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version 1.7, 2010/12/21 13:53:51 version 1.8, 2011/07/22 07:38:17
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      $           PIVMIN, GAPTOL, Z, WANTNC, NEGCNT, ZTZ, MINGMA,       $           PIVMIN, GAPTOL, Z, WANTNC, NEGCNT, ZTZ, MINGMA,
      $           R, ISUPPZ, NRMINV, RESID, RQCORR, WORK )       $           R, ISUPPZ, NRMINV, RESID, RQCORR, WORK )
 *  *
 *  -- 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 ..
       LOGICAL            WANTNC        LOGICAL            WANTNC
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 *  *
 *  ZLAR1V computes the (scaled) r-th column of the inverse of  *  ZLAR1V computes the (scaled) r-th column of the inverse of
 *  the sumbmatrix in rows B1 through BN of the tridiagonal matrix  *  the sumbmatrix in rows B1 through BN of the tridiagonal matrix
 *  L D L^T - sigma I. When sigma is close to an eigenvalue, the  *  L D L**T - sigma I. When sigma is close to an eigenvalue, the
 *  computed vector is an accurate eigenvector. Usually, r corresponds  *  computed vector is an accurate eigenvector. Usually, r corresponds
 *  to the index where the eigenvector is largest in magnitude.  *  to the index where the eigenvector is largest in magnitude.
 *  The following steps accomplish this computation :  *  The following steps accomplish this computation :
 *  (a) Stationary qd transform,  L D L^T - sigma I = L(+) D(+) L(+)^T,  *  (a) Stationary qd transform,  L D L**T - sigma I = L(+) D(+) L(+)**T,
 *  (b) Progressive qd transform, L D L^T - sigma I = U(-) D(-) U(-)^T,  *  (b) Progressive qd transform, L D L**T - sigma I = U(-) D(-) U(-)**T,
 *  (c) Computation of the diagonal elements of the inverse of  *  (c) Computation of the diagonal elements of the inverse of
 *      L D L^T - sigma I by combining the above transforms, and choosing  *      L D L**T - sigma I by combining the above transforms, and choosing
 *      r as the index where the diagonal of the inverse is (one of the)  *      r as the index where the diagonal of the inverse is (one of the)
 *      largest in magnitude.  *      largest in magnitude.
 *  (d) Computation of the (scaled) r-th column of the inverse using the  *  (d) Computation of the (scaled) r-th column of the inverse using the
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 *  =========  *  =========
 *  *
 *  N        (input) INTEGER  *  N        (input) INTEGER
 *           The order of the matrix L D L^T.  *           The order of the matrix L D L**T.
 *  *
 *  B1       (input) INTEGER  *  B1       (input) INTEGER
 *           First index of the submatrix of L D L^T.  *           First index of the submatrix of L D L**T.
 *  *
 *  BN       (input) INTEGER  *  BN       (input) INTEGER
 *           Last index of the submatrix of L D L^T.  *           Last index of the submatrix of L D L**T.
 *  *
 *  LAMBDA    (input) DOUBLE PRECISION  *  LAMBDA    (input) DOUBLE PRECISION
 *           The shift. In order to compute an accurate eigenvector,  *           The shift. In order to compute an accurate eigenvector,
 *           LAMBDA should be a good approximation to an eigenvalue  *           LAMBDA should be a good approximation to an eigenvalue
 *           of L D L^T.  *           of L D L**T.
 *  *
 *  L        (input) DOUBLE PRECISION array, dimension (N-1)  *  L        (input) DOUBLE PRECISION array, dimension (N-1)
 *           The (n-1) subdiagonal elements of the unit bidiagonal matrix  *           The (n-1) subdiagonal elements of the unit bidiagonal matrix
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 *  *
 *  NEGCNT   (output) INTEGER  *  NEGCNT   (output) INTEGER
 *           If WANTNC is .TRUE. then NEGCNT = the number of pivots < pivmin  *           If WANTNC is .TRUE. then NEGCNT = the number of pivots < pivmin
 *           in the  matrix factorization L D L^T, and NEGCNT = -1 otherwise.  *           in the  matrix factorization L D L**T, and NEGCNT = -1 otherwise.
 *  *
 *  ZTZ      (output) DOUBLE PRECISION  *  ZTZ      (output) DOUBLE PRECISION
 *           The square of the 2-norm of Z.  *           The square of the 2-norm of Z.
 *  *
 *  MINGMA   (output) DOUBLE PRECISION  *  MINGMA   (output) DOUBLE PRECISION
 *           The reciprocal of the largest (in magnitude) diagonal  *           The reciprocal of the largest (in magnitude) diagonal
 *           element of the inverse of L D L^T - sigma I.  *           element of the inverse of L D L**T - sigma I.
 *  *
 *  R        (input/output) INTEGER  *  R        (input/output) INTEGER
 *           The twist index for the twisted factorization used to  *           The twist index for the twisted factorization used to
 *           compute Z.  *           compute Z.
 *           On input, 0 <= R <= N. If R is input as 0, R is set to  *           On input, 0 <= R <= N. If R is input as 0, R is set to
 *           the index where (L D L^T - sigma I)^{-1} is largest  *           the index where (L D L**T - sigma I)^{-1} is largest
 *           in magnitude. If 1 <= R <= N, R is unchanged.  *           in magnitude. If 1 <= R <= N, R is unchanged.
 *           On output, R contains the twist index used to compute Z.  *           On output, R contains the twist index used to compute Z.
 *           Ideally, R designates the position of the maximum entry in the  *           Ideally, R designates the position of the maximum entry in the
Removed from v.1.7  
changed lines
  Added in v.1.8

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