This routine is deprecated and has been replaced by routine SGEQP3.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.

M

          M is INTEGER


          The number of rows of the matrix A. M >= 0.

N

          N is INTEGER


          The number of columns of the matrix A. N >= 0

A

          A is 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

          LDA is INTEGER


          The leading dimension of the array A. LDA >= max(1,M).

JPVT

          JPVT is 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

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


          The scalar factors of the elementary reflectors.

WORK

          WORK is REAL array, dimension (3*N)

INFO

          INFO is INTEGER


          = 0:  successful exit


          < 0:  if INFO = -i, the i-th argument had an illegal value

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

November 2011

  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.