SRC/cgeqp3.f(3)            Library Functions Manual            SRC/cgeqp3.f(3)

NAME
       SRC/cgeqp3.f

SYNOPSIS
   Functions/Subroutines
       subroutine cgeqp3 (m, n, a, lda, jpvt, tau, work, lwork, rwork, info)
           CGEQP3

Function/Subroutine Documentation
   subroutine cgeqp3 (integer m, integer n, complex, dimension( lda, * ) a,
       integer lda, integer, dimension( * ) jpvt, complex, dimension( * ) tau,
       complex, dimension( * ) work, integer lwork, real, dimension( * )
       rwork, integer info)
       CGEQP3

       Purpose:


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

       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 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

           !>          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(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

           !>          TAU is COMPLEX array, dimension (min(M,N))
           !>          The scalar factors of the elementary reflectors.
           !>

           WORK

           !>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
           !>          On exit, if INFO=0, WORK(1) returns the optimal LWORK.
           !>

           LWORK

           !>          LWORK is 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

           !>          RWORK is REAL array, dimension (2*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.

       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 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).
           !>

       Contributors:
           G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
           X. Sun, Computer Science Dept., Duke University, USA

       Definition at line 157 of file cgeqp3.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                 SRC/cgeqp3.f(3)