diff --git a/src/cad/Java2JS.java b/src/cad/Java2JS.java new file mode 100644 index 00000000..0d095786 --- /dev/null +++ b/src/cad/Java2JS.java @@ -0,0 +1,136 @@ +package cad; + +import java.util.ArrayList; +import java.util.Collections; +import java.util.List; +import java.util.Scanner; +import java.util.regex.MatchResult; +import java.util.regex.Matcher; +import java.util.regex.Pattern; + +public class Java2JS { + + List comments = new ArrayList<>(); + int initCount = 0; + + public void convert() { + + Scanner scanner = new Scanner(Java2JS.class.getResourceAsStream("lm.in")); + + String text = scanner.useDelimiter("\\A").next(); + + text = rplc(text, "(?= comment.start() && matcher.start() < comment.end()) { + return true; + } + } + return false; + } + + + private String rplcParams(String text) { + + buildComment(text); + + Pattern p = Pattern.compile("this\\.[^\\(]+=\\s*function\\s*\\((.+)\\)"); + Matcher matcher = p.matcher(text); + + List replacements = new ArrayList<>(); + + while (matcher.find()) { + replacements.add(matcher.toMatchResult()); + } + + Collections.reverse(replacements); + + int off = text.length(); + StringBuilder out = new StringBuilder(); + for (MatchResult m : replacements) { + if (isComment(m)) continue; + out.insert(0, text.substring(m.end(1), off)); + String sst = m.group(); + out.insert(0, sst.replaceAll("(?This implementation should work even for over-determined systems + * (i.e. systems having more point than equations). Over-determined systems + * are solved by ignoring the point which have the smallest impact according + * to their jacobian column norm. Only the rank of the matrix and some loop bounds + * are changed to implement this.

+ * + *

The resolution engine is a simple translation of the MINPACK lmder routine with minor + * changes. The changes include the over-determined resolution, the use of + * inherited convergence checker and the Q.R. decomposition which has been + * rewritten following the algorithm described in the + * P. Lascaux and R. Theodor book Analyse numérique matricielle + * appliquée à l'art de l'ingénieur, Masson 1986.

+ *

The authors of the original fortran version are: + *

+ * The redistribution policy for MINPACK is available here, for convenience, it + * is reproduced below.

