/*
void MH_CondDegreeHexad
Select three edges A1->A2, B1->B2, C1->C2 at random and rotate them to
A1->B2, B1->C2, and C1->A2.
Note that while all the *1s need to be distinct and all the *2s
need to be distinct and all dyads to be created must be empty and
meaningful (i.e. not loops), it's OK if A1=C2, B1=A2, and/or
C1=B2. Indeed, "reversing" the cyclical triangle is the one
operation that tetradic toggles can't accomplish.
Note that this must *never* be called for undirected networks.
*/
void MH_CondDegreeHexad(MHproposal *MHp, Network *nwp) {
Vertex A1, A2, B1, B2, C1, C2;
if(MHp->ntoggles == 0) { /* Initialize */
MHp->ntoggles=6;
return;
}
GetRandEdge(&A1, &A2, nwp);
do{
GetRandEdge(&B1, &B2, nwp);
}while(B1==A1 || B2==A1 || B2==A2 || EdgetreeSearch(A1, B2, nwp->outedges));
do{
GetRandEdge(&C1, &C2, nwp);
}while(C1==A1 || C1==B1 || C1==A2 || C2==A2 || C2==B2 || C2==B1 || EdgetreeSearch(B1, C2, nwp->outedges) || EdgetreeSearch(C1, A2, nwp->outedges));
Mtail[0]=A1; Mhead[0]=A2;
Mtail[1]=A1; Mhead[1]=B2;
Mtail[2]=B1; Mhead[2]=B2;
Mtail[3]=B1; Mhead[3]=C2;
Mtail[4]=C1; Mhead[4]=C2;
Mtail[5]=C1; Mhead[5]=A2;
}
/*****************
Edge DesignMissing (see EdgetreeSearch)
*****************/
Edge DesignMissing (Vertex a, Vertex b, Network *mnwp) {
int miss;
miss = EdgetreeSearch(a,b,mnwp->outedges);
if(mnwp->directed_flag){
miss += EdgetreeSearch(a,b,mnwp->inedges);
}
return(miss);
}
int GetRandNonedge(Vertex *tail, Vertex *head, Network *nwp) {
Edge ndyads = DYADCOUNT(nwp->nnodes, nwp->bipartite, nwp->directed_flag);
if(ndyads-nwp->nedges==0) return(0);
/* There are two ways to get a random nonedge: 1) keep trying dyads
at random until you find one that's not an edge or 2) generate i
at random and find ith nonedge. Method 1 works better in sparse
networks, while Method 2, which runs in deterministic time, works
better in dense networks.
The expected number of attempts for Method 1 is 1/(1-e/d) =
d/(d-e), where e is the number of edges and d is the number of
dyads.
*/
// FIXME: The constant maxEattempts needs to be tuned.
const unsigned int maxEattempts=10;
unsigned int Eattempts = ndyads/(ndyads-nwp->nedges);
Edge rane;
if(Eattempts>maxEattempts){
// If the network is too dense, use the deterministic-time method:
rane=1 + unif_rand() * (ndyads-nwp->nedges);
FindithNonedge(tail, head, rane, nwp);
}else{
do{
GetRandDyad(tail, head, nwp);
}while(EdgetreeSearch(*tail, *head, nwp->outedges));
}
return 1;
}
int AddEdgeToTrees(Vertex head, Vertex tail, Gptr g){
if (EdgetreeSearch(head, tail, g.outedges) == 0) {
AddHalfedgeToTree(head, tail, g.outedges, g.next_outedge);
AddHalfedgeToTree(tail, head, g.inedges, g.next_inedge);
++g.outdegree[head];
++g.indegree[tail];
++(*g.n_edges);
return 1;
}
return 0;
}
int AddEdgeToTrees(Vertex tail, Vertex head, Network *nwp){
if (EdgetreeSearch(tail, head, nwp->outedges) == 0) {
AddHalfedgeToTree(tail, head, nwp->outedges, &(nwp->last_outedge));
AddHalfedgeToTree(head, tail, nwp->inedges, &(nwp->last_inedge));
++nwp->outdegree[tail];
++nwp->indegree[head];
++nwp->nedges;
CheckEdgetreeFull(nwp);
return 1;
}
return 0;
}
/********************
void MH_BipartiteHammingTNT
Tie/no tie: Gives at least 50% chance of
proposing a toggle of an existing edge, as opposed
to simple random toggles that rarely do so in sparse
networks
MSH: The name Hamming is a hack for the Hamming proposals
It is no different the MH_BipartiteTNT
***********************/
void MH_BipartiteHammingTNT (MHproposal *MHp, Network *nwp)
{
/* *** don't forget, edges are (tail, head) now */
Vertex tail, head;
Edge nddyads=nwp[1].nedges;
int nd, nc;
static double comp=0.5;
static double odds;
static Dyad ndyads;
static Edge nnodes;
static Edge nb1;
if(MHp->ntoggles == 0) { /* Initialize */
MHp->ntoggles=1;
odds = comp/(1.0-comp);
nnodes = nwp[0].nnodes;
nb1 = nwp[0].bipartite;
ndyads = DYADCOUNT(nnodes, nb1, 0);
return;
}
if (unif_rand() < comp && nddyads > 0) { /* Select a discordant dyad at random */
GetRandEdge(Mtail, Mhead, &nwp[1]);
nd = nddyads;
nc = ndyads-nd;
/* Fixme! Not sure whether the ratio is calculated correctly here.
