SLAHQR(3F) SLAHQR(3F)
SLAHQR - i an auxiliary routine called by SHSEQR to update the
eigenvalues and Schur decomposition already computed by SHSEQR, by
dealing with the Hessenberg submatrix in rows and columns ILO to IHI
SUBROUTINE SLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI, ILOZ, IHIZ,
Z, LDZ, INFO )
LOGICAL WANTT, WANTZ
INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N
REAL H( LDH, * ), WI( * ), WR( * ), Z( LDZ, * )
SLAHQR is an auxiliary routine called by SHSEQR to update the eigenvalues
and Schur decomposition already computed by SHSEQR, by dealing with the
Hessenberg submatrix in rows and columns ILO to IHI.
WANTT (input) LOGICAL
= .TRUE. : the full Schur form T is required;
= .FALSE.: only eigenvalues are required.
WANTZ (input) LOGICAL
= .TRUE. : the matrix of Schur vectors Z is required;
= .FALSE.: Schur vectors are not required.
N (input) INTEGER
The order of the matrix H. N >= 0.
ILO (input) INTEGER
IHI (input) INTEGER It is assumed that H is already upper
quasi-triangular in rows and columns IHI+1:N, and that
H(ILO,ILO-1) = 0 (unless ILO = 1). SLAHQR 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 (input/output) REAL array, dimension (LDH,N)
On entry, the upper Hessenberg matrix H. On exit, if WANTT is
.TRUE., H is upper quasi-triangular in rows and columns ILO:IHI,
with any 2-by-2 diagonal blocks in standard form. If WANTT is
.FALSE., the contents of H are unspecified on exit.
LDH (input) INTEGER
The leading dimension of the array H. LDH >= max(1,N).
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SLAHQR(3F) SLAHQR(3F)
WR (output) REAL array, dimension (N)
WI (output) REAL array, dimension (N) The real and imaginary
parts, respectively, of the computed eigenvalues ILO to IHI are
stored in the corresponding elements of WR and WI. If two
eigenvalues are computed as a complex conjugate pair, they are
stored in consecutive elements of WR and WI, say the i-th and
(i+1)th, with WI(i) > 0 and WI(i+1) < 0. If WANTT is .TRUE., the
eigenvalues are stored in the same order as on the diagonal of
the Schur form returned in H, with WR(i) = H(i,i), and, if
H(i:i+1,i:i+1) is a 2-by-2 diagonal block, WI(i) =
sqrt(H(i+1,i)*H(i,i+1)) and WI(i+1) = -WI(i).
ILOZ (input) INTEGER
IHIZ (input) INTEGER Specify the rows of Z to which
transformations must be applied if WANTZ is .TRUE.. 1 <= ILOZ <=
ILO; IHI <= IHIZ <= N.
Z (input/output) REAL array, dimension (LDZ,N)
If WANTZ is .TRUE., on entry Z must contain the current matrix Z
of transformations accumulated by SHSEQR, and 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.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= max(1,N).
INFO (output) INTEGER
= 0: successful exit
> 0: SLAHQR failed to compute all the eigenvalues ILO to IHI in a
total of 30*(IHI-ILO+1) iterations; if INFO = i, elements i+1:ihi
of WR and WI contain those eigenvalues which have been
successfully computed.
SLAHQR(3F) SLAHQR(3F)
SLAHQR - i an auxiliary routine called by SHSEQR to update the
eigenvalues and Schur decomposition already computed by SHSEQR, by
dealing with the Hessenberg submatrix in rows and columns ILO to IHI
SUBROUTINE SLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI, ILOZ, IHIZ,
Z, LDZ, INFO )
LOGICAL WANTT, WANTZ
INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N
REAL H( LDH, * ), WI( * ), WR( * ), Z( LDZ, * )
SLAHQR is an auxiliary routine called by SHSEQR to update the eigenvalues
and Schur decomposition already computed by SHSEQR, by dealing with the
Hessenberg submatrix in rows and columns ILO to IHI.
WANTT (input) LOGICAL
= .TRUE. : the full Schur form T is required;
= .FALSE.: only eigenvalues are required.
WANTZ (input) LOGICAL
= .TRUE. : the matrix of Schur vectors Z is required;
= .FALSE.: Schur vectors are not required.
N (input) INTEGER
The order of the matrix H. N >= 0.
ILO (input) INTEGER
IHI (input) INTEGER It is assumed that H is already upper
quasi-triangular in rows and columns IHI+1:N, and that
H(ILO,ILO-1) = 0 (unless ILO = 1). SLAHQR 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 (input/output) REAL array, dimension (LDH,N)
On entry, the upper Hessenberg matrix H. On exit, if WANTT is
.TRUE., H is upper quasi-triangular in rows and columns ILO:IHI,
with any 2-by-2 diagonal blocks in standard form. If WANTT is
.FALSE., the contents of H are unspecified on exit.
LDH (input) INTEGER
The leading dimension of the array H. LDH >= max(1,N).
Page 1
SLAHQR(3F) SLAHQR(3F)
WR (output) REAL array, dimension (N)
WI (output) REAL array, dimension (N) The real and imaginary
parts, respectively, of the computed eigenvalues ILO to IHI are
stored in the corresponding elements of WR and WI. If two
eigenvalues are computed as a complex conjugate pair, they are
stored in consecutive elements of WR and WI, say the i-th and
(i+1)th, with WI(i) > 0 and WI(i+1) < 0. If WANTT is .TRUE., the
eigenvalues are stored in the same order as on the diagonal of
the Schur form returned in H, with WR(i) = H(i,i), and, if
H(i:i+1,i:i+1) is a 2-by-2 diagonal block, WI(i) =
sqrt(H(i+1,i)*H(i,i+1)) and WI(i+1) = -WI(i).
ILOZ (input) INTEGER
IHIZ (input) INTEGER Specify the rows of Z to which
transformations must be applied if WANTZ is .TRUE.. 1 <= ILOZ <=
ILO; IHI <= IHIZ <= N.
Z (input/output) REAL array, dimension (LDZ,N)
If WANTZ is .TRUE., on entry Z must contain the current matrix Z
of transformations accumulated by SHSEQR, and 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.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= max(1,N).
INFO (output) INTEGER
= 0: successful exit
> 0: SLAHQR failed to compute all the eigenvalues ILO to IHI in a
total of 30*(IHI-ILO+1) iterations; if INFO = i, elements i+1:ihi
of WR and WI contain those eigenvalues which have been
successfully computed.
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