# SGEQRF (3) - Linux Manuals

sgeqrf.f -

## SYNOPSIS

### Functions/Subroutines

subroutine sgeqrf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
SGEQRF

## Function/Subroutine Documentation

### subroutine sgeqrf (integerM, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( * )TAU, real, dimension( * )WORK, integerLWORK, integerINFO)

SGEQRF

Purpose:

``` SGEQRF 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 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 min(m,n) 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 (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
```

LWORK

```          LWORK is INTEGER
The dimension of the array WORK.  LWORK >= max(1,N).
For optimum performance LWORK >= N*NB, where NB is
the optimal blocksize.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
```

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:

November 2011

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 137 of file sgeqrf.f.

## Author

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