# ungbr - Man Page

{un,or}gbr: generate Q, P from gebrd

## Synopsis

### Functions

subroutine cungbr (vect, m, n, k, a, lda, tau, work, lwork, info)
CUNGBR
subroutine dorgbr (vect, m, n, k, a, lda, tau, work, lwork, info)
DORGBR
subroutine sorgbr (vect, m, n, k, a, lda, tau, work, lwork, info)
SORGBR
subroutine zungbr (vect, m, n, k, a, lda, tau, work, lwork, info)
ZUNGBR

## Function Documentation

### subroutine cungbr (character vect, integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer lwork, integer info)

CUNGBR

Purpose:

``` CUNGBR generates one of the complex unitary matrices Q or P**H
determined by CGEBRD when reducing a complex matrix A to bidiagonal
form: A = Q * B * P**H.  Q and P**H are defined as products of
elementary reflectors H(i) or G(i) respectively.

If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
is of order M:
if m >= k, Q = H(1) H(2) . . . H(k) and CUNGBR returns the first n
columns of Q, where m >= n >= k;
if m < k, Q = H(1) H(2) . . . H(m-1) and CUNGBR returns Q as an
M-by-M matrix.

If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**H
is of order N:
if k < n, P**H = G(k) . . . G(2) G(1) and CUNGBR returns the first m
rows of P**H, where n >= m >= k;
if k >= n, P**H = G(n-1) . . . G(2) G(1) and CUNGBR returns P**H as
an N-by-N matrix.```
Parameters

VECT

```          VECT is CHARACTER*1
Specifies whether the matrix Q or the matrix P**H is
required, as defined in the transformation applied by CGEBRD:
= 'Q':  generate Q;
= 'P':  generate P**H.```

M

```          M is INTEGER
The number of rows of the matrix Q or P**H to be returned.
M >= 0.```

N

```          N is INTEGER
The number of columns of the matrix Q or P**H to be returned.
N >= 0.
If VECT = 'Q', M >= N >= min(M,K);
if VECT = 'P', N >= M >= min(N,K).```

K

```          K is INTEGER
If VECT = 'Q', the number of columns in the original M-by-K
matrix reduced by CGEBRD.
If VECT = 'P', the number of rows in the original K-by-N
matrix reduced by CGEBRD.
K >= 0.```

A

```          A is COMPLEX array, dimension (LDA,N)
On entry, the vectors which define the elementary reflectors,
as returned by CGEBRD.
On exit, the M-by-N matrix Q or P**H.```

LDA

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

TAU

```          TAU is COMPLEX array, dimension
(min(M,K)) if VECT = 'Q'
(min(N,K)) if VECT = 'P'
TAU(i) must contain the scalar factor of the elementary
reflector H(i) or G(i), which determines Q or P**H, as
returned by CGEBRD in its array argument TAUQ or TAUP.```

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 >= max(1,min(M,N)).
For optimum performance LWORK >= min(M,N)*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 156 of file cungbr.f.

### subroutine dorgbr (character vect, integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer lwork, integer info)

DORGBR

Purpose:

``` DORGBR generates one of the real orthogonal matrices Q or P**T
determined by DGEBRD when reducing a real matrix A to bidiagonal
form: A = Q * B * P**T.  Q and P**T are defined as products of
elementary reflectors H(i) or G(i) respectively.

If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
is of order M:
if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the first n
columns of Q, where m >= n >= k;
if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an
M-by-M matrix.

If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T
is of order N:
if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m
rows of P**T, where n >= m >= k;
if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as
an N-by-N matrix.```
Parameters

VECT

```          VECT is CHARACTER*1
Specifies whether the matrix Q or the matrix P**T is
required, as defined in the transformation applied by DGEBRD:
= 'Q':  generate Q;
= 'P':  generate P**T.```

M

```          M is INTEGER
The number of rows of the matrix Q or P**T to be returned.
M >= 0.```

N

```          N is INTEGER
The number of columns of the matrix Q or P**T to be returned.
N >= 0.
If VECT = 'Q', M >= N >= min(M,K);
if VECT = 'P', N >= M >= min(N,K).```

K

```          K is INTEGER
If VECT = 'Q', the number of columns in the original M-by-K
matrix reduced by DGEBRD.
If VECT = 'P', the number of rows in the original K-by-N
matrix reduced by DGEBRD.
K >= 0.```

A

```          A is DOUBLE PRECISION array, dimension (LDA,N)
On entry, the vectors which define the elementary reflectors,
as returned by DGEBRD.
On exit, the M-by-N matrix Q or P**T.```

LDA

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

TAU

```          TAU is DOUBLE PRECISION array, dimension
(min(M,K)) if VECT = 'Q'
(min(N,K)) if VECT = 'P'
TAU(i) must contain the scalar factor of the elementary
reflector H(i) or G(i), which determines Q or P**T, as
returned by DGEBRD in its array argument TAUQ or TAUP.```

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,min(M,N)).
For optimum performance LWORK >= min(M,N)*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 156 of file dorgbr.f.

