Provided by: liblapack-doc_3.3.1-1_all #### NAME

```       LAPACK-3 - routine i deprecated and has been replaced by routine SGEQP3

```

#### SYNOPSIS

```       SUBROUTINE SGEQPF( M, N, A, LDA, JPVT, TAU, WORK, INFO )

INTEGER        INFO, LDA, M, N

INTEGER        JPVT( * )

REAL           A( LDA, * ), TAU( * ), WORK( * )

```

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```       This routine is deprecated and has been replaced by routine SGEQP3.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

```

#### ARGUMENTS

```        M       (input) INTEGER
The number of rows of the matrix A. M >= 0.

N       (input) INTEGER
The number of columns of the matrix A. N >= 0

A       (input/output) 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     (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).

JPVT    (input/output) 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     (output) REAL array, dimension (min(M,N))
The scalar factors of the elementary reflectors.

WORK    (workspace) REAL array, dimension (3*N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

```

#### FURTHERDETAILS

```        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.

LAPACK deprecated computational routine (veApril 20111)                          SGEQPF(3lapack)
```