Visible to Intel only — GUID: GUID-9B559E6E-C7C5-441F-BC60-8DFF6679C912
Visible to Intel only — GUID: GUID-9B559E6E-C7C5-441F-BC60-8DFF6679C912
?larrb
Provides limited bisection to locate eigenvalues for more accuracy.
Syntax
call slarrb( n, d, lld, ifirst, ilast, rtol1, rtol2, offset, w, wgap, werr, work, iwork, pivmin, spdiam, twist, info )
call dlarrb( n, d, lld, ifirst, ilast, rtol1, rtol2, offset, w, wgap, werr, work, iwork, pivmin, spdiam, twist, info )
Include Files
- mkl.fi
Description
Given the relatively robust representation (RRR) L*D*LT, the routine does "limited" bisection to refine the eigenvalues of L*D*LT, 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.
Input Parameters
- n
-
INTEGER. The order of the matrix.
- d
-
REAL for slarrb
DOUBLE PRECISION for dlarrb
Array, DIMENSION (n). The n diagonal elements of the diagonal matrix D.
- lld
-
REAL for slarrb
DOUBLE PRECISION for dlarrb
Array, DIMENSION (n-1).
The n-1 elements Li*Li*Di.
- ifirst
-
INTEGER. The index of the first eigenvalue to be computed.
- ilast
-
INTEGER. The index of the last eigenvalue to be computed.
- rtol1, rtol2
-
REAL for slarrb
DOUBLE PRECISION for dlarrb
Tolerance for the convergence of the bisection intervals. An interval [left, right] has converged if RIGHT-LEFT.LT.MAX( rtol1*gap, rtol2*max(|left|,|right|) ), where gap is the (estimated) distance to the nearest eigenvalue.
- offset
-
INTEGER. Offset for the arrays w, wgap and werr, that is, the ifirst-offset through ilast-offset elements of these arrays are to be used.
- w
-
REAL for slarrb
DOUBLE PRECISION for dlarrb
Array, DIMENSION (n). On input, w( ifirst-offset ) through w( ilast-offset ) are estimates of the eigenvalues of L*D*LT indexed ifirst through ilast.
- wgap
-
REAL for slarrb
DOUBLE PRECISION for dlarrb
Array, DIMENSION (n-1). The estimated gaps between consecutive eigenvalues of L*D*LT, that is, wgap(i-offset) is the gap between eigenvalues i and i+1. Note that if IFIRST.EQ.ILAST then wgap(ifirst-offset) must be set to 0.
- werr
-
REAL for slarrb
DOUBLE PRECISION for dlarrb
Array, DIMENSION (n). On input, werr(ifirst-offset) through werr(ilast-offset) are the errors in the estimates of the corresponding elements in w.
- work
-
REAL for slarrb
DOUBLE PRECISION for dlarrb
Workspace array, DIMENSION (2*n).
- pivmin
-
REAL for slarrb
DOUBLE PRECISION for dlarrb
The minimum pivot in the Sturm sequence.
- spdiam
-
REAL for slarrb
DOUBLE PRECISION for dlarrb
The spectral diameter of the matrix.
- twist
-
INTEGER. The twist index for the twisted factorization that is used for the negcount.
twist = n: Compute negcount from L*D*LT - lambda*i = L+* D+ *L+T
twist = n: Compute negcount from L*D*LT - lambda*i = U-*D-*U-T
twist = n: Compute negcount from L*D*LT - lambda*i = Nr*D r*Nr
- iwork
-
INTEGER.
Workspace array, DIMENSION (2*n).
Output Parameters
- w
-
On output, the estimates of the eigenvalues are "refined".
- wgap
-
On output, the gaps are refined.
- werr
-
On output, "refined" errors in the estimates of w.
- info
-
INTEGER.
Error flag.