Check out the similar ratio calculations for other TNT proposals. */
MHp->logratio += log((nd*1.0) / (odds*(nc+1)));
/* MHp->ratio = (1.0*(nce-1)*(ncn-1)) / (nde*ndn*odds); */
/* MHp->ratio = 1.0; */
/* Rprintf("disconcord nd %d nc %d nddyads %d MHp->ratio %f\n", */
/* nd, nc, nddyads, MHp->ratio); */
}else{
/* select a concordant dyad at random */
do{
tail = 1 + unif_rand() * nb1;
head = 1 + nb1 + unif_rand() * (nnodes - nb1);
}while(EdgetreeSearch(tail,head,nwp[1].outedges)!=0);
Mtail[0]=tail;
Mhead[0]=head;
nd = nddyads;
nc = ndyads-nd;
/* Fixme! Not sure whether the ratio is calculated correctly here.
Check out the similar ratio calculations for other TNT proposals. */
MHp->logratio += log((odds*nc) / ((nd+1)*1.0));
/* Rprintf("concord nd %d nc %d nddyads %d MHp->ratio %f\n", */
/* nd, nc, nddyads, MHp->ratio); */
}
/* Rprintf("h0 %d t0 %d h1 %d t1 %d\n", Mtail[0], Mhead[0], */
/* Mtail[1], Mhead[1]); */
}
/*****************
int DeleteHalfedgeFromTree
Delete the TreeNode with value b from the tree rooted at edges[a].
Return 0 if no such TreeNode exists, 1 otherwise. Also update the
value of *last_edge appropriately.
*****************/
int DeleteHalfedgeFromTree(Vertex a, Vertex b, TreeNode *edges,
Edge *last_edge){
Edge x, z, root=(Edge)a;
TreeNode *xptr, *zptr, *ptr;
if ((z=EdgetreeSearch(a, b, edges))==0) /* z is the current TreeNode. */
return 0; /* This edge doesn't exist, so return 0 */
/* First, determine which node to splice out; this is z. If the current
z has two children, then we'll actually splice out its successor. */
if ((zptr=edges+z)->left != 0 && zptr->right != 0) {
if(unif_rand()<0.5)
z=EdgetreeSuccessor(edges, z);
else
z=EdgetreePredecessor(edges, z);
zptr->value = (ptr=edges+z)->value;
zptr=ptr;
}
/* Set x to the child of z (there is at most one). */
if ((x=zptr->left) == 0)
x = zptr->right;
/* Splice out node z */
if (z == root) {
zptr->value = (xptr=edges+x)->value;
if (x != 0) {
if ((zptr->left=xptr->left) != 0)
(edges+zptr->left)->parent = z;
if ((zptr->right=xptr->right) != 0)
(edges+zptr->right)->parent = z;
zptr=edges+(z=x);
} else
return 1;
} else {
if (x != 0)
(xptr=edges+x)->parent = zptr->parent;
if (z==(ptr=(edges+zptr->parent))->left)
ptr->left = x;
else
ptr->right = x;
}
/* Clear z node, update *last_edge if necessary. */
zptr->value=0;
if(z!=root){
RelocateHalfedge(*last_edge,z,edges);
(*last_edge)--;
}
return 1;
}
void MH_CondB2Degree(MHproposal *MHp, Network *nwp) {
Vertex A1, A2, B1;
if(MHp->ntoggles == 0) { /* Initialize */
MHp->ntoggles=2;
return;
}
do{
GetRandEdge(&A1, &A2, nwp);
B1 = 1 + unif_rand() * nwp->bipartite;
}while(A1==B1 || A2==B1 || EdgetreeSearch(B1, A2, nwp->outedges));
//Rprintf("A1 %d A2 %d B1 %d B2 %d\n",A1,A2,B1,B2);
//Rprintf("in A1 %d A2 %d B1 %d B2 %d\n",A1,A2,B1,B2);
Mtail[0]=A1; Mhead[0]=A2;
Mtail[1]=B1; Mhead[1]=A2;
}
/********************
void MH_BipartiteHammingConstantEdges
Chooses a pair of toggles - one a tie and one not.