+ * + * + * + * + *
+ * Minpack Copyright Notice (1999) University of Chicago. + * All rights reserved + *
+ * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + *
    + *
  1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer.
    2. + *
  2. Redistributions in binary form must reproduce the above + * copyright notice, this list of conditions and the following + * disclaimer in the documentation and/or other materials provided + * with the distribution.
    3. + *
  3. The end-user documentation included with the redistribution, if any, + * must include the following acknowledgment: + * This product includes software developed by the University of + * Chicago, as Operator of Argonne National Laboratory. + * Alternately, this acknowledgment may appear in the software itself, + * if and wherever such third-party acknowledgments normally appear.
    4. + *
  4. WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS" + * WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE + * UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND + * THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR + * IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES + * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE + * OR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY + * OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR + * USEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF + * THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4) + * DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION + * UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL + * BE CORRECTED.
    5. + *
  5. LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT + * HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF + * ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT, + * INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF + * ANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF + * PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER + * SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT + * (INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE, + * EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE + * POSSIBILITY OF SUCH LOSS OR DAMAGES.
    6. + *
    + * + * @version $Id: LevenbergMarquardtOptimizer.java 1416643 2012-12-03 19:37:14Z tn $ + */ +function LMOptimizer() { + + /** Number of solved point. */ + private int solvedCols; + /** Diagonal elements of the R matrix in the Q.R. decomposition. */ + private double[] diagR; + /** Norms of the columns of the jacobian matrix. */ + private double[] jacNorm; + /** Coefficients of the Householder transforms vectors. */ + private double[] beta; + /** Columns permutation array. */ + private int[] permutation; + /** Rank of the jacobian matrix. */ + private int rank; + /** Levenberg-Marquardt parameter. */ + private double lmPar; + /** Parameters evolution direction associated with lmPar. */ + private double[] lmDir; + /** Positive input variable used in determining the initial step bound. */ + private final double initialStepBoundFactor; + /** Desired relative error in the sum of squares. */ + private final double costRelativeTolerance; + /** Desired relative error in the approximate solution parameters. */ + private final double parRelativeTolerance; + /** Desired max cosine on the orthogonality between the function vector + * and the columns of the jacobian. */ + private final double orthoTolerance; + /** Threshold for QR ranking. */ + private final double qrRankingThreshold; + /** Weighted residuals. */ + private double[] weightedResidual; + /** Weighted Jacobian. */ + private double[][] weightedJacobian; + + /** + * Build an optimizer for least squares problems with default values + * for all the tuning parameters (see the {@link + * #LevenbergMarquardtOptimizer(double,double,double,double,double) + * other contructor}. + * The default values for the algorithm settings are: + * + */ + public X init() { + this.init1(100, 1e-10, 1e-10, 1e-10, Precision.SAFE_MIN); + } + + + + /** + * Build an optimizer for least squares problems with default values + * for some of the tuning parameters (see the {@link + * #LevenbergMarquardtOptimizer(double,double,double,double,double) + * other contructor}. + * The default values for the algorithm settings are: + * + * + * @param costRelativeTolerance Desired relative error in the sum of + * squares. + * @param parRelativeTolerance Desired relative error in the approximate + * solution parameters. + * @param orthoTolerance Desired max cosine on the orthogonality