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zgeqp3.f(3) LAPACK zgeqp3.f(3)

NAME

zgeqp3.f -

SYNOPSIS

Functions/Subroutines


subroutine zgeqp3 (M, N, A, LDA, JPVT, TAU, WORK, LWORK, RWORK, INFO)
ZGEQP3

Function/Subroutine Documentation

subroutine zgeqp3 (integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, integer, dimension( * )JPVT, complex*16, dimension( * )TAU, complex*16, dimension( * )WORK, integerLWORK, double precision, dimension( * )RWORK, integerINFO)

ZGEQP3

Purpose:


ZGEQP3 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 COMPLEX*16 array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the upper triangle of the array contains the
min(M,N)-by-N upper trapezoidal matrix R; the elements below
the diagonal, together with the array TAU, represent the
unitary 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 J-th column of A is permuted
to the front of A*P (a leading column); if JPVT(J)=0,
the J-th column of A is a free column.
On exit, if JPVT(J)=K, then the J-th column of A*P was the
the K-th column of A.

TAU


TAU is COMPLEX*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors.

WORK


WORK is COMPLEX*16 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 >= N+1.
For optimal performance LWORK >= ( 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.

RWORK


RWORK is DOUBLE PRECISION array, dimension (2*N)

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:

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**H
where tau is a complex scalar, and v is a real/complex 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).

Contributors:

G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain X. Sun, Computer Science Dept., Duke University, USA

Definition at line 159 of file zgeqp3.f.

Author

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Tue Sep 25 2012 Version 3.4.2