?larrj

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?larrj

Performs refinement of the initial estimates of the eigenvalues of the matrix T .

Syntax

call slarrj ( n , d , e2 , ifirst , ilast , rtol , offset , w , werr , work , iwork , pivmin, spdiam , info )

call dlarrj ( n , d , e2 , ifirst , ilast , rtol , offset , w , werr , work , iwork , pivmin, spdiam , info )

Include Files

mkl.fi

Description

slarrj dlarrj

Given the initial eigenvalue approximations of T , this routine does bisection to refine the eigenvalues of 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 in werr . During bisection, intervals [a,b] 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 T .
d: REAL for slarrj DOUBLE PRECISION for dlarrj Array, DIMENSION ( n ). Contains n diagonal elements of the matrix T .
e2: REAL for slarrj DOUBLE PRECISION for dlarrj Array, DIMENSION ( n-1 ). Contains (n-1) squared sub-diagonal elements of the T .
ifirst: INTEGER .
ilast: INTEGER .
rtol: REAL for slarrj DOUBLE PRECISION for dlarrj Tolerance for the convergence of the bisection intervals. An interval [a,b] is considered to be converged if (b-a) ≤ rtol*max(|a|,|b|) .
offset: INTEGER .
w: REAL for slarrj DOUBLE PRECISION for dlarrj 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 .
werr: REAL for slarrj DOUBLE PRECISION for dlarrj 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 slarrj DOUBLE PRECISION for dlarrj Workspace array, DIMENSION ( 2*n ).
iwork: INTEGER . Workspace array, DIMENSION ( 2*n ).
pivmin: REAL for slarrj DOUBLE PRECISION for dlarrj The minimum pivot in the Sturm sequence for the matrix T .
spdiam: REAL for slarrj DOUBLE PRECISION for dlarrj The spectral diameter of the matrix T .

Output Parameters

w: On exit, contains the refined estimates of the eigenvalues.
werr: On exit, contains the refined errors in the estimates of the corresponding elements in 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

?larrj

Syntax

Include Files

Description

Input Parameters

Output Parameters