---
name: "ungbr"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/ungbr"
---

# ungbr(3)

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

## NAME

ungbr - {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**

## Detailed Description

## 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

Univ. of Colorado Denver

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

Univ. of Colorado Denver

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

Univ. of Colorado Denver

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

Univ. of Colorado Denver

NAG Ltd.

Definition at line **156** of file **zungbr.f**.

## Author

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