/**
* <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(DMatrixRMaj A)
{
if (!isSquare(A))
{
return(false);
}
EigenDecomposition_F64 <DMatrixRMaj> eig = DecompositionFactory_DDRM.eig(A.numCols, false);
if (eig.inputModified())
{
A = (DMatrixRMaj)A.copy();
}
eig.decompose(A);
for (int i = 0; i < A.numRows; i++)
{
Complex_F64 v = eig.getEigenvalue(i);
if (v.getReal() < 0)
{
return(false);
}
}
return(true);
}
private void checkSplitPerformImplicit()
{
// check for splits
for (int i = x2; i > x1; i--)
{
if (_implicit.isZero(i, i - 1))
{
x1 = i;
splits[numSplits++] = i - 1;
// reduce the scope of what it is looking at
return;
}
}
// first try using known eigenvalues in the same order they were originally found
if (onscript)
{
if (_implicit.steps > _implicit.exceptionalThreshold / 2)
{
onscript = false;
}
else
{
Complex_F64 a = origEigenvalues[indexVal];
// if no splits are found perform an implicit step
if (a.isReal())
{
_implicit.performImplicitSingleStep(x1, x2, a.getReal());
}
else if (x2 - x1 >= 1 && x1 + 2 < N)
{
_implicit.performImplicitDoubleStep(x1, x2, a.real, a.imaginary);
}
else
{
onscript = false;
}
}
}
else
{
// that didn't work so try a modified order
if (x2 - x1 >= 1 && x1 + 2 < N)
{
_implicit.implicitDoubleStep(x1, x2);
}
else
{
_implicit.performImplicitSingleStep(x1, x2, _implicit.A.get(x2, x2));
}
}
}
