?lahqr2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?lahqr2

Updates the eigenvalues and Schur decomposition.

Syntax

call clahqr2 ( wantt , wantz , n , ilo , ihi , h , ldh , w , iloz , ihiz , z , ldz , info )

call zlahqr2 ( wantt , wantz , n , ilo , ihi , h , ldh , w , iloz , ihiz , z , ldz , info )

Include Files

Description

?lahqr2 is an auxiliary routine called by ?hseqr to update the eigenvalues and Schur decomposition already computed by ?hseqr , by dealing with the Hessenberg submatrix in rows and columns ilo to ihi . This version of ?lahqr (not the standard LAPACK version) uses a double-shift algorithm (like LAPACK’s ?lahqr ). Unlike the standard LAPACK convention, this does not assume the subdiagonal is real, nor does it work to preserve this quality if given.

Input Parameters

wantt

LOGICAL.

= .TRUE. : the full Schur form T is required;

= .FALSE. : only eigenvalues are required.

wantz

LOGICAL.

= .TRUE. : the matrix of Schur vectors Z is required;

= .FALSE. : Schur vectors are not required.

n

INTEGER.

The order of the matrix H . n >= 0.

ilo , ihi

INTEGER.

It is assumed that the matrix H is upper triangular in rows and columns ihi +1 :n , and that matrix element H(ilo,ilo-1)= 0 (unless ilo = 1). ?lahqr works primarily with the Hessenberg submatrix in rows and columns ilo to ihi , but applies transformations to all of h if wantt is .TRUE. .

1 <= ilo <= max(1, ihi ); ihi <= n .

h

COMPLEX for clahqr2 DOUBLE COMPLEX for zlahqr2

Array, size ( ldh , n ) .

On entry, the upper Hessenberg matrix H .

ldh

INTEGER.

The leading dimension of the array h . ldh >= max(1, n ).

iloz , ihiz

INTEGER.

Specify the rows of Z to which transformations must be applied if wantz is .TRUE. .

1 <= iloz <= ilo ; ihi <= ihiz <= n .

z

COMPLEX for clahqr2 DOUBLE COMPLEX for zlahqr2

Array, size (ldz,n)) .

If wantz is .TRUE. , on entry z must contain the current matrix Z of transformations. If wantz is .FALSE. , z is not referenced.

ldz

INTEGER.

The leading dimension of the array z . ldz >= max(1, n ).

Output Parameters

h

On exit, if wantt is .TRUE. , h is upper triangular in rows and columns ilo : ihi . If wantt is .FALSE. , the contents of h are unspecified on exit.

w

COMPLEX for clahqr2 DOUBLE COMPLEX for zlahqr2 Array, size ( n )

The computed eigenvalues ilo to ihi are stored in the corresponding elements of w . If wantt is .TRUE. , the eigenvalues are stored in the same order as on the diagonal of the Schur form returned in h , with w(i) = h(i,i)w[i] = H(i, i) .

z

If wantz is .TRUE. , on exit z has been updated; transformations are applied only to the submatrix Z ( iloz : ihiz , ilo : ihi ). If wantz is .FALSE. , z is not referenced.

info

INTEGER.

= 0: successful exit

> 0: if info = i , ?lahqr failed to compute all the eigenvalues ilo to ihi in a total of 30*( ihi - ilo +1) iterations; elements i +1: ihi of w contain those eigenvalues which have been successfully computed.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?lahqr2

Syntax

Include Files

Description

Input Parameters

Output Parameters