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authorGeorgey2017-07-05 11:40:43 +0530
committerGeorgey2017-07-05 11:40:43 +0530
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treeb343c0ee5609433c80e0de1db8b6886c9126dc2d /thirdparty/linux/include/coin/amd.h
parent5b72577efe080c5294b32d804e4d26351fef30bc (diff)
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Added linux shared libraries and header files for int and ecos functions
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+/* ========================================================================= */
+/* === AMD: approximate minimum degree ordering =========================== */
+/* ========================================================================= */
+
+/* ------------------------------------------------------------------------- */
+/* AMD Version 2.2, Copyright (c) 2007 by Timothy A. Davis, */
+/* Patrick R. Amestoy, and Iain S. Duff. See ../README.txt for License. */
+/* email: DrTimothyAldenDavis@gmail.com */
+/* ------------------------------------------------------------------------- */
+
+/* AMD finds a symmetric ordering P of a matrix A so that the Cholesky
+ * factorization of P*A*P' has fewer nonzeros and takes less work than the
+ * Cholesky factorization of A. If A is not symmetric, then it performs its
+ * ordering on the matrix A+A'. Two sets of user-callable routines are
+ * provided, one for int integers and the other for SuiteSparse_long integers.
+ *
+ * The method is based on the approximate minimum degree algorithm, discussed
+ * in Amestoy, Davis, and Duff, "An approximate degree ordering algorithm",
+ * SIAM Journal of Matrix Analysis and Applications, vol. 17, no. 4, pp.
+ * 886-905, 1996. This package can perform both the AMD ordering (with
+ * aggressive absorption), and the AMDBAR ordering (without aggressive
+ * absorption) discussed in the above paper. This package differs from the
+ * Fortran codes discussed in the paper:
+ *
+ * (1) it can ignore "dense" rows and columns, leading to faster run times
+ * (2) it computes the ordering of A+A' if A is not symmetric
+ * (3) it is followed by a depth-first post-ordering of the assembly tree
+ * (or supernodal elimination tree)
+ *
+ * For historical reasons, the Fortran versions, amd.f and amdbar.f, have
+ * been left (nearly) unchanged. They compute the identical ordering as
+ * described in the above paper.
+ */
+
+#ifndef AMD_H
+#define AMD_H
+
+/* make it easy for C++ programs to include AMD */
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* get the definition of size_t: */
+#include <stddef.h>
+
+#include "SuiteSparse_config.h"
+
+int amd_order /* returns AMD_OK, AMD_OK_BUT_JUMBLED,
+ * AMD_INVALID, or AMD_OUT_OF_MEMORY */
+(
+ int n, /* A is n-by-n. n must be >= 0. */
+ const int Ap [ ], /* column pointers for A, of size n+1 */
+ const int Ai [ ], /* row indices of A, of size nz = Ap [n] */
+ int P [ ], /* output permutation, of size n */
+ double Control [ ], /* input Control settings, of size AMD_CONTROL */
+ double Info [ ] /* output Info statistics, of size AMD_INFO */
+) ;
+
+SuiteSparse_long amd_l_order /* see above for description of arguments */
+(
+ SuiteSparse_long n,
+ const SuiteSparse_long Ap [ ],
+ const SuiteSparse_long Ai [ ],
+ SuiteSparse_long P [ ],
+ double Control [ ],
+ double Info [ ]
+) ;
+
+/* Input arguments (not modified):
+ *
+ * n: the matrix A is n-by-n.
+ * Ap: an int/SuiteSparse_long array of size n+1, containing column
+ * pointers of A.
+ * Ai: an int/SuiteSparse_long array of size nz, containing the row
+ * indices of A, where nz = Ap [n].
+ * Control: a double array of size AMD_CONTROL, containing control
+ * parameters. Defaults are used if Control is NULL.
+ *
+ * Output arguments (not defined on input):
+ *
+ * P: an int/SuiteSparse_long array of size n, containing the output
+ * permutation. If row i is the kth pivot row, then P [k] = i. In
+ * MATLAB notation, the reordered matrix is A (P,P).
