public MomentumSolver3(
SixDoFJoint rootJoint,
RigidBody elevator,
ReferenceFrame centerOfMassFrame,
TwistCalculator twistCalculator,
LinearSolver<DenseMatrix64F> jacobianSolver,
double controlDT,
YoVariableRegistry parentRegistry) {
this.rootJoint = rootJoint;
this.jointsInOrder = ScrewTools.computeSupportAndSubtreeJoints(rootJoint.getSuccessor());
this.motionConstraintHandler =
new MotionConstraintHandler("solver3", jointsInOrder, twistCalculator, null, registry);
this.centroidalMomentumMatrix = new CentroidalMomentumMatrix(elevator, centerOfMassFrame);
this.previousCentroidalMomentumMatrix =
new DenseMatrix64F(
centroidalMomentumMatrix.getMatrix().getNumRows(),
centroidalMomentumMatrix.getMatrix().getNumCols());
this.centroidalMomentumMatrixDerivative =
new DenseMatrix64F(
centroidalMomentumMatrix.getMatrix().getNumRows(),
centroidalMomentumMatrix.getMatrix().getNumCols());
yoPreviousCentroidalMomentumMatrix =
new DoubleYoVariable[previousCentroidalMomentumMatrix.getNumRows()]
[previousCentroidalMomentumMatrix.getNumCols()];
MatrixYoVariableConversionTools.populateYoVariables(
yoPreviousCentroidalMomentumMatrix, "previousCMMatrix", registry);
this.controlDT = controlDT;
nDegreesOfFreedom = ScrewTools.computeDegreesOfFreedom(jointsInOrder);
this.b = new DenseMatrix64F(SpatialMotionVector.SIZE, 1);
this.v = new DenseMatrix64F(nDegreesOfFreedom, 1);
// nullspaceMotionConstraintEnforcer = new
// EqualityConstraintEnforcer(LinearSolverFactory.pseudoInverse(true));
equalityConstraintEnforcer =
new EqualityConstraintEnforcer(LinearSolverFactory.pseudoInverse(true));
solver = LinearSolverFactory.pseudoInverse(true);
parentRegistry.addChild(registry);
reset();
}
/**
* Computes inverse coefficients
*
* @param border
* @param forward Forward coefficients.
* @param inverse Inverse used in the inner portion of the data stream.
* @return
*/
private static WlBorderCoef<WlCoef_F32> computeBorderCoefficients(
BorderIndex1D border, WlCoef_F32 forward, WlCoef_F32 inverse) {
int N = Math.max(forward.getScalingLength(), forward.getWaveletLength());
N += N % 2;
N *= 2;
border.setLength(N);
// Because the wavelet transform is a linear invertible system the inverse coefficients
// can be found by creating a matrix and inverting the matrix. Boundary conditions are then
// extracted from this inverted matrix.
DenseMatrix64F A = new DenseMatrix64F(N, N);
for (int i = 0; i < N; i += 2) {
for (int j = 0; j < forward.scaling.length; j++) {
int index = border.getIndex(j + i + forward.offsetScaling);
A.add(i, index, forward.scaling[j]);
}
for (int j = 0; j < forward.wavelet.length; j++) {
int index = border.getIndex(j + i + forward.offsetWavelet);
A.add(i + 1, index, forward.wavelet[j]);
}
}
LinearSolver<DenseMatrix64F> solver = LinearSolverFactory.linear(N);
if (!solver.setA(A) || solver.quality() < 1e-5) {
throw new IllegalArgumentException("Can't invert matrix");
}
DenseMatrix64F A_inv = new DenseMatrix64F(N, N);
solver.invert(A_inv);
int numBorder = UtilWavelet.borderForwardLower(inverse) / 2;
WlBorderCoefFixed<WlCoef_F32> ret = new WlBorderCoefFixed<>(numBorder, numBorder + 1);
ret.setInnerCoef(inverse);
// add the lower coefficients first
for (int i = 0; i < ret.getLowerLength(); i++) {
computeLowerCoef(inverse, A_inv, ret, i * 2);
}
// add upper coefficients
for (int i = 0; i < ret.getUpperLength(); i++) {
computeUpperCoef(inverse, N, A_inv, ret, i * 2);
}
return ret;
}
/**
* Computes the most dominant eigen vector of A using an inverted shifted matrix. The inverted
* shifted matrix is defined as <b>B = (A - αI)<sup>-1</sup></b> and can converge faster if
* α is chosen wisely.
