
sgeqrt.f(3) LAPACK sgeqrt.f(3)
NAME
sgeqrt.f 
SYNOPSIS
Functions/Subroutines
subroutine sgeqrt (M, N, NB, A, LDA, T, LDT, WORK, INFO)
SGEQRT
Function/Subroutine Documentation
subroutine sgeqrt (integerM, integerN, integerNB, real, dimension( lda, * )A, integerLDA,
real, dimension( ldt, * )T, integerLDT, real, dimension( * )WORK, integerINFO)
SGEQRT
Purpose:
SGEQRT computes a blocked QR factorization of a real MbyN matrix A
using the compact WY representation of 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.
NB
NB is INTEGER
The block size to be used in the blocked QR. MIN(M,N) >= NB >= 1.
A
A is REAL array, dimension (LDA,N)
On entry, the MbyN matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)byN upper trapezoidal matrix R (R is
upper triangular if M >= N); the elements below the diagonal
are the columns of V.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
T
T is REAL 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 >= NB.
WORK
WORK is REAL array, dimension (NB*N)
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = i, the ith 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 V stores the elementary reflectors H(i) in the ith column
below the diagonal. For example, if M=5 and N=3, the matrix V is
V = ( 1 )
( v1 1 )
( v1 v2 1 )
( v1 v2 v3 )
( v1 v2 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/NB), where each
block is of order NB except for the last block, which is of order
IB = K  (B1)*NB. For each of the B blocks, a upper triangular block
reflector factor is computed: T1, T2, ..., TB. The NBbyNB (and IBbyIB
for the last block) T's are stored in the NBbyN matrix T as
T = (T1 T2 ... TB).
Definition at line 142 of file sgeqrt.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 sgeqrt.f(3) 
