---
name: "sgerqf.f"
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/sgerqf.f"
---

# sgerqf.f(3)

## NAME

SRC/sgerqf.f

## SYNOPSIS

### Functions/Subroutines

subroutine **sgerqf** (m, n, a, lda, tau, work, lwork, info)\
 **SGERQF**

## Function/Subroutine Documentation

### subroutine sgerqf (integer m, integer n, real, dimension( lda, \* ) a, integer lda, real, dimension( \* ) tau, real, dimension( \* ) work, integer lwork, integer info)

**SGERQF**

**Purpose:**

```
!>
!> SGERQF computes an RQ factorization of a real M-by-N matrix A:
!> A = R * Q.
!>
```

**Parameters**

*M*

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

*N*

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

*A*

```
!>          A is REAL array, dimension (LDA,N)
!>          On entry, the M-by-N matrix A.
!>          On exit,
!>          if m <= n, the upper triangle of the subarray
!>          A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R;
!>          if m >= n, the elements on and above the (m-n)-th subdiagonal
!>          contain the M-by-N upper trapezoidal matrix R;
!>          the remaining elements, with the array TAU, represent the
!>          orthogonal matrix Q as a product of min(m,n) elementary
!>          reflectors (see Further Details).
!>
```

*LDA*

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

*TAU*

```
!>          TAU is REAL array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors (see Further
!>          Details).
!>
```

*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 >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise.
!>          For optimum performance LWORK >= M*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.

**Further Details:**

```
!>
!>  The matrix Q is represented as a product of elementary reflectors
!>
!>     Q = H(1) H(2) . . . H(k), where k = min(m,n).
!>
!>  Each H(i) has the form
!>
!>     H(i) = I - tau * v * v**T
!>
!>  where tau is a real scalar, and v is a real vector with
!>  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
!>  A(m-k+i,1:n-k+i-1), and tau in TAU(i).
!>
```

Definition at line **138** of file **sgerqf.f**.

## Author

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