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


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



           INTEGER        INFO, LDA, LWORK, M, N

           INTEGER        JPVT( * )

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


       SGEQP3  computes  a QR factorization with column pivoting of a matrix A:  A*P = Q*R  using
       Level 3 BLAS.


        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) REAL 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
                orthogonal matrix Q as a product of min(M,N) elementary

        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) REAL array, dimension (min(M,N))
                The scalar factors of the elementary reflectors.

        WORK    (workspace/output) REAL 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 >= 3*N+1.
                For optimal performance LWORK >= 2*N+( 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.

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


        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**T
        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                            SGEQP3(3lapack)