dgerqf.f man page

dgerqf.f —

Synopsis

Functions/Subroutines

subroutine dgerqf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
DGERQF

Function/Subroutine Documentation

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

DGERQF

Purpose:

DGERQF 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 min(m,n) 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 (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The dimension of the array WORK.  LWORK >= max(1,M).
For optimum performance LWORK >= M*NB, where NB is
the optimal blocksize.

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.

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:

November 2011

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 139 of file dgerqf.f.

Author

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Referenced By

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

Sat Nov 16 2013 Version 3.4.2 LAPACK