMD_MIN (cur_score, max_score) ; |
| 1390 | COLAMD_ASSERT (cur_score >= 0) ; |
| 1391 | |
| 1392 | /* store updated score */ |
| 1393 | Col [col].shared2.score = cur_score ; |
| 1394 | |
| 1395 | /* === Place column back in degree list ========================= */ |
| 1396 | |
| 1397 | COLAMD_ASSERT (min_score >= 0) ; |
| 1398 | COLAMD_ASSERT (min_score <= n_col) ; |
| 1399 | COLAMD_ASSERT (cur_score >= 0) ; |
| 1400 | COLAMD_ASSERT (cur_score <= n_col) ; |
| 1401 | COLAMD_ASSERT (head [cur_score] >= COLAMD_EMPTY) ; |
| 1402 | next_col = head [cur_score] ; |
| 1403 | Col [col].shared4.degree_next = next_col ; |
| 1404 | Col [col].shared3.prev = COLAMD_EMPTY ; |
| 1405 | if (next_col != COLAMD_EMPTY) |
| 1406 | { |
| 1407 | Col [next_col].shared3.prev = col ; |
| 1408 | } |
| 1409 | head [cur_score] = col ; |
| 1410 | |
| 1411 | /* see if this score is less than current min */ |
| 1412 | min_score = COLAMD_MIN (min_score, cur_score) ; |
| 1413 | |
| 1414 | } |
| 1415 | |
| 1416 | /* === Resurrect the new pivot row ================================== */ |
| 1417 | |
| 1418 | if (pivot_row_degree > 0) |
| 1419 | { |
| 1420 | /* update pivot row length to reflect any cols that were killed */ |
| 1421 | /* during super-col detection and mass elimination */ |
| 1422 | Row [pivot_row].start = pivot_row_start ; |
| 1423 | Row [pivot_row].length = (Index) (new_rp - &A[pivot_row_start]) ; |
| 1424 | Row [pivot_row].shared1.degree = pivot_row_degree ; |
| 1425 | Row [pivot_row].shared2.mark = 0 ; |
| 1426 | /* pivot row is no longer dead */ |
| 1427 | } |
| 1428 | } |
| 1429 | |
| 1430 | /* === All principal columns have now been ordered ====================== */ |
| 1431 | |
| 1432 | return (ngarbage) ; |
| 1433 | } |
| 1434 | |
| 1435 | |
| 1436 | /* ========================================================================== */ |
| 1437 | /* === order_children ======================================================= */ |
| 1438 | /* ========================================================================== */ |
| 1439 | |
| 1440 | /* |
| 1441 | The find_ordering routine has ordered all of the principal columns (the |
| 1442 | representatives of the supercolumns). The non-principal columns have not |
| 1443 | yet been ordered. This routine orders those columns by walking up the |
| 1444 | parent tree (a column is a child of the column which absorbed it). The |
| 1445 | final permutation vector is then placed in p [0 ... n_col-1], with p [0] |
| 1446 | being the first column, and p [n_col-1] being the last. It doesn't look |
| 1447 | like it at first glance, but be assured that this routine takes time linear |
| 1448 | in the number of columns. Although not immediately obvious, the time |
| 1449 | taken by this routine is O (n_col), that is, linear in the number of |
| 1450 | columns. Not user-callable. |
| 1451 | */ |
| 1452 | template <typename Index> |
| 1453 | static inline void order_children |
| 1454 | ( |
| 1455 | /* === Parameters ======================================================= */ |
| 1456 | |
| 1457 | Index n_col, /* number of columns of A */ |
| 1458 | colamd_col<Index> Col [], /* of size n_col+1 */ |
| 1459 | Index p [] /* p [0 ... n_col-1] is the column permutation*/ |
| 1460 | ) |
| 1461 | { |
| 1462 | /* === Local variables ================================================== */ |
| 1463 | |
| 1464 | Index i ; /* loop counter for all columns */ |
| 1465 | Index c ; /* column index */ |
| 1466 | Index parent ; /* index of column's parent */ |
| 1467 | Index order ; /* column's order */ |
| 1468 | |
| 1469 | /* === Order each non-principal column ================================== */ |