+ * Info: a double array of size AMD_INFO, containing statistical
+ * information. Ignored if Info is NULL.
+ *
+ * On input, the matrix A is stored in column-oriented form. The row indices
+ * of nonzero entries in column j are stored in Ai [Ap [j] ... Ap [j+1]-1].
+ *
+ * If the row indices appear in ascending order in each column, and there
+ * are no duplicate entries, then amd_order is slightly more efficient in
+ * terms of time and memory usage. If this condition does not hold, a copy
+ * of the matrix is created (where these conditions do hold), and the copy is
+ * ordered. This feature is new to v2.0 (v1.2 and earlier required this
+ * condition to hold for the input matrix).
+ *
+ * Row indices must be in the range 0 to
+ * n-1. Ap [0] must be zero, and thus nz = Ap [n] is the number of nonzeros
+ * in A. The array Ap is of size n+1, and the array Ai is of size nz = Ap [n].
+ * The matrix does not need to be symmetric, and the diagonal does not need to
+ * be present (if diagonal entries are present, they are ignored except for
+ * the output statistic Info [AMD_NZDIAG]). The arrays Ai and Ap are not
+ * modified. This form of the Ap and Ai arrays to represent the nonzero
+ * pattern of the matrix A is the same as that used internally by MATLAB.
+ * If you wish to use a more flexible input structure, please see the
+ * umfpack_*_triplet_to_col routines in the UMFPACK package, at
+ * http://www.suitesparse.com.
+ *
+ * Restrictions: n >= 0. Ap [0] = 0. Ap [j] <= Ap [j+1] for all j in the
+ * range 0 to n-1. nz = Ap [n] >= 0. Ai [0..nz-1] must be in the range 0
+ * to n-1. Finally, Ai, Ap, and P must not be NULL. If any of these
+ * restrictions are not met, AMD returns AMD_INVALID.
+ *
+ * AMD returns:
+ *
+ * AMD_OK if the matrix is valid and sufficient memory can be allocated to
+ * perform the ordering.
+ *
+ * AMD_OUT_OF_MEMORY if not enough memory can be allocated.
+ *
+ * AMD_INVALID if the input arguments n, Ap, Ai are invalid, or if P is
+ * NULL.
+ *
+ * AMD_OK_BUT_JUMBLED if the matrix had unsorted columns, and/or duplicate
+ * entries, but was otherwise valid.
+ *
+ * The AMD routine first forms the pattern of the matrix A+A', and then
+ * computes a fill-reducing ordering, P. If P [k] = i, then row/column i of
+ * the original is the kth pivotal row. In MATLAB notation, the permuted
+ * matrix is A (P,P), except that 0-based indexing is used instead of the
+ * 1-based indexing in MATLAB.
+ *
+ * The Control array is used to set various parameters for AMD. If a NULL
+ * pointer is passed, default values are used. The Control array is not
+ * modified.
+ *
+ * Control [AMD_DENSE]: controls the threshold for "dense" rows/columns.
+ * A dense row/column in A+A' can cause AMD to spend a lot of time in
+ * ordering the matrix. If Control [AMD_DENSE] >= 0, rows/columns
+ * with more than Control [AMD_DENSE] * sqrt (n) entries are ignored
+ * during the ordering, and placed last in the output order. The
+ * default value of Control [AMD_DENSE] is 10. If negative, no
+ * rows/columns are treated as "dense". Rows/columns with 16 or
+ * fewer off-diagonal entries are never considered "dense".
+ *
+ * Control [AMD_AGGRESSIVE]: controls whether or not to use aggressive
+ * absorption, in which a prior element is absorbed into the current
+ * element if is a subset of the current element, even if it is not
+ * adjacent to the current pivot element (refer to Amestoy, Davis,
+ * & Duff, 1996, for more details). The default value is nonzero,
+ * which means to perform aggressive absorption. This nearly always
+ * leads to a better ordering (because the approximate degrees are
+ * more accurate) and a lower execution time. There are cases where
+ * it can lead to a slightly worse ordering, however. To turn it off,
+ * set Control [AMD_AGGRESSIVE] to 0.
