sgeqp3(3)

NAME

SGEQP3 - compute a QR factorization with column pivoting

of a matrix A

SYNOPSIS

SUBROUTINE  SGEQP3(  M, N, A, LDA, JPVT, TAU, WORK, LWORK,
INFO )
    INTEGER        INFO, LDA, LWORK, M, N
    INTEGER        JPVT( * )
    REAL           A( LDA, * ), TAU( * ), WORK( * )

PURPOSE

SGEQP3 computes a QR factorization with column pivoting of

a matrix A: A*P = Q*R using Level 3 BLAS.

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 trape

zoidal 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(J).ne.0, the J-th column of A is

permuted to the front of A*P (a leading column); if JPVT(J)=0,

the J-th column of A is a free column. On exit, if JPVT(J)=K,

then the J-th column of A*P was the the K-th column of A.

TAU (output) REAL array, dimension (min(M,N))

The scalar factors of the elementary reflectors.

WORK (workspace/output) REAL array, dimension (LWORK)

On exit, if INFO=0, WORK(1) returns the optimal

LWORK.

LWORK (input) INTEGER

The dimension of the array WORK. LWORK >= 3*N+1.

For optimal performance LWORK >= 2*N+( N+1 )*NB, where NB is the

optimal blocksize.

If LWORK = -1, then a workspace query is assumed;

the routine only calculates the optimal size of the WORK array,

returns this value as the first entry of the WORK array, and no

error message related to LWORK is issued by XERBLA.

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(k), where k = min(m,n).

Each H(i) has the form

H(i) = I - tau * v * v'

where tau is a real/complex scalar, and v is a real/com

plex 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), and tau in TAU(i).

Based on contributions by

G. Quintana-Orti, Depto. de Informatica, Universidad

Jaime I, Spain
X. Sun, Computer Science Dept., Duke University, USA

LAPACK version 3.0 15 June 2000

SGEQP3(3)