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