# geqr2 - Man Page

geqr2: QR factor, level 2

## Synopsis

### Functions

subroutine cgeqr2 (m, n, a, lda, tau, work, info)
CGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.
subroutine dgeqr2 (m, n, a, lda, tau, work, info)
DGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.
subroutine sgeqr2 (m, n, a, lda, tau, work, info)
SGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.
subroutine zgeqr2 (m, n, a, lda, tau, work, info)
ZGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.

## Function Documentation

### subroutine cgeqr2 (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)

CGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

``` CGEQR2 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;
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 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

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).```

Definition at line 129 of file cgeqr2.f.

### subroutine dgeqr2 (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)

DGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

``` DGEQR2 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;
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 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

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).```

Definition at line 129 of file dgeqr2.f.

### subroutine sgeqr2 (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info)

SGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

``` SGEQR2 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;
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 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

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).```

Definition at line 129 of file sgeqr2.f.

### subroutine zgeqr2 (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info)

ZGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

``` ZGEQR2 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;
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 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

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).```

Definition at line 129 of file zgeqr2.f.

## Author

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## Info

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK