dgeqlf.f (3) Linux Manual Page
dgeqlf.f –
Synopsis
Functions/Subroutines
subroutine dgeqlf (M, N, A, LDA, TAU, WORK, LWORK, INFO)DGEQLF
Function/Subroutine Documentation
subroutine dgeqlf (integerM, integerN, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( * )TAU, double precision, dimension( * )WORK, integerLWORK, integerINFO)
DGEQLF Purpose:
DGEQLF computes a QL factorization of a real M-by-N matrix A:
A = Q * L.
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 lower triangle of the subarray
A(m-n+1:m,1:n) contains the N-by-N lower triangular matrix L;
if m <= n, the elements on and below the (n-m)-th
superdiagonal contain the M-by-N lower trapezoidal matrix L;
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 (MAX(1,LWORK))
LWORK
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.LWORK is INTEGER
INFO
The dimension of the array WORK. LWORK >= max(1,N).
For optimum performance LWORK >= N*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 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(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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
A(1:m-k+i-1,n-k+i), and tau in TAU(i).
Definition at line 139 of file dgeqlf.f.