# sgeqr2.f - Man Page

SRC/sgeqr2.f

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

### 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.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sgeqr2(3) is an alias of sgeqr2.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK