--- /dev/null
+/*
+ * Jalview - A Sequence Alignment Editor and Viewer ($$Version-Rel$$)
+ * Copyright (C) $$Year-Rel$$ The Jalview Authors
+ *
+ * This file is part of Jalview.
+ *
+ * Jalview is free software: you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License
+ * as published by the Free Software Foundation, either version 3
+ * of the License, or (at your option) any later version.
+ *
+ * Jalview is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty
+ * of MERCHANTABILITY or FITNESS FOR A PARTICULAR
+ * PURPOSE. See the GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with Jalview. If not, see <http://www.gnu.org/licenses/>.
+ * The Jalview Authors are detailed in the 'AUTHORS' file.
+ */
+
+/*
+* Copyright 2018-2022 Kathy Su, Kay Diederichs
+*
+* This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
+*
+* This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
+*
+* You should have received a copy of the GNU General Public License along with this program. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+/**
+* Ported from https://doi.org/10.1107/S2059798317000699 by
+* @AUTHOR MorellThomas
+*/
+
+package jalview.analysis;
+
+import jalview.bin.Console;
+import jalview.math.MatrixI;
+import jalview.math.Matrix;
+import jalview.math.MiscMath;
+
+import java.lang.Math;
+import java.lang.System;
+import java.util.Arrays;
+import java.util.ArrayList;
+import java.util.Comparator;
+import java.util.Map.Entry;
+import java.util.TreeMap;
+
+import org.apache.commons.math3.linear.Array2DRowRealMatrix;
+import org.apache.commons.math3.linear.SingularValueDecomposition;
+
+/**
+ * A class to model rectangular matrices of double values and operations on them
+ */
+public class ccAnalysis
+{
+ private byte dim = 0; //dimensions
+
+ private MatrixI scoresOld; //input scores
+
+ public ccAnalysis(MatrixI scores, byte dim)
+ {
+ // round matrix to .4f to be same as in pasimap
+ for (int i = 0; i < scores.height(); i++)
+ {
+ for (int j = 0; j < scores.width(); j++)
+ {
+ if (!Double.isNaN(scores.getValue(i,j)))
+ {
+ scores.setValue(i, j, (double) Math.round(scores.getValue(i,j) * (int) 10000) / 10000);
+ }
+ }
+ }
+ this.scoresOld = scores;
+ this.dim = dim;
+ }
+
+ /**
+ * Initialise a distrust-score for each hypothesis (h) of hSigns
+ * distrust = conHypNum - proHypNum
+ *
+ * @param hSigns ~ hypothesis signs (+/-) for each sequence
+ * @param scores ~ input score matrix
+ *
+ * @return distrustScores
+ */
+ private int[] initialiseDistrusts(byte[] hSigns, MatrixI scores)
+ {
+ int[] distrustScores = new int[scores.width()];
+
+ // loop over symmetric matrix
+ for (int i = 0; i < scores.width(); i++)
+ {
+ byte hASign = hSigns[i];
+ int conHypNum = 0;
+ int proHypNum = 0;
+
+ for (int j = 0; j < scores.width(); j++)
+ {
+ double cell = scores.getRow(i)[j]; // value at [i][j] in scores
+ byte hBSign = hSigns[j];
+ if (!Double.isNaN(cell))
+ {
+ byte cellSign = (byte) Math.signum(cell); //check if sign of matrix value fits hyptohesis
+ if (cellSign == hASign * hBSign)
+ {
+ proHypNum++;
+ } else {
+ conHypNum++;
+ }
+ }
+ }
+ distrustScores[i] = conHypNum - proHypNum; //create distrust score for each sequence
+ }
+ return distrustScores;
+ }
+
+ /**
+ * Optemise hypothesis concerning the sign of the hypothetical value for each hSigns by interpreting the pairwise correlation coefficients as scalar products