| 1470 | |
| 1471 | for (i = 0 ; i < n_col ; i++) |
| 1472 | { |
| 1473 | /* find an un-ordered non-principal column */ |
| 1474 | COLAMD_ASSERT (COL_IS_DEAD (i)) ; |
| 1475 | if (!COL_IS_DEAD_PRINCIPAL (i) && Col [i].shared2.order == COLAMD_EMPTY) |
| 1476 | { |
| 1477 | parent = i ; |
| 1478 | /* once found, find its principal parent */ |
| 1479 | do |
| 1480 | { |
| 1481 | parent = Col [parent].shared1.parent ; |
| 1482 | } while (!COL_IS_DEAD_PRINCIPAL (parent)) ; |
| 1483 | |
| 1484 | /* now, order all un-ordered non-principal columns along path */ |
| 1485 | /* to this parent. collapse tree at the same time */ |
| 1486 | c = i ; |
| 1487 | /* get order of parent */ |
| 1488 | order = Col [parent].shared2.order ; |
| 1489 | |
| 1490 | do |
| 1491 | { |
| 1492 | COLAMD_ASSERT (Col [c].shared2.order == COLAMD_EMPTY) ; |
| 1493 | |
| 1494 | /* order this column */ |
| 1495 | Col [c].shared2.order = order++ ; |
| 1496 | /* collaps tree */ |
| 1497 | Col [c].shared1.parent = parent ; |
| 1498 | |
| 1499 | /* get immediate parent of this column */ |
| 1500 | c = Col [c].shared1.parent ; |
| 1501 | |
| 1502 | /* continue until we hit an ordered column. There are */ |
| 1503 | /* guarranteed not to be anymore unordered columns */ |
| 1504 | /* above an ordered column */ |
| 1505 | } while (Col [c].shared2.order == COLAMD_EMPTY) ; |
| 1506 | |
| 1507 | /* re-order the super_col parent to largest order for this group */ |
| 1508 | Col [parent].shared2.order = order ; |
| 1509 | } |
| 1510 | } |
| 1511 | |
| 1512 | /* === Generate the permutation ========================================= */ |
| 1513 | |
| 1514 | for (c = 0 ; c < n_col ; c++) |
| 1515 | { |
| 1516 | p [Col [c].shared2.order] = c ; |
| 1517 | } |
| 1518 | } |
| 1519 | |
| 1520 | |
| 1521 | /* ========================================================================== */ |
| 1522 | /* === detect_super_cols ==================================================== */ |
| 1523 | /* ========================================================================== */ |
| 1524 | |
| 1525 | /* |
| 1526 | Detects supercolumns by finding matches between columns in the hash buckets. |
| 1527 | Check amongst columns in the set A [row_start ... row_start + row_length-1]. |
| 1528 | The columns under consideration are currently *not* in the degree lists, |
| 1529 | and have already been placed in the hash buckets. |
| 1530 | |
| 1531 | The hash bucket for columns whose hash function is equal to h is stored |
| 1532 | as follows: |
| 1533 | |
| 1534 | if head [h] is >= 0, then head [h] contains a degree list, so: |
| 1535 | |
| 1536 | head [h] is the first column in degree bucket h. |
| 1537 | Col [head [h]].headhash gives the first column in hash bucket h. |
| 1538 | |
| 1539 | otherwise, the degree list is empty, and: |
| 1540 | |
| 1541 | -(head [h] + 2) is the first column in hash bucket h. |
| 1542 | |
| 1543 | For a column c in a hash bucket, Col [c].shared3.prev is NOT a "previous |
| 1544 | column" pointer. Col [c].shared3.hash is used instead as the hash number |
| 1545 | for that column. The value of Col [c].shared4.hash_next is the next column |
| 1546 | in the same hash bucket. |
| 1547 | |
| 1548 | Assuming no, or "few" hash collisions, the time taken by this routine is |
| 1549 | linear in the sum of the sizes (lengths) of each column whose score has |
| 1550 | just been computed in the approximate degree computation. |
| 1551 | Not user-callable. |
| 1552 | */ |
| 1553 | template <typename Index> |
| 1554 | static void detect_super_cols |
| 1555 | ( |
| 1556 | /* === Parameters ======================================================= */ |
