subroutine zgelqt (M, N, MB, A, LDA, T, LDT, WORK, INFO)
ZGELQT
ZGELQT
Purpose:
ZGELQT computes a blocked LQ factorization of a complex M-by-N matrix A using the compact WY representation of Q.
Parameters:
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.
MB
MB is INTEGER
The block size to be used in the blocked QR. MIN(M,N) >= MB >= 1.
A
A is COMPLEX*16 array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and below the diagonal of the array
contain the M-by-MIN(M,N) lower trapezoidal matrix L (L is
lower triangular if M <= N); the elements above the diagonal
are the rows of V.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
T
T is COMPLEX*16 array, dimension (LDT,MIN(M,N))
The upper triangular block reflectors stored in compact form
as a sequence of upper triangular blocks. See below
for further details.
LDT
LDT is INTEGER
The leading dimension of the array T. LDT >= MB.
WORK
WORK is COMPLEX*16 array, dimension (MB*N)
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Author:
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
Further Details:
The matrix V stores the elementary reflectors H(i) in the i-th row
above the diagonal. For example, if M=5 and N=3, the matrix V is
V = ( 1 v1 v1 v1 v1 )
( 1 v2 v2 v2 )
( 1 v3 v3 )
where the vi's represent the vectors which define H(i), which are returned
in the matrix A. The 1's along the diagonal of V are not stored in A.
Let K=MIN(M,N). The number of blocks is B = ceiling(K/MB), where each
block is of order MB except for the last block, which is of order
IB = K - (B-1)*MB. For each of the B blocks, a upper triangular block
reflector factor is computed: T1, T2, ..., TB. The MB-by-MB (and IB-by-IB
for the last block) T's are stored in the MB-by-K matrix T as
T = (T1 T2 ... TB).
Definition at line 141 of file zgelqt.f.
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