+ *
+ * @param hSigns ~ hypothesis signs (+/-)
+ * @param distrustScores
+ * @param scores ~ input score matrix
+ *
+ * @return hSigns
+ */
+ private byte[] optimiseHypothesis(byte[] hSigns, int[] distrustScores, MatrixI scores)
+ {
+ // get maximum distrust score
+ int[] maxes = MiscMath.findMax(distrustScores);
+ int maxDistrustIndex = maxes[0];
+ int maxDistrust = maxes[1];
+
+ // if hypothesis is not optimal yet
+ if (maxDistrust > 0)
+ {
+ //toggle sign for hI with maximum distrust
+ hSigns[maxDistrustIndex] *= -1;
+ // update distrust at same position
+ distrustScores[maxDistrustIndex] *= -1;
+
+ // also update distrust scores for all hI that were not changed
+ byte hASign = hSigns[maxDistrustIndex];
+ for (int NOTmaxDistrustIndex = 0; NOTmaxDistrustIndex < distrustScores.length; NOTmaxDistrustIndex++)
+ {
+ if (NOTmaxDistrustIndex != maxDistrustIndex)
+ {
+ byte hBSign = hSigns[NOTmaxDistrustIndex];
+ double cell = scores.getValue(maxDistrustIndex, NOTmaxDistrustIndex);
+
+ // distrust only changed if not NaN
+ if (!Double.isNaN(cell))
+ {
+ byte cellSign = (byte) Math.signum(cell);
+ // if sign of cell matches hypothesis decrease distrust by 2 because 1 more value supporting and 1 less contradicting
+ // else increase by 2
+ if (cellSign == hASign * hBSign)
+ {
+ distrustScores[NOTmaxDistrustIndex] -= 2;
+ } else {
+ distrustScores[NOTmaxDistrustIndex] += 2;
+ }
+ }
+ }
+ }
+ //further optimisation necessary
+ return optimiseHypothesis(hSigns, distrustScores, scores);
+
+ } else {
+ return hSigns;
+ }
+ }
+
+ /**
+ * takes the a symmetric MatrixI as input scores which may contain Double.NaN
+ * approximate the missing values using hypothesis optimisation
+ *
+ * runs analysis
+ *
+ * @param scores ~ score matrix
+ *
+ * @return
+ */
+ public MatrixI run () throws Exception
+ {
+ //initialse eigenMatrix and repMatrix
+ MatrixI eigenMatrix = scoresOld.copy();
+ MatrixI repMatrix = scoresOld.copy();
+ try
+ {
+ /*
+ * Calculate correction factor for 2nd and higher eigenvalue(s).
+ * This correction is NOT needed for the 1st eigenvalue, because the
+ * unknown (=NaN) values of the matrix are approximated by presuming
+ * 1-dimensional vectors as the basis of the matrix interpretation as dot
+ * products.
+ */
+
+ System.out.println("Input correlation matrix:");
+ eigenMatrix.print(System.out, "%1.4f ");
+
+ int matrixWidth = eigenMatrix.width(); // square matrix, so width == height
+ int matrixElementsTotal = (int) Math.pow(matrixWidth, 2); //total number of elemts
+
+ float correctionFactor = (float) (matrixElementsTotal - eigenMatrix.countNaN()) / (float) matrixElementsTotal;
+
+ /*
+ * Calculate hypothetical value (1-dimensional vector) h_i for each
+ * dataset by interpreting the given correlation coefficients as scalar
+ * products.
+ */
+
+ /*
+ * Memory for current hypothesis concerning sign of each h_i.
+ * List of signs for all h_i in the encoding:
+ * * 1: positive
+ * * 0: zero
+ * * -1: negative
+ * Initial hypothesis: all signs are positive.
+ */
+ byte[] hSigns = new byte[matrixWidth];
+ Arrays.fill(hSigns, (byte) 1);
+
+ //Estimate signs for each h_i by refining hypothesis on signs.
+ hSigns = optimiseHypothesis(hSigns, initialiseDistrusts(hSigns, eigenMatrix), eigenMatrix);
+
+
+ //Estimate absolute values for each h_i by determining sqrt of mean of
+ //non-NaN absolute values for every row.
