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template<typename T>
void larrb(integer *n, T *d, T *lld, integer *ifirst, integer *ilast, T *rtol1, T *rtol2, integer *offset, T *w, T *wgap, T *werr, T *work, integer *iwork, T *pivmin, T *spdiam, integer *twist, integer *info)# LARRB provides limited bisection to locate eigenvalues for more accuracy.
Purpose:
Given the relatively robust representation(RRR) L D L^T, SLARRB does "limited" bisection to refine the eigenvalues of L D L^T, W(IFIRST-OFFSET) through W(ILAST-OFFSET), 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 WERR and WGAP, respectively. During bisection, intervals [left, right] are maintained by storing their mid-points and semi-widths in the arrays W and WERR respectively.
- Parameters:
N – [in]
N is INTEGER
The order of the matrix.
D – [in]
D is REAL array, dimension (N)
The N diagonal elements of the diagonal matrix D.
LLD – [in]
LLD is REAL array, dimension (N-1)
The (N-1) elements L(i)*L(i)*D(i).
IFIRST – [in]
IFIRST is INTEGER
The index of the first eigenvalue to be computed.
ILAST – [in]
ILAST is INTEGER
The index of the last eigenvalue to be computed.
RTOL1 – [in] RTOL1 is REAL
RTOL2 – [in]
RTOL2 is REAL
Tolerance for the convergence of the bisection intervals. An interval [LEFT,RIGHT] has converged if RIGHT-LEFT < MAX(RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|)) where GAP is the (estimated) distance to the nearest eigenvalue.
OFFSET – [in]
OFFSET is INTEGER
Offset for the arrays W, WGAP and WERR, i.e., the IFIRST-OFFSET through ILAST-OFFSET elements of these arrays are to be used.
W – [inout]
W is REAL array, dimension (N)
On input, W(IFIRST-OFFSET) through W(ILAST-OFFSET) are estimates of the eigenvalues of L D L^T indexed IFIRST through ILAST.
On output, these estimates are refined.WGAP – [inout]
WGAP is REAL array, dimension (N-1)
On input, the (estimated) gaps between consecutive eigenvalues of L D L^T, i.e., WGAP(I-OFFSET) is the gap between eigenvalues I and I+1. Note that if IFIRST = ILAST then WGAP(IFIRST-OFFSET) must be set to ZERO.
On output, these gaps are refined.WERR – [inout]
WERR is REAL array, dimension (N)
On input, WERR(IFIRST-OFFSET) through WERR(ILAST-OFFSET) are the errors in the estimates of the corresponding elements in W. On output, these errors are refined.
WORK – [out]
WORK is REAL array, dimension (2*N)
Workspace.
IWORK – [out]
IWORK is INTEGER array, dimension (2*N)
Workspace.
PIVMIN – [in]
PIVMIN is REAL
The minimum pivot in the Sturm sequence.
SPDIAM – [in]
SPDIAM is REAL
The spectral diameter of the matrix.
TWIST – [in]
TWIST is INTEGER
The twist index for the twisted factorization that is used for the negcount.
TWIST = N: Compute negcount from L D L^T - LAMBDA I = L+ D+ L+^T
TWIST = 1: Compute negcount from L D L^T - LAMBDA I = U- D- U-^T
TWIST = R: Compute negcount from L D L^T - LAMBDA I = N(r) D(r) N(r)INFO – [out]
INFO is INTEGER
Error flag.