/**
* Initializes the receiver.
*
* @param initialCapacity the initial capacity of the receiver.
* @param minLoadFactor the minLoadFactor of the receiver.
* @param maxLoadFactor the maxLoadFactor of the receiver.
* @throws IllegalArgumentException if <tt>initialCapacity < 0 || (minLoadFactor < 0.0 ||
* minLoadFactor >= 1.0) || (maxLoadFactor <= 0.0 || maxLoadFactor >= 1.0) || (minLoadFactor
* >= maxLoadFactor)</tt>.
*/
protected void setUp(int initialCapacity, double minLoadFactor, double maxLoadFactor) {
int capacity = initialCapacity;
super.setUp(capacity, minLoadFactor, maxLoadFactor);
capacity = nextPrime(capacity);
if (capacity == 0) capacity = 1; // open addressing needs at least one FREE slot at any time.
this.table = new int[capacity];
this.values = new double[capacity];
this.state = new byte[capacity];
// memory will be exhausted long before this pathological case happens, anyway.
this.minLoadFactor = minLoadFactor;
if (capacity == PrimeFinder.largestPrime) this.maxLoadFactor = 1.0;
else this.maxLoadFactor = maxLoadFactor;
this.distinct = 0;
this.freeEntries = capacity; // delta
// lowWaterMark will be established upon first expansion.
// establishing it now (upon instance construction) would immediately make the table shrink upon
// first put(...).
// After all the idea of an "initialCapacity" implies violating lowWaterMarks when an object is
// young.
// See ensureCapacity(...)
this.lowWaterMark = 0;
this.highWaterMark = chooseHighWaterMark(capacity, this.maxLoadFactor);
}
/**
* Clears the receiver, then adds all (key,value) pairs of <tt>other</tt>values to it.
*
* @param other the other map to be copied into the receiver.
*/
public void assign(AbstractIntDoubleMap other) {
if (!(other instanceof OpenIntDoubleHashMap)) {
super.assign(other);
return;
}
OpenIntDoubleHashMap source = (OpenIntDoubleHashMap) other;
OpenIntDoubleHashMap copy = (OpenIntDoubleHashMap) source.copy();
this.values = copy.values;
this.table = copy.table;
this.state = copy.state;
this.freeEntries = copy.freeEntries;
this.distinct = copy.distinct;
this.lowWaterMark = copy.lowWaterMark;
this.highWaterMark = copy.highWaterMark;
this.minLoadFactor = copy.minLoadFactor;
this.maxLoadFactor = copy.maxLoadFactor;
}
/**
* 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;
}