+ double[] hAbs = MiscMath.sqrt(eigenMatrix.absolute().meanRow());
+
+ //Combine estimated signs with absolute values in obtain total value for
+ //each h_i.
+ double[] hValues = MiscMath.elementwiseMultiply(hSigns, hAbs);
+
+ /*Complement symmetric matrix by using the scalar products of estimated
+ *values of h_i to replace NaN-cells.
+ *Matrix positions that have estimated values
+ *(only for diagonal and upper off-diagonal values, due to the symmetry
+ *the positions of the lower-diagonal values can be inferred).
+ List of tuples (row_idx, column_idx).*/
+
+ ArrayList<int[]> estimatedPositions = new ArrayList<int[]>();
+
+ // for off-diagonal cells
+ for (int rowIndex = 0; rowIndex < matrixWidth - 1; rowIndex++)
+ {
+ for (int columnIndex = rowIndex + 1; columnIndex < matrixWidth; columnIndex++)
+ {
+ double cell = eigenMatrix.getValue(rowIndex, columnIndex);
+ if (Double.isNaN(cell))
+ {
+ //calculate scalar product as new cell value
+ cell = hValues[rowIndex] * hValues[columnIndex];
+ //fill in new value in cell and symmetric partner
+ eigenMatrix.setValue(rowIndex, columnIndex, cell);
+ eigenMatrix.setValue(columnIndex, rowIndex, cell);
+ //save positions of estimated values
+ estimatedPositions.add(new int[]{rowIndex, columnIndex});
+ }
+ }
+ }
+
+ // for diagonal cells
+ for (int diagonalIndex = 0; diagonalIndex < matrixWidth; diagonalIndex++)
+ {
+ double cell = Math.pow(hValues[diagonalIndex], 2);
+ eigenMatrix.setValue(diagonalIndex, diagonalIndex, cell);
+ estimatedPositions.add(new int[]{diagonalIndex, diagonalIndex});
+ }
+
+ /*Refine total values of each h_i:
+ *Initialise h_values of the hypothetical non-existant previous iteration
+ *with the correct format but with impossible values.
+ Needed for exit condition of otherwise endless loop.*/
+ System.out.print("initial values: [ ");
+ for (double h : hValues)
+ {
+ System.out.print(String.format("%1.4f, ", h));
+ }
+ System.out.println(" ]");
+
+
+ double[] hValuesOld = new double[matrixWidth];
+
+ int iterationCount = 0;
+
+ // repeat unitl values of h do not significantly change anymore
+ while (true)
+ {
+ for (int hIndex = 0; hIndex < matrixWidth; hIndex++)
+ {
+ double newH = Arrays.stream(MiscMath.elementwiseMultiply(hValues, eigenMatrix.getRow(hIndex))).sum() / Arrays.stream(MiscMath.elementwiseMultiply(hValues, hValues)).sum();
+ hValues[hIndex] = newH;
+ }
+
+ System.out.print(String.format("iteration %d: [ ", iterationCount));
+ for (double h : hValues)
+ {
+ System.out.print(String.format("%1.4f, ", h));
+ }
+ System.out.println(" ]");
+
+ //update values of estimated positions
+ for (int[] pair : estimatedPositions) // pair ~ row, col
+ {
+ double newVal = hValues[pair[0]] * hValues[pair[1]];
+ eigenMatrix.setValue(pair[0], pair[1], newVal);
+ eigenMatrix.setValue(pair[1], pair[0], newVal);
+ }
+
+ iterationCount++;
+
+ //exit loop as soon as new values are similar to the last iteration
+ if (MiscMath.allClose(hValues, hValuesOld, 0d, 1e-05d, false))
+ {
+ break;
+ }
+
+ //save hValues for comparison in the next iteration
+ System.arraycopy(hValues, 0, hValuesOld, 0, hValues.length);
+ }
+
+ //-----------------------------
+ //Use complemented symmetric matrix to calculate final representative
+ //vectors.
