lib/network/modules/KamadaKawai.js
// distance finding algorithm
import FloydWarshall from "./components/algorithms/FloydWarshall.js"
/**
* KamadaKawai positions the nodes initially based on
*
* "AN ALGORITHM FOR DRAWING GENERAL UNDIRECTED GRAPHS"
* -- Tomihisa KAMADA and Satoru KAWAI in 1989
*
* Possible optimizations in the distance calculation can be implemented.
*/
class KamadaKawai {
/**
* @param {Object} body
* @param {number} edgeLength
* @param {number} edgeStrength
*/
constructor(body, edgeLength, edgeStrength) {
this.body = body;
this.springLength = edgeLength;
this.springConstant = edgeStrength;
this.distanceSolver = new FloydWarshall();
}
/**
* Not sure if needed but can be used to update the spring length and spring constant
* @param {Object} options
*/
setOptions(options) {
if (options) {
if (options.springLength) {
this.springLength = options.springLength;
}
if (options.springConstant) {
this.springConstant = options.springConstant;
}
}
}
/**
* Position the system
* @param {Array.<Node>} nodesArray
* @param {Array.<vis.Edge>} edgesArray
* @param {boolean} [ignoreClusters=false]
*/
solve(nodesArray, edgesArray, ignoreClusters = false) {
// get distance matrix
let D_matrix = this.distanceSolver.getDistances(this.body, nodesArray, edgesArray); // distance matrix
// get the L Matrix
this._createL_matrix(D_matrix);
// get the K Matrix
this._createK_matrix(D_matrix);
// initial E Matrix
this._createE_matrix();
// calculate positions
let threshold = 0.01;
let innerThreshold = 1;
let iterations = 0;
let maxIterations = Math.max(1000, Math.min(10 * this.body.nodeIndices.length, 6000));
let maxInnerIterations = 5;
let maxEnergy = 1e9;
let highE_nodeId = 0, dE_dx = 0, dE_dy = 0, delta_m = 0, subIterations = 0;
while (maxEnergy > threshold && iterations < maxIterations) {
iterations += 1;
[highE_nodeId, maxEnergy, dE_dx, dE_dy] = this._getHighestEnergyNode(ignoreClusters);
delta_m = maxEnergy;
subIterations = 0;
while (delta_m > innerThreshold && subIterations < maxInnerIterations) {
subIterations += 1;
this._moveNode(highE_nodeId, dE_dx, dE_dy);
[delta_m, dE_dx, dE_dy] = this._getEnergy(highE_nodeId);
}
}
}
/**
* get the node with the highest energy
* @param {boolean} ignoreClusters
* @returns {number[]}
* @private
*/
_getHighestEnergyNode(ignoreClusters) {
let nodesArray = this.body.nodeIndices;
let nodes = this.body.nodes;
let maxEnergy = 0;
let maxEnergyNodeId = nodesArray[0];
let dE_dx_max = 0, dE_dy_max = 0;
for (let nodeIdx = 0; nodeIdx < nodesArray.length; nodeIdx++) {
let m = nodesArray[nodeIdx];
// by not evaluating nodes with predefined positions we should only move nodes that have no positions.
if ((nodes[m].predefinedPosition === false || nodes[m].isCluster === true && ignoreClusters === true) || nodes[m].options.fixed.x === true || nodes[m].options.fixed.y === true) {
let [delta_m,dE_dx,dE_dy] = this._getEnergy(m);
if (maxEnergy < delta_m) {
maxEnergy = delta_m;
maxEnergyNodeId = m;
dE_dx_max = dE_dx;
dE_dy_max = dE_dy;
}
}
}
return [maxEnergyNodeId, maxEnergy, dE_dx_max, dE_dy_max];
}
/**
* calculate the energy of a single node
* @param {Node.id} m
* @returns {number[]}
* @private
*/
_getEnergy(m) {
let [dE_dx,dE_dy] = this.E_sums[m];
let delta_m = Math.sqrt(Math.pow(dE_dx, 2) + Math.pow(dE_dy, 2));
return [delta_m, dE_dx, dE_dy];
}
/**
* move the node based on it's energy
* the dx and dy are calculated from the linear system proposed by Kamada and Kawai
* @param {number} m
* @param {number} dE_dx
* @param {number} dE_dy
* @private
*/
_moveNode(m, dE_dx, dE_dy) {
let nodesArray = this.body.nodeIndices;
let nodes = this.body.nodes;
let d2E_dx2 = 0;
let d2E_dxdy = 0;
let d2E_dy2 = 0;
let x_m = nodes[m].x;
let y_m = nodes[m].y;
let km = this.K_matrix[m];
let lm = this.L_matrix[m];
for (let iIdx = 0; iIdx < nodesArray.length; iIdx++) {
let i = nodesArray[iIdx];
if (i !== m) {
let x_i = nodes[i].x;
