slaorhr_col_getrfnp.f(3)

NAME
slaorhr_col_getrfnp.f

SYNOPSIS

  Functions/Subroutines
subroutine slaorhr_col_getrfnp (M, N, A, LDA, D, INFO)
SLAORHR_COL_GETRFNP

Function/Subroutine Documentation

  subroutine slaorhr_col_getrfnp (integer M, integer N, real, dimension( lda, * ) A, integer LDA, real, dimension( * ) D, integer INFO)

Purpose:

     SLAORHR_COL_GETRFNP computes the modified LU factorization without
     pivoting of a real general M-by-N matrix A. The factorization has
     the form:
         A - S = L * U,
     where:
        S is a m-by-n diagonal sign matrix with the diagonal D, so that
        D(i) = S(i,i), 1 <= i <= min(M,N). The diagonal D is constructed
        as D(i)=-SIGN(A(i,i)), where A(i,i) is the value after performing
        i-1 steps of Gaussian elimination. This means that the diagonal
        element at each step of 'modified' Gaussian elimination is
        at least one in absolute value (so that division-by-zero not
        not possible during the division by the diagonal element);
        L is a M-by-N lower triangular matrix with unit diagonal elements
        (lower trapezoidal if M > N);
        and U is a M-by-N upper triangular matrix
        (upper trapezoidal if M < N).
     This routine is an auxiliary routine used in the Householder
     reconstruction routine SORHR_COL. In SORHR_COL, this routine is
     applied to an M-by-N matrix A with orthonormal columns, where each
     element is bounded by one in absolute value. With the choice of
     the matrix S above, one can show that the diagonal element at each
     step of Gaussian elimination is the largest (in absolute value) in
     the column on or below the diagonal, so that no pivoting is required
     for numerical stability [1].
     For more details on the Householder reconstruction algorithm,
     including the modified LU factorization, see [1].
     This is the blocked right-looking version of the algorithm,
     calling Level 3 BLAS to update the submatrix. To factorize a block,
     this routine calls the recursive routine SLAORHR_COL_GETRFNP2.
     [1] 'Reconstructing Householder vectors from tall-skinny QR',
         G. Ballard, J. Demmel, L. Grigori, M. Jacquelin, H.D. Nguyen,
         E. Solomonik, J. Parallel Distrib. Comput.,
         vol. 85, pp. 3-31, 2015.

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 to be factored.
              On exit, the factors L and U from the factorization
              A-S=L*U; the unit diagonal elements of L are not stored.

    LDA

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

    D

              D is REAL array, dimension min(M,N)
              The diagonal elements of the diagonal M-by-N sign matrix S,
              D(i) = S(i,i), where 1 <= i <= min(M,N). The elements can
              be only plus or minus one.

    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.

Contributors:

     November 2019, Igor Kozachenko,
                    Computer Science Division,
                    University of California, Berkeley

Definition at line 145 of file slaorhr_col_getrfnp.f.

Author

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