# dgerq2.f man page

dgerq2.f —

## Synopsis

### Functions/Subroutines

subroutinedgerq2(M, N, A, LDA, TAU, WORK, INFO)DGERQ2computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

## Function/Subroutine Documentation

### subroutine dgerq2 (integerM, integerN, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( * )TAU, double precision, dimension( * )WORK, integerINFO)

**DGERQ2** computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

**Purpose:**

```
DGERQ2 computes an RQ factorization of a real m by n matrix A:
A = R * Q.
```

**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, if m <= n, the upper triangle of the subarray
A(1:m,n-m+1:n) contains the m by m upper triangular matrix R;
if m >= n, the elements on and above the (m-n)-th subdiagonal
contain the m by n upper trapezoidal matrix R; the remaining
elements, 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.

**Date:**

September 2012

**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(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
A(m-k+i,1:n-k+i-1), and tau in TAU(i).
```

Definition at line 124 of file dgerq2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

dgerq2(3) is an alias of dgerq2.f(3).