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sgeqrf.f(3) LAPACK sgeqrf.f(3)

NAME

sgeqrf.f

SYNOPSIS

Functions/Subroutines


subroutine sgeqrf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
SGEQRF VARIANT: left-looking Level 3 BLAS version of the algorithm.

Function/Subroutine Documentation

subroutine sgeqrf (integer M, integer N, real, dimension( lda, * ) A, integer LDA, real, dimension( * ) TAU, real, dimension( * ) WORK, integer LWORK, integer INFO)

SGEQRF VARIANT: left-looking Level 3 BLAS version of the algorithm. Purpose:


SGEQRF computes a QR factorization of a real M-by-N matrix A:
A = Q * R.
This is the left-looking Level 3 BLAS version of the algorithm.

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.

A


A is REAL array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix R (R is
upper triangular if m >= n); the elements below the diagonal,
with the array TAU, represent the orthogonal matrix Q as a
product of min(m,n) elementary reflectors (see Further
Details).

LDA


LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).

TAU


TAU is REAL array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).

WORK


WORK is REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK


LWORK is INTEGER


The dimension of the array WORK. The dimension can be divided into three parts.


1) The part for the triangular factor T. If the very last T is not bigger
than any of the rest, then this part is NB x ceiling(K/NB), otherwise,
NB x (K-NT), where K = min(M,N) and NT is the dimension of the very last T


2) The part for the very last T when T is bigger than any of the rest T.
The size of this part is NT x NT, where NT = K - ceiling ((K-NX)/NB) x NB,
where K = min(M,N), NX is calculated by
NX = MAX( 0, ILAENV( 3, 'SGEQRF', ' ', M, N, -1, -1 ) )


3) The part for dlarfb is of size max((N-M)*K, (N-M)*NB, K*NB, NB*NB)


So LWORK = part1 + part2 + part3


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


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:

December 2016

Further Details


The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with
v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).

Definition at line 151 of file VARIANTS/qr/LL/sgeqrf.f.

Author

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