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Diff for /rpl/lapack/lapack/zlabrd.f between versions 1.3 and 1.8

version 1.3, 2010/08/06 15:28:55 version 1.8, 2011/07/22 07:38:16
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       SUBROUTINE ZLABRD( M, N, NB, A, LDA, D, E, TAUQ, TAUP, X, LDX, Y,        SUBROUTINE ZLABRD( M, N, NB, A, LDA, D, E, TAUQ, TAUP, X, LDX, Y,
      $                   LDY )       $                   LDY )
 *  *
 *  -- LAPACK auxiliary routine (version 3.2) --  *  -- LAPACK auxiliary routine (version 3.3.1) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     November 2006  *  -- April 2011                                                      --
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER            LDA, LDX, LDY, M, N, NB        INTEGER            LDA, LDX, LDY, M, N, NB
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 *  *
 *  ZLABRD reduces the first NB rows and columns of a complex general  *  ZLABRD reduces the first NB rows and columns of a complex general
 *  m by n matrix A to upper or lower real bidiagonal form by a unitary  *  m by n matrix A to upper or lower real bidiagonal form by a unitary
 *  transformation Q' * A * P, and returns the matrices X and Y which  *  transformation Q**H * A * P, and returns the matrices X and Y which
 *  are needed to apply the transformation to the unreduced part of A.  *  are needed to apply the transformation to the unreduced part of A.
 *  *
 *  If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower  *  If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower
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 *  *
 *  Each H(i) and G(i) has the form:  *  Each H(i) and G(i) has the form:
 *  *
 *     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'  *     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H
 *  *
 *  where tauq and taup are complex scalars, and v and u are complex  *  where tauq and taup are complex scalars, and v and u are complex
 *  vectors.  *  vectors.
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 *  A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).  *  A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
 *  *
 *  The elements of the vectors v and u together form the m-by-nb matrix  *  The elements of the vectors v and u together form the m-by-nb matrix
 *  V and the nb-by-n matrix U' which are needed, with X and Y, to apply  *  V and the nb-by-n matrix U**H which are needed, with X and Y, to apply
 *  the transformation to the unreduced part of the matrix, using a block  *  the transformation to the unreduced part of the matrix, using a block
 *  update of the form:  A := A - V*Y' - X*U'.  *  update of the form:  A := A - V*Y**H - X*U**H.
 *  *
 *  The contents of A on exit are illustrated by the following examples  *  The contents of A on exit are illustrated by the following examples
 *  with nb = 2:  *  with nb = 2:
Removed from v.1.3  
changed lines
  Added in v.1.8

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