# zlaqr5.f man page

zlaqr5.f —

## Synopsis

### Functions/Subroutines

subroutinezlaqr5(WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, S, H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U, LDU, NV, WV, LDWV, NH, WH, LDWH)ZLAQR5performs a single small-bulge multi-shift QR sweep.

## Function/Subroutine Documentation

### subroutine zlaqr5 (logicalWANTT, logicalWANTZ, integerKACC22, integerN, integerKTOP, integerKBOT, integerNSHFTS, complex*16, dimension( * )S, complex*16, dimension( ldh, * )H, integerLDH, integerILOZ, integerIHIZ, complex*16, dimension( ldz, * )Z, integerLDZ, complex*16, dimension( ldv, * )V, integerLDV, complex*16, dimension( ldu, * )U, integerLDU, integerNV, complex*16, dimension( ldwv, * )WV, integerLDWV, integerNH, complex*16, dimension( ldwh, * )WH, integerLDWH)

**ZLAQR5** performs a single small-bulge multi-shift QR sweep.

**Purpose:**

```
ZLAQR5, called by ZLAQR0, performs a
single small-bulge multi-shift QR sweep.
```

**Parameters:**

*WANTT*

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

*WANTZ*

```
WANTZ is logical scalar
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
orthogonal updates.
= 0: ZLAQR5 does not accumulate reflections and does not
use matrix-matrix multiply to update far-from-diagonal
matrix entries.
= 1: ZLAQR5 accumulates reflections and uses matrix-matrix
multiply to update the far-from-diagonal matrix entries.
= 2: ZLAQR5 accumulates reflections, uses matrix-matrix
multiply to update the far-from-diagonal matrix entries,
and takes advantage of 2-by-2 block structure during
matrix multiplies.
```

*N*

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

*KTOP*

`KTOP is integer scalar`

*KBOT*

```
KBOT is integer scalar
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 scalar
NSHFTS gives the number of simultaneous shifts. NSHFTS
must be positive and even.
```

*S*

```
S is COMPLEX*16 array of size (NSHFTS)
S contains the shifts of origin that define the multi-
shift QR sweep. On output S may be reordered.
```

*H*

```
H is COMPLEX*16 array of size (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 scalar
LDH is the leading dimension of H just as declared in the
calling procedure. LDH.GE.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 .LE. ILOZ .LE. IHIZ .LE. N
```

*Z*

```
Z is COMPLEX*16 array of size (LDZ,IHI)
If WANTZ = .TRUE., then the QR Sweep unitary
similarity transformation is accumulated into
Z(ILOZ:IHIZ,ILO:IHI) from the right.
If WANTZ = .FALSE., then Z is unreferenced.
```

*LDZ*

```
LDZ is integer scalar
LDA is the leading dimension of Z just as declared in
the calling procedure. LDZ.GE.N.
```

*V*

`V is COMPLEX*16 array of size (LDV,NSHFTS/2)`

*LDV*

```
LDV is integer scalar
LDV is the leading dimension of V as declared in the
calling procedure. LDV.GE.3.
```

*U*

```
U is COMPLEX*16 array of size
(LDU,3*NSHFTS-3)
```

*LDU*

```
LDU is integer scalar
LDU is the leading dimension of U just as declared in the
in the calling subroutine. LDU.GE.3*NSHFTS-3.
```

*NH*

```
NH is integer scalar
NH is the number of columns in array WH available for
workspace. NH.GE.1.
```

*WH*

`WH is COMPLEX*16 array of size (LDWH,NH)`

*LDWH*

```
LDWH is integer scalar
Leading dimension of WH just as declared in the
calling procedure. LDWH.GE.3*NSHFTS-3.
```

*NV*

```
NV is integer scalar
NV is the number of rows in WV agailable for workspace.
NV.GE.1.
```

*WV*

```
WV is COMPLEX*16 array of size
(LDWV,3*NSHFTS-3)
```

*LDWV*

```
LDWV is integer scalar
LDWV is the leading dimension of WV as declared in the
in the calling subroutine. LDWV.GE.NV.
```

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

September 2012

**Contributors:**

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

**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.

Definition at line 250 of file zlaqr5.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zlaqr5(3) is an alias of zlaqr5.f(3).