dgeqpf(3)

NAME

dgeqpf.f –

SYNOPSIS

Functions/Subroutines

subroutine dgeqpf (M, N, A, LDA, JPVT, TAU, WORK, INFO)
DGEQPF

Function/Subroutine Documentation

subroutine dgeqpf (integerM, integerN, double precision, dimension( lda, * )A, integerLDA, integer, dimension( * )JPVT, double precision, dimension( * )TAU, double precision, dimension( * )WORK, integerINFO)

DGEQPF

Purpose:

 This routine is deprecated and has been replaced by routine DGEQP3.
 DGEQPF computes a QR factorization with column pivoting of a
 real M-by-N matrix A: A*P = Q*R.

 

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 DOUBLE PRECISION 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 triangular 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 (i).ne.0, the i - th column of A is permuted to the front of A *P(a leading column);
if JPVT (i)
= 0,
    the i - th column of A is a free column.On exit, if JPVT (i) = k, then the i - th column of A *P was the k - th column of A.

TAU

          TAU is DOUBLE PRECISION array, dimension (min(M,N))
          The scalar factors of the elementary reflectors.

WORK

          WORK is DOUBLE PRECISION array, dimension (3*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:

November 2011

Further Details:

The matrix Q is represented as a product of elementary reflectors
    Q = H(1) H(2)...H(n)
            Each
            H(i)
has the form
    H = I - tau * v * v * *T 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)
    .The matrix P is represented in jpvt as follows : If
                                                      jpvt(j) = i then the jth column of P is the ith canonical unit vector.Partial column norm updating strategy modified by
                                                                Z.Drmac
                                                                and Z.Bujanovic,
                                                      Dept.of Mathematics,
                                                      University of Zagreb, Croatia.--April 2011 --For more details see LAPACK Working Note 176.

 

Definition at line 143 of file dgeqpf.f.

Author

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