CGERQF (3) Linux Manual Page
cgerqf.f –
Synopsis
Functions/Subroutines
subroutine cgerqf (M, N, A, LDA, TAU, WORK, LWORK, INFO)CGERQF
Function/Subroutine Documentation
subroutine cgerqf (integerM, integerN, complex, dimension( lda, * )A, integerLDA, complex, dimension( * )TAU, complex, dimension( * )WORK, integerLWORK, integerINFO)
CGERQF Purpose:
CGERQF computes an RQ factorization of a complex 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 COMPLEX 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
unitary matrix Q as a product of min(m,n) elementary
reflectors (see Further Details).LDA is INTEGER
TAU
The leading dimension of the array A. LDA >= max(1,M).TAU is COMPLEX array, dimension (min(M,N))
WORK
The scalar factors of the elementary reflectors (see Further
Details).WORK is COMPLEX 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,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 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 H(2)**H . . . H(k)**H, where k = min(m,n).
Each H(i) has the form
H(i) = I – tau * v * v**H
where tau is a complex scalar, and v is a complex vector with
v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(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 cgerqf.f.