?larrb

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

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

slarrb dlarrb

Given the relatively robust representation (RRR) L*D*L^:code:`T` , the routine does “limited” bisection to refine the eigenvalues of L*D*L^:code:`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^:code:`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^:code:`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