*
* @param A An invertible square matrix matrix.
* @param alpha Shifting factor.
* @return If it converged or not.
*/
public boolean computeShiftInvert(DenseMatrix64F A, double alpha) {
initPower(A);
LinearSolver solver = LinearSolverFactory.linear(A.numCols);
SpecializedOps.addIdentity(A, B, -alpha);
solver.setA(B);
boolean converged = false;
for (int i = 0; i < maxIterations && !converged; i++) {
solver.solve(q0, q1);
double s = NormOps.normPInf(q1);
CommonOps.divide(q1, s, q2);
converged = checkConverged(A);
}
return converged;
}
private void estimateCPM() {
logger.info("Start EJML Estimation");
numIterations = 0;
boolean estimationDone = false;
DenseMatrix64F eL_hat = null;
DenseMatrix64F eP_hat = null;
DenseMatrix64F rhsL = null;
DenseMatrix64F rhsP = null;
// normalize master coordinates for stability -- only master!
TDoubleArrayList yMasterNorm = new TDoubleArrayList();
TDoubleArrayList xMasterNorm = new TDoubleArrayList();
for (int i = 0; i < yMaster.size(); i++) {
yMasterNorm.add(PolyUtils.normalize2(yMaster.getQuick(i), normWin.linelo, normWin.linehi));
xMasterNorm.add(PolyUtils.normalize2(xMaster.getQuick(i), normWin.pixlo, normWin.pixhi));
}
// helper variables
int winL;
int winP;
int maxWSum_idx = 0;
while (!estimationDone) {
String codeBlockMessage = "LS ESTIMATION PROCEDURE";
StopWatch stopWatch = new StopWatch();
StopWatch clock = new StopWatch();
clock.start();
stopWatch.setTag(codeBlockMessage);
stopWatch.start();
logger.info("Start iteration: {}" + numIterations);
/** Remove identified outlier from previous estimation */
if (numIterations != 0) {
logger.info(
"Removing observation {}, idxList {}, from observation vector."
+ index.getQuick(maxWSum_idx)
+ maxWSum_idx);
index.removeAt(maxWSum_idx);
yMasterNorm.removeAt(maxWSum_idx);
xMasterNorm.removeAt(maxWSum_idx);
yOffset.removeAt(maxWSum_idx);
xOffset.removeAt(maxWSum_idx);
// only for outlier removal
yMaster.removeAt(maxWSum_idx);
xMaster.removeAt(maxWSum_idx);
ySlave.removeAt(maxWSum_idx);
xSlave.removeAt(maxWSum_idx);
coherence.removeAt(maxWSum_idx);
// also take care of slave pins
slaveGCPList.remove(maxWSum_idx);
// if (demRefinement) {
// ySlaveGeometry.removeAt(maxWSum_idx);
// xSlaveGeometry.removeAt(maxWSum_idx);
// }
}
/** Check redundancy */
numObservations = index.size(); // Number of points > threshold
if (numObservations < numUnknowns) {
logger.severe(
"coregpm: Number of windows > threshold is smaller than parameters solved for.");
throw new ArithmeticException(
"coregpm: Number of windows > threshold is smaller than parameters solved for.");
}
// work with normalized values
DenseMatrix64F A =
new DenseMatrix64F(
SystemOfEquations.constructDesignMatrix_loop(
yMasterNorm.toArray(), xMasterNorm.toArray(), cpmDegree));
logger.info("TIME FOR SETUP of SYSTEM : {}" + stopWatch.lap("setup"));
RowD1Matrix64F Qy_1; // vector
double meanValue;
switch (cpmWeight) {
case "linear":
logger.info("Using sqrt(coherence) as weights");
Qy_1 = DenseMatrix64F.wrap(numObservations, 1, coherence.toArray());
// Normalize weights to avoid influence on estimated var.factor
logger.info("Normalizing covariance matrix for LS estimation");
meanValue = CommonOps.elementSum(Qy_1) / numObservations;
CommonOps.divide(meanValue, Qy_1); // normalize vector
break;
case "quadratic":
logger.info("Using coherence as weights.");
Qy_1 = DenseMatrix64F.wrap(numObservations, 1, coherence.toArray());
CommonOps.elementMult(Qy_1, Qy_1);
// Normalize weights to avoid influence on estimated var.factor
