gtsam/spqr_mini/cholmod_core.h

2291 lines
94 KiB
C

/* ========================================================================== */
/* === Include/cholmod_core.h =============================================== */
/* ========================================================================== */
/* -----------------------------------------------------------------------------
* CHOLMOD/Include/cholmod_core.h.
* Copyright (C) 2005-2006, Univ. of Florida. Author: Timothy A. Davis
* CHOLMOD/Include/cholmod_core.h is licensed under Version 2.1 of the GNU
* Lesser General Public License. See lesser.txt for a text of the license.
* CHOLMOD is also available under other licenses; contact authors for details.
* http://www.cise.ufl.edu/research/sparse
* -------------------------------------------------------------------------- */
/* CHOLMOD Core module: basic CHOLMOD objects and routines.
* Required by all CHOLMOD modules. Requires no other module or package.
*
* The CHOLMOD modules are:
*
* Core basic data structures and definitions
* Check check/print the 5 CHOLMOD objects, & 3 types of integer vectors
* Cholesky sparse Cholesky factorization
* Modify sparse Cholesky update/downdate/row-add/row-delete
* MatrixOps sparse matrix functions (add, multiply, norm, ...)
* Supernodal supernodal sparse Cholesky factorization
* Partition graph-partitioning based orderings
*
* The CHOLMOD objects:
* --------------------
*
* cholmod_common parameters, statistics, and workspace
* cholmod_sparse a sparse matrix in compressed column form
* cholmod_factor an LL' or LDL' factorization
* cholmod_dense a dense matrix
* cholmod_triplet a sparse matrix in "triplet" form
*
* The Core module described here defines the CHOLMOD data structures, and
* basic operations on them. To create and solve a sparse linear system Ax=b,
* the user must create A and b, populate them with values, and then pass them
* to the routines in the CHOLMOD Cholesky module. There are two primary
* methods for creating A: (1) allocate space for a column-oriented sparse
* matrix and fill it with pattern and values, or (2) create a triplet form
* matrix and convert it to a sparse matrix. The latter option is simpler.
*
* The matrices b and x are typically dense matrices, but can also be sparse.
* You can allocate and free them as dense matrices with the
* cholmod_allocate_dense and cholmod_free_dense routines.
*
* The cholmod_factor object contains the symbolic and numeric LL' or LDL'
* factorization of sparse symmetric matrix. The matrix must be positive
* definite for an LL' factorization. It need only be symmetric and have well-
* conditioned leading submatrices for it to have an LDL' factorization
* (CHOLMOD does not pivot for numerical stability). It is typically created
* with the cholmod_factorize routine in the Cholesky module, but can also
* be initialized to L=D=I in the Core module and then modified by the Modify
* module. It must be freed with cholmod_free_factor, defined below.
*
* The Core routines for each object are described below. Each list is split
* into two parts: the primary routines and secondary routines.
*
* ============================================================================
* === cholmod_common =========================================================
* ============================================================================
*
* The Common object contains control parameters, statistics, and
* You must call cholmod_start before calling any other CHOLMOD routine, and
* must call cholmod_finish as your last call to CHOLMOD, with two exceptions:
* you may call cholmod_print_common and cholmod_check_common in the Check
* module after calling cholmod_finish.
*
* cholmod_start first call to CHOLMOD
* cholmod_finish last call to CHOLMOD
* -----------------------------
* cholmod_defaults restore default parameters
* cholmod_maxrank maximum rank for update/downdate
* cholmod_allocate_work allocate workspace in Common
* cholmod_free_work free workspace in Common
* cholmod_clear_flag clear Flag workspace in Common
* cholmod_error called when CHOLMOD encounters an error
* cholmod_dbound for internal use in CHOLMOD only
* cholmod_hypot compute sqrt (x*x + y*y) accurately
* cholmod_divcomplex complex division, c = a/b
*
* ============================================================================
* === cholmod_sparse =========================================================
* ============================================================================
*
* A sparse matrix is held in compressed column form. In the basic type
* ("packed", which corresponds to a MATLAB sparse matrix), an n-by-n matrix
* with nz entries is held in three arrays: p of size n+1, i of size nz, and x
* of size nz. Row indices of column j are held in i [p [j] ... p [j+1]-1] and
* in the same locations in x. There may be no duplicate entries in a column.
* Row indices in each column may be sorted or unsorted (CHOLMOD keeps track).
* A->stype determines the storage mode: 0 if both upper/lower parts are stored,
* -1 if A is symmetric and just tril(A) is stored, +1 if symmetric and triu(A)
* is stored.
*
* cholmod_allocate_sparse allocate a sparse matrix
* cholmod_free_sparse free a sparse matrix
* -----------------------------
* cholmod_reallocate_sparse change the size (# entries) of sparse matrix
* cholmod_nnz number of nonzeros in a sparse matrix
* cholmod_speye sparse identity matrix
* cholmod_spzeros sparse zero matrix
* cholmod_transpose transpose a sparse matrix
* cholmod_ptranspose transpose/permute a sparse matrix
* cholmod_transpose_unsym transpose/permute an unsymmetric sparse matrix
* cholmod_transpose_sym transpose/permute a symmetric sparse matrix
* cholmod_sort sort row indices in each column of sparse matrix
* cholmod_band C = tril (triu (A,k1), k2)
* cholmod_band_inplace A = tril (triu (A,k1), k2)
* cholmod_aat C = A*A'
* cholmod_copy_sparse C = A, create an exact copy of a sparse matrix
* cholmod_copy C = A, with possible change of stype
* cholmod_add C = alpha*A + beta*B
* cholmod_sparse_xtype change the xtype of a sparse matrix
*
* ============================================================================
* === cholmod_factor =========================================================
* ============================================================================
*
* The data structure for an LL' or LDL' factorization is too complex to
* describe in one sentence. This object can hold the symbolic analysis alone,
* or in combination with a "simplicial" (similar to a sparse matrix) or
* "supernodal" form of the numerical factorization. Only the routine to free
* a factor is primary, since a factor object is created by the factorization
* routine (cholmod_factorize). It must be freed with cholmod_free_factor.
*
* cholmod_free_factor free a factor
* -----------------------------
* cholmod_allocate_factor allocate a factor (LL' or LDL')
* cholmod_reallocate_factor change the # entries in a factor
* cholmod_change_factor change the type of factor (e.g., LDL' to LL')
* cholmod_pack_factor pack the columns of a factor
* cholmod_reallocate_column resize a single column of a factor
* cholmod_factor_to_sparse create a sparse matrix copy of a factor
* cholmod_copy_factor create a copy of a factor
* cholmod_factor_xtype change the xtype of a factor
*
* Note that there is no cholmod_sparse_to_factor routine to create a factor
* as a copy of a sparse matrix. It could be done, after a fashion, but a
* lower triangular sparse matrix would not necessarily have a chordal graph,
* which would break the many CHOLMOD routines that rely on this property.
*
* ============================================================================
* === cholmod_dense ==========================================================
* ============================================================================
*
* The solve routines and some of the MatrixOps and Modify routines use dense
* matrices as inputs. These are held in column-major order. With a leading
* dimension of d, the entry in row i and column j is held in x [i+j*d].
*
* cholmod_allocate_dense allocate a dense matrix
* cholmod_free_dense free a dense matrix
* -----------------------------
* cholmod_zeros allocate a dense matrix of all zeros
* cholmod_ones allocate a dense matrix of all ones
* cholmod_eye allocate a dense identity matrix
* cholmod_sparse_to_dense create a dense matrix copy of a sparse matrix
* cholmod_dense_to_sparse create a sparse matrix copy of a dense matrix
* cholmod_copy_dense create a copy of a dense matrix
* cholmod_copy_dense2 copy a dense matrix (pre-allocated)
* cholmod_dense_xtype change the xtype of a dense matrix
*
* ============================================================================
* === cholmod_triplet ========================================================
* ============================================================================
*
* A sparse matrix held in triplet form is the simplest one for a user to
* create. It consists of a list of nz entries in arbitrary order, held in
* three arrays: i, j, and x, each of length nk. The kth entry is in row i[k],
* column j[k], with value x[k]. There may be duplicate values; if A(i,j)
* appears more than once, its value is the sum of the entries with those row
* and column indices.
*
* cholmod_allocate_triplet allocate a triplet matrix
* cholmod_triplet_to_sparse create a sparse matrix copy of a triplet matrix
* cholmod_free_triplet free a triplet matrix
* -----------------------------
* cholmod_reallocate_triplet change the # of entries in a triplet matrix
* cholmod_sparse_to_triplet create a triplet matrix copy of a sparse matrix
* cholmod_copy_triplet create a copy of a triplet matrix
* cholmod_triplet_xtype change the xtype of a triplet matrix
*
* ============================================================================
* === memory management ======================================================
* ============================================================================
*
* cholmod_malloc malloc wrapper
* cholmod_calloc calloc wrapper
* cholmod_free free wrapper
* cholmod_realloc realloc wrapper
* cholmod_realloc_multiple realloc wrapper for multiple objects
*
* ============================================================================
* === Core CHOLMOD prototypes ================================================
* ============================================================================
*
* All CHOLMOD routines (in all modules) use the following protocol for return
* values, with one exception:
*
* int TRUE (1) if successful, or FALSE (0) otherwise.
* (exception: cholmod_divcomplex)
* UF_long a value >= 0 if successful, or -1 otherwise.
* double a value >= 0 if successful, or -1 otherwise.
* size_t a value > 0 if successful, or 0 otherwise.
* void * a non-NULL pointer to newly allocated memory if
* successful, or NULL otherwise.
* cholmod_sparse * a non-NULL pointer to a newly allocated matrix
* if successful, or NULL otherwise.
* cholmod_factor * a non-NULL pointer to a newly allocated factor
* if successful, or NULL otherwise.
* cholmod_triplet * a non-NULL pointer to a newly allocated triplet
* matrix if successful, or NULL otherwise.
* cholmod_dense * a non-NULL pointer to a newly allocated triplet
* matrix if successful, or NULL otherwise.
*
* The last parameter to all routines is always a pointer to the CHOLMOD
* Common object.
*
* TRUE and FALSE are not defined here, since they may conflict with the user
* program. A routine that described here returning TRUE or FALSE returns 1
* or 0, respectively. Any TRUE/FALSE parameter is true if nonzero, false if
* zero.
*/
#ifndef CHOLMOD_CORE_H
#define CHOLMOD_CORE_H
/* ========================================================================== */
/* === CHOLMOD version ====================================================== */
/* ========================================================================== */
/* All versions of CHOLMOD will include the following definitions.
* As an example, to test if the version you are using is 1.3 or later:
*
* if (CHOLMOD_VERSION >= CHOLMOD_VER_CODE (1,3)) ...
*
* This also works during compile-time:
*
* #if CHOLMOD_VERSION >= CHOLMOD_VER_CODE (1,3)
* printf ("This is version 1.3 or later\n") ;
* #else
* printf ("This is version is earlier than 1.3\n") ;
* #endif
*/
#define CHOLMOD_DATE "Nov 30, 2009"
#define CHOLMOD_VER_CODE(main,sub) ((main) * 1000 + (sub))
#define CHOLMOD_MAIN_VERSION 1
#define CHOLMOD_SUB_VERSION 7
#define CHOLMOD_SUBSUB_VERSION 2
#define CHOLMOD_VERSION \
CHOLMOD_VER_CODE(CHOLMOD_MAIN_VERSION,CHOLMOD_SUB_VERSION)
/* ========================================================================== */
/* === non-CHOLMOD include files ============================================ */
/* ========================================================================== */
/* This is the only non-CHOLMOD include file imposed on the user program.
* It required for size_t definition used here. CHOLMOD itself includes other
* ANSI C89 standard #include files, but does not expose them to the user.
*
* CHOLMOD assumes that your C compiler is ANSI C89 compliant. It does not make
* use of ANSI C99 features.
*/
#include <stddef.h>
#include <stdlib.h>
/* ========================================================================== */
/* === CHOLMOD objects ====================================================== */
/* ========================================================================== */
/* Each CHOLMOD object has its own type code. */
#define CHOLMOD_COMMON 0
#define CHOLMOD_SPARSE 1
#define CHOLMOD_FACTOR 2
#define CHOLMOD_DENSE 3
#define CHOLMOD_TRIPLET 4
/* ========================================================================== */
/* === CHOLMOD Common ======================================================= */
/* ========================================================================== */
/* itype defines the types of integer used: */
#define CHOLMOD_INT 0 /* all integer arrays are int */
#define CHOLMOD_INTLONG 1 /* most are int, some are UF_long */
#define CHOLMOD_LONG 2 /* all integer arrays are UF_long */
/* The itype of all parameters for all CHOLMOD routines must match.
* FUTURE WORK: CHOLMOD_INTLONG is not yet supported.
*/
/* dtype defines what the numerical type is (double or float): */
#define CHOLMOD_DOUBLE 0 /* all numerical values are double */
#define CHOLMOD_SINGLE 1 /* all numerical values are float */
/* The dtype of all parameters for all CHOLMOD routines must match.
*
* Scalar floating-point values are always passed as double arrays of size 2
* (for the real and imaginary parts). They are typecast to float as needed.
* FUTURE WORK: the float case is not supported yet.
*/
/* xtype defines the kind of numerical values used: */
#define CHOLMOD_PATTERN 0 /* pattern only, no numerical values */
#define CHOLMOD_REAL 1 /* a real matrix */
#define CHOLMOD_COMPLEX 2 /* a complex matrix (ANSI C99 compatible) */
#define CHOLMOD_ZOMPLEX 3 /* a complex matrix (MATLAB compatible) */
/* The xtype of all parameters for all CHOLMOD routines must match.
*
* CHOLMOD_PATTERN: x and z are ignored.
* CHOLMOD_DOUBLE: x is non-null of size nzmax, z is ignored.
* CHOLMOD_COMPLEX: x is non-null of size 2*nzmax doubles, z is ignored.
* CHOLMOD_ZOMPLEX: x and z are non-null of size nzmax
*
* In the real case, z is ignored. The kth entry in the matrix is x [k].
* There are two methods for the complex case. In the ANSI C99-compatible
* CHOLMOD_COMPLEX case, the real and imaginary parts of the kth entry
* are in x [2*k] and x [2*k+1], respectively. z is ignored. In the
* MATLAB-compatible CHOLMOD_ZOMPLEX case, the real and imaginary
* parts of the kth entry are in x [k] and z [k].
*
* Scalar floating-point values are always passed as double arrays of size 2
* (real and imaginary parts). The imaginary part of a scalar is ignored if
* the routine operates on a real matrix.
*
* These Modules support complex and zomplex matrices, with a few exceptions:
*
* Check all routines
* Cholesky all routines
* Core all except cholmod_aat, add, band, copy
* Demo all routines
* Partition all routines
* Supernodal all routines support any real, complex, or zomplex input.
* There will never be a supernodal zomplex L; a complex
* supernodal L is created if A is zomplex.
* Tcov all routines
* Valgrind all routines
*
* These Modules provide partial support for complex and zomplex matrices:
*
* MATLAB all routines support real and zomplex only, not complex,
* with the exception of ldlupdate, which supports
* real matrices only. This is a minor constraint since
* MATLAB's matrices are all real or zomplex.
* MatrixOps only norm_dense, norm_sparse, and sdmult support complex
* and zomplex
*
* These Modules do not support complex and zomplex matrices at all:
*
* Modify all routines support real matrices only
*/
/* Definitions for cholmod_common: */
#define CHOLMOD_MAXMETHODS 9 /* maximum number of different methods that */
/* cholmod_analyze can try. Must be >= 9. */
/* Common->status values. zero means success, negative means a fatal error,
* positive is a warning. */
#define CHOLMOD_OK 0 /* success */
#define CHOLMOD_NOT_INSTALLED (-1) /* failure: method not installed */
#define CHOLMOD_OUT_OF_MEMORY (-2) /* failure: out of memory */
#define CHOLMOD_TOO_LARGE (-3) /* failure: integer overflow occured */
#define CHOLMOD_INVALID (-4) /* failure: invalid input */
#define CHOLMOD_NOT_POSDEF (1) /* warning: matrix not pos. def. */
#define CHOLMOD_DSMALL (2) /* warning: D for LDL' or diag(L) or */
/* LL' has tiny absolute value */
/* ordering method (also used for L->ordering) */
#define CHOLMOD_NATURAL 0 /* use natural ordering */
#define CHOLMOD_GIVEN 1 /* use given permutation */
#define CHOLMOD_AMD 2 /* use minimum degree (AMD) */
#define CHOLMOD_METIS 3 /* use METIS' nested dissection */
#define CHOLMOD_NESDIS 4 /* use CHOLMOD's version of nested dissection:*/
/* node bisector applied recursively, followed
* by constrained minimum degree (CSYMAMD or
* CCOLAMD) */
#define CHOLMOD_COLAMD 5 /* use AMD for A, COLAMD for A*A' */
/* POSTORDERED is not a method, but a result of natural ordering followed by a
* weighted postorder. It is used for L->ordering, not method [ ].ordering. */
#define CHOLMOD_POSTORDERED 6 /* natural ordering, postordered. */
/* supernodal strategy (for Common->supernodal) */
#define CHOLMOD_SIMPLICIAL 0 /* always do simplicial */
#define CHOLMOD_AUTO 1 /* select simpl/super depending on matrix */
#define CHOLMOD_SUPERNODAL 2 /* always do supernodal */
typedef struct cholmod_common_struct
{
/* ---------------------------------------------------------------------- */
/* parameters for symbolic/numeric factorization and update/downdate */
/* ---------------------------------------------------------------------- */
double dbound ; /* Smallest absolute value of diagonal entries of D
* for LDL' factorization and update/downdate/rowadd/
* rowdel, or the diagonal of L for an LL' factorization.
* Entries in the range 0 to dbound are replaced with dbound.
* Entries in the range -dbound to 0 are replaced with -dbound. No
* changes are made to the diagonal if dbound <= 0. Default: zero */
double grow0 ; /* For a simplicial factorization, L->i and L->x can
* grow if necessary. grow0 is the factor by which
* it grows. For the initial space, L is of size MAX (1,grow0) times
* the required space. If L runs out of space, the new size of L is
* MAX(1.2,grow0) times the new required space. If you do not plan on
* modifying the LDL' factorization in the Modify module, set grow0 to
* zero (or set grow2 to 0, see below). Default: 1.2 */
double grow1 ;
size_t grow2 ; /* For a simplicial factorization, each column j of L
* is initialized with space equal to
* grow1*L->ColCount[j] + grow2. If grow0 < 1, grow1 < 1, or grow2 == 0,
* then the space allocated is exactly equal to L->ColCount[j]. If the
* column j runs out of space, it increases to grow1*need + grow2 in
* size, where need is the total # of nonzeros in that column. If you do
* not plan on modifying the factorization in the Modify module, set
* grow2 to zero. Default: grow1 = 1.2, grow2 = 5. */
size_t maxrank ; /* rank of maximum update/downdate. Valid values:
* 2, 4, or 8. A value < 2 is set to 2, and a
* value > 8 is set to 8. It is then rounded up to the next highest
* power of 2, if not already a power of 2. Workspace (Xwork, below) of
* size nrow-by-maxrank double's is allocated for the update/downdate.
* If an update/downdate of rank-k is requested, with k > maxrank,
* it is done in steps of maxrank. Default: 8, which is fastest.
* Memory usage can be reduced by setting maxrank to 2 or 4.
*/
double supernodal_switch ; /* supernodal vs simplicial factorization */
int supernodal ; /* If Common->supernodal <= CHOLMOD_SIMPLICIAL
* (0) then cholmod_analyze performs a
* simplicial analysis. If >= CHOLMOD_SUPERNODAL (2), then a supernodal
* analysis is performed. If == CHOLMOD_AUTO (1) and
* flop/nnz(L) < Common->supernodal_switch, then a simplicial analysis
* is done. A supernodal analysis done otherwise.
* Default: CHOLMOD_AUTO. Default supernodal_switch = 40 */
int final_asis ; /* If TRUE, then ignore the other final_* parameters
* (except for final_pack).
* The factor is left as-is when done. Default: TRUE.*/
int final_super ; /* If TRUE, leave a factor in supernodal form when
* supernodal factorization is finished. If FALSE,
* then convert to a simplicial factor when done.
* Default: TRUE */
int final_ll ; /* If TRUE, leave factor in LL' form when done.
* Otherwise, leave in LDL' form. Default: FALSE */
int final_pack ; /* If TRUE, pack the columns when done. If TRUE, and
* cholmod_factorize is called with a symbolic L, L is
* allocated with exactly the space required, using L->ColCount. If you
* plan on modifying the factorization, set Common->final_pack to FALSE,
* and each column will be given a little extra slack space for future
* growth in fill-in due to updates. Default: TRUE */
int final_monotonic ; /* If TRUE, ensure columns are monotonic when done.
* Default: TRUE */
int final_resymbol ;/* if cholmod_factorize performed a supernodal
* factorization, final_resymbol is true, and
* final_super is FALSE (convert a simplicial numeric factorization),
* then numerically zero entries that resulted from relaxed supernodal
* amalgamation are removed. This does not remove entries that are zero
* due to exact numeric cancellation, since doing so would break the
* update/downdate rowadd/rowdel routines. Default: FALSE. */
/* supernodal relaxed amalgamation parameters: */
double zrelax [3] ;
size_t nrelax [3] ;
/* Let ns be the total number of columns in two adjacent supernodes.
* Let z be the fraction of zero entries in the two supernodes if they
* are merged (z includes zero entries from prior amalgamations). The
* two supernodes are merged if:
* (ns <= nrelax [0]) || (no new zero entries added) ||
* (ns <= nrelax [1] && z < zrelax [0]) ||
* (ns <= nrelax [2] && z < zrelax [1]) || (z < zrelax [2])
*
* Default parameters result in the following rule:
* (ns <= 4) || (no new zero entries added) ||
* (ns <= 16 && z < 0.8) || (ns <= 48 && z < 0.1) || (z < 0.05)
*/
int prefer_zomplex ; /* X = cholmod_solve (sys, L, B, Common) computes
* x=A\b or solves a related system. If L and B are
* both real, then X is real. Otherwise, X is returned as
* CHOLMOD_COMPLEX if Common->prefer_zomplex is FALSE, or
* CHOLMOD_ZOMPLEX if Common->prefer_zomplex is TRUE. This parameter
* is needed because there is no supernodal zomplex L. Suppose the
* caller wants all complex matrices to be stored in zomplex form
* (MATLAB, for example). A supernodal L is returned in complex form
* if A is zomplex. B can be real, and thus X = cholmod_solve (L,B)
* should return X as zomplex. This cannot be inferred from the input
* arguments L and B. Default: FALSE, since all data types are
* supported in CHOLMOD_COMPLEX form and since this is the native type
* of LAPACK and the BLAS. Note that the MATLAB/cholmod.c mexFunction
* sets this parameter to TRUE, since MATLAB matrices are in
* CHOLMOD_ZOMPLEX form.
*/
int prefer_upper ; /* cholmod_analyze and cholmod_factorize work
* fastest when a symmetric matrix is stored in
* upper triangular form when a fill-reducing ordering is used. In
* MATLAB, this corresponds to how x=A\b works. When the matrix is
* ordered as-is, they work fastest when a symmetric matrix is in lower
* triangular form. In MATLAB, R=chol(A) does the opposite. This
* parameter affects only how cholmod_read returns a symmetric matrix.
* If TRUE (the default case), a symmetric matrix is always returned in
* upper-triangular form (A->stype = 1). */
int quick_return_if_not_posdef ; /* if TRUE, the supernodal numeric
* factorization will return quickly if
* the matrix is not positive definite. Default: FALSE. */
/* ---------------------------------------------------------------------- */
/* printing and error handling options */
/* ---------------------------------------------------------------------- */
int print ; /* print level. Default: 3 */
int precise ; /* if TRUE, print 16 digits. Otherwise print 5 */
int (*print_function) (const char *, ...) ; /* pointer to printf */
int try_catch ; /* if TRUE, then ignore errors; CHOLMOD is in the middle
* of a try/catch block. No error message is printed
* and the Common->error_handler function is not called. */
void (*error_handler) (int status, const char *file,
int line, const char *message) ;
/* Common->error_handler is the user's error handling routine. If not
* NULL, this routine is called if an error occurs in CHOLMOD. status
* can be CHOLMOD_OK (0), negative for a fatal error, and positive for
* a warning. file is a string containing the name of the source code
* file where the error occured, and line is the line number in that
* file. message is a string describing the error in more detail. */
/* ---------------------------------------------------------------------- */
/* ordering options */
/* ---------------------------------------------------------------------- */
/* The cholmod_analyze routine can try many different orderings and select
* the best one. It can also try one ordering method multiple times, with
* different parameter settings. The default is to use three orderings,
* the user's permutation (if provided), AMD which is the fastest ordering
* and generally gives good fill-in, and METIS. CHOLMOD's nested dissection
* (METIS with a constrained AMD) usually gives a better ordering than METIS
* alone (by about 5% to 10%) but it takes more time.
*
* If you know the method that is best for your matrix, set Common->nmethods
* to 1 and set Common->method [0] to the set of parameters for that method.
* If you set it to 1 and do not provide a permutation, then only AMD will
* be called.
*
* If METIS is not available, the default # of methods tried is 2 (the user
* permutation, if any, and AMD).
*
* To try other methods, set Common->nmethods to the number of methods you
* want to try. The suite of default methods and their parameters is
* described in the cholmod_defaults routine, and summarized here:
*
* Common->method [i]:
* i = 0: user-provided ordering (cholmod_analyze_p only)
* i = 1: AMD (for both A and A*A')
* i = 2: METIS
* i = 3: CHOLMOD's nested dissection (NESDIS), default parameters
* i = 4: natural
* i = 5: NESDIS with nd_small = 20000
* i = 6: NESDIS with nd_small = 4, no constrained minimum degree
* i = 7: NESDIS with no dense node removal
* i = 8: AMD for A, COLAMD for A*A'
*
* You can modify the suite of methods you wish to try by modifying
* Common.method [...] after calling cholmod_start or cholmod_defaults.
*
* For example, to use AMD, followed by a weighted postordering:
*
* Common->nmethods = 1 ;
* Common->method [0].ordering = CHOLMOD_AMD ;
* Common->postorder = TRUE ;
*
* To use the natural ordering (with no postordering):
*
* Common->nmethods = 1 ;
* Common->method [0].ordering = CHOLMOD_NATURAL ;
* Common->postorder = FALSE ;
*
* If you are going to factorize hundreds or more matrices with the same
* nonzero pattern, you may wish to spend a great deal of time finding a
* good permutation. In this case, try setting Common->nmethods to 9.
* The time spent in cholmod_analysis will be very high, but you need to
* call it only once.
*
* cholmod_analyze sets Common->current to a value between 0 and nmethods-1.
* Each ordering method uses the set of options defined by this parameter.
*/
int nmethods ; /* The number of ordering methods to try. Default: 0.
* nmethods = 0 is a special case. cholmod_analyze
* will try the user-provided ordering (if given) and AMD. Let fl and
* lnz be the flop count and nonzeros in L from AMD's ordering. Let
* anz be the number of nonzeros in the upper or lower triangular part
* of the symmetric matrix A. If fl/lnz < 500 or lnz/anz < 5, then this
* is a good ordering, and METIS is not attempted. Otherwise, METIS is
* tried. The best ordering found is used. If nmethods > 0, the
* methods used are given in the method[ ] array, below. The first
* three methods in the default suite of orderings is (1) use the given
* permutation (if provided), (2) use AMD, and (3) use METIS. Maximum
* allowed value is CHOLMOD_MAXMETHODS. */
int current ; /* The current method being tried. Default: 0. Valid
* range is 0 to nmethods-1. */
int selected ; /* The best method found. */
/* The suite of ordering methods and parameters: */
struct cholmod_method_struct
{
/* statistics for this method */
double lnz ; /* nnz(L) excl. zeros from supernodal amalgamation,
* for a "pure" L */
double fl ; /* flop count for a "pure", real simplicial LL'
* factorization, with no extra work due to
* amalgamation. Subtract n to get the LDL' flop count. Multiply
* by about 4 if the matrix is complex or zomplex. */
/* ordering method parameters */
double prune_dense ;/* dense row/col control for AMD, SYMAMD, CSYMAMD,
* and NESDIS (cholmod_nested_dissection). For a
* symmetric n-by-n matrix, rows/columns with more than
* MAX (16, prune_dense * sqrt (n)) entries are removed prior to
* ordering. They appear at the end of the re-ordered matrix.
*
* If prune_dense < 0, only completely dense rows/cols are removed.
*
* This paramater is also the dense column control for COLAMD and
* CCOLAMD. For an m-by-n matrix, columns with more than
* MAX (16, prune_dense * sqrt (MIN (m,n))) entries are removed prior
* to ordering. They appear at the end of the re-ordered matrix.
* CHOLMOD factorizes A*A', so it calls COLAMD and CCOLAMD with A',
* not A. Thus, this parameter affects the dense *row* control for
* CHOLMOD's matrix, and the dense *column* control for COLAMD and
* CCOLAMD.
*
* Removing dense rows and columns improves the run-time of the
* ordering methods. It has some impact on ordering quality
* (usually minimal, sometimes good, sometimes bad).
*
* Default: 10. */
double prune_dense2 ;/* dense row control for COLAMD and CCOLAMD.
* Rows with more than MAX (16, dense2 * sqrt (n))
* for an m-by-n matrix are removed prior to ordering. CHOLMOD's
* matrix is transposed before ordering it with COLAMD or CCOLAMD,
* so this controls the dense *columns* of CHOLMOD's matrix, and
* the dense *rows* of COLAMD's or CCOLAMD's matrix.
*
* If prune_dense2 < 0, only completely dense rows/cols are removed.
*
* Default: -1. Note that this is not the default for COLAMD and
* CCOLAMD. -1 is best for Cholesky. 10 is best for LU. */
double nd_oksep ; /* in NESDIS, when a node separator is computed, it
* discarded if nsep >= nd_oksep*n, where nsep is
* the number of nodes in the separator, and n is the size of the
* graph being cut. Valid range is 0 to 1. If 1 or greater, the
* separator is discarded if it consists of the entire graph.
* Default: 1 */
double other1 [4] ; /* future expansion */
size_t nd_small ; /* do not partition graphs with fewer nodes than
* nd_small, in NESDIS. Default: 200 (same as
* METIS) */
size_t other2 [4] ; /* future expansion */
int aggressive ; /* Aggresive absorption in AMD, COLAMD, SYMAMD,
* CCOLAMD, and CSYMAMD. Default: TRUE */
int order_for_lu ; /* CCOLAMD can be optimized to produce an ordering
* for LU or Cholesky factorization. CHOLMOD only
* performs a Cholesky factorization. However, you may wish to use
* CHOLMOD as an interface for CCOLAMD but use it for your own LU
* factorization. In this case, order_for_lu should be set to FALSE.