| 1557 | |
| 1558 | colamd_col<Index> Col [], /* of size n_col+1 */ |
| 1559 | Index A [], /* row indices of A */ |
| 1560 | Index head [], /* head of degree lists and hash buckets */ |
| 1561 | Index row_start, /* pointer to set of columns to check */ |
| 1562 | Index row_length /* number of columns to check */ |
| 1563 | ) |
| 1564 | { |
| 1565 | /* === Local variables ================================================== */ |
| 1566 | |
| 1567 | Index hash ; /* hash value for a column */ |
| 1568 | Index *rp ; /* pointer to a row */ |
| 1569 | Index c ; /* a column index */ |
| 1570 | Index super_c ; /* column index of the column to absorb into */ |
| 1571 | Index *cp1 ; /* column pointer for column super_c */ |
| 1572 | Index *cp2 ; /* column pointer for column c */ |
| 1573 | Index length ; /* length of column super_c */ |
| 1574 | Index prev_c ; /* column preceding c in hash bucket */ |
| 1575 | Index i ; /* loop counter */ |
| 1576 | Index *rp_end ; /* pointer to the end of the row */ |
| 1577 | Index col ; /* a column index in the row to check */ |
| 1578 | Index head_column ; /* first column in hash bucket or degree list */ |
| 1579 | Index first_col ; /* first column in hash bucket */ |
| 1580 | |
| 1581 | /* === Consider each column in the row ================================== */ |
| 1582 | |
| 1583 | rp = &A [row_start] ; |
| 1584 | rp_end = rp + row_length ; |
| 1585 | while (rp < rp_end) |
| 1586 | { |
| 1587 | col = *rp++ ; |
| 1588 | if (COL_IS_DEAD (col)) |
| 1589 | { |
| 1590 | continue ; |
| 1591 | } |
| 1592 | |
| 1593 | /* get hash number for this column */ |
| 1594 | hash = Col [col].shared3.hash ; |
| 1595 | COLAMD_ASSERT (hash <= n_col) ; |
| 1596 | |
| 1597 | /* === Get the first column in this hash bucket ===================== */ |
| 1598 | |
| 1599 | head_column = head [hash] ; |
| 1600 | if (head_column > COLAMD_EMPTY) |
| 1601 | { |
| 1602 | first_col = Col [head_column].shared3.headhash ; |
| 1603 | } |
| 1604 | else |
| 1605 | { |
| 1606 | first_col = - (head_column + 2) ; |
| 1607 | } |
| 1608 | |
| 1609 | /* === Consider each column in the hash bucket ====================== */ |
| 1610 | |
| 1611 | for (super_c = first_col ; super_c != COLAMD_EMPTY ; |
| 1612 | super_c = Col [super_c].shared4.hash_next) |
| 1613 | { |
| 1614 | COLAMD_ASSERT (COL_IS_ALIVE (super_c)) ; |
| 1615 | COLAMD_ASSERT (Col [super_c].shared3.hash == hash) ; |
| 1616 | length = Col [super_c].length ; |
| 1617 | |
| 1618 | /* prev_c is the column preceding column c in the hash bucket */ |
| 1619 | prev_c = super_c ; |
| 1620 | |
| 1621 | /* === Compare super_c with all columns after it ================ */ |
| 1622 | |
| 1623 | for (c = Col [super_c].shared4.hash_next ; |
| 1624 | c != COLAMD_EMPTY ; c = Col [c].shared4.hash_next) |
| 1625 | { |
| 1626 | COLAMD_ASSERT (c != super_c) ; |
| 1627 | COLAMD_ASSERT (COL_IS_ALIVE (c)) ; |
| 1628 | COLAMD_ASSERT (Col [c].shared3.hash == hash) ; |
| 1629 | |
| 1630 | /* not identical if lengths or scores are different */ |
| 1631 | if (Col [c].length != length || |
| 1632 | Col [c].shared2.score != Col [super_c].shared2.score) |
| 1633 | { |
| 1634 | prev_c = c ; |
| 1635 | continue ; |
| 1636 | } |
| 1637 | |
| 1638 | /* compare the two columns */ |
| 1639 | cp1 = &A [Col [super_c].start] ; |
| 1640 | cp2 = &A [Col [c].start] ; |
| 1641 | |
| 1642 | for (i = 0 ; i < length ; i++) |
| 1643 | { |
| 1644 | /* the columns are "clean" (no dead rows) */ |
| 1645 | COLAMD_ASSERT (ROW_IS_ALIVE (*cp1)) ; |
| 1646 | COLAMD_ASSERT (ROW_IS_ALIVE (*cp2)) ; |
| 1647 | /* row indices will same order for both supercols, */ |
