Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3 - computes a QR factorization with column pivoting of a matrix A

SYNOPSIS

       SUBROUTINE CGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, RWORK, INFO )

           INTEGER        INFO, LDA, LWORK, M, N

           INTEGER        JPVT( * )

           REAL           RWORK( * )

           COMPLEX        A( LDA, * ), TAU( * ), WORK( * )

PURPOSE

       CGEQP3  computes  a QR factorization with column pivoting of a matrix A:  A*P = Q*R  using
       Level 3 BLAS.

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

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

        WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
                On exit, if INFO=0, WORK(1) returns the optimal LWORK.

        LWORK   (input) 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   (workspace) REAL array, dimension (2*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(k), where k = min(m,n).
        Each H(i) has the form
           H(i) = I - tau * v * v**H
        where tau is a real/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).
        Based on contributions by
          G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
          X. Sun, Computer Science Dept., Duke University, USA

 LAPACK routine (version 3.3.1)             April 2011                            CGEQP3(3lapack)