```      SUBROUTINE SLAR1V( N, B1, BN, LAMBDA, D, L, LD, LLD,
\$           PIVMIN, GAPTOL, Z, WANTNC, NEGCNT, ZTZ, MINGMA,
\$           R, ISUPPZ, NRMINV, RESID, RQCORR, WORK )
*
*  -- LAPACK auxiliary routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
LOGICAL            WANTNC
INTEGER   B1, BN, N, NEGCNT, R
REAL               GAPTOL, LAMBDA, MINGMA, NRMINV, PIVMIN, RESID,
\$                   RQCORR, ZTZ
*     ..
*     .. Array Arguments ..
INTEGER            ISUPPZ( * )
REAL               D( * ), L( * ), LD( * ), LLD( * ),
\$                  WORK( * )
REAL             Z( * )
*     ..
*
*  Purpose
*  =======
*
*  SLAR1V computes the (scaled) r-th column of the inverse of
*  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
*  computed vector is an accurate eigenvector. Usually, r corresponds
*  to the index where the eigenvector is largest in magnitude.
*  The following steps accomplish this computation :
*  (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,
*  (c) Computation of the diagonal elements of the inverse of
*      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)
*      largest in magnitude.
*  (d) Computation of the (scaled) r-th column of the inverse using the
*      twisted factorization obtained by combining the top part of the
*      the stationary and the bottom part of the progressive transform.
*
*  Arguments
*  =========
*
*  N        (input) INTEGER
*           The order of the matrix L D L^T.
*
*  B1       (input) INTEGER
*           First index of the submatrix of L D L^T.
*
*  BN       (input) INTEGER
*           Last index of the submatrix of L D L^T.
*
*  LAMBDA    (input) REAL
*           The shift. In order to compute an accurate eigenvector,
*           LAMBDA should be a good approximation to an eigenvalue
*           of L D L^T.
*
*  L        (input) REAL             array, dimension (N-1)
*           The (n-1) subdiagonal elements of the unit bidiagonal matrix
*           L, in elements 1 to N-1.
*
*  D        (input) REAL             array, dimension (N)
*           The n diagonal elements of the diagonal matrix D.
*
*  LD       (input) REAL             array, dimension (N-1)
*           The n-1 elements L(i)*D(i).
*
*  LLD      (input) REAL             array, dimension (N-1)
*           The n-1 elements L(i)*L(i)*D(i).
*
*  PIVMIN   (input) REAL
*           The minimum pivot in the Sturm sequence.
*
*  GAPTOL   (input) REAL
*           Tolerance that indicates when eigenvector entries are negligible
*           w.r.t. their contribution to the residual.
*
*  Z        (input/output) REAL             array, dimension (N)
*           On input, all entries of Z must be set to 0.
*           On output, Z contains the (scaled) r-th column of the
*           inverse. The scaling is such that Z(R) equals 1.
*
*  WANTNC   (input) LOGICAL
*           Specifies whether NEGCNT has to be computed.
*
*  NEGCNT   (output) INTEGER
*           If WANTNC is .TRUE. then NEGCNT = the number of pivots < pivmin
*           in the  matrix factorization L D L^T, and NEGCNT = -1 otherwise.
*
*  ZTZ      (output) REAL
*           The square of the 2-norm of Z.
*
*  MINGMA   (output) REAL
*           The reciprocal of the largest (in magnitude) diagonal
*           element of the inverse of L D L^T - sigma I.
*
*  R        (input/output) INTEGER
*           The twist index for the twisted factorization used to
*           compute Z.
*           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
*           in magnitude. If 1 <= R <= N, R is unchanged.
*           On output, R contains the twist index used to compute Z.
*           Ideally, R designates the position of the maximum entry in the
*           eigenvector.
*
*  ISUPPZ   (output) INTEGER array, dimension (2)
*           The support of the vector in Z, i.e., the vector Z is
*           nonzero only in elements ISUPPZ(1) through ISUPPZ( 2 ).
*
*  NRMINV   (output) REAL
*           NRMINV = 1/SQRT( ZTZ )
*
*  RESID    (output) REAL
*           The residual of the FP vector.
*           RESID = ABS( MINGMA )/SQRT( ZTZ )
*
*  RQCORR   (output) REAL
*           The Rayleigh Quotient correction to LAMBDA.
*           RQCORR = MINGMA*TMP
*
*  WORK     (workspace) REAL             array, dimension (4*N)
*
*  Further Details
*  ===============
*
*  Based on contributions by
*     Beresford Parlett, University of California, Berkeley, USA
*     Jim Demmel, University of California, Berkeley, USA
*     Inderjit Dhillon, University of Texas, Austin, USA
*     Osni Marques, LBNL/NERSC, USA
*     Christof Voemel, University of California, Berkeley, USA
*
*  =====================================================================
*
*     .. Parameters ..
