---
name: "gerq2"
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/gerq2"
---

# gerq2(3)

gerq2: RQ factor, level 2

## NAME

gerq2 - gerq2: RQ factor, level 2

## SYNOPSIS

### Functions

subroutine **cgerq2** (m, n, a, lda, tau, work, info)\
 **CGERQ2** computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.  subroutine **dgerq2** (m, n, a, lda, tau, work, info)\
 **DGERQ2** computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.  subroutine **sgerq2** (m, n, a, lda, tau, work, info)\
 **SGERQ2** computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.  subroutine **zgerq2** (m, n, a, lda, tau, work, info)\
 **ZGERQ2** computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

## Detailed Description

## Function Documentation

### subroutine cgerq2 (integer m, integer n, complex, dimension( lda, \* ) a, integer lda, complex, dimension( \* ) tau, complex, dimension( \* ) work, integer info)

**CGERQ2** computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

**Purpose:**

```
!>
!> CGERQ2 computes an RQ factorization of a complex 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 COMPLEX 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 unitary matrix
!>          Q as a product of elementary reflectors (see Further
!>          Details).
!>
```

*LDA*

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

*TAU*

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

*WORK*

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

*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 H(2)**H . . . H(k)**H, where k = min(m,n).
!>
!>  Each H(i) has the form
!>
!>     H(i) = I - tau * v * v**H
!>
!>  where tau is a complex scalar, and v is a complex vector with
!>  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(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 **122** of file **cgerq2.f**.

### subroutine dgerq2 (integer m, integer n, double precision, dimension( lda, \* ) a, integer lda, double precision, dimension( \* ) tau, double precision, dimension( \* ) work, integer info)

**DGERQ2** computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

**Purpose:**

```
!>
!> DGERQ2 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 DOUBLE PRECISION 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 elementary reflectors (see Further
!>          Details).
!>
```

*LDA*

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

*TAU*

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

*WORK*

```
!>          WORK is DOUBLE PRECISION array, dimension (M)
!>
```

*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 **122** of file **dgerq2.f**.

### subroutine sgerq2 (integer m, integer n, real, dimension( lda, \* ) a, integer lda, real, dimension( \* ) tau, real, dimension( \* ) work, integer info)

**SGERQ2** computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

**Purpose:**

```
!>
!> SGERQ2 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 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 (M)
!>
```

*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 **122** of file **sgerq2.f**.

### subroutine zgerq2 (integer m, integer n, complex\*16, dimension( lda, \* ) a, integer lda, complex\*16, dimension( \* ) tau, complex\*16, dimension( \* ) work, integer info)

**ZGERQ2** computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

**Purpose:**

```
!>
!> ZGERQ2 computes an RQ factorization of a complex 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 COMPLEX*16 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 unitary matrix
!>          Q as a product of elementary reflectors (see Further
!>          Details).
!>
```

*LDA*

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

*TAU*

```
!>          TAU is COMPLEX*16 array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors (see Further
!>          Details).
!>
```

*WORK*

```
!>          WORK is COMPLEX*16 array, dimension (M)
!>
```

*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 H(2)**H . . . H(k)**H, where k = min(m,n).
!>
!>  Each H(i) has the form
!>
!>     H(i) = I - tau * v * v**H
!>
!>  where tau is a complex scalar, and v is a complex vector with
!>  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(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 **122** of file **zgerq2.f**.

## Author

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