| 1648 | /* no gather scatter nessasary */ |
| 1649 | if (*cp1++ != *cp2++) |
| 1650 | { |
| 1651 | break ; |
| 1652 | } |
| 1653 | } |
| 1654 | |
| 1655 | /* the two columns are different if the for-loop "broke" */ |
| 1656 | if (i != length) |
| 1657 | { |
| 1658 | prev_c = c ; |
| 1659 | continue ; |
| 1660 | } |
| 1661 | |
| 1662 | /* === Got it! two columns are identical =================== */ |
| 1663 | |
| 1664 | COLAMD_ASSERT (Col [c].shared2.score == Col [super_c].shared2.score) ; |
| 1665 | |
| 1666 | Col [super_c].shared1.thickness += Col [c].shared1.thickness ; |
| 1667 | Col [c].shared1.parent = super_c ; |
| 1668 | KILL_NON_PRINCIPAL_COL (c) ; |
| 1669 | /* order c later, in order_children() */ |
| 1670 | Col [c].shared2.order = COLAMD_EMPTY ; |
| 1671 | /* remove c from hash bucket */ |
| 1672 | Col [prev_c].shared4.hash_next = Col [c].shared4.hash_next ; |
| 1673 | } |
| 1674 | } |
| 1675 | |
| 1676 | /* === Empty this hash bucket ======================================= */ |
| 1677 | |
| 1678 | if (head_column > COLAMD_EMPTY) |
| 1679 | { |
| 1680 | /* corresponding degree list "hash" is not empty */ |
| 1681 | Col [head_column].shared3.headhash = COLAMD_EMPTY ; |
| 1682 | } |
| 1683 | else |
| 1684 | { |
| 1685 | /* corresponding degree list "hash" is empty */ |
| 1686 | head [hash] = COLAMD_EMPTY ; |
| 1687 | } |
| 1688 | } |
| 1689 | } |
| 1690 | |
| 1691 | |
| 1692 | /* ========================================================================== */ |
| 1693 | /* === garbage_collection =================================================== */ |
| 1694 | /* ========================================================================== */ |
| 1695 | |
| 1696 | /* |
| 1697 | Defragments and compacts columns and rows in the workspace A. Used when |
| 1698 | all avaliable memory has been used while performing row merging. Returns |
| 1699 | the index of the first free position in A, after garbage collection. The |
| 1700 | time taken by this routine is linear is the size of the array A, which is |
| 1701 | itself linear in the number of nonzeros in the input matrix. |
| 1702 | Not user-callable. |
| 1703 | */ |
| 1704 | template <typename Index> |
| 1705 | static Index garbage_collection /* returns the new value of pfree */ |
| 1706 | ( |
| 1707 | /* === Parameters ======================================================= */ |
| 1708 | |
| 1709 | Index n_row, /* number of rows */ |
| 1710 | Index n_col, /* number of columns */ |
| 1711 | Colamd_Row<Index> Row [], /* row info */ |
| 1712 | colamd_col<Index> Col [], /* column info */ |
| 1713 | Index A [], /* A [0 ... Alen-1] holds the matrix */ |
| 1714 | Index *pfree /* &A [0] ... pfree is in use */ |
| 1715 | ) |
| 1716 | { |
| 1717 | /* === Local variables ================================================== */ |
| 1718 | |
| 1719 | Index *psrc ; /* source pointer */ |
| 1720 | Index *pdest ; /* destination pointer */ |
| 1721 | Index j ; /* counter */ |
| 1722 | Index r ; /* a row index */ |
| 1723 | Index c ; /* a column index */ |
| 1724 | Index length ; /* length of a row or column */ |
| 1725 | |
| 1726 | /* === Defragment the columns =========================================== */ |
| 1727 | |
| 1728 | pdest = &A[0] ; |
| 1729 | for (c = 0 ; c < n_col ; c++) |
| 1730 | { |
| 1731 | if (COL_IS_ALIVE (c)) |
| 1732 | { |
| 1733 | psrc = &A [Col [c].start] ; |
| 1734 | |
| 1735 | /* move and compact the column */ |
| 1736 | COLAMD_ASSERT (pdest <= psrc) ; |
| 1737 | Col [c].start = (Index) (pdest - &A [0]) ; |
| 1738 | length = Col [c].length ; |
| 1739 | for (j = 0 ; j < length ; j++) |