REAL               ZERO, ONE
PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )

*     ..
*     .. Local Scalars ..
LOGICAL            SAWNAN1, SAWNAN2
INTEGER            I, INDLPL, INDP, INDS, INDUMN, NEG1, NEG2, R1,
\$                   R2
REAL               DMINUS, DPLUS, EPS, S, TMP
*     ..
*     .. External Functions ..
LOGICAL SISNAN
REAL               SLAMCH
EXTERNAL           SISNAN, SLAMCH
*     ..
*     .. Intrinsic Functions ..
INTRINSIC          ABS
*     ..
*     .. Executable Statements ..
*
EPS = SLAMCH( 'Precision' )

IF( R.EQ.0 ) THEN
R1 = B1
R2 = BN
ELSE
R1 = R
R2 = R
END IF

*     Storage for LPLUS
INDLPL = 0
*     Storage for UMINUS
INDUMN = N
INDS = 2*N + 1
INDP = 3*N + 1

IF( B1.EQ.1 ) THEN
WORK( INDS ) = ZERO
ELSE
WORK( INDS+B1-1 ) = LLD( B1-1 )
END IF

*
*     Compute the stationary transform (using the differential form)
*     until the index R2.
*
SAWNAN1 = .FALSE.
NEG1 = 0
S = WORK( INDS+B1-1 ) - LAMBDA
DO 50 I = B1, R1 - 1
DPLUS = D( I ) + S
WORK( INDLPL+I ) = LD( I ) / DPLUS
IF(DPLUS.LT.ZERO) NEG1 = NEG1 + 1
WORK( INDS+I ) = S*WORK( INDLPL+I )*L( I )
S = WORK( INDS+I ) - LAMBDA
50   CONTINUE
SAWNAN1 = SISNAN( S )
IF( SAWNAN1 ) GOTO 60
DO 51 I = R1, R2 - 1
DPLUS = D( I ) + S
WORK( INDLPL+I ) = LD( I ) / DPLUS
WORK( INDS+I ) = S*WORK( INDLPL+I )*L( I )
S = WORK( INDS+I ) - LAMBDA
51   CONTINUE
SAWNAN1 = SISNAN( S )
*
60   CONTINUE
IF( SAWNAN1 ) THEN
*        Runs a slower version of the above loop if a NaN is detected
NEG1 = 0
S = WORK( INDS+B1-1 ) - LAMBDA
DO 70 I = B1, R1 - 1
DPLUS = D( I ) + S
IF(ABS(DPLUS).LT.PIVMIN) DPLUS = -PIVMIN
WORK( INDLPL+I ) = LD( I ) / DPLUS
IF(DPLUS.LT.ZERO) NEG1 = NEG1 + 1
WORK( INDS+I ) = S*WORK( INDLPL+I )*L( I )
IF( WORK( INDLPL+I ).EQ.ZERO )
\$                      WORK( INDS+I ) = LLD( I )
S = WORK( INDS+I ) - LAMBDA
70      CONTINUE
DO 71 I = R1, R2 - 1
DPLUS = D( I ) + S
IF(ABS(DPLUS).LT.PIVMIN) DPLUS = -PIVMIN
WORK( INDLPL+I ) = LD( I ) / DPLUS
WORK( INDS+I ) = S*WORK( INDLPL+I )*L( I )
IF( WORK( INDLPL+I ).EQ.ZERO )
\$                      WORK( INDS+I ) = LLD( I )
S = WORK( INDS+I ) - LAMBDA
71      CONTINUE
END IF
*
*     Compute the progressive transform (using the differential form)
*     until the index R1
*
SAWNAN2 = .FALSE.
