private void init(WeightFunction weightFunction, BasesFunction baseFunction) {
this.weightFunction = weightFunction;
this.basesFunction = baseFunction;
final int baseDim = baseFunction.getDim();
A = new DenseMatrix64F(baseDim, baseDim);
A_x = new DenseMatrix64F(baseDim, baseDim);
A_y = new DenseMatrix64F(baseDim, baseDim);
As = new DenseMatrix64F[] {A, A_x, A_y};
B = new ArrayList<>(baseDim);
B_x = new ArrayList<>(baseDim);
B_y = new ArrayList<>(baseDim);
Bs = Arrays.asList(B, B_x, B_y);
for (ArrayList<TDoubleArrayList> tB : Bs) {
for (int i = 0; i < baseDim; i++) {
tB.add(new TDoubleArrayList(ShapeFunctionUtils2D.MAX_NODES_SIZE_GUESS));
}
}
gamma = new DenseMatrix64F(baseDim, 1);
gamma_x = new DenseMatrix64F(baseDim, 1);
gamma_y = new DenseMatrix64F(baseDim, 1);
ps_arr = new double[3][baseDim];
p = DenseMatrix64F.wrap(ps_arr[0].length, 1, ps_arr[0]);
p_x = DenseMatrix64F.wrap(ps_arr[1].length, 1, ps_arr[1]);
p_y = DenseMatrix64F.wrap(ps_arr[2].length, 1, ps_arr[2]);
tv = new DenseMatrix64F(baseDim, 1);
luSolver = new LinearSolverLu(new LUDecompositionAlt());
A_bak = new DenseMatrix64F(baseDim, baseDim);
}
/**
* Converts a vector from eigen space into sample space.
*
* @param eigenData Eigen space data.
* @return Sample space projection.
*/
public double[] eigenToSampleSpace(double[] eigenData) {
if (eigenData.length != numComponents)
throw new IllegalArgumentException("Unexpected sample length");
DenseMatrix64F s = new DenseMatrix64F(A.getNumCols(), 1);
DenseMatrix64F r = DenseMatrix64F.wrap(numComponents, 1, eigenData);
CommonOps.multTransA(V_t, r, s);
DenseMatrix64F mean = DenseMatrix64F.wrap(A.getNumCols(), 1, this.mean);
CommonOps.add(s, mean, s);
return s.data;
}
/**
* Computes the dot product of each basis vector against the sample. Can be used as a measure for
* membership in the training sample set. High values correspond to a better fit.
*
* @param sample Sample of original data.
* @return Higher value indicates it is more likely to be a member of input dataset.
*/
public double response(double[] sample) {
if (sample.length != A.numCols)
throw new IllegalArgumentException("Expected input vector to be in sample space");
DenseMatrix64F dots = new DenseMatrix64F(numComponents, 1);
DenseMatrix64F s = DenseMatrix64F.wrap(A.numCols, 1, sample);
CommonOps.mult(V_t, s, dots);
return NormOps.normF(dots);
}
/**
* Converts a vector from sample space into eigen space.
*
* @param sampleData Sample space data.
* @return Eigen space projection.
*/
public double[] sampleToEigenSpace(double[] sampleData) {
if (sampleData.length != A.getNumCols())
throw new IllegalArgumentException("Unexpected sample length");
DenseMatrix64F mean = DenseMatrix64F.wrap(A.getNumCols(), 1, this.mean);
DenseMatrix64F s = new DenseMatrix64F(A.getNumCols(), 1, true, sampleData);
DenseMatrix64F r = new DenseMatrix64F(numComponents, 1);
CommonOps.sub(s, mean, s);
CommonOps.mult(V_t, s, r);
return r.data;
}
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();
}