# ungtr - Man Page

{un,or}gtr: generate Q from hetrd

## Synopsis

### Functions

subroutine cungtr (uplo, n, a, lda, tau, work, lwork, info)
CUNGTR
subroutine dorgtr (uplo, n, a, lda, tau, work, lwork, info)
DORGTR
subroutine sorgtr (uplo, n, a, lda, tau, work, lwork, info)
SORGTR
subroutine zungtr (uplo, n, a, lda, tau, work, lwork, info)
ZUNGTR

## Function Documentation

### subroutine cungtr (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer lwork, integer info)

CUNGTR

Purpose:

``` CUNGTR generates a complex unitary matrix Q which is defined as the
product of n-1 elementary reflectors of order N, as returned by
CHETRD:

if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),

if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).```
Parameters

UPLO

```          UPLO is CHARACTER*1
= 'U': Upper triangle of A contains elementary reflectors
from CHETRD;
= 'L': Lower triangle of A contains elementary reflectors
from CHETRD.```

N

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

A

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

LDA

```          LDA is INTEGER
The leading dimension of the array A. LDA >= 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 CHETRD.```

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 >= N-1.
For optimum performance LWORK >= (N-1)*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 122 of file cungtr.f.

### subroutine dorgtr (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer lwork, integer info)

DORGTR

Purpose:

``` DORGTR generates a real orthogonal matrix Q which is defined as the
product of n-1 elementary reflectors of order N, as returned by
DSYTRD:

if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),

if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).```
Parameters

UPLO

```          UPLO is CHARACTER*1
= 'U': Upper triangle of A contains elementary reflectors
from DSYTRD;
= 'L': Lower triangle of A contains elementary reflectors
from DSYTRD.```

N

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

A

```          A is DOUBLE PRECISION array, dimension (LDA,N)
On entry, the vectors which define the elementary reflectors,
as returned by DSYTRD.
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 DSYTRD.```

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 >= max(1,N-1).
For optimum performance LWORK >= (N-1)*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 122 of file dorgtr.f.

### subroutine sorgtr (character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer lwork, integer info)

SORGTR

Purpose:

``` SORGTR generates a real orthogonal matrix Q which is defined as the
product of n-1 elementary reflectors of order N, as returned by
SSYTRD:

if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),

if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).```
Parameters

UPLO

```          UPLO is CHARACTER*1
= 'U': Upper triangle of A contains elementary reflectors
from SSYTRD;
= 'L': Lower triangle of A contains elementary reflectors
from SSYTRD.```

N

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

A

```          A is REAL array, dimension (LDA,N)
On entry, the vectors which define the elementary reflectors,
as returned by SSYTRD.
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 SSYTRD.```

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 >= max(1,N-1).
For optimum performance LWORK >= (N-1)*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 122 of file sorgtr.f.

### subroutine zungtr (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer lwork, integer info)

ZUNGTR

Purpose:

``` ZUNGTR generates a complex unitary matrix Q which is defined as the
product of n-1 elementary reflectors of order N, as returned by
ZHETRD:

if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),

if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).```
Parameters

UPLO

```          UPLO is CHARACTER*1
= 'U': Upper triangle of A contains elementary reflectors
from ZHETRD;
= 'L': Lower triangle of A contains elementary reflectors
from ZHETRD.```

N

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

A

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

LDA

```          LDA is INTEGER
The leading dimension of the array A. LDA >= 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 ZHETRD.```

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 >= N-1.
For optimum performance LWORK >= (N-1)*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