+ *
+ * Control [2..4] are not used in the current version, but may be used in
+ * future versions.
+ *
+ * The Info array provides statistics about the ordering on output. If it is
+ * not present, the statistics are not returned. This is not an error
+ * condition.
+ *
+ * Info [AMD_STATUS]: the return value of AMD, either AMD_OK,
+ * AMD_OK_BUT_JUMBLED, AMD_OUT_OF_MEMORY, or AMD_INVALID.
+ *
+ * Info [AMD_N]: n, the size of the input matrix
+ *
+ * Info [AMD_NZ]: the number of nonzeros in A, nz = Ap [n]
+ *
+ * Info [AMD_SYMMETRY]: the symmetry of the matrix A. It is the number
+ * of "matched" off-diagonal entries divided by the total number of
+ * off-diagonal entries. An entry A(i,j) is matched if A(j,i) is also
+ * an entry, for any pair (i,j) for which i != j. In MATLAB notation,
+ * S = spones (A) ;
+ * B = tril (S, -1) + triu (S, 1) ;
+ * symmetry = nnz (B & B') / nnz (B) ;
+ *
+ * Info [AMD_NZDIAG]: the number of entries on the diagonal of A.
+ *
+ * Info [AMD_NZ_A_PLUS_AT]: the number of nonzeros in A+A', excluding the
+ * diagonal. If A is perfectly symmetric (Info [AMD_SYMMETRY] = 1)
+ * with a fully nonzero diagonal, then Info [AMD_NZ_A_PLUS_AT] = nz-n
+ * (the smallest possible value). If A is perfectly unsymmetric
+ * (Info [AMD_SYMMETRY] = 0, for an upper triangular matrix, for
+ * example) with no diagonal, then Info [AMD_NZ_A_PLUS_AT] = 2*nz
+ * (the largest possible value).
+ *
+ * Info [AMD_NDENSE]: the number of "dense" rows/columns of A+A' that were
+ * removed from A prior to ordering. These are placed last in the
+ * output order P.
+ *
+ * Info [AMD_MEMORY]: the amount of memory used by AMD, in bytes. In the
+ * current version, this is 1.2 * Info [AMD_NZ_A_PLUS_AT] + 9*n
+ * times the size of an integer. This is at most 2.4nz + 9n. This
+ * excludes the size of the input arguments Ai, Ap, and P, which have
+ * a total size of nz + 2*n + 1 integers.
+ *
+ * Info [AMD_NCMPA]: the number of garbage collections performed.
+ *
+ * Info [AMD_LNZ]: the number of nonzeros in L (excluding the diagonal).
+ * This is a slight upper bound because mass elimination is combined
+ * with the approximate degree update. It is a rough upper bound if
+ * there are many "dense" rows/columns. The rest of the statistics,
+ * below, are also slight or rough upper bounds, for the same reasons.
+ * The post-ordering of the assembly tree might also not exactly
+ * correspond to a true elimination tree postordering.
+ *
+ * Info [AMD_NDIV]: the number of divide operations for a subsequent LDL'
+ * or LU factorization of the permuted matrix A (P,P).
+ *
+ * Info [AMD_NMULTSUBS_LDL]: the number of multiply-subtract pairs for a
+ * subsequent LDL' factorization of A (P,P).
+ *
+ * Info [AMD_NMULTSUBS_LU]: the number of multiply-subtract pairs for a
+ * subsequent LU factorization of A (P,P), assuming that no numerical
+ * pivoting is required.
+ *
+ * Info [AMD_DMAX]: the maximum number of nonzeros in any column of L,
+ * including the diagonal.
+ *
+ * Info [14..19] are not used in the current version, but may be used in
+ * future versions.