meanValue = CommonOps.elementSum(Qy_1) / numObservations;
logger.info("Normalizing covariance matrix for LS estimation.");
CommonOps.divide(meanValue, Qy_1); // normalize vector
break;
case "bamler":
// TODO: see Bamler papers IGARSS 2000 and 2004
logger.warning("Bamler weighting method NOT IMPLEMENTED, falling back to None.");
Qy_1 = onesEJML(numObservations);
break;
case "none":
logger.info("No weighting.");
Qy_1 = onesEJML(numObservations);
break;
default:
Qy_1 = onesEJML(numObservations);
break;
}
logger.info("TIME FOR SETUP of VC diag matrix: {}" + stopWatch.lap("diag VC matrix"));
/** tempMatrix_1 matrices */
final DenseMatrix64F yL_matrix = DenseMatrix64F.wrap(numObservations, 1, yOffset.toArray());
final DenseMatrix64F yP_matrix = DenseMatrix64F.wrap(numObservations, 1, xOffset.toArray());
logger.info("TIME FOR SETUP of TEMP MATRICES: {}" + stopWatch.lap("Temp matrices"));
/** normal matrix */
final DenseMatrix64F N =
new DenseMatrix64F(numUnknowns, numUnknowns); // = A_transpose.mmul(Qy_1_diag.mmul(A));
/*
// fork/join parallel implementation
RowD1Matrix64F result = A.copy();
DiagXMat dd = new DiagXMat(Qy_1, A, 0, A.numRows, result);
ForkJoinPool pool = new ForkJoinPool();
pool.invoke(dd);
CommonOps.multAddTransA(A, dd.result, N);
*/
CommonOps.multAddTransA(A, diagxmat(Qy_1, A), N);
DenseMatrix64F Qx_hat = N.copy();
logger.info("TIME FOR SETUP of NORMAL MATRIX: {}" + stopWatch.lap("Normal matrix"));
/** right hand sides */
// azimuth
rhsL = new DenseMatrix64F(numUnknowns, 1); // A_transpose.mmul(Qy_1_diag.mmul(yL_matrix));
CommonOps.multAddTransA(1d, A, diagxmat(Qy_1, yL_matrix), rhsL);
// range
rhsP = new DenseMatrix64F(numUnknowns, 1); // A_transpose.mmul(Qy_1_diag.mmul(yP_matrix));
CommonOps.multAddTransA(1d, A, diagxmat(Qy_1, yP_matrix), rhsP);
logger.info("TIME FOR SETUP of RightHand Side: {}" + stopWatch.lap("Right-hand-side"));
LinearSolver<DenseMatrix64F> solver = LinearSolverFactory.leastSquares(100, 100);
/** compute solution */
if (!solver.setA(Qx_hat)) {
throw new IllegalArgumentException("Singular Matrix");
}
solver.solve(rhsL, rhsL);
solver.solve(rhsP, rhsP);
logger.info("TIME FOR SOLVING of System: {}" + stopWatch.lap("Solving System"));
/** inverting of Qx_hat for stability check */
solver.invert(Qx_hat);
logger.info("TIME FOR INVERSION OF N: {}" + stopWatch.lap("Inversion of N"));
/** test inversion and check stability: max(abs([N*inv(N) - E)) ?= 0 */
DenseMatrix64F tempMatrix_1 = new DenseMatrix64F(N.numRows, N.numCols);
CommonOps.mult(N, Qx_hat, tempMatrix_1);
CommonOps.subEquals(
tempMatrix_1, CommonOps.identity(tempMatrix_1.numRows, tempMatrix_1.numCols));
double maxDeviation = CommonOps.elementMaxAbs(tempMatrix_1);
if (maxDeviation > .01) {
logger.severe(
"COREGPM: maximum deviation N*inv(N) from unity = {}. This is larger than 0.01"
+ maxDeviation);
throw new IllegalStateException("COREGPM: maximum deviation N*inv(N) from unity)");
} else if (maxDeviation > .001) {
logger.warning(
"COREGPM: maximum deviation N*inv(N) from unity = {}. This is between 0.01 and 0.001"
+ maxDeviation);
}
logger.info("TIME FOR STABILITY CHECK: {}" + stopWatch.lap("Stability Check"));
logger.info("Coeffs in Azimuth direction: {}" + rhsL.toString());
logger.info("Coeffs in Range direction: {}" + rhsP.toString());
logger.info("Max Deviation: {}" + maxDeviation);
logger.info("System Quality: {}" + solver.quality());
/** some other stuff if the scale is okay */
DenseMatrix64F Qe_hat = new DenseMatrix64F(numObservations, numObservations);