MSH: The name Hamming is a hack for the Hamming proposals
It is no different the MH_BipartiteConstantEdges
***********************/
void MH_BipartiteHammingConstantEdges (MHproposal *MHp, Network *nwp)
{
/* *** don't forget, edges are (tail, head) now */
Vertex tail, head;
Edge nedges=nwp[0].nedges, nddyads=nwp[1].nedges;
int nde, ndn, nce, ncn;
static double comp=0.5;
static double odds;
static Dyad ndyads;
static Edge nnodes;
static Edge nb1;
if(MHp->ntoggles == 0) { /* Initialize */
MHp->ntoggles=2;
odds = comp/(1.0-comp);
nnodes = nwp[0].nnodes;
nb1 = nwp[0].bipartite;
ndyads = DYADCOUNT(nnodes, nb1, 0);
return;
}
if (unif_rand() < comp && nddyads > 0) { /* Select a discordant pair of tie/nontie at random */
/* First, select discord edge at random */
do{
GetRandEdge(Mtail, Mhead, &nwp[1]);
}while(EdgetreeSearch(Mtail[0], Mhead[0], nwp[0].outedges) == 0);
tail=Mtail[0];
head=Mhead[0];
/* Next, select discord non-edge at random */
/* *** don't forget, edges are (tail, head) now */
do{
GetRandEdge(Mtail, Mhead, &nwp[1]);
}while(EdgetreeSearch(Mtail[0], Mhead[0], nwp[0].outedges) != 0);
Mtail[1]=Mtail[0];
Mhead[1]=Mhead[0];
Mtail[0]=tail;
Mhead[0]=head;
nde = nddyads / 2;
ndn = nddyads / 2;
nce = nedges-nde;
ncn = ndyads-nedges-ndn;
/* MHp->ratio = (nddyads*nddyads) / (odds*(nnodes-nddyads-2)*(nnodes-nddyads-2)); */
MHp->logratio += log((nde*ndn*1.0) / (odds*(nce+1)*(ncn+1)));
/* MHp->ratio = (1.0*(nce-1)*(ncn-1)) / (nde*ndn*odds); */
/* MHp->ratio = 1.0; */
/* Rprintf("disconcord nde %d nce %d ndn %d ncn %d nddyads %d MHp->ratio %f\n", */
/* nde, nce, ndn,ncn,nddyads, MHp->ratio); */
}else{
/* First, select concordant edge at random */
do{
GetRandEdge(Mtail, Mhead, &nwp[0]);
}while(EdgetreeSearch(Mtail[0], Mhead[0], nwp[1].outedges) == 0);
/* Next, select concord non-edge at random */
do{
tail = 1 + unif_rand() * nb1;
head = 1 + nb1 + unif_rand() * (nnodes - nb1);
}while((EdgetreeSearch(tail,head,nwp[0].outedges)!=0) ||
(EdgetreeSearch(tail,head,nwp[1].outedges)!=0));
Mtail[1]=tail;
Mhead[1]=head;
nde = nddyads / 2;
ndn = nddyads / 2;
nce = nedges-nde;
ncn = ndyads-nedges-ndn;
/* MHp->ratio = ((nnodes-nddyads)*(nnodes-nddyads)) / (odds*(nddyads+2)*(nddyads+2)); */
if(nddyads > 4){
MHp->logratio += log((odds*nce*ncn) / ((nde+1)*(ndn+1)*1.0));
/* MHp->ratio = ((nde+1)*(ndn+1)*odds) / (1.0*nce*ncn); */
}else{
MHp->logratio += 100000000.0;
}
/* Rprintf("concord nde %d nce %d ndn %d ncn %d nddyads %d MHp->ratio %f\n", */
/* nde, nce, ndn,ncn,nddyads, MHp->ratio); */
}
/* Rprintf("h0 %d t0 %d h1 %d t1 %d\n", Mtail[0], Mhead[0], */
/* Mtail[1], Mhead[1]); */
}
/*********************
void MH_BipartiteCondDegreeDist
Pick three nodes -- tail, head, alter -- such that
* tail shares an edge with head
* tail does not share an edge with A
* deg(head) = deg(A) + 1
Then, propose swapping the (tail,head) edge for a (tail,A) edge so that
deg(tail) stays the same while deg(head) and deg(A) swap
with one another.