+
+ //Eigendecomposition.
+ eigenMatrix.tred();
+ eigenMatrix.tqli();
+
+ System.out.println("eigenmatrix");
+ eigenMatrix.print(System.out, "%8.2f");
+ System.out.println();
+ System.out.println("uncorrected eigenvalues");
+ eigenMatrix.printD(System.out, "%2.4f ");
+ System.out.println();
+
+ double[] eigenVals = eigenMatrix.getD();
+
+ TreeMap<Double, Integer> eigenPairs = new TreeMap<>(Comparator.reverseOrder());
+ for (int i = 0; i < eigenVals.length; i++)
+ {
+ eigenPairs.put(eigenVals[i], i);
+ }
+
+ // matrix of representative eigenvectors (each row is a vector)
+ double[][] _repMatrix = new double[eigenVals.length][dim];
+ double[][] _oldMatrix = new double[eigenVals.length][dim];
+ double[] correctedEigenValues = new double[dim];
+
+ int l = 0;
+ for (Entry<Double, Integer> pair : eigenPairs.entrySet())
+ {
+ double eigenValue = pair.getKey();
+ int column = pair.getValue();
+ double[] eigenVector = eigenMatrix.getColumn(column);
+ //for 2nd and higher eigenvalues
+ if (l >= 1)
+ {
+ eigenValue /= correctionFactor;
+ }
+ correctedEigenValues[l] = eigenValue;
+ for (int j = 0; j < eigenVector.length; j++)
+ {
+ _repMatrix[j][l] = (eigenValue < 0) ? 0.0 : - Math.sqrt(eigenValue) * eigenVector[j];
+ double tmpOldScore = scoresOld.getColumn(column)[j];
+ _oldMatrix[j][dim - l - 1] = (Double.isNaN(tmpOldScore)) ? 0.0 : tmpOldScore;
+ }
+ l++;
+ if (l >= dim)
+ {
+ break;
+ }
+ }
+
+ System.out.println("correctedEigenValues");
+ MiscMath.print(correctedEigenValues, "%2.4f ");
+
+ repMatrix = new Matrix(_repMatrix);
+ repMatrix.setD(correctedEigenValues);
+ MatrixI oldMatrix = new Matrix(_oldMatrix);
+
+ MatrixI dotMatrix = repMatrix.postMultiply(repMatrix.transpose());
+
+ double rmsd = scoresOld.rmsd(dotMatrix);
+
+ System.out.println("iteration, rmsd, maxDiff, rmsdDiff");
+ System.out.println(String.format("0, %8.5f, -, -", rmsd));
+ // Refine representative vectors by minimising sum-of-squared deviates between dotMatrix and original score matrix
+ for (int iteration = 1; iteration < 21; iteration++) // arbitrarily set to 20
+ {
+ MatrixI repMatrixOLD = repMatrix.copy();
+ MatrixI dotMatrixOLD = dotMatrix.copy();
+
+ // for all rows/hA in the original matrix
+ for (int hAIndex = 0; hAIndex < oldMatrix.height(); hAIndex++)
+ {
+ double[] row = oldMatrix.getRow(hAIndex);
+ double[] hA = repMatrix.getRow(hAIndex);
+ hAIndex = hAIndex;
+ //find least-squares-solution fo rdifferences between original scores and representative vectors
+ double[] hAlsm = leastSquaresOptimisation(repMatrix, scoresOld, hAIndex);
+ // update repMatrix with new hAlsm
+ for (int j = 0; j < repMatrix.width(); j++)
+ {
+ repMatrix.setValue(hAIndex, j, hAlsm[j]);
+ }
+ }
+
+ // dot product of representative vecotrs yields a matrix with values approximating the correlation matrix
+ dotMatrix = repMatrix.postMultiply(repMatrix.transpose());
+ // calculate rmsd between approximation and correlation matrix
+ rmsd = scoresOld.rmsd(dotMatrix);
+
+ // calculate maximum change of representative vectors of current iteration
