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# dgeqpf

```
NAME
DGEQPF - compute a QR factorization with column pivoting of
a real M-by-N matrix A

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
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) elemen-
tary 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.
```