between + * the function vector and the columns of the Jacobian. + */ + public X init0(double costRelativeTolerance, + double parRelativeTolerance, + double orthoTolerance) { + this.init1(100, + costRelativeTolerance, parRelativeTolerance, orthoTolerance, + Precision.SAFE_MIN); + } + + /** + * The arguments control the behaviour of the default convergence checking + * procedure. + * Additional criteria can defined through the setting of a {@link + * ConvergenceChecker}. + * + * @param initialStepBoundFactor Positive input variable used in + * determining the initial step bound. This bound is set to the + * product of initialStepBoundFactor and the euclidean norm of + * {@code diag * x} if non-zero, or else to {@code initialStepBoundFactor} + * itself. In most cases factor should lie in the interval + * {@code (0.1, 100.0)}. {@code 100} is a generally recommended value. + * @param costRelativeTolerance Desired relative error in the sum of + * squares. + * @param parRelativeTolerance Desired relative error in the approximate + * solution parameters. + * @param orthoTolerance Desired max cosine on the orthogonality between + * the function vector and the columns of the Jacobian. + * @param threshold Desired threshold for QR ranking. If the squared norm + * of a column vector is smaller or equal to this threshold during QR + * decomposition, it is considered to be a zero vector and hence the rank + * of the matrix is reduced. + */ + public X init1(double initialStepBoundFactor, + double costRelativeTolerance, + double parRelativeTolerance, + double orthoTolerance, + double threshold) { + this.initialStepBoundFactor = initialStepBoundFactor; + this.costRelativeTolerance = costRelativeTolerance; + this.parRelativeTolerance = parRelativeTolerance; + this.orthoTolerance = orthoTolerance; + this.qrRankingThreshold = threshold; + } + + /** {@inheritDoc} */ + @Override + protected PointVectorValuePair doOptimize() { + final int nR = getTarget().length; // Number of observed data. + final double[] currentPoint = getStartPoint(); + final int nC = currentPoint.length; // Number of parameters. + + // arrays shared with the other private methods + solvedCols = FastMath.min(nR, nC); + diagR = new double[nC]; + jacNorm = new double[nC]; + beta = new double[nC]; + permutation = new int[nC]; + lmDir = new double[nC]; + + // local point + double delta = 0; + double xNorm = 0; + double[] diag = new double[nC]; + double[] oldX = new double[nC]; + double[] oldRes = new double[nR]; + double[] oldObj = new double[nR]; + double[] qtf = new double[nR]; + double[] work1 = new double[nC]; + double[] work2 = new double[nC]; + double[] work3 = new double[nC]; + + final RealMatrix weightMatrixSqrt = getWeightSquareRoot(); + + // Evaluate the function at the starting point and calculate its norm. + double[] currentObjective = computeObjectiveValue(currentPoint); + double[] currentResiduals = computeResiduals(currentObjective); + PointVectorValuePair current = new PointVectorValuePair(currentPoint, currentObjective); + double currentCost = computeCost(currentResiduals); + + // Outer loop. + lmPar = 0; + boolean firstIteration = true; + int iter = 0; + final ConvergenceChecker checker = getConvergenceChecker(); + while (true) { + ++iter; + final PointVectorValuePair previous = current; + + // QR decomposition of the jacobian matrix + qrDecomposition(computeWeightedJacobian(currentPoint)); + + weightedResidual = weightMatrixSqrt.operate(currentResiduals); + for (int i = 0; i < nR; i++) { + qtf[i] = weightedResidual[i]; + } + + // compute Qt.res + qTy(qtf); + + // now we don't need Q anymore, + // so let jacobian contain the R matrix with its diagonal elements + for (int k = 0; k < solvedCols; ++k) { + int pk = permutation[k]; + weightedJacobian[k][pk] = diagR[pk]; + } + + if (firstIteration) { + // scale the point according to the norms of the columns + // of the initial jacobian + xNorm = 0; + for (int k = 0; k < nC; ++k) { + double dk = jacNorm[k]; + if (dk == 0) { + dk = 1.0; + } + double xk = dk * currentPoint[k]; + xNorm += xk * xk; + diag[k] = dk; + } + xNorm = FastMath.sqrt(xNorm); + + // initialize the step bound delta + delta = (xNorm == 0) ? initialStepBoundFactor : (initialStepBoundFactor * xNorm); + } + + // check orthogonality between function vector and jacobian columns + double maxCosine = 0; + if (currentCost != 0) { + for (int j = 0; j < solvedCols; ++j) { + int pj = permutation[j]; + double s = jacNorm[pj]; + if (s != 0) { + double sum = 0; + for (int i = 0; i <= j; ++i) { + sum += weightedJacobian[i][pj] * qtf[i]; + } + maxCosine = FastMath.max(maxCosine, FastMath.abs(sum) / (s * currentCost)); + } + } + } + if (maxCosine <= orthoTolerance) { + // Convergence has been reached. + setCost(currentCost); + return current; + } + + // rescale if necessary + for (int j = 0; j < nC; ++j) { + diag[j] = FastMath.max(diag[j], jacNorm[j]); + } + + // Inner loop. + for (double ratio = 0; ratio < 1.0e-4;) { + + // save the state + for (int j = 0; j < solvedCols; ++j) { + int pj = permutation[j]; + oldX[pj] = currentPoint[pj]; + } + final double previousCost = currentCost; + double[] tmpVec = weightedResidual; + weightedResidual = oldRes; + oldRes = tmpVec; + tmpVec = currentObjective; + currentObjective = oldObj; + oldObj = tmpVec; + + // determine the Levenberg-Marquardt parameter + determineLMParameter(qtf, delta, diag, work1, work2, work3); + + // compute the new point and the norm of the evolution direction + double lmNorm = 0; + for (int j = 0; j < solvedCols; ++j) { + int pj = permutation[j]; + lmDir[pj] = -lmDir[pj]; + currentPoint[pj] = oldX[pj] + lmDir[pj]; + double s = diag[pj] * lmDir[pj]; + lmNorm += s * s; + } + lmNorm = FastMath.sqrt(lmNorm); + // on the first iteration, adjust the initial step bound. + if (firstIteration) { + delta = FastMath.min(delta, lmNorm); + } + + // Evaluate the function at x + p and calculate its norm. + currentObjective = computeObjectiveValue(currentPoint); + currentResiduals = computeResiduals(currentObjective); + current = new PointVectorValuePair(currentPoint, currentObjective); + currentCost = computeCost(currentResiduals); + + // compute the scaled actual reduction + double actRed = -1.0; + if (0.1 * currentCost < previousCost) { + double r = currentCost / previousCost; + actRed = 1.0 - r * r; + } + + // compute the scaled predicted reduction + // and the scaled directional derivative + for (int j = 0; j < solvedCols; ++j) { + int pj = permutation[j]; + double dirJ = lmDir[pj]; + work1[j] = 0; + for (int i = 0; i <= j; ++i) { + work1[i] += weightedJacobian[i][pj] * dirJ; + } + } + double coeff1 = 0; + for (int j = 0; j < solvedCols; ++j) { + coeff1 += work1[j] * work1[j]; + } + double pc2 = previousCost * previousCost; + coeff1 = coeff1 / pc2; + double coeff2 = lmPar * lmNorm * lmNorm / pc2; + double preRed = coeff1 + 2 * coeff2; + double dirDer = -(coeff1 + coeff2); + + // ratio of the actual to the predicted reduction + ratio = (preRed == 0) ? 0 : (actRed / preRed); + + // update the step bound + if (ratio <= 0.25) { + double tmp = + (actRed < 0) ? (0.5 * dirDer / (dirDer + 0.5 * actRed)) : 0.5; + if ((0.1 * currentCost >= previousCost) || (tmp < 0.1)) { + tmp = 0.1; + } + delta = tmp * FastMath.min(delta, 10.0 * lmNorm); + lmPar /= tmp; + } else if ((lmPar == 0) || (ratio >= 0.75)) { + delta = 2 * lmNorm; + lmPar *= 0.5; + } + + // test for successful iteration. + if (ratio >= 1.0e-4) { + // successful iteration, update the norm + firstIteration = false; + xNorm = 0; + for (int k = 0; k < nC; ++k) { + double xK = diag[k] * currentPoint[k]; + xNorm += xK * xK; + } + xNorm = FastMath.sqrt(xNorm); + + // tests for convergence. + if (checker != null) { + // we use the vectorial convergence checker + if (checker.converged(iter, previous, current)) { + setCost(currentCost); + return current; + } + } + } else { + // failed iteration, reset the previous values + currentCost = previousCost; + for (int j = 0; j < solvedCols; ++j) { + int pj = permutation[j]; + currentPoint[pj] = oldX[pj]; + } + tmpVec = weightedResidual; + weightedResidual = oldRes; + oldRes = tmpVec; + tmpVec = currentObjective; + currentObjective = oldObj; + oldObj = tmpVec; + // Reset "current" to previous values. + current = new PointVectorValuePair(currentPoint, currentObjective); + } + + // Default convergence criteria. + if ((FastMath.abs(actRed) <= costRelativeTolerance && + preRed <= costRelativeTolerance && + ratio <= 2.0) || + delta <= parRelativeTolerance * xNorm) { + setCost(currentCost); + return current; + } + + // tests for termination and stringent tolerances + // (2.2204e-16 is the machine epsilon for IEEE754) + if ((FastMath.abs(actRed) <= 2.2204e-16) && (preRed <= 2.2204e-16) && (ratio <= 2.0)) { + throw "TOO_SMALL_COST_RELATIVE_TOLERANCE: " + costRelativeTolerance; + } else if (delta <= 2.2204e-16 * xNorm) { + throw "TOO_SMALL_PARAMETERS_RELATIVE_TOLERANCE: " + parRelativeTolerance; + } else if (maxCosine <= 2.2204e-16) { + throw "TOO_SMALL_ORTHOGONALITY_TOLERANCE: " + orthoTolerance; + } + } + } + } + + /** + * Determine the Levenberg-Marquardt parameter. + *

    This implementation is a translation in Java of the MINPACK + * lmpar + * routine.

    + *

    This method sets the lmPar and lmDir attributes.

    + *

    The authors of the original fortran function are:

    + *
      + *
    • Argonne National Laboratory. MINPACK project. March 1980
      • + *
    • Burton S. Garbow
      • + *
    • Kenneth E. Hillstrom
      • + *
    • Jorge J. More
      • + *
    + *

    Luc Maisonobe did the Java translation.

    + * + * @param qy array containing qTy + * @param delta upper bound on the euclidean norm of diagR * lmDir + * @param diag diagonal matrix + * @param work1 work array + * @param work2 work array + * @param work3 work array + */ + private void determineLMParameter(double[] qy, double delta, double[] diag, + double[] work1, double[] work2, double[] work3) { + final int nC = weightedJacobian[0].length; + + // compute and store in x the gauss-newton direction, if the + // jacobian is rank-deficient, obtain a least squares solution + for (int j = 0; j < rank; ++j) { + lmDir[permutation[j]] = qy[j]; + } + for (int j = rank; j < nC; ++j) { + lmDir[permutation[j]] = 0; + } + for (int k = rank - 1; k >= 0; --k) { + int pk = permutation[k]; + double ypk = lmDir[pk] / diagR[pk]; + for (int i = 0; i < k; ++i) { + lmDir[permutation[i]] -= ypk * weightedJacobian[i][pk]; + } + lmDir[pk] = ypk; + } + + // evaluate the function at the origin, and test + // for acceptance of the Gauss-Newton direction + double dxNorm = 0; + for (int j = 0; j < solvedCols; ++j) { + int pj = permutation[j]; + double s = diag[pj] * lmDir[pj]; + work1[pj] = s; + dxNorm += s * s; + } + dxNorm = FastMath.sqrt(dxNorm); + double fp = dxNorm - delta; + if (fp <= 0.1 * delta) { + lmPar = 0; + return; + } + + // if the jacobian is not rank deficient, the Newton step provides + // a lower bound, parl, for the zero of the function, + // otherwise set this bound to zero + double sum2; + double parl = 0; + if (rank == solvedCols) { + for (int j = 0; j < solvedCols; ++j) { + int pj = permutation[j]; + work1[pj] *= diag[pj] / dxNorm; + } + sum2 = 0; + for (int j = 0; j < solvedCols; ++j) { + int pj = permutation[j]; + double sum = 0; + for (int i = 0; i < j; ++i) { + sum += weightedJacobian[i][pj] * work1[permutation[i]]; + } + double s = (work1[pj] - sum) / diagR[pj]; + work1[pj] = s; + sum2 += s * s; + } + parl = fp / (delta * sum2); + } + + // calculate an upper bound, paru, for the zero of the function + sum2 = 0; + for (int j = 0; j < solvedCols; ++j) { + int pj = permutation[j]; + double sum = 0; + for (int i = 0; i <= j; ++i) { + sum += weightedJacobian[i][pj] * qy[i]; + } + sum /= diag[pj]; + sum2 += sum * sum; + } + double gNorm = FastMath.sqrt(sum2); + double paru = gNorm / delta; + if (paru == 0) { + // 2.2251e-308 is the smallest positive real for IEE754 + paru = 2.2251e-308 / FastMath.min(delta, 0.1); + } + + // if the input par lies outside of the interval (parl,paru), + // set par to the closer endpoint + lmPar = FastMath.min(paru, FastMath.max(lmPar, parl)); + if (lmPar == 0) { + lmPar = gNorm / dxNorm; + } + + for (int countdown = 10; countdown >= 0; --countdown) { + + // evaluate the function at the current value of lmPar + if (lmPar == 0) { + lmPar = FastMath.max(2.2251e-308, 0.001 * paru); + } + double sPar = FastMath.sqrt(lmPar); + for (int j = 0; j < solvedCols; ++j) { + int pj = permutation[j]; + work1[pj] = sPar * diag[pj]; + } + determineLMDirection(qy, work1, work2, work3); + + dxNorm = 0; + for (int j = 0; j < solvedCols; ++j) { + int pj = permutation[j]; + double s = diag[pj] * lmDir[pj]; + work3[pj] = s; + dxNorm += s * s; + } + dxNorm = FastMath.sqrt(dxNorm); + double previousFP = fp; + fp = dxNorm - delta; + + // if the function is small enough, accept the current value + // of lmPar, also test for the exceptional cases where parl is zero + if ((FastMath.abs(fp) <= 0.1 * delta) || + ((parl == 0) && (fp <= previousFP) && (previousFP < 0))) { + return; + } + + // compute the Newton correction + for (int j = 0; j < solvedCols; ++j) { + int pj = permutation[j]; + work1[pj] = work3[pj] * diag[pj] / dxNorm; + } + for (int j = 0; j < solvedCols; ++j) { + int pj = permutation[j]; + work1[pj] /= work2[j]; + double tmp = work1[pj]; + for (int i = j + 1; i < solvedCols; ++i) { + work1[permutation[i]] -= weightedJacobian[i][pj] * tmp; + } + } + sum2 = 0; + for (int j = 0; j < solvedCols; ++j) { + double s = work1[permutation[j]]; + sum2 += s * s; + } + double correction = fp / (delta * sum2); + + // depending on the sign of the function, update parl or paru. + if (fp > 0) { + parl = FastMath.max(parl, lmPar); + } else if (fp < 0) { + paru = FastMath.min(paru, lmPar); + } + + // compute an improved estimate for lmPar + lmPar = FastMath.max(parl, lmPar + correction); + + } + } + + /** + * Solve a*x = b and d*x = 0 in the least squares sense. + *

    This implementation is a translation in Java of the MINPACK + * qrsolv + * routine.

    + *

    This method sets the lmDir and lmDiag attributes.

    + *

    The authors of the original fortran function are:

    + *
      + *
    • Argonne National Laboratory. MINPACK project. March 1980
      • + *
    • Burton S. Garbow
      • + *
    • Kenneth E. Hillstrom
      • + *
    • Jorge J. More
      • + *
    + *

    Luc Maisonobe did the Java translation.

    + * + * @param qy array containing qTy + * @param diag diagonal matrix + * @param lmDiag diagonal elements associated with lmDir + * @param work work array + */ + private void determineLMDirection(double[] qy, double[] diag, + double[] lmDiag, double[] work) { + + // copy R and Qty to preserve input and initialize s + // in particular, save the diagonal elements of R in lmDir + for (int j = 0; j < solvedCols; ++j) { + int pj = permutation[j]; + for (int i = j + 1; i < solvedCols; ++i) { + weightedJacobian[i][pj] = weightedJacobian[j][permutation[i]]; + } + lmDir[j] = diagR[pj]; + work[j] = qy[j]; + } + + // eliminate the diagonal matrix d using a Givens rotation + for (int j = 0; j < solvedCols; ++j) { + + // prepare the row of d to be eliminated, locating the + // diagonal element using p from the Q.R. factorization + int pj = permutation[j]; + double dpj = diag[pj]; + if (dpj != 0) { + Arrays.fill(lmDiag, j + 1, lmDiag.length, 0); + } + lmDiag[j] = dpj; + + // the transformations to eliminate the row of d + // modify only a single element of Qty + // beyond the first n, which is initially zero. + double qtbpj = 0; + for (int k = j; k < solvedCols; ++k) { + int pk = permutation[k]; + + // determine a Givens rotation which eliminates the + // appropriate element in the current row of d + if (lmDiag[k] != 0) { + + final double sin; + final double cos; + double rkk = weightedJacobian[k][pk]; + if (FastMath.abs(rkk) < FastMath.abs(lmDiag[k])) { + final double cotan = rkk / lmDiag[k]; + sin = 1.0 / FastMath.sqrt(1.0 + cotan * cotan); + cos = sin * cotan; + } else { + final double tan = lmDiag[k] / rkk; + cos = 1.0 / FastMath.sqrt(1.0 + tan * tan); + sin = cos * tan; + } + + // compute the modified diagonal element of R and + // the modified element of (Qty,0) + weightedJacobian[k][pk] = cos * rkk + sin * lmDiag[k]; + final double temp = cos * work[k] + sin * qtbpj; + qtbpj = -sin * work[k] + cos * qtbpj; + work[k] = temp; + + // accumulate the tranformation in the row of s + for (int i = k + 1; i < solvedCols; ++i) { + double rik = weightedJacobian[i][pk]; + final double temp2 = cos * rik + sin * lmDiag[i]; + lmDiag[i] = -sin * rik + cos * lmDiag[i]; + weightedJacobian[i][pk] = temp2; + } + } + } + + // store the diagonal element of s and restore + // the corresponding diagonal element of R + lmDiag[j] = weightedJacobian[j][permutation[j]]; + weightedJacobian[j][permutation[j]] = lmDir[j]; + } + + // solve the triangular system for z, if the system is + // singular, then obtain a least squares solution + int nSing = solvedCols; + for (int j = 0; j < solvedCols; ++j) { + if ((lmDiag[j] == 0) && (nSing == solvedCols)) { + nSing = j; + } + if (nSing < solvedCols) { + work[j] = 0; + } + } + if (nSing > 0) { + for (int j = nSing - 1; j >= 0; --j) { + int pj = permutation[j]; + double sum = 0; + for (int i = j + 1; i < nSing; ++i) { + sum += weightedJacobian[i][pj] * work[i]; + } + work[j] = (work[j] - sum) / lmDiag[j]; + } + } + + // permute the components of z back to components of lmDir + for (int j = 0; j < lmDir.length; ++j) { + lmDir[permutation[j]] = work[j]; + } + } + + /** + * Decompose a matrix A as A.P = Q.R using Householder transforms. + *

