SRC/zgeqrfp.f(3)

NAME
SRC/zgeqrfp.f

SYNOPSIS

  Functions/Subroutines
subroutine zgeqrfp (m, n, a, lda, tau, work, lwork, info)
ZGEQRFP

Function/Subroutine Documentation

  subroutine zgeqrfp (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer lwork, integer info)

ZGEQRFP

Purpose:

     ZGEQR2P computes a QR factorization of a complex M-by-N matrix A:
        A = Q * ( R ),
                ( 0 )
     where:
        Q is a M-by-M orthogonal matrix;
        R is an upper-triangular N-by-N matrix with nonnegative diagonal
        entries;
        0 is a (M-N)-by-N zero matrix, if M > N.

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*16 array, dimension (LDA,N)
              On entry, the M-by-N matrix A.
              On exit, the elements on and above the diagonal of the array
              contain the min(M,N)-by-N upper trapezoidal matrix R (R is
              upper triangular if m >= n). The diagonal entries of R
              are real and nonnegative; The elements below the diagonal,
              with the array TAU, represent the unitary matrix Q as a
              product of min(m,n) elementary reflectors (see Further
              Details).

    LDA

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

    TAU

              TAU is COMPLEX*16 array, dimension (min(M,N))
              The scalar factors of the elementary reflectors (see Further
              Details).

    WORK

              WORK is COMPLEX*16 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 >= max(1,N).
              For optimum performance LWORK >= N*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

              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 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).
     See Lapack Working Note 203 for details

Definition at line 148 of file zgeqrfp.f.

Author

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