List of usage examples for org.apache.commons.math3.exception MathIllegalStateException MathIllegalStateException
public MathIllegalStateException(Localizable pattern, Object... args)
From source file:com.itemanalysis.psychometrics.optimization.BOBYQAOptimizer.java
/** * The arguments N, NPT, X, XL, XU, RHOBEG, RHOEND, IPRINT and MAXFUN * are identical to the corresponding arguments in SUBROUTINE BOBYQA. * XBASE holds a shift of origin that should reduce the contributions * from rounding errors to values of the model and Lagrange functions. * XPT is a two-dimensional array that holds the coordinates of the * interpolation points relative to XBASE. * FVAL holds the values of F at the interpolation points. * XOPT is set to the displacement from XBASE of the trust region centre. * GOPT holds the gradientAt of the quadratic model at XBASE+XOPT. * HQ holds the explicit second derivatives of the quadratic model. * PQ contains the parameters of the implicit second derivatives of the * quadratic model.// w w w.ja v a 2s .c om * BMAT holds the last N columns of H. * ZMAT holds the factorization of the leading NPT by NPT submatrix of H, * this factorization being ZMAT times ZMAT^T, which provides both the * correct rank and positive semi-definiteness. * NDIM is the first dimension of BMAT and has the value NPT+N. * SL and SU hold the differences XL-XBASE and XU-XBASE, respectively. * All the components of every XOPT are going to satisfy the bounds * SL(I) .LEQ. XOPT(I) .LEQ. SU(I), with appropriate equalities when * XOPT is on a constraint boundary. * XNEW is chosen by SUBROUTINE TRSBOX or ALTMOV. Usually XBASE+XNEW is the * vector of variables for the next call of CALFUN. XNEW also satisfies * the SL and SU constraints in the way that has just been mentioned. * XALT is an alternative to XNEW, chosen by ALTMOV, that may replace XNEW * in order to increase the denominator in the updating of UPDATE. * D is reserved for a trial step from XOPT, which is usually XNEW-XOPT. * VLAG contains the values of the Lagrange functions at a new point X. * They are part of a product that requires VLAG to be of length NDIM. * W is a one-dimensional array that is used for working space. Its length * must be at least 3*NDIM = 3*(NPT+N). * * @param lowerBound Lower bounds. * @param upperBound Upper bounds. * @return the value of the objective at the optimum. */ private double bobyqb(double[] lowerBound, double[] upperBound) { printMethod(); // XXX final int n = currentBest.getDimension(); final int npt = numberOfInterpolationPoints; final int np = n + 1; final int nptm = npt - np; final int nh = n * np / 2; final ArrayRealVector work1 = new ArrayRealVector(n); final ArrayRealVector work2 = new ArrayRealVector(npt); final ArrayRealVector work3 = new ArrayRealVector(npt); double cauchy = Double.NaN; double alpha = Double.NaN; double dsq = Double.NaN; double crvmin = Double.NaN; // Set some constants. // Parameter adjustments // Function Body // The call of PRELIM sets the elements of XBASE, XPT, FVAL, GOPT, HQ, PQ, // BMAT and ZMAT for the first iteration, with the corresponding values of // of NF and KOPT, which are the number of calls of CALFUN so far and the // index of the interpolation point at the trust region centre. Then the // initial XOPT is set too. The branch to label 720 occurs if MAXFUN is // less than NPT. GOPT will be updated if KOPT is different from KBASE. trustRegionCenterInterpolationPointIndex = 0; prelim(lowerBound, upperBound); double xoptsq = ZERO; for (int i = 0; i < n; i++) { trustRegionCenterOffset.setEntry(i, interpolationPoints.getEntry(trustRegionCenterInterpolationPointIndex, i)); // Computing 2nd power final double deltaOne = trustRegionCenterOffset.getEntry(i); xoptsq += deltaOne * deltaOne; } double fsave = fAtInterpolationPoints.getEntry(0); final int kbase = 0; // Complete the settings that are required for the iterative procedure. int ntrits = 0; int itest = 0; int knew = 0; int nfsav = getEvaluations(); double rho = initialTrustRegionRadius; double delta = rho; double diffa = ZERO; double diffb = ZERO; double diffc = ZERO; double f = ZERO; double beta = ZERO; double adelt = ZERO; double denom = ZERO; double ratio = ZERO; double dnorm = ZERO; double scaden = ZERO; double biglsq = ZERO; double distsq = ZERO; // Update GOPT if necessary before the first iteration and after each // call of RESCUE that makes a call of CALFUN. int state = 20; for (;;) switch (state) { case 20: { printState(20); // XXX if (trustRegionCenterInterpolationPointIndex != kbase) { int ih = 0; for (int j = 0; j < n; j++) { for (int i = 0; i <= j; i++) { if (i < j) { gradientAtTrustRegionCenter.setEntry(j, gradientAtTrustRegionCenter.getEntry(j) + modelSecondDerivativesValues.getEntry(ih) * trustRegionCenterOffset.getEntry(i)); } gradientAtTrustRegionCenter.setEntry(i, gradientAtTrustRegionCenter.getEntry(i) + modelSecondDerivativesValues.getEntry(ih) * trustRegionCenterOffset.getEntry(j)); ih++; } } if (getEvaluations() > npt) { for (int k = 0; k < npt; k++) { double temp = ZERO; for (int j = 0; j < n; j++) { temp += interpolationPoints.getEntry(k, j) * trustRegionCenterOffset.getEntry(j); } temp *= modelSecondDerivativesParameters.getEntry(k); for (int i = 0; i < n; i++) { gradientAtTrustRegionCenter.setEntry(i, gradientAtTrustRegionCenter.getEntry(i) + temp * interpolationPoints.getEntry(k, i)); } } // throw new PathIsExploredException(); // XXX } } // Generate the next point in the trust region that provides a small value // of the