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dgerq2.f(3) LAPACK dgerq2.f(3)

NAME

dgerq2.f

SYNOPSIS

Functions/Subroutines


subroutine dgerq2 (M, N, A, LDA, TAU, WORK, INFO)
DGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

Function/Subroutine Documentation

subroutine dgerq2 (integer M, integer N, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) TAU, double precision, dimension( * ) WORK, integer INFO)

DGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:


DGERQ2 computes an RQ factorization of a real m by n matrix A:
A = R * 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, if m <= n, the upper triangle of the subarray
A(1:m,n-m+1:n) contains the m by m upper triangular matrix R;
if m >= n, the elements on and above the (m-n)-th subdiagonal
contain the m by n upper trapezoidal matrix R; the remaining
elements, 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:

December 2016

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(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
A(m-k+i,1:n-k+i-1), and tau in TAU(i).

Definition at line 125 of file dgerq2.f.

Author

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Tue Nov 14 2017 Version 3.8.0