---
name: "sormbr"
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/sormbr.f"
---

# sormbr(3)

Part of [sormbr.f(3)](/sormbr.f/3.md).

## NAME

SRC/sormbr.f

## SYNOPSIS

### Functions/Subroutines

subroutine **sormbr** (vect, side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)\
 **SORMBR**

## Function/Subroutine Documentation

### subroutine sormbr (character vect, character side, character trans, integer m, integer n, integer k, real, dimension( lda, \* ) a, integer lda, real, dimension( \* ) tau, real, dimension( ldc, \* ) c, integer ldc, real, dimension( \* ) work, integer lwork, integer info)

**SORMBR**

**Purpose:**

```
!>
!> If VECT = 'Q', SORMBR overwrites the general real M-by-N matrix C
!> with
!>                 SIDE = 'L'     SIDE = 'R'
!> TRANS = 'N':      Q * C          C * Q
!> TRANS = 'T':      Q**T * C       C * Q**T
!>
!> If VECT = 'P', SORMBR overwrites the general real M-by-N matrix C
!> with
!>                 SIDE = 'L'     SIDE = 'R'
!> TRANS = 'N':      P * C          C * P
!> TRANS = 'T':      P**T * C       C * P**T
!>
!> Here Q and P**T are the orthogonal matrices 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) and G(i)
!> respectively.
!>
!> Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
!> order of the orthogonal matrix Q or P**T that is applied.
!>
!> If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
!> if nq >= k, Q = H(1) H(2) . . . H(k);
!> if nq < k, Q = H(1) H(2) . . . H(nq-1).
!>
!> If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
!> if k < nq, P = G(1) G(2) . . . G(k);
!> if k >= nq, P = G(1) G(2) . . . G(nq-1).
!>
```

**Parameters**

*VECT*

```
!>          VECT is CHARACTER*1
!>          = 'Q': apply Q or Q**T;
!>          = 'P': apply P or P**T.
!>
```

*SIDE*

```
!>          SIDE is CHARACTER*1
!>          = 'L': apply Q, Q**T, P or P**T from the Left;
!>          = 'R': apply Q, Q**T, P or P**T from the Right.
!>
```

*TRANS*

```
!>          TRANS is CHARACTER*1
!>          = 'N':  No transpose, apply Q  or P;
!>          = 'T':  Transpose, apply Q**T or P**T.
!>
```

*M*

```
!>          M is INTEGER
!>          The number of rows of the matrix C. M >= 0.
!>
```

*N*

```
!>          N is INTEGER
!>          The number of columns of the matrix C. N >= 0.
!>
```

*K*

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

*A*

```
!>          A is REAL array, dimension
!>                                (LDA,min(nq,K)) if VECT = 'Q'
!>                                (LDA,nq)        if VECT = 'P'
!>          The vectors which define the elementary reflectors H(i) and
!>          G(i), whose products determine the matrices Q and P, as
!>          returned by SGEBRD.
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the array A.
!>          If VECT = 'Q', LDA >= max(1,nq);
!>          if VECT = 'P', LDA >= max(1,min(nq,K)).
!>
```

*TAU*

```
!>          TAU is REAL array, dimension (min(nq,K))
!>          TAU(i) must contain the scalar factor of the elementary
!>          reflector H(i) or G(i) which determines Q or P, as returned
!>          by SGEBRD in the array argument TAUQ or TAUP.
!>
```

*C*

```
!>          C is REAL array, dimension (LDC,N)
!>          On entry, the M-by-N matrix C.
!>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q
!>          or P*C or P**T*C or C*P or C*P**T.
!>
```

*LDC*

```
!>          LDC is INTEGER
!>          The leading dimension of the array C. LDC >= max(1,M).
!>
```

*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.
!>          If SIDE = 'L', LWORK >= max(1,N);
!>          if SIDE = 'R', LWORK >= max(1,M).
!>          For optimum performance LWORK >= N*NB if SIDE = 'L', and
!>          LWORK >= M*NB if SIDE = 'R', 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 **194** of file **sormbr.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.