
sgeqp3.f(3) LAPACK sgeqp3.f(3)
NAME
sgeqp3.f 
SYNOPSIS
Functions/Subroutines
subroutine sgeqp3 (M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO)
SGEQP3
Function/Subroutine Documentation
subroutine sgeqp3 (integerM, integerN, real, dimension( lda, * )A, integerLDA, integer,
dimension( * )JPVT, real, dimension( * )TAU, real, dimension( * )WORK, integerLWORK,
integerINFO)
SGEQP3
Purpose:
SGEQP3 computes a QR factorization with column pivoting of a
matrix A: A*P = Q*R using Level 3 BLAS.
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 MbyN matrix A.
On exit, the upper triangle of the array contains the
min(M,N)byN upper trapezoidal matrix R; the elements below
the diagonal, together with the array TAU, represent the
orthogonal matrix Q as a product of min(M,N) elementary
reflectors.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
JPVT
JPVT is INTEGER array, dimension (N)
On entry, if JPVT(J).ne.0, the Jth column of A is permuted
to the front of A*P (a leading column); if JPVT(J)=0,
the Jth column of A is a free column.
On exit, if JPVT(J)=K, then the Jth column of A*P was the
the Kth column of A.
TAU
TAU is REAL array, dimension (min(M,N))
The scalar factors of the elementary reflectors.
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. LWORK >= 3*N+1.
For optimal performance LWORK >= 2*N+( N+1 )*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
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:
September 2012
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**T
where tau is a real scalar, and v is a real/complex vector
with v(1:i1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in
A(i+1:m,i), and tau in TAU(i).
Contributors:
G. QuintanaOrti, Depto. de Informatica, Universidad Jaime I, Spain X. Sun, Computer
Science Dept., Duke University, USA
Definition at line 152 of file sgeqp3.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 sgeqp3.f(3) 
