?larrb

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 10/15/2026

Version

Public

?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*L^T , the routine 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.

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 L_{i}*L_{i}*D_{i} .
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*L^T 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*L^T , 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.
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 .

Now it is not used and always is set to 0.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?larrb

Syntax

Include Files

Description

Input Parameters

Output Parameters