public static OptimisationReport NiuDunLaFuSunStep(
MatrixChains chain, double[] angles, boolean printStep) {
// see: http://code.google.com/p/efficient-java-matrix-library/wiki/SolvingLinearSystems
int l = angles.length;
DenseMatrix64F J = get2d(chain, angles);
DenseMatrix64F grad = get1d(chain, angles);
DenseMatrix64F propose = vector(l);
boolean solved = CommonOps.solve(J, grad, propose);
for (int i = 0; i < l; ++i) {
if (Double.isNaN(propose.data[i])) {
solved = false;
}
}
OptimisationReport togo = new OptimisationReport();
try {
if (!solved) {
throw new RuntimeException("Failed to solve update equation");
}
CommonOps.scale(-1, propose);
if (printStep) {
EigenDecomposition<DenseMatrix64F> decomp = DecompositionFactory.eigSymm(l, false);
boolean posed = decomp.decompose(J);
if (!posed) {
throw new RuntimeException("Failed to decompose matrix");
}
double[] eigs = eigs(decomp);
System.out.println("Computed eigenvalues " + printVec(eigs));
togo.eigenvalues = eigs;
}
tryProposal(chain, propose, grad, angles, printStep, togo);
} catch (Exception e) {
System.out.println(
"Failed to find suitable proposal from Newton step - trying gradient step");
propose.set(grad);
CommonOps.scale(-1, propose);
tryProposal(chain, propose, grad, angles, printStep, togo);
}
return togo;
}
private static boolean verifyProposal(
MatrixChains chain,
double[] angles,
double[] newAng,
DenseMatrix64F grad,
DenseMatrix64F propose,
OptimisationReport report) {
for (int i = 0; i < newAng.length; ++i) {
if (newAng[i] <= 0 || newAng[i] >= 2 * Math.PI) {
System.out.println("Rejected out of range angle " + newAng[i] + " at index " + i);
return false;
}
}
double descent = dot(grad.data, propose.data);
if (descent > 0) {
throw new RuntimeException("Non-reducing gradient direction with slope " + descent);
}
double oldF = f(chain, angles);
double newF = f(chain, newAng);
if (newF > oldF + 1e-4 * descent) {
System.out.println("Rejected failure of descent step to " + newF);
return false;
}
DenseMatrix64F newGrad = get1d(chain, newAng);
// These would both be negative numbers reflecting correct gradient direction
double newDescent = dot(newGrad.data, propose.data);
if (newDescent < 0.99 * descent) {
System.out.println(
"Rejected failure of gradient reduce step from " + descent + " to " + newDescent);
return false;
}
report.fval = newF;
report.gradn = Math.sqrt(dot(newGrad.data, newGrad.data));
report.angles = newAng;
return true;
}
public static OptimisationReport runNewton(MatrixChains chains, double[] angles) {
System.out.println("f: " + Newton.f(chains, angles));
System.out.println();
DenseMatrix64F dby1 = Newton.get1d(chains, angles);
System.out.println("dby1: " + dby1);
System.out.println("numDiff: " + Newton.numDiff1d(chains, angles, 1e-6));
System.out.println();
DenseMatrix64F dby11 = Newton.get2d(chains, angles);
System.out.println("dby11: " + dby11);
System.out.println("numDiff: " + Newton.numDiff2d(chains, angles, 1e-5));
OptimisationReport report = runNewtonRun(chains, angles, 25);
if (report.gradn >= chains.tolerance) {
report.status = "FAILED";
} else {
int minIndex = diagnoseEigenvalues(report.eigenvalues);
if (minIndex == -1) {
report.status = "RIGID";
} else {
report.status = "LOOSE";
chains.regularise = 1e-1;
chains.initialPoint = angles;
System.out.println("Beginning 2nd run with regularisation " + chains.regularise);
report = runNewtonRun(chains, angles, 30);
report.status = (report.gradn >= chains.tolerance) ? "LOOSE-FAILED" : "LOOSE";
System.out.println("Original vector was " + printVec(angles));
chains.regularise = 1e-4;
chains.initialPoint = report.angles;
System.out.println("Beginning 3nd run with regularisation " + chains.regularise);
report = runNewtonRun(chains, report.angles, 30);
report.status = (report.gradn >= chains.tolerance) ? "LOOSE-FAILED" : "LOOSE";
System.out.println("Original vector was " + printVec(angles));
}
}
System.out.println("Optimisation concluded - the configuration is " + report.status);
return report;
}
