public void decode() {
int v = vec.get(idx);
if (WAHBitSet.isAFill(v)) {
fillWord = (isOneFill(v) ? ALLONES : 0);
nWords = v & MAXCNT;
fill = true;
} else {
nWords = 1;
fill = false;
}
}
// this function tries to advance the run by nWords
// sometimes it is not possible, in that case it returns how much it advanced.
public int inc(int nWords) {
int orig = nWords;
nWords--;
while (nWords > 0) {
++idx;
int v = vec.get(idx);
if (isAFill(v)) {
int words = v & MAXCNT;
if (words > nWords) {
--idx;
break;
}
nWords -= words;
} else {
nWords--;
}
}
return orig - nWords;
}
private void setBit(int ind, int val) {
assert val == 0 || val == 1;
if (ind >= numBits()) {
int diff = ind - numBits() + 1;
if (active.nbits > 0) {
if (ind + 1 >= nbits + MAXBITS) {
diff -= MAXBITS - active.nbits;
active.val <<= (MAXBITS - active.nbits);
if (diff == 0) active.val += (val != 0 ? 1 : 0);
appendLiteral();
} else {
active.nbits += diff;
active.val <<= diff;
active.val += (val != 0 ? 1 : 0);
diff = 0;
}
}
if (diff != 0) {
int w = diff / MAXBITS;
diff -= w * MAXBITS;
if (diff != 0) {
if (w > 1) {
appendCounter(0, w);
} else if (w != 0) {
appendLiteral();
}
active.nbits = diff;
active.val += (val != 0 ? 1 : 0);
} else if (val != 0) {
if (w > 2) {
appendCounter(0, w - 1);
} else if (w == 2) {
appendLiteral();
}
active.val = 1;
appendLiteral();
} else {
if (w > 1) {
appendCounter(0, w);
} else if (w != 0) {
appendLiteral();
}
}
}
if (numBits() != ind + 1) logger.warning("Warning");
if (nset != 0) nset += (val != 0 ? 1 : 0);
return;
} else if (ind >= nbits) { // modify an active bit
int u = active.val;
if (val != 0) {
active.val |= (1 << (active.nbits - (ind - nbits) - 1));
} else {
active.val &= ~(1 << (active.nbits - (ind - nbits) - 1));
}
if (nset != 0 && (u != active.val)) nset += (val != 0 ? 1 : -1);
return;
} else if (vec.size() * MAXBITS == nbits) { // uncompressed
int i = ind / MAXBITS;
int u = vec.get(i);
int w = (1 << (SECONDBIT - (ind % MAXBITS)));
if (val != 0) vec.setQuick(i, u |= w);
else vec.setQuick(i, u &= ~w);
if (nset != 0 && (vec.getQuick(i) != u)) nset += (val != 0 ? 1 : -1);
return;
}
// the code after this has not been verified at all...
// should proceed with caution.
// compressed bit vector --
// the bit to be modified is in vec
if (RUN_UNTESTED_CODE) {
int idx = 0;
int compressed = 0, cnt = 0, ind1 = 0, ind0 = ind;
int current = 0; // current bit value
while ((ind0 > 0) && (idx < vec.size())) {
int v = vec.getQuick(idx);
if (isAFill(v)) { // a fill
cnt = ((v) & MAXCNT) * MAXBITS;
if (cnt > ind0) { // found the location
current = (isOneFill(v) ? 1 : 0);
compressed = 1;
ind1 = ind0;
ind0 = 0;
} else {
ind0 -= cnt;
ind1 = ind0;
++idx;
}
} else { // a literal word
cnt = MAXBITS;
if (MAXBITS > ind0) { // found the location
current = (1 & ((v) >>> (SECONDBIT - ind0)));
compressed = 0;
ind1 = ind0;
ind0 = 0;
} else {
ind0 -= MAXBITS;
ind1 = ind0;
++idx;
}
}
} // while (ind...
if (ind1 == 0) { // set current and compressed
int v = vec.getQuick(idx);
if (isAFill(v)) {
cnt = (v & MAXCNT) * MAXBITS;
current = (isOneFill(v) ? 1 : 0);
compressed = 1;
} else {
cnt = MAXBITS;
current = (v >>> SECONDBIT);
compressed = 0;
}
}
if (ind0 > 0) // has not found the right location yet.
{
if (ind0 < active.nbits) { // in the active word
ind1 = (1 << (active.nbits - ind0 - 1));
if (val != 0) {
active.val |= ind1;
} else {
active.val &= ~ind1;
}
} else { // extends the current bit vector
ind1 = ind0 - active.nbits - 1;
appendWord(HEADER0 | (ind1 / MAXBITS));
for (ind1 %= MAXBITS; ind1 > 0; --ind1) addOneBit(0);
addOneBit(val != 0 ? 1 : 0);
}
if (nset != 0) nset += val != 0 ? 1 : -1;
return;
}
// locate the bit to be changed, lots of work hidden here
if (current == val) return; // nothing to do
int v = vec.getQuick(idx);
// need to actually modify the bit
if (compressed == 0) {
// toggle a single bit of a literal word
v ^= (1 << (SECONDBIT - ind1));
vec.setQuick(idx, v);
} else if (ind1 < MAXBITS) {
// bit to be modified is in the first word, two pieces
--v;
vec.set(idx, v);
if ((v & MAXCNT) == 1) {
v = (current != 0) ? ALLONES : 0;
vec.setQuick(idx, v);
}
int w = 1 << (SECONDBIT - ind1);
if (val == 0) w ^= ALLONES;
vec.beforeInsert(idx, w);
idx++;
} else if (cnt - ind1 <= MAXBITS) {
// bit to be modified is in the last word, two pieces
--(v);
vec.setQuick(idx, v);
if ((v & MAXCNT) == 1) {
v = (current != 0) ? ALLONES : 0;
vec.setQuick(idx, v);
}
int w = 1 << (cnt - ind1 - 1);
if (val == 0) w ^= ALLONES;
++idx;
vec.beforeInsert(idx, w);
} else { // the counter breaks into three pieces
int u[] = new int[2], w;
u[0] = ind1 / MAXBITS;
w = (v & MAXCNT) - u[0] - 1;
u[1] = 1 << (SECONDBIT - ind1 + u[0] * MAXBITS);
if (val == 0) {
u[0] = (u[0] > 1) ? (HEADER1 | u[0]) : (ALLONES);
u[1] ^= ALLONES;
w = (w > 1) ? (HEADER1 | w) : (ALLONES);
} else {
u[0] = (u[0] > 1) ? (HEADER0 | u[0]) : 0;
w = (w > 1) ? (HEADER0 | w) : 0;
}
vec.setQuick(idx, w);
vec.beforeInsertAllOf(idx, Arrays.asList(u));
}
if (nset != 0) nset += val != 0 ? 1 : -1;
} else {
throw new AssertionError("Untested code detected, would rather die than run this");
}
}
/**
* Returns the best cut of a graph w.r.t. the degree of dissimilarity between points of different
* partitions and the degree of similarity between points of the same partition.
*
* @param W the weight matrix of the graph
* @return an array of two elements, each of these contains the points of a partition
*/
protected static int[][] bestCut(DoubleMatrix2D W) {
int n = W.columns();
// Builds the diagonal matrices D and D^(-1/2) (represented as their diagonals)
DoubleMatrix1D d = DoubleFactory1D.dense.make(n);
DoubleMatrix1D d_minus_1_2 = DoubleFactory1D.dense.make(n);
for (int i = 0; i < n; i++) {
double d_i = W.viewRow(i).zSum();
d.set(i, d_i);
d_minus_1_2.set(i, 1 / Math.sqrt(d_i));
}
DoubleMatrix2D D = DoubleFactory2D.sparse.diagonal(d);
// System.out.println("DoubleMatrix2D :\n"+D.toString());
DoubleMatrix2D X = D.copy();
// System.out.println("DoubleMatrix2D copy :\n"+X.toString());
// X = D^(-1/2) * (D - W) * D^(-1/2)
X.assign(W, Functions.minus);
// System.out.println("DoubleMatrix2D X: (D-W) :\n"+X.toString());
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
X.set(i, j, X.get(i, j) * d_minus_1_2.get(i) * d_minus_1_2.get(j));
// Computes the eigenvalues and the eigenvectors of X
EigenvalueDecomposition e = new EigenvalueDecomposition(X);
DoubleMatrix1D lambda = e.getRealEigenvalues();
// Selects the eigenvector z_2 associated with the second smallest eigenvalue
// Creates a map that contains the pairs <index, eigenvalue>
AbstractIntDoubleMap map = new OpenIntDoubleHashMap(n);
for (int i = 0; i < n; i++) map.put(i, Math.abs(lambda.get(i)));
IntArrayList list = new IntArrayList();
// Sorts the map on the value
map.keysSortedByValue(list);
// Gets the index of the second smallest element
int i_2 = list.get(1);
// y_2 = D^(-1/2) * z_2
DoubleMatrix1D y_2 = e.getV().viewColumn(i_2).copy();
y_2.assign(d_minus_1_2, Functions.mult);
// Creates a map that contains the pairs <i, y_2[i]>
map.clear();
for (int i = 0; i < n; i++) map.put(i, y_2.get(i));
// Sorts the map on the value
map.keysSortedByValue(list);
// Search the element in the map previuosly ordered that minimizes the cut
// of the partition
double best_cut = Double.POSITIVE_INFINITY;
int[][] partition = new int[2][];
// The array v contains all the elements of the graph ordered by their
// projection on vector y_2
int[] v = list.elements();
// For each admissible splitting point i
for (int i = 1; i < n; i++) {
// The array a contains all the elements that have a projection on vector
// y_2 less or equal to the one of i-th element
// The array b contains the remaining elements
int[] a = new int[i];
int[] b = new int[n - i];
System.arraycopy(v, 0, a, 0, i);
System.arraycopy(v, i, b, 0, n - i);
double cut = Ncut(W, a, b, v);
if (cut < best_cut) {
best_cut = cut;
partition[0] = a;
partition[1] = b;
}
}
// System.out.println("Partition:");
// UtilsJS.printMatrix(partition);
return partition;
}
