SRC/dtzrzf.f(3)

NAME
SRC/dtzrzf.f

SYNOPSIS

  Functions/Subroutines
subroutine dtzrzf (m, n, a, lda, tau, work, lwork, info)
DTZRZF

Function/Subroutine Documentation

  subroutine dtzrzf (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer lwork, integer info)

DTZRZF

Purpose:

    !>
    !> DTZRZF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A
    !> to upper triangular form by means of orthogonal transformations.
    !>
    !> The upper trapezoidal matrix A is factored as
    !>
    !>    A = ( R  0 ) * Z,
    !>
    !> where Z is an N-by-N orthogonal matrix and R is an M-by-M upper
    !> triangular matrix.
    !>

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 >= M.
    !>

    A

    !>          A is DOUBLE PRECISION array, dimension (LDA,N)
    !>          On entry, the leading M-by-N upper trapezoidal part of the
    !>          array A must contain the matrix to be factorized.
    !>          On exit, the leading M-by-M upper triangular part of A
    !>          contains the upper triangular matrix R, and elements M+1 to
    !>          N of the first M rows of A, with the array TAU, represent the
    !>          orthogonal matrix Z as a product of M elementary reflectors.
    !>

    LDA

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

    TAU

    !>          TAU is DOUBLE PRECISION array, dimension (M)
    !>          The scalar factors of the elementary reflectors.
    !>

    WORK

    !>          WORK is DOUBLE PRECISION 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.

Contributors:
    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

    !>
    !>  The N-by-N matrix Z can be computed by
    !>
    !>     Z =  Z(1)*Z(2)* ... *Z(M)
    !>
    !>  where each N-by-N Z(k) is given by
    !>
    !>     Z(k) = I - tau(k)*v(k)*v(k)**T
    !>
    !>  with v(k) is the kth row vector of the M-by-N matrix
    !>
    !>     V = ( I   A(:,M+1:N) )
    !>
    !>  I is the M-by-M identity matrix, A(:,M+1:N)
    !>  is the output stored in A on exit from DTZRZF,
    !>  and tau(k) is the kth element of the array TAU.
    !>
    !>

Definition at line 150 of file dtzrzf.f.

Author

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