quadratic model subject to the constraints on the variables. // The int NTRITS is set to the number "trust region" iterations that // have occurred since the last "alternative" iteration. If the length // of XNEW-XOPT is less than HALF*RHO, however, then there is a branch to // label 650 or 680 with NTRITS=-1, instead of calculating F at XNEW. } case 60: { printState(60); // XXX final ArrayRealVector gnew = new ArrayRealVector(n); final ArrayRealVector xbdi = new ArrayRealVector(n); final ArrayRealVector s = new ArrayRealVector(n); final ArrayRealVector hs = new ArrayRealVector(n); final ArrayRealVector hred = new ArrayRealVector(n); final double[] dsqCrvmin = trsbox(delta, gnew, xbdi, s, hs, hred); dsq = dsqCrvmin[0]; crvmin = dsqCrvmin[1]; // Computing MIN double deltaOne = delta; double deltaTwo = Math.sqrt(dsq); dnorm = Math.min(deltaOne, deltaTwo); if (dnorm < HALF * rho) { ntrits = -1; // Computing 2nd power deltaOne = TEN * rho; distsq = deltaOne * deltaOne; if (getEvaluations() <= nfsav + 2) { state = 650; break; } // The following choice between labels 650 and 680 depends on whether or // not our work with the current RHO seems to be complete. Either RHO is // decreased or termination occurs if the errors in the quadratic model at // the last three interpolation points compare favourably with predictions // of likely improvements to the model within distance HALF*RHO of XOPT. // Computing MAX deltaOne = Math.max(diffa, diffb); final double errbig = Math.max(deltaOne, diffc); final double frhosq = rho * ONE_OVER_EIGHT * rho; if (crvmin > ZERO && errbig > frhosq * crvmin) { state = 650; break; } final double bdtol = errbig / rho; for (int j = 0; j < n; j++) { double bdtest = bdtol; if (newPoint.getEntry(j) == lowerDifference.getEntry(j)) { bdtest = work1.getEntry(j); } if (newPoint.getEntry(j) == upperDifference.getEntry(j)) { bdtest = -work1.getEntry(j); } if (bdtest < bdtol) { double curv = modelSecondDerivativesValues.getEntry((j + j * j) / 2); for (int k = 0; k < npt; k++) { // Computing 2nd power final double d1 = interpolationPoints.getEntry(k, j); curv += modelSecondDerivativesParameters.getEntry(k) * (d1 * d1); } bdtest += HALF * curv * rho; if (bdtest < bdtol) { state = 650; break; } // throw new PathIsExploredException(); // XXX } } state = 680; break; } ++ntrits; // Severe cancellation is likely to occur if XOPT is too far from XBASE. // If the following test holds, then XBASE is shifted so that XOPT becomes // zero. The appropriate changes are made to BMAT and to the second // derivatives of the current model, beginning with the changes to BMAT // that do not depend on ZMAT. VLAG is used temporarily for working space. } case 90: { printState(90); // XXX if (dsq <= xoptsq * ONE_OVER_A_THOUSAND) { final double fracsq = xoptsq * ONE_OVER_FOUR; double sumpq = ZERO; // final RealVector sumVector // = new ArrayRealVector(npt, -HALF * xoptsq).add(interpolationPoints.operate(trustRegionCenter)); for (int k = 0; k < npt; k++) { sumpq += modelSecondDerivativesParameters.getEntry(k); double sum = -HALF * xoptsq; for (int i = 0; i < n; i++) { sum += interpolationPoints.getEntry(k, i) * trustRegionCenterOffset.getEntry(i); } // sum = sumVector.getEntry(k); // XXX "testAckley" and "testDiffPow" fail. work2.setEntry(k, sum); final double temp = fracsq - HALF * sum; for (int i = 0; i < n; i++) { work1.setEntry(i, bMatrix.getEntry(k, i)); lagrangeValuesAtNewPoint.setEntry(i, sum * interpolationPoints.getEntry(k, i) + temp * trustRegionCenterOffset.getEntry(i)); final int ip = npt + i; for (int j = 0; j <= i; j++) { bMatrix.setEntry(ip, j, bMatrix.getEntry(ip, j) + work1.getEntry(i) * lagrangeValuesAtNewPoint.getEntry(j) + lagrangeValuesAtNewPoint.getEntry(i) * work1.getEntry(j)); } } } // Then the revisions of BMAT that depend on ZMAT are calculated. for (int m = 0; m < nptm; m++) { double sumz = ZERO; double sumw = ZERO; for (int k = 0; k < npt; k++) { sumz += zMatrix.getEntry(k, m); lagrangeValuesAtNewPoint.setEntry(k, work2.getEntry(k) * zMatrix.getEntry(k, m)); sumw += lagrangeValuesAtNewPoint.getEntry(k); } for (int j = 0; j < n; j++) { double sum = (fracsq * sumz - HALF * sumw) * trustRegionCenterOffset.getEntry(j); for (int k = 0; k < npt; k++) { sum += lagrangeValuesAtNewPoint.getEntry(k) * interpolationPoints.getEntry(k, j); } work1.setEntry(j, sum); for (int k = 0; k < npt; k++) { bMatrix.setEntry(k, j, bMatrix.getEntry(k, j) + sum * zMatrix.getEntry(k, m)); } } for (int i = 0; i < n; i++) { final int ip = i + npt; final double temp = work1.getEntry(i); for (int j = 0; j <= i; j++) { bMatrix.setEntry(ip, j, bMatrix.getEntry(ip, j) + temp * work1.getEntry(j)); } } } // The following instructions complete the shift, including the changes // to the second derivative parameters of the quadratic model. int ih = 0; for (int j = 0; j < n; j++) { work1.setEntry(j, -HALF * sumpq * trustRegionCenterOffset.getEntry(j)); for (int k = 0; k < npt; k++) { work1.setEntry(j, work1.getEntry(j) + modelSecondDerivativesParameters.getEntry(k) * interpolationPoints.getEntry(k, j)); interpolationPoints.setEntry(k, j, interpolationPoints.getEntry(k, j) - trustRegionCenterOffset.getEntry(j)); } for (int i = 0; i <= j; i++) { modelSecondDerivativesValues.setEntry(ih, modelSecondDerivativesValues.getEntry(ih) + work1.getEntry(i) * trustRegionCenterOffset.getEntry(j) + trustRegionCenterOffset.getEntry(i) * work1.getEntry(j)); bMatrix.setEntry(npt + i, j, bMatrix.getEntry(npt + j, i)); ih++; } } for (int i = 0; i < n; i++) { originShift.setEntry(i, originShift.getEntry(i) + trustRegionCenterOffset.getEntry(i)); newPoint.setEntry(i, newPoint.getEntry(i) - trustRegionCenterOffset.getEntry(i)); lowerDifference.setEntry(i, lowerDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i)); upperDifference.setEntry(i, upperDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i)); trustRegionCenterOffset.setEntry(i, ZERO); } xoptsq = ZERO; } if (ntrits == 0) { state = 210; break; } state = 230; break; // XBASE is also moved to XOPT by a call of RESCUE. This calculation is // more expensive than the previous shift, because new matrices BMAT and // ZMAT are generated from scratch, which may include the replacement of // interpolation points whose positions seem to be causing near linear // dependence in the interpolation conditions. Therefore RESCUE is called // only if rounding errors have reduced by at least a factor of two the // denominator of the formula for updating the H matrix. It provides a // useful safeguard, but is not invoked in most applications of BOBYQA. } case 210: { printState(210); // XXX // Pick two alternative vectors of variables, relative to XBASE, that // are suitable as new positions of the KNEW-th interpolation point. // Firstly, XNEW is set to the point on a line through XOPT and another // interpolation point that minimizes the predicted value of the next // denominator, subject to ||XNEW - XOPT|| .LEQ. ADELT and to the SL // and SU bounds. Secondly, XALT is set to the best feasible point on // a constrained version of the Cauchy step of the KNEW-th Lagrange // function, the corresponding value of the square of this function // being returned in CAUCHY. The choice between these alternatives is // going to be made when the denominator is calculated. final double[] alphaCauchy = altmov(knew, adelt); alpha = alphaCauchy[0]; cauchy = alphaCauchy[1]; for (int i = 0; i < n; i++) { trialStepPoint.setEntry(i, newPoint.getEntry(i) - trustRegionCenterOffset.getEntry(i)); } // Calculate VLAG and BETA for the current choice of D. The scalar // product of D with XPT(K,.) is going to be held in W(NPT+K) for // use when VQUAD is calculated. } case 230: { printState(230); // XXX for (int k = 0; k < npt; k++) { double suma = ZERO; double sumb = ZERO; double sum = ZERO; for (int j = 0; j < n; j++) { suma += interpolationPoints.getEntry(k, j) * trialStepPoint.getEntry(j); sumb += interpolationPoints.getEntry(k, j) * trustRegionCenterOffset.getEntry(j); sum += bMatrix.getEntry(k, j) * trialStepPoint.getEntry(j); } work3.setEntry(k, suma * (HALF * suma + sumb)); lagrangeValuesAtNewPoint.setEntry(k, sum); work2.setEntry(k, suma); } beta = ZERO; for (int m = 0; m < nptm; m++) { double sum = ZERO; for (int k = 0; k < npt; k++) { sum += zMatrix.getEntry(k, m) * work3.getEntry(k); } beta -= sum * sum; for (int k = 0; k < npt; k++) { lagrangeValuesAtNewPoint.setEntry(k, lagrangeValuesAtNewPoint.getEntry(k) + sum * zMatrix.getEntry(k, m)); } } dsq = ZERO; double bsum = ZERO; double dx = ZERO; for (int j = 0; j < n; j++) { // Computing 2nd power final double d1 = trialStepPoint.getEntry(j); dsq += d1 * d1; double sum = ZERO; for (int k = 0; k < npt; k++) { sum += work3.getEntry(k) * bMatrix.getEntry(k, j); } bsum += sum * trialStepPoint.getEntry(j); final int jp = npt + j; for (int i = 0; i < n; i++) { sum += bMatrix.getEntry(jp, i) * trialStepPoint.getEntry(i); } lagrangeValuesAtNewPoint.setEntry(jp, sum); bsum += sum * trialStepPoint.getEntry(j); dx += trialStepPoint.getEntry(j) * trustRegionCenterOffset.getEntry(j); } beta = dx * dx + dsq * (xoptsq + dx + dx + HALF * dsq) + beta - bsum; // Original // beta += dx * dx + dsq * (xoptsq + dx + dx + HALF * dsq) - bsum; // XXX "testAckley" and "testDiffPow" fail. // beta = dx * dx + dsq * (xoptsq + 2 * dx + HALF * dsq) + beta - bsum; // XXX "testDiffPow" fails. lagrangeValuesAtNewPoint.setEntry(trustRegionCenterInterpolationPointIndex, lagrangeValuesAtNewPoint.getEntry(trustRegionCenterInterpolationPointIndex) + ONE); // If NTRITS is zero, the denominator may be increased by replacing // the step D of ALTMOV by a Cauchy step. Then RESCUE may be called if // rounding errors have damaged the chosen denominator. if (ntrits == 0) { // Computing 2nd power final double d1 = lagrangeValuesAtNewPoint.getEntry(knew); denom = d1 * d1 + alpha * beta; if (denom < cauchy && cauchy > ZERO) { for (int i = 0; i < n; i++) { newPoint.setEntry(i, alternativeNewPoint.getEntry(i)); trialStepPoint.setEntry(i, newPoint.getEntry(i) - trustRegionCenterOffset.getEntry(i)); } cauchy = ZERO; // XXX Useful statement? state = 230; break; } // Alternatively, if NTRITS is positive, then set KNEW to the index of // the next interpolation point to be deleted to make room for a trust // region step. Again RESCUE may be called if rounding errors have damaged_ // the chosen denominator, which is the reason for attempting to select // KNEW before calculating the next value of the objective function. } else { final double delsq = delta * delta; scaden = ZERO; biglsq = ZERO; knew = 0; for (int k = 0; k < npt; k++) { if (k == trustRegionCenterInterpolationPointIndex) { continue; } double hdiag = ZERO; for (int m = 0; m < nptm; m++) { // Computing 2nd power final double d1 = zMatrix.getEntry(k, m); hdiag += d1 * d1; } // Computing 2nd power final double d2 = lagrangeValuesAtNewPoint.getEntry(k); final double den = beta * hdiag + d2 * d2; distsq = ZERO; for (int j = 0; j < n; j++) { // Computing 2nd power final double d3 = interpolationPoints.getEntry(k, j) - trustRegionCenterOffset.getEntry(j); distsq += d3 * d3; } // Computing MAX // Computing 2nd power final double d4 = distsq / delsq; final double temp = Math.max(ONE, d4 * d4); if (temp * den > scaden) { scaden = temp * den; knew = k; denom = den; } // Computing MAX // Computing 2nd power final double d5 = lagrangeValuesAtNewPoint.getEntry(k); biglsq = Math.max(biglsq, temp * (d5 * d5)); } } // Put the variables for the next calculation of the objective function // in XNEW, with any adjustments for the bounds. // Calculate the value of the objective function at XBASE+XNEW, unless // the limit on the number of calculations of F has been reached. } case 360: { printState(360); // XXX for (int i = 0; i < n; i++) { // Computing MIN // Computing MAX final double d3 = lowerBound[i]; final double d4 = originShift.getEntry(i) + newPoint.getEntry(i); final double d1 = Math.max(d3, d4); final double d2 = upperBound[i]; currentBest.setEntry(i, Math.min(d1, d2)); if (newPoint.getEntry(i) == lowerDifference.getEntry(i)) { currentBest.setEntry(i, lowerBound[i]); } if (newPoint.getEntry(i) == upperDifference.getEntry(i)) { currentBest.setEntry(i, upperBound[i]); } } f = computeObjectiveValue(currentBest.toArray()); if (!isMinimize) f = -f; if (ntrits == -1) { fsave = f; state = 720; break; } // Use the quadratic model to predict the change in F due to the step D, // and set DIFF to the error of this prediction. final double fopt = fAtInterpolationPoints.getEntry(trustRegionCenterInterpolationPointIndex); double vquad = ZERO; int ih = 0; for (int j = 0; j < n; j++) { vquad += trialStepPoint.getEntry(j) * gradientAtTrustRegionCenter.getEntry(j); for (int i = 0; i <= j; i++) { double temp = trialStepPoint.getEntry(i) * trialStepPoint.getEntry(j); if (i == j) { temp *= HALF; } vquad += modelSecondDerivativesValues.getEntry(ih) * temp; ih++; } } for (int k = 0; k < npt; k++) { // Computing 2nd power final double d1 = work2.getEntry(k); final double d2 = d1 * d1; // "d1" must be squared first to prevent test failures. vquad += HALF * modelSecondDerivativesParameters.getEntry(k) * d2; } final double diff = f - fopt - vquad; diffc = diffb; diffb = diffa; diffa = Math.abs(diff); if (dnorm > rho) { nfsav = getEvaluations(); } // Pick the next value of DELTA after a trust region step. if (ntrits > 0) { if (vquad >= ZERO) { throw new MathIllegalStateException(LocalizedFormats.TRUST_REGION_STEP_FAILED, vquad); } ratio = (f - fopt) / vquad; final double hDelta = HALF * delta; if (ratio <= ONE_OVER_TEN) { // Computing MIN delta = Math.min(hDelta, dnorm); } else if (ratio <= .7) { // Computing MAX delta = Math.max(hDelta, dnorm); } else { // Computing MAX delta = Math.max(hDelta, 2 * dnorm); } if (delta <= rho * 1.5) { delta = rho; } // Recalculate KNEW and DENOM if the new F is less than FOPT. if (f < fopt) { final int ksav = knew; final double densav = denom; final double delsq = delta * delta; scaden = ZERO; biglsq = ZERO; knew = 0; for (int k = 0; k < npt; k++) { double hdiag = ZERO; for (int m = 0; m < nptm; m++) { // Computing 2nd power final double d1 = zMatrix.getEntry(k, m); hdiag += d1 * d1; } // Computing 2nd power final double d1 = lagrangeValuesAtNewPoint.getEntry(k); final double den = beta * hdiag + d1 * d1; distsq = ZERO; for (int j = 0; j < n; j++) { // Computing 2nd power final double d2 = interpolationPoints.getEntry(k, j) - newPoint.getEntry(j); distsq += d2 * d2; } // Computing MAX // Computing 2nd power final double d3 = distsq / delsq; final double temp = Math.max(ONE, d3 * d3); if (temp * den > scaden) { scaden = temp * den; knew = k; denom = den; } // Computing MAX // Computing 2nd power final double d4 = lagrangeValuesAtNewPoint.getEntry(k); final double d5 = temp * (d4 * d4); biglsq = Math.max(biglsq, d5); } if (scaden <= HALF * biglsq) { knew = ksav; denom = densav; } } } // Update BMAT and ZMAT, so that the KNEW-th interpolation point can be // moved. Also update the second derivative terms of the model. update(beta, denom, knew); ih = 0; final double pqold = modelSecondDerivativesParameters.getEntry(knew); modelSecondDerivativesParameters.setEntry(knew, ZERO); for (int i = 0; i < n; i++) { final double temp = pqold * interpolationPoints.getEntry(knew, i); for (int j = 0; j <= i; j++) { modelSecondDerivativesValues.setEntry(ih, modelSecondDerivativesValues.getEntry(ih) + temp * interpolationPoints.getEntry(knew, j)); ih++; } } for (int m = 0; m < nptm; m++) { final double temp = diff * zMatrix.getEntry(knew, m); for (int k = 0; k < npt; k++) { modelSecondDerivativesParameters.setEntry(k, modelSecondDerivativesParameters.getEntry(k) + temp * zMatrix.getEntry(k, m)); } } // Include the new interpolation point, and make the changes to GOPT at // the old XOPT that are caused by the updating of the quadratic model. fAtInterpolationPoints.setEntry(knew, f); for (int i = 0; i < n; i++) { interpolationPoints.setEntry(knew, i, newPoint.getEntry(i)); work1.setEntry(i, bMatrix.getEntry(knew, i)); } for (int k = 0; k < npt; k++) { double suma = ZERO; for (int m = 0; m < nptm; m++) { suma += zMatrix.getEntry(knew, m) * zMatrix.getEntry(k, m); } double sumb = ZERO; for (int j = 0; j < n; j++) { sumb += interpolationPoints.getEntry(k, j) * trustRegionCenterOffset.getEntry(j); } final double temp = suma * sumb; for (int i = 0; i < n; i++) { work1.setEntry(i, work1.getEntry(i) + temp * interpolationPoints.getEntry(k, i)); } } for (int i = 0; i < n; i++) { gradientAtTrustRegionCenter.setEntry(i, gradientAtTrustRegionCenter.getEntry(i) + diff * work1.getEntry(i)); } // Update XOPT, GOPT and KOPT if the new calculated F is less than FOPT. if (f < fopt) { trustRegionCenterInterpolationPointIndex = knew; xoptsq = ZERO; ih = 0; for (int j = 0; j < n; j++) { trustRegionCenterOffset.setEntry(j, newPoint.getEntry(j)); // Computing 2nd power final double d1 = trustRegionCenterOffset.getEntry(j); xoptsq += d1 * d1; for (int i = 0; i <= j; i++) { if (i < j) { gradientAtTrustRegionCenter.setEntry(j, gradientAtTrustRegionCenter.getEntry(j) + modelSecondDerivativesValues.getEntry(ih) * trialStepPoint.getEntry(i)); } gradientAtTrustRegionCenter.setEntry(i, gradientAtTrustRegionCenter.getEntry(i) + modelSecondDerivativesValues.getEntry(ih) * trialStepPoint.getEntry(j)); ih++; } } for (int k = 0; k < npt; k++) { double temp = ZERO; for (int j = 0; j < n; j++) { temp += interpolationPoints.getEntry(k, j) * trialStepPoint.getEntry(j); } temp *= modelSecondDerivativesParameters.getEntry(k); for (int i = 0; i < n; i++) { gradientAtTrustRegionCenter.setEntry(i, gradientAtTrustRegionCenter.getEntry(i) + temp * interpolationPoints.getEntry(k, i)); } } } // Calculate the parameters of the least Frobenius norm interpolant to // the current data, the gradientAt of this interpolant at XOPT being put // into VLAG(NPT+I), I=1,2,...,N. if (ntrits > 0) { for (int k = 0; k < npt; k++) { lagrangeValuesAtNewPoint.setEntry(k, fAtInterpolationPoints.getEntry(k) - fAtInterpolationPoints.getEntry(trustRegionCenterInterpolationPointIndex)); work3.setEntry(k, ZERO); } for (int j = 0; j < nptm; j++) { double sum = ZERO; for (int k = 0; k < npt; k++) { sum += zMatrix.getEntry(k, j) * lagrangeValuesAtNewPoint.getEntry(k); } for (int k = 0; k < npt; k++) { work3.setEntry(k, work3.getEntry(k) + sum * zMatrix.getEntry(k, j)); } } for (int k = 0; k < npt; k++) { double sum = ZERO; for (int j = 0; j < n; j++) { sum += interpolationPoints.getEntry(k, j) * trustRegionCenterOffset.getEntry(j); } work2.setEntry(k, work3.getEntry(k)); work3.setEntry(k, sum * work3.getEntry(k)); } double gqsq = ZERO; double gisq = ZERO; for (int i = 0; i < n; i++) { double sum = ZERO; for (int k = 0; k < npt; k++) { sum += bMatrix.getEntry(k, i) * lagrangeValuesAtNewPoint.getEntry(k) + interpolationPoints.getEntry(k, i) * work3.getEntry(k); } if (trustRegionCenterOffset.getEntry(i) == lowerDifference.getEntry(i)) { // Computing MIN // Computing 2nd power final double d1 = Math.min(ZERO, gradientAtTrustRegionCenter.getEntry(i)); gqsq += d1 * d1; // Computing 2nd power final double d2 = Math.min(ZERO, sum); gisq += d2 * d2; } else if (trustRegionCenterOffset.getEntry(i) == upperDifference.getEntry(i)) { // Computing MAX // Computing 2nd power final double d1 = Math.max(ZERO, gradientAtTrustRegionCenter.getEntry(i)); gqsq += d1 * d1; // Computing 2nd power final double d2 = Math.max(ZERO, sum); gisq += d2 * d2; } else { // Computing 2nd power final double d1 = gradientAtTrustRegionCenter.getEntry(i); gqsq += d1 * d1; gisq += sum * sum; } lagrangeValuesAtNewPoint.setEntry(npt + i, sum); } // Test whether to replace the new quadratic model by the least Frobenius // norm interpolant, making the replacement if the test is satisfied. ++itest; if (gqsq < TEN * gisq) { itest = 0; } if (itest >= 3) { for (int i = 0, max = Math.max(npt, nh); i < max; i++) { if (i < n) { gradientAtTrustRegionCenter.setEntry(i, lagrangeValuesAtNewPoint.getEntry(npt + i)); } if (i < npt) { modelSecondDerivativesParameters.setEntry(i, work2.getEntry(i)); } if (i < nh) { modelSecondDerivativesValues.setEntry(i, ZERO); } itest = 0; } } } // If a trust region step has provided a sufficient decrease in F, then // branch for another trust region calculation. The case NTRITS=0 occurs // when the new interpolation point was reached by an alternative step. if (ntrits == 0) { state = 60; break; } if (f <= fopt + ONE_OVER_TEN * vquad) { state = 60; break; } // Alternatively, find out if the interpolation points are close enough // to the best point so far. // Computing MAX // Computing 2nd power final double d1 = TWO * delta; // Computing 2nd power final double d2 = TEN * rho; distsq = Math.max(d1 * d1, d2 * d2); } case 650: { printState(650); // XXX knew = -1; for (int k = 0; k < npt; k++) { double sum = ZERO; for (int j = 0; j < n; j++) { // Computing 2nd power final double d1 = interpolationPoints.getEntry(k, j) - trustRegionCenterOffset.getEntry(j); sum += d1 * d1; } if (sum > distsq) { knew = k; distsq = sum; } } // If KNEW is positive, then ALTMOV finds alternative new positions for // the KNEW-th interpolation point within distance ADELT of XOPT. It is // reached via label 90. Otherwise, there is a branch to label 60 for // another trust region iteration, unless the calculations with the // current RHO are complete. if (knew >= 0) { final double dist = Math.sqrt(distsq); if (ntrits == -1) { // Computing MIN delta = Math.min(ONE_OVER_TEN * delta, HALF * dist); if (delta <= rho * 1.5) { delta = rho; } } ntrits = 0; // Computing MAX // Computing MIN final double d1 = Math.min(ONE_OVER_TEN * dist, delta); adelt = Math.max(d1, rho); dsq = adelt * adelt; state = 90; break; } if (ntrits == -1) { state = 680; break; } if (ratio > ZERO) { state = 60; break; } if (Math.max(delta, dnorm) > rho) { state = 60; break; } // The calculations with the current value of RHO are complete. Pick the // next values of RHO and DELTA. } case 680: { printState(680); // XXX if (rho > stoppingTrustRegionRadius) { delta = HALF * rho; ratio = rho / stoppingTrustRegionRadius; if (ratio <= SIXTEEN) { rho = stoppingTrustRegionRadius; } else if (ratio <= TWO_HUNDRED_FIFTY) { rho = Math.sqrt(ratio) * stoppingTrustRegionRadius; } else { rho *= ONE_OVER_TEN; } delta = Math.max(delta, rho); ntrits = 0; nfsav = getEvaluations(); state = 60; break; } // Return from the calculation, after another Newton-Raphson step, if // it is too short to have been tried before. if (ntrits == -1) { state = 360; break; } } case 720: { printState(720); // XXX if (fAtInterpolationPoints.getEntry(trustRegionCenterInterpolationPointIndex) <= fsave) { for (int i = 0; i < n; i++) { // Computing MIN // Computing MAX final double d3 = lowerBound[i]; final double d4 = originShift.getEntry(i) + trustRegionCenterOffset.getEntry(i); final double d1 = Math.max(d3, d4); final double d2 = upperBound[i]; currentBest.setEntry(i, Math.min(d1, d2)); if (trustRegionCenterOffset.getEntry(i) == lowerDifference.getEntry(i)) { currentBest.setEntry(i, lowerBound[i]); } if (trustRegionCenterOffset.getEntry(i) == upperDifference.getEntry(i)) { currentBest.setEntry(i, upperBound[i]); } } f = fAtInterpolationPoints.getEntry(trustRegionCenterInterpolationPointIndex); } return f; } default: { throw new MathIllegalStateException(LocalizedFormats.SIMPLE_MESSAGE, "bobyqb"); } } }
From source file:com.itemanalysis.psychometrics.optimization.BOBYQAOptimizer.java
/** * A version of the truncated conjugate gradientAt is applied. If a line * search is restricted by a constraint, then the procedure is restarted, * the values of the variables that are at their bounds being fixed. If * the trust region boundary is reached, then further changes may be made * to D, each one being in the two dimensional space that is spanned * by the current D and the gradientAt of Q at XOPT+D, staying on the trust * region boundary. Termination occurs when the reduction in Q seems to * be close to the greatest reduction that can be achieved. * The arguments N, NPT, XPT, XOPT, GOPT, HQ, PQ, SL and SU have the same * meanings as the corresponding arguments of BOBYQB. * DELTA is the trust region radius for the present calculation, which * seeks a small value of the quadratic model within distance DELTA of * XOPT subject to the bounds on the variables. * XNEW will be set to a new vector of variables that is approximately * the one that minimizes the quadratic model within the trust region * subject to the SL and SU constraints on the variables. It satisfies * as equations the bounds that become active during the calculation. * D is the calculated trial step from XOPT, generated iteratively from an * initial value of zero. Thus XNEW is XOPT+D after the final iteration. * GNEW holds the gradientAt of the quadratic model at XOPT+D. It is updated * when D is updated./* w w w . java2 s.c o m*/ * xbdi.get( is a working space vector. For I=1,2,...,N, the element xbdi.get((I) is * set to -1.0, 0.0, or 1.0, the value being nonzero if and only if the * I-th variable has become fixed at a bound, the bound being SL(I) or * SU(I) in the case xbdi.get((I)=-1.0 or xbdi.get((I)=1.0, respectively. This * information is accumulated during the construction of XNEW. * The arrays S, HS and HRED are also used for working space. They hold the * current search direction, and the changes in the gradientAt of Q along S * and the reduced D, respectively, where the reduced D is the same as D, * except that the components of the fixed variables are zero. * DSQ will be set to the square of the length of XNEW-XOPT. * CRVMIN is set to zero if D reaches the trust region boundary. Otherwise * it is set to the least curvature of H that occurs in the conjugate * gradientAt searches that are not restricted by any constraints. The * value CRVMIN=-1.0D0 is set, however, if all of these searches are * constrained. * @param delta * @param gnew * @param xbdi * @param s * @param hs * @param hred */ private double[] trsbox(double delta, ArrayRealVector gnew, ArrayRealVector xbdi, ArrayRealVector s, ArrayRealVector hs, ArrayRealVector hred) { printMethod(); // XXX final int n = currentBest.getDimension(); final int npt = numberOfInterpolationPoints; double dsq = Double.NaN; double crvmin = Double.NaN; // Local variables double ds; int iu; double dhd, dhs, cth, shs, sth, ssq, beta = 0, sdec, blen; int iact = -1; int nact = 0; double angt = 0, qred; int isav; double temp = 0, xsav = 0, xsum = 0, angbd = 0, dredg = 0, sredg = 0; int iterc; double resid = 0, delsq = 0, ggsav = 0, tempa = 0, tempb = 0, redmax = 0, dredsq = 0, redsav = 0, gredsq = 0, rednew = 0; int itcsav = 0; double rdprev = 0, rdnext = 0, stplen = 0, stepsq = 0; int itermax = 0; // Set some constants. // Function Body // The sign of GOPT(I) gives the sign of the change to the I-th variable // that will reduce Q from its value at XOPT. Thus xbdi.get((I) shows whether // or not to fix the I-th variable at one of its bounds initially, with // NACT being set to the number of fixed variables. D and GNEW are also // set for the first iteration. DELSQ is the upper bound on the sum of // squares of the free variables. QRED is the reduction in Q so far. iterc = 0; nact = 0; for (int i = 0; i < n; i++) { xbdi.setEntry(i, ZERO); if (trustRegionCenterOffset.getEntry(i) <= lowerDifference.getEntry(i)) { if (gradientAtTrustRegionCenter.getEntry(i) >= ZERO) { xbdi.setEntry(i, MINUS_ONE); } } else if (trustRegionCenterOffset.getEntry(i) >= upperDifference.getEntry(i)) { if (gradientAtTrustRegionCenter.getEntry(i) <= ZERO) { xbdi.setEntry(i, ONE); } } if (xbdi.getEntry(i) != ZERO) { ++nact; } trialStepPoint.setEntry(i, ZERO); gnew.setEntry(i, gradientAtTrustRegionCenter.getEntry(i)); } delsq = delta * delta; qred = ZERO; crvmin = MINUS_ONE; // Set the next search direction of the conjugate gradientAt method. It is // the steepest descent direction initially and when the iterations are // restarted because a variable has just been fixed by a bound, and of // course the components of the fixed variables are zero. ITERMAX is an // upper bound on the indices of the conjugate gradientAt iterations. int state = 20; for (;;) { switch (state) { case 20: { printState(20); // XXX beta = ZERO; } case 30: { printState(30); // XXX stepsq = ZERO; for (int i = 0; i < n; i++) { if (xbdi.getEntry(i) != ZERO) { s.setEntry(i, ZERO); } else if (beta == ZERO) { s.setEntry(i, -gnew.getEntry(i)); } else { s.setEntry(i, beta * s.getEntry(i) - gnew.getEntry(i)); } // Computing 2nd power final double d1 = s.getEntry(i); stepsq += d1 * d1; } if (stepsq == ZERO) { state = 190; break; } if (beta == ZERO) { gredsq = stepsq; itermax = iterc + n - nact; } if (gredsq * delsq <= qred * 1e-4 * qred) { state = 190; break; } // Multiply the search direction by the second derivative matrix of Q and // calculate some scalars for the choice of steplength. Then set BLEN to // the length of the the step to the trust region boundary and STPLEN to // the steplength, ignoring the simple bounds. state = 210; break; } case 50: { printState(50); // XXX resid = delsq; ds = ZERO; shs = ZERO; for (int i = 0; i < n; i++) { if (xbdi.getEntry(i) == ZERO) { // Computing 2nd power final double d1 = trialStepPoint.getEntry(i); resid -= d1 * d1; ds += s.getEntry(i) * trialStepPoint.getEntry(i); shs += s.getEntry(i) * hs.getEntry(i); } } if (resid <= ZERO) { state = 90; break; } temp = Math.sqrt(stepsq * resid + ds * ds); if (ds < ZERO) { blen = (temp - ds) / stepsq; } else { blen = resid / (temp + ds); } stplen = blen; if (shs > ZERO) { // Computing MIN stplen = Math.min(blen, gredsq / shs); } // Reduce STPLEN if necessary in order to preserve the simple bounds, // letting IACT be the index of the new constrained variable. iact = -1; for (int i = 0; i < n; i++) { if (s.getEntry(i) != ZERO) { xsum = trustRegionCenterOffset.getEntry(i) + trialStepPoint.getEntry(i); if (s.getEntry(i) > ZERO) { temp = (upperDifference.getEntry(i) - xsum) / s.getEntry(i); } else { temp = (lowerDifference.getEntry(i) - xsum) / s.getEntry(i); } if (temp < stplen) { stplen = temp; iact = i; } } } // Update CRVMIN, GNEW and D. Set SDEC to the decrease that occurs in Q. sdec = ZERO; if (stplen > ZERO) { ++iterc; temp = shs / stepsq; if (iact == -1 && temp > ZERO) { crvmin = Math.min(crvmin, temp); if (crvmin == MINUS_ONE) { crvmin = temp; } } ggsav = gredsq; gredsq = ZERO; for (int i = 0; i < n; i++) { gnew.setEntry(i, gnew.getEntry(i) + stplen * hs.getEntry(i)); if (xbdi.getEntry(i) == ZERO) { // Computing 2nd power final double d1 = gnew.getEntry(i); gredsq += d1 * d1; } trialStepPoint.setEntry(i, trialStepPoint.getEntry(i) + stplen * s.getEntry(i)); } // Computing MAX final double d1 = stplen * (ggsav - HALF * stplen * shs); sdec = Math.max(d1, ZERO); qred += sdec; } // Restart the conjugate gradientAt method if it has hit a new bound. if (iact >= 0) { ++nact; xbdi.setEntry(iact, ONE); if (s.getEntry(iact) < ZERO) { xbdi.setEntry(iact, MINUS_ONE); } // Computing 2nd power final double d1 = trialStepPoint.getEntry(iact); delsq -= d1 * d1; if (delsq <= ZERO) { state = 190; break; } state = 20; break; } // If STPLEN is less than BLEN, then either apply another conjugate // gradientAt iteration or RETURN. if (stplen < blen) { if (iterc == itermax) { state = 190; break; } if (sdec <= qred * .01) { state = 190; break; } beta = gredsq / ggsav; state = 30; break; } } case 90: { printState(90); // XXX crvmin = ZERO; // Prepare for the alternative iteration by calculating some scalars // and by multiplying the reduced D by the second derivative matrix of // Q, where S holds the reduced D in the call of GGMULT. } case 100: { printState(100); // XXX if (nact >= n - 1) { state = 190; break; } dredsq = ZERO; dredg = ZERO; gredsq = ZERO; for (int i = 0; i < n; i++) { if (xbdi.getEntry(i) == ZERO) { // Computing 2nd power double d1 = trialStepPoint.getEntry(i); dredsq += d1 * d1; dredg += trialStepPoint.getEntry(i) * gnew.getEntry(i); // Computing 2nd power d1 = gnew.getEntry(i); gredsq += d1 * d1; s.setEntry(i, trialStepPoint.getEntry(i)); } else { s.setEntry(i, ZERO); } } itcsav = iterc; state = 210; break; // Let the search direction S be a linear combination of the reduced D // and the reduced G that is orthogonal to the reduced D. } case 120: { printState(120); // XXX ++iterc; temp = gredsq * dredsq - dredg * dredg; if (temp <= qred * 1e-4 * qred) { state = 190; break; } temp = Math.sqrt(temp); for (int i = 0; i < n; i++) { if (xbdi.getEntry(i) == ZERO) { s.setEntry(i, (dredg * trialStepPoint.getEntry(i) - dredsq * gnew.getEntry(i)) / temp); } else { s.setEntry(i, ZERO); } } sredg = -temp; // By considering the simple bounds on the variables, calculate an upper // bound on the tangent of half the angle of the alternative iteration, // namely ANGBD, except that, if already a free variable has reached a // bound, there is a branch back to label 100 after fixing that variable. angbd = ONE; iact = -1; for (int i = 0; i < n; i++) { if (xbdi.getEntry(i) == ZERO) { tempa = trustRegionCenterOffset.getEntry(i) + trialStepPoint.getEntry(i) - lowerDifference.getEntry(i); tempb = upperDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i) - trialStepPoint.getEntry(i); if (tempa <= ZERO) { ++nact; xbdi.setEntry(i, MINUS_ONE); state = 100; break; } else if (tempb <= ZERO) { ++nact; xbdi.setEntry(i, ONE); state = 100; break; } // Computing 2nd power double d1 = trialStepPoint.getEntry(i); // Computing 2nd power double d2 = s.getEntry(i); ssq = d1 * d1 + d2 * d2; // Computing 2nd power d1 = trustRegionCenterOffset.getEntry(i) - lowerDifference.getEntry(i); temp = ssq - d1 * d1; if (temp > ZERO) { temp = Math.sqrt(temp) - s.getEntry(i); if (angbd * temp > tempa) { angbd = tempa / temp; iact = i; xsav = MINUS_ONE; } } // Computing 2nd power d1 = upperDifference.getEntry(i) - trustRegionCenterOffset.getEntry(i); temp = ssq - d1 * d1; if (temp > ZERO) { temp = Math.sqrt(temp) + s.getEntry(i); if (angbd * temp > tempb) { angbd = tempb / temp; iact = i; xsav = ONE; } } } } // Calculate HHD and some curvatures for the alternative iteration. state = 210; break; } case 150: { printState(150); // XXX shs = ZERO; dhs = ZERO; dhd = ZERO; for (int i = 0; i < n; i++) { if (xbdi.getEntry(i) == ZERO) { shs += s.getEntry(i) * hs.getEntry(i); dhs += trialStepPoint.getEntry(i) * hs.getEntry(i); dhd += trialStepPoint.getEntry(i) * hred.getEntry(i); } } // Seek the greatest reduction in Q for a range of equally spaced values // of ANGT in [0,ANGBD], where ANGT is the tangent of half the angle of // the alternative iteration. redmax = ZERO; isav = -1; redsav = ZERO; iu = (int) (angbd * 17. + 3.1); for (int i = 0; i < iu; i++) { angt = angbd * i / iu; sth = (angt + angt) / (ONE + angt * angt); temp = shs + angt * (angt * dhd - dhs - dhs); rednew = sth * (angt * dredg - sredg - HALF * sth * temp); if (rednew > redmax) { redmax = rednew; isav = i; rdprev = redsav; } else if (i == isav + 1) { rdnext = rednew; } redsav = rednew; } // Return if the reduction is zero. Otherwise, set the sine and cosine // of the angle of the alternative iteration, and calculate SDEC. if (isav < 0) { state = 190; break; } if (isav < iu) { temp = (rdnext - rdprev) / (redmax + redmax - rdprev - rdnext); angt = angbd * (isav + HALF * temp) / iu; } cth = (ONE - angt * angt) / (ONE + angt * angt); sth = (angt + angt) / (ONE + angt * angt); temp = shs + angt * (angt * dhd - dhs - dhs); sdec = sth * (angt * dredg - sredg - HALF * sth * temp); if (sdec <= ZERO) { state = 190; break; } // Update GNEW, D and HRED. If the angle of the alternative iteration // is restricted by a bound on a free variable, that variable is fixed // at the bound. dredg = ZERO; gredsq = ZERO; for (int i = 0; i < n; i++) { gnew.setEntry(i, gnew.getEntry(i) + (cth - ONE) * hred.getEntry(i) + sth * hs.getEntry(i)); if (xbdi.getEntry(i) == ZERO) { trialStepPoint.setEntry(i, cth * trialStepPoint.getEntry(i) + sth * s.getEntry(i)); dredg += trialStepPoint.getEntry(i) * gnew.getEntry(i); // Computing 2nd power final double d1 = gnew.getEntry(i); gredsq += d1 * d1; } hred.setEntry(i, cth * hred.getEntry(i) + sth * hs.getEntry(i)); } qred += sdec; if (iact >= 0 && isav == iu) { ++nact; xbdi.setEntry(iact, xsav); state = 100; break; } // If SDEC is sufficiently small, then RETURN after setting XNEW to // XOPT+D, giving careful attention to the bounds. if (sdec > qred * .01) { state = 120; break; } } case 190: { printState(190); // XXX dsq = ZERO; for (int i = 0; i < n; i++) { // Computing MAX // Computing MIN final double min = Math.min(trustRegionCenterOffset.getEntry(i) + trialStepPoint.getEntry(i), upperDifference.getEntry(i)); newPoint.setEntry(i, Math.max(min, lowerDifference.getEntry(i))); if (xbdi.getEntry(i) == MINUS_ONE) { newPoint.setEntry(i, lowerDifference.getEntry(i)); } if (xbdi.getEntry(i) == ONE) { newPoint.setEntry(i, upperDifference.getEntry(i)); } trialStepPoint.setEntry(i, newPoint.getEntry(i) - trustRegionCenterOffset.getEntry(i)); // Computing 2nd power final double d1 = trialStepPoint.getEntry(i); dsq += d1 * d1; } return new double[] { dsq, crvmin }; // The following instructions multiply the current S-vector by the second // derivative matrix of the quadratic model, putting the product in HS. // They are reached from three different parts of the software above and // they can be regarded as an external subroutine. } case 210: { printState(210); // XXX int ih = 0; for (int j = 0; j < n; j++) { hs.setEntry(j, ZERO); for (int i = 0; i <= j; i++) { if (i < j) { hs.setEntry(j, hs.getEntry(j) + modelSecondDerivativesValues.getEntry(ih) * s.getEntry(i)); } hs.setEntry(i, hs.getEntry(i) + modelSecondDerivativesValues.getEntry(ih) * s.getEntry(j)); ih++; } } final RealVector tmp = interpolationPoints.operate(s).ebeMultiply(modelSecondDerivativesParameters); for (int k = 0; k < npt; k++) { if (modelSecondDerivativesParameters.getEntry(k) != ZERO) { for (int i = 0; i < n; i++) { hs.setEntry(i, hs.getEntry(i) + tmp.getEntry(k) * interpolationPoints.getEntry(k, i)); } } } if (crvmin != ZERO) { state = 50; break; } if (iterc > itcsav) { state = 150; break; } for (int i = 0; i < n; i++) { hred.setEntry(i, hs.getEntry(i)); } state = 120; break; } default: { throw new MathIllegalStateException(LocalizedFormats.SIMPLE_MESSAGE, "trsbox"); } } } }
From source file:org.matheclipse.core.stat.descriptive.SymbolicGeometricMean.java
/** * Throws IllegalStateException if n > 0. *//*www . j a v a2s . com*/ private void checkEmpty() { if (getN() > 0) { throw new MathIllegalStateException(LocalizedFormats.VALUES_ADDED_BEFORE_CONFIGURING_STATISTIC, getN()); } }