dgerq2.f (3) Linux Manual Page
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 (integerM, integerN, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( * )TAU, double precision, dimension( * )WORK, integerINFO)
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
N
The number of rows of the matrix A. M >= 0.N is INTEGER
A
The number of columns of the matrix A. N >= 0.A is DOUBLE PRECISION array, dimension (LDA,N)
LDA
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 is INTEGER
TAU
The leading dimension of the array A. LDA >= max(1,M).TAU is DOUBLE PRECISION array, dimension (min(M,N))
WORK
The scalar factors of the elementary reflectors (see Further
Details).WORK is DOUBLE PRECISION array, dimension (M)
INFOINFO 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(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 124 of file dgerq2.f.