* When factorizing in CHOLMOD itself, you should *** NEVER *** set
* this parameter FALSE. Default: TRUE. */
int nd_compress ; /* If TRUE, compress the graph and subgraphs before
* partitioning them in NESDIS. Default: TRUE */
int nd_camd ; /* If 1, follow the nested dissection ordering
* with a constrained minimum degree ordering that
* respects the partitioning just found (using CAMD). If 2, use
* CSYMAMD instead. If you set nd_small very small, you may not need
* this ordering, and can save time by setting it to zero (no
* constrained minimum degree ordering). Default: 1. */
int nd_components ; /* The nested dissection ordering finds a node
* separator that splits the graph into two parts,
* which may be unconnected. If nd_components is TRUE, each of
* these connected components is split independently. If FALSE,
* each part is split as a whole, even if it consists of more than
* one connected component. Default: FALSE */
/* fill-reducing ordering to use */
int ordering ;
size_t other3 [4] ; /* future expansion */
} method [CHOLMOD_MAXMETHODS + 1] ;
int postorder ; /* If TRUE, cholmod_analyze follows the ordering with a
* weighted postorder of the elimination tree. Improves
* supernode amalgamation. Does not affect fundamental nnz(L) and
* flop count. Default: TRUE. */
/* ---------------------------------------------------------------------- */
/* memory management routines */
/* ---------------------------------------------------------------------- */
void *(*malloc_memory) (size_t) ; /* pointer to malloc */
void *(*realloc_memory) (void *, size_t) ; /* pointer to realloc */
void (*free_memory) (void *) ; /* pointer to free */
void *(*calloc_memory) (size_t, size_t) ; /* pointer to calloc */
/* ---------------------------------------------------------------------- */
/* routines for complex arithmetic */
/* ---------------------------------------------------------------------- */
int (*complex_divide) (double ax, double az, double bx, double bz,
double *cx, double *cz) ;
/* flag = complex_divide (ax, az, bx, bz, &cx, &cz) computes the complex
* division c = a/b, where ax and az hold the real and imaginary part
* of a, and b and c are stored similarly. flag is returned as 1 if
* a divide-by-zero occurs, or 0 otherwise. By default, the function
* pointer Common->complex_divide is set equal to cholmod_divcomplex.
*/
double (*hypotenuse) (double x, double y) ;
/* s = hypotenuse (x,y) computes s = sqrt (x*x + y*y), but does so more
* accurately. By default, the function pointer Common->hypotenuse is
* set equal to cholmod_hypot. See also the hypot function in the C99
* standard, which has an identical syntax and function. If you have
* a C99-compliant compiler, you can set Common->hypotenuse = hypot. */
/* ---------------------------------------------------------------------- */
/* METIS workarounds */
/* ---------------------------------------------------------------------- */
double metis_memory ; /* This is a parameter for CHOLMOD's interface to
* METIS, not a parameter to METIS itself. METIS
* uses an amount of memory that is difficult to estimate precisely
* beforehand. If it runs out of memory, it terminates your program.
* All routines in CHOLMOD except for CHOLMOD's interface to METIS
* return an error status and safely return to your program if they run
* out of memory. To mitigate this problem, the CHOLMOD interface
* can allocate a single block of memory equal in size to an empirical
* upper bound of METIS's memory usage times the Common->metis_memory
* parameter, and then immediately free it. It then calls METIS. If
* this pre-allocation fails, it is possible that METIS will fail as
* well, and so CHOLMOD returns with an out-of-memory condition without
* calling METIS.
*
* METIS_NodeND (used in the CHOLMOD_METIS ordering option) with its
* default parameter settings typically uses about (4*nz+40n+4096)
* times sizeof(int) memory, where nz is equal to the number of entries
* in A for the symmetric case or AA' if an unsymmetric matrix is
* being ordered (where nz includes both the upper and lower parts
* of A or AA'). The observed "upper bound" (with 2 exceptions),
* measured in an instrumented copy of METIS 4.0.1 on thousands of
* matrices, is (10*nz+50*n+4096) * sizeof(int). Two large matrices
* exceeded this bound, one by almost a factor of 2 (Gupta/gupta2).
*
* If your program is terminated by METIS, try setting metis_memory to
* 2.0, or even higher if needed. By default, CHOLMOD assumes that METIS
* does not have this problem (so that CHOLMOD will work correctly when
* this issue is fixed in METIS). Thus, the default value is zero.
* This work-around is not guaranteed anyway.
*
* If a matrix exceeds this predicted memory usage, AMD is attempted
* instead. It, too, may run out of memory, but if it does so it will
* not terminate your program.
*/
double metis_dswitch ; /* METIS_NodeND in METIS 4.0.1 gives a seg */
size_t metis_nswitch ; /* fault with one matrix of order n = 3005 and
* nz = 6,036,025. This is a very dense graph.
* The workaround is to use AMD instead of METIS for matrices of dimension
* greater than Common->metis_nswitch (default 3000) or more and with
* density of Common->metis_dswitch (default 0.66) or more.
* cholmod_nested_dissection has no problems with the same matrix, even
* though it uses METIS_NodeComputeSeparator on this matrix. If this
* seg fault does not affect you, set metis_nswitch to zero or less,
* and CHOLMOD will not switch to AMD based just on the density of the
* matrix (it will still switch to AMD if the metis_memory parameter
* causes the switch).
*/
/* ---------------------------------------------------------------------- */
/* workspace */
/* ---------------------------------------------------------------------- */
/* CHOLMOD has several routines that take less time than the size of
* workspace they require. Allocating and initializing the workspace would
* dominate the run time, unless workspace is allocated and initialized
* just once. CHOLMOD allocates this space when needed, and holds it here
* between calls to CHOLMOD. cholmod_start sets these pointers to NULL
* (which is why it must be the first routine called in CHOLMOD).
* cholmod_finish frees the workspace (which is why it must be the last
* call to CHOLMOD).
*/
size_t nrow ; /* size of Flag and Head */
UF_long mark ; /* mark value for Flag array */
size_t iworksize ; /* size of Iwork. Upper bound: 6*nrow+ncol */
size_t xworksize ; /* size of Xwork, in bytes.
* maxrank*nrow*sizeof(double) for update/downdate.
* 2*nrow*sizeof(double) otherwise */
/* initialized workspace: contents needed between calls to CHOLMOD */
void *Flag ; /* size nrow, an integer array. Kept cleared between
* calls to cholmod rouines (Flag [i] < mark) */
void *Head ; /* size nrow+1, an integer array. Kept cleared between
* calls to cholmod routines (Head [i] = EMPTY) */
void *Xwork ; /* a double array. Its size varies. It is nrow for
* most routines (cholmod_rowfac, cholmod_add,
* cholmod_aat, cholmod_norm, cholmod_ssmult) for the real case, twice
* that when the input matrices are complex or zomplex. It is of size
* 2*nrow for cholmod_rowadd and cholmod_rowdel. For cholmod_updown,
* its size is maxrank*nrow where maxrank is 2, 4, or 8. Kept cleared
* between calls to cholmod (set to zero). */
/* uninitialized workspace, contents not needed between calls to CHOLMOD */
void *Iwork ; /* size iworksize, 2*nrow+ncol for most routines,
* up to 6*nrow+ncol for cholmod_analyze. */
int itype ; /* If CHOLMOD_LONG, Flag, Head, and Iwork are UF_long.
* Otherwise all three arrays are int. */
int dtype ; /* double or float */
/* Common->itype and Common->dtype are used to define the types of all
* sparse matrices, triplet matrices, dense matrices, and factors
* created using this Common struct. The itypes and dtypes of all
* parameters to all CHOLMOD routines must match. */
int no_workspace_reallocate ; /* this is an internal flag, used as a
* precaution by cholmod_analyze. It is normally false. If true,
* cholmod_allocate_work is not allowed to reallocate any workspace;
* they must use the existing workspace in Common (Iwork, Flag, Head,
* and Xwork). Added for CHOLMOD v1.1 */
/* ---------------------------------------------------------------------- */
/* statistics */
/* ---------------------------------------------------------------------- */
/* fl and lnz are set only in cholmod_analyze and cholmod_rowcolcounts,
* in the Cholesky modudle. modfl is set only in the Modify module. */
int status ; /* error code */
double fl ; /* LL' flop count from most recent analysis */
double lnz ; /* fundamental nz in L */
double anz ; /* nonzeros in tril(A) if A is symmetric/lower,
* triu(A) if symmetric/upper, or tril(A*A') if
* unsymmetric, in last call to cholmod_analyze. */
double modfl ; /* flop count from most recent update/downdate/
* rowadd/rowdel (excluding flops to modify the
* solution to Lx=b, if computed) */
size_t malloc_count ; /* # of objects malloc'ed minus the # free'd*/
size_t memory_usage ; /* peak memory usage in bytes */
size_t memory_inuse ; /* current memory usage in bytes */
double nrealloc_col ; /* # of column reallocations */
double nrealloc_factor ;/* # of factor reallocations due to col. reallocs */
double ndbounds_hit ; /* # of times diagonal modified by dbound */
double rowfacfl ; /* # of flops in last call to cholmod_rowfac */
double aatfl ; /* # of flops to compute A(:,f)*A(:,f)' */
/* ---------------------------------------------------------------------- */
/* future expansion */
/* ---------------------------------------------------------------------- */
/* To allow CHOLMOD to be updated without recompiling the user application,
* additional space is set aside here for future statistics, parameters,
* and workspace. Note: additional entries were added in v1.1 to the
* method array, above, and thus v1.0 and v1.1 are not binary compatible.
*
* v1.1 to the current version are binary compatible.
