# include <stdlib.h>
# include <limits.h>
# include <math.h>
# include <stdio.h>
# include "csparse.h"
cs *cs_add ( const cs *A, const cs *B, double alpha, double beta )
/*
Purpose:
CS_ADD computes C = alpha*A + beta*B for sparse A and B.
Reference:
Timothy Davis,
Direct Methods for Sparse Linear Systems,
SIAM, Philadelphia, 2006.
*/
{
int p, j, nz = 0, anz, *Cp, *Ci, *Bp, m, n, bnz, *w, values ;
double *x, *Bx, *Cx ;
cs *C ;
if (!A || !B) return (NULL) ; /* check inputs */
m = A->m ; anz = A->p [A->n] ;
n = B->n ; Bp = B->p ; Bx = B->x ; bnz = Bp [n] ;
w = cs_calloc (m, sizeof (int)) ;
values = (A->x != NULL) && (Bx != NULL) ;
x = values ? cs_malloc (m, sizeof (double)) : NULL ;
C = cs_spalloc (m, n, anz + bnz, values, 0) ;
if (!C || !w || (values && !x)) return (cs_done (C, w, x, 0)) ;
Cp = C->p ; Ci = C->i ; Cx = C->x ;
for (j = 0 ; j < n ; j++)
{
Cp [j] = nz ; /* column j of C starts here */
nz = cs_scatter (A, j, alpha, w, x, j+1, C, nz) ; /* alpha*A(:,j)*/
nz = cs_scatter (B, j, beta, w, x, j+1, C, nz) ; /* beta*B(:,j) */
if (values) for (p = Cp [j] ; p < nz ; p++) Cx [p] = x [Ci [p]] ;
}
Cp [n] = nz ; /* finalize the last column of C */
cs_sprealloc (C, 0) ; /* remove extra space from C */
return (cs_done (C, w, x, 1)) ; /* success; free workspace, return C */
}
static int cs_wclear (int mark, int lemax, int *w, int n)
/*
Purpose:
CS_WCLEAR clears W.
Reference:
Timothy Davis,
Direct Methods for Sparse Linear Systems,
SIAM, Philadelphia, 2006.
*/
{
int k ;
if (mark < 2 || (mark + lemax < 0))
{
for (k = 0 ; k < n ; k++) if (w [k] != 0) w [k] = 1 ;
mark = 2 ;
}
return (mark) ; /* at this point, w [0..n-1] < mark holds */
}
/* keep off-diagonal entries; drop diagonal entries */
static int cs_diag (int i, int j, double aij, void *other)
{
return (i != j);
}
/* p = amd(A+A') if symmetric is true, or amd(A'A) otherwise */
int *cs_amd ( const cs *A, int order )
/*
Purpose:
CS_AMD carries out the approximate minimum degree algorithm.
Reference:
Timothy Davis,
Direct Methods for Sparse Linear Systems,
SIAM, Philadelphia, 2006.
Parameters:
Input, int ORDER:
-1:natural,
0:Cholesky,
1:LU,
2:QR
*/
{
cs *C, *A2, *AT ;
int *Cp, *Ci, *last, *ww, *len, *nv, *next, *P, *head, *elen, *degree, *w,
*hhead, *ATp, *ATi, d, dk, dext, lemax = 0, e, elenk, eln, i, j, k, k1,
k2, k3, jlast, ln, dense, nzmax, mindeg = 0, nvi, nvj, nvk, mark, wnvi,
ok, cnz, nel = 0, p, p1, p2, p3, p4, pj, pk, pk1, pk2, pn, q, n, m ;
unsigned int h ;
/* --- Construct matrix C ----------------------------------------------- */
if (!A || order < 0) return (NULL) ; /* check inputs; quick return */
AT = cs_transpose (A, 0) ; /* compute A' */
if (!AT) return (NULL) ;
m = A->m ; n = A->n ;
dense = CS_MAX (16, 10 * sqrt ((double) n)) ; /* find dense threshold */
dense = CS_MIN (n-2, dense) ;
if (order == 0 && n == m)
{
C = cs_add (A, AT, 0, 0) ; /* C = A+A' */
}
else if (order == 1)
{
ATp = AT->p ; /* drop dense columns from AT */
ATi = AT->i ;
for (p2 = 0, j = 0 ; j < m ; j++)
{
p = ATp [j] ; /* column j of AT starts here */
ATp [j] = p2 ; /* new column j starts here */
if (ATp [j+1] - p > dense) continue ; /* skip dense col j */
for ( ; p < ATp [j+1] ; p++) ATi [p2++] = ATi [p] ;
}
ATp [m] = p2 ; /* finalize AT */
A2 = cs_transpose (AT, 0) ; /* A2 = AT' */
C = A2 ? cs_multiply (AT, A2) : NULL ; /* C=A'*A with no dense rows */
cs_spfree (A2) ;
}
else
{
C = cs_multiply (AT, A) ; /* C=A'*A */
}
cs_spfree (AT) ;
if (!C) return (NULL) ;
P = cs_malloc (n+1, sizeof (int)) ; /* allocate result */
