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latmio_dir_connected.cpp
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latmio_dir_connected.cpp
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#include <cmath>
#include "bct.h"
/*
* Returns a latticized graph with equivalent degree sequence to the original
* weighted directed graph, and with preserved connectedness. On average, each
* edge is rewired ITER times. Out-strength is preserved for weighted graphs,
* while in-strength is not.
*/
MATRIX_T* BCT_NAMESPACE::latmio_dir_connected(const MATRIX_T* R, int ITER) {
if (safe_mode) check_status(R, SQUARE | DIRECTED, "latmio_dir_connected");
gsl_rng* rng = get_rng();
// n=length(R);
int n = length(R);
// D=zeros(n);
MATRIX_T* D = zeros(n);
// u=[0 min([mod(1:n-1,n);mod(n-1:-1:1,n)])];
VECTOR_T* seq1 = sequence(1, n - 1);
VECTOR_T* seq2 = sequence(n - 1, -1, 1);
MATRIX_T* seq1_seq2 = concatenate_columns(seq1, seq2);
VECTOR_ID(free)(seq1);
VECTOR_ID(free)(seq2);
VECTOR_T* min_seq1_seq2 = min(seq1_seq2);
MATRIX_ID(free)(seq1_seq2);
VECTOR_T* u = concatenate(0.0, min_seq1_seq2);
VECTOR_ID(free)(min_seq1_seq2);
// for v=1:ceil(n/2)
for (int v = 1; v <= (int)std::ceil((FP_T)n / 2.0); v++) {
// D(n-v+1,:)=u([v+1:n 1:v]);
VECTOR_T* u_indices1 = sequence(v, n - 1);
VECTOR_T* u_indices2 = sequence(0, v - 1);
VECTOR_T* u_indices = concatenate(u_indices1, u_indices2);
VECTOR_ID(free)(u_indices1);
VECTOR_ID(free)(u_indices2);
VECTOR_T* u_idx = ordinal_index(u, u_indices);
VECTOR_ID(free)(u_indices);
MATRIX_ID(set_row)(D, n - v, u_idx);
VECTOR_ID(free)(u_idx);
// D(v,:)=D(n-v+1,n:-1:1);
VECTOR_T* D_rows = VECTOR_ID(alloc)(1);
VECTOR_ID(set)(D_rows, 0, (FP_T)(n - v));
VECTOR_T* D_cols = sequence(n - 1, -1, 0);
MATRIX_T* D_idx = ordinal_index(D, D_rows, D_cols);
VECTOR_ID(free)(D_rows);
VECTOR_ID(free)(D_cols);
VECTOR_T* D_idx_v = to_vector(D_idx);
MATRIX_ID(free)(D_idx);
MATRIX_ID(set_row)(D, v - 1, D_idx_v);
VECTOR_ID(free)(D_idx_v);
}
// [i j]=find(R);
MATRIX_T* find_R = find_ij(R);
VECTOR_ID(view) i = MATRIX_ID(column)(find_R, 0);
VECTOR_ID(view) j = MATRIX_ID(column)(find_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 ~(R(a,d) || R(c,b))
if (fp_zero(MATRIX_ID(get)(_R, a, d)) && fp_zero(MATRIX_ID(get)(_R, c, b))) {
// if (D(a,b)+D(c,d))>=(D(a,d)+D(c,b))
if (fp_greater_or_equal(MATRIX_ID(get)(D, a, b) + MATRIX_ID(get)(D, c, d),
MATRIX_ID(get)(D, a, d) + MATRIX_ID(get)(D, c, b))) {
// if ~(any([R(a,c) R(d,b) R(d,c)]) && any([R(c,a) R(b,d) R(b,a)]))
VECTOR_T* _R_idx_1 = VECTOR_ID(alloc)(3);
VECTOR_ID(set)(_R_idx_1, 0, MATRIX_ID(get)(_R, a, c));
VECTOR_ID(set)(_R_idx_1, 1, MATRIX_ID(get)(_R, d, b));
VECTOR_ID(set)(_R_idx_1, 2, MATRIX_ID(get)(_R, d, c));
VECTOR_T* _R_idx_2 = VECTOR_ID(alloc)(3);
VECTOR_ID(set)(_R_idx_2, 0, MATRIX_ID(get)(_R, c, a));
VECTOR_ID(set)(_R_idx_2, 1, MATRIX_ID(get)(_R, b, d));
VECTOR_ID(set)(_R_idx_2, 2, MATRIX_ID(get)(_R, b, a));
bool any_R_idx_1_and_any_R_idx_2 = any(_R_idx_1) && any(_R_idx_2);
VECTOR_ID(free)(_R_idx_1);
VECTOR_ID(free)(_R_idx_2);
if (!any_R_idx_1_and_any_R_idx_2) {
// P=R([a c],:);
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)c);
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(1,d)=1;
MATRIX_ID(set)(P, 0, b, 0.0);
MATRIX_ID(set)(P, 0, d, 1.0);
// P(2,d)=0; P(2,b)=1;
MATRIX_ID(set)(P, 1, d, 0.0);
MATRIX_ID(set)(P, 1, b, 1.0);
// PN=P;
MATRIX_T* PN = copy(P);
// PN(1,a)=1; PN(2,c)=1;
MATRIX_ID(set)(PN, 0, a, 1.0);
MATRIX_ID(set)(PN, 1, c, 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);
// PN=PN+P
MATRIX_ID(add)(PN, P);
// 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(PN(1,[b c])) && any(PN(2,[d a]))
VECTOR_T* PN_idx_1 = VECTOR_ID(alloc)(2);
VECTOR_ID(set)(PN_idx_1, 0, MATRIX_ID(get)(PN, 0, b));
VECTOR_ID(set)(PN_idx_1, 1, MATRIX_ID(get)(PN, 0, c));
VECTOR_T* PN_idx_2 = VECTOR_ID(alloc)(2);
VECTOR_ID(set)(PN_idx_2, 0, MATRIX_ID(get)(PN, 1, d));
VECTOR_ID(set)(PN_idx_2, 1, MATRIX_ID(get)(PN, 1, a));
bool any_PN_idx_1_and_any_PN_idx_2 = any(PN_idx_1) && any(PN_idx_2);
VECTOR_ID(free)(PN_idx_1);
VECTOR_ID(free)(PN_idx_2);
if (any_PN_idx_1_and_any_PN_idx_2) {
// break
break;
}
}
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(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);
// 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)(D);
MATRIX_ID(free)(find_R);
return _R;
}