+ MatrixI diff = repMatrix.subtract(repMatrixOLD).absolute();
+ double maxDiff = 0.0;
+ for (int i = 0; i < diff.height(); i++)
+ {
+ for (int j = 0; j < diff.width(); j++)
+ {
+ maxDiff = (diff.getValue(i, j) > maxDiff) ? diff.getValue(i, j) : maxDiff;
+ }
+ }
+
+ // calculate rmsd between current and previous estimation
+ double rmsdDiff = dotMatrix.rmsd(dotMatrixOLD);
+
+ System.out.println(String.format("%d, %8.5f, %8.5f, %8.5f", iteration, rmsd, maxDiff, rmsdDiff));
+
+ if (!(Math.abs(maxDiff) > 1e-06))
+ {
+ repMatrix = repMatrixOLD.copy();
+ break;
+ }
+ }
+
+
+ } catch (Exception q)
+ {
+ Console.error("Error computing cc_analysis: " + q.getMessage());
+ q.printStackTrace();
+ }
+ System.out.println("final coordinates:");
+ repMatrix.print(System.out, "%1.8f ");
+ return repMatrix;
+ }
+
+ /**
+ * Create equations system using information on originally known
+ * pairwise correlation coefficients (parsed from infile) and the
+ * representative result vectors
+ *
+ * Each equation has the format:
+ * hA * hA - pairwiseCC = 0
+ * with:
+ * hA: unknown variable
+ * hB: known representative vector
+ * pairwiseCC: known pairwise correlation coefficien
+ *
+ * The resulting equations system is overdetermined, if there are more
+ * equations than unknown elements
+ *
+ * @param x ~ unknown n-dimensional column-vector
+ * (needed for generating equations system, NOT to be specified by user).
+ * @param hAIndex ~ index of currently optimised representative result vector.
+ * @param h ~ matrix with row-wise listing of representative result vectors.
+ * @param originalRow ~ matrix-row of originally parsed pairwise correlation coefficients.
+ *
+ * @return
+ */
+ private double[] originalToEquasionSystem(double[] hA, MatrixI repMatrix, MatrixI scoresOld, int hAIndex)
+ {
+ double[] originalRow = scoresOld.getRow(hAIndex);
+ int nans = MiscMath.countNaN(originalRow);
+ double[] result = new double[originalRow.length - nans];
+
+ //for all pairwiseCC in originalRow
+ int resultIndex = 0;
+ for (int hBIndex = 0; hBIndex < originalRow.length; hBIndex++)
+ {
+ double pairwiseCC = originalRow[hBIndex];
+ // if not NaN -> create new equation and add it to the system
+ if (!Double.isNaN(pairwiseCC))
+ {
+ double[] hB = repMatrix.getRow(hBIndex);
+ result[resultIndex++] = MiscMath.sum(MiscMath.elementwiseMultiply(hA, hB)) - pairwiseCC;
+ } else {
+ }
+ }
+ return result;
+ }
+
+ /**
+ * returns the jacobian matrix
+ * @param repMatrix ~ matrix of representative vectors
+ * @param hAIndex ~ current row index
+ *
+ * @return
+ */
+ private MatrixI approximateDerivative(MatrixI repMatrix, MatrixI scoresOld, int hAIndex)
+ {
+ //hA = x0
+ double[] hA = repMatrix.getRow(hAIndex);
+ double[] f0 = originalToEquasionSystem(hA, repMatrix, scoresOld, hAIndex);
+ double[] signX0 = new double[hA.length];
+ double[] xAbs = new double[hA.length];
+ for (int i = 0; i < hA.length; i++)
+ {
+ signX0[i] = (hA[i] >= 0) ? 1 : -1;
+ xAbs[i] = (Math.abs(hA[i]) >= 1.0) ? Math.abs(hA[i]) : 1.0;
+ }
