SRC/cgerqf.f(3)

NAME
SRC/cgerqf.f

SYNOPSIS

  Functions/Subroutines
subroutine cgerqf (m, n, a, lda, tau, work, lwork, info)
CGERQF

Function/Subroutine Documentation

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

CGERQF

Purpose:

    !>
    !> CGERQF computes an RQ factorization of a complex M-by-N matrix A:
    !> A = R * Q.
    !>

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,
    !>          if m <= n, the upper triangle of the subarray
    !>          A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R;
    !>          if m >= n, the elements on and above the (m-n)-th subdiagonal
    !>          contain the M-by-N upper trapezoidal matrix R;
    !>          the remaining elements, 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 array, dimension (min(M,N))
    !>          The scalar factors of the elementary reflectors (see Further
    !>          Details).
    !>

    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 >= 1, if MIN(M,N) = 0, and LWORK >= M, otherwise.
    !>          For optimum performance LWORK >= M*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 H(2)**H . . . H(k)**H, 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(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on
    !>  exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).
    !>

Definition at line 138 of file cgerqf.f.

Author

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