# sgeqpf.f (3) - Linux Manuals

sgeqpf.f -

## SYNOPSIS

### Functions/Subroutines

subroutine sgeqpf (M, N, A, LDA, JPVT, TAU, WORK, INFO)
SGEQPF

## Function/Subroutine Documentation

### subroutine sgeqpf (integerM, integerN, real, dimension( lda, * )A, integerLDA, integer, dimension( * )JPVT, real, dimension( * )TAU, real, dimension( * )WORK, integerINFO)

SGEQPF

Purpose:

``` This routine is deprecated and has been replaced by routine SGEQP3.

SGEQPF computes a QR factorization with column pivoting of a
real M-by-N matrix A: A*P = 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 upper triangle of the array contains the
min(M,N)-by-N upper triangular matrix R; the elements
below the diagonal, together with the array TAU,
represent the orthogonal matrix Q as a product of
min(m,n) elementary reflectors.
```

LDA

```          LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
```

JPVT

```          JPVT is INTEGER array, dimension (N)
On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted
to the front of A*P (a leading column); if JPVT(i) = 0,
the i-th column of A is a free column.
On exit, if JPVT(i) = k, then the i-th column of A*P
was the k-th column of A.
```

TAU

```          TAU is REAL array, dimension (min(M,N))
The scalar factors of the elementary reflectors.
```

WORK

```          WORK is REAL array, dimension (3*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.

Date:

November 2011

Further Details:

```  The matrix Q is represented as a product of elementary reflectors

Q = H(1) H(2) . . . H(n)

Each H(i) has the form

H = 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).

The matrix P is represented in jpvt as follows: If
jpvt(j) = i
then the jth column of P is the ith canonical unit vector.

Partial column norm updating strategy modified by
Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
University of Zagreb, Croatia.
-- April 2011                                                      --
For more details see LAPACK Working Note 176.
```

Definition at line 143 of file sgeqpf.f.

## Author

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