+ double rstep = Math.pow(Math.ulp(1.0), 0.5);
+
+ double[] h = new double [hA.length];
+ for (int i = 0; i < hA.length; i++)
+ {
+ h[i] = rstep * signX0[i] * xAbs[i];
+ }
+
+ int m = f0.length;
+ int n = hA.length;
+ double[][] jTransposed = new double[n][m];
+ for (int i = 0; i < h.length; i++)
+ {
+ double[] x = new double[h.length];
+ System.arraycopy(hA, 0, x, 0, h.length);
+ x[i] += h[i];
+ double dx = x[i] - hA[i];
+ double[] df = originalToEquasionSystem(x, repMatrix, scoresOld, hAIndex);
+ for (int j = 0; j < df.length; j++)
+ {
+ df[j] -= f0[j];
+ jTransposed[i][j] = df[j] / dx;
+ }
+ }
+ MatrixI J = new Matrix(jTransposed).transpose();
+ return J;
+ }
+
+ /**
+ * norm of regularized (by alpha) least-squares solution minus Delta
+ * @param alpha
+ * @param suf
+ * @param s
+ * @param Delta
+ *
+ * @return
+ */
+ private double[] phiAndDerivative(double alpha, double[] suf, double[] s, double Delta)
+ {
+ double[] denom = MiscMath.elementwiseAdd(MiscMath.elementwiseMultiply(s, s), alpha);
+ double pNorm = MiscMath.norm(MiscMath.elementwiseDivide(suf, denom));
+ double phi = pNorm - Delta;
+ // - sum ( suf**2 / denom**3) / pNorm
+ double phiPrime = - MiscMath.sum(MiscMath.elementwiseDivide(MiscMath.elementwiseMultiply(suf, suf), MiscMath.elementwiseMultiply(MiscMath.elementwiseMultiply(denom, denom), denom))) / pNorm;
+ return new double[]{phi, phiPrime};
+ }
+
+ /**
+ * class holding the result of solveLsqTrustRegion
+ */
+ private class TrustRegion
+ {
+ private double[] step;
+ private double alpha;
+ private int iteration;
+
+ public TrustRegion(double[] step, double alpha, int iteration)
+ {
+ this.step = step;
+ this.alpha = alpha;
+ this.iteration = iteration;
+ }
+
+ public double[] getStep()
+ {
+ return this.step;
+ }
+
+ public double getAlpha()
+ {
+ return this.alpha;
+ }
+
+ public int getIteration()
+ {
+ return this.iteration;
+ }
+ }
+
+ /**
+ * solve a trust-region problem arising in least-squares optimisation
+ * @param n ~ number of variables
+ * @param m ~ number of residuals
+ * @param uf
+ * @param s ~ singular values of J
+ * @param V ~ transpose of VT
+ * @param Delta ~ radius of a trust region
+ * @param alpha ~ initial guess for alpha
+ *
+ * @return
+ */
+ private TrustRegion solveLsqTrustRegion(int n, int m, double[] uf, double[] s, MatrixI V, double Delta, double alpha)
+ {
+ double[] suf = MiscMath.elementwiseMultiply(s, uf);
+
+ //check if J has full rank and tr Gauss-Newton step
+ boolean fullRank = false;
+ if (m >= n)
+ {
+ double threshold = s[0] * Math.ulp(1.0) * m;
+ fullRank = s[s.length - 1] > threshold;
+ }
+ if (fullRank)
+ {
+ double[] p = MiscMath.elementwiseMultiply(V.sumProduct(MiscMath.elementwiseDivide(uf, s)), -1);
+ if (MiscMath.norm(p) <= Delta)
+ {
+ TrustRegion result = new TrustRegion(p, 0.0, 0);
+ return result;
+ }
+ }
+
+ double alphaUpper = MiscMath.norm(suf) / Delta;
+ double alphaLower = 0.0;
+ if (fullRank)
+ {
+ double[] phiAndPrime = phiAndDerivative(0.0, suf, s, Delta);
+ alphaLower = - phiAndPrime[0] / phiAndPrime[1];
