sgelq2.f - Man Page

SRC/sgelq2.f

Synopsis

Functions/Subroutines

subroutine sgelq2 (m, n, a, lda, tau, work, info)
SGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

Function/Subroutine Documentation

subroutine sgelq2 (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info)

SGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.  

Purpose:

 SGELQ2 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

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 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 REAL array, dimension (min(M,N))
          The scalar factors of the elementary reflectors (see Further
          Details).

WORK

          WORK is REAL 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.

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 128 of file sgelq2.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page sgelq2(3) is an alias of sgelq2.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK