sgeqrt3.f(3) LAPACK sgeqrt3.f(3)
recursive subroutine sgeqrt3 (M, N, A, LDA, T, LDT, INFO)
SGEQRT3 recursively computes a QR factorization of a general real or complex matrix
using the compact WY representation of Q.
recursive subroutine sgeqrt3 (integerM, integerN, real, dimension( lda, * )A, integerLDA,
real, dimension( ldt, * )T, integerLDT, integerINFO)
SGEQRT3 recursively computes a QR factorization of a general real or complex matrix using
the compact WY representation of Q.
SGEQRT3 recursively computes a QR factorization of a real M-by-N
matrix A, using the compact WY representation of Q.
Based on the algorithm of Elmroth and Gustavson,
IBM J. Res. Develop. Vol 44 No. 4 July 2000.
M is INTEGER
The number of rows of the matrix A. M >= N.
N is INTEGER
The number of columns of the matrix A. N >= 0.
A is REAL array, dimension (LDA,N)
On entry, the real M-by-N matrix A. On exit, the elements on and
above the diagonal contain the N-by-N upper triangular matrix R; the
elements below the diagonal are the columns of V. See below for
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
T is REAL array, dimension (LDT,N)
The N-by-N upper triangular factor of the block reflector.
The elements on and above the diagonal contain the block
reflector T; the elements below the diagonal are not used.
See below for further details.
LDT is INTEGER
The leading dimension of the array T. LDT >= max(1,N).
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
The matrix V stores the elementary reflectors H(i) in the i-th 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. The
block reflector H is then given by
H = I - V * T * V**T
where V**T is the transpose of V.
For details of the algorithm, see Elmroth and Gustavson (cited above).
Definition at line 133 of file sgeqrt3.f.
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Version 3.4.2 Tue Sep 25 2012 sgeqrt3.f(3)