NEG2 = 0
WORK( INDP+BN-1 ) = D( BN ) - LAMBDA
DO 80 I = BN - 1, R1, -1
DMINUS = LLD( I ) + WORK( INDP+I )
TMP = D( I ) / DMINUS
IF(DMINUS.LT.ZERO) NEG2 = NEG2 + 1
WORK( INDUMN+I ) = L( I )*TMP
WORK( INDP+I-1 ) = WORK( INDP+I )*TMP - LAMBDA
80   CONTINUE
TMP = WORK( INDP+R1-1 )
SAWNAN2 = SISNAN( TMP )

IF( SAWNAN2 ) THEN
*        Runs a slower version of the above loop if a NaN is detected
NEG2 = 0
DO 100 I = BN-1, R1, -1
DMINUS = LLD( I ) + WORK( INDP+I )
IF(ABS(DMINUS).LT.PIVMIN) DMINUS = -PIVMIN
TMP = D( I ) / DMINUS
IF(DMINUS.LT.ZERO) NEG2 = NEG2 + 1
WORK( INDUMN+I ) = L( I )*TMP
WORK( INDP+I-1 ) = WORK( INDP+I )*TMP - LAMBDA
IF( TMP.EQ.ZERO )
\$          WORK( INDP+I-1 ) = D( I ) - LAMBDA
100     CONTINUE
END IF
*
*     Find the index (from R1 to R2) of the largest (in magnitude)
*     diagonal element of the inverse
*
MINGMA = WORK( INDS+R1-1 ) + WORK( INDP+R1-1 )
IF( MINGMA.LT.ZERO ) NEG1 = NEG1 + 1
IF( WANTNC ) THEN
NEGCNT = NEG1 + NEG2
ELSE
NEGCNT = -1
ENDIF
IF( ABS(MINGMA).EQ.ZERO )
\$   MINGMA = EPS*WORK( INDS+R1-1 )
R = R1
DO 110 I = R1, R2 - 1
TMP = WORK( INDS+I ) + WORK( INDP+I )
IF( TMP.EQ.ZERO )
\$      TMP = EPS*WORK( INDS+I )
IF( ABS( TMP ).LE.ABS( MINGMA ) ) THEN
MINGMA = TMP
R = I + 1
END IF
110  CONTINUE
*
*     Compute the FP vector: solve N^T v = e_r
*
ISUPPZ( 1 ) = B1
ISUPPZ( 2 ) = BN
Z( R ) = ONE
ZTZ = ONE
*
*     Compute the FP vector upwards from R
*
IF( .NOT.SAWNAN1 .AND. .NOT.SAWNAN2 ) THEN
DO 210 I = R-1, B1, -1
Z( I ) = -( WORK( INDLPL+I )*Z( I+1 ) )
IF( (ABS(Z(I))+ABS(Z(I+1)))* ABS(LD(I)).LT.GAPTOL )
\$           THEN
Z( I ) = ZERO
ISUPPZ( 1 ) = I + 1
GOTO 220
ENDIF
ZTZ = ZTZ + Z( I )*Z( I )
210     CONTINUE
220     CONTINUE
ELSE
*        Run slower loop if NaN occurred.
DO 230 I = R - 1, B1, -1
IF( Z( I+1 ).EQ.ZERO ) THEN
Z( I ) = -( LD( I+1 ) / LD( I ) )*Z( I+2 )
ELSE
Z( I ) = -( WORK( INDLPL+I )*Z( I+1 ) )
END IF
IF( (ABS(Z(I))+ABS(Z(I+1)))* ABS(LD(I)).LT.GAPTOL )
\$           THEN
Z( I ) = ZERO
ISUPPZ( 1 ) = I + 1
GO TO 240
END IF
ZTZ = ZTZ + Z( I )*Z( I )
230     CONTINUE
240     CONTINUE
ENDIF

*     Compute the FP vector downwards from R in blocks of size BLKSIZ
IF( .NOT.SAWNAN1 .AND. .NOT.SAWNAN2 ) THEN
DO 250 I = R, BN-1
Z( I+1 ) = -( WORK( INDUMN+I )*Z( I ) )
IF( (ABS(Z(I))+ABS(Z(I+1)))* ABS(LD(I)).LT.GAPTOL )
\$         THEN
Z( I+1 ) = ZERO
ISUPPZ( 2 ) = I
GO TO 260
END IF
ZTZ = ZTZ + Z( I+1 )*Z( I+1 )
250     CONTINUE
260     CONTINUE
ELSE
*        Run slower loop if NaN occurred.
DO 270 I = R, BN - 1
IF( Z( I ).EQ.ZERO ) THEN
Z( I+1 ) = -( LD( I-1 ) / LD( I ) )*Z( I-1 )
ELSE
Z( I+1 ) = -( WORK( INDUMN+I )*Z( I ) )
END IF
IF( (ABS(Z(I))+ABS(Z(I+1)))* ABS(LD(I)).LT.GAPTOL )
\$           THEN
Z( I+1 ) = ZERO
ISUPPZ( 2 ) = I
GO TO 280
END IF
ZTZ = ZTZ + Z( I+1 )*Z( I+1 )
270     CONTINUE
280     CONTINUE
END IF
*
*     Compute quantities for convergence test
*
TMP = ONE / ZTZ
NRMINV = SQRT( TMP )
RESID = ABS( MINGMA )*NRMINV
RQCORR = MINGMA*TMP
*
*
RETURN
*
*     End of SLAR1V
*
END

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