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randmio_und_connected.cpp
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#include "bct.h"
/*
* Returns a randomized graph with equivalent degree sequence to the original
* weighted undirected graph, and with preserved connectedness. On average,
* each edge is rewired ITER times. Strength distributions are not preserved
* for weighted graphs.
*/
MATRIX_T* BCT_NAMESPACE::randmio_und_connected(const MATRIX_T* R, int ITER) {
if (safe_mode) check_status(R, SQUARE | UNDIRECTED, "randmio_und_connected");
gsl_rng* rng = get_rng();
// [i j]=find(tril(R));
MATRIX_T* tril_R = tril(R);
MATRIX_T* find_tril_R = find_ij(tril_R);
MATRIX_ID(free)(tril_R);
VECTOR_ID(view) i = MATRIX_ID(column)(find_tril_R, 0);
VECTOR_ID(view) j = MATRIX_ID(column)(find_tril_R, 1);
// K=length(i);
int K = length(&i.vector);
// ITER=K*ITER;
ITER = K * ITER;
MATRIX_T* _R = copy(R);
// for iter=1:ITER
for (int iter = 1; iter <= ITER; iter++) {
// while 1
while (true) {
// rewire = 1
bool rewire = true;
int e1, e2;
int a, b, c, d;
// while 1
while (true) {
// e1=ceil(K*rand);
e1 = gsl_rng_uniform_int(rng, K);
// e2=ceil(K*rand);
e2 = gsl_rng_uniform_int(rng, K);
// while (e2==e1),
while (e2 == e1) {
// e2=ceil(K*rand);
e2 = gsl_rng_uniform_int(rng, K);
}
// a=i(e1); b=j(e1);
a = (int)VECTOR_ID(get)(&i.vector, e1);
b = (int)VECTOR_ID(get)(&j.vector, e1);
// c=i(e2); d=j(e2);
c = (int)VECTOR_ID(get)(&i.vector, e2);
d = (int)VECTOR_ID(get)(&j.vector, e2);
// if all(a~=[c d]) && all(b~=[c d]);
if (a != c && a != d && b != c && b != d) {
// break
break;
}
}
// if rand>0.5
if (gsl_rng_uniform(rng) > 0.5) {
// i(e2)=d; j(e2)=c;
VECTOR_ID(set)(&i.vector, e2, (FP_T)d);
VECTOR_ID(set)(&j.vector, e2, (FP_T)c);
// c=i(e2); d=j(e2);
c = (int)VECTOR_ID(get)(&i.vector, e2);
d = (int)VECTOR_ID(get)(&j.vector, e2);
}
// if ~(R(a,d) || R(c,b))
if (fp_zero(MATRIX_ID(get)(_R, a, d)) && fp_zero(MATRIX_ID(get)(_R, c, b))) {
// if ~(R(a,c) || R(b,d))
if (fp_zero(MATRIX_ID(get)(_R, a, c)) && fp_zero(MATRIX_ID(get)(_R, b, d))) {
// P=R([a d],:);
VECTOR_T* _R_rows = VECTOR_ID(alloc)(2);
VECTOR_ID(set)(_R_rows, 0, (FP_T)a);
VECTOR_ID(set)(_R_rows, 1, (FP_T)d);
VECTOR_T* _R_cols = sequence(0, _R->size2 - 1);
MATRIX_T* P = ordinal_index(_R, _R_rows, _R_cols);
VECTOR_ID(free)(_R_rows);
VECTOR_ID(free)(_R_cols);
// P(1,b)=0; P(2,c)=0;
MATRIX_ID(set)(P, 0, b, 0.0);
MATRIX_ID(set)(P, 1, c, 0.0);
// PN=P;
MATRIX_T* PN = copy(P);
// PN(:,d)=1; PN(:,a)=1;
VECTOR_ID(view) PN_col_d = MATRIX_ID(column)(PN, d);
