/**
* The scale of the trifocal tensor is arbitrary. However there are situations when comparing
* results that using a consistent scale is useful. This function normalizes the sensor such that
* its Euclidean length (the f-norm) is equal to one.
*/
public void normalizeScale() {
double sum = 0;
sum += SpecializedOps.elementSumSq(T1);
sum += SpecializedOps.elementSumSq(T2);
sum += SpecializedOps.elementSumSq(T3);
double n = Math.sqrt(sum);
CommonOps.scale(1.0 / n, T1);
CommonOps.scale(1.0 / n, T2);
CommonOps.scale(1.0 / n, T3);
}
/**
* Extracts a row or column from this matrix. The returned vector will either be a row or column
* vector depending on the input type.
*
* @param extractRow If true a row will be extracted.
* @param element The row or column the vector is contained in.
* @return Extracted vector.
*/
public T extractVector(boolean extractRow, int element) {
int length = extractRow ? mat.numCols : mat.numRows;
T ret = extractRow ? createMatrix(1, length) : createMatrix(length, 1);
if (extractRow) {
SpecializedOps.subvector(mat, element, 0, length, true, 0, ret.getMatrix());
} else {
SpecializedOps.subvector(mat, 0, element, length, false, 0, ret.getMatrix());
}
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;
}
/**
* Computes the most dominant eigen vector of A using a shifted matrix. The shifted matrix is
* defined as <b>B = A - αI</b> and can converge faster if α is chosen wisely. In
* general it is easier to choose a value for α that will converge faster with the
* shift-invert strategy than this one.
*
* @param A The matrix.
* @param alpha Shifting factor.
* @return If it converged or not.
*/
public boolean computeShiftDirect(DenseMatrix64F A, double alpha) {
SpecializedOps.addIdentity(A, B, -alpha);
return computeDirect(B);
}