ww = cs_malloc (8*(n+1), sizeof (int)) ;/* get workspace */
len = ww ; nv = ww + (n+1) ; next = ww + 2*(n+1) ;
head = ww + 3*(n+1) ; elen = ww + 4*(n+1) ; degree = ww + 5*(n+1) ;
w = ww + 6*(n+1) ; hhead = ww + 7*(n+1) ;
last = P ; /* use P as workspace for last */
cs_fkeep (C, &cs_diag, NULL) ; /* drop diagonal entries */
Cp = C->p ;
cnz = Cp [n] ;
if (!cs_sprealloc (C, cnz+cnz/5+2*n)) return (cs_idone (P, C, ww, 0)) ;
/* --- Initialize quotient graph ---------------------------------------- */
for (k = 0 ; k < n ; k++) len [k] = Cp [k+1] - Cp [k] ;
len [n] = 0 ;
nzmax = C->nzmax ;
Ci = C->i ;
for (i = 0 ; i <= n ; i++)
{
head [i] = -1 ; /* degree list i is empty */
last [i] = -1 ;
next [i] = -1 ;
hhead [i] = -1 ; /* hash list i is empty */
nv [i] = 1 ; /* node i is just one node */
w [i] = 1 ; /* node i is alive */
elen [i] = 0 ; /* Ek of node i is empty */
degree [i] = len [i] ; /* degree of node i */
}
mark = cs_wclear (0, 0, w, n) ; /* clear w */
elen [n] = -2 ; /* n is a dead element */
Cp [n] = -1 ; /* n is a root of assembly tree */
w [n] = 0 ; /* n is a dead element */
/* --- Initialize degree lists ------------------------------------------ */
for (i = 0 ; i < n ; i++)
{
d = degree [i] ;
if (d == 0) /* node i is empty */
{
elen [i] = -2 ; /* element i is dead */
nel++ ;
Cp [i] = -1 ; /* i is a root of assemby tree */
w [i] = 0 ;
}
else if (d > dense) /* node i is dense */
{
nv [i] = 0 ; /* absorb i into element n */
elen [i] = -1 ; /* node i is dead */
nel++ ;
Cp [i] = CS_FLIP (n) ;
nv [n]++ ;
}
else
{
if (head [d] != -1) last [head [d]] = i ;
next [i] = head [d] ; /* put node i in degree list d */
head [d] = i ;
}
}
while (nel < n) /* while (selecting pivots) do */
{
/* --- Select node of minimum approximate degree -------------------- */
for (k = -1 ; mindeg < n && (k = head [mindeg]) == -1 ; mindeg++) ;
if (next [k] != -1) last [next [k]] = -1 ;
head [mindeg] = next [k] ; /* remove k from degree list */
elenk = elen [k] ; /* elenk = |Ek| */
nvk = nv [k] ; /* # of nodes k represents */
nel += nvk ; /* nv[k] nodes of A eliminated */
/* --- Garbage collection ------------------------------------------- */
if (elenk > 0 && cnz + mindeg >= nzmax)
{
for (j = 0 ; j < n ; j++)
{
if ((p = Cp [j]) >= 0) /* j is a live node or element */
{
Cp [j] = Ci [p] ; /* save first entry of object */
Ci [p] = CS_FLIP (j) ; /* first entry is now CS_FLIP(j) */
}
}
for (q = 0, p = 0 ; p < cnz ; ) /* scan all of memory */
{
if ((j = CS_FLIP (Ci [p++])) >= 0) /* found object j */
{
Ci [q] = Cp [j] ; /* restore first entry of object */
Cp [j] = q++ ; /* new pointer to object j */
for (k3 = 0 ; k3 < len [j]-1 ; k3++) Ci [q++] = Ci [p++] ;
}
}
cnz = q ; /* Ci [cnz...nzmax-1] now free */
}
/* --- Construct new element ---------------------------------------- */
dk = 0 ;
nv [k] = -nvk ; /* flag k as in Lk */
p = Cp [k] ;
pk1 = (elenk == 0) ? p : cnz ; /* do in place if elen[k] == 0 */
pk2 = pk1 ;
for (k1 = 1 ; k1 <= elenk + 1 ; k1++)
{
if (k1 > elenk)
{
e = k ; /* search the nodes in k */
pj = p ; /* list of nodes starts at Ci[pj]*/
ln = len [k] - elenk ; /* length of list of nodes in k */
}
else
{
e = Ci [p++] ; /* search the nodes in e */
pj = Cp [e] ;
ln = len [e] ; /* length of list of nodes in e */
}
for (k2 = 1 ; k2 <= ln ; k2++)
{
i = Ci [pj++] ;
if ((nvi = nv [i]) <= 0) continue ; /* node i dead, or seen */
dk += nvi ; /* degree[Lk] += size of node i */
nv [i] = -nvi ; /* negate nv[i] to denote i in Lk*/
Ci [pk2++] = i ; /* place i in Lk */
if (next [i] != -1) last [next [i]] =