---
name: "dgeqpf"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/dgeqpf/3lapack"
---

# dgeqpf(3lapack)

routine i deprecated and has been replaced by routine DGEQP3

## NAME

DGEQPF - routine i deprecated and has been replaced by routine DGEQP3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This routine is deprecated and has been replaced by routine DGEQP3.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.\