*********************/
void MH_BipartiteCondDegreeDist (MHproposal *MHp, Network *nwp) {
int valid, count;
Edge e;
Vertex tail, head, A, tailin, tailout, headdeg, Adeg, minA, maxA, i, k;
double u;
TreeNode *tail_edges;
Vertex *headA_degrees;
/* *** don't forget, edges are (tail, head) now */
if(MHp->ntoggles == 0) { /* Initialize */
MHp->ntoggles=2;
return;
}
MHp->logratio += 0; /* By symmetry: P(choosing tail,head,A) must equal */
/* P(choosing tail,A,head after head and A swap roles), */
/* which makes the ratio equal to 1. */
for(valid = count = 0; valid == 0 && count<MAX_TRIES/10; count++) {
tailin = tailout = 0;
/* choose a node at random; ensure it has some edges */
while (tailin + tailout == 0) {
u = unif_rand();
if (u < .5) { /* Pick "male" and "female" nodes with equal prob */
tail = 1 + unif_rand() * nwp->bipartite;
} else {
tail = 1 + nwp->bipartite + unif_rand() * (nwp->nnodes - nwp->bipartite);
}
tailin = nwp->indegree[tail];
tailout = nwp->outdegree[tail];
}
/* select an edge to/from tail at random */
k = (int)(unif_rand() * (tailout + tailin));
if (k < tailout) { /* we chose an outedge */
tail_edges = nwp->outedges;
i = k;
headA_degrees = nwp->indegree;
} else { /* we chose an inedge */
tail_edges = nwp->inedges;
i = k - tailout;
headA_degrees = nwp->outdegree;
}
/* Find ith edge in correct edgetree for tail; this will be (tail,head) or (head,tail) */
e=EdgetreeMinimum(tail_edges, tail);
while (i-- > 0) {
e=EdgetreeSuccessor(tail_edges, e);
}
head = tail_edges[e].value;
headdeg = nwp->directed_flag ? headA_degrees[head] : nwp->indegree[head] + nwp->outdegree[head];
/* Now choose alter at random */
/* Now search for eligible alters */
minA = (u<.5) ? 1 + nwp->bipartite : 1 ;
maxA = (u<.5) ? nwp->nnodes : nwp->bipartite;
i=0;
for (A=minA; A<=maxA; A++) {
Adeg = nwp->directed_flag ? headA_degrees[A] : nwp->indegree[A] + nwp->outdegree[A];
/* To be a valid choice, alter (A) must not be tied to tail and it must have */
/* a degree one less than the head */
if (headdeg == Adeg + 1 && EdgetreeSearch(tail, A, tail_edges) == 0) {
if (nwp->directed_flag || EdgetreeSearch(A, tail, tail_edges) ==0) {
i++;
}
}
} /* After for-loop, i is # of eligible alters. */
if (i>0) {
valid = 1;
i = 1 + unif_rand()*i; /* Pick an eligible alter at random */
for (A=minA; i>0; A++) {
Adeg = nwp->directed_flag ? headA_degrees[A] : nwp->indegree[A] + nwp->outdegree[A];
/* To be a valid choice, alter (A) must not be tied to tail and it must have */
/* a degree one less than the head */
if (headdeg == Adeg + 1 && EdgetreeSearch(tail, A, tail_edges) == 0) {
if (nwp->directed_flag || EdgetreeSearch(A, tail, tail_edges) ==0) {
i--; /* By counting down, when i==0 we have the selected A. */
}
}
}
}
}
if ( (!nwp->directed_flag && tail > head) ||
(nwp->directed_flag && k < tailout) )
{
Mtail[0] = head;
Mhead[0] = tail;
}else{
Mtail[0] = tail;
Mhead[0] = head;
}
if(!valid) {
Mtail[1] = Mtail[0];
Mhead[1] = Mtail[0];
} else {
if ( (!nwp->directed_flag && tail > A) ||
(nwp->directed_flag && k < tailout) )
{
Mtail[0] = A;
Mhead[0] = tail;
}else{
Mtail[0] = tail;
Mhead[0] = A;
}
}
}