NAME

dgelq2.f -

SYNOPSIS


Functions/Subroutines


subroutine dgelq2 (M, N, A, LDA, TAU, WORK, INFO)
DGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

Function/Subroutine Documentation

subroutine dgelq2 (integerM, integerN, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( * )TAU, double precision, dimension( * )WORK, integerINFO)

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

Purpose:

 DGELQ2 computes an LQ factorization of a real m by n matrix A:
 A = L * Q.


 

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 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).


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 (M)


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.

Date:

September 2012

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).


 

Definition at line 122 of file dgelq2.f.

Author

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