zgerqf.f(3)

NAME
zgerqf.f

SYNOPSIS

  Functions/Subroutines
subroutine zgerqf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
ZGERQF

Function/Subroutine Documentation

  subroutine zgerqf (integer M, integer N, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( * ) TAU, complex*16, dimension( * ) WORK, integer LWORK, integer INFO)

Purpose:

     ZGERQF 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*16 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*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,M).
              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 137 of file zgerqf.f.

Author

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