SGEQPF (3lapack)

compute a QR factorization with column pivoting of a real M-by-N matrix A

SYNOPSIS

  SUBROUTINE SGEQPF( M, N, A, LDA, JPVT, TAU, WORK, INFO )

      INTEGER        INFO, LDA, M, N

      INTEGER        JPVT( * )

      REAL           A( LDA, * ), TAU( * ), WORK( * )

PURPOSE

  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.