dgeqpf(3S)

NAME
     DGEQPF - routine is deprecated and has been replaced by routine DGEQP3

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

         INTEGER        INFO, LDA, M, N

         INTEGER        JPVT( * )

         DOUBLE         PRECISION A( LDA, * ), TAU( * ), WORK( * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

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     This routine is deprecated and has been replaced by routine DGEQP3.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) INTEGER
             The number of rows of the matrix A. M >= 0.

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

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

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

     WORK    (workspace) DOUBLE PRECISION array, dimension (3*N)

     INFO    (output) 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'

     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.


SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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