cgerq2.f(3)

NAME
cgerq2.f -

SYNOPSIS

  Functions/Subroutines

subroutine cgerq2 (M, N, A, LDA, TAU, WORK, INFO)
CGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

Function/Subroutine Documentation

  subroutine cgerq2 (integerM, integerN, complex, dimension( lda, * )A, integerLDA, complex, dimension( * )TAU, complex, dimension( * )WORK, integerINFO)

CGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

     CGERQ2 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 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 (M)

    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.

Date:
    September 2012

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 124 of file cgerq2.f.

Author

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