DenseMatrix64F tempMatrix_2 = new DenseMatrix64F(numObservations, numUnknowns);
CommonOps.mult(A, Qx_hat, tempMatrix_2);
CommonOps.multTransB(-1, tempMatrix_2, A, Qe_hat);
scaleInputDiag(Qe_hat, Qy_1);
// solution: Azimuth
DenseMatrix64F yL_hat = new DenseMatrix64F(numObservations, 1);
eL_hat = new DenseMatrix64F(numObservations, 1);
CommonOps.mult(A, rhsL, yL_hat);
CommonOps.sub(yL_matrix, yL_hat, eL_hat);
// solution: Range
DenseMatrix64F yP_hat = new DenseMatrix64F(numObservations, 1);
eP_hat = new DenseMatrix64F(numObservations, 1);
CommonOps.mult(A, rhsP, yP_hat);
CommonOps.sub(yP_matrix, yP_hat, eP_hat);
logger.info("TIME FOR DATA preparation for TESTING: {}" + stopWatch.lap("Testing Setup"));
/** overal model test (variance factor) */
double overAllModelTest_L = 0;
double overAllModelTest_P = 0;
for (int i = 0; i < numObservations; i++) {
overAllModelTest_L += FastMath.pow(eL_hat.get(i), 2) * Qy_1.get(i);
overAllModelTest_P += FastMath.pow(eP_hat.get(i), 2) * Qy_1.get(i);
}
overAllModelTest_L =
(overAllModelTest_L / FastMath.pow(SIGMA_L, 2)) / (numObservations - numUnknowns);
overAllModelTest_P =
(overAllModelTest_P / FastMath.pow(SIGMA_P, 2)) / (numObservations - numUnknowns);
logger.info("Overall Model Test Lines: {}" + overAllModelTest_L);
logger.info("Overall Model Test Pixels: {}" + overAllModelTest_P);
logger.info("TIME FOR OMT: {}" + stopWatch.lap("OMT"));
/** ---------------------- DATASNOPING ----------------------------------- * */
/** Assumed Qy diag */
/** initialize */
DenseMatrix64F wTest_L = new DenseMatrix64F(numObservations, 1);
DenseMatrix64F wTest_P = new DenseMatrix64F(numObservations, 1);
for (int i = 0; i < numObservations; i++) {
wTest_L.set(i, eL_hat.get(i) / (Math.sqrt(Qe_hat.get(i, i)) * SIGMA_L));
wTest_P.set(i, eP_hat.get(i) / (Math.sqrt(Qe_hat.get(i, i)) * SIGMA_P));
}
/** find maxima's */
// azimuth
winL = absArgmax(wTest_L);
double maxWinL = Math.abs(wTest_L.get(winL));
logger.info(
"maximum wtest statistic azimuth = {} for window number: {} "
+ maxWinL
+ index.getQuick(winL));
// range
winP = absArgmax(wTest_P);
double maxWinP = Math.abs(wTest_P.get(winP));
logger.info(
"maximum wtest statistic range = {} for window number: {} "
+ maxWinP
+ index.getQuick(winP));
/** use summed wTest in Azimuth and Range direction for outlier detection */
DenseMatrix64F wTestSum = new DenseMatrix64F(numObservations);
for (int i = 0; i < numObservations; i++) {
wTestSum.set(i, FastMath.pow(wTest_L.get(i), 2) + FastMath.pow(wTest_P.get(i), 2));
}
maxWSum_idx = absArgmax(wTest_P);
double maxWSum = wTest_P.get(winP);
logger.info(
"Detected outlier: summed sqr.wtest = {}; observation: {}"
+ maxWSum
+ index.getQuick(maxWSum_idx));
/** Test if we are estimationDone yet */
// check on number of observations
if (numObservations <= numUnknowns) {
logger.warning("NO redundancy! Exiting iterations.");
estimationDone = true; // cannot remove more than this
}
// check on test k_alpha
if (Math.max(maxWinL, maxWinP) <= criticalValue) {
// all tests accepted?
logger.info("All outlier tests accepted! (final solution computed)");
estimationDone = true;
}
if (numIterations >= maxIterations) {
logger.info("max. number of iterations reached (exiting loop).");
estimationDone = true; // we reached max. (or no max_iter specified)
}
/** Only warn if last iteration has been estimationDone */
if (estimationDone) {
if (overAllModelTest_L > 10) {
logger.warning(
"COREGPM: Overall Model Test, Lines = {} is larger than 10. (Suggest model or a priori sigma not correct.)"
