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TASSEL 6 is a software package to evaluate traits association. Feature Tables are at the heart of the package where, a feature is a range of positions or a single position. Row in the that table are taxon.

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// UPGMATree.java
//
// (c) 1999-2001 PAL Development Core Team
//
// This package may be distributed under the
// terms of the Lesser GNU General Public License (LGPL)
// Known bugs and limitations:
// - computational complexity O(numSeqs^3)
//   (this could be brought down to O(numSeqs^2)
//   but this needs more clever programming ...)
package net.maizegenetics.taxa.tree;

import net.maizegenetics.taxa.distance.DistanceMatrix;

/**
 * constructs a UPGMA tree from pairwise distances
 *
 * @author Korbinian Strimmer
 * @author Alexei Drummond
 */
public class UPGMATree extends SimpleTree {

    /**
     * constructor UPGMA tree
     *
     * @param m distance matrix
     */
    public UPGMATree(DistanceMatrix m) {
        if (m.getSize() < 2) {
            new IllegalArgumentException("LESS THAN 2 TAXA IN DISTANCE MATRIX");
        }
        if (!m.isSymmetric()) {
            new IllegalArgumentException("UNSYMMETRIC DISTANCE MATRIX");
        }

        init(m);

        while (true) {
            findNextPair();
            newBranchLengths();

            if (numClusters == 2) {
                break;
            }

            newCluster();
        }

        finish();
        createNodeList();
    }

    private int numClusters;
    private int besti, abi;
    private int bestj, abj;
    private int[] alias;
    private double[][] distance;

    private double[] height;
    private int[] oc;

    private double getDist(int a, int b) {
        return distance[alias[a]][alias[b]];
    }

    private void init(DistanceMatrix m) {
        numClusters = m.getSize();

        distance = m.getClonedDistances();

        for (int i = 0; i < numClusters; i++) {
            Node tmp = NodeFactory.createNode();
            tmp.setIdentifier(m.getTaxon(i));
            getRoot().addChild(tmp);
        }

        alias = new int[numClusters];
        for (int i = 0; i < numClusters; i++) {
            alias[i] = i;
        }

        height = new double[numClusters];
        oc = new int[numClusters];
        for (int i = 0; i < numClusters; i++) {
            height[i] = 0.0;
            oc[i] = 1;
        }
    }

    private void finish() {
        distance = null;
    }

    private void findNextPair() {
        besti = 0;
        bestj = 1;
        double dmin = getDist(0, 1);
        for (int i = 0; i < numClusters - 1; i++) {
            for (int j = i + 1; j < numClusters; j++) {
                if (getDist(i, j) < dmin) {
                    dmin = getDist(i, j);
                    besti = i;
                    bestj = j;
                }
            }
        }
        abi = alias[besti];
        abj = alias[bestj];
    }

    private void newBranchLengths() {
        double dij = getDist(besti, bestj);

        getRoot().getChild(besti).setBranchLength(dij / 2.0 - height[abi]);
        getRoot().getChild(bestj).setBranchLength(dij / 2.0 - height[abj]);
    }

    private void newCluster() {
        // Update distances
        for (int k = 0; k < numClusters; k++) {
            if (k != besti && k != bestj) {
                int ak = alias[k];
                distance[ak][abi] = distance[abi][ak] = updatedDistance(besti, bestj, k);
            }
        }
        distance[abi][abi] = 0.0;

        // Update UPGMA variables
        height[abi] = getDist(besti, bestj) / 2.0;
        oc[abi] += oc[abj];

        // Index besti now represent the new cluster
        NodeUtils.joinChilds(getRoot(), besti, bestj);

        // Update alias
        for (int i = bestj; i < numClusters - 1; i++) {
            alias[i] = alias[i + 1];
        }

        numClusters--;
    }

    /**
     * compute updated distance between the new cluster (i,j) to any other
     * cluster k
     */
    private double updatedDistance(int i, int j, int k) {
        int ai = alias[i];
        int aj = alias[j];

        double ocsum = (double) (oc[ai] + oc[aj]);

        return (oc[ai] / ocsum) * getDist(k, i)
                + (oc[aj] / ocsum) * getDist(k, j);
    }

}