NAME¶

SGEQPF - routine i deprecated and has been replaced by routine SGEQP3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This routine is deprecated and has been replaced by routine SGEQP3. SGEQPF 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) 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 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) 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 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.