let y_i = nodes[i].y;
let kmat = km[i];
let lmat = lm[i];
let denominator = 1.0 / Math.pow(Math.pow(x_m - x_i, 2) + Math.pow(y_m - y_i, 2), 1.5);
d2E_dx2 += kmat * (1 - lmat * Math.pow(y_m - y_i, 2) * denominator);
d2E_dxdy += kmat * (lmat * (x_m - x_i) * (y_m - y_i) * denominator);
d2E_dy2 += kmat * (1 - lmat * Math.pow(x_m - x_i, 2) * denominator);
}
}
// make the variable names easier to make the solving of the linear system easier to read
let A = d2E_dx2, B = d2E_dxdy, C = dE_dx, D = d2E_dy2, E = dE_dy;
// solve the linear system for dx and dy
let dy = (C / A + E / B) / (B / A - D / B);
let dx = -(B * dy + C) / A;
// move the node
nodes[m].x += dx;
nodes[m].y += dy;
// Recalculate E_matrix (should be incremental)
this._updateE_matrix(m);
}
/**
* Create the L matrix: edge length times shortest path
* @param {Object} D_matrix
* @private
*/
_createL_matrix(D_matrix) {
let nodesArray = this.body.nodeIndices;
let edgeLength = this.springLength;
this.L_matrix = [];
for (let i = 0; i < nodesArray.length; i++) {
this.L_matrix[nodesArray[i]] = {};
for (let j = 0; j < nodesArray.length; j++) {
this.L_matrix[nodesArray[i]][nodesArray[j]] = edgeLength * D_matrix[nodesArray[i]][nodesArray[j]];
}
}
}
/**
* Create the K matrix: spring constants times shortest path
* @param {Object} D_matrix
* @private
*/
_createK_matrix(D_matrix) {
let nodesArray = this.body.nodeIndices;
let edgeStrength = this.springConstant;
this.K_matrix = [];
for (let i = 0; i < nodesArray.length; i++) {
this.K_matrix[nodesArray[i]] = {};
for (let j = 0; j < nodesArray.length; j++) {
this.K_matrix[nodesArray[i]][nodesArray[j]] = edgeStrength * Math.pow(D_matrix[nodesArray[i]][nodesArray[j]], -2);
}
}
}
/**
* Create matrix with all energies between nodes
* @private
*/
_createE_matrix() {
let nodesArray = this.body.nodeIndices;
let nodes = this.body.nodes;
this.E_matrix = {};
this.E_sums = {};
for (let mIdx = 0; mIdx < nodesArray.length; mIdx++) {
this.E_matrix[nodesArray[mIdx]] = [];
}
for (let mIdx = 0; mIdx < nodesArray.length; mIdx++) {
let m = nodesArray[mIdx];
let x_m = nodes[m].x;
let y_m = nodes[m].y;
let dE_dx = 0;
let dE_dy = 0;
for (let iIdx = mIdx; iIdx < nodesArray.length; iIdx++) {
let i = nodesArray[iIdx];
if (i !== m) {
let x_i = nodes[i].x;
let y_i = nodes[i].y;
let denominator = 1.0 / Math.sqrt(Math.pow(x_m - x_i, 2) + Math.pow(y_m - y_i, 2));
this.E_matrix[m][iIdx] = [
this.K_matrix[m][i] * ((x_m - x_i) - this.L_matrix[m][i] * (x_m - x_i) * denominator),
this.K_matrix[m][i] * ((y_m - y_i) - this.L_matrix[m][i] * (y_m - y_i) * denominator)
];
this.E_matrix[i][mIdx] = this.E_matrix[m][iIdx];
dE_dx += this.E_matrix[m][iIdx][0];
dE_dy += this.E_matrix[m][iIdx][1];
}
}
//Store sum
this.E_sums[m] = [dE_dx, dE_dy];
}
}
/**
* Update method, just doing single column (rows are auto-updated) (update all sums)
*
* @param {number} m
* @private
*/
_updateE_matrix(m) {
let nodesArray = this.body.nodeIndices;
let nodes = this.body.nodes;
let colm = this.E_matrix[m];
let kcolm = this.K_matrix[m];
let lcolm = this.L_matrix[m];
let x_m = nodes[m].x;
let y_m = nodes[m].y;
let dE_dx = 0;
let dE_dy = 0;
for (let iIdx = 0; iIdx < nodesArray.length; iIdx++) {
let i = nodesArray[iIdx];
if (i !== m) {
//Keep old energy value for sum modification below
let cell = colm[iIdx];
let oldDx = cell[0];
let oldDy = cell[1];
//Calc new energy:
let x_i = nodes[i].x;
let y_i = nodes[i].y;
let denominator = 1.0 / Math.sqrt(Math.pow(x_m - x_i, 2) + Math.pow(y_m - y_i, 2));
let dx = kcolm[i] * ((x_m - x_i) - lcolm[i] * (x_m - x_i) * denominator);
let dy = kcolm[i] * ((y_m - y_i) - lcolm[i] * (y_m - y_i) * denominator);
colm[iIdx] = [dx, dy];
dE_dx += dx;
dE_dy += dy;
//add new energy to sum of each column
let sum = this.E_sums[i];
sum[0] += (dx-oldDx);
sum[1] += (dy-oldDy);
}
}
//Store sum at -1 index
this.E_sums[m] = [dE_dx, dE_dy];
}
}
export default KamadaKawai;