/**
* <p>
* The condition number of a matrix is used to measure the sensitivity of the linear
* system <b>Ax=b</b>. A value near one indicates that it is a well conditioned matrix.<br>
* <br>
* κ<sub>p</sub> = ||A||<sub>p</sub>||A<sup>-1</sup>||<sub>p</sub>
* </p>
* <p>
* If the matrix is not square then the condition of either A<sup>T</sup>A or AA<sup>T</sup> is computed.
* <p>
* @param A The matrix.
* @param p p-norm
* @return The condition number.
*/
public static double conditionP(DMatrixRMaj A, double p)
{
if (p == 2)
{
return(conditionP2(A));
}
else if (A.numRows == A.numCols)
{
// square matrices are the typical case
DMatrixRMaj A_inv = new DMatrixRMaj(A.numRows, A.numCols);
if (!CommonOps_DDRM.invert(A, A_inv))
{
throw new ArgumentException("A can't be inverted.");
}
return(normP(A, p) * normP(A_inv, p));
}
else
{
DMatrixRMaj pinv = new DMatrixRMaj(A.numCols, A.numRows);
CommonOps_DDRM.pinv(A, pinv);
return(normP(A, p) * normP(pinv, p));
}
}
/// <summary>
/// Computes the Moore-Penrose pseudo-inverse.
/// </summary>
public override SimpleMatrixD pseudoInverse()
{
SimpleMatrixD ret = createMatrix(mat.getNumCols(), mat.getNumRows());
CommonOps_DDRM.pinv(mat, ret.getMatrix());
return(ret);
}