DGEQPF(3) routine i deprecated and has been replaced by routine DGEQP3

## SYNOPSIS

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

INTEGER INFO, LDA, M, N

INTEGER JPVT( * )

DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )

## PURPOSE

This routine is deprecated and has been replaced by routine DGEQP3. DGEQPF 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors.
WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

## 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'
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.

June 2006.
For more details see LAPACK Working Note 176.