*/
/* ---------------------------------------------------------------------- */
double other1 [10] ;
double SPQR_xstat [4] ; /* for SuiteSparseQR statistics */
/* SuiteSparseQR control parameters: */
double SPQR_grain ; /* task size is >= max (total flops / grain) */
double SPQR_small ; /* task size is >= small */
/* ---------------------------------------------------------------------- */
UF_long SPQR_istat [10] ; /* for SuiteSparseQR statistics */
UF_long other2 [6] ; /* reduced from size 16 in v1.6 */
/* ---------------------------------------------------------------------- */
int other3 [10] ; /* reduced from size 16 in v1.1. */
int prefer_binary ; /* cholmod_read_triplet converts a symmetric
* pattern-only matrix into a real matrix. If
* prefer_binary is FALSE, the diagonal entries are set to 1 + the degree
* of the row/column, and off-diagonal entries are set to -1 (resulting
* in a positive definite matrix if the diagonal is zero-free). Most
* symmetric patterns are the pattern a positive definite matrix. If
* this parameter is TRUE, then the matrix is returned with a 1 in each
* entry, instead. Default: FALSE. Added in v1.3. */
/* control parameter (added for v1.2): */
int default_nesdis ; /* Default: FALSE. If FALSE, then the default
* ordering strategy (when Common->nmethods == 0)
* is to try the given ordering (if present), AMD, and then METIS if AMD
* reports high fill-in. If Common->default_nesdis is TRUE then NESDIS
* is used instead in the default strategy. */
/* statistic (added for v1.2): */
int called_nd ; /* TRUE if the last call to
* cholmod_analyze called NESDIS or METIS. */
int blas_ok ; /* FALSE if BLAS int overflow; TRUE otherwise */
/* SuiteSparseQR control parameters: */
int SPQR_shrink ; /* controls stack realloc method */
int SPQR_nthreads ; /* number of TBB threads, 0 = auto */
/* ---------------------------------------------------------------------- */
size_t other4 [16] ;
/* ---------------------------------------------------------------------- */
void *other5 [16] ;
} cholmod_common ;
/* -------------------------------------------------------------------------- */
/* cholmod_start: first call to CHOLMOD */
/* -------------------------------------------------------------------------- */
int cholmod_start
(
cholmod_common *Common
) ;
int cholmod_l_start (cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_finish: last call to CHOLMOD */
/* -------------------------------------------------------------------------- */
int cholmod_finish
(
cholmod_common *Common
) ;
int cholmod_l_finish (cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_defaults: restore default parameters */
/* -------------------------------------------------------------------------- */
int cholmod_defaults
(
cholmod_common *Common
) ;
int cholmod_l_defaults (cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_maxrank: return valid maximum rank for update/downdate */
/* -------------------------------------------------------------------------- */
size_t cholmod_maxrank /* returns validated value of Common->maxrank */
(
/* ---- input ---- */
size_t n, /* A and L will have n rows */
/* --------------- */
cholmod_common *Common
) ;
size_t cholmod_l_maxrank (size_t, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_allocate_work: allocate workspace in Common */
/* -------------------------------------------------------------------------- */
int cholmod_allocate_work
(
/* ---- input ---- */
size_t nrow, /* size: Common->Flag (nrow), Common->Head (nrow+1) */
size_t iworksize, /* size of Common->Iwork */
size_t xworksize, /* size of Common->Xwork */
/* --------------- */
cholmod_common *Common
) ;
int cholmod_l_allocate_work (size_t, size_t, size_t, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_free_work: free workspace in Common */
/* -------------------------------------------------------------------------- */
int cholmod_free_work
(
cholmod_common *Common
) ;
int cholmod_l_free_work (cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_clear_flag: clear Flag workspace in Common */
/* -------------------------------------------------------------------------- */
/* use a macro for speed */
#define CHOLMOD_CLEAR_FLAG(Common) \
{ \
Common->mark++ ; \
if (Common->mark <= 0) \
{ \
Common->mark = EMPTY ; \
CHOLMOD (clear_flag) (Common) ; \
} \
}
UF_long cholmod_clear_flag
(
cholmod_common *Common
) ;
UF_long cholmod_l_clear_flag (cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_error: called when CHOLMOD encounters an error */
/* -------------------------------------------------------------------------- */
int cholmod_error
(
/* ---- input ---- */
int status, /* error status */
const char *file, /* name of source code file where error occured */
int line, /* line number in source code file where error occured*/
const char *message,/* error message */
/* --------------- */
cholmod_common *Common
) ;
int cholmod_l_error (int, const char *, int, const char *, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_dbound: for internal use in CHOLMOD only */
/* -------------------------------------------------------------------------- */
double cholmod_dbound /* returns modified diagonal entry of D or L */
(
/* ---- input ---- */
double dj, /* diagonal entry of D for LDL' or L for LL' */
/* --------------- */
cholmod_common *Common
) ;
double cholmod_l_dbound (double, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_hypot: compute sqrt (x*x + y*y) accurately */
/* -------------------------------------------------------------------------- */
double cholmod_hypot
(
/* ---- input ---- */
double x, double y
) ;
double cholmod_l_hypot (double, double) ;
/* -------------------------------------------------------------------------- */
/* cholmod_divcomplex: complex division, c = a/b */
/* -------------------------------------------------------------------------- */
int cholmod_divcomplex /* return 1 if divide-by-zero, 0 otherise */
(
/* ---- input ---- */
double ar, double ai, /* real and imaginary parts of a */
double br, double bi, /* real and imaginary parts of b */
/* ---- output --- */
double *cr, double *ci /* real and imaginary parts of c */
) ;
int cholmod_l_divcomplex (double, double, double, double, double *, double *) ;
/* ========================================================================== */
/* === Core/cholmod_sparse ================================================== */
/* ========================================================================== */
/* A sparse matrix stored in compressed-column form. */
typedef struct cholmod_sparse_struct
{
size_t nrow ; /* the matrix is nrow-by-ncol */
size_t ncol ;
size_t nzmax ; /* maximum number of entries in the matrix */
/* pointers to int or UF_long: */
void *p ; /* p [0..ncol], the column pointers */
void *i ; /* i [0..nzmax-1], the row indices */
/* for unpacked matrices only: */
void *nz ; /* nz [0..ncol-1], the # of nonzeros in each col. In
* packed form, the nonzero pattern of column j is in
* A->i [A->p [j] ... A->p [j+1]-1]. In unpacked form, column j is in
* A->i [A->p [j] ... A->p [j]+A->nz[j]-1] instead. In both cases, the
* numerical values (if present) are in the corresponding locations in
* the array x (or z if A->xtype is CHOLMOD_ZOMPLEX). */
/* pointers to double or float: */
void *x ; /* size nzmax or 2*nzmax, if present */
void *z ; /* size nzmax, if present */
int stype ; /* Describes what parts of the matrix are considered:
*
* 0: matrix is "unsymmetric": use both upper and lower triangular parts
* (the matrix may actually be symmetric in pattern and value, but
* both parts are explicitly stored and used). May be square or
* rectangular.
* >0: matrix is square and symmetric, use upper triangular part.
* Entries in the lower triangular part are ignored.
* <0: matrix is square and symmetric, use lower triangular part.
* Entries in the upper triangular part are ignored.
*
* Note that stype>0 and stype<0 are different for cholmod_sparse and
* cholmod_triplet. See the cholmod_triplet data structure for more
* details.
*/
int itype ; /* CHOLMOD_INT: p, i, and nz are int.
* CHOLMOD_INTLONG: p is UF_long, i and nz are int.
* CHOLMOD_LONG: p, i, and nz are UF_long. */
int xtype ; /* pattern, real, complex, or zomplex */
int dtype ; /* x and z are double or float */
int sorted ; /* TRUE if columns are sorted, FALSE otherwise */
int packed ; /* TRUE if packed (nz ignored), FALSE if unpacked
* (nz is required) */
} cholmod_sparse ;
/* -------------------------------------------------------------------------- */
/* cholmod_allocate_sparse: allocate a sparse matrix */
/* -------------------------------------------------------------------------- */
cholmod_sparse *cholmod_allocate_sparse
(
/* ---- input ---- */
size_t nrow, /* # of rows of A */
size_t ncol, /* # of columns of A */
size_t nzmax, /* max # of nonzeros of A */
int sorted, /* TRUE if columns of A sorted, FALSE otherwise */
int packed, /* TRUE if A will be packed, FALSE otherwise */
int stype, /* stype of A */
int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */
/* --------------- */
cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_allocate_sparse (size_t, size_t, size_t, int, int,
int, int, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_free_sparse: free a sparse matrix */
/* -------------------------------------------------------------------------- */
int cholmod_free_sparse
(
/* ---- in/out --- */
cholmod_sparse **A, /* matrix to deallocate, NULL on output */
/* --------------- */
cholmod_common *Common
) ;
int cholmod_l_free_sparse (cholmod_sparse **, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_reallocate_sparse: change the size (# entries) of sparse matrix */
/* -------------------------------------------------------------------------- */
int cholmod_reallocate_sparse
(
/* ---- input ---- */
size_t nznew, /* new # of entries in A */
/* ---- in/out --- */
cholmod_sparse *A, /* matrix to reallocate */
/* --------------- */
cholmod_common *Common
) ;
int cholmod_l_reallocate_sparse ( size_t, cholmod_sparse *, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_nnz: return number of nonzeros in a sparse matrix */
/* -------------------------------------------------------------------------- */
UF_long cholmod_nnz
(
/* ---- input ---- */
cholmod_sparse *A,
/* --------------- */
cholmod_common *Common
) ;
UF_long cholmod_l_nnz (cholmod_sparse *, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_speye: sparse identity matrix */
/* -------------------------------------------------------------------------- */
cholmod_sparse *cholmod_speye
(
/* ---- input ---- */
size_t nrow, /* # of rows of A */
size_t ncol, /* # of columns of A */
int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */
/* --------------- */
cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_speye (size_t, size_t, int, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_spzeros: sparse zero matrix */
/* -------------------------------------------------------------------------- */
cholmod_sparse *cholmod_spzeros
(
/* ---- input ---- */
size_t nrow, /* # of rows of A */
size_t ncol, /* # of columns of A */
size_t nzmax, /* max # of nonzeros of A */
int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */
/* --------------- */
cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_spzeros (size_t, size_t, size_t, int,
cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_transpose: transpose a sparse matrix */
/* -------------------------------------------------------------------------- */
/* Return A' or A.' The "values" parameter is 0, 1, or 2 to denote the pattern
* transpose, the array transpose (A.'), and the complex conjugate transpose
* (A').
*/
cholmod_sparse *cholmod_transpose
(
/* ---- input ---- */
cholmod_sparse *A, /* matrix to transpose */
int values, /* 0: pattern, 1: array transpose, 2: conj. transpose */
/* --------------- */
cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_transpose (cholmod_sparse *, int, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_transpose_unsym: transpose an unsymmetric sparse matrix */
/* -------------------------------------------------------------------------- */
/* Compute F = A', A (:,f)', or A (p,f)', where A is unsymmetric and F is
* already allocated. See cholmod_transpose for a simpler routine. */
int cholmod_transpose_unsym
(
/* ---- input ---- */
cholmod_sparse *A, /* matrix to transpose */
int values, /* 0: pattern, 1: array transpose, 2: conj. transpose */
int *Perm, /* size nrow, if present (can be NULL) */
int *fset, /* subset of 0:(A->ncol)-1 */
size_t fsize, /* size of fset */
/* ---- output --- */
cholmod_sparse *F, /* F = A', A(:,f)', or A(p,f)' */
/* --------------- */
cholmod_common *Common
) ;
int cholmod_l_transpose_unsym (cholmod_sparse *, int, UF_long *, UF_long *,
size_t, cholmod_sparse *, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_transpose_sym: transpose a symmetric sparse matrix */
/* -------------------------------------------------------------------------- */
/* Compute F = A' or A (p,p)', where A is symmetric and F is already allocated.
* See cholmod_transpose for a simpler routine. */
int cholmod_transpose_sym
(
/* ---- input ---- */
cholmod_sparse *A, /* matrix to transpose */
int values, /* 0: pattern, 1: array transpose, 2: conj. transpose */
int *Perm, /* size nrow, if present (can be NULL) */
/* ---- output --- */
cholmod_sparse *F, /* F = A' or A(p,p)' */
/* --------------- */
cholmod_common *Common
) ;
int cholmod_l_transpose_sym (cholmod_sparse *, int, UF_long *, cholmod_sparse *,
cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_ptranspose: transpose a sparse matrix */
/* -------------------------------------------------------------------------- */
/* Return A' or A(p,p)' if A is symmetric. Return A', A(:,f)', or A(p,f)' if
* A is unsymmetric. */
cholmod_sparse *cholmod_ptranspose
(
/* ---- input ---- */
cholmod_sparse *A, /* matrix to transpose */
int values, /* 0: pattern, 1: array transpose, 2: conj. transpose */
int *Perm, /* if non-NULL, F = A(p,f) or A(p,p) */
int *fset, /* subset of 0:(A->ncol)-1 */
size_t fsize, /* size of fset */
/* --------------- */
cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_ptranspose (cholmod_sparse *, int, UF_long *,
UF_long *, size_t, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_sort: sort row indices in each column of sparse matrix */
/* -------------------------------------------------------------------------- */
int cholmod_sort
(
/* ---- in/out --- */
cholmod_sparse *A, /* matrix to sort */
/* --------------- */
cholmod_common *Common
) ;
int cholmod_l_sort (cholmod_sparse *, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_band: C = tril (triu (A,k1), k2) */
/* -------------------------------------------------------------------------- */
cholmod_sparse *cholmod_band
(
/* ---- input ---- */
cholmod_sparse *A, /* matrix to extract band matrix from */
UF_long k1, /* ignore entries below the k1-st diagonal */
UF_long k2, /* ignore entries above the k2-nd diagonal */
int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) */
/* --------------- */
cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_band (cholmod_sparse *, UF_long, UF_long, int,
cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_band_inplace: A = tril (triu (A,k1), k2) */
/* -------------------------------------------------------------------------- */
int cholmod_band_inplace
(
/* ---- input ---- */
UF_long k1, /* ignore entries below the k1-st diagonal */
UF_long k2, /* ignore entries above the k2-nd diagonal */
int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) */
/* ---- in/out --- */
cholmod_sparse *A, /* matrix from which entries not in band are removed */
/* --------------- */
cholmod_common *Common
) ;
int cholmod_l_band_inplace (UF_long, UF_long, int, cholmod_sparse *,
cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_aat: C = A*A' or A(:,f)*A(:,f)' */
/* -------------------------------------------------------------------------- */
cholmod_sparse *cholmod_aat
(
/* ---- input ---- */
cholmod_sparse *A, /* input matrix; C=A*A' is constructed */
int *fset, /* subset of 0:(A->ncol)-1 */
size_t fsize, /* size of fset */
int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag),
* -2: pattern only, no diagonal, add 50%+n extra
* space to C */
/* --------------- */
cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_aat (cholmod_sparse *, UF_long *, size_t, int,
cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_copy_sparse: C = A, create an exact copy of a sparse matrix */
/* -------------------------------------------------------------------------- */
cholmod_sparse *cholmod_copy_sparse
(
/* ---- input ---- */
cholmod_sparse *A, /* matrix to copy */
/* --------------- */
cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_copy_sparse (cholmod_sparse *, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_copy: C = A, with possible change of stype */
/* -------------------------------------------------------------------------- */
cholmod_sparse *cholmod_copy
(
/* ---- input ---- */
cholmod_sparse *A, /* matrix to copy */
int stype, /* requested stype of C */
int mode, /* >0: numerical, 0: pattern, <0: pattern (no diag) */
/* --------------- */
cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_copy (cholmod_sparse *, int, int, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_add: C = alpha*A + beta*B */
/* -------------------------------------------------------------------------- */
cholmod_sparse *cholmod_add
(
/* ---- input ---- */
cholmod_sparse *A, /* matrix to add */
cholmod_sparse *B, /* matrix to add */
double alpha [2], /* scale factor for A */
double beta [2], /* scale factor for B */
int values, /* if TRUE compute the numerical values of C */
int sorted, /* if TRUE, sort columns of C */
/* --------------- */
cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_add (cholmod_sparse *, cholmod_sparse *, double *,
double *, int, int, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_sparse_xtype: change the xtype of a sparse matrix */
/* -------------------------------------------------------------------------- */
int cholmod_sparse_xtype
(
/* ---- input ---- */
int to_xtype, /* requested xtype (pattern, real, complex, zomplex) */
/* ---- in/out --- */
cholmod_sparse *A, /* sparse matrix to change */
/* --------------- */
cholmod_common *Common
) ;
int cholmod_l_sparse_xtype (int, cholmod_sparse *, cholmod_common *) ;
/* ========================================================================== */
/* === Core/cholmod_factor ================================================== */
/* ========================================================================== */
/* A symbolic and numeric factorization, either simplicial or supernodal.
* In all cases, the row indices in the columns of L are kept sorted. */
typedef struct cholmod_factor_struct
{
/* ---------------------------------------------------------------------- */
/* for both simplicial and supernodal factorizations */
/* ---------------------------------------------------------------------- */
size_t n ; /* L is n-by-n */
size_t minor ; /* If the factorization failed, L->minor is the column
* at which it failed (in the range 0 to n-1). A value
* of n means the factorization was successful or
* the matrix has not yet been factorized. */
/* ---------------------------------------------------------------------- */
/* symbolic ordering and analysis */
/* ---------------------------------------------------------------------- */
void *Perm ; /* size n, permutation used */
void *ColCount ; /* size n, column counts for simplicial L */
/* ---------------------------------------------------------------------- */
/* simplicial factorization */
/* ---------------------------------------------------------------------- */
size_t nzmax ; /* size of i and x */
void *p ; /* p [0..ncol], the column pointers */
void *i ; /* i [0..nzmax-1], the row indices */
void *x ; /* x [0..nzmax-1], the numerical values */
void *z ;
void *nz ; /* nz [0..ncol-1], the # of nonzeros in each column.
* i [p [j] ... p [j]+nz[j]-1] contains the row indices,
* and the numerical values are in the same locatins
* in x. The value of i [p [k]] is always k. */
void *next ; /* size ncol+2. next [j] is the next column in i/x */
void *prev ; /* size ncol+2. prev [j] is the prior column in i/x.
* head of the list is ncol+1, and the tail is ncol. */
/* ---------------------------------------------------------------------- */
/* supernodal factorization */
/* ---------------------------------------------------------------------- */
/* Note that L->x is shared with the simplicial data structure. L->x has
* size L->nzmax for a simplicial factor, and size L->xsize for a supernodal
* factor. */
size_t nsuper ; /* number of supernodes */
size_t ssize ; /* size of s, integer part of supernodes */
size_t xsize ; /* size of x, real part of supernodes */
size_t maxcsize ; /* size of largest update matrix */
size_t maxesize ; /* max # of rows in supernodes, excl. triangular part */
void *super ; /* size nsuper+1, first col in each supernode */
void *pi ; /* size nsuper+1, pointers to integer patterns */
void *px ; /* size nsuper+1, pointers to real parts */
void *s ; /* size ssize, integer part of supernodes */
/* ---------------------------------------------------------------------- */
/* factorization type */
/* ---------------------------------------------------------------------- */
int ordering ; /* ordering method used */
int is_ll ; /* TRUE if LL', FALSE if LDL' */
int is_super ; /* TRUE if supernodal, FALSE if simplicial */
int is_monotonic ; /* TRUE if columns of L appear in order 0..n-1.
* Only applicable to simplicial numeric types. */
/* There are 8 types of factor objects that cholmod_factor can represent
* (only 6 are used):
*
* Numeric types (xtype is not CHOLMOD_PATTERN)
* --------------------------------------------
*
* simplicial LDL': (is_ll FALSE, is_super FALSE). Stored in compressed
* column form, using the simplicial components above (nzmax, p, i,
* x, z, nz, next, and prev). The unit diagonal of L is not stored,
* and D is stored in its place. There are no supernodes.
*
* simplicial LL': (is_ll TRUE, is_super FALSE). Uses the same storage
* scheme as the simplicial LDL', except that D does not appear.
* The first entry of each column of L is the diagonal entry of
* that column of L.
*
* supernodal LDL': (is_ll FALSE, is_super TRUE). Not used.
* FUTURE WORK: add support for supernodal LDL'
*
* supernodal LL': (is_ll TRUE, is_super TRUE). A supernodal factor,
* using the supernodal components described above (nsuper, ssize,
* xsize, maxcsize, maxesize, super, pi, px, s, x, and z).
*
*
* Symbolic types (xtype is CHOLMOD_PATTERN)
* -----------------------------------------
*
* simplicial LDL': (is_ll FALSE, is_super FALSE). Nothing is present
* except Perm and ColCount.
*
* simplicial LL': (is_ll TRUE, is_super FALSE). Identical to the
* simplicial LDL', except for the is_ll flag.
*
* supernodal LDL': (is_ll FALSE, is_super TRUE). Not used.
* FUTURE WORK: add support for supernodal LDL'
*
* supernodal LL': (is_ll TRUE, is_super TRUE). A supernodal symbolic
* factorization. The simplicial symbolic information is present
* (Perm and ColCount), as is all of the supernodal factorization
* except for the numerical values (x and z).
*/
int itype ; /* The integer arrays are Perm, ColCount, p, i, nz,
* next, prev, super, pi, px, and s. If itype is
* CHOLMOD_INT, all of these are int arrays.
* CHOLMOD_INTLONG: p, pi, px are UF_long, others int.
