dtzrzf.f(3)

NAME
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.

Date:
    April 2012

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 153 of file dtzrzf.f.

Author

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