# unghr - Man Page

{un,or}ghr: generate Q from gehrd

## Synopsis

### Functions

subroutine cunghr (n, ilo, ihi, a, lda, tau, work, lwork, info)
CUNGHR
subroutine dorghr (n, ilo, ihi, a, lda, tau, work, lwork, info)
DORGHR
subroutine sorghr (n, ilo, ihi, a, lda, tau, work, lwork, info)
SORGHR
subroutine zunghr (n, ilo, ihi, a, lda, tau, work, lwork, info)
ZUNGHR

## Function Documentation

### subroutine cunghr (integer n, integer ilo, integer ihi, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer lwork, integer info)

CUNGHR

Purpose:

``` CUNGHR generates a complex unitary matrix Q which is defined as the
product of IHI-ILO elementary reflectors of order N, as returned by
CGEHRD:

Q = H(ilo) H(ilo+1) . . . H(ihi-1).```
Parameters

N

```          N is INTEGER
The order of the matrix Q. N >= 0.```

ILO

`          ILO is INTEGER`

IHI

```          IHI is INTEGER

ILO and IHI must have the same values as in the previous call
of CGEHRD. Q is equal to the unit matrix except in the
submatrix Q(ilo+1:ihi,ilo+1:ihi).
1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.```

A

```          A is COMPLEX array, dimension (LDA,N)
On entry, the vectors which define the elementary reflectors,
as returned by CGEHRD.
On exit, the N-by-N unitary matrix Q.```

LDA

```          LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).```

TAU

```          TAU is COMPLEX array, dimension (N-1)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by CGEHRD.```

WORK

```          WORK is COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.```

LWORK

```          LWORK is INTEGER
The dimension of the array WORK. LWORK >= IHI-ILO.
For optimum performance LWORK >= (IHI-ILO)*NB, where NB is
the optimal blocksize.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.```

INFO

```          INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 125 of file cunghr.f.

### subroutine dorghr (integer n, integer ilo, integer ihi, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer lwork, integer info)

DORGHR

Purpose:

``` DORGHR generates a real orthogonal matrix Q which is defined as the
product of IHI-ILO elementary reflectors of order N, as returned by
DGEHRD:

Q = H(ilo) H(ilo+1) . . . H(ihi-1).```
Parameters

N

```          N is INTEGER
The order of the matrix Q. N >= 0.```

ILO

`          ILO is INTEGER`

IHI

```          IHI is INTEGER

ILO and IHI must have the same values as in the previous call
of DGEHRD. Q is equal to the unit matrix except in the
submatrix Q(ilo+1:ihi,ilo+1:ihi).
1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.```

A

```          A is DOUBLE PRECISION array, dimension (LDA,N)
On entry, the vectors which define the elementary reflectors,
as returned by DGEHRD.
On exit, the N-by-N orthogonal matrix Q.```

LDA

```          LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).```

TAU

```          TAU is DOUBLE PRECISION array, dimension (N-1)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEHRD.```

WORK

```          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.```

LWORK

```          LWORK is INTEGER
The dimension of the array WORK. LWORK >= IHI-ILO.
For optimum performance LWORK >= (IHI-ILO)*NB, where NB is
the optimal blocksize.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.```

INFO

```          INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 125 of file dorghr.f.

### subroutine sorghr (integer n, integer ilo, integer ihi, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer lwork, integer info)

SORGHR

Purpose:

``` SORGHR generates a real orthogonal matrix Q which is defined as the
product of IHI-ILO elementary reflectors of order N, as returned by
SGEHRD:

Q = H(ilo) H(ilo+1) . . . H(ihi-1).```
Parameters

N

```          N is INTEGER
The order of the matrix Q. N >= 0.```

ILO

`          ILO is INTEGER`

IHI

```          IHI is INTEGER

ILO and IHI must have the same values as in the previous call
of SGEHRD. Q is equal to the unit matrix except in the
submatrix Q(ilo+1:ihi,ilo+1:ihi).
1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.```

A

```          A is REAL array, dimension (LDA,N)
On entry, the vectors which define the elementary reflectors,
as returned by SGEHRD.
On exit, the N-by-N orthogonal matrix Q.```

LDA

```          LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).```

TAU

```          TAU is REAL array, dimension (N-1)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by SGEHRD.```

WORK

```          WORK is REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.```

LWORK

```          LWORK is INTEGER
The dimension of the array WORK. LWORK >= IHI-ILO.
For optimum performance LWORK >= (IHI-ILO)*NB, where NB is
the optimal blocksize.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.```

INFO

```          INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 125 of file sorghr.f.

### subroutine zunghr (integer n, integer ilo, integer ihi, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer lwork, integer info)

ZUNGHR

Purpose:

``` ZUNGHR generates a complex unitary matrix Q which is defined as the
product of IHI-ILO elementary reflectors of order N, as returned by
ZGEHRD:

Q = H(ilo) H(ilo+1) . . . H(ihi-1).```
Parameters

N

```          N is INTEGER
The order of the matrix Q. N >= 0.```

ILO

`          ILO is INTEGER`

IHI

```          IHI is INTEGER

ILO and IHI must have the same values as in the previous call
of ZGEHRD. Q is equal to the unit matrix except in the
submatrix Q(ilo+1:ihi,ilo+1:ihi).
1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.```

A

```          A is COMPLEX*16 array, dimension (LDA,N)
On entry, the vectors which define the elementary reflectors,
as returned by ZGEHRD.
On exit, the N-by-N unitary matrix Q.```

LDA

```          LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).```

TAU

```          TAU is COMPLEX*16 array, dimension (N-1)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZGEHRD.```

WORK

```          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.```

LWORK

```          LWORK is INTEGER
The dimension of the array WORK. LWORK >= IHI-ILO.
For optimum performance LWORK >= (IHI-ILO)*NB, where NB is
the optimal blocksize.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.```

INFO

```          INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value```
Author

Univ. of Tennessee

Univ. of California Berkeley