* CHOLMOD_LONG: all integer arrays are UF_long. */
int xtype ; /* pattern, real, complex, or zomplex */
int dtype ; /* x and z double or float */
} cholmod_factor ;
/* -------------------------------------------------------------------------- */
/* cholmod_allocate_factor: allocate a factor (symbolic LL' or LDL') */
/* -------------------------------------------------------------------------- */
cholmod_factor *cholmod_allocate_factor
(
/* ---- input ---- */
size_t n, /* L is n-by-n */
/* --------------- */
cholmod_common *Common
) ;
cholmod_factor *cholmod_l_allocate_factor (size_t, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_free_factor: free a factor */
/* -------------------------------------------------------------------------- */
int cholmod_free_factor
(
/* ---- in/out --- */
cholmod_factor **L, /* factor to free, NULL on output */
/* --------------- */
cholmod_common *Common
) ;
int cholmod_l_free_factor (cholmod_factor **, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_reallocate_factor: change the # entries in a factor */
/* -------------------------------------------------------------------------- */
int cholmod_reallocate_factor
(
/* ---- input ---- */
size_t nznew, /* new # of entries in L */
/* ---- in/out --- */
cholmod_factor *L, /* factor to modify */
/* --------------- */
cholmod_common *Common
) ;
int cholmod_l_reallocate_factor (size_t, cholmod_factor *, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_change_factor: change the type of factor (e.g., LDL' to LL') */
/* -------------------------------------------------------------------------- */
int cholmod_change_factor
(
/* ---- input ---- */
int to_xtype, /* to CHOLMOD_PATTERN, _REAL, _COMPLEX, _ZOMPLEX */
int to_ll, /* TRUE: convert to LL', FALSE: LDL' */
int to_super, /* TRUE: convert to supernodal, FALSE: simplicial */
int to_packed, /* TRUE: pack simplicial columns, FALSE: do not pack */
int to_monotonic, /* TRUE: put simplicial columns in order, FALSE: not */
/* ---- in/out --- */
cholmod_factor *L, /* factor to modify */
/* --------------- */
cholmod_common *Common
) ;
int cholmod_l_change_factor ( int, int, int, int, int, cholmod_factor *,
cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_pack_factor: pack the columns of a factor */
/* -------------------------------------------------------------------------- */
/* Pack the columns of a simplicial factor. Unlike cholmod_change_factor,
* it can pack the columns of a factor even if they are not stored in their
* natural order (non-monotonic). */
int cholmod_pack_factor
(
/* ---- in/out --- */
cholmod_factor *L, /* factor to modify */
/* --------------- */
cholmod_common *Common
) ;
int cholmod_l_pack_factor (cholmod_factor *, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_reallocate_column: resize a single column of a factor */
/* -------------------------------------------------------------------------- */
int cholmod_reallocate_column
(
/* ---- input ---- */
size_t j, /* the column to reallocate */
size_t need, /* required size of column j */
/* ---- in/out --- */
cholmod_factor *L, /* factor to modify */
/* --------------- */
cholmod_common *Common
) ;
int cholmod_l_reallocate_column (size_t, size_t, cholmod_factor *,
cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_factor_to_sparse: create a sparse matrix copy of a factor */
/* -------------------------------------------------------------------------- */
/* Only operates on numeric factors, not symbolic ones */
cholmod_sparse *cholmod_factor_to_sparse
(
/* ---- in/out --- */
cholmod_factor *L, /* factor to copy, converted to symbolic on output */
/* --------------- */
cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_factor_to_sparse (cholmod_factor *,
cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_copy_factor: create a copy of a factor */
/* -------------------------------------------------------------------------- */
cholmod_factor *cholmod_copy_factor
(
/* ---- input ---- */
cholmod_factor *L, /* factor to copy */
/* --------------- */
cholmod_common *Common
) ;
cholmod_factor *cholmod_l_copy_factor (cholmod_factor *, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_factor_xtype: change the xtype of a factor */
/* -------------------------------------------------------------------------- */
int cholmod_factor_xtype
(
/* ---- input ---- */
int to_xtype, /* requested xtype (real, complex, or zomplex) */
/* ---- in/out --- */
cholmod_factor *L, /* factor to change */
/* --------------- */
cholmod_common *Common
) ;
int cholmod_l_factor_xtype (int, cholmod_factor *, cholmod_common *) ;
/* ========================================================================== */
/* === Core/cholmod_dense =================================================== */
/* ========================================================================== */
/* A dense matrix in column-oriented form. It has no itype since it contains
* no integers. Entry in row i and column j is located in x [i+j*d].
*/
typedef struct cholmod_dense_struct
{
size_t nrow ; /* the matrix is nrow-by-ncol */
size_t ncol ;
size_t nzmax ; /* maximum number of entries in the matrix */
size_t d ; /* leading dimension (d >= nrow must hold) */
void *x ; /* size nzmax or 2*nzmax, if present */
void *z ; /* size nzmax, if present */
int xtype ; /* pattern, real, complex, or zomplex */
int dtype ; /* x and z double or float */
} cholmod_dense ;
/* -------------------------------------------------------------------------- */
/* cholmod_allocate_dense: allocate a dense matrix (contents uninitialized) */
/* -------------------------------------------------------------------------- */
cholmod_dense *cholmod_allocate_dense
(
/* ---- input ---- */
size_t nrow, /* # of rows of matrix */
size_t ncol, /* # of columns of matrix */
size_t d, /* leading dimension */
int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */
/* --------------- */
cholmod_common *Common
) ;
cholmod_dense *cholmod_l_allocate_dense (size_t, size_t, size_t, int,
cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_zeros: allocate a dense matrix and set it to zero */
/* -------------------------------------------------------------------------- */
cholmod_dense *cholmod_zeros
(
/* ---- input ---- */
size_t nrow, /* # of rows of matrix */
size_t ncol, /* # of columns of matrix */
int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */
/* --------------- */
cholmod_common *Common
) ;
cholmod_dense *cholmod_l_zeros (size_t, size_t, int, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_ones: allocate a dense matrix and set it to all ones */
/* -------------------------------------------------------------------------- */
cholmod_dense *cholmod_ones
(
/* ---- input ---- */
size_t nrow, /* # of rows of matrix */
size_t ncol, /* # of columns of matrix */
int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */
/* --------------- */
cholmod_common *Common
) ;
cholmod_dense *cholmod_l_ones (size_t, size_t, int, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_eye: allocate a dense matrix and set it to the identity matrix */
/* -------------------------------------------------------------------------- */
cholmod_dense *cholmod_eye
(
/* ---- input ---- */
size_t nrow, /* # of rows of matrix */
size_t ncol, /* # of columns of matrix */
int xtype, /* CHOLMOD_REAL, _COMPLEX, or _ZOMPLEX */
/* --------------- */
cholmod_common *Common
) ;
cholmod_dense *cholmod_l_eye (size_t, size_t, int, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_free_dense: free a dense matrix */
/* -------------------------------------------------------------------------- */
int cholmod_free_dense
(
/* ---- in/out --- */
cholmod_dense **X, /* dense matrix to deallocate, NULL on output */
/* --------------- */
cholmod_common *Common
) ;
int cholmod_l_free_dense (cholmod_dense **, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_sparse_to_dense: create a dense matrix copy of a sparse matrix */
/* -------------------------------------------------------------------------- */
cholmod_dense *cholmod_sparse_to_dense
(
/* ---- input ---- */
cholmod_sparse *A, /* matrix to copy */
/* --------------- */
cholmod_common *Common
) ;
cholmod_dense *cholmod_l_sparse_to_dense (cholmod_sparse *,
cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_dense_to_sparse: create a sparse matrix copy of a dense matrix */
/* -------------------------------------------------------------------------- */
cholmod_sparse *cholmod_dense_to_sparse
(
/* ---- input ---- */
cholmod_dense *X, /* matrix to copy */
int values, /* TRUE if values to be copied, FALSE otherwise */
/* --------------- */
cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_dense_to_sparse (cholmod_dense *, int,
cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_copy_dense: create a copy of a dense matrix */
/* -------------------------------------------------------------------------- */
cholmod_dense *cholmod_copy_dense
(
/* ---- input ---- */
cholmod_dense *X, /* matrix to copy */
/* --------------- */
cholmod_common *Common
) ;
cholmod_dense *cholmod_l_copy_dense (cholmod_dense *, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_copy_dense2: copy a dense matrix (pre-allocated) */
/* -------------------------------------------------------------------------- */
int cholmod_copy_dense2
(
/* ---- input ---- */
cholmod_dense *X, /* matrix to copy */
/* ---- output --- */
cholmod_dense *Y, /* copy of matrix X */
/* --------------- */
cholmod_common *Common
) ;
int cholmod_l_copy_dense2 (cholmod_dense *, cholmod_dense *, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_dense_xtype: change the xtype of a dense matrix */
/* -------------------------------------------------------------------------- */
int cholmod_dense_xtype
(
/* ---- input ---- */
int to_xtype, /* requested xtype (real, complex,or zomplex) */
/* ---- in/out --- */
cholmod_dense *X, /* dense matrix to change */
/* --------------- */
cholmod_common *Common
) ;
int cholmod_l_dense_xtype (int, cholmod_dense *, cholmod_common *) ;
/* ========================================================================== */
/* === Core/cholmod_triplet ================================================= */
/* ========================================================================== */
/* A sparse matrix stored in triplet form. */
typedef struct cholmod_triplet_struct
{
size_t nrow ; /* the matrix is nrow-by-ncol */
size_t ncol ;
size_t nzmax ; /* maximum number of entries in the matrix */
size_t nnz ; /* number of nonzeros in the matrix */
void *i ; /* i [0..nzmax-1], the row indices */
void *j ; /* j [0..nzmax-1], the column indices */
void *x ; /* size nzmax or 2*nzmax, if present */
void *z ; /* size nzmax, if present */
int stype ; /* Describes what parts of the matrix are considered:
*
* 0: matrix is "unsymmetric": use both upper and lower triangular parts
* (the matrix may actually be symmetric in pattern and value, but
* both parts are explicitly stored and used). May be square or
* rectangular.
* >0: matrix is square and symmetric. Entries in the lower triangular
* part are transposed and added to the upper triangular part when
* the matrix is converted to cholmod_sparse form.
* <0: matrix is square and symmetric. Entries in the upper triangular
* part are transposed and added to the lower triangular part when
* the matrix is converted to cholmod_sparse form.
*
* Note that stype>0 and stype<0 are different for cholmod_sparse and
* cholmod_triplet. The reason is simple. You can permute a symmetric
* triplet matrix by simply replacing a row and column index with their
* new row and column indices, via an inverse permutation. Suppose
* P = L->Perm is your permutation, and Pinv is an array of size n.
* Suppose a symmetric matrix A is represent by a triplet matrix T, with
* entries only in the upper triangular part. Then the following code:
*
* Ti = T->i ;
* Tj = T->j ;
* for (k = 0 ; k < n ; k++) Pinv [P [k]] = k ;
* for (k = 0 ; k < nz ; k++) Ti [k] = Pinv [Ti [k]] ;
* for (k = 0 ; k < nz ; k++) Tj [k] = Pinv [Tj [k]] ;
*
* creates the triplet form of C=P*A*P'. However, if T initially
* contains just the upper triangular entries (T->stype = 1), after
* permutation it has entries in both the upper and lower triangular
* parts. These entries should be transposed when constructing the
* cholmod_sparse form of A, which is what cholmod_triplet_to_sparse
* does. Thus:
*
* C = cholmod_triplet_to_sparse (T, 0, &Common) ;
*
* will return the matrix C = P*A*P'.
*
* Since the triplet matrix T is so simple to generate, it's quite easy
* to remove entries that you do not want, prior to converting T to the
* cholmod_sparse form. So if you include these entries in T, CHOLMOD
* assumes that there must be a reason (such as the one above). Thus,
* no entry in a triplet matrix is ever ignored.
*/
int itype ; /* CHOLMOD_LONG: i and j are UF_long. Otherwise int. */
int xtype ; /* pattern, real, complex, or zomplex */
int dtype ; /* x and z are double or float */
} cholmod_triplet ;
/* -------------------------------------------------------------------------- */
/* cholmod_allocate_triplet: allocate a triplet matrix */
/* -------------------------------------------------------------------------- */
cholmod_triplet *cholmod_allocate_triplet
(
/* ---- input ---- */
size_t nrow, /* # of rows of T */
size_t ncol, /* # of columns of T */
size_t nzmax, /* max # of nonzeros of T */
int stype, /* stype of T */
int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */
/* --------------- */
cholmod_common *Common
) ;
cholmod_triplet *cholmod_l_allocate_triplet (size_t, size_t, size_t, int, int,
cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_free_triplet: free a triplet matrix */
/* -------------------------------------------------------------------------- */
int cholmod_free_triplet
(
/* ---- in/out --- */
cholmod_triplet **T, /* triplet matrix to deallocate, NULL on output */
/* --------------- */
cholmod_common *Common
) ;
int cholmod_l_free_triplet (cholmod_triplet **, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_reallocate_triplet: change the # of entries in a triplet matrix */
/* -------------------------------------------------------------------------- */
int cholmod_reallocate_triplet
(
/* ---- input ---- */
size_t nznew, /* new # of entries in T */
/* ---- in/out --- */
cholmod_triplet *T, /* triplet matrix to modify */
/* --------------- */
cholmod_common *Common
) ;
int cholmod_l_reallocate_triplet (size_t, cholmod_triplet *, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_sparse_to_triplet: create a triplet matrix copy of a sparse matrix*/
/* -------------------------------------------------------------------------- */
cholmod_triplet *cholmod_sparse_to_triplet
(
/* ---- input ---- */
cholmod_sparse *A, /* matrix to copy */
/* --------------- */
cholmod_common *Common
) ;
cholmod_triplet *cholmod_l_sparse_to_triplet (cholmod_sparse *,
cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_triplet_to_sparse: create a sparse matrix copy of a triplet matrix*/
/* -------------------------------------------------------------------------- */
cholmod_sparse *cholmod_triplet_to_sparse
(
/* ---- input ---- */
cholmod_triplet *T, /* matrix to copy */
size_t nzmax, /* allocate at least this much space in output matrix */
/* --------------- */
cholmod_common *Common
) ;
cholmod_sparse *cholmod_l_triplet_to_sparse (cholmod_triplet *, size_t,
cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_copy_triplet: create a copy of a triplet matrix */
/* -------------------------------------------------------------------------- */
cholmod_triplet *cholmod_copy_triplet
(
/* ---- input ---- */
cholmod_triplet *T, /* matrix to copy */
/* --------------- */
cholmod_common *Common
) ;
cholmod_triplet *cholmod_l_copy_triplet (cholmod_triplet *, cholmod_common *) ;
/* -------------------------------------------------------------------------- */
/* cholmod_triplet_xtype: change the xtype of a triplet matrix */
/* -------------------------------------------------------------------------- */
int cholmod_triplet_xtype
(
/* ---- input ---- */
int to_xtype, /* requested xtype (pattern, real, complex,or zomplex)*/
/* ---- in/out --- */
cholmod_triplet *T, /* triplet matrix to change */
/* --------------- */
cholmod_common *Common
) ;
int cholmod_l_triplet_xtype (int, cholmod_triplet *, cholmod_common *) ;
/* ========================================================================== */
/* === Core/cholmod_memory ================================================== */
/* ========================================================================== */
/* The user may make use of these, just like malloc and free. You can even
* malloc an object and safely free it with cholmod_free, and visa versa
* (except that the memory usage statistics will be corrupted). These routines
* do differ from malloc and free. If cholmod_free is given a NULL pointer,
* for example, it does nothing (unlike the ANSI free). cholmod_realloc does
* not return NULL if given a non-NULL pointer and a nonzero size, even if it
* fails (it returns the original pointer and sets an error code in
* Common->status instead).
*
* CHOLMOD keeps track of the amount of memory it has allocated, and so the
* cholmod_free routine also takes the size of the object being freed. This
* is only used for statistics. If you, the user of CHOLMOD, pass the wrong
* size, the only consequence is that the memory usage statistics will be
* corrupted.
*/
void *cholmod_malloc /* returns pointer to the newly malloc'd block */
(
/* ---- input ---- */
size_t n, /* number of items */
size_t size, /* size of each item */
/* --------------- */
cholmod_common *Common
) ;
void *cholmod_l_malloc (size_t, size_t, cholmod_common *) ;
void *cholmod_calloc /* returns pointer to the newly calloc'd block */
(
/* ---- input ---- */
size_t n, /* number of items */
size_t size, /* size of each item */
/* --------------- */
cholmod_common *Common
) ;
void *cholmod_l_calloc (size_t, size_t, cholmod_common *) ;
void *cholmod_free /* always returns NULL */
(
/* ---- input ---- */
size_t n, /* number of items */
size_t size, /* size of each item */
/* ---- in/out --- */
void *p, /* block of memory to free */
/* --------------- */
cholmod_common *Common
) ;
void *cholmod_l_free (size_t, size_t, void *, cholmod_common *) ;
void *cholmod_realloc /* returns pointer to reallocated block */
(
/* ---- input ---- */
size_t nnew, /* requested # of items in reallocated block */
size_t size, /* size of each item */
/* ---- in/out --- */
void *p, /* block of memory to realloc */
size_t *n, /* current size on input, nnew on output if successful*/
/* --------------- */
cholmod_common *Common
) ;
void *cholmod_l_realloc (size_t, size_t, void *, size_t *, cholmod_common *) ;
int cholmod_realloc_multiple
(
/* ---- input ---- */
size_t nnew, /* requested # of items in reallocated blocks */
int nint, /* number of int/UF_long blocks */
int xtype, /* CHOLMOD_PATTERN, _REAL, _COMPLEX, or _ZOMPLEX */
/* ---- in/out --- */
void **I, /* int or UF_long block */
void **J, /* int or UF_long block */
void **X, /* complex, double, or float block */
void **Z, /* zomplex case only: double or float block */
size_t *n, /* current size of the I,J,X,Z blocks on input,
* nnew on output if successful */
/* --------------- */
cholmod_common *Common
) ;
int cholmod_l_realloc_multiple (size_t, int, int, void **, void **, void **,
void **, size_t *, cholmod_common *) ;
/* ========================================================================== */
/* === symmetry types ======================================================= */
/* ========================================================================== */
#define CHOLMOD_MM_RECTANGULAR 1
#define CHOLMOD_MM_UNSYMMETRIC 2
#define CHOLMOD_MM_SYMMETRIC 3
#define CHOLMOD_MM_HERMITIAN 4
#define CHOLMOD_MM_SKEW_SYMMETRIC 5
#define CHOLMOD_MM_SYMMETRIC_POSDIAG 6
#define CHOLMOD_MM_HERMITIAN_POSDIAG 7
/* ========================================================================== */
/* === Numerical relop macros =============================================== */
/* ========================================================================== */
/* These macros correctly handle the NaN case.
*
* CHOLMOD_IS_NAN(x):
* True if x is NaN. False otherwise. The commonly-existing isnan(x)
* function could be used, but it's not in Kernighan & Ritchie 2nd edition
* (ANSI C89). It may appear in <math.h>, but I'm not certain about
* portability. The expression x != x is true if and only if x is NaN,
* according to the IEEE 754 floating-point standard.
*
* CHOLMOD_IS_ZERO(x):
* True if x is zero. False if x is nonzero, NaN, or +/- Inf.
* This is (x == 0) if the compiler is IEEE 754 compliant.
*
* CHOLMOD_IS_NONZERO(x):
* True if x is nonzero, NaN, or +/- Inf. False if x zero.
* This is (x != 0) if the compiler is IEEE 754 compliant.
*
* CHOLMOD_IS_LT_ZERO(x):
* True if x is < zero or -Inf. False if x is >= 0, NaN, or +Inf.
* This is (x < 0) if the compiler is IEEE 754 compliant.
*
* CHOLMOD_IS_GT_ZERO(x):
* True if x is > zero or +Inf. False if x is <= 0, NaN, or -Inf.
* This is (x > 0) if the compiler is IEEE 754 compliant.
*
* CHOLMOD_IS_LE_ZERO(x):
* True if x is <= zero or -Inf. False if x is > 0, NaN, or +Inf.
* This is (x <= 0) if the compiler is IEEE 754 compliant.
*/
#ifdef CHOLMOD_WINDOWS
/* Yes, this is exceedingly ugly. Blame Microsoft, which hopelessly */
/* violates the IEEE 754 floating-point standard in a bizarre way. */
/* If you're using an IEEE 754-compliant compiler, then x != x is true */
/* iff x is NaN. For Microsoft, (x < x) is true iff x is NaN. */
/* So either way, this macro safely detects a NaN. */
#define CHOLMOD_IS_NAN(x) (((x) != (x)) || (((x) < (x))))
#define CHOLMOD_IS_ZERO(x) (((x) == 0.) && !CHOLMOD_IS_NAN(x))
#define CHOLMOD_IS_NONZERO(x) (((x) != 0.) || CHOLMOD_IS_NAN(x))
#define CHOLMOD_IS_LT_ZERO(x) (((x) < 0.) && !CHOLMOD_IS_NAN(x))
#define CHOLMOD_IS_GT_ZERO(x) (((x) > 0.) && !CHOLMOD_IS_NAN(x))
#define CHOLMOD_IS_LE_ZERO(x) (((x) <= 0.) && !CHOLMOD_IS_NAN(x))
#else
/* These all work properly, according to the IEEE 754 standard ... except on */
/* a PC with windows. Works fine in Linux on the same PC... */
#define CHOLMOD_IS_NAN(x) ((x) != (x))
#define CHOLMOD_IS_ZERO(x) ((x) == 0.)
#define CHOLMOD_IS_NONZERO(x) ((x) != 0.)
#define CHOLMOD_IS_LT_ZERO(x) ((x) < 0.)
#define CHOLMOD_IS_GT_ZERO(x) ((x) > 0.)
#define CHOLMOD_IS_LE_ZERO(x) ((x) <= 0.)
#endif
#endif