inline static void f_centroid( t_float * const b, const t_float a, const t_float stc, const t_float s, const t_float t) {
*b = s*a - stc + t*(*b);
#ifndef FE_INVALID
if (fc_isnan(*b)) {
throw(nan_error());
}
#if HAVE_DIAGNOSTIC
#pragma GCC diagnostic pop
#endif
#endif
}
inline static void f_median( t_float * const b, const t_float a, const t_float c_4) {
*b = (a+(*b))*.5 - c_4;
#ifndef FE_INVALID
#if HAVE_DIAGNOSTIC
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wfloat-equal"
#endif
if (fc_isnan(*b)) {
throw(nan_error());
}
#if HAVE_DIAGNOSTIC
#pragma GCC diagnostic pop
#endif
#endif
}
inline static void f_average( t_float * const b, const t_float a, const t_float s, const t_float t) {
*b = s*a + t*(*b);
#ifndef FE_INVALID
#if HAVE_DIAGNOSTIC
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wfloat-equal"
#endif
if (fc_isnan(*b)) {
throw(nan_error());
}
#if HAVE_DIAGNOSTIC
#pragma GCC diagnostic pop
#endif
#endif
}
inline static void f_ward( t_float * const b, const t_float a, const t_float c, const t_float s, const t_float t, const t_float v) {
*b = ( (v+s)*a - v*c + (v+t)*(*b) ) / (s+t+v);
//*b = a+(*b)-(t*a+s*(*b)+v*c)/(s+t+v);
#ifndef FE_INVALID
#if HAVE_DIAGNOSTIC
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wfloat-equal"
#endif
if (fc_isnan(*b)) {
throw(nan_error());
}
#if HAVE_DIAGNOSTIC
#pragma GCC diagnostic pop
#endif
#endif
}
double sqeuclidean(t_index const i1, t_index const i2) const {
double dev, dist;
int count, j;
count = 0;
dist = 0;
double * p1 = x+i1*nc;
double * p2 = x+i2*nc;
for(j = 0 ; j < nc ; ++j) {
if(both_non_NA(*p1, *p2)) {
dev = (*p1 - *p2);
if(!ISNAN(dev)) {
dist += dev * dev;
++count;
}
}
++p1;
++p2;
}
if(count == 0) return NA_REAL;
if(count != nc) dist /= (static_cast<double>(count)/static_cast<double>(nc));
//return sqrt(dist);
// we take the square root later
if (check_NaN) {
#if HAVE_DIAGNOSTIC
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wfloat-equal"
#endif
if (fc_isnan(dist))
throw(nan_error());
#if HAVE_DIAGNOSTIC
#pragma GCC diagnostic pop
#endif
}
return dist;
}
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
}
void MST_linkage_core(const t_index N, const t_float * const D,
cluster_result & Z2) {
/*
N: integer, number of data points
D: condensed distance matrix N*(N-1)/2
Z2: output data structure
The basis of this algorithm is an algorithm by Rohlf:
F. James Rohlf, Hierarchical clustering using the minimum spanning tree,
The Computer Journal, vol. 16, 1973, p. 93–95.
*/
t_index i;
t_index idx2;
doubly_linked_list active_nodes(N);
auto_array_ptr<t_float> d(N);
t_index prev_node;
t_float min;
// first iteration
idx2 = 1;
min = std::numeric_limits<t_float>::infinity();
for (i=1; i<N; ++i) {
d[i] = D[i-1];
#if HAVE_DIAGNOSTIC
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wfloat-equal"
#endif
if (d[i] < min) {
min = d[i];
idx2 = i;
}
else if (fc_isnan(d[i]))
throw (nan_error());
#if HAVE_DIAGNOSTIC
#pragma GCC diagnostic pop
#endif
}
Z2.append(0, idx2, min);
for (t_index j=1; j<N-1; ++j) {
prev_node = idx2;
active_nodes.remove(prev_node);
idx2 = active_nodes.succ[0];
min = d[idx2];
for (i=idx2; i<prev_node; i=active_nodes.succ[i]) {
t_float tmp = D_(i, prev_node);
#if HAVE_DIAGNOSTIC
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wfloat-equal"
#endif
if (tmp < d[i])
d[i] = tmp;
else if (fc_isnan(tmp))
throw (nan_error());
#if HAVE_DIAGNOSTIC
#pragma GCC diagnostic pop
#endif
if (d[i] < min) {
min = d[i];
idx2 = i;
}
}
for (; i<N; i=active_nodes.succ[i]) {
t_float tmp = D_(prev_node, i);
#if HAVE_DIAGNOSTIC
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wfloat-equal"
#endif
if (d[i] > tmp)
d[i] = tmp;
else if (fc_isnan(tmp))
throw (nan_error());
#if HAVE_DIAGNOSTIC
#pragma GCC diagnostic pop
#endif
if (d[i] < min) {
min = d[i];
idx2 = i;
}
}
Z2.append(prev_node, idx2, min);
}
}