    As suggested in the P. Lascaux and R. Theodor book + * Analyse numérique matricielle appliquée à + * l'art de l'ingénieur (Masson, 1986), instead of representing + * the Householder transforms with uk unit vectors such that: + * 

    +     * Hk = I - 2uk.ukt
+     *
    + * we use k non-unit vectors such that: + * 
    +     * Hk = I - betakvk.vkt
+     *
    + * where vk = ak - alphak ek. + * The betak coefficients are provided upon exit as recomputing + * them from the vk vectors would be costly.

    + *

    This decomposition handles rank deficient cases since the tranformations + * are performed in non-increasing columns norms order thanks to columns + * pivoting. The diagonal elements of the R matrix are therefore also in + * non-increasing absolute values order.

    + * + * @param jacobian Weighted Jacobian matrix at the current point. + * @exception ConvergenceException if the decomposition cannot be performed + */ + private void qrDecomposition(RealMatrix jacobian) { + // Code in this class assumes that the weighted Jacobian is -(W^(1/2) J), + // hence the multiplication by -1. + weightedJacobian = jacobian.scalarMultiply(-1).getData(); + + final int nR = weightedJacobian.length; + final int nC = weightedJacobian[0].length; + + // initializations + for (int k = 0; k < nC; ++k) { + permutation[k] = k; + double norm2 = 0; + for (int i = 0; i < nR; ++i) { + double akk = weightedJacobian[i][k]; + norm2 += akk * akk; + } + jacNorm[k] = FastMath.sqrt(norm2); + } + + // transform the matrix column after column + for (int k = 0; k < nC; ++k) { + + // select the column with the greatest norm on active components + int nextColumn = -1; + double ak2 = Double.NEGATIVE_INFINITY; + for (int i = k; i < nC; ++i) { + double norm2 = 0; + for (int j = k; j < nR; ++j) { + double aki = weightedJacobian[j][permutation[i]]; + norm2 += aki * aki; + } + if (!isFinite(norm2)) { + throw "UNABLE_TO_PERFORM_QR_DECOMPOSITION_ON_JACOBIAN"; + } + if (norm2 > ak2) { + nextColumn = i; + ak2 = norm2; + } + } + if (ak2 <= qrRankingThreshold) { + rank = k; + return; + } + int pk = permutation[nextColumn]; + permutation[nextColumn] = permutation[k]; + permutation[k] = pk; + + // choose alpha such that Hk.u = alpha ek + double akk = weightedJacobian[k][pk]; + double alpha = (akk > 0) ? -FastMath.sqrt(ak2) : FastMath.sqrt(ak2); + double betak = 1.0 / (ak2 - akk * alpha); + beta[pk] = betak; + + // transform the current column + diagR[pk] = alpha; + weightedJacobian[k][pk] -= alpha; + + // transform the remaining columns + for (int dk = nC - 1 - k; dk > 0; --dk) { + double gamma = 0; + for (int j = k; j < nR; ++j) { + gamma += weightedJacobian[j][pk] * weightedJacobian[j][permutation[k + dk]]; + } + gamma *= betak; + for (int j = k; j < nR; ++j) { + weightedJacobian[j][permutation[k + dk]] -= gamma * weightedJacobian[j][pk]; + } + } + } + rank = solvedCols; + } + + /** + * Compute the product Qt.y for some Q.R. decomposition. + * + * @param y vector to multiply (will be overwritten with the result) + */ + private void qTy(double[] y) { + final int nR = weightedJacobian.length; + final int nC = weightedJacobian[0].length; + + for (int k = 0; k < nC; ++k) { + int pk = permutation[k]; + double gamma = 0; + for (int i = k; i < nR; ++i) { + gamma += weightedJacobian[i][pk] * y[i]; + } + gamma *= beta[pk]; + for (int i = k; i < nR; ++i) { + y[i] -= gamma * weightedJacobian[i][pk]; + } + } + } +} diff --git a/web/app/optim/lm.js b/web/app/optim/lm.js new file mode 100644 index 00000000..e69de29b