---
name: "gelq2"
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/gelq2"
---

# gelq2(3)

gelq2: LQ factor, level 2

## NAME

gelq2 - gelq2: LQ factor, level 2

## SYNOPSIS

### Functions

subroutine **cgelq2** (m, n, a, lda, tau, work, info)\
 **CGELQ2** computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.  subroutine **dgelq2** (m, n, a, lda, tau, work, info)\
 **DGELQ2** computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.  subroutine **sgelq2** (m, n, a, lda, tau, work, info)\
 **SGELQ2** computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.  subroutine **zgelq2** (m, n, a, lda, tau, work, info)\
 **ZGELQ2** computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

## Detailed Description

## Function Documentation

### subroutine cgelq2 (integer m, integer n, complex, dimension( lda, \* ) a, integer lda, complex, dimension( \* ) tau, complex, dimension( \* ) work, integer info)

**CGELQ2** computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

**Purpose:**

```
!>
!> CGELQ2 computes an LQ factorization of a complex m-by-n matrix A:
!>
!>    A = ( L 0 ) *  Q
!>
!> where:
!>
!>    Q is a n-by-n orthogonal matrix;
!>    L is a lower-triangular m-by-m matrix;
!>    0 is a m-by-(n-m) zero matrix, if m < n.
!>
!>
```

**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, the elements on and below the diagonal of the array
!>          contain the m by min(m,n) lower trapezoidal matrix L (L is
!>          lower triangular if m <= n); the elements above the diagonal,
!>          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(k)**H . . . H(2)**H H(1)**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(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
!>  A(i,i+1:n), and tau in TAU(i).
!>
```

Definition at line **128** of file **cgelq2.f**.

### subroutine dgelq2 (integer m, integer n, double precision, dimension( lda, \* ) a, integer lda, double precision, dimension( \* ) tau, double precision, dimension( \* ) work, integer info)

**DGELQ2** computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

**Purpose:**

```
!>
!> DGELQ2 computes an LQ factorization of a real m-by-n matrix A:
!>
!>    A = ( L 0 ) *  Q
!>
!> where:
!>
!>    Q is a n-by-n orthogonal matrix;
!>    L is a lower-triangular m-by-m matrix;
!>    0 is a m-by-(n-m) zero matrix, if m < n.
!>
!>
```

**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, the elements on and below the diagonal of the array
!>          contain the m by min(m,n) lower trapezoidal matrix L (L is
!>          lower triangular if m <= n); the elements above the diagonal,
!>          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(k) . . . H(2) H(1), 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(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
!>  and tau in TAU(i).
!>
```

Definition at line **128** of file **dgelq2.f**.

### subroutine sgelq2 (integer m, integer n, real, dimension( lda, \* ) a, integer lda, real, dimension( \* ) tau, real, dimension( \* ) work, integer info)

**SGELQ2** computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

**Purpose:**

```
!>
!> SGELQ2 computes an LQ factorization of a real m-by-n matrix A:
!>
!>    A = ( L 0 ) *  Q
!>
!> where:
!>
!>    Q is a n-by-n orthogonal matrix;
!>    L is a lower-triangular m-by-m matrix;
!>    0 is a m-by-(n-m) zero matrix, if m < n.
!>
!>
```

**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, the elements on and below the diagonal of the array
!>          contain the m by min(m,n) lower trapezoidal matrix L (L is
!>          lower triangular if m <= n); the elements above the diagonal,
!>          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(k) . . . H(2) H(1), 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(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
!>  and tau in TAU(i).
!>
```

Definition at line **128** of file **sgelq2.f**.

### subroutine zgelq2 (integer m, integer n, complex\*16, dimension( lda, \* ) a, integer lda, complex\*16, dimension( \* ) tau, complex\*16, dimension( \* ) work, integer info)

**ZGELQ2** computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

**Purpose:**

```
!>
!> ZGELQ2 computes an LQ factorization of a complex m-by-n matrix A:
!>
!>    A = ( L 0 ) *  Q
!>
!> where:
!>
!>    Q is a n-by-n orthogonal matrix;
!>    L is a lower-triangular m-by-m matrix;
!>    0 is a m-by-(n-m) zero matrix, if m < n.
!>
!>
```

**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, the elements on and below the diagonal of the array
!>          contain the m by min(m,n) lower trapezoidal matrix L (L is
!>          lower triangular if m <= n); the elements above the diagonal,
!>          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(k)**H . . . H(2)**H H(1)**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(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
!>  A(i,i+1:n), and tau in TAU(i).
!>
```

Definition at line **128** of file **zgelq2.f**.

## Author

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