claqr5.f - Man Page

SRC/claqr5.f

Synopsis

Functions/Subroutines

subroutine claqr5 (wantt, wantz, kacc22, n, ktop, kbot, nshfts, s, h, ldh, iloz, ihiz, z, ldz, v, ldv, u, ldu, nv, wv, ldwv, nh, wh, ldwh)
CLAQR5 performs a single small-bulge multi-shift QR sweep.

Function/Subroutine Documentation

subroutine claqr5 (logical wantt, logical wantz, integer kacc22, integer n, integer ktop, integer kbot, integer nshfts, complex, dimension( * ) s, complex, dimension( ldh, * ) h, integer ldh, integer iloz, integer ihiz, complex, dimension( ldz, * ) z, integer ldz, complex, dimension( ldv, * ) v, integer ldv, complex, dimension( ldu, * ) u, integer ldu, integer nv, complex, dimension( ldwv, * ) wv, integer ldwv, integer nh, complex, dimension( ldwh, * ) wh, integer ldwh)

CLAQR5 performs a single small-bulge multi-shift QR sweep.

Purpose:

```    CLAQR5 called by CLAQR0 performs a
single small-bulge multi-shift QR sweep.```
Parameters

WANTT

```          WANTT is LOGICAL
WANTT = .true. if the triangular Schur factor
is being computed.  WANTT is set to .false. otherwise.```

WANTZ

```          WANTZ is LOGICAL
WANTZ = .true. if the unitary Schur factor is being
computed.  WANTZ is set to .false. otherwise.```

KACC22

```          KACC22 is INTEGER with value 0, 1, or 2.
Specifies the computation mode of far-from-diagonal
= 0: CLAQR5 does not accumulate reflections and does not
use matrix-matrix multiply to update far-from-diagonal
matrix entries.
= 1: CLAQR5 accumulates reflections and uses matrix-matrix
multiply to update the far-from-diagonal matrix entries.
= 2: Same as KACC22 = 1. This option used to enable exploiting
the 2-by-2 structure during matrix multiplications, but
this is no longer supported.```

N

```          N is INTEGER
N is the order of the Hessenberg matrix H upon which this
subroutine operates.```

KTOP

`          KTOP is INTEGER`

KBOT

```          KBOT is INTEGER
These are the first and last rows and columns of an
isolated diagonal block upon which the QR sweep is to be
applied. It is assumed without a check that
either KTOP = 1  or   H(KTOP,KTOP-1) = 0
and
either KBOT = N  or   H(KBOT+1,KBOT) = 0.```

NSHFTS

```          NSHFTS is INTEGER
NSHFTS gives the number of simultaneous shifts.  NSHFTS
must be positive and even.```

S

```          S is COMPLEX array, dimension (NSHFTS)
S contains the shifts of origin that define the multi-
shift QR sweep.  On output S may be reordered.```

H

```          H is COMPLEX array, dimension (LDH,N)
On input H contains a Hessenberg matrix.  On output a
multi-shift QR sweep with shifts SR(J)+i*SI(J) is applied
to the isolated diagonal block in rows and columns KTOP
through KBOT.```

LDH

```          LDH is INTEGER
LDH is the leading dimension of H just as declared in the
calling procedure.  LDH >= MAX(1,N).```

ILOZ

`          ILOZ is INTEGER`

IHIZ

```          IHIZ is INTEGER
Specify the rows of Z to which transformations must be
applied if WANTZ is .TRUE.. 1 <= ILOZ <= IHIZ <= N```

Z

```          Z is COMPLEX array, dimension (LDZ,IHIZ)
If WANTZ = .TRUE., then the QR Sweep unitary
similarity transformation is accumulated into
Z(ILOZ:IHIZ,ILOZ:IHIZ) from the right.
If WANTZ = .FALSE., then Z is unreferenced.```

LDZ

```          LDZ is INTEGER
LDA is the leading dimension of Z just as declared in
the calling procedure. LDZ >= N.```

V

`          V is COMPLEX array, dimension (LDV,NSHFTS/2)`

LDV

```          LDV is INTEGER
LDV is the leading dimension of V as declared in the
calling procedure.  LDV >= 3.```

U

`          U is COMPLEX array, dimension (LDU,2*NSHFTS)`

LDU

```          LDU is INTEGER
LDU is the leading dimension of U just as declared in the
in the calling subroutine.  LDU >= 2*NSHFTS.```

NV

```          NV is INTEGER
NV is the number of rows in WV agailable for workspace.
NV >= 1.```

WV

`          WV is COMPLEX array, dimension (LDWV,2*NSHFTS)`

LDWV

```          LDWV is INTEGER
LDWV is the leading dimension of WV as declared in the
in the calling subroutine.  LDWV >= NV.```

NH

```          NH is INTEGER
NH is the number of columns in array WH available for
workspace. NH >= 1.```

WH

`          WH is COMPLEX array, dimension (LDWH,NH)`

LDWH

```          LDWH is INTEGER
Leading dimension of WH just as declared in the
calling procedure.  LDWH >= 2*NSHFTS.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Contributors:

Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA

Lars Karlsson, Daniel Kressner, and Bruno Lang

Thijs Steel, Department of Computer science, KU Leuven, Belgium

References:

K. Braman, R. Byers and R. Mathias, The Multi-Shift QR Algorithm Part I: Maintaining Well Focused Shifts, and Level 3 Performance, SIAM Journal of Matrix Analysis, volume 23, pages 929--947, 2002.

Lars Karlsson, Daniel Kressner, and Bruno Lang, Optimally packed chains of bulges in multishift QR algorithms. ACM Trans. Math. Softw. 40, 2, Article 12 (February 2014).

Definition at line 254 of file claqr5.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page claqr5(3) is an alias of claqr5.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK