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Diff for /rpl/lapack/lapack/dlabrd.f between versions 1.7 and 1.8

version 1.7, 2010/12/21 13:53:28 version 1.8, 2011/07/22 07:38:06
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       SUBROUTINE DLABRD( M, N, NB, A, LDA, D, E, TAUQ, TAUP, X, LDX, Y,        SUBROUTINE DLABRD( 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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 *  *
 *  DLABRD reduces the first NB rows and columns of a real general  *  DLABRD reduces the first NB rows and columns of a real general
 *  m by n matrix A to upper or lower bidiagonal form by an orthogonal  *  m by n matrix A to upper or lower bidiagonal form by an orthogonal
 *  transformation Q' * A * P, and returns the matrices X and Y which  *  transformation Q**T * 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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 *          of A.  *          of A.
 *  *
 *  LDX     (input) INTEGER  *  LDX     (input) INTEGER
 *          The leading dimension of the array X. LDX >= M.  *          The leading dimension of the array X. LDX >= max(1,M).
 *  *
 *  Y       (output) DOUBLE PRECISION array, dimension (LDY,NB)  *  Y       (output) DOUBLE PRECISION array, dimension (LDY,NB)
 *          The n-by-nb matrix Y required to update the unreduced part  *          The n-by-nb matrix Y required to update the unreduced part
 *          of A.  *          of A.
 *  *
 *  LDY     (input) INTEGER  *  LDY     (input) INTEGER
 *          The leading dimension of the array Y. LDY >= N.  *          The leading dimension of the array Y. LDY >= max(1,N).
 *  *
 *  Further Details  *  Further Details
 *  ===============  *  ===============
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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**T  and G(i) = I - taup * u * u**T
 *  *
 *  where tauq and taup are real scalars, and v and u are real vectors.  *  where tauq and taup are real scalars, and v and u are real 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**T 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**T - X*U**T.
 *  *
 *  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.1.7  
changed lines
  Added in v.1.8

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