+ */
+
+/* ------------------------------------------------------------------------- */
+/* direct interface to AMD */
+/* ------------------------------------------------------------------------- */
+
+/* amd_2 is the primary AMD ordering routine. It is not meant to be
+ * user-callable because of its restrictive inputs and because it destroys
+ * the user's input matrix. It does not check its inputs for errors, either.
+ * However, if you can work with these restrictions it can be faster than
+ * amd_order and use less memory (assuming that you can create your own copy
+ * of the matrix for AMD to destroy). Refer to AMD/Source/amd_2.c for a
+ * description of each parameter. */
+
+void amd_2
+(
+ int n,
+ int Pe [ ],
+ int Iw [ ],
+ int Len [ ],
+ int iwlen,
+ int pfree,
+ int Nv [ ],
+ int Next [ ],
+ int Last [ ],
+ int Head [ ],
+ int Elen [ ],
+ int Degree [ ],
+ int W [ ],
+ double Control [ ],
+ double Info [ ]
+) ;
+
+void amd_l2
+(
+ SuiteSparse_long n,
+ SuiteSparse_long Pe [ ],
+ SuiteSparse_long Iw [ ],
+ SuiteSparse_long Len [ ],
+ SuiteSparse_long iwlen,
+ SuiteSparse_long pfree,
+ SuiteSparse_long Nv [ ],
+ SuiteSparse_long Next [ ],
+ SuiteSparse_long Last [ ],
+ SuiteSparse_long Head [ ],
+ SuiteSparse_long Elen [ ],
+ SuiteSparse_long Degree [ ],
+ SuiteSparse_long W [ ],
+ double Control [ ],
+ double Info [ ]
+) ;
+
+/* ------------------------------------------------------------------------- */
+/* amd_valid */
+/* ------------------------------------------------------------------------- */
+
+/* Returns AMD_OK or AMD_OK_BUT_JUMBLED if the matrix is valid as input to
+ * amd_order; the latter is returned if the matrix has unsorted and/or
+ * duplicate row indices in one or more columns. Returns AMD_INVALID if the
+ * matrix cannot be passed to amd_order. For amd_order, the matrix must also
+ * be square. The first two arguments are the number of rows and the number
+ * of columns of the matrix. For its use in AMD, these must both equal n.
+ *
+ * NOTE: this routine returned TRUE/FALSE in v1.2 and earlier.
+ */
+
+int amd_valid
+(
+ int n_row, /* # of rows */
+ int n_col, /* # of columns */
+ const int Ap [ ], /* column pointers, of size n_col+1 */
+ const int Ai [ ] /* row indices, of size Ap [n_col] */
+) ;
+
+SuiteSparse_long amd_l_valid
+(
+ SuiteSparse_long n_row,
+ SuiteSparse_long n_col,
+ const SuiteSparse_long Ap [ ],
+ const SuiteSparse_long Ai [ ]
+) ;
+
+/* ------------------------------------------------------------------------- */
+/* AMD memory manager and printf routines */
+/* ------------------------------------------------------------------------- */
+
+/* The user can redefine these to change the malloc, free, and printf routines
+ * that AMD uses. */
+
+#ifndef EXTERN
+#define EXTERN extern
+#endif
+
+EXTERN void *(*amd_malloc) (size_t) ; /* pointer to malloc */
+EXTERN void (*amd_free) (void *) ; /* pointer to free */
+EXTERN void *(*amd_realloc) (void *, size_t) ; /* pointer to realloc */
+EXTERN void *(*amd_calloc) (size_t, size_t) ; /* pointer to calloc */
+EXTERN int (*amd_printf) (const char *, ...) ; /* pointer to printf */
+
+/* ------------------------------------------------------------------------- */
+/* AMD Control and Info arrays */
+/* ------------------------------------------------------------------------- */
+
+/* amd_defaults: sets the default control settings */
+void amd_defaults (double Control [ ]) ;
+void amd_l_defaults (double Control [ ]) ;
+
+/* amd_control: prints the control settings */
+void amd_control (double Control [ ]) ;
+void amd_l_control (double Control [ ]) ;
+
+/* amd_info: prints the statistics */
+void amd_info (double Info [ ]) ;
+void amd_l_info (double Info [ ]) ;
+
+#define AMD_CONTROL 5 /* size of Control array */
+#define AMD_INFO 20 /* size of Info array */
+
+/* contents of Control */
+#define AMD_DENSE 0 /* "dense" if degree > Control [0] * sqrt (n) */
+#define AMD_AGGRESSIVE 1 /* do aggressive absorption if Control [1] != 0 */
+
+/* default Control settings */
+#define AMD_DEFAULT_DENSE 10.0 /* default "dense" degree 10*sqrt(n) */
+#define AMD_DEFAULT_AGGRESSIVE 1 /* do aggressive absorption by default */
+
+/* contents of Info */
+#define AMD_STATUS 0 /* return value of amd_order and amd_l_order */
+#define AMD_N 1 /* A is n-by-n */
+#define AMD_NZ 2 /* number of nonzeros in A */
+#define AMD_SYMMETRY 3 /* symmetry of pattern (1 is sym., 0 is unsym.) */
+#define AMD_NZDIAG 4 /* # of entries on diagonal */
+#define AMD_NZ_A_PLUS_AT 5 /* nz in A+A' */
+#define AMD_NDENSE 6 /* number of "dense" rows/columns in A */
+#define AMD_MEMORY 7 /* amount of memory used by AMD */
+#define AMD_NCMPA 8 /* number of garbage collections in AMD */
+#define AMD_LNZ 9 /* approx. nz in L, excluding the diagonal */
+#define AMD_NDIV 10 /* number of fl. point divides for LU and LDL' */
+#define AMD_NMULTSUBS_LDL 11 /* number of fl. point (*,-) pairs for LDL' */
+#define AMD_NMULTSUBS_LU 12 /* number of fl. point (*,-) pairs for LU */
+#define AMD_DMAX 13 /* max nz. in any column of L, incl. diagonal */
+
+/* ------------------------------------------------------------------------- */
+/* return values of AMD */
+/* ------------------------------------------------------------------------- */
+
+#define AMD_OK 0 /* success */
+#define AMD_OUT_OF_MEMORY -1 /* malloc failed, or problem too large */
+#define AMD_INVALID -2 /* input arguments are not valid */
+#define AMD_OK_BUT_JUMBLED 1 /* input matrix is OK for amd_order, but
+ * columns were not sorted, and/or duplicate entries were present. AMD had
+ * to do extra work before ordering the matrix. This is a warning, not an
+ * error. */
+
+/* ========================================================================== */
+/* === AMD version ========================================================== */
+/* ========================================================================== */
+
+/* AMD Version 1.2 and later include the following definitions.
+ * As an example, to test if the version you are using is 1.2 or later:
+ *
+ * #ifdef AMD_VERSION
+ * if (AMD_VERSION >= AMD_VERSION_CODE (1,2)) ...
+ * #endif
+ *
+ * This also works during compile-time:
+ *
+ * #if defined(AMD_VERSION) && (AMD_VERSION >= AMD_VERSION_CODE (1,2))
+ * printf ("This is version 1.2 or later\n") ;
+ * #else
+ * printf ("This is an early version\n") ;
+ * #endif
+ *
+ * Versions 1.1 and earlier of AMD do not include a #define'd version number.
+ */
+
+#define AMD_DATE "Jun 20, 2012"
+#define AMD_VERSION_CODE(main,sub) ((main) * 1000 + (sub))
+#define AMD_MAIN_VERSION 2
+#define AMD_SUB_VERSION 3
+#define AMD_SUBSUB_VERSION 1
+#define AMD_VERSION AMD_VERSION_CODE(AMD_MAIN_VERSION,AMD_SUB_VERSION)
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif