sgeqpf(3)

NAME

SGEQPF - routine is deprecated and has been replaced by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This routine is deprecated and has been replaced by rou

tine SGEQP3. SGEQPF computes a QR factorization with column piv

oting 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 ar

ray 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 ille

gal value

FURTHER DETAILS

The matrix Q is represented as a product of elementary re

flectors

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.

LAPACK test version 3.0 15 June 2000

SGEQPF(3)