+ }
+
+ alpha = (!fullRank && alpha == 0.0) ? alpha = Math.max(0.001 * alphaUpper, Math.pow(alphaLower * alphaUpper, 0.5)) : alpha;
+
+ int iteration = 0;
+ while (iteration < 10) // 10 is default max_iter
+ {
+ alpha = (alpha < alphaLower || alpha > alphaUpper) ? alpha = Math.max(0.001 * alphaUpper, Math.pow(alphaLower * alphaUpper, 0.5)) : alpha;
+ double[] phiAndPrime = phiAndDerivative(alpha, suf, s, Delta);
+ double phi = phiAndPrime[0];
+ double phiPrime = phiAndPrime[1];
+
+ alphaUpper = (phi < 0) ? alpha : alphaUpper;
+ double ratio = phi / phiPrime;
+ alphaLower = Math.max(alphaLower, alpha - ratio);
+ alpha -= (phi + Delta) * ratio / Delta;
+
+ if (Math.abs(phi) < 0.01 * Delta) // default rtol set to 0.01
+ {
+ break;
+ }
+ iteration++;
+ }
+
+ // p = - V.dot( suf / (s**2 + alpha))
+ double[] tmp = MiscMath.elementwiseDivide(suf, MiscMath.elementwiseAdd(MiscMath.elementwiseMultiply(s, s), alpha));
+ double[] p = MiscMath.elementwiseMultiply(V.sumProduct(tmp), -1);
+
+ // Make the norm of p equal to Delta, p is changed only slightly during this.
+ // It is done to prevent p lie outside of the trust region
+ p = MiscMath.elementwiseMultiply(p, Delta / MiscMath.norm(p));
+
+ TrustRegion result = new TrustRegion(p, alpha, iteration + 1);
+ return result;
+ }
+
+ /**
+ * compute values of a quadratic function arising in least squares
+ * function: 0.5 * s.T * (J.T * J + diag) * s + g.T * s
+ *
+ * @param J ~ jacobian matrix
+ * @param g ~ gradient
+ * @param s ~ steps and rows
+ *
+ * @return
+ */
+ private double evaluateQuadratic(MatrixI J, double[] g, double[] s)
+ {
+
+ double[] Js = J.sumProduct(s);
+ double q = MiscMath.dot(Js, Js);
+ double l = MiscMath.dot(s, g);
+
+ return 0.5 * q + l;
+ }
+
+ /**
+ * update the radius of a trust region based on the cost reduction
+ *
+ * @param Delta
+ * @param actualReduction
+ * @param predictedReduction
+ * @param stepNorm
+ * @param boundHit
+ *
+ * @return
+ */
+ private double[] updateTrustRegionRadius(double Delta, double actualReduction, double predictedReduction, double stepNorm, boolean boundHit)
+ {
+ double ratio = 0;
+ if (predictedReduction > 0)
+ {
+ ratio = actualReduction / predictedReduction;
+ } else if (predictedReduction == 0 && actualReduction == 0) {
+ ratio = 1;
+ } else {
+ ratio = 0;
+ }
+
+ if (ratio < 0.25)
+ {
+ Delta = 0.25 * stepNorm;
+ } else if (ratio > 0.75 && boundHit) {
+ Delta *= 2.0;
+ }
+
+ return new double[]{Delta, ratio};
+ }
+
+ /**
+ * trust region reflective algorithm
+ * @param repMatrix ~ Matrix containing representative vectors
+ * @param scoresOld ~ Matrix containing initial observations
+ * @param index ~ current row index
+ * @param J ~ jacobian matrix
+ *
+ * @return
+ */
+ private double[] trf(MatrixI repMatrix, MatrixI scoresOld, int index, MatrixI J)
+ {
+ //hA = x0
+ double[] hA = repMatrix.getRow(index);
+ double[] f0 = originalToEquasionSystem(hA, repMatrix, scoresOld, index);
+ int nfev = 1;
+ int m = J.height();
+ int n = J.width();
+ double cost = 0.5 * MiscMath.dot(f0, f0);
