?larrf

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?larrf

Finds a new relatively robust representation such that at least one of the eigenvalues is relatively isolated.

Syntax

call slarrf ( n , d , l , ld , clstrt , clend , w , wgap , werr , spdiam , clgapl , clgapr , pivmin , sigma , dplus , lplus , work , info )

call dlarrf ( n , d , l , ld , clstrt , clend , w , wgap , werr , spdiam , clgapl , clgapr , pivmin , sigma , dplus , lplus , work , info )

Include Files

mkl.fi

Description

slarrf dlarrf

Given the initial representation L*D*L^:code:`T` and its cluster of close eigenvalues (in a relative measure), w ( clstrt ), w ( clstrt +1), … w ( clend ), the routine ?larrf finds a new relatively robust representation

L*D*L^{T} - σ_{i}*I = L(+)*D(+)*L(+)^{T}

such that at least one of the eigenvalues of L (+)* D* (+)* L (+) ^:code:`T` is relatively isolated.

Input Parameters

n: INTEGER . The order of the matrix (subblock, if the matrix is splitted).
d: REAL for slarrf DOUBLE PRECISION for dlarrf Array, DIMENSION ( n ). The n diagonal elements of the diagonal matrix D .
l: REAL for slarrf DOUBLE PRECISION for dlarrf Array, DIMENSION ( n -1). The ( n -1) subdiagonal elements of the unit bidiagonal matrix L .
ld: REAL for slarrf DOUBLE PRECISION for dlarrf Array, DIMENSION ( n -1). The n -1 elements L_i * D_i .
clstrt: INTEGER . The index of the first eigenvalue in the cluster.
clend: INTEGER . The index of the last eigenvalue in the cluster.
w: REAL for slarrf DOUBLE PRECISION for dlarrf Array, DIMENSION ≥ ( clend - clstrt +1). The eigenvalue approximations of L*D*L^:code:`T` in ascending order. w ( clstrt ) through w ( clend ) form the cluster of relatively close eigenvalues.
wgap: REAL for slarrf DOUBLE PRECISION for dlarrf Array, DIMENSION ≥ ( clend - clstrt +1). The separation from the right neighbor eigenvalue in w .
werr: REAL for slarrf DOUBLE PRECISION for dlarrf Array, DIMENSION ≥ ( clend - clstrt +1). On input, werr contains the semiwidth of the uncertainty interval of the corresponding eigenvalue approximation in w .
spdiam: REAL for slarrf DOUBLE PRECISION for dlarrf Estimate of the spectral diameter obtained from the Gerschgorin intervals.
clgapl , clgapr: REAL for slarrf DOUBLE PRECISION for dlarrf Absolute gap on each end of the cluster. Set by the calling routine to protect against shifts too close to eigenvalues outside the cluster.
pivmin: REAL for slarrf DOUBLE PRECISION for dlarrf The minimum pivot allowed in the Sturm sequence.
work: REAL for slarrf DOUBLE PRECISION for dlarrf Workspace array, DIMENSION (2* n ).

Output Parameters

wgap: On output, the gaps are refined.
sigma: REAL for slarrf DOUBLE PRECISION for dlarrf The shift used to form L (+)* D* (+)* L (+) ^:code:`T` .
dplus: REAL for slarrf DOUBLE PRECISION for dlarrf Array, DIMENSION ( n ). The n diagonal elements of the diagonal matrix D (+).
lplus: REAL for slarrf DOUBLE PRECISION for dlarrf Array, DIMENSION ( n ). The first ( n -1) elements of lplus contain the subdiagonal elements of the unit bidiagonal matrix L (+).

info

INTEGER .

Signals processing OK (=0) or failure (=1)

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?larrf

Syntax

Include Files

Description

Input Parameters

Output Parameters