| 1740 | { |
| 1741 | r = *psrc++ ; |
| 1742 | if (ROW_IS_ALIVE (r)) |
| 1743 | { |
| 1744 | *pdest++ = r ; |
| 1745 | } |
| 1746 | } |
| 1747 | Col [c].length = (Index) (pdest - &A [Col [c].start]) ; |
| 1748 | } |
| 1749 | } |
| 1750 | |
| 1751 | /* === Prepare to defragment the rows =================================== */ |
| 1752 | |
| 1753 | for (r = 0 ; r < n_row ; r++) |
| 1754 | { |
| 1755 | if (ROW_IS_ALIVE (r)) |
| 1756 | { |
| 1757 | if (Row [r].length == 0) |
| 1758 | { |
| 1759 | /* this row is of zero length. cannot compact it, so kill it */ |
| 1760 | COLAMD_DEBUG3 (("Defrag row kill\n")) ; |
| 1761 | KILL_ROW (r) ; |
| 1762 | } |
| 1763 | else |
| 1764 | { |
| 1765 | /* save first column index in Row [r].shared2.first_column */ |
| 1766 | psrc = &A [Row [r].start] ; |
| 1767 | Row [r].shared2.first_column = *psrc ; |
| 1768 | COLAMD_ASSERT (ROW_IS_ALIVE (r)) ; |
| 1769 | /* flag the start of the row with the one's complement of row */ |
| 1770 | *psrc = ONES_COMPLEMENT (r) ; |
| 1771 | |
| 1772 | } |
| 1773 | } |
| 1774 | } |
| 1775 | |
| 1776 | /* === Defragment the rows ============================================== */ |
| 1777 | |
| 1778 | psrc = pdest ; |
| 1779 | while (psrc < pfree) |
| 1780 | { |
| 1781 | /* find a negative number ... the start of a row */ |
| 1782 | if (*psrc++ < 0) |
| 1783 | { |
| 1784 | psrc-- ; |
| 1785 | /* get the row index */ |
| 1786 | r = ONES_COMPLEMENT (*psrc) ; |
| 1787 | COLAMD_ASSERT (r >= 0 && r < n_row) ; |
| 1788 | /* restore first column index */ |
| 1789 | *psrc = Row [r].shared2.first_column ; |
| 1790 | COLAMD_ASSERT (ROW_IS_ALIVE (r)) ; |
| 1791 | |
| 1792 | /* move and compact the row */ |
| 1793 | COLAMD_ASSERT (pdest <= psrc) ; |
| 1794 | Row [r].start = (Index) (pdest - &A [0]) ; |
| 1795 | length = Row [r].length ; |
| 1796 | for (j = 0 ; j < length ; j++) |
| 1797 | { |
| 1798 | c = *psrc++ ; |
| 1799 | if (COL_IS_ALIVE (c)) |
| 1800 | { |
| 1801 | *pdest++ = c ; |
| 1802 | } |
| 1803 | } |
| 1804 | Row [r].length = (Index) (pdest - &A [Row [r].start]) ; |
| 1805 | |
| 1806 | } |
| 1807 | } |
| 1808 | /* ensure we found all the rows */ |
| 1809 | COLAMD_ASSERT (debug_rows == 0) ; |
| 1810 | |
| 1811 | /* === Return the new value of pfree ==================================== */ |
| 1812 | |
| 1813 | return ((Index) (pdest - &A [0])) ; |
| 1814 | } |
| 1815 | |
| 1816 | |
| 1817 | /* ========================================================================== */ |
| 1818 | /* === clear_mark =========================================================== */ |
| 1819 | /* ========================================================================== */ |
| 1820 | |
| 1821 | /* |
| 1822 | Clears the Row [].shared2.mark array, and returns the new tag_mark. |
| 1823 | Return value is the new tag_mark. Not user-callable. |
| 1824 | */ |
| 1825 | template <typename Index> |
| 1826 | static inline Index clear_mark /* return the new value for tag_mark */ |
| 1827 | ( |
| 1828 | /* === Parameters ======================================================= */ |
| 1829 | |
| 1830 | Index n_row, /* number of rows in A */ |
| 1831 | Colamd_Row<Index> Row [] /* Row [0 ... n_row-1].shared2.mark is set to zero */ |
| 1832 | ) |
| 1833 | { |
| 1834 | /* === Local variables ================================================== */ |
| 1835 | |
| 1836 | Index r ; |
| 1837 | |
| 1838 | for (r = 0 ; r < n_row ; r++) |
| 1839 | { |
| 1840 | if (ROW_IS_ALIVE (r)) |
| 1841 | { |
| 1842 | Row [r].shared2.mark = 0 ; |
| 1843 | } |
| 1844 | } |
| 1845 | return (1) ; |
| 1846 | } |
| 1847 | |
| 1848 | |
| 1849 | } // namespace internal |
| 1850 | #endif |