---
name: "cgerqs.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/cgerqs.f"
---

# cgerqs.f(3)

## NAME

TESTING/LIN/cgerqs.f

## SYNOPSIS

### Functions/Subroutines

subroutine **cgerqs** (m, n, nrhs, a, lda, tau, b, ldb, work, lwork, info)\
 **CGERQS**

## Function/Subroutine Documentation

### subroutine cgerqs (integer m, integer n, integer nrhs, complex, dimension( lda, \* ) a, integer lda, complex, dimension( \* ) tau, complex, dimension( ldb, \* ) b, integer ldb, complex, dimension( lwork ) work, integer lwork, integer info)

**CGERQS**

**Purpose:**

```
!>
!> Compute a minimum-norm solution
!>     min || A*X - B ||
!> using the RQ factorization
!>     A = R*Q
!> computed by CGERQF.
!>
```

**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 >= M >= 0.
!>
```

*NRHS*

```
!>          NRHS is INTEGER
!>          The number of columns of B.  NRHS >= 0.
!>
```

*A*

```
!>          A is COMPLEX array, dimension (LDA,N)
!>          Details of the RQ factorization of the original matrix A as
!>          returned by CGERQF.
!>
```

*LDA*

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

*TAU*

```
!>          TAU is COMPLEX array, dimension (M)
!>          Details of the orthogonal matrix Q.
!>
```

*B*

```
!>          B is COMPLEX array, dimension (LDB,NRHS)
!>          On entry, the right hand side vectors for the linear system.
!>          On exit, the solution vectors X.  Each solution vector
!>          is contained in rows 1:N of a column of B.
!>
```

*LDB*

```
!>          LDB is INTEGER
!>          The leading dimension of the array B. LDB >= max(1,N).
!>
```

*WORK*

```
!>          WORK is COMPLEX array, dimension (LWORK)
!>
```

*LWORK*

```
!>          LWORK is INTEGER
!>          The length of the array WORK.  LWORK must be at least NRHS,
!>          and should be at least NRHS*NB, where NB is the block size
!>          for this environment.
!>
```

*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 **120** of file **cgerqs.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.