static void NN_chain_core(const t_index N, t_float * const D, t_members * const members, cluster_result & Z2) {
/*
N: integer
D: condensed distance matrix N*(N-1)/2
Z2: output data structure
This is the NN-chain algorithm, described on page 86 in the following book:
Fionn Murtagh, Multidimensional Clustering Algorithms,
Vienna, Würzburg: Physica-Verlag, 1985.
This implementation does not give defined results when NaN or Inf values
are present in the array D.
*/
t_index i;
auto_array_ptr<t_index> NN_chain(N);
t_index NN_chain_tip = 0;
t_index idx1, idx2;
t_float size1, size2;
doubly_linked_list AR(N);
t_float min;
for (t_index j=0; j<N-1; j++) {
if (NN_chain_tip <= 3) {
NN_chain[0] = idx1 = AR.start;
NN_chain_tip = 1;
idx2 = AR.succ[idx1];
min = D_(idx1,idx2);
for (i=AR.succ[idx2]; i<N; i=AR.succ[i]) {
if (D_(idx1,i) < min) {
min = D_(idx1,i);
idx2 = i;
}
}
} // a: idx1 b: idx2
else {
NN_chain_tip -= 3;
idx1 = NN_chain[NN_chain_tip-1];
idx2 = NN_chain[NN_chain_tip];
min = idx1<idx2 ? D_(idx1,idx2) : D_(idx2,idx1);
} // a: idx1 b: idx2
do {
NN_chain[NN_chain_tip] = idx2;
for (i=AR.start; i<idx2; i=AR.succ[i]) {
if (D_(i,idx2) < min) {
min = D_(i,idx2);
idx1 = i;
}
}
for (i=AR.succ[idx2]; i<N; i=AR.succ[i]) {
if (D_(idx2,i) < min) {
min = D_(idx2,i);
idx1 = i;
}
}
idx2 = idx1;
idx1 = NN_chain[NN_chain_tip++];
} while (idx2 != NN_chain[NN_chain_tip-2]);
Z2.append(idx1, idx2, min);
if (idx1>idx2) {
t_index tmp = idx1;
idx1 = idx2;
idx2 = tmp;
}
if (method==METHOD_METR_AVERAGE ||
method==METHOD_METR_WARD) {
size1 = static_cast<t_float>(members[idx1]);
size2 = static_cast<t_float>(members[idx2]);
members[idx2] += members[idx1];
}
// Remove the smaller index from the valid indices (AR).
AR.remove(idx1);
switch (method) {
case METHOD_METR_SINGLE:
/*
Single linkage.
Characteristic: new distances are never longer than the old distances.
*/
// Update the distance matrix in the range [start, idx1).
for (i=AR.start; i<idx1; i=AR.succ[i])
f_single(&D_(i, idx2), D_(i, idx1) );
// Update the distance matrix in the range (idx1, idx2).
for (; i<idx2; i=AR.succ[i])
f_single(&D_(i, idx2), D_(idx1, i) );
// Update the distance matrix in the range (idx2, N).
for (i=AR.succ[idx2]; i<N; i=AR.succ[i])
f_single(&D_(idx2, i), D_(idx1, i) );
break;
case METHOD_METR_COMPLETE:
/*
Complete linkage.
Characteristic: new distances are never shorter than the old distances.
*/
// Update the distance matrix in the range [start, idx1).
for (i=AR.start; i<idx1; i=AR.succ[i])
f_complete(&D_(i, idx2), D_(i, idx1) );
// Update the distance matrix in the range (idx1, idx2).
for (; i<idx2; i=AR.succ[i])
f_complete(&D_(i, idx2), D_(idx1, i) );
// Update the distance matrix in the range (idx2, N).
for (i=AR.succ[idx2]; i<N; i=AR.succ[i])
f_complete(&D_(idx2, i), D_(idx1, i) );
break;
case METHOD_METR_AVERAGE: {
/*
Average linkage.
Shorter and longer distances can occur.
*/
// Update the distance matrix in the range [start, idx1).
t_float s = size1/(size1+size2);
t_float t = size2/(size1+size2);
for (i=AR.start; i<idx1; i=AR.succ[i])
f_average(&D_(i, idx2), D_(i, idx1), s, t );
// Update the distance matrix in the range (idx1, idx2).
for (; i<idx2; i=AR.succ[i])
f_average(&D_(i, idx2), D_(idx1, i), s, t );
// Update the distance matrix in the range (idx2, N).
for (i=AR.succ[idx2]; i<N; i=AR.succ[i])
f_average(&D_(idx2, i), D_(idx1, i), s, t );
break;
}
case METHOD_METR_WEIGHTED:
/*
Weighted linkage.