+ overAllModelTest_L);
}
if (overAllModelTest_P > 10) {
logger.warning(
"COREGPM: Overall Model Test, Pixels = {} is larger than 10. (Suggest model or a priori sigma not correct.)"
+ overAllModelTest_P);
}
/** if a priori sigma is correct, max wtest should be something like 1.96 */
if (Math.max(maxWinL, maxWinP) > 200.0) {
logger.warning(
"Recommendation: remove window number: {} and re-run step COREGPM. max. wtest is: {}."
+ index.get(winL)
+ Math.max(maxWinL, maxWinP));
}
}
logger.info("TIME FOR wTestStatistics: {}" + stopWatch.lap("WTEST"));
logger.info("Total Estimation TIME: {}" + clock.getElapsedTime());
numIterations++; // update counter here!
} // only warn when iterating
yError = eL_hat.getData();
xError = eP_hat.getData();
yCoef = rhsL.getData();
xCoef = rhsP.getData();
}
/**
* Computes the Sampson distance residual for a set of observations given a homography matrix. For
* use in least-squares non-linear optimization algorithms. The full 9 elements of the 3x3 matrix
* are used to parameterize. This has an extra redundant parameter, but is much simpler and should
* not affect the final result.
*
* <p>R. Hartley, and A. Zisserman, "Multiple View Geometry in Computer Vision", 2nd Ed, Cambridge
* 2003
*
* @author Peter Abeles
*/
public class HomographyResidualSampson
implements ModelObservationResidualN<DenseMatrix64F, AssociatedPair> {
DenseMatrix64F H;
Point2D_F64 temp = new Point2D_F64();
DenseMatrix64F J = new DenseMatrix64F(2, 4);
DenseMatrix64F JJ = new DenseMatrix64F(2, 2);
DenseMatrix64F e = new DenseMatrix64F(2, 1);
DenseMatrix64F x = new DenseMatrix64F(2, 1);
DenseMatrix64F error = new DenseMatrix64F(4, 1);
LinearSolver<DenseMatrix64F> solver = LinearSolverFactory.linear(2);
@Override
public void setModel(DenseMatrix64F F) {
this.H = F;
}
@Override
public int computeResiduals(AssociatedPair p, double[] residuals, int index) {
GeometryMath_F64.mult(H, p.p1, temp);
double top1 = error1(p.p1.x, p.p1.y, p.p2.x, p.p2.y);
double top2 = error2(p.p1.x, p.p1.y, p.p2.x, p.p2.y);
computeJacobian(p.p1, p.p2);
// JJ = J*J'
CommonOps.multTransB(J, J, JJ);
// solve JJ'*x = -e
e.data[0] = -top1;
e.data[1] = -top2;
if (solver.setA(JJ)) {
solver.solve(e, x);
// -J'(J*J')^-1*e
CommonOps.multTransA(J, x, error);
residuals[index++] = error.data[0];
residuals[index++] = error.data[1];
residuals[index++] = error.data[2];
residuals[index++] = error.data[3];
} else {
residuals[index++] = 0;
residuals[index++] = 0;
residuals[index++] = 0;
residuals[index++] = 0;
}
return index;
}
/** x2 = H*x1 */
public double error1(double x1, double y1, double x2, double y2) {
double ret;
ret = -(x1 * H.get(1, 0) + y1 * H.get(1, 1) + H.get(1, 2));
ret += y2 * (x1 * H.get(2, 0) + y1 * H.get(2, 1) + H.get(2, 2));
return ret;
}
public double error2(double x1, double y1, double x2, double y2) {
double ret;
ret = (x1 * H.get(0, 0) + y1 * H.get(0, 1) + H.get(0, 2));
ret -= x2 * (x1 * H.get(2, 0) + y1 * H.get(2, 1) + H.get(2, 2));
return ret;
}
public void computeJacobian(Point2D_F64 x1, Point2D_F64 x2) {
J.data[0] = -H.get(1, 0) + x2.y * H.get(2, 0);
J.data[1] = -H.get(1, 1) + x2.y * H.get(2, 1);
J.data[2] = 0;
J.data[3] = x1.x * H.get(2, 0) + x1.y * H.get(2, 1) + H.get(2, 2);
J.data[4] = H.get(0, 0) - x2.x * H.get(2, 0);
J.data[5] = H.get(0, 1) - x2.x * H.get(2, 1);
J.data[6] = -J.data[3];
J.data[7] = 0;
}
@Override
public int getN() {
return 4;
}
}