DGEQPF(l) — LAPACK test routine (version 2.0)

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) 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.