+ double[] g = J.transpose().sumProduct(f0);
+ double Delta = MiscMath.norm(hA);
+ int maxNfev = hA.length * 100;
+ double alpha = 0.0; // "Levenberg-Marquardt" parameter
+
+ double gNorm = 0;
+ boolean terminationStatus = false;
+ int iteration = 0;
+
+ while (true)
+ {
+ gNorm = MiscMath.norm(g);
+ if (terminationStatus || nfev == maxNfev)
+ {
+ break;
+ }
+ SingularValueDecomposition svd = new SingularValueDecomposition(new Array2DRowRealMatrix(J.asArray()));
+ MatrixI U = new Matrix(svd.getU().getData());
+ double[] s = svd.getSingularValues();
+ MatrixI V = new Matrix(svd.getV().getData()).transpose();
+ double[] uf = U.transpose().sumProduct(f0);
+
+ double actualReduction = -1;
+ double[] xNew = new double[hA.length];
+ double[] fNew = new double[f0.length];
+ double costNew = 0;
+ double stepHnorm = 0;
+
+ while (actualReduction <= 0 && nfev < maxNfev)
+ {
+ TrustRegion trustRegion = solveLsqTrustRegion(n, m, uf, s, V, Delta, alpha);
+ double[] stepH = trustRegion.getStep();
+ alpha = trustRegion.getAlpha();
+ int nIterations = trustRegion.getIteration();
+ double predictedReduction = - (evaluateQuadratic(J, g, stepH));
+
+ xNew = MiscMath.elementwiseAdd(hA, stepH);
+ fNew = originalToEquasionSystem(xNew, repMatrix, scoresOld, index);
+ nfev++;
+
+ stepHnorm = MiscMath.norm(stepH);
+
+ if (MiscMath.countNaN(fNew) > 0)
+ {
+ Delta = 0.25 * stepHnorm;
+ continue;
+ }
+
+ // usual trust-region step quality estimation
+ costNew = 0.5 * MiscMath.dot(fNew, fNew);
+ actualReduction = cost - costNew;
+
+ double[] updatedTrustRegion = updateTrustRegionRadius(Delta, actualReduction, predictedReduction, stepHnorm, stepHnorm > (0.95 * Delta));
+ double DeltaNew = updatedTrustRegion[0];
+ double ratio = updatedTrustRegion[1];
+
+ // default ftol and xtol = 1e-8
+ boolean ftolSatisfied = actualReduction < (1e-8 * cost) && ratio > 0.25;
+ boolean xtolSatisfied = stepHnorm < (1e-8 * (1e-8 + MiscMath.norm(hA)));
+ terminationStatus = ftolSatisfied || xtolSatisfied;
+ if (terminationStatus)
+ {
+ break;
+ }
+
+ alpha *= Delta / DeltaNew;
+ Delta = DeltaNew;
+
+ }
+ if (actualReduction > 0)
+ {
+ hA = xNew;
+ f0 = fNew;
+ cost = costNew;
+
+ J = approximateDerivative(repMatrix, scoresOld, index);
+
+ g = J.transpose().sumProduct(f0);
+ } else {
+ stepHnorm = 0;
+ actualReduction = 0;
+ }
+ iteration++;
+ }
+
+ return hA;
+ }
+
+ /**
+ * performs the least squares optimisation
+ * adapted from https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.least_squares.html#scipy.optimize.least_squares
+ *
+ * @param repMatrix ~ Matrix containing representative vectors
+ * @param scoresOld ~ Matrix containing initial observations
+ * @param index ~ current row index
+ *
+ * @return
+ */
+ private double[] leastSquaresOptimisation(MatrixI repMatrix, MatrixI scoresOld, int index)
+ {
+ MatrixI J = approximateDerivative(repMatrix, scoresOld, index);
+ double[] result = trf(repMatrix, scoresOld, index, J);
+ return result;
+ }
+
+}
git://source.jalview.org / jalview.git / blobdiff