VECTOR_ID(set_all)(&PN_col_d.vector, 1.0);
VECTOR_ID(view) PN_col_a = MATRIX_ID(column)(PN, a);
VECTOR_ID(set_all)(&PN_col_a.vector, 1.0);
// while 1
while (true) {
// P(1,:)=any(R(P(1,:)~=0,:),1);
VECTOR_ID(view) P_row_0 = MATRIX_ID(row)(P, 0);
VECTOR_T* P_row_0_neq_0 = compare_elements(&P_row_0.vector, fp_not_equal, 0.0);
VECTOR_T* _R_cols = sequence(0, _R->size2 - 1);
MATRIX_T* _R_idx = log_ord_index(_R, P_row_0_neq_0, _R_cols);
VECTOR_ID(free)(P_row_0_neq_0);
if (_R_idx != NULL) {
VECTOR_T* any__R_idx = any(_R_idx, 1);
MATRIX_ID(free)(_R_idx);
MATRIX_ID(set_row)(P, 0, any__R_idx);
VECTOR_ID(free)(any__R_idx);
} else {
VECTOR_ID(set_zero)(&P_row_0.vector);
}
// P(2,:)=any(R(P(2,:)~=0,:),1);
VECTOR_ID(view) P_row_1 = MATRIX_ID(row)(P, 0);
VECTOR_T* P_row_1_neq_0 = compare_elements(&P_row_1.vector, fp_not_equal, 0.0);
_R_idx = log_ord_index(_R, P_row_1_neq_0, _R_cols);
VECTOR_ID(free)(P_row_1_neq_0);
VECTOR_ID(free)(_R_cols);
if (_R_idx != NULL) {
VECTOR_T* any__R_idx = any(_R_idx, 1);
MATRIX_ID(free)(_R_idx);
MATRIX_ID(set_row)(P, 1, any__R_idx);
VECTOR_ID(free)(any__R_idx);
} else {
VECTOR_ID(set_zero)(&P_row_1.vector);
}
// P=P.*(~PN);
MATRIX_T* not_PN = logical_not(PN);
MATRIX_ID(mul_elements)(P, not_PN);
MATRIX_ID(free)(not_PN);
// if ~all(any(P,2))
VECTOR_T* any_P = any(P, 2);
bool all_any_P = all(any_P);
VECTOR_ID(free)(any_P);
if (!all_any_P) {
// rewire=0;
rewire = false;
// break
break;
}
// elseif any(any(P(:,[b c])))
VECTOR_ID(view) P_col_b = MATRIX_ID(column)(P, b);
VECTOR_ID(view) P_col_c = MATRIX_ID(column)(P, c);
MATRIX_T* P_idx = concatenate_rows(&P_col_b.vector, &P_col_c.vector);
VECTOR_T* any_P_idx = any(P_idx);
MATRIX_ID(free)(P_idx);
bool any_any_P_idx = any(any_P_idx);
VECTOR_ID(free)(any_P_idx);
if (any_any_P_idx) {
// break
break;
}
// PN=PN+P;
MATRIX_ID(add)(PN, P);
}
MATRIX_ID(free)(P);
MATRIX_ID(free)(PN);
}
// if rewire
if (rewire) {
// R(a,d)=R(a,b); R(a,b)=0;
MATRIX_ID(set)(_R, a, d, MATRIX_ID(get)(_R, a, b));
MATRIX_ID(set)(_R, a, b, 0.0);
// R(d,a)=R(b,a); R(b,a)=0;
MATRIX_ID(set)(_R, d, a, MATRIX_ID(get)(_R, b, a));
MATRIX_ID(set)(_R, b, a, 0.0);
// R(c,b)=R(c,d); R(c,d)=0;
MATRIX_ID(set)(_R, c, b, MATRIX_ID(get)(_R, c, d));
MATRIX_ID(set)(_R, c, d, 0.0);
// R(b,c)=R(d,c); R(d,c)=0;
MATRIX_ID(set)(_R, b, c, MATRIX_ID(get)(_R, d, c));
MATRIX_ID(set)(_R, d, c, 0.0);
// j(e1) = d;
VECTOR_ID(set)(&j.vector, e1, (FP_T)d);
// j(e2) = b;
VECTOR_ID(set)(&j.vector, e2, (FP_T)b);
// break;
break;
}
}
}
}
MATRIX_ID(free)(find_tril_R);
return _R;
}