# dgeqr2.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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dgeqr2.f

## SYNOPSIS

### Functions/Subroutines

subroutine dgeqr2 (M, N, A, LDA, TAU, WORK, INFO)
DGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.

## Function/Subroutine Documentation

### 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.
```

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

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

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 123 of file dgeqr2.f.

## Author

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