public static double quality(DMatrixRMaj orig, DMatrixRMaj U, DMatrixRMaj W, DMatrixRMaj Vt)
{
// foundA = U*W*Vt
DMatrixRMaj UW = new DMatrixRMaj(U.numRows, W.numCols);
CommonOps_DDRM.mult(U, W, UW);
DMatrixRMaj foundA = new DMatrixRMaj(UW.numRows, Vt.numCols);
CommonOps_DDRM.mult(UW, Vt, foundA);
double normA = NormOps_DDRM.normF(foundA);
return(SpecializedOps_DDRM.diffNormF(orig, foundA) / normA);
}
/**
* <p>
* The vector associated will the smallest singular value is returned as the null space
* of the decomposed system. A right null space is returned if 'isRight' is set to true,
* and a left null space if false.
* </p>
*
* @param svd A precomputed decomposition. Not modified.
* @param isRight true for right null space and false for left null space. Right is more commonly used.
* @param nullVector Optional storage for a vector for the null space. Modified.
* @return Vector in V associated with smallest singular value..
*/
public static DMatrixRMaj nullVector(SingularValueDecomposition_F64 <DMatrixRMaj> svd,
bool isRight,
DMatrixRMaj nullVector)
{
int N = svd.numberOfSingularValues();
double[] s = svd.getSingularValues();
DMatrixRMaj A = isRight ? svd.getV(null, true) : svd.getU(null, false);
if (isRight)
{
if (A.numRows != svd.numCols())
{
throw new ArgumentException("Can't compute the null space using a compact SVD for a matrix of this size.");
}
if (nullVector == null)
{
nullVector = new DMatrixRMaj(svd.numCols(), 1);
}
else
{
nullVector.reshape(svd.numCols(), 1);
}
}
else
{
if (A.numCols != svd.numRows())
{
throw new ArgumentException("Can't compute the null space using a compact SVD for a matrix of this size.");
}
if (nullVector == null)
{
nullVector = new DMatrixRMaj(svd.numRows(), 1);
}
else
{
nullVector.reshape(svd.numRows(), 1);
}
}
int smallestIndex = -1;
if (isRight && svd.numCols() > svd.numRows())
{
smallestIndex = svd.numCols() - 1;
}
else if (!isRight && svd.numCols() < svd.numRows())
{
smallestIndex = svd.numRows() - 1;
}
else
{
// find the smallest singular value
double smallestValue = Double.MaxValue;
for (int i = 0; i < N; i++)
{
if (s[i] < smallestValue)
{
smallestValue = s[i];
smallestIndex = i;
}
}
}
// extract the null space
if (isRight)
{
SpecializedOps_DDRM.subvector(A, smallestIndex, 0, A.numRows, true, 0, nullVector);
}
else
{
SpecializedOps_DDRM.subvector(A, 0, smallestIndex, A.numRows, false, 0, nullVector);
}
return(nullVector);
}
public double quality()
{
return(SpecializedOps_DDRM.qualityTriangular(decomposer.getQR()));
}
public DMatrixRMaj getRowPivot(DMatrixRMaj pivot)
{
return(SpecializedOps_DDRM.pivotMatrix(pivot, this.pivot, LU.numRows, false));
}