Shorter and longer distances can occur.
*/
// Update the distance matrix in the range [start, idx1).
for (i=AR.start; i<idx1; i=AR.succ[i])
f_weighted(&D_(i, idx2), D_(i, idx1) );
// Update the distance matrix in the range (idx1, idx2).
for (; i<idx2; i=AR.succ[i])
f_weighted(&D_(i, idx2), D_(idx1, i) );
// Update the distance matrix in the range (idx2, N).
for (i=AR.succ[idx2]; i<N; i=AR.succ[i])
f_weighted(&D_(idx2, i), D_(idx1, i) );
break;
case METHOD_METR_WARD:
/*
Ward linkage.
Shorter and longer distances can occur, not smaller than min(d1,d2)
but maybe bigger than max(d1,d2).
*/
// Update the distance matrix in the range [start, idx1).
//t_float v = static_cast<t_float>(members[i]);
for (i=AR.start; i<idx1; i=AR.succ[i])
f_ward(&D_(i, idx2), D_(i, idx1), min,
size1, size2, static_cast<t_float>(members[i]) );
// Update the distance matrix in the range (idx1, idx2).
for (; i<idx2; i=AR.succ[i])
f_ward(&D_(i, idx2), D_(idx1, i), min,
size1, size2, static_cast<t_float>(members[i]) );
// Update the distance matrix in the range (idx2, N).
for (i=AR.succ[idx2]; i<N; i=AR.succ[i])
f_ward(&D_(idx2, i), D_(idx1, i), min,
size1, size2, static_cast<t_float>(members[i]) );
break;
}
}
}
static void NN_chain_core(const t_index N, t_float * const D, t_members * const members, cluster_result & Z2) {
/*
N: integer
D: condensed distance matrix N*(N-1)/2
Z2: output data structure
This is the NN-chain algorithm, described on page 86 in the following book:
Fionn Murtagh, Multidimensional Clustering Algorithms,
Vienna, Würzburg: Physica-Verlag, 1985.
*/
t_index i;
auto_array_ptr<t_index> NN_chain(N);
t_index NN_chain_tip = 0;
t_index idx1, idx2;
t_float size1, size2;
doubly_linked_list active_nodes(N);
t_float min;
for (t_float const * DD=D; DD!=D+(static_cast<std::ptrdiff_t>(N)*(N-1)>>1);
++DD) {
#if HAVE_DIAGNOSTIC
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wfloat-equal"
#endif
if (fc_isnan(*DD)) {
throw(nan_error());
}
#if HAVE_DIAGNOSTIC
#pragma GCC diagnostic pop
#endif
}
#ifdef FE_INVALID
if (feclearexcept(FE_INVALID)) throw fenv_error();
#endif
for (t_index j=0; j<N-1; ++j) {
if (NN_chain_tip <= 3) {
NN_chain[0] = idx1 = active_nodes.start;
NN_chain_tip = 1;
idx2 = active_nodes.succ[idx1];
min = D_(idx1,idx2);
for (i=active_nodes.succ[idx2]; i<N; i=active_nodes.succ[i]) {
if (D_(idx1,i) < min) {
min = D_(idx1,i);
idx2 = i;
}
}
} // a: idx1 b: idx2
else {
NN_chain_tip -= 3;
idx1 = NN_chain[NN_chain_tip-1];
idx2 = NN_chain[NN_chain_tip];
min = idx1<idx2 ? D_(idx1,idx2) : D_(idx2,idx1);
} // a: idx1 b: idx2
do {
NN_chain[NN_chain_tip] = idx2;
for (i=active_nodes.start; i<idx2; i=active_nodes.succ[i]) {
if (D_(i,idx2) < min) {
min = D_(i,idx2);
idx1 = i;
}
}
for (i=active_nodes.succ[idx2]; i<N; i=active_nodes.succ[i]) {
if (D_(idx2,i) < min) {
min = D_(idx2,i);
idx1 = i;
}
}
idx2 = idx1;
idx1 = NN_chain[NN_chain_tip++];
} while (idx2 != NN_chain[NN_chain_tip-2]);
Z2.append(idx1, idx2, min);
if (idx1>idx2) {
t_index tmp = idx1;
idx1 = idx2;
idx2 = tmp;
}
if (method==METHOD_METR_AVERAGE ||
method==METHOD_METR_WARD) {
size1 = static_cast<t_float>(members[idx1]);
size2 = static_cast<t_float>(members[idx2]);
members[idx2] += members[idx1];
}
// Remove the smaller index from the valid indices (active_nodes).
active_nodes.remove(idx1);
switch (method) {
case METHOD_METR_SINGLE:
/*
Single linkage.
