Provides limited bisection to locate eigenvalues for more accuracy.
Given the relatively robust representation (RRR)
?larrb2does "limited" bisection to refine the eigenvalues of
,to more accuracy. Initial guesses for these eigenvalues are input in
w, the corresponding estimate of the error in these guesses and their gaps are input in
wgap, respectively. During bisection, intervals [
right] are maintained by storing their mid-points and semi-widths in the arrays
There are very few minor differences between larrb from LAPACK and this current
?larrb2. The most important reason for creating this nearly identical copy is profiling: in the ScaLAPACK MRRR algorithm, eigenvalue computation using
?larrb2is used for refinement in the construction of the representation tree, as opposed to the initial computation of the eigenvalues for the root RRR which uses
?larrb. When profiling, this allows an easy quantification of refinement work vs. computing eigenvalues of the root.
- INTEGERThe order of the matrix.
- REALforslarrb2DOUBLE PRECISIONfordlarrb2Array of sizen.Thendiagonal elements of the diagonal matrixD.
- REALforslarrb2DOUBLE PRECISIONfordlarrb2Array of sizen-1.The (n-1) elements.l*il*id(i)
- INTEGERThe index of the first eigenvalue to be computed.
- INTEGERThe index of the last eigenvalue to be computed.
- REALforslarrb2DOUBLE PRECISIONfordlarrb2Tolerance for the convergence of the bisection intervals.An interval [left,right] has converged ifright-left< max (rtol1*gap,rtol2* max(|left|, |right|)) wheregapis the (estimated) distance to the nearest eigenvalue.
- INTEGEROffset for the arraysw,wgapand