LAPACK 3.11.0
LAPACK: Linear Algebra PACKage

◆ dgelq2()

subroutine dgelq2 ( integer  M,
integer  N,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( * )  TAU,
double precision, dimension( * )  WORK,
integer  INFO 
)

DGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

Download DGELQ2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 DGELQ2 computes an LQ factorization of a real m-by-n matrix A:

    A = ( L 0 ) *  Q

 where:

    Q is a n-by-n orthogonal matrix;
    L is a lower-triangular m-by-m matrix;
    0 is a m-by-(n-m) zero matrix, if m < n.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix A.  N >= 0.
[in,out]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the m by n matrix A.
          On exit, the elements on and below the diagonal of the array
          contain the m by min(m,n) lower trapezoidal matrix L (L is
          lower triangular if m <= n); the elements above the diagonal,
          with the array TAU, represent the orthogonal matrix Q as a
          product of elementary reflectors (see Further Details).
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).
[out]TAU
          TAU is DOUBLE PRECISION array, dimension (min(M,N))
          The scalar factors of the elementary reflectors (see Further
          Details).
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (M)
[out]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(k) . . . H(2) H(1), 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:n) is stored on exit in A(i,i+1:n),
  and tau in TAU(i).