?larrj

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

Download PDF

ID 766686

Date 10/15/2026

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

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.

Select Your Language

Using Intel.com Search

Quick Links

Recent Searches

Advanced Search

Only search in

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?larrj

Syntax

Include Files

Description

Input Parameters

Output Parameters