DGEQPF(3)      LAPACK routine of NEC Numeric Library Collection      DGEQPF(3)



NAME
       DGEQPF

SYNOPSIS
       SUBROUTINE DGEQPF (M, N, A, LDA, JPVT, TAU, WORK, INFO)



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            This routine is deprecated and has been replaced by routine DGEQP3.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.




ARGUMENTS
           M         (input)
                     M is INTEGER
                     The number of rows of the matrix A. M >= 0.

           N         (input)
                     N is INTEGER
                     The number of columns of the matrix A. N >= 0

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

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

           WORK      (output)
                     WORK is DOUBLE PRECISION array, dimension (3*N)

           INFO      (output)
                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value






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.




LAPACK routine                  31 October 2017                      DGEQPF(3)