// returns the energy of i (looping over all other nodes)
private double getDeltaM(
int i,
DenseDoubleMatrix2D lMatrix,
DenseDoubleMatrix2D kMatrix,
double[] xPos,
double[] yPos) {
int nNodes = lMatrix.rows();
double deltaM = 0;
double xPartial = 0;
double yPartial = 0;
double dx, dy, dd;
for (int j = 0; j < nNodes; j++) {
if (i != j) {
dx = xPos[i] - xPos[j];
dy = yPos[i] - yPos[j];
dd = Math.sqrt(dx * dx + dy * dy);
double kMatrixVal = kMatrix.getQuick(i, j);
double lMatrixVal = lMatrix.getQuick(i, j);
xPartial += kMatrixVal * (dx - lMatrixVal * dx / dd);
yPartial += kMatrixVal * (dy - lMatrixVal * dy / dd);
}
}
// deltaM = sqrt(xPartial^2+yPartial^2)
deltaM = Math.sqrt(xPartial * xPartial + yPartial * yPartial);
return deltaM;
}
// the bulk of the KK inner loop, estimates location of local minima
private double[] getDeltas(
int i,
DenseDoubleMatrix2D lMatrix,
DenseDoubleMatrix2D kMatrix,
double[] xPos,
double[] yPos) {
// solve deltaM partial eqns to figure out new position for node of index i
// where deltaM is close to 0 (or less then epsilon)
int nNodes = lMatrix.rows();
double[] deltas = new double[2]; // holds x and y coords to return
double dx, dy, dd;
// double deltaX, deltaY;
double xPartial = 0;
double yPartial = 0;
double xxPartial = 0;
double xyPartial = 0;
double yxPartial = 0;
double yyPartial = 0;
for (int j = 0; j < nNodes; j++) {
if (i != j) {
dx = xPos[i] - xPos[j];
dy = yPos[i] - yPos[j];
dd = Math.sqrt(dx * dx + dy * dy);
double kMatrixVal = kMatrix.getQuick(i, j);
double lMatrixVal = lMatrix.getQuick(i, j);
double ddCubed = dd * dd * dd;
xPartial += kMatrixVal * (dx - lMatrixVal * dx / dd);
yPartial += kMatrixVal * (dy - lMatrixVal * dy / dd);
xxPartial += kMatrixVal * (1 - lMatrixVal * dy * dy / ddCubed);
xyPartial += kMatrixVal * (lMatrixVal * dx * dy / ddCubed);
yxPartial += kMatrixVal * (lMatrixVal * dy * dx / ddCubed);
yyPartial += kMatrixVal * (1 - lMatrixVal * dx * dx / ddCubed);
}
}
// calculate x and y position difference using partials
deltas[0] =
((-xPartial) * yyPartial - xyPartial * (-yPartial))
/ (xxPartial * yyPartial - xyPartial * yxPartial);
deltas[1] =
(xxPartial * (-yPartial) - (-xPartial) * yxPartial)
/ (xxPartial * yyPartial - xyPartial * yxPartial);
return deltas;
}
// calculate the diameter of the graph (longest shortest path)
// requires that path lengths are calc'd first
private int getDiam(DenseDoubleMatrix2D distMatrix) {
int nNodes = distMatrix.rows();
double graphDiam = 0;
for (int i = 0; i < nNodes; i++) {
for (int j = 0; j < nNodes; j++) {
graphDiam = Math.max(graphDiam, distMatrix.getQuick(i, j));
}
}
return (int) graphDiam;
}
// set up matrix of desired edge lengths using L*d[i][j]
private DenseDoubleMatrix2D calcLMatrix(DenseDoubleMatrix2D distMatrix, double optDist) {
int nNodes = distMatrix.rows();
DenseDoubleMatrix2D lMatrix = new DenseDoubleMatrix2D(nNodes, nNodes);
for (int i = 0; i < nNodes; i++) {
for (int j = 0; j < nNodes; j++) {
lMatrix.setQuick(i, j, (optDist * distMatrix.getQuick(i, j)));
}
}
return lMatrix;
}
private double getEnergy(
DenseDoubleMatrix2D lMatrix, DenseDoubleMatrix2D kMatrix, double[] xPos, double[] yPos) {
int nNodes = lMatrix.rows();
double energy = 0;
double dx, dy, lij;
int limit = nNodes - 1;
// for all pairs..
for (int i = 0; i < limit; i++) {
for (int j = i + 1; j < nNodes; j++) {
dx = xPos[i] - xPos[j];
dy = yPos[i] - yPos[j];
lij = lMatrix.getQuick(i, j);
energy +=
0.5
* kMatrix.getQuick(i, j)
* (dx * dx + dy * dy + lij * lij - 2 * lij * Math.sqrt(dx * dx + dy * dy));
}
}
return energy;
}
// set up matrix of spring forces between pairs using K/(d[i][j]^2)
private DenseDoubleMatrix2D calcKMatrix(DenseDoubleMatrix2D distMatrix, double spring) {
int nNodes = distMatrix.rows();
DenseDoubleMatrix2D kMatrix = new DenseDoubleMatrix2D(nNodes, nNodes);
for (int i = 0; i < nNodes; i++) {
for (int j = 0; j < nNodes; j++) {
double distMVal = distMatrix.getQuick(i, j);
kMatrix.setQuick(i, j, (spring / (distMVal * distMVal)));
}
}
return kMatrix;
}
/**
* Copies the matrix elements from the specified DenseDoubleMatrix2D. The matrix element at ij is
* set to 0 if the element at DoubleMatrix[i][j] = 0, otherwise the matrix element at ij is set to
* 1.
*
* @param m the actual matrix data for this AdjacencyMatrix
*/
public void setMatrix(DenseDoubleMatrix2D m) {
int rows = m.rows();
int cols = m.columns();
matrix = new BitMatrix2D(rows, cols);
for (int i = 0; i < rows; i++) {
for (int j = 0; j < cols; j++) {
matrix.set(i, j, (byte) m.getQuick(i, j));
}
}
}
