dgeqrfp.f - Man Page

subroutine dgeqrfp (m, n, a, lda, tau, work, lwork, info)
DGEQRFP

DGEQRFP  

Purpose:

 DGEQR2P computes a QR factorization of a real M-by-N matrix A:

    A = Q * ( R ),
            ( 0 )

 where:

    Q is a M-by-M orthogonal matrix;
    R is an upper-triangular N-by-N matrix with nonnegative diagonal
    entries;
    0 is a (M-N)-by-N zero matrix, if M > N.

Parameters

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 DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the M-by-N matrix A.
          On exit, the elements on and above the diagonal of the array
          contain the min(M,N)-by-N upper trapezoidal matrix R (R is
          upper triangular if m >= n). The diagonal entries of R
          are nonnegative; the elements below the diagonal,
          with the array TAU, represent the orthogonal matrix Q as a
          product of min(m,n) elementary reflectors (see Further
          Details).

LDA

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

TAU

          TAU is DOUBLE PRECISION array, dimension (min(M,N))
          The scalar factors of the elementary reflectors (see Further
          Details).

WORK

          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.  LWORK >= max(1,N).
          For optimum performance LWORK >= N*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

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

  The matrix Q is represented as a product of elementary reflectors

     Q = H(1) H(2) . . . H(k), where k = min(m,n).

  Each H(i) has the form

     H(i) = 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),
  and tau in TAU(i).

 See Lapack Working Note 203 for details

Definition at line 148 of file dgeqrfp.f.