### subroutine sorgbr (character vect, integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer lwork, integer info)

SORGBR

Purpose:

``` SORGBR generates one of the real orthogonal matrices Q or P**T
determined by SGEBRD when reducing a real matrix A to bidiagonal
form: A = Q * B * P**T.  Q and P**T are defined as products of
elementary reflectors H(i) or G(i) respectively.

If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
is of order M:
if m >= k, Q = H(1) H(2) . . . H(k) and SORGBR returns the first n
columns of Q, where m >= n >= k;
if m < k, Q = H(1) H(2) . . . H(m-1) and SORGBR returns Q as an
M-by-M matrix.

If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T
is of order N:
if k < n, P**T = G(k) . . . G(2) G(1) and SORGBR returns the first m
rows of P**T, where n >= m >= k;
if k >= n, P**T = G(n-1) . . . G(2) G(1) and SORGBR returns P**T as
an N-by-N matrix.```
Parameters

VECT

```          VECT is CHARACTER*1
Specifies whether the matrix Q or the matrix P**T is
required, as defined in the transformation applied by SGEBRD:
= 'Q':  generate Q;
= 'P':  generate P**T.```

M

```          M is INTEGER
The number of rows of the matrix Q or P**T to be returned.
M >= 0.```

N

```          N is INTEGER
The number of columns of the matrix Q or P**T to be returned.
N >= 0.
If VECT = 'Q', M >= N >= min(M,K);
if VECT = 'P', N >= M >= min(N,K).```

K

```          K is INTEGER
If VECT = 'Q', the number of columns in the original M-by-K
matrix reduced by SGEBRD.
If VECT = 'P', the number of rows in the original K-by-N
matrix reduced by SGEBRD.
K >= 0.```

A

```          A is REAL array, dimension (LDA,N)
On entry, the vectors which define the elementary reflectors,
as returned by SGEBRD.
On exit, the M-by-N matrix Q or P**T.```

LDA

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

TAU

```          TAU is REAL array, dimension
(min(M,K)) if VECT = 'Q'
(min(N,K)) if VECT = 'P'
TAU(i) must contain the scalar factor of the elementary
reflector H(i) or G(i), which determines Q or P**T, as
returned by SGEBRD in its array argument TAUQ or TAUP.```

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,min(M,N)).
For optimum performance LWORK >= min(M,N)*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 156 of file sorgbr.f.

### subroutine zungbr (character vect, integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer lwork, integer info)

ZUNGBR

Purpose:

``` ZUNGBR generates one of the complex unitary matrices Q or P**H
determined by ZGEBRD when reducing a complex matrix A to bidiagonal
form: A = Q * B * P**H.  Q and P**H are defined as products of
elementary reflectors H(i) or G(i) respectively.

If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
is of order M:
if m >= k, Q = H(1) H(2) . . . H(k) and ZUNGBR returns the first n
columns of Q, where m >= n >= k;
if m < k, Q = H(1) H(2) . . . H(m-1) and ZUNGBR returns Q as an
M-by-M matrix.

If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**H
is of order N:
if k < n, P**H = G(k) . . . G(2) G(1) and ZUNGBR returns the first m
rows of P**H, where n >= m >= k;
if k >= n, P**H = G(n-1) . . . G(2) G(1) and ZUNGBR returns P**H as
an N-by-N matrix.```
Parameters

VECT

```          VECT is CHARACTER*1
Specifies whether the matrix Q or the matrix P**H is
required, as defined in the transformation applied by ZGEBRD:
= 'Q':  generate Q;
= 'P':  generate P**H.```

M

```          M is INTEGER
The number of rows of the matrix Q or P**H to be returned.
M >= 0.```

N

```          N is INTEGER
The number of columns of the matrix Q or P**H to be returned.
N >= 0.
If VECT = 'Q', M >= N >= min(M,K);
if VECT = 'P', N >= M >= min(N,K).```

K

```          K is INTEGER
If VECT = 'Q', the number of columns in the original M-by-K
matrix reduced by ZGEBRD.
If VECT = 'P', the number of rows in the original K-by-N
matrix reduced by ZGEBRD.
K >= 0.```

A

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

LDA

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

TAU

```          TAU is COMPLEX*16 array, dimension
(min(M,K)) if VECT = 'Q'
(min(N,K)) if VECT = 'P'
TAU(i) must contain the scalar factor of the elementary
reflector H(i) or G(i), which determines Q or P**H, as
returned by ZGEBRD in its array argument TAUQ or TAUP.```

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 >= max(1,min(M,N)).
For optimum performance LWORK >= min(M,N)*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