Provided by: liblapack-doc_3.3.1-1_all

**NAME**

LAPACK-3 - routine i deprecated and has been replaced by routine SGEQP3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This routine is deprecated and has been replaced by routine SGEQP3.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**T 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. -- April 2011 -- For more details see LAPACK Working Note 176. LAPACK deprecated computational routine (veApril 20111) SGEQPF(3lapack)