sgelq2.f man page

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 (integerM, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( * )TAU, real, dimension( * )WORK, integerINFO)

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 * 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 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.

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 sgelq2.f.

Author

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Referenced By

sgelq2(3) is an alias of sgelq2.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK