/**
* <p>
* Computes a metric which measures the the quality of an eigen value decomposition. If a
* value is returned that is close to or smaller than 1e-15 then it is within machine precision.
* </p>
* <p>
* EVD quality is defined as:<br>
* <br>
* Quality = ||A*V - V*D|| / ||A*V||.
* </p>
*
* @param orig The original matrix. Not modified.
* @param eig EVD of the original matrix. Not modified.
* @return The quality of the decomposition.
*/
public static float quality(FMatrixRMaj orig, EigenDecomposition_F32 <FMatrixRMaj> eig)
{
FMatrixRMaj A = orig;
FMatrixRMaj V = EigenOps_FDRM.createMatrixV(eig);
FMatrixRMaj D = EigenOps_FDRM.createMatrixD(eig);
// L = A*V
FMatrixRMaj L = new FMatrixRMaj(A.numRows, V.numCols);
CommonOps_FDRM.mult(A, V, L);
// R = V*D
FMatrixRMaj R = new FMatrixRMaj(V.numRows, D.numCols);
CommonOps_FDRM.mult(V, D, R);
FMatrixRMaj diff = new FMatrixRMaj(L.numRows, L.numCols);
CommonOps_FDRM.subtract(L, R, diff);
float top = NormOps_FDRM.normF(diff);
float bottom = NormOps_FDRM.normF(L);
float error = top / bottom;
return(error);
}
public static float quality(FMatrixRMaj orig, FMatrixRMaj U, FMatrixRMaj W, FMatrixRMaj Vt)
{
// foundA = U*W*Vt
FMatrixRMaj UW = new FMatrixRMaj(U.numRows, W.numCols);
CommonOps_FDRM.mult(U, W, UW);
FMatrixRMaj foundA = new FMatrixRMaj(UW.numRows, Vt.numCols);
CommonOps_FDRM.mult(UW, Vt, foundA);
float normA = NormOps_FDRM.normF(foundA);
return(SpecializedOps_FDRM.diffNormF(orig, foundA) / normA);
}
