/**
* <p>
* Checks to see if the matrix is positive semidefinite:
* </p>
* <p>
* x<sup>T</sup> A x ≥ 0<br>
* for all x where x is a non-zero vector and A is a symmetric matrix.
* </p>
*
* @param A square symmetric matrix. Not modified.
*
* @return True if it is positive semidefinite and false if it is not.
*/
public static bool isPositiveSemidefinite(FMatrixRMaj A)
{
if (!isSquare(A))
{
return(false);
}
EigenDecomposition_F32 <FMatrixRMaj> eig = DecompositionFactory_FDRM.eig(A.numCols, false);
if (eig.inputModified())
{
A = (FMatrixRMaj)A.copy();
}
eig.decompose(A);
for (int i = 0; i < A.numRows; i++)
{
Complex_F32 v = eig.getEigenvalue(i);
if (v.getReal() < 0)
{
return(false);
}
}
return(true);
}
public virtual bool decompose(FMatrixRMaj orig)
{
A.set(orig);
symmetric = MatrixFeatures_FDRM.isSymmetric(A, tol);
return(symmetric ? symmetricAlg.decompose(A) : generalAlg.decompose(A));
}
