sgerqf.f(3)

NAME
sgerqf.f -

SYNOPSIS

  Functions/Subroutines
subroutine sgerqf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
SGERQF

Function/Subroutine Documentation

  subroutine sgerqf (integerM, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( * )TAU, real, dimension( * )WORK, integerLWORK, integerINFO)

SGERQF

Purpose:

     SGERQF computes an RQ factorization of a real 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 REAL 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
              orthogonal 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 REAL array, dimension (min(M,N))
              The scalar factors of the elementary reflectors (see Further
              Details).

    WORK

              WORK is REAL 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.

Date:
    November 2011

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**T
      where tau is a real scalar, and v is a real vector with
      v(n-k+i+1:n) = 0 and v(n-k+i) = 1; 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 139 of file sgerqf.f.

Author

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