Characteristic: new distances are never longer than the old distances.
*/
// Update the distance matrix in the range [start, idx1).
for (i=active_nodes.start; i<idx1; i=active_nodes.succ[i])
f_single(&D_(i, idx2), D_(i, idx1) );
// Update the distance matrix in the range (idx1, idx2).
for (; i<idx2; i=active_nodes.succ[i])
f_single(&D_(i, idx2), D_(idx1, i) );
// Update the distance matrix in the range (idx2, N).
for (i=active_nodes.succ[idx2]; i<N; i=active_nodes.succ[i])
f_single(&D_(idx2, i), D_(idx1, i) );
break;
case METHOD_METR_COMPLETE:
/*
Complete linkage.
Characteristic: new distances are never shorter than the old distances.
*/
// Update the distance matrix in the range [start, idx1).
for (i=active_nodes.start; i<idx1; i=active_nodes.succ[i])
f_complete(&D_(i, idx2), D_(i, idx1) );
// Update the distance matrix in the range (idx1, idx2).
for (; i<idx2; i=active_nodes.succ[i])
f_complete(&D_(i, idx2), D_(idx1, i) );
// Update the distance matrix in the range (idx2, N).
for (i=active_nodes.succ[idx2]; i<N; i=active_nodes.succ[i])
f_complete(&D_(idx2, i), D_(idx1, i) );
break;
case METHOD_METR_AVERAGE: {
/*
Average linkage.
Shorter and longer distances can occur.
*/
// Update the distance matrix in the range [start, idx1).
t_float s = size1/(size1+size2);
t_float t = size2/(size1+size2);
for (i=active_nodes.start; i<idx1; i=active_nodes.succ[i])
f_average(&D_(i, idx2), D_(i, idx1), s, t );
// Update the distance matrix in the range (idx1, idx2).
for (; i<idx2; i=active_nodes.succ[i])
f_average(&D_(i, idx2), D_(idx1, i), s, t );
// Update the distance matrix in the range (idx2, N).
for (i=active_nodes.succ[idx2]; i<N; i=active_nodes.succ[i])
f_average(&D_(idx2, i), D_(idx1, i), s, t );
break;
}
case METHOD_METR_WEIGHTED:
/*
Weighted linkage.
Shorter and longer distances can occur.
*/
// Update the distance matrix in the range [start, idx1).
for (i=active_nodes.start; i<idx1; i=active_nodes.succ[i])
f_weighted(&D_(i, idx2), D_(i, idx1) );
// Update the distance matrix in the range (idx1, idx2).
for (; i<idx2; i=active_nodes.succ[i])
f_weighted(&D_(i, idx2), D_(idx1, i) );
// Update the distance matrix in the range (idx2, N).
for (i=active_nodes.succ[idx2]; i<N; i=active_nodes.succ[i])
f_weighted(&D_(idx2, i), D_(idx1, i) );
break;
case METHOD_METR_WARD:
/*
Ward linkage.
Shorter and longer distances can occur, not smaller than min(d1,d2)
but maybe bigger than max(d1,d2).
*/
// Update the distance matrix in the range [start, idx1).
//t_float v = static_cast<t_float>(members[i]);
for (i=active_nodes.start; i<idx1; i=active_nodes.succ[i])
f_ward(&D_(i, idx2), D_(i, idx1), min,
size1, size2, static_cast<t_float>(members[i]) );
// Update the distance matrix in the range (idx1, idx2).
for (; i<idx2; i=active_nodes.succ[i])
f_ward(&D_(i, idx2), D_(idx1, i), min,
size1, size2, static_cast<t_float>(members[i]) );
// Update the distance matrix in the range (idx2, N).
for (i=active_nodes.succ[idx2]; i<N; i=active_nodes.succ[i])
f_ward(&D_(idx2, i), D_(idx1, i), min,
size1, size2, static_cast<t_float>(members[i]) );
break;
default:
throw std::runtime_error(std::string("Invalid method."));
}
}
#ifdef FE_INVALID
if (fetestexcept(FE_INVALID)) throw fenv_error();
#endif
}