---
name: "geqr2p"
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/geqr2p"
---

# geqr2p(3)

geqr2p: QR factor, diag( R ) ≥ 0, level 2

## NAME

geqr2p - geqr2p: QR factor, diag( R ) ≥ 0, level 2

## SYNOPSIS

### Functions

subroutine **cgeqr2p** (m, n, a, lda, tau, work, info)\
 **CGEQR2P** computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.  subroutine **dgeqr2p** (m, n, a, lda, tau, work, info)\
 **DGEQR2P** computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.  subroutine **sgeqr2p** (m, n, a, lda, tau, work, info)\
 **SGEQR2P** computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.  subroutine **zgeqr2p** (m, n, a, lda, tau, work, info)\
 **ZGEQR2P** computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.

## Detailed Description

## Function Documentation

### subroutine cgeqr2p (integer m, integer n, complex, dimension( lda, \* ) a, integer lda, complex, dimension( \* ) tau, complex, dimension( \* ) work, integer info)

**CGEQR2P** computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.

**Purpose:**

```
!>
!> CGEQR2P computes a QR factorization of a complex m-by-n matrix A:
!>
!>    A = Q * ( R ),
!>            ( 0 )
!>
!> where:
!>
!>    Q is a m-by-m orthogonal matrix;
!>    R is an upper-triangular n-by-n matrix with nonnegative diagonal
!>    entries;
!>    0 is a (m-n)-by-n 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 above the diagonal of the array
!>          contain the min(m,n) by n upper trapezoidal matrix R (R is
!>          upper triangular if m >= n). The diagonal entries of R are
!>          real and nonnegative; the elements below 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 (N)
!>
```

*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**H
!>
!>  where tau is a complex scalar, and v is a complex vector with
!>  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
!>  and tau in TAU(i).
!>
!> See Lapack Working Note 203 for details
!>
```

Definition at line **133** of file **cgeqr2p.f**.

### subroutine dgeqr2p (integer m, integer n, double precision, dimension( lda, \* ) a, integer lda, double precision, dimension( \* ) tau, double precision, dimension( \* ) work, integer info)

**DGEQR2P** computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.

**Purpose:**

```
!>
!> DGEQR2P computes a QR factorization of a real m-by-n matrix A:
!>
!>    A = Q * ( R ),
!>            ( 0 )
!>
!> where:
!>
!>    Q is a m-by-m orthogonal matrix;
!>    R is an upper-triangular n-by-n matrix with nonnegative diagonal
!>    entries;
!>    0 is a (m-n)-by-n 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 above the diagonal of the array
!>          contain the min(m,n) by n upper trapezoidal matrix R (R is
!>          upper triangular if m >= n). The diagonal entries of R are
!>          nonnegative; the elements below 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 (N)
!>
```

*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(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
!>  and tau in TAU(i).
!>
!> See Lapack Working Note 203 for details
!>
```

Definition at line **133** of file **dgeqr2p.f**.

### subroutine sgeqr2p (integer m, integer n, real, dimension( lda, \* ) a, integer lda, real, dimension( \* ) tau, real, dimension( \* ) work, integer info)

**SGEQR2P** computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.

**Purpose:**

```
!>
!> SGEQR2P computes a QR factorization of a real m-by-n matrix A:
!>
!>    A = Q * ( R ),
!>            ( 0 )
!>
!> where:
!>
!>    Q is a m-by-m orthogonal matrix;
!>    R is an upper-triangular n-by-n matrix with nonnegative diagonal
!>    entries;
!>    0 is a (m-n)-by-n 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 above the diagonal of the array
!>          contain the min(m,n) by n upper trapezoidal matrix R (R is
!>          upper triangular if m >= n). The diagonal entries of R
!>          are nonnegative; the elements below 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 (N)
!>
```

*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(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
!>  and tau in TAU(i).
!>
!> See Lapack Working Note 203 for details
!>
```

Definition at line **133** of file **sgeqr2p.f**.

### subroutine zgeqr2p (integer m, integer n, complex\*16, dimension( lda, \* ) a, integer lda, complex\*16, dimension( \* ) tau, complex\*16, dimension( \* ) work, integer info)

**ZGEQR2P** computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algorithm.

**Purpose:**

```
!>
!> ZGEQR2P computes a QR factorization of a complex m-by-n matrix A:
!>
!>    A = Q * ( R ),
!>            ( 0 )
!>
!> where:
!>
!>    Q is a m-by-m orthogonal matrix;
!>    R is an upper-triangular n-by-n matrix with nonnegative diagonal
!>    entries;
!>    0 is a (m-n)-by-n 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 above the diagonal of the array
!>          contain the min(m,n) by n upper trapezoidal matrix R (R is
!>          upper triangular if m >= n). The diagonal entries of R
!>          are real and nonnegative; the elements below 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 (N)
!>
```

*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**H
!>
!>  where tau is a complex scalar, and v is a complex vector with
!>  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
!>  and tau in TAU(i).
!>
!> See Lapack Working Note 203 for details
!>
```

Definition at line **133** of file **zgeqr2p.f**.

## Author

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